premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is patient or creative is both not generous and humble. Everyone who is not wise or humble is generous and vice versa. If lucy is generous or not quiet then lucy is not tall. If fred is either patient or not generous then alice is rich. Everyone who is not curious or not patient is both not wise and not calm. If alice is either wise or brave then someone is both not happy and not brave. Everyone who is wise is both strong and humble. Everyone who is rich is both not strong and not calm and vice versa. Everyone who is either strong or not funny is not happy or not funny and vice versa. Everyone who is brave or not calm is kind or not funny. If someone is humble then alice is not happy and vice versa. If john is not brave then mary is either old or not kind and vice versa. Everyone who is either not rich or funny is either not kind or old. Everyone who is both not old and not generous is patient or not kind. Someone is not old. Someone is not quiet or tall. Lucy is either quiet or not tall. Someone is either not happy or not funny. Someone is either wise or not brave. Alice is either not brave or rich. | Mary is not generous. | contradiction | (![X]:((patient(X)|creative(X))=>(~generous(X)&humble(X))))&
(![X]:((~wise(X)|humble(X))<=>generous(X)))&
(((generous(lucy)|~quiet(lucy)))=>(~tall(lucy)))&
(((patient(fred)<~>~generous(fred)))=>(rich(alice)))&
(![X]:((~curious(X)|~patient(X))=>(~wise(X)&~calm(X))))&
(((wise(alice)<~>brave(alice)))=>(?[X]:((~happy(X)&~brave(X)))))&
(![X]:(wise(X)=>(strong(X)&humble(X))))&
(![X]:(rich(X)<=>(~strong(X)&~calm(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~happy(X)|~funny(X))))&
(![X]:((brave(X)|~calm(X))=>(kind(X)|~funny(X))))&
((?[X]:(humble(X)))<=>(~happy(alice)))&
((~brave(john))<=>((old(mary)<~>~kind(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(~kind(X)<~>old(X))))&
(![X]:((~old(X)&~generous(X))=>(patient(X)|~kind(X))))&
(?[X]:(~old(X)))&
(?[X]:((~quiet(X)|tall(X))))&
((quiet(lucy)<~>~tall(lucy)))&
(?[X]:((~happy(X)<~>~funny(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
((~brave(alice)<~>rich(alice))) | ~generous(mary) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1361058705168257917931311
% SZS output start Proof for 1361058705168257917931311
2. ! [X0] : ((humble(X0) | ~wise(X0)) <=> generous(X0)) [input p1]
7. ! [X0] : (wise(X0) => (humble(X0) & strong(X0))) [input p6]
21. ~generous(mary) [input hypothesis]
29. ! [X0] : ((humble(X0) & strong(X0)) | ~wise(X0)) [ennf transformation 7]
35. ! [X0] : (((humble(X0) | ~wise(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) & wise(X0)))) [nnf transformation 2]
36. ! [X0] : ((humble(X0) | ~wise(X0) | ~generous(X0)) & (generous(X0) | (~humble(X0) & wise(X0)))) [flattening 35]
65. wise(X0) | generous(X0) [cnf transformation 36]
66. ~humble(X0) | generous(X0) [cnf transformation 36]
79. ~wise(X0) | humble(X0) [cnf transformation 29]
112. ~generous(mary) [cnf transformation 21]
235. humble(X0) | generous(X0) [resolution 79,65]
236. generous(X0) [subsumption resolution 235,66]
237. $false [resolution 236,112]
% SZS output end Proof for 1361058705168257917931311
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not happy is patient or not quiet.
Everyone who is not tall is patient or tall.
Everyone who is either quiet or generous is both not rich and not funny.
Everyone who is either not strong or patient is humble or wise and vice versa.
If lucy is both quiet and not quiet then susan is curious and vice versa.
Everyone who is either not quiet or not tall is either not brave or not creative and vice versa.
If someone is either kind or not brave then someone is patient or kind and vice versa.
If someone is both quiet and not tall then alice is both tall and happy and vice versa.
If susan is either not patient or brave then john is old or strong and vice versa.
Everyone who is not old or not strong is both funny and kind and vice versa.
Everyone who is either not curious or happy is not calm.
Everyone who is not generous is brave or kind and vice versa.
Everyone who is strong or calm is quiet and vice versa.
Everyone who is not generous is humble.
Everyone who is both not rich and generous is not kind and vice versa.
Everyone who is not calm is not rich and vice versa.
Someone is not wise.
Susan is not strong or generous.
Alice is brave or patient.
John is either wise or not brave.
John is either not patient or not quiet.
Someone is funny or not creative.
John is not brave.
Lucy is not tall. | Lucy is quiet. | entailment | (![X]:((~patient(X)<~>~happy(X))=>(patient(X)|~quiet(X))))&
(![X]:(~tall(X)=>(patient(X)|tall(X))))&
(![X]:((quiet(X)<~>generous(X))=>(~rich(X)&~funny(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)|wise(X))))&
(((quiet(lucy)&~quiet(lucy)))<=>(curious(susan)))&
(![X]:((~quiet(X)<~>~tall(X))<=>(~brave(X)<~>~creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((quiet(X)&~tall(X))))<=>((tall(alice)&happy(alice))))&
(((~patient(susan)<~>brave(susan)))<=>((old(john)|strong(john))))&
(![X]:((~old(X)|~strong(X))<=>(funny(X)&kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>~calm(X)))&
(![X]:(~generous(X)<=>(brave(X)|kind(X))))&
(![X]:((strong(X)|calm(X))<=>quiet(X)))&
(![X]:(~generous(X)=>humble(X)))&
(![X]:((~rich(X)&generous(X))<=>~kind(X)))&
(![X]:(~calm(X)<=>~rich(X)))&
(?[X]:(~wise(X)))&
((~strong(susan)|generous(susan)))&
((brave(alice)|patient(alice)))&
((wise(john)<~>~brave(john)))&
((~patient(john)<~>~quiet(john)))&
(?[X]:((funny(X)|~creative(X))))&
(~brave(john))&
(~tall(lucy)) | quiet(lucy) | [
"p1",
"p3",
"p9",
"p11",
"p12",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1178361045342894993284507
% SZS output start Proof for 1178361045342894993284507
2. ! [X0] : (~tall(X0) => (tall(X0) | patient(X0))) [input p1]
4. ! [X0] : ((~strong(X0) <~> patient(X0)) <=> (wise(X0) | humble(X0))) [input p3]
10. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (kind(X0) & funny(X0))) [input p9]
12. ! [X0] : (~generous(X0) <=> (kind(X0) | brave(X0))) [input p11]
13. ! [X0] : ((calm(X0) | strong(X0)) <=> quiet(X0)) [input p12]
14. ! [X0] : (~generous(X0) => humble(X0)) [input p13]
24. ~tall(lucy) [input p23]
25. ~quiet(lucy) [input hypothesis]
29. ! [X0] : ((tall(X0) | patient(X0)) | tall(X0)) [ennf transformation 2]
30. ! [X0] : (tall(X0) | patient(X0) | tall(X0)) [flattening 29]
33. ! [X0] : (humble(X0) | generous(X0)) [ennf transformation 14]
36. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [nnf transformation 4]
37. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [flattening 36]
53. ! [X0] : (((~strong(X0) | ~old(X0)) | (~kind(X0) | ~funny(X0))) & ((kind(X0) & funny(X0)) | (strong(X0) & old(X0)))) [nnf transformation 10]
54. ! [X0] : ((~strong(X0) | ~old(X0) | ~kind(X0) | ~funny(X0)) & ((kind(X0) & funny(X0)) | (strong(X0) & old(X0)))) [flattening 53]
56. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & ((kind(X0) | brave(X0)) | generous(X0))) [nnf transformation 12]
57. ! [X0] : ((~generous(X0) | (~kind(X0) & ~brave(X0))) & (kind(X0) | brave(X0) | generous(X0))) [flattening 56]
58. ! [X0] : (((calm(X0) | strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [nnf transformation 13]
59. ! [X0] : ((calm(X0) | strong(X0) | ~quiet(X0)) & (quiet(X0) | (~calm(X0) & ~strong(X0)))) [flattening 58]
71. tall(X0) | patient(X0) | tall(X0) [cnf transformation 30]
80. ~humble(X0) | strong(X0) | ~patient(X0) [cnf transformation 37]
112. kind(X0) | strong(X0) [cnf transformation 54]
118. ~kind(X0) | ~generous(X0) [cnf transformation 57]
119. ~strong(X0) | quiet(X0) [cnf transformation 59]
122. humble(X0) | generous(X0) [cnf transformation 33]
137. ~tall(lucy) [cnf transformation 24]
138. ~quiet(lucy) [cnf transformation 25]
139. tall(X0) | patient(X0) [duplicate literal removal 71]
146. 2 <=> quiet(lucy) [avatar definition]
148. ~quiet(lucy) <- (~2) [avatar component clause 146]
278. ~2 [avatar split clause 138,146]
282. ~generous(X0) | strong(X0) [resolution 118,112]
294. patient(lucy) [resolution 139,137]
313. strong(X0) | ~patient(X0) | generous(X0) [resolution 80,122]
314. ~patient(X0) | strong(X0) [subsumption resolution 313,282]
315. strong(lucy) [resolution 314,294]
327. quiet(lucy) [resolution 315,119]
328. $false <- (~2) [subsumption resolution 327,148]
329. 2 [avatar contradiction clause 328]
330. $false [avatar sat refutation 278,329]
% SZS output end Proof for 1178361045342894993284507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not happy and creative then someone is both not brave and not patient. If susan is both not rich and not funny then john is both curious and strong. Everyone who is not wise is both rich and wise and vice versa. Everyone who is generous or funny is either curious or happy. Everyone who is generous is both not patient and funny and vice versa. If someone is quiet then someone is both not strong and not curious and vice versa. Everyone who is either not happy or tall is both not quiet and not brave. Everyone who is both not tall and rich is either patient or not calm and vice versa. If someone is not brave then alice is not strong or brave. If paul is wise or not tall then mary is both not strong and generous and vice versa. If someone is not kind then someone is either brave or not creative and vice versa. Everyone who is either not brave or curious is both not funny and curious and vice versa. If lucy is creative or not patient then john is quiet and vice versa. If john is not creative or not strong then susan is both not rich and tall. Everyone who is either happy or rich is both not old and not humble and vice versa. Everyone who is both not humble and not wise is either not patient or not old and vice versa. Someone is not brave. Someone is either not humble or tall. Someone is either not creative or not quiet. John is happy. Someone is creative. Someone is not rich or not quiet. Someone is either not quiet or tall. | Paul is calm. | neutral | (((~happy(susan)&creative(susan)))=>(?[X]:((~brave(X)&~patient(X)))))&
(((~rich(susan)&~funny(susan)))=>((curious(john)&strong(john))))&
(![X]:(~wise(X)<=>(rich(X)&wise(X))))&
(![X]:((generous(X)|funny(X))=>(curious(X)<~>happy(X))))&
(![X]:(generous(X)<=>(~patient(X)&funny(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~happy(X)<~>tall(X))=>(~quiet(X)&~brave(X))))&
(![X]:((~tall(X)&rich(X))<=>(patient(X)<~>~calm(X))))&
((?[X]:(~brave(X)))=>((~strong(alice)|brave(alice))))&
(((wise(paul)|~tall(paul)))<=>((~strong(mary)&generous(mary))))&
((?[X]:(~kind(X)))<=>(?[X]:((brave(X)<~>~creative(X)))))&
(![X]:((~brave(X)<~>curious(X))<=>(~funny(X)&curious(X))))&
(((creative(lucy)|~patient(lucy)))<=>(quiet(john)))&
(((~creative(john)|~strong(john)))=>((~rich(susan)&tall(susan))))&
(![X]:((happy(X)<~>rich(X))<=>(~old(X)&~humble(X))))&
(![X]:((~humble(X)&~wise(X))<=>(~patient(X)<~>~old(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~humble(X)<~>tall(X))))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(happy(john))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~quiet(X))))&
(?[X]:((~quiet(X)<~>tall(X)))) | calm(paul) | [] | null | 0 |
If fred is both old and not funny then mary is either rich or not kind and vice versa.
Everyone who is not brave or not wise is not funny or not kind and vice versa.
If fred is funny then someone is both creative and not rich.
Everyone who is happy is not creative.
If lucy is not tall or curious then susan is either wise or humble and vice versa.
If someone is calm or happy then someone is funny or not funny and vice versa.
If john is either not curious or not creative then paul is either kind or not funny and vice versa.
Everyone who is either brave or funny is not quiet or curious.
Everyone who is not curious or strong is wise and vice versa.
If someone is both strong and creative then paul is strong or not kind and vice versa.
Everyone who is either quiet or humble is not patient and vice versa.
If susan is both not humble and not rich then someone is not curious or not humble and vice versa.
Everyone who is creative or wise is rich or not humble and vice versa.
Everyone who is tall or not wise is tall or not quiet and vice versa.
Everyone who is brave is either not old or strong and vice versa.
Susan is either quiet or not happy.
Lucy is not rich.
Someone is either not strong or calm.
Someone is either strong or funny.
Susan is old.
Lucy is kind.
Someone is tall or not old.
Someone is rich or not tall. | John is not happy. | neutral | (((old(fred)&~funny(fred)))<=>((rich(mary)<~>~kind(mary))))&
(![X]:((~brave(X)|~wise(X))<=>(~funny(X)|~kind(X))))&
((funny(fred))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:(happy(X)=>~creative(X)))&
(((~tall(lucy)|curious(lucy)))<=>((wise(susan)<~>humble(susan))))&
((?[X]:((calm(X)|happy(X))))<=>(?[X]:((funny(X)|~funny(X)))))&
(((~curious(john)<~>~creative(john)))<=>((kind(paul)<~>~funny(paul))))&
(![X]:((brave(X)<~>funny(X))=>(~quiet(X)|curious(X))))&
(![X]:((~curious(X)|strong(X))<=>wise(X)))&
((?[X]:((strong(X)&creative(X))))<=>((strong(paul)|~kind(paul))))&
(![X]:((quiet(X)<~>humble(X))<=>~patient(X)))&
(((~humble(susan)&~rich(susan)))<=>(?[X]:((~curious(X)|~humble(X)))))&
(![X]:((creative(X)|wise(X))<=>(rich(X)|~humble(X))))&
(![X]:((tall(X)|~wise(X))<=>(tall(X)|~quiet(X))))&
(![X]:(brave(X)<=>(~old(X)<~>strong(X))))&
((quiet(susan)<~>~happy(susan)))&
(~rich(lucy))&
(?[X]:((~strong(X)<~>calm(X))))&
(?[X]:((strong(X)<~>funny(X))))&
(old(susan))&
(kind(lucy))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:((rich(X)|~tall(X)))) | ~happy(john) | [] | null | 0 |
Everyone who is both not creative and kind is either happy or not tall.
If someone is both funny and not calm then susan is both not patient and generous.
Everyone who is quiet or not strong is not strong or not kind and vice versa.
If someone is both curious and kind then someone is both not rich and generous and vice versa.
If susan is both not quiet and not generous then someone is funny.
Everyone who is brave is not funny and vice versa.
Everyone who is calm is both not old and calm and vice versa.
If paul is not curious then john is patient and vice versa.
Everyone who is brave or not old is either not quiet or strong.
If john is not funny or not calm then someone is both not humble and not curious.
Everyone who is strong is both not strong and strong and vice versa.
Everyone who is both strong and funny is not quiet and vice versa.
If someone is both old and kind then lucy is either creative or not kind.
Everyone who is generous or tall is funny or old.
Everyone who is both not funny and kind is curious.
If someone is either not funny or curious then someone is either not brave or not quiet.
Lucy is either generous or tall.
John is not brave.
Someone is either not curious or strong.
Someone is wise.
Susan is not wise.
Someone is calm or not tall.
Paul is not humble or not calm.
Paul is both happy and not kind. | Paul is not curious. | neutral | (![X]:((~creative(X)&kind(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((funny(X)&~calm(X))))=>((~patient(susan)&generous(susan))))&
(![X]:((quiet(X)|~strong(X))<=>(~strong(X)|~kind(X))))&
((?[X]:((curious(X)&kind(X))))<=>(?[X]:((~rich(X)&generous(X)))))&
(((~quiet(susan)&~generous(susan)))=>(?[X]:(funny(X))))&
(![X]:(brave(X)<=>~funny(X)))&
(![X]:(calm(X)<=>(~old(X)&calm(X))))&
((~curious(paul))<=>(patient(john)))&
(![X]:((brave(X)|~old(X))=>(~quiet(X)<~>strong(X))))&
(((~funny(john)|~calm(john)))=>(?[X]:((~humble(X)&~curious(X)))))&
(![X]:(strong(X)<=>(~strong(X)&strong(X))))&
(![X]:((strong(X)&funny(X))<=>~quiet(X)))&
((?[X]:((old(X)&kind(X))))=>((creative(lucy)<~>~kind(lucy))))&
(![X]:((generous(X)|tall(X))=>(funny(X)|old(X))))&
(![X]:((~funny(X)&kind(X))=>curious(X)))&
((?[X]:((~funny(X)<~>curious(X))))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
((generous(lucy)<~>tall(lucy)))&
(~brave(john))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:(wise(X)))&
(~wise(susan))&
(?[X]:((calm(X)|~tall(X))))&
((~humble(paul)|~calm(paul)))&
((happy(paul)&~kind(paul))) | ~curious(paul) | [] | null | 0 |
Everyone who is not brave is tall and vice versa.
Everyone who is creative or tall is funny or not tall.
If someone is funny or happy then someone is not funny or not generous and vice versa.
If susan is not kind or generous then someone is either curious or generous and vice versa.
Everyone who is both calm and not curious is funny and vice versa.
Everyone who is not old is both not humble and not tall and vice versa.
If someone is not creative or wise then someone is both not humble and quiet and vice versa.
If someone is both patient and not funny then paul is either not old or happy and vice versa.
If someone is not funny then john is happy or funny and vice versa.
If someone is either funny or not brave then someone is both strong and not strong.
Everyone who is either not strong or quiet is not tall.
If someone is not humble then someone is either humble or not humble.
Everyone who is both not curious and not funny is both not quiet and not calm.
Everyone who is not happy or not calm is both wise and not wise and vice versa.
Everyone who is funny or curious is not patient and vice versa.
If someone is both not quiet and not kind then someone is rich.
Fred is either not brave or rich.
Someone is both rich and not old.
Someone is either not patient or not generous.
Someone is kind or not creative.
Someone is not happy or not funny.
Lucy is not funny or curious.
Someone is either humble or not curious. | Paul is old. | contradiction | (![X]:(~brave(X)<=>tall(X)))&
(![X]:((creative(X)|tall(X))=>(funny(X)|~tall(X))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:((~funny(X)|~generous(X)))))&
(((~kind(susan)|generous(susan)))<=>(?[X]:((curious(X)<~>generous(X)))))&
(![X]:((calm(X)&~curious(X))<=>funny(X)))&
(![X]:(~old(X)<=>(~humble(X)&~tall(X))))&
((?[X]:((~creative(X)|wise(X))))<=>(?[X]:((~humble(X)&quiet(X)))))&
((?[X]:((patient(X)&~funny(X))))<=>((~old(paul)<~>happy(paul))))&
((?[X]:(~funny(X)))<=>((happy(john)|funny(john))))&
((?[X]:((funny(X)<~>~brave(X))))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((~curious(X)&~funny(X))=>(~quiet(X)&~calm(X))))&
(![X]:((~happy(X)|~calm(X))<=>(wise(X)&~wise(X))))&
(![X]:((funny(X)|curious(X))<=>~patient(X)))&
((?[X]:((~quiet(X)&~kind(X))))=>(?[X]:(rich(X))))&
((~brave(fred)<~>rich(fred)))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:((~patient(X)<~>~generous(X))))&
(?[X]:((kind(X)|~creative(X))))&
(?[X]:((~happy(X)|~funny(X))))&
((~funny(lucy)|curious(lucy)))&
(?[X]:((humble(X)<~>~curious(X)))) | old(paul) | [
"p4",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1146842913263846098589568
% SZS output start Proof for 1146842913263846098589568
5. ! [X0] : ((~curious(X0) & calm(X0)) <=> funny(X0)) [input p4]
8. ? [X0] : (~funny(X0) & patient(X0)) <=> (~old(paul) <~> happy(paul)) [input p7]
14. ! [X0] : ((~calm(X0) | ~happy(X0)) <=> (~wise(X0) & wise(X0))) [input p13]
15. ! [X0] : ((curious(X0) | funny(X0)) <=> ~patient(X0)) [input p14]
24. old(paul) [input hypothesis]
49. ! [X0] : (((~curious(X0) & calm(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~calm(X0)))) [nnf transformation 5]
50. ! [X0] : (((~curious(X0) & calm(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~calm(X0))) [flattening 49]
58. (? [X0] : (~funny(X0) & patient(X0)) | ((~old(paul) | ~happy(paul)) & (happy(paul) | old(paul)))) & (((~happy(paul) | old(paul)) & (happy(paul) | ~old(paul))) | ! [X0] : (funny(X0) | ~patient(X0))) [nnf transformation 8]
59. (? [X0] : (~funny(X0) & patient(X0)) | ((~old(paul) | ~happy(paul)) & (happy(paul) | old(paul)))) & (((~happy(paul) | old(paul)) & (happy(paul) | ~old(paul))) | ! [X1] : (funny(X1) | ~patient(X1))) [rectify 58]
60. ? [X0] : (~funny(X0) & patient(X0)) => (~funny(sK5) & patient(sK5)) [choice axiom]
61. ((~funny(sK5) & patient(sK5)) | ((~old(paul) | ~happy(paul)) & (happy(paul) | old(paul)))) & (((~happy(paul) | old(paul)) & (happy(paul) | ~old(paul))) | ! [X1] : (funny(X1) | ~patient(X1))) [skolemisation 59,60]
76. ! [X0] : (((~calm(X0) | ~happy(X0)) | (wise(X0) | ~wise(X0))) & ((~wise(X0) & wise(X0)) | (calm(X0) & happy(X0)))) [nnf transformation 14]
77. ! [X0] : ((~calm(X0) | ~happy(X0) | wise(X0) | ~wise(X0)) & ((~wise(X0) & wise(X0)) | (calm(X0) & happy(X0)))) [flattening 76]
78. ! [X0] : (((curious(X0) | funny(X0)) | patient(X0)) & (~patient(X0) | (~curious(X0) & ~funny(X0)))) [nnf transformation 15]
79. ! [X0] : ((curious(X0) | funny(X0) | patient(X0)) & (~patient(X0) | (~curious(X0) & ~funny(X0)))) [flattening 78]
110. ~calm(X0) | curious(X0) | funny(X0) [cnf transformation 50]
124. patient(sK5) | ~old(paul) | ~happy(paul) [cnf transformation 61]
126. ~funny(sK5) | ~old(paul) | ~happy(paul) [cnf transformation 61]
140. wise(X0) | happy(X0) [cnf transformation 77]
141. wise(X0) | calm(X0) [cnf transformation 77]
142. ~wise(X0) | happy(X0) [cnf transformation 77]
143. ~wise(X0) | calm(X0) [cnf transformation 77]
146. ~patient(X0) | ~curious(X0) [cnf transformation 79]
160. old(paul) [cnf transformation 24]
253. 22 <=> happy(paul) [avatar definition]
255. ~happy(paul) <- (~22) [avatar component clause 253]
257. 23 <=> old(paul) [avatar definition]
261. 24 <=> funny(sK5) [avatar definition]
263. ~funny(sK5) <- (~24) [avatar component clause 261]
264. ~22 | ~23 | ~24 [avatar split clause 126,261,257,253]
267. 25 <=> patient(sK5) [avatar definition]
269. patient(sK5) <- (25) [avatar component clause 267]
270. ~22 | ~23 | 25 [avatar split clause 124,267,257,253]
306. calm(X0) [subsumption resolution 141,143]
307. happy(X0) [subsumption resolution 140,142]
357. 23 [avatar split clause 160,257]
360. $false <- (~22) [subsumption resolution 255,307]
361. 22 [avatar contradiction clause 360]
373. ~curious(sK5) <- (25) [resolution 146,269]
385. curious(X0) | funny(X0) [resolution 110,306]
407. funny(sK5) <- (25) [resolution 385,373]
410. $false <- (~24, 25) [subsumption resolution 407,263]
411. 24 | ~25 [avatar contradiction clause 410]
414. $false [avatar sat refutation 264,270,357,361,411]
% SZS output end Proof for 1146842913263846098589568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not creative is both curious and calm.
If john is both wise and not happy then someone is tall and vice versa.
Everyone who is both tall and not strong is either funny or not old.
Everyone who is humble is either not generous or curious and vice versa.
Everyone who is both curious and not old is patient or funny.
Everyone who is not humble is generous or wise.
If john is both brave and not tall then someone is patient or generous and vice versa.
Everyone who is both not wise and not funny is brave or not rich and vice versa.
If alice is either not curious or not rich then john is funny.
Everyone who is either creative or wise is both not curious and not funny and vice versa.
If susan is not old then fred is patient or not generous.
Everyone who is not curious is both not strong and rich and vice versa.
If someone is humble or not curious then john is either not creative or not old and vice versa.
Everyone who is not quiet or not tall is generous or not tall and vice versa.
If someone is old then fred is either not wise or generous and vice versa.
If john is both not rich and wise then fred is not happy or not humble and vice versa.
Someone is both not generous and not happy.
Fred is not funny.
Alice is not funny.
Fred is strong.
Someone is either not humble or not curious.
Fred is either quiet or not generous.
Someone is either rich or kind.
Alice is not old. | John is not patient. | neutral | (![X]:((happy(X)|~creative(X))=>(curious(X)&calm(X))))&
(((wise(john)&~happy(john)))<=>(?[X]:(tall(X))))&
(![X]:((tall(X)&~strong(X))=>(funny(X)<~>~old(X))))&
(![X]:(humble(X)<=>(~generous(X)<~>curious(X))))&
(![X]:((curious(X)&~old(X))=>(patient(X)|funny(X))))&
(![X]:(~humble(X)=>(generous(X)|wise(X))))&
(((brave(john)&~tall(john)))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:((~wise(X)&~funny(X))<=>(brave(X)|~rich(X))))&
(((~curious(alice)<~>~rich(alice)))=>(funny(john)))&
(![X]:((creative(X)<~>wise(X))<=>(~curious(X)&~funny(X))))&
((~old(susan))=>((patient(fred)|~generous(fred))))&
(![X]:(~curious(X)<=>(~strong(X)&rich(X))))&
((?[X]:((humble(X)|~curious(X))))<=>((~creative(john)<~>~old(john))))&
(![X]:((~quiet(X)|~tall(X))<=>(generous(X)|~tall(X))))&
((?[X]:(old(X)))<=>((~wise(fred)<~>generous(fred))))&
(((~rich(john)&wise(john)))<=>((~happy(fred)|~humble(fred))))&
(?[X]:((~generous(X)&~happy(X))))&
(~funny(fred))&
(~funny(alice))&
(strong(fred))&
(?[X]:((~humble(X)<~>~curious(X))))&
((quiet(fred)<~>~generous(fred)))&
(?[X]:((rich(X)<~>kind(X))))&
(~old(alice)) | ~patient(john) | [] | null | 0 |
If paul is not calm then mary is both happy and quiet. Everyone who is both strong and not patient is generous or not funny and vice versa. Everyone who is not wise or not rich is not kind or not curious. If someone is both not strong and creative then someone is not wise or wise. Everyone who is quiet is not kind and vice versa. If alice is not funny or strong then mary is either not funny or quiet. If alice is either not old or not calm then someone is both not creative and not curious. Everyone who is not rich or curious is both tall and humble and vice versa. Everyone who is kind or rich is not generous or not curious and vice versa. Everyone who is both not old and not wise is not quiet. If mary is both rich and strong then someone is wise or rich. Everyone who is not funny is rich or not brave and vice versa. Everyone who is not patient or not generous is either not curious or brave and vice versa. Everyone who is not rich or happy is not calm and vice versa. If fred is both curious and tall then someone is either strong or calm and vice versa. Everyone who is curious or not quiet is not generous. Someone is both generous and not creative. Someone is not humble. Alice is wise. Someone is old. Someone is either creative or quiet. Alice is not generous or funny. Someone is not wise. | Mary is not generous. | entailment | ((~calm(paul))=>((happy(mary)&quiet(mary))))&
(![X]:((strong(X)&~patient(X))<=>(generous(X)|~funny(X))))&
(![X]:((~wise(X)|~rich(X))=>(~kind(X)|~curious(X))))&
((?[X]:((~strong(X)&creative(X))))=>(?[X]:((~wise(X)|wise(X)))))&
(![X]:(quiet(X)<=>~kind(X)))&
(((~funny(alice)|strong(alice)))=>((~funny(mary)<~>quiet(mary))))&
(((~old(alice)<~>~calm(alice)))=>(?[X]:((~creative(X)&~curious(X)))))&
(![X]:((~rich(X)|curious(X))<=>(tall(X)&humble(X))))&
(![X]:((kind(X)|rich(X))<=>(~generous(X)|~curious(X))))&
(![X]:((~old(X)&~wise(X))=>~quiet(X)))&
(((rich(mary)&strong(mary)))=>(?[X]:((wise(X)|rich(X)))))&
(![X]:(~funny(X)<=>(rich(X)|~brave(X))))&
(![X]:((~patient(X)|~generous(X))<=>(~curious(X)<~>brave(X))))&
(![X]:((~rich(X)|happy(X))<=>~calm(X)))&
(((curious(fred)&tall(fred)))<=>(?[X]:((strong(X)<~>calm(X)))))&
(![X]:((curious(X)|~quiet(X))=>~generous(X)))&
(?[X]:((generous(X)&~creative(X))))&
(?[X]:(~humble(X)))&
(wise(alice))&
(?[X]:(old(X)))&
(?[X]:((creative(X)<~>quiet(X))))&
((~generous(alice)|funny(alice)))&
(?[X]:(~wise(X))) | ~generous(mary) | [
"p1",
"p2",
"p4",
"p5",
"p8",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8126989595894482744684117
% SZS output start Proof for 8126989595894482744684117
2. ! [X0] : ((~patient(X0) & strong(X0)) <=> (~funny(X0) | generous(X0))) [input p1]
3. ! [X0] : ((~rich(X0) | ~wise(X0)) => (~curious(X0) | ~kind(X0))) [input p2]
5. ! [X0] : (quiet(X0) <=> ~kind(X0)) [input p4]
6. (strong(alice) | ~funny(alice)) => (~funny(mary) <~> quiet(mary)) [input p5]
9. ! [X0] : ((rich(X0) | kind(X0)) <=> (~curious(X0) | ~generous(X0))) [input p8]
12. ! [X0] : (~funny(X0) <=> (~brave(X0) | rich(X0))) [input p11]
13. ! [X0] : ((~generous(X0) | ~patient(X0)) <=> (~curious(X0) <~> brave(X0))) [input p12]
16. ! [X0] : ((~quiet(X0) | curious(X0)) => ~generous(X0)) [input p15]
24. generous(mary) [input hypothesis]
27. ! [X0] : ((~curious(X0) | ~kind(X0)) | (rich(X0) & wise(X0))) [ennf transformation 3]
28. ! [X0] : (~curious(X0) | ~kind(X0) | (rich(X0) & wise(X0))) [flattening 27]
30. (~funny(mary) <~> quiet(mary)) | (~strong(alice) & funny(alice)) [ennf transformation 6]
36. ! [X0] : (~generous(X0) | (quiet(X0) & ~curious(X0))) [ennf transformation 16]
37. ! [X0] : (((~patient(X0) & strong(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (patient(X0) | ~strong(X0)))) [nnf transformation 2]
38. ! [X0] : (((~patient(X0) & strong(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | patient(X0) | ~strong(X0))) [flattening 37]
42. ! [X0] : ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))) [nnf transformation 5]
43. ((~quiet(mary) | funny(mary)) & (quiet(mary) | ~funny(mary))) | (~strong(alice) & funny(alice)) [nnf transformation 30]
49. ! [X0] : (((rich(X0) | kind(X0)) | (curious(X0) & generous(X0))) & ((~curious(X0) | ~generous(X0)) | (~rich(X0) & ~kind(X0)))) [nnf transformation 9]
50. ! [X0] : ((rich(X0) | kind(X0) | (curious(X0) & generous(X0))) & (~curious(X0) | ~generous(X0) | (~rich(X0) & ~kind(X0)))) [flattening 49]
53. ! [X0] : ((~funny(X0) | (brave(X0) & ~rich(X0))) & ((~brave(X0) | rich(X0)) | funny(X0))) [nnf transformation 12]
54. ! [X0] : ((~funny(X0) | (brave(X0) & ~rich(X0))) & (~brave(X0) | rich(X0) | funny(X0))) [flattening 53]
55. ! [X0] : (((~generous(X0) | ~patient(X0)) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (generous(X0) & patient(X0)))) [nnf transformation 13]
56. ! [X0] : ((~generous(X0) | ~patient(X0) | ((~curious(X0) | ~brave(X0)) & (brave(X0) | curious(X0)))) & (((~brave(X0) | curious(X0)) & (brave(X0) | ~curious(X0))) | (generous(X0) & patient(X0)))) [flattening 55]
78. ~generous(X0) | strong(X0) [cnf transformation 38]
83. ~curious(X0) | ~kind(X0) | rich(X0) [cnf transformation 28]
85. ~kind(X0) | ~quiet(X0) [cnf transformation 42]
89. ~quiet(mary) | funny(mary) | funny(alice) [cnf transformation 43]
90. ~quiet(mary) | funny(mary) | ~strong(alice) [cnf transformation 43]
102. kind(X0) | rich(X0) | generous(X0) [cnf transformation 50]
103. curious(X0) | kind(X0) | rich(X0) [cnf transformation 50]
107. ~rich(X0) | ~funny(X0) [cnf transformation 54]
108. ~funny(X0) | brave(X0) [cnf transformation 54]
112. ~brave(X0) | curious(X0) | generous(X0) [cnf transformation 56]
124. ~curious(X0) | ~generous(X0) [cnf transformation 36]
125. ~generous(X0) | quiet(X0) [cnf transformation 36]
135. generous(mary) [cnf transformation 24]
141. 2 <=> quiet(mary) [avatar definition]
143. quiet(mary) <- (2) [avatar component clause 141]
151. 4 <=> strong(alice) [avatar definition]
155. 5 <=> funny(mary) [avatar definition]
158. ~4 | 5 | ~2 [avatar split clause 90,141,155,151]
160. 6 <=> funny(alice) [avatar definition]
162. funny(alice) <- (6) [avatar component clause 160]
163. 6 | 5 | ~2 [avatar split clause 89,141,155,160]
187. 11 <=> rich(mary) [avatar definition]
188. rich(mary) <- (11) [avatar component clause 187]
244. 23 <=> generous(alice) [avatar definition]
245. generous(alice) <- (23) [avatar component clause 244]
246. ~generous(alice) <- (~23) [avatar component clause 244]
263. quiet(mary) [resolution 125,135]
297. kind(X6) | rich(X6) | ~generous(X6) [resolution 103,124]
308. kind(X6) | rich(X6) [subsumption resolution 297,102]
356. 2 [avatar split clause 263,141]
361. brave(alice) <- (6) [resolution 162,108]
426. curious(alice) | generous(alice) <- (6) [resolution 361,112]
429. curious(alice) <- (6, ~23) [subsumption resolution 426,246]
439. ~funny(mary) <- (11) [resolution 188,107]
454. ~quiet(X0) | rich(X0) [resolution 308,85]
490. ~kind(alice) | rich(alice) <- (6, ~23) [resolution 429,83]
498. rich(alice) <- (6, ~23) [subsumption resolution 490,308]
511. rich(mary) <- (2) [resolution 454,143]
535. ~funny(alice) <- (6, ~23) [resolution 498,107]
537. $false <- (6, ~23) [subsumption resolution 535,162]
538. ~6 | 23 [avatar contradiction clause 537]
551. strong(alice) <- (23) [resolution 245,78]
556. 4 | ~23 [avatar split clause 551,244,151]
557. ~5 | ~11 [avatar split clause 439,187,155]
559. 11 | ~2 [avatar split clause 511,141,187]
569. $false [avatar sat refutation 158,163,356,538,556,557,559]
% SZS output end Proof for 8126989595894482744684117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is not wise then someone is not calm or not humble.
If someone is either not creative or not happy then someone is both not tall and not calm and vice versa.
If someone is not strong or strong then someone is both happy and not tall and vice versa.
If someone is generous or not humble then john is both not creative and not quiet and vice versa.
If alice is either not old or not humble then lucy is funny or not quiet and vice versa.
Everyone who is both not patient and rich is curious or quiet and vice versa.
If someone is both not generous and not quiet then someone is tall or patient.
If someone is either old or not patient then alice is either rich or brave and vice versa.
Everyone who is both not kind and not calm is either funny or not wise.
Everyone who is strong or not creative is not creative.
If susan is either happy or not calm then someone is tall and vice versa.
If someone is either happy or creative then fred is either creative or not calm.
Everyone who is either not strong or not patient is either not tall or kind.
Everyone who is patient is both not patient and creative and vice versa.
Everyone who is creative is creative or not curious and vice versa.
If susan is funny or humble then susan is not humble and vice versa.
Susan is both not humble and not old.
Paul is not calm or not quiet.
Someone is both tall and calm.
John is not calm.
Mary is either funny or not kind.
Someone is not old. | Alice is rich. | entailment | ((~wise(paul))=>(?[X]:((~calm(X)|~humble(X)))))&
((?[X]:((~creative(X)<~>~happy(X))))<=>(?[X]:((~tall(X)&~calm(X)))))&
((?[X]:((~strong(X)|strong(X))))<=>(?[X]:((happy(X)&~tall(X)))))&
((?[X]:((generous(X)|~humble(X))))<=>((~creative(john)&~quiet(john))))&
(((~old(alice)<~>~humble(alice)))<=>((funny(lucy)|~quiet(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(curious(X)|quiet(X))))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((tall(X)|patient(X)))))&
((?[X]:((old(X)<~>~patient(X))))<=>((rich(alice)<~>brave(alice))))&
(![X]:((~kind(X)&~calm(X))=>(funny(X)<~>~wise(X))))&
(![X]:((strong(X)|~creative(X))=>~creative(X)))&
(((happy(susan)<~>~calm(susan)))<=>(?[X]:(tall(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((creative(fred)<~>~calm(fred))))&
(![X]:((~strong(X)<~>~patient(X))=>(~tall(X)<~>kind(X))))&
(![X]:(patient(X)<=>(~patient(X)&creative(X))))&
(![X]:(creative(X)<=>(creative(X)|~curious(X))))&
(((funny(susan)|humble(susan)))<=>(~humble(susan)))&
((~humble(susan)&~old(susan)))&
((~calm(paul)|~quiet(paul)))&
(?[X]:((tall(X)&calm(X))))&
(~calm(john))&
((funny(mary)<~>~kind(mary)))&
(?[X]:(~old(X))) | rich(alice) | [
"p5",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8729015435527288961829850
% SZS output start Proof for 8729015435527288961829850
6. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (quiet(X0) | curious(X0))) [input p5]
14. ! [X0] : (patient(X0) <=> (creative(X0) & ~patient(X0))) [input p13]
15. ! [X0] : (creative(X0) <=> (~curious(X0) | creative(X0))) [input p14]
23. ~rich(alice) [input hypothesis]
53. ! [X0] : (((rich(X0) & ~patient(X0)) | (~quiet(X0) & ~curious(X0))) & ((quiet(X0) | curious(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 6]
54. ! [X0] : (((rich(X0) & ~patient(X0)) | (~quiet(X0) & ~curious(X0))) & (quiet(X0) | curious(X0) | ~rich(X0) | patient(X0))) [flattening 53]
69. ! [X0] : ((patient(X0) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [nnf transformation 14]
70. ! [X0] : ((patient(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | ~patient(X0))) [flattening 69]
71. ! [X0] : ((creative(X0) | (curious(X0) & ~creative(X0))) & ((~curious(X0) | creative(X0)) | ~creative(X0))) [nnf transformation 15]
72. ! [X0] : ((creative(X0) | (curious(X0) & ~creative(X0))) & (~curious(X0) | creative(X0) | ~creative(X0))) [flattening 71]
106. ~curious(X0) | rich(X0) [cnf transformation 54]
133. ~patient(X0) | ~patient(X0) [cnf transformation 70]
135. patient(X0) | ~creative(X0) | patient(X0) [cnf transformation 70]
138. curious(X0) | creative(X0) [cnf transformation 72]
151. ~rich(alice) [cnf transformation 23]
154. ~patient(X0) [duplicate literal removal 133]
155. ~creative(X0) | patient(X0) [duplicate literal removal 135]
284. 29 <=> rich(alice) [avatar definition]
285. ~rich(alice) <- (~29) [avatar component clause 284]
371. ~29 [avatar split clause 151,284]
379. rich(X0) | creative(X0) [resolution 138,106]
402. creative(alice) <- (~29) [resolution 379,285]
416. patient(alice) <- (~29) [resolution 402,155]
417. $false <- (~29) [subsumption resolution 416,154]
418. 29 [avatar contradiction clause 417]
419. $false [avatar sat refutation 371,418]
% SZS output end Proof for 8729015435527288961829850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or old then someone is either calm or funny and vice versa.
Everyone who is not brave or quiet is both not brave and not funny.
If someone is rich or strong then lucy is not funny and vice versa.
Everyone who is not quiet is both not strong and creative and vice versa.
If lucy is both not curious and not creative then someone is both not creative and rich.
Everyone who is not kind or generous is quiet or not rich and vice versa.
If someone is both generous and not curious then someone is either not kind or not quiet and vice versa.
Everyone who is both not old and funny is patient or tall and vice versa.
Everyone who is both generous and not patient is creative and vice versa.
Everyone who is either not strong or not humble is not funny.
If someone is both not strong and not happy then john is both not wise and patient and vice versa.
Everyone who is not curious or calm is old.
If someone is strong or wise then mary is both funny and generous and vice versa.
Everyone who is not quiet is either old or curious and vice versa.
Everyone who is not creative or not curious is both not wise and not strong.
Everyone who is not creative or happy is either not old or happy and vice versa.
Lucy is both rich and old.
Alice is not patient or not happy.
Paul is either calm or not kind.
Someone is not curious or not kind.
Lucy is humble.
Someone is funny or quiet. | Lucy is not calm. | entailment | ((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:((calm(X)<~>funny(X)))))&
(![X]:((~brave(X)|quiet(X))=>(~brave(X)&~funny(X))))&
((?[X]:((rich(X)|strong(X))))<=>(~funny(lucy)))&
(![X]:(~quiet(X)<=>(~strong(X)&creative(X))))&
(((~curious(lucy)&~creative(lucy)))=>(?[X]:((~creative(X)&rich(X)))))&
(![X]:((~kind(X)|generous(X))<=>(quiet(X)|~rich(X))))&
((?[X]:((generous(X)&~curious(X))))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
(![X]:((~old(X)&funny(X))<=>(patient(X)|tall(X))))&
(![X]:((generous(X)&~patient(X))<=>creative(X)))&
(![X]:((~strong(X)<~>~humble(X))=>~funny(X)))&
((?[X]:((~strong(X)&~happy(X))))<=>((~wise(john)&patient(john))))&
(![X]:((~curious(X)|calm(X))=>old(X)))&
((?[X]:((strong(X)|wise(X))))<=>((funny(mary)&generous(mary))))&
(![X]:(~quiet(X)<=>(old(X)<~>curious(X))))&
(![X]:((~creative(X)|~curious(X))=>(~wise(X)&~strong(X))))&
(![X]:((~creative(X)|happy(X))<=>(~old(X)<~>happy(X))))&
((rich(lucy)&old(lucy)))&
((~patient(alice)|~happy(alice)))&
((calm(paul)<~>~kind(paul)))&
(?[X]:((~curious(X)|~kind(X))))&
(humble(lucy))&
(?[X]:((funny(X)|quiet(X)))) | ~calm(lucy) | [
"p0",
"p2",
"p3",
"p7",
"p9",
"p11",
"p13",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1874980764326651088673033
% SZS output start Proof for 1874980764326651088673033
1. ? [X0] : (~tall(X0) <~> old(X0)) <=> ? [X0] : (calm(X0) <~> funny(X0)) [input p0]
3. ? [X0] : (strong(X0) | rich(X0)) <=> ~funny(lucy) [input p2]
4. ! [X0] : (~quiet(X0) <=> (creative(X0) & ~strong(X0))) [input p3]
8. ! [X0] : ((funny(X0) & ~old(X0)) <=> (tall(X0) | patient(X0))) [input p7]
10. ! [X0] : ((~strong(X0) <~> ~humble(X0)) => ~funny(X0)) [input p9]
12. ! [X0] : ((calm(X0) | ~curious(X0)) => old(X0)) [input p11]
14. ! [X0] : (~quiet(X0) <=> (old(X0) <~> curious(X0))) [input p13]
16. ! [X0] : ((happy(X0) | ~creative(X0)) <=> (~old(X0) <~> happy(X0))) [input p15]
21. humble(lucy) [input p20]
23. calm(lucy) [input hypothesis]
24. ? [X0] : (~tall(X0) <~> old(X0)) <=> ? [X1] : (calm(X1) <~> funny(X1)) [rectify 1]
29. ! [X0] : (~funny(X0) | (~strong(X0) <=> ~humble(X0))) [ennf transformation 10]
30. ! [X0] : (old(X0) | (~calm(X0) & curious(X0))) [ennf transformation 12]
32. (? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ! [X1] : ((calm(X1) | ~funny(X1)) & (funny(X1) | ~calm(X1)))) & (? [X1] : ((~funny(X1) | ~calm(X1)) & (funny(X1) | calm(X1))) | ! [X0] : ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) [nnf transformation 24]
33. (? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ! [X1] : ((calm(X1) | ~funny(X1)) & (funny(X1) | ~calm(X1)))) & (? [X2] : ((~funny(X2) | ~calm(X2)) & (funny(X2) | calm(X2))) | ! [X3] : ((~tall(X3) | ~old(X3)) & (old(X3) | tall(X3)))) [rectify 32]
34. ? [X0] : ((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) => ((~old(sK0) | tall(sK0)) & (old(sK0) | ~tall(sK0))) [choice axiom]
35. ? [X2] : ((~funny(X2) | ~calm(X2)) & (funny(X2) | calm(X2))) => ((~funny(sK1) | ~calm(sK1)) & (funny(sK1) | calm(sK1))) [choice axiom]
36. (((~old(sK0) | tall(sK0)) & (old(sK0) | ~tall(sK0))) | ! [X1] : ((calm(X1) | ~funny(X1)) & (funny(X1) | ~calm(X1)))) & (((~funny(sK1) | ~calm(sK1)) & (funny(sK1) | calm(sK1))) | ! [X3] : ((~tall(X3) | ~old(X3)) & (old(X3) | tall(X3)))) [skolemisation 33,35,34]
37. (? [X0] : (strong(X0) | rich(X0)) | funny(lucy)) & (~funny(lucy) | ! [X0] : (~strong(X0) & ~rich(X0))) [nnf transformation 3]
38. (? [X0] : (strong(X0) | rich(X0)) | funny(lucy)) & (~funny(lucy) | ! [X1] : (~strong(X1) & ~rich(X1))) [rectify 37]
39. ? [X0] : (strong(X0) | rich(X0)) => (strong(sK2) | rich(sK2)) [choice axiom]
40. ((strong(sK2) | rich(sK2)) | funny(lucy)) & (~funny(lucy) | ! [X1] : (~strong(X1) & ~rich(X1))) [skolemisation 38,39]
41. ! [X0] : ((~quiet(X0) | (~creative(X0) | strong(X0))) & ((creative(X0) & ~strong(X0)) | quiet(X0))) [nnf transformation 4]
42. ! [X0] : ((~quiet(X0) | ~creative(X0) | strong(X0)) & ((creative(X0) & ~strong(X0)) | quiet(X0))) [flattening 41]
52. ! [X0] : (((funny(X0) & ~old(X0)) | (~tall(X0) & ~patient(X0))) & ((tall(X0) | patient(X0)) | (~funny(X0) | old(X0)))) [nnf transformation 8]
53. ! [X0] : (((funny(X0) & ~old(X0)) | (~tall(X0) & ~patient(X0))) & (tall(X0) | patient(X0) | ~funny(X0) | old(X0))) [flattening 52]
56. ! [X0] : (~funny(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) [nnf transformation 29]
67. ! [X0] : ((~quiet(X0) | ((old(X0) | ~curious(X0)) & (curious(X0) | ~old(X0)))) & (((~curious(X0) | ~old(X0)) & (curious(X0) | old(X0))) | quiet(X0))) [nnf transformation 14]
68. ! [X0] : (((happy(X0) | ~creative(X0)) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~happy(X0) & creative(X0)))) [nnf transformation 16]
69. ! [X0] : ((happy(X0) | ~creative(X0) | ((~old(X0) | ~happy(X0)) & (happy(X0) | old(X0)))) & (((~happy(X0) | old(X0)) & (happy(X0) | ~old(X0))) | (~happy(X0) & creative(X0)))) [flattening 68]
81. ~old(sK0) | tall(sK0) | funny(X1) | ~calm(X1) [cnf transformation 36]
88. ~funny(lucy) | ~strong(X1) [cnf transformation 40]
91. creative(X0) | quiet(X0) [cnf transformation 42]
107. ~old(X0) | ~tall(X0) [cnf transformation 53]
113. ~humble(X0) | ~funny(X0) | strong(X0) [cnf transformation 56]
119. curious(X0) | old(X0) [cnf transformation 30]
129. ~quiet(X0) | old(X0) | ~curious(X0) [cnf transformation 67]
137. ~happy(X0) | old(X0) | ~happy(X0) [cnf transformation 69]
138. happy(X0) | ~creative(X0) | happy(X0) | old(X0) [cnf transformation 69]
146. humble(lucy) [cnf transformation 21]
148. calm(lucy) [cnf transformation 23]
149. ~happy(X0) | old(X0) [duplicate literal removal 137]
150. ~creative(X0) | happy(X0) | old(X0) [duplicate literal removal 138]
155. 2 <=> tall(sK0) [avatar definition]
157. tall(sK0) <- (2) [avatar component clause 155]
159. 3 <=> old(sK0) [avatar definition]
160. old(sK0) <- (3) [avatar component clause 159]
161. ~old(sK0) <- (~3) [avatar component clause 159]
164. 4 <=> ! [X1] : (funny(X1) | ~calm(X1)) [avatar definition]
165. ~calm(X1) | funny(X1) <- (4) [avatar component clause 164]
166. 4 | 2 | ~3 [avatar split clause 81,159,155,164]
170. 5 <=> ! [X3] : (~tall(X3) | ~old(X3)) [avatar definition]
171. ~old(X3) | ~tall(X3) <- (5) [avatar component clause 170]
188. 9 <=> funny(lucy) [avatar definition]
189. ~funny(lucy) <- (~9) [avatar component clause 188]
201. 12 <=> ! [X1] : ~strong(X1) [avatar definition]
202. ~strong(X1) <- (12) [avatar component clause 201]
203. 12 | ~9 [avatar split clause 88,188,201]
257. 5 [avatar split clause 107,170]
305. ~quiet(X0) | old(X0) [subsumption resolution 129,119]
428. ~funny(lucy) | strong(lucy) [resolution 113,146]
530. funny(lucy) <- (4) [resolution 165,148]
531. $false <- (4, ~9) [subsumption resolution 530,189]
532. ~4 | 9 [avatar contradiction clause 531]
534. ~tall(sK0) <- (3, 5) [resolution 160,171]
544. $false <- (2, 3, 5) [subsumption resolution 534,157]
545. ~2 | ~3 | ~5 [avatar contradiction clause 544]
551. happy(X0) | old(X0) | quiet(X0) [resolution 150,91]
554. old(X0) | quiet(X0) [subsumption resolution 551,149]
555. old(X0) [subsumption resolution 554,305]
617. $false <- (~3) [resolution 555,161]
618. 3 [avatar contradiction clause 617]
620. 64 <=> strong(lucy) [avatar definition]
622. strong(lucy) <- (64) [avatar component clause 620]
623. 64 | ~9 [avatar split clause 428,188,620]
627. $false <- (12, 64) [subsumption resolution 622,202]
628. ~12 | ~64 [avatar contradiction clause 627]
629. $false [avatar sat refutation 166,203,257,532,545,618,623,628]
% SZS output end Proof for 1874980764326651088673033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either wise or not wise then someone is both humble and not wise. If paul is not calm then paul is both wise and rich. If someone is either quiet or not creative then susan is not quiet and vice versa. Everyone who is both not strong and brave is not humble and vice versa. If someone is strong or not curious then mary is not brave or calm. Everyone who is not strong or kind is old or not funny and vice versa. If john is either not humble or calm then lucy is tall or patient and vice versa. Everyone who is calm is happy. Everyone who is both rich and not patient is either generous or not wise and vice versa. If susan is both rich and not patient then john is not tall and vice versa. Everyone who is kind or not quiet is either old or patient and vice versa. Everyone who is generous or creative is either not tall or curious and vice versa. If alice is both not funny and generous then someone is both happy and tall and vice versa. If someone is both happy and generous then alice is either not curious or brave. If paul is either happy or not calm then mary is both wise and not tall and vice versa. If paul is either brave or not strong then someone is both not generous and not quiet and vice versa. Someone is not patient or not generous. Someone is both creative and not quiet. Someone is both old and not kind. Someone is both not kind and calm. Someone is not old. Someone is not brave. John is both curious and strong. | Lucy is not funny. | neutral | (((wise(mary)<~>~wise(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((~calm(paul))=>((wise(paul)&rich(paul))))&
((?[X]:((quiet(X)<~>~creative(X))))<=>(~quiet(susan)))&
(![X]:((~strong(X)&brave(X))<=>~humble(X)))&
((?[X]:((strong(X)|~curious(X))))=>((~brave(mary)|calm(mary))))&
(![X]:((~strong(X)|kind(X))<=>(old(X)|~funny(X))))&
(((~humble(john)<~>calm(john)))<=>((tall(lucy)|patient(lucy))))&
(![X]:(calm(X)=>happy(X)))&
(![X]:((rich(X)&~patient(X))<=>(generous(X)<~>~wise(X))))&
(((rich(susan)&~patient(susan)))<=>(~tall(john)))&
(![X]:((kind(X)|~quiet(X))<=>(old(X)<~>patient(X))))&
(![X]:((generous(X)|creative(X))<=>(~tall(X)<~>curious(X))))&
(((~funny(alice)&generous(alice)))<=>(?[X]:((happy(X)&tall(X)))))&
((?[X]:((happy(X)&generous(X))))=>((~curious(alice)<~>brave(alice))))&
(((happy(paul)<~>~calm(paul)))<=>((wise(mary)&~tall(mary))))&
(((brave(paul)<~>~strong(paul)))<=>(?[X]:((~generous(X)&~quiet(X)))))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((old(X)&~kind(X))))&
(?[X]:((~kind(X)&calm(X))))&
(?[X]:(~old(X)))&
(?[X]:(~brave(X)))&
((curious(john)&strong(john))) | ~funny(lucy) | [] | null | 0 |
If someone is both calm and not humble then someone is both not strong and happy and vice versa.
If fred is not generous or not happy then paul is not humble and vice versa.
If mary is generous then someone is either tall or not quiet and vice versa.
Everyone who is either not strong or old is both strong and tall and vice versa.
Everyone who is not quiet or happy is not curious or rich.
Everyone who is not kind or not calm is not curious.
Everyone who is happy is both not kind and strong.
Everyone who is wise is either not brave or tall and vice versa.
If someone is both not creative and strong then someone is both wise and calm.
Everyone who is both not kind and kind is funny or not patient and vice versa.
Everyone who is either not curious or quiet is both old and creative.
If fred is not patient or not quiet then lucy is either not kind or not patient and vice versa.
Everyone who is not tall or not calm is wise and vice versa.
Everyone who is not quiet or calm is either humble or happy.
If fred is both brave and not old then someone is both curious and not rich.
Everyone who is not brave is not kind or kind and vice versa.
John is not brave or brave.
Someone is both not rich and old.
Someone is not calm or tall.
Paul is funny or not brave.
Susan is either generous or not old.
Paul is not brave.
Lucy is both old and wise. | Paul is patient. | entailment | ((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~strong(X)&happy(X)))))&
(((~generous(fred)|~happy(fred)))<=>(~humble(paul)))&
((generous(mary))<=>(?[X]:((tall(X)<~>~quiet(X)))))&
(![X]:((~strong(X)<~>old(X))<=>(strong(X)&tall(X))))&
(![X]:((~quiet(X)|happy(X))=>(~curious(X)|rich(X))))&
(![X]:((~kind(X)|~calm(X))=>~curious(X)))&
(![X]:(happy(X)=>(~kind(X)&strong(X))))&
(![X]:(wise(X)<=>(~brave(X)<~>tall(X))))&
((?[X]:((~creative(X)&strong(X))))=>(?[X]:((wise(X)&calm(X)))))&
(![X]:((~kind(X)&kind(X))<=>(funny(X)|~patient(X))))&
(![X]:((~curious(X)<~>quiet(X))=>(old(X)&creative(X))))&
(((~patient(fred)|~quiet(fred)))<=>((~kind(lucy)<~>~patient(lucy))))&
(![X]:((~tall(X)|~calm(X))<=>wise(X)))&
(![X]:((~quiet(X)|calm(X))=>(humble(X)<~>happy(X))))&
(((brave(fred)&~old(fred)))=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:(~brave(X)<=>(~kind(X)|kind(X))))&
((~brave(john)|brave(john)))&
(?[X]:((~rich(X)&old(X))))&
(?[X]:((~calm(X)|tall(X))))&
((funny(paul)|~brave(paul)))&
((generous(susan)<~>~old(susan)))&
(~brave(paul))&
((old(lucy)&wise(lucy))) | patient(paul) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 3786875125456934437388085
% SZS output start Proof for 3786875125456934437388085
10. ! [X0] : ((kind(X0) & ~kind(X0)) <=> (~patient(X0) | funny(X0))) [input p9]
24. ~patient(paul) [input hypothesis]
51. ! [X0] : (((kind(X0) & ~kind(X0)) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | (~kind(X0) | kind(X0)))) [nnf transformation 10]
52. ! [X0] : (((kind(X0) & ~kind(X0)) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | ~kind(X0) | kind(X0))) [flattening 51]
97. ~kind(X0) | patient(X0) [cnf transformation 52]
99. kind(X0) | patient(X0) [cnf transformation 52]
130. ~patient(paul) [cnf transformation 24]
197. patient(X0) [subsumption resolution 97,99]
250. $false [subsumption resolution 130,197]
% SZS output end Proof for 3786875125456934437388085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative then someone is not patient or strong.
If mary is not kind then someone is either kind or not calm and vice versa.
Everyone who is both not strong and creative is tall and vice versa.
Everyone who is rich is both creative and not happy and vice versa.
Everyone who is not generous or not calm is humble or brave.
Everyone who is either not brave or brave is brave.
If susan is strong then someone is patient.
Everyone who is generous is either not calm or not happy.
If someone is calm then alice is both not quiet and curious.
Everyone who is quiet is either not old or curious.
Everyone who is both not funny and not calm is both calm and not brave and vice versa.
Everyone who is generous or quiet is both not strong and not generous.
If john is not strong or brave then someone is not quiet or creative.
If paul is either rich or not generous then someone is either wise or not patient and vice versa.
If john is not strong or not funny then someone is not wise or not old.
If someone is either generous or funny then mary is either not old or rich.
Someone is curious.
Someone is either patient or not tall.
Someone is brave or not calm.
Fred is either not tall or not old.
John is quiet or funny.
Alice is not patient.
Lucy is either wise or old.
Someone is not brave or brave. | Lucy is not generous. | entailment | ((?[X]:(creative(X)))=>(?[X]:((~patient(X)|strong(X)))))&
((~kind(mary))<=>(?[X]:((kind(X)<~>~calm(X)))))&
(![X]:((~strong(X)&creative(X))<=>tall(X)))&
(![X]:(rich(X)<=>(creative(X)&~happy(X))))&
(![X]:((~generous(X)|~calm(X))=>(humble(X)|brave(X))))&
(![X]:((~brave(X)<~>brave(X))=>brave(X)))&
((strong(susan))=>(?[X]:(patient(X))))&
(![X]:(generous(X)=>(~calm(X)<~>~happy(X))))&
((?[X]:(calm(X)))=>((~quiet(alice)&curious(alice))))&
(![X]:(quiet(X)=>(~old(X)<~>curious(X))))&
(![X]:((~funny(X)&~calm(X))<=>(calm(X)&~brave(X))))&
(![X]:((generous(X)|quiet(X))=>(~strong(X)&~generous(X))))&
(((~strong(john)|brave(john)))=>(?[X]:((~quiet(X)|creative(X)))))&
(((rich(paul)<~>~generous(paul)))<=>(?[X]:((wise(X)<~>~patient(X)))))&
(((~strong(john)|~funny(john)))=>(?[X]:((~wise(X)|~old(X)))))&
((?[X]:((generous(X)<~>funny(X))))=>((~old(mary)<~>rich(mary))))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)<~>~tall(X))))&
(?[X]:((brave(X)|~calm(X))))&
((~tall(fred)<~>~old(fred)))&
((quiet(john)|funny(john)))&
(~patient(alice))&
((wise(lucy)<~>old(lucy)))&
(?[X]:((~brave(X)|brave(X)))) | ~generous(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3603996503666989940531637
% SZS output start Proof for 3603996503666989940531637
12. ! [X0] : ((quiet(X0) | generous(X0)) => (~generous(X0) & ~strong(X0))) [input p11]
25. generous(lucy) [input hypothesis]
34. ! [X0] : ((~generous(X0) & ~strong(X0)) | (~quiet(X0) & ~generous(X0))) [ennf transformation 12]
102. ~generous(X0) | ~generous(X0) [cnf transformation 34]
131. generous(lucy) [cnf transformation 25]
132. ~generous(X0) [duplicate literal removal 102]
299. $false [subsumption resolution 131,132]
% SZS output end Proof for 3603996503666989940531637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not quiet then someone is either not calm or not brave. If someone is either kind or not quiet then susan is not creative or not calm and vice versa. Everyone who is both not calm and funny is curious and vice versa. If someone is not patient then someone is quiet and vice versa. Everyone who is both funny and generous is both kind and funny. Everyone who is both not curious and brave is both not wise and wise. If susan is both rich and not rich then someone is either creative or not generous and vice versa. Everyone who is both kind and rich is both not humble and not funny. Everyone who is either happy or creative is either tall or not humble and vice versa. Everyone who is not curious is tall. If someone is both not rich and not happy then someone is kind. If mary is either not kind or generous then someone is wise or not curious. Everyone who is both calm and not quiet is not happy or wise. If someone is not strong or funny then someone is either not old or not quiet and vice versa. Everyone who is both not brave and not rich is not strong and vice versa. If paul is both quiet and rich then alice is either tall or humble. Someone is rich. Someone is both humble and calm. Mary is not generous. Someone is either tall or not tall. Someone is not brave or tall. Susan is both not generous and not funny. Someone is either not calm or not quiet. Someone is not old or not kind. | Lucy is brave. | neutral | ((~quiet(lucy))=>(?[X]:((~calm(X)<~>~brave(X)))))&
((?[X]:((kind(X)<~>~quiet(X))))<=>((~creative(susan)|~calm(susan))))&
(![X]:((~calm(X)&funny(X))<=>curious(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(quiet(X))))&
(![X]:((funny(X)&generous(X))=>(kind(X)&funny(X))))&
(![X]:((~curious(X)&brave(X))=>(~wise(X)&wise(X))))&
(((rich(susan)&~rich(susan)))<=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:((kind(X)&rich(X))=>(~humble(X)&~funny(X))))&
(![X]:((happy(X)<~>creative(X))<=>(tall(X)<~>~humble(X))))&
(![X]:(~curious(X)=>tall(X)))&
((?[X]:((~rich(X)&~happy(X))))=>(?[X]:(kind(X))))&
(((~kind(mary)<~>generous(mary)))=>(?[X]:((wise(X)|~curious(X)))))&
(![X]:((calm(X)&~quiet(X))=>(~happy(X)|wise(X))))&
((?[X]:((~strong(X)|funny(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((~brave(X)&~rich(X))<=>~strong(X)))&
(((quiet(paul)&rich(paul)))=>((tall(alice)<~>humble(alice))))&
(?[X]:(rich(X)))&
(?[X]:((humble(X)&calm(X))))&
(~generous(mary))&
(?[X]:((tall(X)<~>~tall(X))))&
(?[X]:((~brave(X)|tall(X))))&
((~generous(susan)&~funny(susan)))&
(?[X]:((~calm(X)<~>~quiet(X))))&
(?[X]:((~old(X)|~kind(X)))) | brave(lucy) | [] | null | 0 |
If someone is either not rich or calm then someone is tall and vice versa.
Everyone who is not funny is creative and vice versa.
Everyone who is either brave or kind is not tall.
If mary is not calm or patient then someone is both not brave and not strong.
Everyone who is not curious is not generous or not old and vice versa.
If mary is both not happy and not brave then fred is not patient and vice versa.
Everyone who is not curious or not wise is both curious and not patient.
If john is not strong or rich then alice is creative or tall and vice versa.
Everyone who is both happy and wise is wise or not strong and vice versa.
Everyone who is both not funny and old is either brave or not generous and vice versa.
If someone is both creative and not happy then lucy is both not calm and rich.
Everyone who is rich is not calm and vice versa.
Everyone who is either not humble or not quiet is not kind or not old.
Lucy is not strong or not funny.
Someone is funny or not patient.
Someone is both kind and not tall.
Susan is not brave.
Susan is both old and not brave. | Susan is not creative. | entailment | ((?[X]:((~rich(X)<~>calm(X))))<=>(?[X]:(tall(X))))&
(![X]:(~funny(X)<=>creative(X)))&
(![X]:((brave(X)<~>kind(X))=>~tall(X)))&
(((~calm(mary)|patient(mary)))=>(?[X]:((~brave(X)&~strong(X)))))&
(![X]:(~curious(X)<=>(~generous(X)|~old(X))))&
(((~happy(mary)&~brave(mary)))<=>(~patient(fred)))&
(![X]:((~curious(X)|~wise(X))=>(curious(X)&~patient(X))))&
(((~strong(john)|rich(john)))<=>((creative(alice)|tall(alice))))&
(![X]:((happy(X)&wise(X))<=>(wise(X)|~strong(X))))&
(![X]:((~funny(X)&old(X))<=>(brave(X)<~>~generous(X))))&
((?[X]:((creative(X)&~happy(X))))=>((~calm(lucy)&rich(lucy))))&
(![X]:(rich(X)<=>~calm(X)))&
(![X]:((~humble(X)<~>~quiet(X))=>(~kind(X)|~old(X))))&
((~strong(lucy)|~funny(lucy)))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:((kind(X)&~tall(X))))&
(~brave(susan))&
((old(susan)&~brave(susan))) | ~creative(susan) | [
"p1",
"p4",
"p6",
"p9",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7054678712930826592366265
% SZS output start Proof for 7054678712930826592366265
2. ! [X0] : (~funny(X0) <=> creative(X0)) [input p1]
5. ! [X0] : (~curious(X0) <=> (~old(X0) | ~generous(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | ~curious(X0)) => (~patient(X0) & curious(X0))) [input p6]
10. ! [X0] : ((old(X0) & ~funny(X0)) <=> (brave(X0) <~> ~generous(X0))) [input p9]
17. ~brave(susan) [input p16]
18. ~brave(susan) & old(susan) [input p17]
19. creative(susan) [input hypothesis]
21. ! [X0] : ((~old(X0) | ~generous(X0)) => ~curious(X0)) [unused predicate definition removal 5]
24. ! [X0] : (~curious(X0) | (old(X0) & generous(X0))) [ennf transformation 21]
25. ! [X0] : ((~patient(X0) & curious(X0)) | (wise(X0) & curious(X0))) [ennf transformation 7]
34. ! [X0] : ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))) [nnf transformation 2]
44. ! [X0] : (((old(X0) & ~funny(X0)) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) & (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | (~old(X0) | funny(X0)))) [nnf transformation 10]
45. ! [X0] : (((old(X0) & ~funny(X0)) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) & (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | ~old(X0) | funny(X0))) [flattening 44]
57. ~creative(X0) | ~funny(X0) [cnf transformation 34]
64. ~curious(X0) | generous(X0) [cnf transformation 24]
69. curious(X0) | curious(X0) [cnf transformation 25]
82. ~old(X0) | brave(X0) | ~generous(X0) | funny(X0) [cnf transformation 45]
98. ~brave(susan) [cnf transformation 17]
99. old(susan) [cnf transformation 18]
101. creative(susan) [cnf transformation 19]
102. curious(X0) [duplicate literal removal 69]
216. ~funny(susan) [resolution 57,101]
218. generous(X0) [resolution 64,102]
239. brave(susan) | ~generous(susan) | funny(susan) [resolution 82,99]
243. ~generous(susan) | funny(susan) [subsumption resolution 239,98]
244. funny(susan) [subsumption resolution 243,218]
245. $false [subsumption resolution 244,216]
% SZS output end Proof for 7054678712930826592366265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not tall.
Everyone who is either rich or not brave is both not quiet and patient.
Everyone who is both old and not brave is not old or brave.
Everyone who is not strong is old or not brave and vice versa.
If john is both not funny and not happy then paul is both patient and creative.
Everyone who is not tall or not calm is not rich.
If mary is strong or old then alice is calm and vice versa.
If paul is either not patient or calm then alice is both not kind and wise.
Everyone who is not tall is not kind or not old.
Everyone who is either not generous or humble is both strong and not funny.
Everyone who is either patient or not humble is both not strong and not humble and vice versa.
Everyone who is not creative is both not old and humble.
Everyone who is not generous is both humble and happy.
Everyone who is both not curious and not rich is curious or funny and vice versa.
Everyone who is rich or not calm is humble.
Everyone who is happy is humble.
Lucy is both wise and not funny.
Someone is both creative and not old.
Someone is either not funny or not strong.
Someone is old or patient.
Someone is old or not happy.
Someone is either not old or not humble.
Someone is tall or not curious. | Lucy is rich. | entailment | (![X]:((~wise(X)<~>curious(X))=>~tall(X)))&
(![X]:((rich(X)<~>~brave(X))=>(~quiet(X)&patient(X))))&
(![X]:((old(X)&~brave(X))=>(~old(X)|brave(X))))&
(![X]:(~strong(X)<=>(old(X)|~brave(X))))&
(((~funny(john)&~happy(john)))=>((patient(paul)&creative(paul))))&
(![X]:((~tall(X)|~calm(X))=>~rich(X)))&
(((strong(mary)|old(mary)))<=>(calm(alice)))&
(((~patient(paul)<~>calm(paul)))=>((~kind(alice)&wise(alice))))&
(![X]:(~tall(X)=>(~kind(X)|~old(X))))&
(![X]:((~generous(X)<~>humble(X))=>(strong(X)&~funny(X))))&
(![X]:((patient(X)<~>~humble(X))<=>(~strong(X)&~humble(X))))&
(![X]:(~creative(X)=>(~old(X)&humble(X))))&
(![X]:(~generous(X)=>(humble(X)&happy(X))))&
(![X]:((~curious(X)&~rich(X))<=>(curious(X)|funny(X))))&
(![X]:((rich(X)|~calm(X))=>humble(X)))&
(![X]:(happy(X)=>humble(X)))&
((wise(lucy)&~funny(lucy)))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((~funny(X)<~>~strong(X))))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((old(X)|~happy(X))))&
(?[X]:((~old(X)<~>~humble(X))))&
(?[X]:((tall(X)|~curious(X)))) | rich(lucy) | [
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2772338832190130743416024
% SZS output start Proof for 2772338832190130743416024
14. ! [X0] : ((~rich(X0) & ~curious(X0)) <=> (funny(X0) | curious(X0))) [input p13]
17. ~funny(lucy) & wise(lucy) [input p16]
24. ~rich(lucy) [input hypothesis]
53. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & ((funny(X0) | curious(X0)) | (rich(X0) | curious(X0)))) [nnf transformation 14]
54. ! [X0] : (((~rich(X0) & ~curious(X0)) | (~funny(X0) & ~curious(X0))) & (funny(X0) | curious(X0) | rich(X0) | curious(X0))) [flattening 53]
97. funny(X0) | curious(X0) | rich(X0) | curious(X0) [cnf transformation 54]
98. ~curious(X0) | ~curious(X0) [cnf transformation 54]
106. ~funny(lucy) [cnf transformation 17]
115. ~rich(lucy) [cnf transformation 24]
116. funny(X0) | curious(X0) | rich(X0) [duplicate literal removal 97]
117. ~curious(X0) [duplicate literal removal 98]
159. funny(X0) | rich(X0) [subsumption resolution 116,117]
206. rich(lucy) [resolution 159,106]
209. $false [subsumption resolution 206,115]
% SZS output end Proof for 2772338832190130743416024
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or curious is not funny.
If paul is not tall or not rich then someone is either tall or kind and vice versa.
Everyone who is either not curious or humble is both funny and curious.
Everyone who is not generous or funny is both not creative and not quiet.
Everyone who is brave or curious is not humble or not tall and vice versa.
Everyone who is not patient is old or happy.
If john is strong or not brave then someone is either not happy or not strong.
Everyone who is not quiet is patient.
If someone is curious then alice is both creative and generous.
Everyone who is not funny is both not wise and patient and vice versa.
If someone is either calm or quiet then mary is curious or not creative.
Everyone who is both not patient and not rich is both tall and creative.
If john is not happy then someone is happy and vice versa.
Everyone who is both creative and wise is not funny or strong and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
Susan is wise.
Someone is both kind and not old.
John is not calm.
Lucy is wise. | Paul is not strong. | entailment | (![X]:((rich(X)|curious(X))=>~funny(X)))&
(((~tall(paul)|~rich(paul)))<=>(?[X]:((tall(X)<~>kind(X)))))&
(![X]:((~curious(X)<~>humble(X))=>(funny(X)&curious(X))))&
(![X]:((~generous(X)|funny(X))=>(~creative(X)&~quiet(X))))&
(![X]:((brave(X)|curious(X))<=>(~humble(X)|~tall(X))))&
(![X]:(~patient(X)=>(old(X)|happy(X))))&
(((strong(john)|~brave(john)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:(~quiet(X)=>patient(X)))&
((?[X]:(curious(X)))=>((creative(alice)&generous(alice))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
(wise(susan))&
(?[X]:((kind(X)&~old(X))))&
(~calm(john))&
(wise(lucy)) | ~strong(paul) | [
"p3",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2004513311717300940944320
% SZS output start Proof for 2004513311717300940944320
4. ! [X0] : ((funny(X0) | ~generous(X0)) => (~quiet(X0) & ~creative(X0))) [input p3]
10. ! [X0] : (~funny(X0) <=> (patient(X0) & ~wise(X0))) [input p9]
14. ! [X0] : ((wise(X0) & creative(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
20. strong(paul) [input hypothesis]
22. ! [X0] : (funny(X0) => (~quiet(X0) & ~creative(X0))) [pure predicate removal 4]
25. ! [X0] : ((~quiet(X0) & ~creative(X0)) | ~funny(X0)) [ennf transformation 22]
46. ! [X0] : ((~funny(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | funny(X0))) [nnf transformation 10]
47. ! [X0] : ((~funny(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | funny(X0))) [flattening 46]
53. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (~wise(X0) | ~creative(X0)))) [nnf transformation 14]
54. ! [X0] : (((wise(X0) & creative(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | ~wise(X0) | ~creative(X0))) [flattening 53]
70. ~creative(X0) | ~funny(X0) [cnf transformation 25]
83. ~wise(X0) | funny(X0) [cnf transformation 47]
94. ~strong(X0) | creative(X0) [cnf transformation 54]
95. wise(X0) | funny(X0) [cnf transformation 54]
110. strong(paul) [cnf transformation 20]
198. funny(X0) [subsumption resolution 95,83]
207. creative(paul) [resolution 94,110]
208. ~funny(paul) [resolution 207,70]
209. $false [subsumption resolution 208,198]
% SZS output end Proof for 2004513311717300940944320
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Susan is not creative. | 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))) | ~creative(susan) | [
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4510264763245962385476562
% SZS output start Proof for 4510264763245962385476562
10. ? [X0] : ~creative(X0) <=> (happy(susan) & ~brave(susan)) [input p9]
15. ! [X0] : (~brave(X0) <=> (~tall(X0) & creative(X0))) [input p14]
23. ~creative(susan) [input hypothesis]
49. (? [X0] : ~creative(X0) | (~happy(susan) | brave(susan))) & ((happy(susan) & ~brave(susan)) | ! [X0] : creative(X0)) [nnf transformation 10]
50. (? [X0] : ~creative(X0) | ~happy(susan) | brave(susan)) & ((happy(susan) & ~brave(susan)) | ! [X0] : creative(X0)) [flattening 49]
51. (? [X0] : ~creative(X0) | ~happy(susan) | brave(susan)) & ((happy(susan) & ~brave(susan)) | ! [X1] : creative(X1)) [rectify 50]
52. ? [X0] : ~creative(X0) => ~creative(sK3) [choice axiom]
53. (~creative(sK3) | ~happy(susan) | brave(susan)) & ((happy(susan) & ~brave(susan)) | ! [X1] : creative(X1)) [skolemisation 51,52]
62. ! [X0] : ((~brave(X0) | (tall(X0) | ~creative(X0))) & ((~tall(X0) & creative(X0)) | brave(X0))) [nnf transformation 15]
63. ! [X0] : ((~brave(X0) | tall(X0) | ~creative(X0)) & ((~tall(X0) & creative(X0)) | brave(X0))) [flattening 62]
107. ~brave(susan) | creative(X1) [cnf transformation 53]
130. brave(X0) | creative(X0) [cnf transformation 63]
142. ~creative(susan) [cnf transformation 23]
209. 14 <=> brave(susan) [avatar definition]
210. ~brave(susan) <- (~14) [avatar component clause 209]
222. 17 <=> ! [X1] : creative(X1) [avatar definition]
223. creative(X1) <- (17) [avatar component clause 222]
225. 17 | ~14 [avatar split clause 107,209,222]
280. creative(susan) <- (~14) [resolution 130,210]
281. $false <- (~14) [subsumption resolution 280,142]
282. 14 [avatar contradiction clause 281]
283. $false <- (17) [resolution 223,142]
286. ~17 [avatar contradiction clause 283]
287. $false [avatar sat refutation 225,282,286]
% SZS output end Proof for 4510264763245962385476562
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or curious then paul is either not curious or not generous.
Everyone who is not rich or not quiet is either not brave or not funny.
Everyone who is both not kind and not generous is both generous and curious and vice versa.
Everyone who is not curious is not old or not patient.
If someone is calm or not kind then mary is either not humble or wise.
If mary is patient or not happy then fred is not happy and vice versa.
If someone is not brave or not humble then alice is not funny and vice versa.
If susan is brave then alice is not kind or strong.
Everyone who is humble is either not generous or kind and vice versa.
If someone is both old and not creative then someone is not rich or funny.
Everyone who is not curious or strong is not kind.
Everyone who is both wise and not happy is both not funny and not tall and vice versa.
Everyone who is kind or strong is either quiet or not patient and vice versa.
Everyone who is both brave and funny is creative.
If fred is both wise and not old then alice is strong or tall and vice versa.
Everyone who is not humble is quiet and vice versa.
Someone is either not strong or not funny.
Lucy is humble or rich.
Someone is tall.
Mary is patient or tall.
Mary is quiet.
Alice is kind.
Paul is patient or curious.
Lucy is both not strong and not curious. | Lucy is not patient. | entailment | ((?[X]:((brave(X)|curious(X))))=>((~curious(paul)<~>~generous(paul))))&
(![X]:((~rich(X)|~quiet(X))=>(~brave(X)<~>~funny(X))))&
(![X]:((~kind(X)&~generous(X))<=>(generous(X)&curious(X))))&
(![X]:(~curious(X)=>(~old(X)|~patient(X))))&
((?[X]:((calm(X)|~kind(X))))=>((~humble(mary)<~>wise(mary))))&
(((patient(mary)|~happy(mary)))<=>(~happy(fred)))&
((?[X]:((~brave(X)|~humble(X))))<=>(~funny(alice)))&
((brave(susan))=>((~kind(alice)|strong(alice))))&
(![X]:(humble(X)<=>(~generous(X)<~>kind(X))))&
((?[X]:((old(X)&~creative(X))))=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((~curious(X)|strong(X))=>~kind(X)))&
(![X]:((wise(X)&~happy(X))<=>(~funny(X)&~tall(X))))&
(![X]:((kind(X)|strong(X))<=>(quiet(X)<~>~patient(X))))&
(![X]:((brave(X)&funny(X))=>creative(X)))&
(((wise(fred)&~old(fred)))<=>((strong(alice)|tall(alice))))&
(![X]:(~humble(X)<=>quiet(X)))&
(?[X]:((~strong(X)<~>~funny(X))))&
((humble(lucy)|rich(lucy)))&
(?[X]:(tall(X)))&
((patient(mary)|tall(mary)))&
(quiet(mary))&
(kind(alice))&
((patient(paul)|curious(paul)))&
((~strong(lucy)&~curious(lucy))) | ~patient(lucy) | [
"p2",
"p8",
"p10",
"p12",
"p15",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6006853299440999146617033
% SZS output start Proof for 6006853299440999146617033
3. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (curious(X0) & generous(X0))) [input p2]
9. ! [X0] : (humble(X0) <=> (~generous(X0) <~> kind(X0))) [input p8]
11. ! [X0] : ((strong(X0) | ~curious(X0)) => ~kind(X0)) [input p10]
13. ! [X0] : ((strong(X0) | kind(X0)) <=> (quiet(X0) <~> ~patient(X0))) [input p12]
16. ! [X0] : (~humble(X0) <=> quiet(X0)) [input p15]
24. ~curious(lucy) & ~strong(lucy) [input p23]
25. patient(lucy) [input hypothesis]
39. ! [X0] : (~kind(X0) | (~strong(X0) & curious(X0))) [ennf transformation 11]
42. ! [X0] : (((~generous(X0) & ~kind(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (generous(X0) | kind(X0)))) [nnf transformation 3]
43. ! [X0] : (((~generous(X0) & ~kind(X0)) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | generous(X0) | kind(X0))) [flattening 42]
51. ! [X0] : ((humble(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) & (((~kind(X0) | generous(X0)) & (kind(X0) | ~generous(X0))) | ~humble(X0))) [nnf transformation 9]
54. ! [X0] : (((strong(X0) | kind(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (~strong(X0) & ~kind(X0)))) [nnf transformation 13]
55. ! [X0] : ((strong(X0) | kind(X0) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (~strong(X0) & ~kind(X0)))) [flattening 54]
58. ! [X0] : ((~humble(X0) | ~quiet(X0)) & (quiet(X0) | humble(X0))) [nnf transformation 16]
70. generous(X0) | generous(X0) | kind(X0) [cnf transformation 43]
84. kind(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 51]
85. ~kind(X0) | generous(X0) | ~humble(X0) [cnf transformation 51]
88. ~kind(X0) | curious(X0) [cnf transformation 39]
94. ~patient(X0) | quiet(X0) | ~kind(X0) [cnf transformation 55]
98. ~patient(X0) | kind(X0) | strong(X0) | ~quiet(X0) [cnf transformation 55]
105. humble(X0) | quiet(X0) [cnf transformation 58]
114. ~strong(lucy) [cnf transformation 24]
115. ~curious(lucy) [cnf transformation 24]
116. patient(lucy) [cnf transformation 25]
117. kind(X0) | generous(X0) [duplicate literal removal 70]
199. ~humble(X0) | generous(X0) [subsumption resolution 85,117]
200. ~humble(X0) | kind(X0) [subsumption resolution 84,199]
248. kind(X0) | quiet(X0) [resolution 200,105]
376. quiet(lucy) | ~kind(lucy) [resolution 94,116]
378. quiet(lucy) [subsumption resolution 376,248]
384. kind(lucy) | strong(lucy) | ~quiet(lucy) [resolution 98,116]
386. kind(lucy) | ~quiet(lucy) [subsumption resolution 384,114]
387. kind(lucy) [subsumption resolution 386,378]
411. curious(lucy) [resolution 387,88]
421. $false [subsumption resolution 411,115]
% SZS output end Proof for 6006853299440999146617033
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not quiet is either not creative or not happy.
If mary is both creative and tall then someone is not old and vice versa.
If susan is wise then someone is both not humble and brave.
If someone is generous or not happy then alice is both generous and kind.
If someone is humble then someone is either not patient or not old and vice versa.
Everyone who is either not generous or generous is both not patient and tall.
If someone is not rich then alice is either not quiet or generous and vice versa.
Everyone who is kind or not wise is either not brave or not funny.
If fred is both curious and not curious then someone is calm or not strong and vice versa.
Everyone who is not creative or brave is either not patient or not tall.
Everyone who is not brave is both old and not rich and vice versa.
Everyone who is old or funny is either not calm or not kind.
If alice is both not creative and strong then paul is both not patient and not funny.
If someone is either not generous or tall then someone is both patient and tall.
If susan is not generous then alice is either old or quiet.
Everyone who is not kind is both strong and not calm.
Alice is strong.
Fred is both not wise and not generous.
Someone is either not creative or not old.
Someone is not rich.
Someone is either not calm or not happy.
Someone is both funny and not rich.
Someone is not kind or not generous.
Paul is patient or not curious. | Susan is not tall. | contradiction | (![X]:((~creative(X)<~>~quiet(X))=>(~creative(X)<~>~happy(X))))&
(((creative(mary)&tall(mary)))<=>(?[X]:(~old(X))))&
((wise(susan))=>(?[X]:((~humble(X)&brave(X)))))&
((?[X]:((generous(X)|~happy(X))))=>((generous(alice)&kind(alice))))&
((?[X]:(humble(X)))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((~generous(X)<~>generous(X))=>(~patient(X)&tall(X))))&
((?[X]:(~rich(X)))<=>((~quiet(alice)<~>generous(alice))))&
(![X]:((kind(X)|~wise(X))=>(~brave(X)<~>~funny(X))))&
(((curious(fred)&~curious(fred)))<=>(?[X]:((calm(X)|~strong(X)))))&
(![X]:((~creative(X)|brave(X))=>(~patient(X)<~>~tall(X))))&
(![X]:(~brave(X)<=>(old(X)&~rich(X))))&
(![X]:((old(X)|funny(X))=>(~calm(X)<~>~kind(X))))&
(((~creative(alice)&strong(alice)))=>((~patient(paul)&~funny(paul))))&
((?[X]:((~generous(X)<~>tall(X))))=>(?[X]:((patient(X)&tall(X)))))&
((~generous(susan))=>((old(alice)<~>quiet(alice))))&
(![X]:(~kind(X)=>(strong(X)&~calm(X))))&
(strong(alice))&
((~wise(fred)&~generous(fred)))&
(?[X]:((~creative(X)<~>~old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((~calm(X)<~>~happy(X))))&
(?[X]:((funny(X)&~rich(X))))&
(?[X]:((~kind(X)|~generous(X))))&
((patient(paul)|~curious(paul))) | ~tall(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3102450611254099536694743
% SZS output start Proof for 3102450611254099536694743
6. ! [X0] : ((~generous(X0) <~> generous(X0)) => (tall(X0) & ~patient(X0))) [input p5]
25. ~tall(susan) [input hypothesis]
31. ! [X0] : ((tall(X0) & ~patient(X0)) | (~generous(X0) <=> generous(X0))) [ennf transformation 6]
53. ! [X0] : ((tall(X0) & ~patient(X0)) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) [nnf transformation 31]
104. tall(X0) | generous(X0) | generous(X0) [cnf transformation 53]
105. tall(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 53]
152. ~tall(susan) [cnf transformation 25]
155. tall(X0) | generous(X0) [duplicate literal removal 104]
156. tall(X0) | ~generous(X0) [duplicate literal removal 105]
234. tall(X0) [subsumption resolution 155,156]
322. $false [subsumption resolution 152,234]
% SZS output end Proof for 3102450611254099536694743
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and not kind is funny or brave and vice versa.
If john is quiet then john is either humble or curious and vice versa.
Everyone who is generous is either tall or quiet.
If someone is either not wise or kind then john is both brave and not strong.
Everyone who is not brave is both brave and not brave.
Everyone who is both calm and not quiet is not brave.
If someone is not old or curious then mary is both calm and humble.
Everyone who is either patient or not old is both happy and curious and vice versa.
Everyone who is both not curious and not happy is not happy and vice versa.
Everyone who is either quiet or not kind is not kind and vice versa.
Everyone who is not quiet or not brave is either humble or happy and vice versa.
Everyone who is not happy or not curious is either not calm or humble.
If someone is curious or not wise then someone is not strong or not generous and vice versa.
Everyone who is not generous or not funny is not generous.
Someone is not funny or happy.
Lucy is not old or brave.
Paul is not quiet or rich. | Mary is generous. | contradiction | (![X]:((~tall(X)&~kind(X))<=>(funny(X)|brave(X))))&
((quiet(john))<=>((humble(john)<~>curious(john))))&
(![X]:(generous(X)=>(tall(X)<~>quiet(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((brave(john)&~strong(john))))&
(![X]:(~brave(X)=>(brave(X)&~brave(X))))&
(![X]:((calm(X)&~quiet(X))=>~brave(X)))&
((?[X]:((~old(X)|curious(X))))=>((calm(mary)&humble(mary))))&
(![X]:((patient(X)<~>~old(X))<=>(happy(X)&curious(X))))&
(![X]:((~curious(X)&~happy(X))<=>~happy(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~kind(X)))&
(![X]:((~quiet(X)|~brave(X))<=>(humble(X)<~>happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(~calm(X)<~>humble(X))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:((~strong(X)|~generous(X)))))&
(![X]:((~generous(X)|~funny(X))=>~generous(X)))&
(?[X]:((~funny(X)|happy(X))))&
((~old(lucy)|brave(lucy)))&
((~quiet(paul)|rich(paul))) | generous(mary) | [
"p0",
"p2",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2409006866344991924363547
% SZS output start Proof for 2409006866344991924363547
1. ! [X0] : ((~kind(X0) & ~tall(X0)) <=> (brave(X0) | funny(X0))) [input p0]
3. ! [X0] : (generous(X0) => (tall(X0) <~> quiet(X0))) [input p2]
5. ! [X0] : (~brave(X0) => (~brave(X0) & brave(X0))) [input p4]
10. ! [X0] : ((quiet(X0) <~> ~kind(X0)) <=> ~kind(X0)) [input p9]
18. generous(mary) [input hypothesis]
21. ! [X0] : ((tall(X0) <~> quiet(X0)) | ~generous(X0)) [ennf transformation 3]
23. ! [X0] : ((~brave(X0) & brave(X0)) | brave(X0)) [ennf transformation 5]
29. ! [X0] : (((~kind(X0) & ~tall(X0)) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | (kind(X0) | tall(X0)))) [nnf transformation 1]
30. ! [X0] : (((~kind(X0) & ~tall(X0)) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | kind(X0) | tall(X0))) [flattening 29]
32. ! [X0] : (((~quiet(X0) | ~tall(X0)) & (quiet(X0) | tall(X0))) | ~generous(X0)) [nnf transformation 21]
38. ! [X0] : ((((kind(X0) | ~quiet(X0)) & (~kind(X0) | quiet(X0))) | kind(X0)) & (~kind(X0) | ((quiet(X0) | kind(X0)) & (~kind(X0) | ~quiet(X0))))) [nnf transformation 10]
51. ~brave(X0) | ~tall(X0) [cnf transformation 30]
58. ~generous(X0) | tall(X0) | quiet(X0) [cnf transformation 32]
64. brave(X0) | brave(X0) [cnf transformation 23]
80. ~kind(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 38]
83. kind(X0) | ~quiet(X0) | kind(X0) [cnf transformation 38]
102. generous(mary) [cnf transformation 18]
103. ~kind(X0) | ~quiet(X0) [duplicate literal removal 80]
104. ~quiet(X0) | kind(X0) [duplicate literal removal 83]
105. brave(X0) [duplicate literal removal 64]
159. ~quiet(X0) [subsumption resolution 103,104]
201. ~tall(X0) [resolution 51,105]
211. tall(mary) | quiet(mary) [resolution 58,102]
212. quiet(mary) [subsumption resolution 211,201]
213. $false [subsumption resolution 212,159]
% SZS output end Proof for 2409006866344991924363547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not happy and vice versa.
Everyone who is both not old and brave is both strong and not humble and vice versa.
If someone is either tall or not creative then paul is not curious or not kind and vice versa.
Everyone who is both rich and not strong is both quiet and not calm and vice versa.
Everyone who is both not quiet and humble is both creative and not humble and vice versa.
Everyone who is both not wise and old is either patient or funny.
Everyone who is not kind is either patient or not humble and vice versa.
Everyone who is both creative and not strong is kind.
Everyone who is both not calm and wise is both funny and not quiet.
If lucy is either not tall or not funny then someone is both funny and not patient and vice versa.
Everyone who is creative is both humble and funny.
Everyone who is creative is either happy or funny.
Everyone who is either not brave or not calm is either not calm or not rich.
Everyone who is both not humble and creative is kind and vice versa.
If mary is either not creative or not rich then john is not quiet.
Everyone who is not happy or tall is either old or calm.
Someone is old or not wise.
Someone is tall.
Someone is not rich.
Fred is either not generous or curious.
Someone is not curious or not generous.
Someone is not funny or tall.
Someone is not tall or old.
Someone is either patient or not happy. | Mary is kind. | contradiction | (![X]:(~old(X)<=>~happy(X)))&
(![X]:((~old(X)&brave(X))<=>(strong(X)&~humble(X))))&
((?[X]:((tall(X)<~>~creative(X))))<=>((~curious(paul)|~kind(paul))))&
(![X]:((rich(X)&~strong(X))<=>(quiet(X)&~calm(X))))&
(![X]:((~quiet(X)&humble(X))<=>(creative(X)&~humble(X))))&
(![X]:((~wise(X)&old(X))=>(patient(X)<~>funny(X))))&
(![X]:(~kind(X)<=>(patient(X)<~>~humble(X))))&
(![X]:((creative(X)&~strong(X))=>kind(X)))&
(![X]:((~calm(X)&wise(X))=>(funny(X)&~quiet(X))))&
(((~tall(lucy)<~>~funny(lucy)))<=>(?[X]:((funny(X)&~patient(X)))))&
(![X]:(creative(X)=>(humble(X)&funny(X))))&
(![X]:(creative(X)=>(happy(X)<~>funny(X))))&
(![X]:((~brave(X)<~>~calm(X))=>(~calm(X)<~>~rich(X))))&
(![X]:((~humble(X)&creative(X))<=>kind(X)))&
(((~creative(mary)<~>~rich(mary)))=>(~quiet(john)))&
(![X]:((~happy(X)|tall(X))=>(old(X)<~>calm(X))))&
(?[X]:((old(X)|~wise(X))))&
(?[X]:(tall(X)))&
(?[X]:(~rich(X)))&
((~generous(fred)<~>curious(fred)))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((~tall(X)|old(X))))&
(?[X]:((patient(X)<~>~happy(X)))) | kind(mary) | [
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6066565677388069804479245
% SZS output start Proof for 6066565677388069804479245
5. ! [X0] : ((humble(X0) & ~quiet(X0)) <=> (~humble(X0) & creative(X0))) [input p4]
14. ! [X0] : ((creative(X0) & ~humble(X0)) <=> kind(X0)) [input p13]
25. kind(mary) [input hypothesis]
47. ! [X0] : (((humble(X0) & ~quiet(X0)) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | (~humble(X0) | quiet(X0)))) [nnf transformation 5]
48. ! [X0] : (((humble(X0) & ~quiet(X0)) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | ~humble(X0) | quiet(X0))) [flattening 47]
57. ! [X0] : (((creative(X0) & ~humble(X0)) | ~kind(X0)) & (kind(X0) | (~creative(X0) | humble(X0)))) [nnf transformation 14]
58. ! [X0] : (((creative(X0) & ~humble(X0)) | ~kind(X0)) & (kind(X0) | ~creative(X0) | humble(X0))) [flattening 57]
96. humble(X0) | humble(X0) | ~creative(X0) [cnf transformation 48]
121. ~kind(X0) | ~humble(X0) [cnf transformation 58]
122. ~kind(X0) | creative(X0) [cnf transformation 58]
139. kind(mary) [cnf transformation 25]
143. ~creative(X0) | humble(X0) [duplicate literal removal 96]
203. 13 <=> creative(mary) [avatar definition]
204. creative(mary) <- (13) [avatar component clause 203]
269. ~humble(mary) [resolution 121,139]
270. creative(mary) [resolution 122,139]
271. 13 [avatar split clause 270,203]
273. humble(mary) <- (13) [resolution 143,204]
274. $false <- (13) [subsumption resolution 273,269]
275. ~13 [avatar contradiction clause 274]
276. $false [avatar sat refutation 271,275]
% SZS output end Proof for 6066565677388069804479245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or rich then john is kind and vice versa.
If someone is generous then someone is both not brave and not curious and vice versa.
Everyone who is not happy or not brave is either kind or not brave and vice versa.
If someone is both not humble and not patient then someone is either rich or funny.
Everyone who is both not kind and curious is either not tall or strong and vice versa.
If susan is creative or not kind then lucy is rich or not brave and vice versa.
If someone is both patient and not kind then someone is both happy and not rich.
Everyone who is wise or creative is not creative or not brave and vice versa.
Everyone who is not strong is either strong or not generous and vice versa.
If someone is wise or not rich then mary is tall or curious.
If mary is kind then someone is not old or not curious and vice versa.
If someone is either not quiet or old then susan is either not wise or brave.
If paul is generous then someone is generous or not kind and vice versa.
Everyone who is either not kind or not strong is quiet or not rich and vice versa.
Everyone who is either not creative or old is either calm or not strong and vice versa.
If susan is both humble and not old then someone is both not rich and not curious and vice versa.
Lucy is either generous or quiet.
Mary is not curious or tall.
Someone is both calm and kind.
Mary is funny.
Paul is not calm.
Someone is not curious. | Lucy is not happy. | entailment | ((?[X]:((tall(X)<~>rich(X))))<=>(kind(john)))&
((?[X]:(generous(X)))<=>(?[X]:((~brave(X)&~curious(X)))))&
(![X]:((~happy(X)|~brave(X))<=>(kind(X)<~>~brave(X))))&
((?[X]:((~humble(X)&~patient(X))))=>(?[X]:((rich(X)<~>funny(X)))))&
(![X]:((~kind(X)&curious(X))<=>(~tall(X)<~>strong(X))))&
(((creative(susan)|~kind(susan)))<=>((rich(lucy)|~brave(lucy))))&
((?[X]:((patient(X)&~kind(X))))=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((wise(X)|creative(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~strong(X)<=>(strong(X)<~>~generous(X))))&
((?[X]:((wise(X)|~rich(X))))=>((tall(mary)|curious(mary))))&
((kind(mary))<=>(?[X]:((~old(X)|~curious(X)))))&
((?[X]:((~quiet(X)<~>old(X))))=>((~wise(susan)<~>brave(susan))))&
((generous(paul))<=>(?[X]:((generous(X)|~kind(X)))))&
(![X]:((~kind(X)<~>~strong(X))<=>(quiet(X)|~rich(X))))&
(![X]:((~creative(X)<~>old(X))<=>(calm(X)<~>~strong(X))))&
(((humble(susan)&~old(susan)))<=>(?[X]:((~rich(X)&~curious(X)))))&
((generous(lucy)<~>quiet(lucy)))&
((~curious(mary)|tall(mary)))&
(?[X]:((calm(X)&kind(X))))&
(funny(mary))&
(~calm(paul))&
(?[X]:(~curious(X))) | ~happy(lucy) | [
"p2",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5306924594508456399680406
% SZS output start Proof for 5306924594508456399680406
3. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> (kind(X0) <~> ~brave(X0))) [input p2]
9. ! [X0] : (~strong(X0) <=> (strong(X0) <~> ~generous(X0))) [input p8]
13. generous(paul) <=> ? [X0] : (~kind(X0) | generous(X0)) [input p12]
23. happy(lucy) [input hypothesis]
41. ! [X0] : (((~brave(X0) | ~happy(X0)) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (brave(X0) & happy(X0)))) [nnf transformation 3]
42. ! [X0] : ((~brave(X0) | ~happy(X0) | ((kind(X0) | brave(X0)) & (~brave(X0) | ~kind(X0)))) & (((brave(X0) | ~kind(X0)) & (~brave(X0) | kind(X0))) | (brave(X0) & happy(X0)))) [flattening 41]
56. ! [X0] : ((~strong(X0) | ((strong(X0) | generous(X0)) & (~generous(X0) | ~strong(X0)))) & (((generous(X0) | ~strong(X0)) & (~generous(X0) | strong(X0))) | strong(X0))) [nnf transformation 9]
62. (generous(paul) | ! [X0] : (kind(X0) & ~generous(X0))) & (? [X0] : (~kind(X0) | generous(X0)) | ~generous(paul)) [nnf transformation 13]
63. (generous(paul) | ! [X0] : (kind(X0) & ~generous(X0))) & (? [X1] : (~kind(X1) | generous(X1)) | ~generous(paul)) [rectify 62]
64. ? [X1] : (~kind(X1) | generous(X1)) => (~kind(sK6) | generous(sK6)) [choice axiom]
65. (generous(paul) | ! [X0] : (kind(X0) & ~generous(X0))) & ((~kind(sK6) | generous(sK6)) | ~generous(paul)) [skolemisation 63,64]
89. brave(X0) | ~kind(X0) | brave(X0) [cnf transformation 42]
90. ~brave(X0) | ~happy(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 42]
110. ~generous(X0) | strong(X0) | strong(X0) [cnf transformation 56]
112. ~strong(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 56]
125. generous(paul) | kind(X0) [cnf transformation 65]
152. happy(lucy) [cnf transformation 23]
153. ~generous(X0) | strong(X0) [duplicate literal removal 110]
154. ~strong(X0) | ~generous(X0) [duplicate literal removal 112]
157. ~kind(X0) | brave(X0) [duplicate literal removal 89]
158. ~happy(X0) | ~brave(X0) | ~kind(X0) [duplicate literal removal 90]
190. 8 <=> ! [X3] : ~generous(X3) [avatar definition]
191. ~generous(X3) <- (8) [avatar component clause 190]
248. ~generous(X0) [subsumption resolution 153,154]
249. 8 [avatar split clause 248,190]
306. 34 <=> ! [X0] : kind(X0) [avatar definition]
307. kind(X0) <- (34) [avatar component clause 306]
309. 35 <=> generous(paul) [avatar definition]
311. generous(paul) <- (35) [avatar component clause 309]
312. 34 | 35 [avatar split clause 125,309,306]
361. $false <- (8, 35) [subsumption resolution 311,191]
362. ~8 | ~35 [avatar contradiction clause 361]
374. brave(X0) <- (34) [resolution 157,307]
427. ~brave(lucy) | ~kind(lucy) [resolution 158,152]
428. ~kind(lucy) <- (34) [subsumption resolution 427,374]
429. $false <- (34) [subsumption resolution 428,307]
430. ~34 [avatar contradiction clause 429]
431. $false [avatar sat refutation 249,312,362,430]
% SZS output end Proof for 5306924594508456399680406
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either generous or not generous then someone is either curious or not brave and vice versa.
Everyone who is not tall is both rich and quiet.
Everyone who is happy is both old and creative and vice versa.
Everyone who is curious is strong or not quiet and vice versa.
Everyone who is strong is wise or funny.
Everyone who is both kind and not kind is either not old or not happy.
Everyone who is both happy and quiet is not curious or quiet.
Everyone who is both wise and patient is either funny or generous.
Everyone who is both not calm and not funny is both not wise and creative.
If alice is old or brave then lucy is both creative and old.
Everyone who is not rich or generous is both not calm and not tall.
If john is quiet or not humble then alice is both kind and not quiet and vice versa.
Everyone who is tall or not kind is either humble or brave and vice versa.
If mary is either not happy or rich then someone is old.
If someone is both rich and not happy then susan is either kind or humble.
Everyone who is either not quiet or not curious is both brave and wise.
Someone is not wise or not rich.
Someone is not strong or funny.
John is calm or brave.
Someone is both not generous and old. | Alice is not wise. | contradiction | (((generous(mary)<~>~generous(mary)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:(~tall(X)=>(rich(X)&quiet(X))))&
(![X]:(happy(X)<=>(old(X)&creative(X))))&
(![X]:(curious(X)<=>(strong(X)|~quiet(X))))&
(![X]:(strong(X)=>(wise(X)|funny(X))))&
(![X]:((kind(X)&~kind(X))=>(~old(X)<~>~happy(X))))&
(![X]:((happy(X)&quiet(X))=>(~curious(X)|quiet(X))))&
(![X]:((wise(X)&patient(X))=>(funny(X)<~>generous(X))))&
(![X]:((~calm(X)&~funny(X))=>(~wise(X)&creative(X))))&
(((old(alice)|brave(alice)))=>((creative(lucy)&old(lucy))))&
(![X]:((~rich(X)|generous(X))=>(~calm(X)&~tall(X))))&
(((quiet(john)|~humble(john)))<=>((kind(alice)&~quiet(alice))))&
(![X]:((tall(X)|~kind(X))<=>(humble(X)<~>brave(X))))&
(((~happy(mary)<~>rich(mary)))=>(?[X]:(old(X))))&
((?[X]:((rich(X)&~happy(X))))=>((kind(susan)<~>humble(susan))))&
(![X]:((~quiet(X)<~>~curious(X))=>(brave(X)&wise(X))))&
(?[X]:((~wise(X)|~rich(X))))&
(?[X]:((~strong(X)|funny(X))))&
((calm(john)|brave(john)))&
(?[X]:((~generous(X)&old(X)))) | ~wise(alice) | [
"p1",
"p3",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 33934167126832995886906
% SZS output start Proof for 33934167126832995886906
2. ! [X0] : (~tall(X0) => (quiet(X0) & rich(X0))) [input p1]
4. ! [X0] : (curious(X0) <=> (~quiet(X0) | strong(X0))) [input p3]
12. (~humble(john) | quiet(john)) <=> (~quiet(alice) & kind(alice)) [input p11]
13. ! [X0] : ((~kind(X0) | tall(X0)) <=> (humble(X0) <~> brave(X0))) [input p12]
16. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) => (wise(X0) & brave(X0))) [input p15]
21. ~wise(alice) [input hypothesis]
26. ! [X0] : ((quiet(X0) & rich(X0)) | tall(X0)) [ennf transformation 2]
35. ! [X0] : ((wise(X0) & brave(X0)) | (~quiet(X0) <=> ~curious(X0))) [ennf transformation 16]
42. ! [X0] : ((curious(X0) | (quiet(X0) & ~strong(X0))) & ((~quiet(X0) | strong(X0)) | ~curious(X0))) [nnf transformation 4]
43. ! [X0] : ((curious(X0) | (quiet(X0) & ~strong(X0))) & (~quiet(X0) | strong(X0) | ~curious(X0))) [flattening 42]
45. ((~humble(john) | quiet(john)) | (quiet(alice) | ~kind(alice))) & ((~quiet(alice) & kind(alice)) | (humble(john) & ~quiet(john))) [nnf transformation 12]
46. (~humble(john) | quiet(john) | quiet(alice) | ~kind(alice)) & ((~quiet(alice) & kind(alice)) | (humble(john) & ~quiet(john))) [flattening 45]
47. ! [X0] : (((~kind(X0) | tall(X0)) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (kind(X0) & ~tall(X0)))) [nnf transformation 13]
48. ! [X0] : ((~kind(X0) | tall(X0) | ((humble(X0) | ~brave(X0)) & (brave(X0) | ~humble(X0)))) & (((~brave(X0) | ~humble(X0)) & (brave(X0) | humble(X0))) | (kind(X0) & ~tall(X0)))) [flattening 47]
53. ! [X0] : ((wise(X0) & brave(X0)) | ((~quiet(X0) | curious(X0)) & (~curious(X0) | quiet(X0)))) [nnf transformation 35]
67. quiet(X0) | tall(X0) [cnf transformation 26]
73. quiet(X0) | curious(X0) [cnf transformation 43]
87. ~quiet(alice) | ~quiet(john) [cnf transformation 46]
88. ~quiet(alice) | humble(john) [cnf transformation 46]
92. ~humble(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 48]
100. brave(X0) | ~curious(X0) | quiet(X0) [cnf transformation 53]
102. wise(X0) | ~curious(X0) | quiet(X0) [cnf transformation 53]
108. ~wise(alice) [cnf transformation 21]
155. 9 <=> quiet(alice) [avatar definition]
159. 10 <=> quiet(john) [avatar definition]
160. ~quiet(john) <- (~10) [avatar component clause 159]
163. 11 <=> humble(john) [avatar definition]
164. humble(john) <- (11) [avatar component clause 163]
167. 11 | ~9 [avatar split clause 88,155,163]
168. ~10 | ~9 [avatar split clause 87,155,159]
197. wise(X0) | quiet(X0) [subsumption resolution 102,73]
199. quiet(X0) | brave(X0) [subsumption resolution 100,73]
206. 18 <=> brave(john) [avatar definition]
208. brave(john) <- (18) [avatar component clause 206]
213. tall(john) <- (~10) [resolution 67,160]
227. quiet(alice) [resolution 197,108]
231. 9 [avatar split clause 227,155]
236. brave(john) <- (~10) [resolution 199,160]
237. 18 | 10 [avatar split clause 236,159,206]
252. ~brave(john) | ~tall(john) <- (11) [resolution 92,164]
254. ~tall(john) <- (11, 18) [subsumption resolution 252,208]
255. $false <- (~10, 11, 18) [subsumption resolution 254,213]
256. 10 | ~11 | ~18 [avatar contradiction clause 255]
257. $false [avatar sat refutation 167,168,231,237,256]
% SZS output end Proof for 33934167126832995886906
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not patient and creative then susan is quiet and vice versa. Everyone who is both generous and not generous is kind or not generous and vice versa. Everyone who is not generous or calm is strong or old. If someone is not quiet or not brave then john is not brave or quiet and vice versa. If paul is quiet or wise then someone is not brave or happy and vice versa. Everyone who is creative is both calm and creative. Everyone who is wise is either not kind or not generous and vice versa. Everyone who is either not patient or not old is not strong or not kind and vice versa. If someone is patient then someone is curious or creative and vice versa. Everyone who is brave is both rich and not creative. Everyone who is both rich and not generous is both not old and not generous. Everyone who is both humble and curious is not happy or funny. Everyone who is not curious is humble and vice versa. If john is brave or curious then fred is curious or happy. If someone is either brave or not calm then someone is not humble and vice versa. If someone is not happy then lucy is humble. Someone is either not old or brave. Someone is tall or not curious. Paul is not creative. Susan is both not brave and not happy. Lucy is not wise or humble. Someone is not rich. | Fred is funny. | neutral | ((?[X]:((~patient(X)&creative(X))))<=>(quiet(susan)))&
(![X]:((generous(X)&~generous(X))<=>(kind(X)|~generous(X))))&
(![X]:((~generous(X)|calm(X))=>(strong(X)|old(X))))&
((?[X]:((~quiet(X)|~brave(X))))<=>((~brave(john)|quiet(john))))&
(((quiet(paul)|wise(paul)))<=>(?[X]:((~brave(X)|happy(X)))))&
(![X]:(creative(X)=>(calm(X)&creative(X))))&
(![X]:(wise(X)<=>(~kind(X)<~>~generous(X))))&
(![X]:((~patient(X)<~>~old(X))<=>(~strong(X)|~kind(X))))&
((?[X]:(patient(X)))<=>(?[X]:((curious(X)|creative(X)))))&
(![X]:(brave(X)=>(rich(X)&~creative(X))))&
(![X]:((rich(X)&~generous(X))=>(~old(X)&~generous(X))))&
(![X]:((humble(X)&curious(X))=>(~happy(X)|funny(X))))&
(![X]:(~curious(X)<=>humble(X)))&
(((brave(john)|curious(john)))=>((curious(fred)|happy(fred))))&
((?[X]:((brave(X)<~>~calm(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(~happy(X)))=>(humble(lucy)))&
(?[X]:((~old(X)<~>brave(X))))&
(?[X]:((tall(X)|~curious(X))))&
(~creative(paul))&
((~brave(susan)&~happy(susan)))&
((~wise(lucy)|humble(lucy)))&
(?[X]:(~rich(X))) | funny(fred) | [] | null | 0 |
If john is both kind and not funny then someone is not creative. Everyone who is either not happy or not quiet is both tall and not creative. Everyone who is quiet is not rich or not calm. If john is either strong or generous then someone is either not brave or not humble and vice versa. Everyone who is not tall is both not curious and not strong. Everyone who is either rich or wise is both not quiet and not humble. Everyone who is either generous or not happy is not generous and vice versa. Everyone who is curious is not kind or humble and vice versa. Everyone who is patient or strong is happy or not kind. If fred is either not curious or old then someone is both not creative and patient and vice versa. Everyone who is humble is not brave or old and vice versa. If susan is both not wise and not rich then alice is generous or not calm and vice versa. If someone is not rich or curious then someone is both not generous and old. If someone is both rich and happy then mary is quiet and vice versa. If john is not happy or curious then susan is old or strong and vice versa. Everyone who is both happy and kind is either not curious or not tall and vice versa. Someone is either not patient or wise. Someone is both calm and humble. Paul is both humble and rich. John is not creative or happy. Someone is either not humble or generous. Alice is calm. Someone is either not generous or funny. | Susan is not humble. | neutral | (((kind(john)&~funny(john)))=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)<~>~quiet(X))=>(tall(X)&~creative(X))))&
(![X]:(quiet(X)=>(~rich(X)|~calm(X))))&
(((strong(john)<~>generous(john)))<=>(?[X]:((~brave(X)<~>~humble(X)))))&
(![X]:(~tall(X)=>(~curious(X)&~strong(X))))&
(![X]:((rich(X)<~>wise(X))=>(~quiet(X)&~humble(X))))&
(![X]:((generous(X)<~>~happy(X))<=>~generous(X)))&
(![X]:(curious(X)<=>(~kind(X)|humble(X))))&
(![X]:((patient(X)|strong(X))=>(happy(X)|~kind(X))))&
(((~curious(fred)<~>old(fred)))<=>(?[X]:((~creative(X)&patient(X)))))&
(![X]:(humble(X)<=>(~brave(X)|old(X))))&
(((~wise(susan)&~rich(susan)))<=>((generous(alice)|~calm(alice))))&
((?[X]:((~rich(X)|curious(X))))=>(?[X]:((~generous(X)&old(X)))))&
((?[X]:((rich(X)&happy(X))))<=>(quiet(mary)))&
(((~happy(john)|curious(john)))<=>((old(susan)|strong(susan))))&
(![X]:((happy(X)&kind(X))<=>(~curious(X)<~>~tall(X))))&
(?[X]:((~patient(X)<~>wise(X))))&
(?[X]:((calm(X)&humble(X))))&
((humble(paul)&rich(paul)))&
((~creative(john)|happy(john)))&
(?[X]:((~humble(X)<~>generous(X))))&
(calm(alice))&
(?[X]:((~generous(X)<~>funny(X)))) | ~humble(susan) | [] | null | 0 |
Everyone who is both creative and not calm is not creative or not happy. Everyone who is either quiet or kind is rich or calm and vice versa. Everyone who is not funny is both not generous and calm and vice versa. If paul is both happy and not wise then someone is wise. Everyone who is not funny or tall is both rich and not tall. Everyone who is calm or tall is both curious and old and vice versa. Everyone who is either not quiet or not patient is both tall and not humble and vice versa. If someone is strong then someone is patient. If alice is both not wise and rich then susan is funny or not humble and vice versa. If someone is both calm and old then someone is not creative or not kind. If lucy is either rich or not humble then someone is brave or kind and vice versa. Everyone who is curious is both strong and not generous and vice versa. Everyone who is calm or not curious is both funny and rich. If someone is happy or funny then someone is not tall and vice versa. Everyone who is both curious and not quiet is both rich and old and vice versa. If mary is either not strong or not funny then someone is both not old and not kind and vice versa. Someone is both not rich and not creative. Someone is old or not rich. Someone is either humble or not creative. Lucy is both not old and humble. Fred is either not patient or humble. Alice is rich. Lucy is either not creative or not wise. | Paul is calm. | contradiction | (![X]:((creative(X)&~calm(X))=>(~creative(X)|~happy(X))))&
(![X]:((quiet(X)<~>kind(X))<=>(rich(X)|calm(X))))&
(![X]:(~funny(X)<=>(~generous(X)&calm(X))))&
(((happy(paul)&~wise(paul)))=>(?[X]:(wise(X))))&
(![X]:((~funny(X)|tall(X))=>(rich(X)&~tall(X))))&
(![X]:((calm(X)|tall(X))<=>(curious(X)&old(X))))&
(![X]:((~quiet(X)<~>~patient(X))<=>(tall(X)&~humble(X))))&
((?[X]:(strong(X)))=>(?[X]:(patient(X))))&
(((~wise(alice)&rich(alice)))<=>((funny(susan)|~humble(susan))))&
((?[X]:((calm(X)&old(X))))=>(?[X]:((~creative(X)|~kind(X)))))&
(((rich(lucy)<~>~humble(lucy)))<=>(?[X]:((brave(X)|kind(X)))))&
(![X]:(curious(X)<=>(strong(X)&~generous(X))))&
(![X]:((calm(X)|~curious(X))=>(funny(X)&rich(X))))&
((?[X]:((happy(X)|funny(X))))<=>(?[X]:(~tall(X))))&
(![X]:((curious(X)&~quiet(X))<=>(rich(X)&old(X))))&
(((~strong(mary)<~>~funny(mary)))<=>(?[X]:((~old(X)&~kind(X)))))&
(?[X]:((~rich(X)&~creative(X))))&
(?[X]:((old(X)|~rich(X))))&
(?[X]:((humble(X)<~>~creative(X))))&
((~old(lucy)&humble(lucy)))&
((~patient(fred)<~>humble(fred)))&
(rich(alice))&
((~creative(lucy)<~>~wise(lucy))) | calm(paul) | [
"p2",
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4991775215200866364322642
% SZS output start Proof for 4991775215200866364322642
3. ! [X0] : (~funny(X0) <=> (calm(X0) & ~generous(X0))) [input p2]
6. ! [X0] : ((tall(X0) | calm(X0)) <=> (old(X0) & curious(X0))) [input p5]
12. ! [X0] : (curious(X0) <=> (~generous(X0) & strong(X0))) [input p11]
13. ! [X0] : ((~curious(X0) | calm(X0)) => (rich(X0) & funny(X0))) [input p12]
24. calm(paul) [input hypothesis]
35. ! [X0] : ((rich(X0) & funny(X0)) | (curious(X0) & ~calm(X0))) [ennf transformation 13]
38. ! [X0] : ((~funny(X0) | (~calm(X0) | generous(X0))) & ((calm(X0) & ~generous(X0)) | funny(X0))) [nnf transformation 3]
39. ! [X0] : ((~funny(X0) | ~calm(X0) | generous(X0)) & ((calm(X0) & ~generous(X0)) | funny(X0))) [flattening 38]
42. ! [X0] : (((tall(X0) | calm(X0)) | (~old(X0) | ~curious(X0))) & ((old(X0) & curious(X0)) | (~tall(X0) & ~calm(X0)))) [nnf transformation 6]
43. ! [X0] : ((tall(X0) | calm(X0) | ~old(X0) | ~curious(X0)) & ((old(X0) & curious(X0)) | (~tall(X0) & ~calm(X0)))) [flattening 42]
58. ! [X0] : ((curious(X0) | (generous(X0) | ~strong(X0))) & ((~generous(X0) & strong(X0)) | ~curious(X0))) [nnf transformation 12]
59. ! [X0] : ((curious(X0) | generous(X0) | ~strong(X0)) & ((~generous(X0) & strong(X0)) | ~curious(X0))) [flattening 58]
88. funny(X0) | calm(X0) [cnf transformation 39]
89. ~funny(X0) | ~calm(X0) | generous(X0) [cnf transformation 39]
95. ~calm(X0) | curious(X0) [cnf transformation 43]
120. ~curious(X0) | ~generous(X0) [cnf transformation 59]
122. funny(X0) | ~calm(X0) [cnf transformation 35]
151. calm(paul) [cnf transformation 24]
240. funny(X0) [subsumption resolution 122,88]
305. curious(paul) [resolution 95,151]
310. ~generous(paul) [resolution 120,305]
340. ~calm(X2) | generous(X2) [resolution 89,240]
449. generous(paul) [resolution 340,151]
450. $false [subsumption resolution 449,310]
% SZS output end Proof for 4991775215200866364322642
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or rich is not patient or not quiet.
If paul is old then someone is either kind or not old.
If someone is either not calm or not patient then someone is wise.
Everyone who is either curious or funny is both not strong and funny and vice versa.
If mary is not quiet or calm then someone is not old or calm.
Everyone who is both not curious and not calm is either not funny or calm.
If alice is either curious or not creative then lucy is both brave and kind and vice versa.
Everyone who is either strong or not patient is either not old or kind and vice versa.
Everyone who is either wise or funny is either not brave or kind and vice versa.
If someone is both brave and creative then someone is both calm and not funny.
If alice is not generous then lucy is not funny.
If someone is quiet or old then someone is calm and vice versa.
Everyone who is both creative and generous is not happy.
Everyone who is either kind or creative is either kind or not quiet and vice versa.
If susan is not wise then alice is both not strong and not wise.
Everyone who is not patient or not kind is both happy and creative and vice versa.
Someone is not creative.
Susan is brave or not old.
Susan is both patient and not tall.
Someone is rich.
Alice is tall.
Someone is either brave or kind.
Paul is curious.
Alice is old. | Mary is calm. | neutral | (![X]:((brave(X)<~>rich(X))=>(~patient(X)|~quiet(X))))&
((old(paul))=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~calm(X)<~>~patient(X))))=>(?[X]:(wise(X))))&
(![X]:((curious(X)<~>funny(X))<=>(~strong(X)&funny(X))))&
(((~quiet(mary)|calm(mary)))=>(?[X]:((~old(X)|calm(X)))))&
(![X]:((~curious(X)&~calm(X))=>(~funny(X)<~>calm(X))))&
(((curious(alice)<~>~creative(alice)))<=>((brave(lucy)&kind(lucy))))&
(![X]:((strong(X)<~>~patient(X))<=>(~old(X)<~>kind(X))))&
(![X]:((wise(X)<~>funny(X))<=>(~brave(X)<~>kind(X))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((calm(X)&~funny(X)))))&
((~generous(alice))=>(~funny(lucy)))&
((?[X]:((quiet(X)|old(X))))<=>(?[X]:(calm(X))))&
(![X]:((creative(X)&generous(X))=>~happy(X)))&
(![X]:((kind(X)<~>creative(X))<=>(kind(X)<~>~quiet(X))))&
((~wise(susan))=>((~strong(alice)&~wise(alice))))&
(![X]:((~patient(X)|~kind(X))<=>(happy(X)&creative(X))))&
(?[X]:(~creative(X)))&
((brave(susan)|~old(susan)))&
((patient(susan)&~tall(susan)))&
(?[X]:(rich(X)))&
(tall(alice))&
(?[X]:((brave(X)<~>kind(X))))&
(curious(paul))&
(old(alice)) | calm(mary) | [] | null | 0 |
If alice is either humble or not wise then someone is not funny.
Everyone who is either not quiet or kind is both curious and brave and vice versa.
Everyone who is creative is kind or generous.
If someone is not rich or happy then mary is not brave or happy.
Everyone who is both not patient and not kind is not curious and vice versa.
If john is not quiet or wise then someone is both curious and not curious and vice versa.
Everyone who is both old and kind is either not old or creative and vice versa.
Everyone who is both not calm and calm is not quiet or not kind and vice versa.
Everyone who is both generous and curious is both creative and tall and vice versa.
Everyone who is old is either not humble or calm.
Everyone who is creative is both humble and not happy.
Everyone who is not wise or not generous is funny and vice versa.
Everyone who is tall or not humble is quiet or not old and vice versa.
If fred is not wise then someone is not happy and vice versa.
Fred is funny.
Someone is not tall or not patient.
Alice is quiet.
Someone is funny or not funny.
Someone is not wise.
Someone is either not quiet or not funny.
Someone is strong or creative. | Alice is humble. | entailment | (((humble(alice)<~>~wise(alice)))=>(?[X]:(~funny(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(curious(X)&brave(X))))&
(![X]:(creative(X)=>(kind(X)|generous(X))))&
((?[X]:((~rich(X)|happy(X))))=>((~brave(mary)|happy(mary))))&
(![X]:((~patient(X)&~kind(X))<=>~curious(X)))&
(((~quiet(john)|wise(john)))<=>(?[X]:((curious(X)&~curious(X)))))&
(![X]:((old(X)&kind(X))<=>(~old(X)<~>creative(X))))&
(![X]:((~calm(X)&calm(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((generous(X)&curious(X))<=>(creative(X)&tall(X))))&
(![X]:(old(X)=>(~humble(X)<~>calm(X))))&
(![X]:(creative(X)=>(humble(X)&~happy(X))))&
(![X]:((~wise(X)|~generous(X))<=>funny(X)))&
(![X]:((tall(X)|~humble(X))<=>(quiet(X)|~old(X))))&
((~wise(fred))<=>(?[X]:(~happy(X))))&
(funny(fred))&
(?[X]:((~tall(X)|~patient(X))))&
(quiet(alice))&
(?[X]:((funny(X)|~funny(X))))&
(?[X]:(~wise(X)))&
(?[X]:((~quiet(X)<~>~funny(X))))&
(?[X]:((strong(X)|creative(X)))) | humble(alice) | [
"p6",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 62238056426123087595371
% SZS output start Proof for 62238056426123087595371
7. ! [X0] : ((kind(X0) & old(X0)) <=> (~old(X0) <~> creative(X0))) [input p6]
8. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p7]
11. ! [X0] : (creative(X0) => (~happy(X0) & humble(X0))) [input p10]
22. ~humble(alice) [input hypothesis]
31. ! [X0] : ((~happy(X0) & humble(X0)) | ~creative(X0)) [ennf transformation 11]
44. ! [X0] : (((kind(X0) & old(X0)) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0)))) & (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | (~kind(X0) | ~old(X0)))) [nnf transformation 7]
45. ! [X0] : (((kind(X0) & old(X0)) | ((~old(X0) | ~creative(X0)) & (creative(X0) | old(X0)))) & (((~creative(X0) | old(X0)) & (creative(X0) | ~old(X0))) | ~kind(X0) | ~old(X0))) [flattening 44]
46. ! [X0] : (((calm(X0) & ~calm(X0)) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 8]
47. ! [X0] : (((calm(X0) & ~calm(X0)) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ~calm(X0) | calm(X0))) [flattening 46]
86. creative(X0) | ~old(X0) | ~kind(X0) | ~old(X0) [cnf transformation 45]
88. old(X0) | creative(X0) | old(X0) [cnf transformation 45]
94. ~calm(X0) | kind(X0) [cnf transformation 47]
96. calm(X0) | kind(X0) [cnf transformation 47]
103. ~creative(X0) | humble(X0) [cnf transformation 31]
121. ~humble(alice) [cnf transformation 22]
122. creative(X0) | ~old(X0) | ~kind(X0) [duplicate literal removal 86]
123. old(X0) | creative(X0) [duplicate literal removal 88]
129. 2 <=> humble(alice) [avatar definition]
130. ~humble(alice) <- (~2) [avatar component clause 129]
166. ~kind(X0) | creative(X0) [subsumption resolution 122,123]
167. kind(X0) [subsumption resolution 94,96]
193. ~2 [avatar split clause 121,129]
197. creative(X0) [resolution 166,167]
198. humble(X0) [resolution 197,103]
199. $false <- (~2) [resolution 198,130]
201. 2 [avatar contradiction clause 199]
202. $false [avatar sat refutation 193,201]
% SZS output end Proof for 62238056426123087595371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not tall is not quiet.
Everyone who is happy is not strong or rich and vice versa.
Everyone who is happy is kind.
If someone is not quiet then someone is either not calm or not generous.
If mary is both happy and humble then someone is either strong or not creative and vice versa.
If lucy is not old then fred is either wise or not quiet.
If someone is not creative or calm then lucy is not happy and vice versa.
Everyone who is either not tall or not old is either not old or not patient and vice versa.
If someone is both curious and kind then someone is not humble or happy.
If mary is either wise or quiet then alice is curious and vice versa.
If someone is both old and not generous then lucy is not wise and vice versa.
Everyone who is not strong or not humble is wise.
If someone is not curious then someone is kind.
Everyone who is both not calm and brave is not funny or humble and vice versa.
If someone is both generous and not kind then alice is not humble and vice versa.
Everyone who is either curious or not humble is both humble and generous.
Alice is both not brave and strong.
Someone is both tall and not old.
John is both not patient and creative.
Someone is brave.
Someone is not tall or old.
Paul is both rich and not creative.
Someone is either not patient or not wise. | Paul is not happy. | contradiction | (![X]:((~wise(X)&~tall(X))=>~quiet(X)))&
(![X]:(happy(X)<=>(~strong(X)|rich(X))))&
(![X]:(happy(X)=>kind(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(((happy(mary)&humble(mary)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
((~old(lucy))=>((wise(fred)<~>~quiet(fred))))&
((?[X]:((~creative(X)|calm(X))))<=>(~happy(lucy)))&
(![X]:((~tall(X)<~>~old(X))<=>(~old(X)<~>~patient(X))))&
((?[X]:((curious(X)&kind(X))))=>(?[X]:((~humble(X)|happy(X)))))&
(((wise(mary)<~>quiet(mary)))<=>(curious(alice)))&
((?[X]:((old(X)&~generous(X))))<=>(~wise(lucy)))&
(![X]:((~strong(X)|~humble(X))=>wise(X)))&
((?[X]:(~curious(X)))=>(?[X]:(kind(X))))&
(![X]:((~calm(X)&brave(X))<=>(~funny(X)|humble(X))))&
((?[X]:((generous(X)&~kind(X))))<=>(~humble(alice)))&
(![X]:((curious(X)<~>~humble(X))=>(humble(X)&generous(X))))&
((~brave(alice)&strong(alice)))&
(?[X]:((tall(X)&~old(X))))&
((~patient(john)&creative(john)))&
(?[X]:(brave(X)))&
(?[X]:((~tall(X)|old(X))))&
((rich(paul)&~creative(paul)))&
(?[X]:((~patient(X)<~>~wise(X)))) | ~happy(paul) | [
"p1",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4963620409351210027518313
% SZS output start Proof for 4963620409351210027518313
2. ! [X0] : (happy(X0) <=> (rich(X0) | ~strong(X0))) [input p1]
22. ~creative(paul) & rich(paul) [input p21]
24. ~happy(paul) [input hypothesis]
37. ! [X0] : ((happy(X0) | (~rich(X0) & strong(X0))) & ((rich(X0) | ~strong(X0)) | ~happy(X0))) [nnf transformation 2]
38. ! [X0] : ((happy(X0) | (~rich(X0) & strong(X0))) & (rich(X0) | ~strong(X0) | ~happy(X0))) [flattening 37]
84. ~rich(X0) | happy(X0) [cnf transformation 38]
138. rich(paul) [cnf transformation 22]
142. ~happy(paul) [cnf transformation 24]
319. happy(paul) [resolution 84,138]
320. $false [subsumption resolution 319,142]
% SZS output end Proof for 4963620409351210027518313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not generous is quiet or not humble and vice versa.
If someone is curious or quiet then someone is not tall.
If alice is not curious then someone is not brave and vice versa.
If someone is not quiet or not funny then someone is tall or patient and vice versa.
If susan is both generous and patient then someone is generous.
Everyone who is wise or rich is not quiet or not kind.
Everyone who is humble is not tall and vice versa.
If someone is either not wise or not tall then someone is calm or quiet.
If lucy is calm then someone is not wise.
Everyone who is both wise and not tall is not humble and vice versa.
Everyone who is either not strong or generous is rich.
If alice is not tall then someone is old and vice versa.
Everyone who is not old or creative is both funny and kind and vice versa.
Everyone who is not creative or humble is not generous or happy and vice versa.
Everyone who is either rich or not tall is patient.
Everyone who is generous or old is either happy or not tall and vice versa.
Someone is both quiet and kind.
Someone is both curious and not patient.
Lucy is not patient.
Mary is funny.
Someone is brave.
John is both not creative and not funny.
Someone is calm.
Someone is happy. | Lucy is not kind. | entailment | (![X]:((~kind(X)|~generous(X))<=>(quiet(X)|~humble(X))))&
((?[X]:((curious(X)|quiet(X))))=>(?[X]:(~tall(X))))&
((~curious(alice))<=>(?[X]:(~brave(X))))&
((?[X]:((~quiet(X)|~funny(X))))<=>(?[X]:((tall(X)|patient(X)))))&
(((generous(susan)&patient(susan)))=>(?[X]:(generous(X))))&
(![X]:((wise(X)|rich(X))=>(~quiet(X)|~kind(X))))&
(![X]:(humble(X)<=>~tall(X)))&
((?[X]:((~wise(X)<~>~tall(X))))=>(?[X]:((calm(X)|quiet(X)))))&
((calm(lucy))=>(?[X]:(~wise(X))))&
(![X]:((wise(X)&~tall(X))<=>~humble(X)))&
(![X]:((~strong(X)<~>generous(X))=>rich(X)))&
((~tall(alice))<=>(?[X]:(old(X))))&
(![X]:((~old(X)|creative(X))<=>(funny(X)&kind(X))))&
(![X]:((~creative(X)|humble(X))<=>(~generous(X)|happy(X))))&
(![X]:((rich(X)<~>~tall(X))=>patient(X)))&
(![X]:((generous(X)|old(X))<=>(happy(X)<~>~tall(X))))&
(?[X]:((quiet(X)&kind(X))))&
(?[X]:((curious(X)&~patient(X))))&
(~patient(lucy))&
(funny(mary))&
(?[X]:(brave(X)))&
((~creative(john)&~funny(john)))&
(?[X]:(calm(X)))&
(?[X]:(happy(X))) | ~kind(lucy) | [
"p0",
"p5",
"p6",
"p9",
"p13",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 847889088208352298435221
% SZS output start Proof for 847889088208352298435221
1. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (~humble(X0) | quiet(X0))) [input p0]
6. ! [X0] : ((rich(X0) | wise(X0)) => (~kind(X0) | ~quiet(X0))) [input p5]
7. ! [X0] : (humble(X0) <=> ~tall(X0)) [input p6]
10. ! [X0] : ((~tall(X0) & wise(X0)) <=> ~humble(X0)) [input p9]
14. ! [X0] : ((humble(X0) | ~creative(X0)) <=> (happy(X0) | ~generous(X0))) [input p13]
15. ! [X0] : ((rich(X0) <~> ~tall(X0)) => patient(X0)) [input p14]
16. ! [X0] : ((old(X0) | generous(X0)) <=> (happy(X0) <~> ~tall(X0))) [input p15]
19. ~patient(lucy) [input p18]
25. kind(lucy) [input hypothesis]
32. ! [X0] : ((~kind(X0) | ~quiet(X0)) | (~rich(X0) & ~wise(X0))) [ennf transformation 6]
33. ! [X0] : (~kind(X0) | ~quiet(X0) | (~rich(X0) & ~wise(X0))) [flattening 32]
37. ! [X0] : (patient(X0) | (rich(X0) <=> ~tall(X0))) [ennf transformation 15]
38. ! [X0] : (((~generous(X0) | ~kind(X0)) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 1]
39. ! [X0] : ((~generous(X0) | ~kind(X0) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | (generous(X0) & kind(X0)))) [flattening 38]
54. ! [X0] : ((humble(X0) | tall(X0)) & (~tall(X0) | ~humble(X0))) [nnf transformation 7]
61. ! [X0] : (((~tall(X0) & wise(X0)) | humble(X0)) & (~humble(X0) | (tall(X0) | ~wise(X0)))) [nnf transformation 10]
62. ! [X0] : (((~tall(X0) & wise(X0)) | humble(X0)) & (~humble(X0) | tall(X0) | ~wise(X0))) [flattening 61]
70. ! [X0] : (((humble(X0) | ~creative(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (~humble(X0) & creative(X0)))) [nnf transformation 14]
71. ! [X0] : ((humble(X0) | ~creative(X0) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | (~humble(X0) & creative(X0)))) [flattening 70]
72. ! [X0] : (patient(X0) | ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0)))) [nnf transformation 37]
73. ! [X0] : (((old(X0) | generous(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (~old(X0) & ~generous(X0)))) [nnf transformation 16]
74. ! [X0] : ((old(X0) | generous(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (~old(X0) & ~generous(X0)))) [flattening 73]
86. ~humble(X0) | quiet(X0) | generous(X0) [cnf transformation 39]
99. ~rich(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 33]
100. ~tall(X0) | ~humble(X0) [cnf transformation 54]
101. tall(X0) | humble(X0) [cnf transformation 54]
107. ~tall(X0) | humble(X0) [cnf transformation 62]
118. ~humble(X0) | ~generous(X0) | happy(X0) [cnf transformation 71]
122. rich(X0) | patient(X0) | tall(X0) [cnf transformation 72]
125. ~happy(X0) | tall(X0) | ~generous(X0) [cnf transformation 74]
133. ~patient(lucy) [cnf transformation 19]
140. kind(lucy) [cnf transformation 25]
179. 10 <=> ! [X1] : ~tall(X1) [avatar definition]
180. ~tall(X1) <- (10) [avatar component clause 179]
236. ~tall(X0) [subsumption resolution 107,100]
237. 10 [avatar split clause 236,179]
260. humble(X1) <- (10) [resolution 101,180]
265. quiet(X0) | generous(X0) <- (10) [resolution 86,260]
295. ~generous(X0) | happy(X0) <- (10) [resolution 118,260]
298. patient(X1) | tall(X1) | ~quiet(X1) | ~kind(X1) [resolution 122,99]
300. ~quiet(X1) | patient(X1) | ~kind(X1) <- (10) [subsumption resolution 298,180]
336. ~kind(X0) | patient(X0) | generous(X0) <- (10) [resolution 300,265]
346. patient(lucy) | generous(lucy) <- (10) [resolution 336,140]
348. generous(lucy) <- (10) [subsumption resolution 346,133]
350. happy(lucy) <- (10) [resolution 348,295]
355. tall(lucy) | ~generous(lucy) <- (10) [resolution 350,125]
358. ~generous(lucy) <- (10) [subsumption resolution 355,180]
359. $false <- (10) [subsumption resolution 358,348]
360. ~10 [avatar contradiction clause 359]
361. $false [avatar sat refutation 237,360]
% SZS output end Proof for 847889088208352298435221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not happy or old and vice versa. If someone is brave or not happy then someone is humble or not wise. Everyone who is not patient or humble is patient and vice versa. If paul is either not old or not quiet then someone is generous and vice versa. Everyone who is strong is not creative or not happy. Everyone who is both not creative and tall is rich and vice versa. If alice is either not curious or not wise then lucy is quiet and vice versa. Everyone who is both not happy and not quiet is both not quiet and quiet. If someone is rich then lucy is either kind or creative. Everyone who is not quiet or wise is not tall or quiet. Everyone who is either not wise or patient is either tall or not patient and vice versa. If someone is either not curious or funny then someone is not quiet. If mary is wise then someone is not tall or brave and vice versa. If someone is calm then john is funny. If someone is calm then mary is either calm or wise. If someone is both not quiet and not tall then someone is either calm or brave and vice versa. Someone is either not funny or patient. Susan is either not wise or not humble. Fred is either strong or not curious. Someone is calm or funny. Someone is not strong. John is kind or not humble. Susan is kind or not tall. | John is old. | contradiction | (![X]:(~old(X)<=>(~happy(X)|old(X))))&
((?[X]:((brave(X)|~happy(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:((~patient(X)|humble(X))<=>patient(X)))&
(((~old(paul)<~>~quiet(paul)))<=>(?[X]:(generous(X))))&
(![X]:(strong(X)=>(~creative(X)|~happy(X))))&
(![X]:((~creative(X)&tall(X))<=>rich(X)))&
(((~curious(alice)<~>~wise(alice)))<=>(quiet(lucy)))&
(![X]:((~happy(X)&~quiet(X))=>(~quiet(X)&quiet(X))))&
((?[X]:(rich(X)))=>((kind(lucy)<~>creative(lucy))))&
(![X]:((~quiet(X)|wise(X))=>(~tall(X)|quiet(X))))&
(![X]:((~wise(X)<~>patient(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((~curious(X)<~>funny(X))))=>(?[X]:(~quiet(X))))&
((wise(mary))<=>(?[X]:((~tall(X)|brave(X)))))&
((?[X]:(calm(X)))=>(funny(john)))&
((?[X]:(calm(X)))=>((calm(mary)<~>wise(mary))))&
((?[X]:((~quiet(X)&~tall(X))))<=>(?[X]:((calm(X)<~>brave(X)))))&
(?[X]:((~funny(X)<~>patient(X))))&
((~wise(susan)<~>~humble(susan)))&
((strong(fred)<~>~curious(fred)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:(~strong(X)))&
((kind(john)|~humble(john)))&
((kind(susan)|~tall(susan))) | old(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 7165660133101332936501677
% SZS output start Proof for 7165660133101332936501677
1. ! [X0] : (~old(X0) <=> (old(X0) | ~happy(X0))) [input p0]
24. old(john) [input hypothesis]
42. ! [X0] : ((~old(X0) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | old(X0))) [nnf transformation 1]
43. ! [X0] : ((~old(X0) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | old(X0))) [flattening 42]
81. ~old(X0) | ~old(X0) [cnf transformation 43]
135. old(john) [cnf transformation 24]
145. ~old(X0) [duplicate literal removal 81]
306. $false [subsumption resolution 135,145]
% SZS output end Proof for 7165660133101332936501677
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or not patient is either not generous or not creative.
Everyone who is happy is not strong or not funny.
Everyone who is not quiet or wise is both brave and old.
If lucy is rich or tall then paul is not humble and vice versa.
Everyone who is creative is not patient.
Everyone who is strong is rich or not kind and vice versa.
Everyone who is both not patient and generous is not brave or curious and vice versa.
Everyone who is generous or funny is both not old and funny.
If someone is either funny or brave then susan is curious or funny.
If someone is funny then paul is both not brave and not rich and vice versa.
Everyone who is either humble or curious is both not wise and patient and vice versa.
If paul is both old and curious then someone is either creative or funny.
Everyone who is generous is both not tall and not creative.
If susan is either creative or not quiet then lucy is not tall or strong.
Everyone who is either not happy or generous is either wise or not brave and vice versa.
Everyone who is both calm and not curious is either old or not kind.
Someone is either curious or not patient.
Someone is humble.
Fred is not happy.
Susan is not generous or happy.
Someone is either not quiet or patient.
Someone is both funny and not strong.
Fred is wise.
Someone is not humble or kind. | Fred is not humble. | entailment | (![X]:((~curious(X)|~patient(X))=>(~generous(X)<~>~creative(X))))&
(![X]:(happy(X)=>(~strong(X)|~funny(X))))&
(![X]:((~quiet(X)|wise(X))=>(brave(X)&old(X))))&
(((rich(lucy)|tall(lucy)))<=>(~humble(paul)))&
(![X]:(creative(X)=>~patient(X)))&
(![X]:(strong(X)<=>(rich(X)|~kind(X))))&
(![X]:((~patient(X)&generous(X))<=>(~brave(X)|curious(X))))&
(![X]:((generous(X)|funny(X))=>(~old(X)&funny(X))))&
((?[X]:((funny(X)<~>brave(X))))=>((curious(susan)|funny(susan))))&
((?[X]:(funny(X)))<=>((~brave(paul)&~rich(paul))))&
(![X]:((humble(X)<~>curious(X))<=>(~wise(X)&patient(X))))&
(((old(paul)&curious(paul)))=>(?[X]:((creative(X)<~>funny(X)))))&
(![X]:(generous(X)=>(~tall(X)&~creative(X))))&
(((creative(susan)<~>~quiet(susan)))=>((~tall(lucy)|strong(lucy))))&
(![X]:((~happy(X)<~>generous(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((calm(X)&~curious(X))=>(old(X)<~>~kind(X))))&
(?[X]:((curious(X)<~>~patient(X))))&
(?[X]:(humble(X)))&
(~happy(fred))&
((~generous(susan)|happy(susan)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((funny(X)&~strong(X))))&
(wise(fred))&
(?[X]:((~humble(X)|kind(X)))) | ~humble(fred) | [
"p2",
"p6",
"p7",
"p10",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6494209085882490187543850
% SZS output start Proof for 6494209085882490187543850
3. ! [X0] : ((wise(X0) | ~quiet(X0)) => (old(X0) & brave(X0))) [input p2]
7. ! [X0] : ((generous(X0) & ~patient(X0)) <=> (curious(X0) | ~brave(X0))) [input p6]
8. ! [X0] : ((funny(X0) | generous(X0)) => (funny(X0) & ~old(X0))) [input p7]
11. ! [X0] : ((humble(X0) <~> curious(X0)) <=> (patient(X0) & ~wise(X0))) [input p10]
23. wise(fred) [input p22]
25. humble(fred) [input hypothesis]
30. ! [X0] : ((old(X0) & brave(X0)) | (~wise(X0) & quiet(X0))) [ennf transformation 3]
32. ! [X0] : ((funny(X0) & ~old(X0)) | (~funny(X0) & ~generous(X0))) [ennf transformation 8]
45. ! [X0] : (((generous(X0) & ~patient(X0)) | (~curious(X0) & brave(X0))) & ((curious(X0) | ~brave(X0)) | (~generous(X0) | patient(X0)))) [nnf transformation 7]
46. ! [X0] : (((generous(X0) & ~patient(X0)) | (~curious(X0) & brave(X0))) & (curious(X0) | ~brave(X0) | ~generous(X0) | patient(X0))) [flattening 45]
53. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [nnf transformation 11]
54. ! [X0] : ((((~curious(X0) | ~humble(X0)) & (curious(X0) | humble(X0))) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | ((humble(X0) | ~curious(X0)) & (curious(X0) | ~humble(X0))))) [flattening 53]
80. ~wise(X0) | old(X0) [cnf transformation 30]
92. ~curious(X0) | generous(X0) [cnf transformation 46]
93. ~old(X0) | ~generous(X0) [cnf transformation 32]
102. ~humble(X0) | curious(X0) | ~wise(X0) [cnf transformation 54]
131. wise(fred) [cnf transformation 23]
133. humble(fred) [cnf transformation 25]
255. old(fred) [resolution 80,131]
264. ~generous(fred) [resolution 93,255]
309. curious(fred) | ~wise(fred) [resolution 102,133]
320. curious(fred) [subsumption resolution 309,131]
330. generous(fred) [resolution 320,92]
331. $false [subsumption resolution 330,264]
% SZS output end Proof for 6494209085882490187543850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not brave and old then fred is both not old and not patient and vice versa. If someone is not rich or kind then susan is either funny or brave and vice versa. If susan is not curious then someone is happy. If susan is calm or rich then paul is both not quiet and not curious. If alice is not creative then alice is either not rich or kind. Everyone who is either creative or not brave is not patient or curious and vice versa. Everyone who is both creative and not old is both not kind and not generous and vice versa. Everyone who is not generous or patient is wise and vice versa. Everyone who is both not quiet and calm is both not generous and not humble and vice versa. If fred is not strong or generous then fred is both not old and not funny and vice versa. Everyone who is both creative and not curious is not quiet or funny and vice versa. If john is not patient then someone is either quiet or humble and vice versa. Everyone who is not curious is curious or not old. Everyone who is either kind or curious is both not calm and kind. If someone is old or patient then alice is wise or calm and vice versa. Everyone who is not kind or quiet is both not creative and not kind. Someone is both not wise and not calm. Someone is either happy or curious. John is quiet. Alice is not funny. Fred is either strong or brave. | Susan is not funny. | entailment | (((~brave(susan)&old(susan)))<=>((~old(fred)&~patient(fred))))&
((?[X]:((~rich(X)|kind(X))))<=>((funny(susan)<~>brave(susan))))&
((~curious(susan))=>(?[X]:(happy(X))))&
(((calm(susan)|rich(susan)))=>((~quiet(paul)&~curious(paul))))&
((~creative(alice))=>((~rich(alice)<~>kind(alice))))&
(![X]:((creative(X)<~>~brave(X))<=>(~patient(X)|curious(X))))&
(![X]:((creative(X)&~old(X))<=>(~kind(X)&~generous(X))))&
(![X]:((~generous(X)|patient(X))<=>wise(X)))&
(![X]:((~quiet(X)&calm(X))<=>(~generous(X)&~humble(X))))&
(((~strong(fred)|generous(fred)))<=>((~old(fred)&~funny(fred))))&
(![X]:((creative(X)&~curious(X))<=>(~quiet(X)|funny(X))))&
((~patient(john))<=>(?[X]:((quiet(X)<~>humble(X)))))&
(![X]:(~curious(X)=>(curious(X)|~old(X))))&
(![X]:((kind(X)<~>curious(X))=>(~calm(X)&kind(X))))&
((?[X]:((old(X)|patient(X))))<=>((wise(alice)|calm(alice))))&
(![X]:((~kind(X)|quiet(X))=>(~creative(X)&~kind(X))))&
(?[X]:((~wise(X)&~calm(X))))&
(?[X]:((happy(X)<~>curious(X))))&
(quiet(john))&
(~funny(alice))&
((strong(fred)<~>brave(fred))) | ~funny(susan) | [
"p6",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6186771339029363534614502
% SZS output start Proof for 6186771339029363534614502
7. ! [X0] : ((~old(X0) & creative(X0)) <=> (~generous(X0) & ~kind(X0))) [input p6]
11. ! [X0] : ((~curious(X0) & creative(X0)) <=> (funny(X0) | ~quiet(X0))) [input p10]
13. ! [X0] : (~curious(X0) => (~old(X0) | curious(X0))) [input p12]
16. ! [X0] : ((quiet(X0) | ~kind(X0)) => (~kind(X0) & ~creative(X0))) [input p15]
22. funny(susan) [input hypothesis]
26. ! [X0] : ((~old(X0) | curious(X0)) | curious(X0)) [ennf transformation 13]
27. ! [X0] : (~old(X0) | curious(X0) | curious(X0)) [flattening 26]
29. ! [X0] : ((~kind(X0) & ~creative(X0)) | (~quiet(X0) & kind(X0))) [ennf transformation 16]
41. ! [X0] : (((~old(X0) & creative(X0)) | (generous(X0) | kind(X0))) & ((~generous(X0) & ~kind(X0)) | (old(X0) | ~creative(X0)))) [nnf transformation 7]
42. ! [X0] : (((~old(X0) & creative(X0)) | generous(X0) | kind(X0)) & ((~generous(X0) & ~kind(X0)) | old(X0) | ~creative(X0))) [flattening 41]
49. ! [X0] : (((~curious(X0) & creative(X0)) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | (curious(X0) | ~creative(X0)))) [nnf transformation 11]
50. ! [X0] : (((~curious(X0) & creative(X0)) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | curious(X0) | ~creative(X0))) [flattening 49]
90. ~creative(X0) | old(X0) | ~kind(X0) [cnf transformation 42]
108. ~funny(X0) | creative(X0) [cnf transformation 50]
110. ~curious(X0) | ~funny(X0) [cnf transformation 50]
115. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 27]
124. ~creative(X0) | kind(X0) [cnf transformation 29]
136. funny(susan) [cnf transformation 22]
138. ~old(X0) | curious(X0) [duplicate literal removal 115]
148. 3 <=> old(susan) [avatar definition]
150. old(susan) <- (3) [avatar component clause 148]
160. 5 <=> funny(susan) [avatar definition]
162. funny(susan) <- (5) [avatar component clause 160]
184. 10 <=> curious(susan) [avatar definition]
185. ~curious(susan) <- (~10) [avatar component clause 184]
186. curious(susan) <- (10) [avatar component clause 184]
307. 5 [avatar split clause 136,160]
311. creative(susan) <- (5) [resolution 108,162]
314. ~funny(susan) <- (10) [resolution 110,186]
315. $false <- (5, 10) [subsumption resolution 314,162]
316. ~5 | ~10 [avatar contradiction clause 315]
318. kind(susan) <- (5) [resolution 124,311]
354. old(susan) | ~kind(susan) <- (5) [resolution 90,311]
363. old(susan) <- (5) [subsumption resolution 354,318]
364. 3 | ~5 [avatar split clause 363,160,148]
370. curious(susan) <- (3) [resolution 150,138]
371. $false <- (3, ~10) [subsumption resolution 370,185]
372. ~3 | 10 [avatar contradiction clause 371]
373. $false [avatar sat refutation 307,316,364,372]
% SZS output end Proof for 6186771339029363534614502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Fred is not brave. | 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)) | ~brave(fred) | [] | null | 0 |
Everyone who is both curious and quiet is not tall or happy and vice versa.
Everyone who is both not curious and not happy is both not kind and patient and vice versa.
Everyone who is either not calm or creative is not brave or not strong and vice versa.
Everyone who is quiet is not quiet or calm.
If someone is not brave then someone is curious and vice versa.
If someone is patient then someone is both wise and happy and vice versa.
If fred is both kind and not patient then someone is either funny or curious.
Everyone who is old or quiet is both creative and not curious and vice versa.
If fred is not calm or not kind then someone is both creative and not patient.
If lucy is creative or not generous then fred is both not rich and not humble and vice versa.
Everyone who is either brave or rich is not old.
Everyone who is rich is either not humble or tall and vice versa.
Everyone who is not quiet or rich is kind and vice versa.
If someone is either not humble or not funny then susan is strong or not kind.
If fred is brave or not wise then mary is not creative.
If john is either not old or kind then lucy is not kind and vice versa.
Someone is both curious and not happy.
Alice is brave or curious.
Someone is both not old and strong.
Mary is tall.
Someone is not quiet or old.
Someone is either not tall or kind. | Fred is not kind. | contradiction | (![X]:((curious(X)&quiet(X))<=>(~tall(X)|happy(X))))&
(![X]:((~curious(X)&~happy(X))<=>(~kind(X)&patient(X))))&
(![X]:((~calm(X)<~>creative(X))<=>(~brave(X)|~strong(X))))&
(![X]:(quiet(X)=>(~quiet(X)|calm(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(curious(X))))&
((?[X]:(patient(X)))<=>(?[X]:((wise(X)&happy(X)))))&
(((kind(fred)&~patient(fred)))=>(?[X]:((funny(X)<~>curious(X)))))&
(![X]:((old(X)|quiet(X))<=>(creative(X)&~curious(X))))&
(((~calm(fred)|~kind(fred)))=>(?[X]:((creative(X)&~patient(X)))))&
(((creative(lucy)|~generous(lucy)))<=>((~rich(fred)&~humble(fred))))&
(![X]:((brave(X)<~>rich(X))=>~old(X)))&
(![X]:(rich(X)<=>(~humble(X)<~>tall(X))))&
(![X]:((~quiet(X)|rich(X))<=>kind(X)))&
((?[X]:((~humble(X)<~>~funny(X))))=>((strong(susan)|~kind(susan))))&
(((brave(fred)|~wise(fred)))=>(~creative(mary)))&
(((~old(john)<~>kind(john)))<=>(~kind(lucy)))&
(?[X]:((curious(X)&~happy(X))))&
((brave(alice)|curious(alice)))&
(?[X]:((~old(X)&strong(X))))&
(tall(mary))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((~tall(X)<~>kind(X)))) | ~kind(fred) | [
"p0",
"p1",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7559408381097918894174436
% SZS output start Proof for 7559408381097918894174436
1. ! [X0] : ((quiet(X0) & curious(X0)) <=> (happy(X0) | ~tall(X0))) [input p0]
2. ! [X0] : ((~happy(X0) & ~curious(X0)) <=> (patient(X0) & ~kind(X0))) [input p1]
6. ? [X0] : patient(X0) <=> ? [X0] : (happy(X0) & wise(X0)) [input p5]
8. ! [X0] : ((quiet(X0) | old(X0)) <=> (~curious(X0) & creative(X0))) [input p7]
13. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> kind(X0)) [input p12]
23. ~kind(fred) [input hypothesis]
25. ? [X0] : patient(X0) <=> ? [X1] : (happy(X1) & wise(X1)) [rectify 6]
35. ! [X0] : (((quiet(X0) & curious(X0)) | (~happy(X0) & tall(X0))) & ((happy(X0) | ~tall(X0)) | (~quiet(X0) | ~curious(X0)))) [nnf transformation 1]
36. ! [X0] : (((quiet(X0) & curious(X0)) | (~happy(X0) & tall(X0))) & (happy(X0) | ~tall(X0) | ~quiet(X0) | ~curious(X0))) [flattening 35]
37. ! [X0] : (((~happy(X0) & ~curious(X0)) | (~patient(X0) | kind(X0))) & ((patient(X0) & ~kind(X0)) | (happy(X0) | curious(X0)))) [nnf transformation 2]
38. ! [X0] : (((~happy(X0) & ~curious(X0)) | ~patient(X0) | kind(X0)) & ((patient(X0) & ~kind(X0)) | happy(X0) | curious(X0))) [flattening 37]
46. (? [X0] : patient(X0) | ! [X1] : (~happy(X1) | ~wise(X1))) & (? [X1] : (happy(X1) & wise(X1)) | ! [X0] : ~patient(X0)) [nnf transformation 25]
47. (? [X0] : patient(X0) | ! [X1] : (~happy(X1) | ~wise(X1))) & (? [X2] : (happy(X2) & wise(X2)) | ! [X3] : ~patient(X3)) [rectify 46]
48. ? [X0] : patient(X0) => patient(sK2) [choice axiom]
49. ? [X2] : (happy(X2) & wise(X2)) => (happy(sK3) & wise(sK3)) [choice axiom]
50. (patient(sK2) | ! [X1] : (~happy(X1) | ~wise(X1))) & ((happy(sK3) & wise(sK3)) | ! [X3] : ~patient(X3)) [skolemisation 47,49,48]
54. ! [X0] : (((quiet(X0) | old(X0)) | (curious(X0) | ~creative(X0))) & ((~curious(X0) & creative(X0)) | (~quiet(X0) & ~old(X0)))) [nnf transformation 8]
55. ! [X0] : ((quiet(X0) | old(X0) | curious(X0) | ~creative(X0)) & ((~curious(X0) & creative(X0)) | (~quiet(X0) & ~old(X0)))) [flattening 54]
62. ! [X0] : (((rich(X0) | ~quiet(X0)) | ~kind(X0)) & (kind(X0) | (~rich(X0) & quiet(X0)))) [nnf transformation 13]
63. ! [X0] : ((rich(X0) | ~quiet(X0) | ~kind(X0)) & (kind(X0) | (~rich(X0) & quiet(X0)))) [flattening 62]
77. ~happy(X0) | curious(X0) [cnf transformation 36]
79. ~happy(X0) | quiet(X0) [cnf transformation 36]
81. patient(X0) | happy(X0) | curious(X0) [cnf transformation 38]
94. happy(sK3) | ~patient(X3) [cnf transformation 50]
101. ~quiet(X0) | ~curious(X0) [cnf transformation 55]
118. kind(X0) | quiet(X0) [cnf transformation 63]
138. ~kind(fred) [cnf transformation 23]
140. patient(X0) | curious(X0) [subsumption resolution 81,77]
167. 7 <=> ! [X3] : ~patient(X3) [avatar definition]
168. ~patient(X3) <- (7) [avatar component clause 167]
170. 8 <=> happy(sK3) [avatar definition]
172. happy(sK3) <- (8) [avatar component clause 170]
173. 7 | 8 [avatar split clause 94,170,167]
180. 10 <=> kind(fred) [avatar definition]
182. ~kind(fred) <- (~10) [avatar component clause 180]
308. ~10 [avatar split clause 138,180]
319. quiet(fred) <- (~10) [resolution 118,182]
323. ~curious(fred) <- (~10) [resolution 319,101]
349. curious(X0) <- (7) [resolution 168,140]
354. $false <- (7, ~10) [resolution 323,349]
355. ~7 | 10 [avatar contradiction clause 354]
372. quiet(sK3) <- (8) [resolution 172,79]
373. curious(sK3) <- (8) [resolution 172,77]
403. ~curious(sK3) <- (8) [resolution 372,101]
405. $false <- (8) [subsumption resolution 403,373]
406. ~8 [avatar contradiction clause 405]
407. $false [avatar sat refutation 173,308,355,406]
% SZS output end Proof for 7559408381097918894174436
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not quiet and creative then susan is both old and funny. If someone is curious or not kind then susan is generous or not generous and vice versa. Everyone who is old or funny is rich or not kind and vice versa. If someone is not tall then mary is not old or not calm. Everyone who is not rich is either not wise or not creative. Everyone who is patient or happy is both creative and not brave. If someone is old or not kind then fred is not tall. If alice is either creative or tall then lucy is either patient or happy. Everyone who is both not funny and not curious is not kind. Everyone who is both not curious and wise is not tall or not generous. Everyone who is creative or not brave is not humble. Everyone who is either funny or brave is not rich. If mary is either not wise or not quiet then mary is either rich or not quiet. Everyone who is either not calm or not humble is not rich or patient and vice versa. If paul is both generous and not funny then someone is either patient or brave and vice versa. Everyone who is generous or not funny is rich or generous. Someone is not creative. Someone is wise or kind. Someone is not happy or not calm. Someone is both rich and not strong. John is either not creative or strong. John is both rich and humble. Someone is strong or happy. Someone is not kind. | John is not patient. | entailment | ((?[X]:((~quiet(X)&creative(X))))=>((old(susan)&funny(susan))))&
((?[X]:((curious(X)|~kind(X))))<=>((generous(susan)|~generous(susan))))&
(![X]:((old(X)|funny(X))<=>(rich(X)|~kind(X))))&
((?[X]:(~tall(X)))=>((~old(mary)|~calm(mary))))&
(![X]:(~rich(X)=>(~wise(X)<~>~creative(X))))&
(![X]:((patient(X)|happy(X))=>(creative(X)&~brave(X))))&
((?[X]:((old(X)|~kind(X))))=>(~tall(fred)))&
(((creative(alice)<~>tall(alice)))=>((patient(lucy)<~>happy(lucy))))&
(![X]:((~funny(X)&~curious(X))=>~kind(X)))&
(![X]:((~curious(X)&wise(X))=>(~tall(X)|~generous(X))))&
(![X]:((creative(X)|~brave(X))=>~humble(X)))&
(![X]:((funny(X)<~>brave(X))=>~rich(X)))&
(((~wise(mary)<~>~quiet(mary)))=>((rich(mary)<~>~quiet(mary))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~rich(X)|patient(X))))&
(((generous(paul)&~funny(paul)))<=>(?[X]:((patient(X)<~>brave(X)))))&
(![X]:((generous(X)|~funny(X))=>(rich(X)|generous(X))))&
(?[X]:(~creative(X)))&
(?[X]:((wise(X)|kind(X))))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((rich(X)&~strong(X))))&
((~creative(john)<~>strong(john)))&
((rich(john)&humble(john)))&
(?[X]:((strong(X)|happy(X))))&
(?[X]:(~kind(X))) | ~patient(john) | [
"p5",
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3103087744292426021681044
% SZS output start Proof for 3103087744292426021681044
6. ! [X0] : ((happy(X0) | patient(X0)) => (~brave(X0) & creative(X0))) [input p5]
11. ! [X0] : ((~brave(X0) | creative(X0)) => ~humble(X0)) [input p10]
22. humble(john) & rich(john) [input p21]
25. patient(john) [input hypothesis]
30. ! [X0] : ((~brave(X0) & creative(X0)) | (~happy(X0) & ~patient(X0))) [ennf transformation 6]
37. ! [X0] : (~humble(X0) | (brave(X0) & ~creative(X0))) [ennf transformation 11]
86. ~patient(X0) | creative(X0) [cnf transformation 30]
98. ~humble(X0) | ~creative(X0) [cnf transformation 37]
128. humble(john) [cnf transformation 22]
131. patient(john) [cnf transformation 25]
269. 30 <=> creative(john) [avatar definition]
271. creative(john) <- (30) [avatar component clause 269]
289. creative(john) [resolution 86,131]
293. 30 [avatar split clause 289,269]
294. ~creative(john) [resolution 98,128]
295. $false <- (30) [subsumption resolution 294,271]
296. ~30 [avatar contradiction clause 295]
297. $false [avatar sat refutation 293,296]
% SZS output end Proof for 3103087744292426021681044
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall or wise then lucy is both generous and quiet.
If alice is not calm or strong then someone is either not calm or not brave and vice versa.
Everyone who is not calm is both calm and not kind and vice versa.
Everyone who is either not funny or wise is both not curious and tall and vice versa.
If someone is not happy then susan is brave.
Everyone who is not strong is both funny and rich.
Everyone who is either not kind or calm is patient.
If susan is not humble or not funny then someone is happy or not creative.
If someone is either not curious or not old then john is either not patient or rich.
Everyone who is not tall or not strong is either creative or patient and vice versa.
Everyone who is both not patient and not tall is either generous or wise.
If john is calm or not tall then someone is either not creative or not patient.
Everyone who is not generous is either tall or old.
Everyone who is both kind and quiet is strong or not kind and vice versa.
If paul is rich or brave then mary is either not funny or not happy and vice versa.
If someone is not old then fred is either funny or not humble and vice versa.
Someone is creative.
Someone is both tall and not generous.
John is not old.
Alice is not humble.
Someone is either humble or not happy.
Fred is either happy or old.
Lucy is both happy and not tall.
Paul is either brave or not patient. | Lucy is creative. | contradiction | ((?[X]:((tall(X)|wise(X))))=>((generous(lucy)&quiet(lucy))))&
(((~calm(alice)|strong(alice)))<=>(?[X]:((~calm(X)<~>~brave(X)))))&
(![X]:(~calm(X)<=>(calm(X)&~kind(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(~curious(X)&tall(X))))&
((?[X]:(~happy(X)))=>(brave(susan)))&
(![X]:(~strong(X)=>(funny(X)&rich(X))))&
(![X]:((~kind(X)<~>calm(X))=>patient(X)))&
(((~humble(susan)|~funny(susan)))=>(?[X]:((happy(X)|~creative(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>((~patient(john)<~>rich(john))))&
(![X]:((~tall(X)|~strong(X))<=>(creative(X)<~>patient(X))))&
(![X]:((~patient(X)&~tall(X))=>(generous(X)<~>wise(X))))&
(((calm(john)|~tall(john)))=>(?[X]:((~creative(X)<~>~patient(X)))))&
(![X]:(~generous(X)=>(tall(X)<~>old(X))))&
(![X]:((kind(X)&quiet(X))<=>(strong(X)|~kind(X))))&
(((rich(paul)|brave(paul)))<=>((~funny(mary)<~>~happy(mary))))&
((?[X]:(~old(X)))<=>((funny(fred)<~>~humble(fred))))&
(?[X]:(creative(X)))&
(?[X]:((tall(X)&~generous(X))))&
(~old(john))&
(~humble(alice))&
(?[X]:((humble(X)<~>~happy(X))))&
((happy(fred)<~>old(fred)))&
((happy(lucy)&~tall(lucy)))&
((brave(paul)<~>~patient(paul))) | creative(lucy) | [
"p2",
"p6",
"p9",
"p13",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2195916745672172073946178
% SZS output start Proof for 2195916745672172073946178
3. ! [X0] : (~calm(X0) <=> (~kind(X0) & calm(X0))) [input p2]
7. ! [X0] : ((~kind(X0) <~> calm(X0)) => patient(X0)) [input p6]
10. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (creative(X0) <~> patient(X0))) [input p9]
14. ! [X0] : ((quiet(X0) & kind(X0)) <=> (~kind(X0) | strong(X0))) [input p13]
23. ~tall(lucy) & happy(lucy) [input p22]
25. creative(lucy) [input hypothesis]
29. ! [X0] : (patient(X0) | (~kind(X0) <=> calm(X0))) [ennf transformation 7]
41. ! [X0] : ((~calm(X0) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | calm(X0))) [nnf transformation 3]
42. ! [X0] : ((~calm(X0) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | calm(X0))) [flattening 41]
45. ! [X0] : (patient(X0) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0)))) [nnf transformation 29]
49. ! [X0] : (((~strong(X0) | ~tall(X0)) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (strong(X0) & tall(X0)))) [nnf transformation 10]
50. ! [X0] : ((~strong(X0) | ~tall(X0) | ((creative(X0) | ~patient(X0)) & (patient(X0) | ~creative(X0)))) & (((~patient(X0) | ~creative(X0)) & (patient(X0) | creative(X0))) | (strong(X0) & tall(X0)))) [flattening 49]
56. ! [X0] : (((quiet(X0) & kind(X0)) | (kind(X0) & ~strong(X0))) & ((~kind(X0) | strong(X0)) | (~quiet(X0) | ~kind(X0)))) [nnf transformation 14]
57. ! [X0] : (((quiet(X0) & kind(X0)) | (kind(X0) & ~strong(X0))) & (~kind(X0) | strong(X0) | ~quiet(X0) | ~kind(X0))) [flattening 56]
83. calm(X0) | calm(X0) [cnf transformation 42]
96. patient(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 45]
105. ~creative(X0) | ~patient(X0) | tall(X0) [cnf transformation 50]
119. kind(X0) | kind(X0) [cnf transformation 57]
142. ~tall(lucy) [cnf transformation 23]
145. creative(lucy) [cnf transformation 25]
147. kind(X0) [duplicate literal removal 119]
148. calm(X0) [duplicate literal removal 83]
204. ~kind(X0) | patient(X0) [subsumption resolution 96,148]
345. patient(X1) [resolution 204,147]
386. ~patient(lucy) | tall(lucy) [resolution 105,145]
391. tall(lucy) [subsumption resolution 386,345]
392. $false [subsumption resolution 391,142]
% SZS output end Proof for 2195916745672172073946178
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not old then paul is not wise and vice versa. Everyone who is funny or tall is both not kind and old and vice versa. Everyone who is both brave and rich is not rich or not patient and vice versa. If john is either not generous or quiet then someone is not patient or rich and vice versa. If susan is kind or not tall then susan is either not happy or rich. If someone is either not rich or patient then john is not wise or not old and vice versa. Everyone who is either happy or not humble is quiet or brave. Everyone who is both curious and quiet is both not old and not tall and vice versa. If someone is happy or strong then mary is not generous. Everyone who is not generous is not patient or not humble and vice versa. Everyone who is both not patient and not happy is old or not rich. Everyone who is not creative is not old or not brave. If susan is not creative or curious then paul is both curious and rich and vice versa. Everyone who is wise is either quiet or old. Everyone who is not brave is not brave or brave and vice versa. If alice is both not generous and quiet then susan is either curious or patient and vice versa. Fred is not wise. Someone is either not rich or funny. Alice is both not brave and strong. John is funny. Alice is both not humble and not old. Susan is patient. Someone is both not kind and rich. | John is not kind. | entailment | ((?[X]:((~happy(X)|~old(X))))<=>(~wise(paul)))&
(![X]:((funny(X)|tall(X))<=>(~kind(X)&old(X))))&
(![X]:((brave(X)&rich(X))<=>(~rich(X)|~patient(X))))&
(((~generous(john)<~>quiet(john)))<=>(?[X]:((~patient(X)|rich(X)))))&
(((kind(susan)|~tall(susan)))=>((~happy(susan)<~>rich(susan))))&
((?[X]:((~rich(X)<~>patient(X))))<=>((~wise(john)|~old(john))))&
(![X]:((happy(X)<~>~humble(X))=>(quiet(X)|brave(X))))&
(![X]:((curious(X)&quiet(X))<=>(~old(X)&~tall(X))))&
((?[X]:((happy(X)|strong(X))))=>(~generous(mary)))&
(![X]:(~generous(X)<=>(~patient(X)|~humble(X))))&
(![X]:((~patient(X)&~happy(X))=>(old(X)|~rich(X))))&
(![X]:(~creative(X)=>(~old(X)|~brave(X))))&
(((~creative(susan)|curious(susan)))<=>((curious(paul)&rich(paul))))&
(![X]:(wise(X)=>(quiet(X)<~>old(X))))&
(![X]:(~brave(X)<=>(~brave(X)|brave(X))))&
(((~generous(alice)&quiet(alice)))<=>((curious(susan)<~>patient(susan))))&
(~wise(fred))&
(?[X]:((~rich(X)<~>funny(X))))&
((~brave(alice)&strong(alice)))&
(funny(john))&
((~humble(alice)&~old(alice)))&
(patient(susan))&
(?[X]:((~kind(X)&rich(X)))) | ~kind(john) | [
"p1",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2715895006102042370274547
% SZS output start Proof for 2715895006102042370274547
2. ! [X0] : ((tall(X0) | funny(X0)) <=> (old(X0) & ~kind(X0))) [input p1]
20. funny(john) [input p19]
24. kind(john) [input hypothesis]
38. ! [X0] : (((tall(X0) | funny(X0)) | (~old(X0) | kind(X0))) & ((old(X0) & ~kind(X0)) | (~tall(X0) & ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : ((tall(X0) | funny(X0) | ~old(X0) | kind(X0)) & ((old(X0) & ~kind(X0)) | (~tall(X0) & ~funny(X0)))) [flattening 38]
72. ~kind(X0) | ~funny(X0) [cnf transformation 39]
132. funny(john) [cnf transformation 20]
138. kind(john) [cnf transformation 24]
270. ~funny(john) [resolution 72,138]
271. $false [subsumption resolution 270,132]
% SZS output end Proof for 2715895006102042370274547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not wise is not creative and vice versa. Everyone who is both not generous and calm is either not wise or not funny. Everyone who is both not quiet and patient is both wise and not funny. Everyone who is not strong is not curious or patient and vice versa. If paul is both not quiet and not patient then someone is both not wise and wise and vice versa. Everyone who is both not brave and brave is both kind and quiet and vice versa. Everyone who is generous is both not calm and not patient and vice versa. Everyone who is either not brave or strong is patient or not wise and vice versa. Everyone who is strong is both strong and not creative. If lucy is not happy then john is old and vice versa. Everyone who is both old and curious is not patient. Everyone who is both not happy and generous is both happy and not generous. Everyone who is both not quiet and brave is either not curious or happy. If someone is both creative and not patient then someone is both tall and strong. Everyone who is both not wise and curious is either not wise or not quiet. If lucy is both not creative and not rich then alice is both creative and not old and vice versa. Fred is humble. Alice is both rich and humble. Someone is not humble. Someone is not brave or funny. Someone is kind or old. Someone is creative or brave. Alice is calm. John is not patient. | Lucy is creative. | neutral | (![X]:((calm(X)<~>~wise(X))<=>~creative(X)))&
(![X]:((~generous(X)&calm(X))=>(~wise(X)<~>~funny(X))))&
(![X]:((~quiet(X)&patient(X))=>(wise(X)&~funny(X))))&
(![X]:(~strong(X)<=>(~curious(X)|patient(X))))&
(((~quiet(paul)&~patient(paul)))<=>(?[X]:((~wise(X)&wise(X)))))&
(![X]:((~brave(X)&brave(X))<=>(kind(X)&quiet(X))))&
(![X]:(generous(X)<=>(~calm(X)&~patient(X))))&
(![X]:((~brave(X)<~>strong(X))<=>(patient(X)|~wise(X))))&
(![X]:(strong(X)=>(strong(X)&~creative(X))))&
((~happy(lucy))<=>(old(john)))&
(![X]:((old(X)&curious(X))=>~patient(X)))&
(![X]:((~happy(X)&generous(X))=>(happy(X)&~generous(X))))&
(![X]:((~quiet(X)&brave(X))=>(~curious(X)<~>happy(X))))&
((?[X]:((creative(X)&~patient(X))))=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~wise(X)&curious(X))=>(~wise(X)<~>~quiet(X))))&
(((~creative(lucy)&~rich(lucy)))<=>((creative(alice)&~old(alice))))&
(humble(fred))&
((rich(alice)&humble(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)|funny(X))))&
(?[X]:((kind(X)|old(X))))&
(?[X]:((creative(X)|brave(X))))&
(calm(alice))&
(~patient(john)) | creative(lucy) | [] | null | 0 |
Everyone who is both not calm and not old is not tall or not strong and vice versa.
If someone is quiet then mary is either generous or not calm and vice versa.
Everyone who is brave is not patient.
Everyone who is not tall is both calm and not strong.
If mary is either old or brave then alice is both rich and not calm.
If mary is either calm or not calm then someone is not wise.
Everyone who is either brave or not happy is either not tall or not kind and vice versa.
If paul is calm then lucy is either not quiet or quiet.
Everyone who is both rich and not creative is not kind or wise.
Everyone who is funny is both old and happy and vice versa.
If alice is both not wise and kind then lucy is not creative or not strong and vice versa.
Everyone who is either not patient or strong is not happy or calm and vice versa.
If someone is not curious or not rich then someone is either quiet or not quiet.
Everyone who is either not wise or not old is not happy or not old and vice versa.
Everyone who is both not brave and not old is not creative.
Everyone who is either happy or not calm is either not rich or wise.
Someone is generous.
Someone is both rich and tall.
Someone is not old.
Someone is both not kind and not brave.
Alice is both creative and not wise.
Fred is not brave or not happy.
Fred is not quiet. | Mary is brave. | neutral | (![X]:((~calm(X)&~old(X))<=>(~tall(X)|~strong(X))))&
((?[X]:(quiet(X)))<=>((generous(mary)<~>~calm(mary))))&
(![X]:(brave(X)=>~patient(X)))&
(![X]:(~tall(X)=>(calm(X)&~strong(X))))&
(((old(mary)<~>brave(mary)))=>((rich(alice)&~calm(alice))))&
(((calm(mary)<~>~calm(mary)))=>(?[X]:(~wise(X))))&
(![X]:((brave(X)<~>~happy(X))<=>(~tall(X)<~>~kind(X))))&
((calm(paul))=>((~quiet(lucy)<~>quiet(lucy))))&
(![X]:((rich(X)&~creative(X))=>(~kind(X)|wise(X))))&
(![X]:(funny(X)<=>(old(X)&happy(X))))&
(((~wise(alice)&kind(alice)))<=>((~creative(lucy)|~strong(lucy))))&
(![X]:((~patient(X)<~>strong(X))<=>(~happy(X)|calm(X))))&
((?[X]:((~curious(X)|~rich(X))))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((~wise(X)<~>~old(X))<=>(~happy(X)|~old(X))))&
(![X]:((~brave(X)&~old(X))=>~creative(X)))&
(![X]:((happy(X)<~>~calm(X))=>(~rich(X)<~>wise(X))))&
(?[X]:(generous(X)))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:(~old(X)))&
(?[X]:((~kind(X)&~brave(X))))&
((creative(alice)&~wise(alice)))&
((~brave(fred)|~happy(fred)))&
(~quiet(fred)) | brave(mary) | [] | null | 0 |
Everyone who is both kind and rich is not generous. Everyone who is kind or happy is not quiet or wise. Everyone who is happy or not old is not tall or not calm and vice versa. Everyone who is tall or not strong is either not generous or not humble and vice versa. Everyone who is generous is not calm or quiet. If someone is either not patient or rich then mary is both funny and generous and vice versa. If someone is kind then mary is either generous or not kind. Everyone who is both tall and not rich is either generous or not funny and vice versa. If fred is either brave or not curious then someone is not quiet. Everyone who is either wise or not tall is wise or strong and vice versa. If alice is not funny or happy then someone is either not quiet or not curious and vice versa. Everyone who is either strong or not generous is both not tall and happy. If someone is both brave and creative then john is not brave or not humble and vice versa. If mary is both funny and humble then someone is brave and vice versa. Everyone who is tall or strong is either quiet or not calm and vice versa. Everyone who is either not creative or not tall is curious. Someone is not tall. Mary is not brave or funny. John is not patient. Fred is both strong and happy. Someone is not generous. Someone is humble. Alice is either not strong or not patient. Someone is not rich. | Mary is not generous. | entailment | (![X]:((kind(X)&rich(X))=>~generous(X)))&
(![X]:((kind(X)|happy(X))=>(~quiet(X)|wise(X))))&
(![X]:((happy(X)|~old(X))<=>(~tall(X)|~calm(X))))&
(![X]:((tall(X)|~strong(X))<=>(~generous(X)<~>~humble(X))))&
(![X]:(generous(X)=>(~calm(X)|quiet(X))))&
((?[X]:((~patient(X)<~>rich(X))))<=>((funny(mary)&generous(mary))))&
((?[X]:(kind(X)))=>((generous(mary)<~>~kind(mary))))&
(![X]:((tall(X)&~rich(X))<=>(generous(X)<~>~funny(X))))&
(((brave(fred)<~>~curious(fred)))=>(?[X]:(~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(wise(X)|strong(X))))&
(((~funny(alice)|happy(alice)))<=>(?[X]:((~quiet(X)<~>~curious(X)))))&
(![X]:((strong(X)<~>~generous(X))=>(~tall(X)&happy(X))))&
((?[X]:((brave(X)&creative(X))))<=>((~brave(john)|~humble(john))))&
(((funny(mary)&humble(mary)))<=>(?[X]:(brave(X))))&
(![X]:((tall(X)|strong(X))<=>(quiet(X)<~>~calm(X))))&
(![X]:((~creative(X)<~>~tall(X))=>curious(X)))&
(?[X]:(~tall(X)))&
((~brave(mary)|funny(mary)))&
(~patient(john))&
((strong(fred)&happy(fred)))&
(?[X]:(~generous(X)))&
(?[X]:(humble(X)))&
((~strong(alice)<~>~patient(alice)))&
(?[X]:(~rich(X))) | ~generous(mary) | [
"p3",
"p7",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2370778367085603875618294
% SZS output start Proof for 2370778367085603875618294
4. ! [X0] : ((~strong(X0) | tall(X0)) <=> (~generous(X0) <~> ~humble(X0))) [input p3]
8. ! [X0] : ((~rich(X0) & tall(X0)) <=> (generous(X0) <~> ~funny(X0))) [input p7]
13. ? [X0] : (creative(X0) & brave(X0)) <=> (~humble(john) | ~brave(john)) [input p12]
14. (humble(mary) & funny(mary)) <=> ? [X0] : brave(X0) [input p13]
25. generous(mary) [input hypothesis]
38. ! [X0] : (((~strong(X0) | tall(X0)) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (strong(X0) & ~tall(X0)))) [nnf transformation 4]
39. ! [X0] : ((~strong(X0) | tall(X0) | ((~generous(X0) | humble(X0)) & (~humble(X0) | generous(X0)))) & (((humble(X0) | generous(X0)) & (~humble(X0) | ~generous(X0))) | (strong(X0) & ~tall(X0)))) [flattening 38]
46. ! [X0] : (((~rich(X0) & tall(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | (rich(X0) | ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((~rich(X0) & tall(X0)) | ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0)))) & (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | rich(X0) | ~tall(X0))) [flattening 46]
59. (? [X0] : (creative(X0) & brave(X0)) | (humble(john) & brave(john))) & ((~humble(john) | ~brave(john)) | ! [X0] : (~creative(X0) | ~brave(X0))) [nnf transformation 13]
60. (? [X0] : (creative(X0) & brave(X0)) | (humble(john) & brave(john))) & (~humble(john) | ~brave(john) | ! [X0] : (~creative(X0) | ~brave(X0))) [flattening 59]
61. (? [X0] : (creative(X0) & brave(X0)) | (humble(john) & brave(john))) & (~humble(john) | ~brave(john) | ! [X1] : (~creative(X1) | ~brave(X1))) [rectify 60]
62. ? [X0] : (creative(X0) & brave(X0)) => (creative(sK3) & brave(sK3)) [choice axiom]
63. ((creative(sK3) & brave(sK3)) | (humble(john) & brave(john))) & (~humble(john) | ~brave(john) | ! [X1] : (~creative(X1) | ~brave(X1))) [skolemisation 61,62]
64. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | (~humble(mary) | ~funny(mary))) [nnf transformation 14]
65. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (? [X0] : brave(X0) | ~humble(mary) | ~funny(mary)) [flattening 64]
66. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (? [X1] : brave(X1) | ~humble(mary) | ~funny(mary)) [rectify 65]
67. ? [X1] : brave(X1) => brave(sK4) [choice axiom]
68. ((humble(mary) & funny(mary)) | ! [X0] : ~brave(X0)) & (brave(sK4) | ~humble(mary) | ~funny(mary)) [skolemisation 66,67]
88. ~humble(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 39]
105. ~funny(X0) | tall(X0) | ~generous(X0) [cnf transformation 47]
128. brave(sK3) | brave(john) [cnf transformation 63]
133. funny(mary) | ~brave(X0) [cnf transformation 68]
134. humble(mary) | ~brave(X0) [cnf transformation 68]
153. generous(mary) [cnf transformation 25]
157. 1 <=> funny(mary) [avatar definition]
158. funny(mary) <- (1) [avatar component clause 157]
161. 2 <=> generous(mary) [avatar definition]
162. generous(mary) <- (2) [avatar component clause 161]
247. 20 <=> brave(john) [avatar definition]
249. brave(john) <- (20) [avatar component clause 247]
252. 21 <=> brave(sK3) [avatar definition]
254. brave(sK3) <- (21) [avatar component clause 252]
256. 20 | 21 [avatar split clause 128,252,247]
262. 23 <=> ! [X0] : ~brave(X0) [avatar definition]
263. ~brave(X0) <- (23) [avatar component clause 262]
265. 24 <=> humble(mary) [avatar definition]
267. humble(mary) <- (24) [avatar component clause 265]
268. 23 | 24 [avatar split clause 134,265,262]
269. 23 | 1 [avatar split clause 133,157,262]
290. 2 [avatar split clause 153,161]
291. $false <- (21, 23) [subsumption resolution 254,263]
292. ~21 | ~23 [avatar contradiction clause 291]
301. ~generous(mary) | ~tall(mary) <- (24) [resolution 88,267]
311. ~tall(mary) <- (2, 24) [subsumption resolution 301,162]
320. tall(mary) | ~generous(mary) <- (1) [resolution 105,158]
322. ~generous(mary) <- (1, 2, 24) [subsumption resolution 320,311]
323. $false <- (1, 2, 24) [subsumption resolution 322,162]
324. ~1 | ~2 | ~24 [avatar contradiction clause 323]
335. $false <- (20, 23) [subsumption resolution 249,263]
336. ~20 | ~23 [avatar contradiction clause 335]
337. $false [avatar sat refutation 256,268,269,290,292,324,336]
% SZS output end Proof for 2370778367085603875618294
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is funny or not patient. Everyone who is happy is both rich and humble and vice versa. Everyone who is not strong or not creative is not quiet or strong and vice versa. Everyone who is both calm and funny is humble or not creative. If lucy is not funny then john is both humble and not kind and vice versa. If someone is both generous and quiet then john is both not tall and not generous and vice versa. Everyone who is patient is both old and not wise and vice versa. If susan is not funny or humble then someone is both not patient and curious. If someone is patient then someone is not funny or generous and vice versa. If lucy is either not curious or not calm then someone is either not tall or not kind and vice versa. If someone is both not creative and not old then someone is both humble and not old and vice versa. Everyone who is either old or not brave is both not kind and not happy. Everyone who is both not patient and wise is calm or kind. Everyone who is both not kind and not happy is either not tall or not quiet and vice versa. Everyone who is not quiet or not generous is old or not generous and vice versa. Everyone who is tall or not calm is both not wise and curious. Alice is not wise. Susan is either not curious or not humble. Someone is both not tall and curious. Fred is calm. Someone is generous or strong. Fred is not brave or patient. Someone is both patient and not strong. Someone is curious or strong. | Lucy is quiet. | neutral | ((?[X]:(~old(X)))=>(?[X]:((funny(X)|~patient(X)))))&
(![X]:(happy(X)<=>(rich(X)&humble(X))))&
(![X]:((~strong(X)|~creative(X))<=>(~quiet(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(humble(X)|~creative(X))))&
((~funny(lucy))<=>((humble(john)&~kind(john))))&
((?[X]:((generous(X)&quiet(X))))<=>((~tall(john)&~generous(john))))&
(![X]:(patient(X)<=>(old(X)&~wise(X))))&
(((~funny(susan)|humble(susan)))=>(?[X]:((~patient(X)&curious(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(((~curious(lucy)<~>~calm(lucy)))<=>(?[X]:((~tall(X)<~>~kind(X)))))&
((?[X]:((~creative(X)&~old(X))))<=>(?[X]:((humble(X)&~old(X)))))&
(![X]:((old(X)<~>~brave(X))=>(~kind(X)&~happy(X))))&
(![X]:((~patient(X)&wise(X))=>(calm(X)|kind(X))))&
(![X]:((~kind(X)&~happy(X))<=>(~tall(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|~generous(X))<=>(old(X)|~generous(X))))&
(![X]:((tall(X)|~calm(X))=>(~wise(X)&curious(X))))&
(~wise(alice))&
((~curious(susan)<~>~humble(susan)))&
(?[X]:((~tall(X)&curious(X))))&
(calm(fred))&
(?[X]:((generous(X)|strong(X))))&
((~brave(fred)|patient(fred)))&
(?[X]:((patient(X)&~strong(X))))&
(?[X]:((curious(X)|strong(X)))) | quiet(lucy) | [] | null | 0 |
Everyone who is either wise or kind is tall or not old and vice versa.
Everyone who is not humble is either not strong or not tall.
Everyone who is both rich and funny is both creative and funny and vice versa.
Everyone who is not generous or not calm is either brave or creative.
Everyone who is generous is either not strong or not curious.
Everyone who is not brave or not old is both patient and not humble.
Everyone who is happy is not brave and vice versa.
Everyone who is not brave is curious and vice versa.
Everyone who is either calm or brave is both not quiet and funny.
If mary is not brave then someone is not happy or strong.
Everyone who is not strong or not brave is funny or rich.
Everyone who is not happy or calm is either creative or kind and vice versa.
If someone is either old or not wise then susan is either brave or old and vice versa.
Everyone who is quiet is both calm and old.
Everyone who is both creative and strong is not curious or wise.
If susan is kind then someone is either quiet or not funny.
Alice is either happy or not calm.
Susan is not patient.
Alice is either not quiet or not strong.
Someone is both not quiet and brave.
Someone is strong or not quiet.
Alice is not creative.
Someone is kind.
Someone is brave or not funny. | Susan is not happy. | entailment | (![X]:((wise(X)<~>kind(X))<=>(tall(X)|~old(X))))&
(![X]:(~humble(X)=>(~strong(X)<~>~tall(X))))&
(![X]:((rich(X)&funny(X))<=>(creative(X)&funny(X))))&
(![X]:((~generous(X)|~calm(X))=>(brave(X)<~>creative(X))))&
(![X]:(generous(X)=>(~strong(X)<~>~curious(X))))&
(![X]:((~brave(X)|~old(X))=>(patient(X)&~humble(X))))&
(![X]:(happy(X)<=>~brave(X)))&
(![X]:(~brave(X)<=>curious(X)))&
(![X]:((calm(X)<~>brave(X))=>(~quiet(X)&funny(X))))&
((~brave(mary))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~strong(X)|~brave(X))=>(funny(X)|rich(X))))&
(![X]:((~happy(X)|calm(X))<=>(creative(X)<~>kind(X))))&
((?[X]:((old(X)<~>~wise(X))))<=>((brave(susan)<~>old(susan))))&
(![X]:(quiet(X)=>(calm(X)&old(X))))&
(![X]:((creative(X)&strong(X))=>(~curious(X)|wise(X))))&
((kind(susan))=>(?[X]:((quiet(X)<~>~funny(X)))))&
((happy(alice)<~>~calm(alice)))&
(~patient(susan))&
((~quiet(alice)<~>~strong(alice)))&
(?[X]:((~quiet(X)&brave(X))))&
(?[X]:((strong(X)|~quiet(X))))&
(~creative(alice))&
(?[X]:(kind(X)))&
(?[X]:((brave(X)|~funny(X)))) | ~happy(susan) | [
"p5",
"p6",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2080801889433550414780688
% SZS output start Proof for 2080801889433550414780688
6. ! [X0] : ((~old(X0) | ~brave(X0)) => (~humble(X0) & patient(X0))) [input p5]
7. ! [X0] : (happy(X0) <=> ~brave(X0)) [input p6]
18. ~patient(susan) [input p17]
25. happy(susan) [input hypothesis]
29. ! [X0] : ((~humble(X0) & patient(X0)) | (old(X0) & brave(X0))) [ennf transformation 6]
45. ! [X0] : ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0))) [nnf transformation 7]
87. patient(X0) | brave(X0) [cnf transformation 29]
91. ~happy(X0) | ~brave(X0) [cnf transformation 45]
123. ~patient(susan) [cnf transformation 18]
132. happy(susan) [cnf transformation 25]
151. 5 <=> brave(susan) [avatar definition]
153. brave(susan) <- (5) [avatar component clause 151]
228. brave(susan) [resolution 87,123]
231. 5 [avatar split clause 228,151]
236. ~brave(susan) [resolution 91,132]
237. $false <- (5) [subsumption resolution 236,153]
238. ~5 [avatar contradiction clause 237]
239. $false [avatar sat refutation 231,238]
% SZS output end Proof for 2080801889433550414780688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or wise is not wise or not calm and vice versa.
Everyone who is wise is calm or not strong.
Everyone who is not quiet is either strong or rich.
If someone is both quiet and not humble then someone is quiet.
Everyone who is either quiet or not funny is not humble and vice versa.
If someone is kind then someone is either happy or not kind and vice versa.
Everyone who is either humble or tall is brave or kind and vice versa.
Everyone who is not strong or quiet is funny and vice versa.
Everyone who is either not calm or not kind is not tall or funny and vice versa.
Everyone who is both not quiet and brave is both not curious and funny and vice versa.
Everyone who is both not humble and not generous is strong.
Everyone who is not kind is rich or generous and vice versa.
If mary is either humble or wise then paul is both not creative and wise and vice versa.
Everyone who is tall is both patient and not brave and vice versa.
Someone is either not wise or quiet.
Someone is generous or strong.
Fred is generous or strong.
John is both not calm and happy. | Paul is not creative. | neutral | (![X]:((~rich(X)<~>wise(X))<=>(~wise(X)|~calm(X))))&
(![X]:(wise(X)=>(calm(X)|~strong(X))))&
(![X]:(~quiet(X)=>(strong(X)<~>rich(X))))&
((?[X]:((quiet(X)&~humble(X))))=>(?[X]:(quiet(X))))&
(![X]:((quiet(X)<~>~funny(X))<=>~humble(X)))&
((?[X]:(kind(X)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((humble(X)<~>tall(X))<=>(brave(X)|kind(X))))&
(![X]:((~strong(X)|quiet(X))<=>funny(X)))&
(![X]:((~calm(X)<~>~kind(X))<=>(~tall(X)|funny(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~curious(X)&funny(X))))&
(![X]:((~humble(X)&~generous(X))=>strong(X)))&
(![X]:(~kind(X)<=>(rich(X)|generous(X))))&
(((humble(mary)<~>wise(mary)))<=>((~creative(paul)&wise(paul))))&
(![X]:(tall(X)<=>(patient(X)&~brave(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:((generous(X)|strong(X))))&
((generous(fred)|strong(fred)))&
((~calm(john)&happy(john))) | ~creative(paul) | [] | null | 0 |
If someone is either not quiet or not happy then someone is not creative.
If lucy is either not generous or old then someone is not strong.
Everyone who is either quiet or wise is strong and vice versa.
If lucy is either creative or kind then someone is generous or strong and vice versa.
Everyone who is not humble or not generous is kind or not patient.
Everyone who is not humble is not wise and vice versa.
If someone is kind or not old then susan is both patient and not quiet.
Everyone who is kind or not funny is both funny and tall.
Everyone who is either quiet or humble is both not humble and humble and vice versa.
Everyone who is not strong or happy is both not calm and not rich and vice versa.
Everyone who is either not wise or not brave is not curious.
If paul is both not happy and patient then someone is both calm and kind.
Everyone who is not curious is tall.
If someone is either not old or generous then someone is both not creative and not generous.
Everyone who is both not curious and curious is either not strong or strong.
If susan is rich or happy then john is both creative and strong and vice versa.
Someone is generous.
Mary is curious or not calm.
Alice is not strong.
Someone is either happy or brave.
Someone is either curious or calm.
Someone is not wise.
John is not kind.
John is calm or not creative. | John is not rich. | entailment | ((?[X]:((~quiet(X)<~>~happy(X))))=>(?[X]:(~creative(X))))&
(((~generous(lucy)<~>old(lucy)))=>(?[X]:(~strong(X))))&
(![X]:((quiet(X)<~>wise(X))<=>strong(X)))&
(((creative(lucy)<~>kind(lucy)))<=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((~humble(X)|~generous(X))=>(kind(X)|~patient(X))))&
(![X]:(~humble(X)<=>~wise(X)))&
((?[X]:((kind(X)|~old(X))))=>((patient(susan)&~quiet(susan))))&
(![X]:((kind(X)|~funny(X))=>(funny(X)&tall(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(~humble(X)&humble(X))))&
(![X]:((~strong(X)|happy(X))<=>(~calm(X)&~rich(X))))&
(![X]:((~wise(X)<~>~brave(X))=>~curious(X)))&
(((~happy(paul)&patient(paul)))=>(?[X]:((calm(X)&kind(X)))))&
(![X]:(~curious(X)=>tall(X)))&
((?[X]:((~old(X)<~>generous(X))))=>(?[X]:((~creative(X)&~generous(X)))))&
(![X]:((~curious(X)&curious(X))=>(~strong(X)<~>strong(X))))&
(((rich(susan)|happy(susan)))<=>((creative(john)&strong(john))))&
(?[X]:(generous(X)))&
((curious(mary)|~calm(mary)))&
(~strong(alice))&
(?[X]:((happy(X)<~>brave(X))))&
(?[X]:((curious(X)<~>calm(X))))&
(?[X]:(~wise(X)))&
(~kind(john))&
((calm(john)|~creative(john))) | ~rich(john) | [
"p2",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 282043632185506162256541
% SZS output start Proof for 282043632185506162256541
3. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> strong(X0)) [input p2]
6. ! [X0] : (~humble(X0) <=> ~wise(X0)) [input p5]
9. ! [X0] : ((quiet(X0) <~> humble(X0)) <=> (humble(X0) & ~humble(X0))) [input p8]
10. ! [X0] : ((happy(X0) | ~strong(X0)) <=> (~rich(X0) & ~calm(X0))) [input p9]
25. rich(john) [input hypothesis]
49. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | ~strong(X0)) & (strong(X0) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 3]
54. ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 6]
55. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | (~humble(X0) | humble(X0))) & ((humble(X0) & ~humble(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [nnf transformation 9]
56. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | ~humble(X0) | humble(X0)) & ((humble(X0) & ~humble(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [flattening 55]
57. ! [X0] : (((happy(X0) | ~strong(X0)) | (rich(X0) | calm(X0))) & ((~rich(X0) & ~calm(X0)) | (~happy(X0) & strong(X0)))) [nnf transformation 10]
58. ! [X0] : ((happy(X0) | ~strong(X0) | rich(X0) | calm(X0)) & ((~rich(X0) & ~calm(X0)) | (~happy(X0) & strong(X0)))) [flattening 57]
85. ~strong(X0) | quiet(X0) | wise(X0) [cnf transformation 49]
86. ~wise(X0) | ~quiet(X0) | ~strong(X0) [cnf transformation 49]
95. ~wise(X0) | humble(X0) [cnf transformation 54]
96. ~humble(X0) | wise(X0) [cnf transformation 54]
102. ~humble(X0) | quiet(X0) | ~humble(X0) [cnf transformation 56]
103. humble(X0) | humble(X0) | ~quiet(X0) [cnf transformation 56]
109. ~rich(X0) | strong(X0) [cnf transformation 58]
137. rich(john) [cnf transformation 25]
138. ~humble(X0) | quiet(X0) [duplicate literal removal 102]
139. ~quiet(X0) | humble(X0) [duplicate literal removal 103]
255. 26 <=> strong(john) [avatar definition]
256. strong(john) <- (26) [avatar component clause 255]
309. strong(john) [resolution 109,137]
310. 26 [avatar split clause 309,255]
313. quiet(john) | wise(john) <- (26) [resolution 85,256]
324. 38 <=> wise(john) [avatar definition]
325. ~wise(john) <- (~38) [avatar component clause 324]
326. wise(john) <- (38) [avatar component clause 324]
328. 39 <=> quiet(john) [avatar definition]
329. ~quiet(john) <- (~39) [avatar component clause 328]
330. quiet(john) <- (39) [avatar component clause 328]
331. 38 | 39 | ~26 [avatar split clause 313,255,328,324]
334. ~quiet(john) | ~strong(john) <- (38) [resolution 326,86]
336. humble(john) <- (38) [resolution 326,95]
337. ~quiet(john) <- (26, 38) [subsumption resolution 334,256]
338. ~39 | ~26 | ~38 [avatar split clause 337,324,255,328]
381. quiet(john) <- (38) [resolution 336,138]
383. $false <- (38, ~39) [subsumption resolution 381,329]
384. ~38 | 39 [avatar contradiction clause 383]
386. humble(john) <- (39) [resolution 330,139]
393. wise(john) <- (39) [resolution 386,96]
394. $false <- (~38, 39) [subsumption resolution 393,325]
395. 38 | ~39 [avatar contradiction clause 394]
396. $false [avatar sat refutation 310,331,338,384,395]
% SZS output end Proof for 282043632185506162256541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or humble is either kind or not rich.
Everyone who is either not calm or not patient is generous.
Everyone who is either not strong or old is either not calm or rich.
Everyone who is both not quiet and not patient is either not strong or not patient and vice versa.
If lucy is not wise then alice is both quiet and funny and vice versa.
Everyone who is both tall and generous is quiet.
If mary is strong then someone is either not humble or not tall.
If john is either tall or not humble then someone is either not happy or quiet.
Everyone who is happy or not strong is brave.
Everyone who is both kind and not curious is both not kind and not rich and vice versa.
If alice is either humble or brave then fred is both not generous and not creative.
If someone is old then someone is both not wise and creative and vice versa.
If lucy is not calm or not patient then someone is both not tall and wise.
If paul is wise or not humble then lucy is either not wise or not patient.
Everyone who is not creative is both curious and not wise.
If someone is humble or generous then someone is both not humble and patient.
Paul is either wise or not humble.
Paul is both not patient and not brave.
Mary is kind.
Susan is calm or brave.
Fred is either not wise or funny.
Someone is humble or not kind.
Someone is either curious or rich. | Fred is funny. | neutral | (![X]:((~tall(X)|humble(X))=>(kind(X)<~>~rich(X))))&
(![X]:((~calm(X)<~>~patient(X))=>generous(X)))&
(![X]:((~strong(X)<~>old(X))=>(~calm(X)<~>rich(X))))&
(![X]:((~quiet(X)&~patient(X))<=>(~strong(X)<~>~patient(X))))&
((~wise(lucy))<=>((quiet(alice)&funny(alice))))&
(![X]:((tall(X)&generous(X))=>quiet(X)))&
((strong(mary))=>(?[X]:((~humble(X)<~>~tall(X)))))&
(((tall(john)<~>~humble(john)))=>(?[X]:((~happy(X)<~>quiet(X)))))&
(![X]:((happy(X)|~strong(X))=>brave(X)))&
(![X]:((kind(X)&~curious(X))<=>(~kind(X)&~rich(X))))&
(((humble(alice)<~>brave(alice)))=>((~generous(fred)&~creative(fred))))&
((?[X]:(old(X)))<=>(?[X]:((~wise(X)&creative(X)))))&
(((~calm(lucy)|~patient(lucy)))=>(?[X]:((~tall(X)&wise(X)))))&
(((wise(paul)|~humble(paul)))=>((~wise(lucy)<~>~patient(lucy))))&
(![X]:(~creative(X)=>(curious(X)&~wise(X))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((~humble(X)&patient(X)))))&
((wise(paul)<~>~humble(paul)))&
((~patient(paul)&~brave(paul)))&
(kind(mary))&
((calm(susan)|brave(susan)))&
((~wise(fred)<~>funny(fred)))&
(?[X]:((humble(X)|~kind(X))))&
(?[X]:((curious(X)<~>rich(X)))) | funny(fred) | [] | null | 0 |
If mary is not curious then john is not old and vice versa.
Everyone who is either not strong or funny is not calm and vice versa.
If john is humble then john is not quiet.
Everyone who is either old or not generous is strong and vice versa.
If lucy is either rich or not curious then alice is either not rich or not creative.
If someone is either not happy or not humble then paul is patient.
Everyone who is both strong and happy is not happy.
Everyone who is both not old and not tall is not quiet.
Everyone who is calm or kind is either not patient or funny and vice versa.
If john is humble then mary is patient.
Everyone who is both wise and kind is not strong and vice versa.
Everyone who is not curious or not humble is either brave or generous.
If someone is both not creative and old then someone is either kind or not patient.
If someone is either wise or not kind then john is not strong and vice versa.
Everyone who is curious or funny is either patient or old.
Everyone who is not humble is wise or brave and vice versa.
Someone is funny or old.
Someone is not brave or patient.
Alice is either not kind or funny.
Mary is both rich and not happy.
Fred is both not patient and happy.
Someone is strong.
Alice is both not patient and not quiet.
Someone is not kind. | Paul is not old. | entailment | ((~curious(mary))<=>(~old(john)))&
(![X]:((~strong(X)<~>funny(X))<=>~calm(X)))&
((humble(john))=>(~quiet(john)))&
(![X]:((old(X)<~>~generous(X))<=>strong(X)))&
(((rich(lucy)<~>~curious(lucy)))=>((~rich(alice)<~>~creative(alice))))&
((?[X]:((~happy(X)<~>~humble(X))))=>(patient(paul)))&
(![X]:((strong(X)&happy(X))=>~happy(X)))&
(![X]:((~old(X)&~tall(X))=>~quiet(X)))&
(![X]:((calm(X)|kind(X))<=>(~patient(X)<~>funny(X))))&
((humble(john))=>(patient(mary)))&
(![X]:((wise(X)&kind(X))<=>~strong(X)))&
(![X]:((~curious(X)|~humble(X))=>(brave(X)<~>generous(X))))&
((?[X]:((~creative(X)&old(X))))=>(?[X]:((kind(X)<~>~patient(X)))))&
((?[X]:((wise(X)<~>~kind(X))))<=>(~strong(john)))&
(![X]:((curious(X)|funny(X))=>(patient(X)<~>old(X))))&
(![X]:(~humble(X)<=>(wise(X)|brave(X))))&
(?[X]:((funny(X)|old(X))))&
(?[X]:((~brave(X)|patient(X))))&
((~kind(alice)<~>funny(alice)))&
((rich(mary)&~happy(mary)))&
((~patient(fred)&happy(fred)))&
(?[X]:(strong(X)))&
((~patient(alice)&~quiet(alice)))&
(?[X]:(~kind(X))) | ~old(paul) | [
"p1",
"p5",
"p6",
"p8",
"p10",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4307614300867557450118861
% SZS output start Proof for 4307614300867557450118861
2. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> ~calm(X0)) [input p1]
6. ? [X0] : (~happy(X0) <~> ~humble(X0)) => patient(paul) [input p5]
7. ! [X0] : ((happy(X0) & strong(X0)) => ~happy(X0)) [input p6]
9. ! [X0] : ((kind(X0) | calm(X0)) <=> (~patient(X0) <~> funny(X0))) [input p8]
11. ! [X0] : ((kind(X0) & wise(X0)) <=> ~strong(X0)) [input p10]
15. ! [X0] : ((funny(X0) | curious(X0)) => (patient(X0) <~> old(X0))) [input p14]
16. ! [X0] : (~humble(X0) <=> (brave(X0) | wise(X0))) [input p15]
21. happy(fred) & ~patient(fred) [input p20]
25. old(paul) [input hypothesis]
31. patient(paul) | ! [X0] : (~happy(X0) <=> ~humble(X0)) [ennf transformation 6]
32. ! [X0] : (~happy(X0) | (~happy(X0) | ~strong(X0))) [ennf transformation 7]
33. ! [X0] : (~happy(X0) | ~happy(X0) | ~strong(X0)) [flattening 32]
37. ! [X0] : ((patient(X0) <~> old(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 15]
39. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | calm(X0)) & (~calm(X0) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 2]
42. patient(paul) | ! [X0] : ((~happy(X0) | humble(X0)) & (~humble(X0) | happy(X0))) [nnf transformation 31]
43. ! [X0] : (((kind(X0) | calm(X0)) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~kind(X0) & ~calm(X0)))) [nnf transformation 9]
44. ! [X0] : ((kind(X0) | calm(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0)))) & (((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | (~kind(X0) & ~calm(X0)))) [flattening 43]
45. ! [X0] : (((kind(X0) & wise(X0)) | strong(X0)) & (~strong(X0) | (~kind(X0) | ~wise(X0)))) [nnf transformation 11]
46. ! [X0] : (((kind(X0) & wise(X0)) | strong(X0)) & (~strong(X0) | ~kind(X0) | ~wise(X0))) [flattening 45]
56. ! [X0] : (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 37]
57. ! [X0] : ((~humble(X0) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | humble(X0))) [nnf transformation 16]
58. ! [X0] : ((~humble(X0) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | humble(X0))) [flattening 57]
72. ~strong(X0) | funny(X0) | calm(X0) [cnf transformation 39]
83. patient(paul) | ~happy(X0) | humble(X0) [cnf transformation 42]
84. ~happy(X0) | ~happy(X0) | ~strong(X0) [cnf transformation 33]
85. ~patient(X0) | funny(X0) | ~calm(X0) [cnf transformation 44]
86. ~kind(X0) | ~patient(X0) | funny(X0) [cnf transformation 44]
93. wise(X0) | strong(X0) [cnf transformation 46]
94. kind(X0) | strong(X0) [cnf transformation 46]
108. ~patient(X0) | ~old(X0) | ~funny(X0) [cnf transformation 56]
110. ~wise(X0) | ~humble(X0) [cnf transformation 58]
119. happy(fred) [cnf transformation 21]
123. old(paul) [cnf transformation 25]
124. ~happy(X0) | ~strong(X0) [duplicate literal removal 84]
156. 7 <=> ! [X0] : (~happy(X0) | humble(X0)) [avatar definition]
157. ~happy(X0) | humble(X0) <- (7) [avatar component clause 156]
159. 8 <=> patient(paul) [avatar definition]
161. patient(paul) <- (8) [avatar component clause 159]
162. 7 | 8 [avatar split clause 83,159,156]
244. ~humble(X0) | strong(X0) [resolution 110,93]
245. ~strong(fred) [resolution 124,119]
341. funny(paul) | ~calm(paul) <- (8) [resolution 85,161]
343. 42 <=> calm(paul) [avatar definition]
345. ~calm(paul) <- (~42) [avatar component clause 343]
347. 43 <=> funny(paul) [avatar definition]
348. ~funny(paul) <- (~43) [avatar component clause 347]
350. ~42 | 43 | ~8 [avatar split clause 341,159,347,343]
351. ~patient(X0) | funny(X0) | strong(X0) [resolution 86,94]
441. ~old(paul) | ~funny(paul) <- (8) [resolution 108,161]
443. ~funny(paul) <- (8) [subsumption resolution 441,123]
444. ~43 | ~8 [avatar split clause 443,159,347]
482. funny(paul) | strong(paul) <- (8) [resolution 351,161]
484. strong(paul) <- (8, ~43) [subsumption resolution 482,348]
505. funny(paul) | calm(paul) <- (8, ~43) [resolution 484,72]
507. calm(paul) <- (8, ~43) [subsumption resolution 505,348]
508. $false <- (8, ~42, ~43) [subsumption resolution 507,345]
509. ~8 | 42 | 43 [avatar contradiction clause 508]
510. humble(fred) <- (7) [resolution 157,119]
513. strong(fred) <- (7) [resolution 510,244]
523. $false <- (7) [subsumption resolution 513,245]
524. ~7 [avatar contradiction clause 523]
525. $false [avatar sat refutation 162,350,444,509,524]
% SZS output end Proof for 4307614300867557450118861
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either humble or rich then someone is either not rich or wise.
Everyone who is either calm or not quiet is not rich.
Everyone who is both not curious and not calm is both funny and not patient.
If mary is either creative or not wise then lucy is both wise and not wise and vice versa.
If someone is either rich or quiet then someone is either old or not funny.
If someone is not kind or brave then paul is either wise or not strong and vice versa.
Everyone who is both not happy and brave is both funny and not rich and vice versa.
Everyone who is not humble or creative is not happy.
If someone is not wise then fred is both humble and not humble.
If alice is both kind and humble then someone is both not tall and creative.
Everyone who is both wise and not tall is strong or rich.
If susan is strong then mary is calm or not old.
Everyone who is old is old or funny and vice versa.
If someone is either not humble or kind then alice is both funny and rich and vice versa.
Everyone who is not humble or not generous is both old and creative.
If susan is not wise or not funny then fred is either happy or not funny and vice versa.
Mary is not rich.
Fred is both kind and not funny.
John is either not tall or not brave.
Someone is not patient.
Alice is rich.
Alice is both patient and creative. | Alice is brave. | contradiction | (((humble(john)<~>rich(john)))=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((calm(X)<~>~quiet(X))=>~rich(X)))&
(![X]:((~curious(X)&~calm(X))=>(funny(X)&~patient(X))))&
(((creative(mary)<~>~wise(mary)))<=>((wise(lucy)&~wise(lucy))))&
((?[X]:((rich(X)<~>quiet(X))))=>(?[X]:((old(X)<~>~funny(X)))))&
((?[X]:((~kind(X)|brave(X))))<=>((wise(paul)<~>~strong(paul))))&
(![X]:((~happy(X)&brave(X))<=>(funny(X)&~rich(X))))&
(![X]:((~humble(X)|creative(X))=>~happy(X)))&
((?[X]:(~wise(X)))=>((humble(fred)&~humble(fred))))&
(((kind(alice)&humble(alice)))=>(?[X]:((~tall(X)&creative(X)))))&
(![X]:((wise(X)&~tall(X))=>(strong(X)|rich(X))))&
((strong(susan))=>((calm(mary)|~old(mary))))&
(![X]:(old(X)<=>(old(X)|funny(X))))&
((?[X]:((~humble(X)<~>kind(X))))<=>((funny(alice)&rich(alice))))&
(![X]:((~humble(X)|~generous(X))=>(old(X)&creative(X))))&
(((~wise(susan)|~funny(susan)))<=>((happy(fred)<~>~funny(fred))))&
(~rich(mary))&
((kind(fred)&~funny(fred)))&
((~tall(john)<~>~brave(john)))&
(?[X]:(~patient(X)))&
(rich(alice))&
((patient(alice)&creative(alice))) | brave(alice) | [
"p6",
"p7",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4605654019768823037774136
% SZS output start Proof for 4605654019768823037774136
7. ! [X0] : ((brave(X0) & ~happy(X0)) <=> (~rich(X0) & funny(X0))) [input p6]
8. ! [X0] : ((creative(X0) | ~humble(X0)) => ~happy(X0)) [input p7]
21. rich(alice) [input p20]
22. creative(alice) & patient(alice) [input p21]
23. brave(alice) [input hypothesis]
30. ! [X0] : (~happy(X0) | (~creative(X0) & humble(X0))) [ennf transformation 8]
53. ! [X0] : (((brave(X0) & ~happy(X0)) | (rich(X0) | ~funny(X0))) & ((~rich(X0) & funny(X0)) | (~brave(X0) | happy(X0)))) [nnf transformation 7]
54. ! [X0] : (((brave(X0) & ~happy(X0)) | rich(X0) | ~funny(X0)) & ((~rich(X0) & funny(X0)) | ~brave(X0) | happy(X0))) [flattening 53]
92. ~brave(X0) | ~rich(X0) | happy(X0) [cnf transformation 54]
96. ~happy(X0) | ~creative(X0) [cnf transformation 30]
126. rich(alice) [cnf transformation 21]
128. creative(alice) [cnf transformation 22]
129. brave(alice) [cnf transformation 23]
257. 28 <=> rich(alice) [avatar definition]
258. rich(alice) <- (28) [avatar component clause 257]
313. 28 [avatar split clause 126,257]
338. ~rich(alice) | happy(alice) [resolution 92,129]
339. happy(alice) <- (28) [subsumption resolution 338,258]
341. ~creative(alice) <- (28) [resolution 339,96]
343. $false <- (28) [subsumption resolution 341,128]
344. ~28 [avatar contradiction clause 343]
347. $false [avatar sat refutation 313,344]
% SZS output end Proof for 4605654019768823037774136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both not calm and kind.
Everyone who is not curious is both not brave and not wise and vice versa.
If someone is both not rich and not strong then lucy is both not generous and quiet and vice versa.
Everyone who is either curious or generous is wise or tall and vice versa.
If someone is both old and not happy then alice is not curious or curious and vice versa.
If lucy is both patient and kind then someone is wise and vice versa.
If someone is not creative or calm then someone is creative or not brave.
If someone is tall or kind then someone is not tall or not funny.
If someone is both not tall and kind then someone is either not old or not generous and vice versa.
Everyone who is both not happy and not tall is not wise or brave.
Everyone who is happy or creative is not happy.
Everyone who is strong is either not calm or not old and vice versa.
If lucy is either not rich or quiet then someone is humble or patient and vice versa.
Everyone who is not patient or not humble is both brave and not quiet.
Everyone who is either kind or not tall is either strong or funny.
If someone is either not tall or generous then someone is tall and vice versa.
Someone is either humble or brave.
Lucy is either humble or wise.
Someone is kind or strong.
Susan is not rich or strong.
Lucy is not patient or not calm.
Susan is both not creative and tall. | Alice is happy. | contradiction | (![X]:(generous(X)=>(~calm(X)&kind(X))))&
(![X]:(~curious(X)<=>(~brave(X)&~wise(X))))&
((?[X]:((~rich(X)&~strong(X))))<=>((~generous(lucy)&quiet(lucy))))&
(![X]:((curious(X)<~>generous(X))<=>(wise(X)|tall(X))))&
((?[X]:((old(X)&~happy(X))))<=>((~curious(alice)|curious(alice))))&
(((patient(lucy)&kind(lucy)))<=>(?[X]:(wise(X))))&
((?[X]:((~creative(X)|calm(X))))=>(?[X]:((creative(X)|~brave(X)))))&
((?[X]:((tall(X)|kind(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
((?[X]:((~tall(X)&kind(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
(![X]:((~happy(X)&~tall(X))=>(~wise(X)|brave(X))))&
(![X]:((happy(X)|creative(X))=>~happy(X)))&
(![X]:(strong(X)<=>(~calm(X)<~>~old(X))))&
(((~rich(lucy)<~>quiet(lucy)))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((~patient(X)|~humble(X))=>(brave(X)&~quiet(X))))&
(![X]:((kind(X)<~>~tall(X))=>(strong(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>generous(X))))<=>(?[X]:(tall(X))))&
(?[X]:((humble(X)<~>brave(X))))&
((humble(lucy)<~>wise(lucy)))&
(?[X]:((kind(X)|strong(X))))&
((~rich(susan)|strong(susan)))&
((~patient(lucy)|~calm(lucy)))&
((~creative(susan)&tall(susan))) | happy(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6079981281448792497313540
% SZS output start Proof for 6079981281448792497313540
11. ! [X0] : ((creative(X0) | happy(X0)) => ~happy(X0)) [input p10]
23. happy(alice) [input hypothesis]
33. ! [X0] : (~happy(X0) | (~creative(X0) & ~happy(X0))) [ennf transformation 11]
117. ~happy(X0) | ~happy(X0) [cnf transformation 33]
150. happy(alice) [cnf transformation 23]
151. ~happy(X0) [duplicate literal removal 117]
362. $false [subsumption resolution 150,151]
% SZS output end Proof for 6079981281448792497313540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or happy is not rich and vice versa.
If someone is either not curious or curious then lucy is not humble and vice versa.
Everyone who is not patient or not strong is either happy or not kind and vice versa.
If fred is not funny or not wise then fred is not creative.
If someone is both tall and strong then susan is both happy and patient.
If someone is not wise or not curious then someone is either not happy or not rich and vice versa.
Everyone who is both quiet and wise is generous.
Everyone who is not strong or not tall is either not strong or not happy.
If someone is creative then someone is calm or not quiet and vice versa.
Everyone who is not quiet is both generous and not rich and vice versa.
Everyone who is either old or not quiet is funny and vice versa.
Everyone who is not strong is tall or not rich.
If someone is either generous or rich then john is tall or happy and vice versa.
Everyone who is both kind and not kind is not creative or not rich and vice versa.
Everyone who is not strong or not kind is both not strong and quiet and vice versa.
Everyone who is kind is patient.
Someone is either not funny or not patient.
Fred is either not brave or not generous.
Susan is generous or not wise.
Someone is either not quiet or not calm.
Paul is both not brave and not generous.
Alice is not brave or not quiet.
Fred is either not generous or not happy. | John is creative. | entailment | (![X]:((brave(X)<~>happy(X))<=>~rich(X)))&
((?[X]:((~curious(X)<~>curious(X))))<=>(~humble(lucy)))&
(![X]:((~patient(X)|~strong(X))<=>(happy(X)<~>~kind(X))))&
(((~funny(fred)|~wise(fred)))=>(~creative(fred)))&
((?[X]:((tall(X)&strong(X))))=>((happy(susan)&patient(susan))))&
((?[X]:((~wise(X)|~curious(X))))<=>(?[X]:((~happy(X)<~>~rich(X)))))&
(![X]:((quiet(X)&wise(X))=>generous(X)))&
(![X]:((~strong(X)|~tall(X))=>(~strong(X)<~>~happy(X))))&
((?[X]:(creative(X)))<=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~quiet(X)<=>(generous(X)&~rich(X))))&
(![X]:((old(X)<~>~quiet(X))<=>funny(X)))&
(![X]:(~strong(X)=>(tall(X)|~rich(X))))&
((?[X]:((generous(X)<~>rich(X))))<=>((tall(john)|happy(john))))&
(![X]:((kind(X)&~kind(X))<=>(~creative(X)|~rich(X))))&
(![X]:((~strong(X)|~kind(X))<=>(~strong(X)&quiet(X))))&
(![X]:(kind(X)=>patient(X)))&
(?[X]:((~funny(X)<~>~patient(X))))&
((~brave(fred)<~>~generous(fred)))&
((generous(susan)|~wise(susan)))&
(?[X]:((~quiet(X)<~>~calm(X))))&
((~brave(paul)&~generous(paul)))&
((~brave(alice)|~quiet(alice)))&
((~generous(fred)<~>~happy(fred))) | creative(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 135130704635917563799167
% SZS output start Proof for 135130704635917563799167
14. ! [X0] : ((~kind(X0) & kind(X0)) <=> (~rich(X0) | ~creative(X0))) [input p13]
24. ~creative(john) [input hypothesis]
61. ! [X0] : (((~kind(X0) & kind(X0)) | (rich(X0) & creative(X0))) & ((~rich(X0) | ~creative(X0)) | (kind(X0) | ~kind(X0)))) [nnf transformation 14]
62. ! [X0] : (((~kind(X0) & kind(X0)) | (rich(X0) & creative(X0))) & (~rich(X0) | ~creative(X0) | kind(X0) | ~kind(X0))) [flattening 61]
120. kind(X0) | creative(X0) [cnf transformation 62]
122. ~kind(X0) | creative(X0) [cnf transformation 62]
142. ~creative(john) [cnf transformation 24]
269. creative(X0) [subsumption resolution 120,122]
324. $false [subsumption resolution 142,269]
% SZS output end Proof for 135130704635917563799167
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm then john is both humble and tall.
If someone is both not brave and happy then alice is both not strong and quiet.
If alice is humble then someone is patient or rich and vice versa.
Everyone who is either not kind or calm is both not tall and not rich and vice versa.
If someone is not tall then someone is either not rich or not brave.
If someone is not generous then someone is not old.
Everyone who is both quiet and not tall is not quiet and vice versa.
Everyone who is both not rich and curious is either tall or not quiet and vice versa.
If lucy is both not kind and not old then someone is either not kind or wise.
If alice is either not old or not wise then alice is quiet or patient and vice versa.
If alice is brave or strong then paul is not patient and vice versa.
Everyone who is either not generous or kind is not strong.
If someone is patient then someone is calm or not generous.
Everyone who is both generous and not wise is either old or happy.
Everyone who is not funny is both funny and not patient and vice versa.
Everyone who is generous or not calm is both not quiet and funny and vice versa.
Fred is either not strong or not brave.
John is tall or not curious.
Someone is not wise.
Someone is either brave or not brave.
Someone is quiet. | John is strong. | contradiction | ((~calm(lucy))=>((humble(john)&tall(john))))&
((?[X]:((~brave(X)&happy(X))))=>((~strong(alice)&quiet(alice))))&
((humble(alice))<=>(?[X]:((patient(X)|rich(X)))))&
(![X]:((~kind(X)<~>calm(X))<=>(~tall(X)&~rich(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
((?[X]:(~generous(X)))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)&~tall(X))<=>~quiet(X)))&
(![X]:((~rich(X)&curious(X))<=>(tall(X)<~>~quiet(X))))&
(((~kind(lucy)&~old(lucy)))=>(?[X]:((~kind(X)<~>wise(X)))))&
(((~old(alice)<~>~wise(alice)))<=>((quiet(alice)|patient(alice))))&
(((brave(alice)|strong(alice)))<=>(~patient(paul)))&
(![X]:((~generous(X)<~>kind(X))=>~strong(X)))&
((?[X]:(patient(X)))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:((generous(X)&~wise(X))=>(old(X)<~>happy(X))))&
(![X]:(~funny(X)<=>(funny(X)&~patient(X))))&
(![X]:((generous(X)|~calm(X))<=>(~quiet(X)&funny(X))))&
((~strong(fred)<~>~brave(fred)))&
((tall(john)|~curious(john)))&
(?[X]:(~wise(X)))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:(quiet(X))) | strong(john) | [
"p3",
"p6",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2385401541023671740579706
% SZS output start Proof for 2385401541023671740579706
4. ! [X0] : ((~kind(X0) <~> calm(X0)) <=> (~rich(X0) & ~tall(X0))) [input p3]
7. ! [X0] : ((~tall(X0) & quiet(X0)) <=> ~quiet(X0)) [input p6]
12. ! [X0] : ((~generous(X0) <~> kind(X0)) => ~strong(X0)) [input p11]
16. ! [X0] : ((~calm(X0) | generous(X0)) <=> (funny(X0) & ~quiet(X0))) [input p15]
22. strong(john) [input hypothesis]
32. ! [X0] : (~strong(X0) | (~generous(X0) <=> kind(X0))) [ennf transformation 12]
40. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | (rich(X0) | tall(X0))) & ((~rich(X0) & ~tall(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~calm(X0) | kind(X0)) & (calm(X0) | ~kind(X0))) | rich(X0) | tall(X0)) & ((~rich(X0) & ~tall(X0)) | ((~kind(X0) | ~calm(X0)) & (calm(X0) | kind(X0))))) [flattening 40]
49. ! [X0] : (((~tall(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | (tall(X0) | ~quiet(X0)))) [nnf transformation 7]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | quiet(X0)) & (~quiet(X0) | tall(X0) | ~quiet(X0))) [flattening 49]
60. ! [X0] : (~strong(X0) | ((~generous(X0) | ~kind(X0)) & (kind(X0) | generous(X0)))) [nnf transformation 32]
67. ! [X0] : (((~calm(X0) | generous(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (calm(X0) & ~generous(X0)))) [nnf transformation 16]
68. ! [X0] : ((~calm(X0) | generous(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | (calm(X0) & ~generous(X0)))) [flattening 67]
85. ~kind(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 41]
93. ~quiet(X0) | tall(X0) | ~quiet(X0) [cnf transformation 50]
94. quiet(X0) | quiet(X0) [cnf transformation 50]
113. ~strong(X0) | kind(X0) | generous(X0) [cnf transformation 60]
121. ~quiet(X0) | ~generous(X0) [cnf transformation 68]
122. ~quiet(X0) | calm(X0) [cnf transformation 68]
133. strong(john) [cnf transformation 22]
136. ~quiet(X0) | tall(X0) [duplicate literal removal 93]
137. quiet(X0) [duplicate literal removal 94]
187. 12 <=> ! [X1] : tall(X1) [avatar definition]
188. tall(X1) <- (12) [avatar component clause 187]
207. tall(X0) [subsumption resolution 136,137]
208. 12 [avatar split clause 207,187]
268. calm(X0) [subsumption resolution 122,137]
269. ~generous(X0) [subsumption resolution 121,137]
296. kind(john) | generous(john) [resolution 113,133]
298. kind(john) [subsumption resolution 296,269]
301. ~tall(john) | ~calm(john) [resolution 298,85]
302. ~calm(john) <- (12) [subsumption resolution 301,188]
303. $false <- (12) [subsumption resolution 302,268]
304. ~12 [avatar contradiction clause 303]
305. $false [avatar sat refutation 208,304]
% SZS output end Proof for 2385401541023671740579706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and not quiet then paul is not kind or creative and vice versa. Everyone who is either not old or patient is either tall or calm and vice versa. Everyone who is not happy or not rich is either not rich or not creative. If someone is funny then susan is either rich or not funny. Everyone who is not brave is both quiet and not tall. Everyone who is not rich or tall is both not calm and not creative. Everyone who is both kind and curious is both not brave and kind. If mary is either generous or curious then alice is both not patient and not happy and vice versa. Everyone who is happy is strong and vice versa. If someone is both quiet and not quiet then someone is not quiet or not kind and vice versa. If someone is generous or patient then alice is both calm and not patient. Everyone who is not curious or not patient is not strong. Everyone who is funny or patient is either not curious or quiet and vice versa. If someone is either tall or not curious then lucy is not curious or patient. If someone is not creative then fred is both not wise and funny. Mary is not wise or not tall. John is kind or not curious. Someone is either humble or not humble. Someone is tall. Someone is either curious or not funny. | Alice is creative. | contradiction | ((?[X]:((wise(X)&~quiet(X))))<=>((~kind(paul)|creative(paul))))&
(![X]:((~old(X)<~>patient(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~happy(X)|~rich(X))=>(~rich(X)<~>~creative(X))))&
((?[X]:(funny(X)))=>((rich(susan)<~>~funny(susan))))&
(![X]:(~brave(X)=>(quiet(X)&~tall(X))))&
(![X]:((~rich(X)|tall(X))=>(~calm(X)&~creative(X))))&
(![X]:((kind(X)&curious(X))=>(~brave(X)&kind(X))))&
(((generous(mary)<~>curious(mary)))<=>((~patient(alice)&~happy(alice))))&
(![X]:(happy(X)<=>strong(X)))&
((?[X]:((quiet(X)&~quiet(X))))<=>(?[X]:((~quiet(X)|~kind(X)))))&
((?[X]:((generous(X)|patient(X))))=>((calm(alice)&~patient(alice))))&
(![X]:((~curious(X)|~patient(X))=>~strong(X)))&
(![X]:((funny(X)|patient(X))<=>(~curious(X)<~>quiet(X))))&
((?[X]:((tall(X)<~>~curious(X))))=>((~curious(lucy)|patient(lucy))))&
((?[X]:(~creative(X)))=>((~wise(fred)&funny(fred))))&
((~wise(mary)|~tall(mary)))&
((kind(john)|~curious(john)))&
(?[X]:((humble(X)<~>~humble(X))))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)<~>~funny(X)))) | creative(alice) | [
"p2",
"p5",
"p8",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2608615287191823460242851
% SZS output start Proof for 2608615287191823460242851
3. ! [X0] : ((~rich(X0) | ~happy(X0)) => (~rich(X0) <~> ~creative(X0))) [input p2]
6. ! [X0] : ((tall(X0) | ~rich(X0)) => (~creative(X0) & ~calm(X0))) [input p5]
9. ! [X0] : (happy(X0) <=> strong(X0)) [input p8]
11. ? [X0] : (patient(X0) | generous(X0)) => (~patient(alice) & calm(alice)) [input p10]
12. ! [X0] : ((~patient(X0) | ~curious(X0)) => ~strong(X0)) [input p11]
21. creative(alice) [input hypothesis]
23. ! [X0] : ((~rich(X0) <~> ~creative(X0)) | (rich(X0) & happy(X0))) [ennf transformation 3]
26. ! [X0] : ((~creative(X0) & ~calm(X0)) | (~tall(X0) & rich(X0))) [ennf transformation 6]
29. (~patient(alice) & calm(alice)) | ! [X0] : (~patient(X0) & ~generous(X0)) [ennf transformation 11]
30. ! [X0] : (~strong(X0) | (patient(X0) & curious(X0))) [ennf transformation 12]
40. ! [X0] : (((creative(X0) | rich(X0)) & (~creative(X0) | ~rich(X0))) | (rich(X0) & happy(X0))) [nnf transformation 23]
44. ! [X0] : ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0))) [nnf transformation 9]
74. ~rich(X0) | ~creative(X0) | happy(X0) [cnf transformation 40]
77. creative(X0) | rich(X0) | rich(X0) [cnf transformation 40]
84. ~creative(X0) | rich(X0) [cnf transformation 26]
94. ~happy(X0) | strong(X0) [cnf transformation 44]
104. ~patient(alice) | ~patient(X0) [cnf transformation 29]
106. ~strong(X0) | patient(X0) [cnf transformation 30]
124. creative(alice) [cnf transformation 21]
125. rich(X0) | creative(X0) [duplicate literal removal 77]
163. rich(X0) [subsumption resolution 84,125]
165. 9 <=> patient(alice) [avatar definition]
166. ~patient(alice) <- (~9) [avatar component clause 165]
169. 10 <=> happy(alice) [avatar definition]
171. happy(alice) <- (10) [avatar component clause 169]
201. 16 <=> ! [X0] : ~patient(X0) [avatar definition]
202. ~patient(X0) <- (16) [avatar component clause 201]
203. 16 | ~9 [avatar split clause 104,165,201]
285. strong(alice) <- (10) [resolution 94,171]
288. patient(alice) <- (10) [resolution 106,285]
289. $false <- (10, 16) [subsumption resolution 288,202]
290. ~10 | ~16 [avatar contradiction clause 289]
292. ~creative(X1) | happy(X1) [resolution 74,163]
293. happy(alice) [resolution 292,124]
296. 10 [avatar split clause 293,169]
297. strong(alice) <- (10) [resolution 171,94]
299. patient(alice) <- (10) [resolution 297,106]
302. $false <- (~9, 10) [subsumption resolution 299,166]
303. 9 | ~10 [avatar contradiction clause 302]
304. $false [avatar sat refutation 203,290,296,303]
% SZS output end Proof for 2608615287191823460242851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not calm is not generous and vice versa.
If someone is not funny or not curious then susan is either humble or strong.
Everyone who is either not patient or not calm is rich and vice versa.
Everyone who is both generous and funny is not quiet or not patient and vice versa.
Everyone who is not wise is old or tall and vice versa.
If someone is not generous then someone is calm and vice versa.
If susan is either not patient or humble then someone is either tall or old.
Everyone who is both not wise and strong is either rich or not calm.
If fred is not creative or not strong then someone is tall or not funny and vice versa.
Everyone who is both not strong and not funny is both not brave and not wise.
If someone is either strong or not kind then someone is both not rich and not humble.
Everyone who is not creative or not quiet is not creative or patient.
Everyone who is generous is both not tall and not kind.
Everyone who is both not old and not brave is not strong or not calm and vice versa.
If someone is either happy or old then fred is generous.
Everyone who is both creative and old is both quiet and humble.
Someone is either not creative or not rich.
Someone is either humble or generous.
Paul is creative or tall.
Someone is kind or creative.
Someone is not curious.
Alice is brave or creative.
Alice is wise.
Mary is not old. | Paul is not old. | entailment | (![X]:((calm(X)<~>~calm(X))<=>~generous(X)))&
((?[X]:((~funny(X)|~curious(X))))=>((humble(susan)<~>strong(susan))))&
(![X]:((~patient(X)<~>~calm(X))<=>rich(X)))&
(![X]:((generous(X)&funny(X))<=>(~quiet(X)|~patient(X))))&
(![X]:(~wise(X)<=>(old(X)|tall(X))))&
((?[X]:(~generous(X)))<=>(?[X]:(calm(X))))&
(((~patient(susan)<~>humble(susan)))=>(?[X]:((tall(X)<~>old(X)))))&
(![X]:((~wise(X)&strong(X))=>(rich(X)<~>~calm(X))))&
(((~creative(fred)|~strong(fred)))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((~strong(X)&~funny(X))=>(~brave(X)&~wise(X))))&
((?[X]:((strong(X)<~>~kind(X))))=>(?[X]:((~rich(X)&~humble(X)))))&
(![X]:((~creative(X)|~quiet(X))=>(~creative(X)|patient(X))))&
(![X]:(generous(X)=>(~tall(X)&~kind(X))))&
(![X]:((~old(X)&~brave(X))<=>(~strong(X)|~calm(X))))&
((?[X]:((happy(X)<~>old(X))))=>(generous(fred)))&
(![X]:((creative(X)&old(X))=>(quiet(X)&humble(X))))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((humble(X)<~>generous(X))))&
((creative(paul)|tall(paul)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:(~curious(X)))&
((brave(alice)|creative(alice)))&
(wise(alice))&
(~old(mary)) | ~old(paul) | [
"p0",
"p2",
"p3",
"p4",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5859780421855052446901066
% SZS output start Proof for 5859780421855052446901066
1. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> ~generous(X0)) [input p0]
3. ! [X0] : ((~patient(X0) <~> ~calm(X0)) <=> rich(X0)) [input p2]
4. ! [X0] : ((funny(X0) & generous(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p3]
5. ! [X0] : (~wise(X0) <=> (tall(X0) | old(X0))) [input p4]
8. ! [X0] : ((strong(X0) & ~wise(X0)) => (rich(X0) <~> ~calm(X0))) [input p7]
14. ! [X0] : ((~brave(X0) & ~old(X0)) <=> (~calm(X0) | ~strong(X0))) [input p13]
25. old(paul) [input hypothesis]
30. ! [X0] : ((rich(X0) <~> ~calm(X0)) | (~strong(X0) | wise(X0))) [ennf transformation 8]
31. ! [X0] : ((rich(X0) <~> ~calm(X0)) | ~strong(X0) | wise(X0)) [flattening 30]
41. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | generous(X0)) & (~generous(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 1]
43. ! [X0] : ((((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~rich(X0)) & (rich(X0) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0))))) [nnf transformation 3]
44. ! [X0] : (((funny(X0) & generous(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~funny(X0) | ~generous(X0)))) [nnf transformation 4]
45. ! [X0] : (((funny(X0) & generous(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~funny(X0) | ~generous(X0))) [flattening 44]
46. ! [X0] : ((~wise(X0) | (~tall(X0) & ~old(X0))) & ((tall(X0) | old(X0)) | wise(X0))) [nnf transformation 5]
47. ! [X0] : ((~wise(X0) | (~tall(X0) & ~old(X0))) & (tall(X0) | old(X0) | wise(X0))) [flattening 46]
56. ! [X0] : (((calm(X0) | ~rich(X0)) & (~calm(X0) | rich(X0))) | ~strong(X0) | wise(X0)) [nnf transformation 31]
66. ! [X0] : (((~brave(X0) & ~old(X0)) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | (brave(X0) | old(X0)))) [nnf transformation 14]
67. ! [X0] : (((~brave(X0) & ~old(X0)) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | brave(X0) | old(X0))) [flattening 66]
79. ~generous(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 41]
80. ~generous(X0) | calm(X0) | calm(X0) [cnf transformation 41]
89. ~rich(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 43]
93. generous(X0) | patient(X0) [cnf transformation 45]
97. ~old(X0) | ~wise(X0) [cnf transformation 47]
105. ~strong(X0) | rich(X0) | ~calm(X0) | wise(X0) [cnf transformation 56]
122. ~old(X0) | strong(X0) [cnf transformation 67]
123. ~old(X0) | calm(X0) [cnf transformation 67]
140. old(paul) [cnf transformation 25]
141. ~generous(X0) | ~calm(X0) [duplicate literal removal 79]
142. ~generous(X0) | calm(X0) [duplicate literal removal 80]
143. ~generous(X0) [subsumption resolution 141,142]
162. patient(X0) [subsumption resolution 93,143]
258. ~wise(paul) [resolution 97,140]
259. strong(paul) [resolution 122,140]
260. calm(paul) [resolution 123,140]
293. rich(paul) | ~calm(paul) | wise(paul) [resolution 105,259]
305. rich(paul) | wise(paul) [subsumption resolution 293,260]
306. rich(paul) [subsumption resolution 305,258]
335. ~patient(paul) | ~calm(paul) [resolution 306,89]
336. ~calm(paul) [subsumption resolution 335,162]
337. $false [subsumption resolution 336,260]
% SZS output end Proof for 5859780421855052446901066
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both strong and creative then someone is not quiet or not humble and vice versa.
If someone is either funny or calm then susan is either not humble or quiet and vice versa.
Everyone who is both wise and not patient is happy.
Everyone who is both brave and wise is either not generous or not wise and vice versa.
If alice is both humble and not curious then paul is not brave or not kind and vice versa.
If someone is not brave or tall then someone is not funny or not tall.
Everyone who is both creative and not kind is not humble.
Everyone who is both generous and not rich is humble or not patient and vice versa.
Everyone who is both not rich and patient is not brave or calm.
Everyone who is both not kind and not wise is not old or humble.
Everyone who is not generous is generous or not patient.
If someone is either not calm or generous then lucy is not patient or not brave and vice versa.
If alice is not funny then alice is both not kind and not old.
If someone is creative then someone is not happy or funny.
If fred is not brave then john is both quiet and humble and vice versa.
If someone is either generous or not strong then mary is tall or not kind and vice versa.
Someone is both not tall and not rich.
Mary is either not happy or not patient.
Paul is not strong.
Someone is not brave or not strong.
John is both patient and funny.
Alice is both strong and tall.
Someone is rich or not rich. | Alice is curious. | contradiction | (((strong(alice)&creative(alice)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
((?[X]:((funny(X)<~>calm(X))))<=>((~humble(susan)<~>quiet(susan))))&
(![X]:((wise(X)&~patient(X))=>happy(X)))&
(![X]:((brave(X)&wise(X))<=>(~generous(X)<~>~wise(X))))&
(((humble(alice)&~curious(alice)))<=>((~brave(paul)|~kind(paul))))&
((?[X]:((~brave(X)|tall(X))))=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((creative(X)&~kind(X))=>~humble(X)))&
(![X]:((generous(X)&~rich(X))<=>(humble(X)|~patient(X))))&
(![X]:((~rich(X)&patient(X))=>(~brave(X)|calm(X))))&
(![X]:((~kind(X)&~wise(X))=>(~old(X)|humble(X))))&
(![X]:(~generous(X)=>(generous(X)|~patient(X))))&
((?[X]:((~calm(X)<~>generous(X))))<=>((~patient(lucy)|~brave(lucy))))&
((~funny(alice))=>((~kind(alice)&~old(alice))))&
((?[X]:(creative(X)))=>(?[X]:((~happy(X)|funny(X)))))&
((~brave(fred))<=>((quiet(john)&humble(john))))&
((?[X]:((generous(X)<~>~strong(X))))<=>((tall(mary)|~kind(mary))))&
(?[X]:((~tall(X)&~rich(X))))&
((~happy(mary)<~>~patient(mary)))&
(~strong(paul))&
(?[X]:((~brave(X)|~strong(X))))&
((patient(john)&funny(john)))&
((strong(alice)&tall(alice)))&
(?[X]:((rich(X)|~rich(X)))) | curious(alice) | [
"p3",
"p4",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5474036736049572527814098
% SZS output start Proof for 5474036736049572527814098
4. ! [X0] : ((wise(X0) & brave(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p3]
5. (~curious(alice) & humble(alice)) <=> (~kind(paul) | ~brave(paul)) [input p4]
8. ! [X0] : ((~rich(X0) & generous(X0)) <=> (~patient(X0) | humble(X0))) [input p7]
11. ! [X0] : (~generous(X0) => (~patient(X0) | generous(X0))) [input p10]
24. curious(alice) [input hypothesis]
36. ! [X0] : ((~patient(X0) | generous(X0)) | generous(X0)) [ennf transformation 11]
37. ! [X0] : (~patient(X0) | generous(X0) | generous(X0)) [flattening 36]
49. ! [X0] : (((wise(X0) & brave(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (~wise(X0) | ~brave(X0)))) [nnf transformation 4]
50. ! [X0] : (((wise(X0) & brave(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | ~wise(X0) | ~brave(X0))) [flattening 49]
51. ((~curious(alice) & humble(alice)) | (kind(paul) & brave(paul))) & ((~kind(paul) | ~brave(paul)) | (curious(alice) | ~humble(alice))) [nnf transformation 5]
52. ((~curious(alice) & humble(alice)) | (kind(paul) & brave(paul))) & (~kind(paul) | ~brave(paul) | curious(alice) | ~humble(alice)) [flattening 51]
56. ! [X0] : (((~rich(X0) & generous(X0)) | (patient(X0) & ~humble(X0))) & ((~patient(X0) | humble(X0)) | (rich(X0) | ~generous(X0)))) [nnf transformation 8]
57. ! [X0] : (((~rich(X0) & generous(X0)) | (patient(X0) & ~humble(X0))) & (~patient(X0) | humble(X0) | rich(X0) | ~generous(X0))) [flattening 56]
94. ~wise(X0) | ~generous(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 50]
99. wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 50]
103. ~curious(alice) | brave(paul) [cnf transformation 52]
110. generous(X0) | patient(X0) [cnf transformation 57]
114. ~patient(X0) | generous(X0) | generous(X0) [cnf transformation 37]
143. curious(alice) [cnf transformation 24]
144. ~patient(X0) | generous(X0) [duplicate literal removal 114]
145. ~wise(X0) | ~generous(X0) | ~brave(X0) [duplicate literal removal 94]
146. ~generous(X0) | wise(X0) [duplicate literal removal 99]
204. ~generous(X0) | ~brave(X0) [subsumption resolution 145,146]
210. 14 <=> curious(alice) [avatar definition]
215. 15 <=> brave(paul) [avatar definition]
217. brave(paul) <- (15) [avatar component clause 215]
218. 15 | ~14 [avatar split clause 103,210,215]
242. generous(X0) [subsumption resolution 144,110]
341. 14 [avatar split clause 143,210]
346. ~brave(X1) [resolution 204,242]
348. $false <- (15) [resolution 346,217]
349. ~15 [avatar contradiction clause 348]
350. $false [avatar sat refutation 218,341,349]
% SZS output end Proof for 5474036736049572527814098
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble or creative then paul is both rich and kind and vice versa.
Everyone who is either not curious or calm is not humble and vice versa.
If someone is funny or wise then someone is humble or tall.
Everyone who is brave is either quiet or not tall and vice versa.
If fred is either not patient or not tall then someone is either not creative or old.
Everyone who is either not tall or humble is not humble.
Everyone who is not kind is either wise or not curious and vice versa.
Everyone who is both quiet and rich is not happy or not kind.
Everyone who is quiet is either funny or not creative and vice versa.
Everyone who is not rich is not patient.
If someone is both quiet and wise then mary is quiet or not tall and vice versa.
If someone is not creative then someone is not creative or not happy and vice versa.
If someone is either not calm or not rich then mary is not creative or not patient and vice versa.
Everyone who is either tall or funny is both kind and not strong.
Everyone who is not strong is both not quiet and wise and vice versa.
Everyone who is old or quiet is not wise and vice versa.
Susan is either quiet or not old.
Paul is not curious or calm.
Someone is both calm and not curious.
Someone is either not brave or not generous.
Paul is kind.
Someone is old or curious.
Someone is happy or not humble. | Mary is humble. | contradiction | ((?[X]:((~humble(X)|creative(X))))<=>((rich(paul)&kind(paul))))&
(![X]:((~curious(X)<~>calm(X))<=>~humble(X)))&
((?[X]:((funny(X)|wise(X))))=>(?[X]:((humble(X)|tall(X)))))&
(![X]:(brave(X)<=>(quiet(X)<~>~tall(X))))&
(((~patient(fred)<~>~tall(fred)))=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:((~tall(X)<~>humble(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(wise(X)<~>~curious(X))))&
(![X]:((quiet(X)&rich(X))=>(~happy(X)|~kind(X))))&
(![X]:(quiet(X)<=>(funny(X)<~>~creative(X))))&
(![X]:(~rich(X)=>~patient(X)))&
((?[X]:((quiet(X)&wise(X))))<=>((quiet(mary)|~tall(mary))))&
((?[X]:(~creative(X)))<=>(?[X]:((~creative(X)|~happy(X)))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((~creative(mary)|~patient(mary))))&
(![X]:((tall(X)<~>funny(X))=>(kind(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~quiet(X)&wise(X))))&
(![X]:((old(X)|quiet(X))<=>~wise(X)))&
((quiet(susan)<~>~old(susan)))&
((~curious(paul)|calm(paul)))&
(?[X]:((calm(X)&~curious(X))))&
(?[X]:((~brave(X)<~>~generous(X))))&
(kind(paul))&
(?[X]:((old(X)|curious(X))))&
(?[X]:((happy(X)|~humble(X)))) | humble(mary) | [
"p5",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 320485871562345613176413
% SZS output start Proof for 320485871562345613176413
6. ! [X0] : ((~tall(X0) <~> humble(X0)) => ~humble(X0)) [input p5]
11. ? [X0] : (wise(X0) & quiet(X0)) <=> (~tall(mary) | quiet(mary)) [input p10]
16. ! [X0] : ((quiet(X0) | old(X0)) <=> ~wise(X0)) [input p15]
24. humble(mary) [input hypothesis]
30. ! [X0] : (~humble(X0) | (~tall(X0) <=> humble(X0))) [ennf transformation 6]
49. ! [X0] : (~humble(X0) | ((~tall(X0) | ~humble(X0)) & (humble(X0) | tall(X0)))) [nnf transformation 30]
52. (? [X0] : (wise(X0) & quiet(X0)) | (tall(mary) & ~quiet(mary))) & ((~tall(mary) | quiet(mary)) | ! [X0] : (~wise(X0) | ~quiet(X0))) [nnf transformation 11]
53. (? [X0] : (wise(X0) & quiet(X0)) | (tall(mary) & ~quiet(mary))) & (~tall(mary) | quiet(mary) | ! [X0] : (~wise(X0) | ~quiet(X0))) [flattening 52]
54. (? [X0] : (wise(X0) & quiet(X0)) | (tall(mary) & ~quiet(mary))) & (~tall(mary) | quiet(mary) | ! [X1] : (~wise(X1) | ~quiet(X1))) [rectify 53]
55. ? [X0] : (wise(X0) & quiet(X0)) => (wise(sK3) & quiet(sK3)) [choice axiom]
56. ((wise(sK3) & quiet(sK3)) | (tall(mary) & ~quiet(mary))) & (~tall(mary) | quiet(mary) | ! [X1] : (~wise(X1) | ~quiet(X1))) [skolemisation 54,55]
68. ! [X0] : (((quiet(X0) | old(X0)) | wise(X0)) & (~wise(X0) | (~quiet(X0) & ~old(X0)))) [nnf transformation 16]
69. ! [X0] : ((quiet(X0) | old(X0) | wise(X0)) & (~wise(X0) | (~quiet(X0) & ~old(X0)))) [flattening 68]
100. ~humble(X0) | ~tall(X0) | ~humble(X0) [cnf transformation 49]
113. quiet(sK3) | tall(mary) [cnf transformation 56]
115. wise(sK3) | tall(mary) [cnf transformation 56]
132. ~wise(X0) | ~quiet(X0) [cnf transformation 69]
144. humble(mary) [cnf transformation 24]
145. ~tall(X0) | ~humble(X0) [duplicate literal removal 100]
210. 15 <=> tall(mary) [avatar definition]
212. tall(mary) <- (15) [avatar component clause 210]
214. 16 <=> wise(sK3) [avatar definition]
216. wise(sK3) <- (16) [avatar component clause 214]
217. 15 | 16 [avatar split clause 115,214,210]
224. 18 <=> quiet(sK3) [avatar definition]
226. quiet(sK3) <- (18) [avatar component clause 224]
227. 15 | 18 [avatar split clause 113,224,210]
230. 19 <=> ! [X1] : (~wise(X1) | ~quiet(X1)) [avatar definition]
231. ~quiet(X1) | ~wise(X1) <- (19) [avatar component clause 230]
282. 19 [avatar split clause 132,230]
334. ~humble(mary) <- (15) [resolution 145,212]
335. $false <- (15) [subsumption resolution 334,144]
336. ~15 [avatar contradiction clause 335]
338. ~wise(sK3) <- (18, 19) [resolution 231,226]
339. $false <- (16, 18, 19) [subsumption resolution 338,216]
340. ~16 | ~18 | ~19 [avatar contradiction clause 339]
341. $false [avatar sat refutation 217,227,282,336,340]
% SZS output end Proof for 320485871562345613176413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and calm is not generous or not strong and vice versa.
Everyone who is happy is both not tall and old and vice versa.
If someone is both not humble and tall then alice is either tall or not happy.
Everyone who is both not wise and not rich is not calm.
If fred is either not kind or old then someone is both not quiet and creative and vice versa.
Everyone who is tall or old is not patient or brave.
Everyone who is either funny or not happy is either not tall or patient and vice versa.
Everyone who is not curious is either tall or happy.
If alice is both not happy and old then john is both rich and brave and vice versa.
If someone is either not strong or not patient then someone is not strong and vice versa.
If john is either not tall or not creative then john is humble or not calm and vice versa.
Everyone who is not wise or calm is funny.
Everyone who is either quiet or not strong is not patient or not old and vice versa.
Everyone who is both not generous and strong is not humble or not calm and vice versa.
Everyone who is both not brave and calm is either wise or tall.
Lucy is not creative.
Someone is either not quiet or not kind.
Someone is either brave or curious.
Susan is kind.
Someone is either not kind or generous. | Alice is not calm. | contradiction | (![X]:((strong(X)&calm(X))<=>(~generous(X)|~strong(X))))&
(![X]:(happy(X)<=>(~tall(X)&old(X))))&
((?[X]:((~humble(X)&tall(X))))=>((tall(alice)<~>~happy(alice))))&
(![X]:((~wise(X)&~rich(X))=>~calm(X)))&
(((~kind(fred)<~>old(fred)))<=>(?[X]:((~quiet(X)&creative(X)))))&
(![X]:((tall(X)|old(X))=>(~patient(X)|brave(X))))&
(![X]:((funny(X)<~>~happy(X))<=>(~tall(X)<~>patient(X))))&
(![X]:(~curious(X)=>(tall(X)<~>happy(X))))&
(((~happy(alice)&old(alice)))<=>((rich(john)&brave(john))))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(~strong(X))))&
(((~tall(john)<~>~creative(john)))<=>((humble(john)|~calm(john))))&
(![X]:((~wise(X)|calm(X))=>funny(X)))&
(![X]:((quiet(X)<~>~strong(X))<=>(~patient(X)|~old(X))))&
(![X]:((~generous(X)&strong(X))<=>(~humble(X)|~calm(X))))&
(![X]:((~brave(X)&calm(X))=>(wise(X)<~>tall(X))))&
(~creative(lucy))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:((brave(X)<~>curious(X))))&
(kind(susan))&
(?[X]:((~kind(X)<~>generous(X)))) | ~calm(alice) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 880882969989489369261461
% SZS output start Proof for 880882969989489369261461
1. ! [X0] : ((calm(X0) & strong(X0)) <=> (~strong(X0) | ~generous(X0))) [input p0]
14. ! [X0] : ((strong(X0) & ~generous(X0)) <=> (~calm(X0) | ~humble(X0))) [input p13]
21. ~calm(alice) [input hypothesis]
32. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & ((~strong(X0) | ~generous(X0)) | (~calm(X0) | ~strong(X0)))) [nnf transformation 1]
33. ! [X0] : (((calm(X0) & strong(X0)) | (strong(X0) & generous(X0))) & (~strong(X0) | ~generous(X0) | ~calm(X0) | ~strong(X0))) [flattening 32]
54. ! [X0] : (((strong(X0) & ~generous(X0)) | (calm(X0) & humble(X0))) & ((~calm(X0) | ~humble(X0)) | (~strong(X0) | generous(X0)))) [nnf transformation 14]
55. ! [X0] : (((strong(X0) & ~generous(X0)) | (calm(X0) & humble(X0))) & (~calm(X0) | ~humble(X0) | ~strong(X0) | generous(X0))) [flattening 54]
69. calm(X0) | generous(X0) [cnf transformation 33]
119. ~generous(X0) | calm(X0) [cnf transformation 55]
132. ~calm(alice) [cnf transformation 21]
223. calm(X0) [subsumption resolution 119,69]
258. $false [subsumption resolution 132,223]
% SZS output end Proof for 880882969989489369261461
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or strong is both strong and not kind and vice versa.
If mary is creative then mary is both brave and strong.
Everyone who is not old or humble is quiet and vice versa.
Everyone who is funny or tall is both not tall and kind.
If someone is both not rich and not wise then alice is curious or not generous and vice versa.
Everyone who is both creative and patient is both patient and not curious.
Everyone who is both happy and creative is curious and vice versa.
If paul is funny or not brave then someone is both creative and not wise.
Everyone who is not funny is either not creative or humble and vice versa.
If susan is rich or not curious then someone is both not tall and not rich.
If mary is either not brave or humble then alice is old and vice versa.
If alice is either old or creative then someone is not quiet and vice versa.
Everyone who is not funny or patient is not calm and vice versa.
Everyone who is both not old and not creative is not tall and vice versa.
Everyone who is not rich is either old or humble.
Someone is not happy.
Paul is not humble or quiet.
Someone is not patient or quiet.
Alice is curious or not calm.
Someone is happy.
Mary is both brave and not patient.
Someone is patient.
Someone is not patient. | Alice is not patient. | neutral | (![X]:((~tall(X)<~>strong(X))<=>(strong(X)&~kind(X))))&
((creative(mary))=>((brave(mary)&strong(mary))))&
(![X]:((~old(X)|humble(X))<=>quiet(X)))&
(![X]:((funny(X)|tall(X))=>(~tall(X)&kind(X))))&
((?[X]:((~rich(X)&~wise(X))))<=>((curious(alice)|~generous(alice))))&
(![X]:((creative(X)&patient(X))=>(patient(X)&~curious(X))))&
(![X]:((happy(X)&creative(X))<=>curious(X)))&
(((funny(paul)|~brave(paul)))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:(~funny(X)<=>(~creative(X)<~>humble(X))))&
(((rich(susan)|~curious(susan)))=>(?[X]:((~tall(X)&~rich(X)))))&
(((~brave(mary)<~>humble(mary)))<=>(old(alice)))&
(((old(alice)<~>creative(alice)))<=>(?[X]:(~quiet(X))))&
(![X]:((~funny(X)|patient(X))<=>~calm(X)))&
(![X]:((~old(X)&~creative(X))<=>~tall(X)))&
(![X]:(~rich(X)=>(old(X)<~>humble(X))))&
(?[X]:(~happy(X)))&
((~humble(paul)|quiet(paul)))&
(?[X]:((~patient(X)|quiet(X))))&
((curious(alice)|~calm(alice)))&
(?[X]:(happy(X)))&
((brave(mary)&~patient(mary)))&
(?[X]:(patient(X)))&
(?[X]:(~patient(X))) | ~patient(alice) | [] | null | 0 |
Everyone who is both not quiet and not humble is funny or humble and vice versa. If someone is not quiet or generous then fred is both not strong and quiet and vice versa. If fred is both kind and not rich then alice is either humble or strong and vice versa. If alice is both strong and tall then someone is not calm or quiet. Everyone who is either funny or not humble is quiet or not curious and vice versa. Everyone who is either not rich or not kind is rich or not patient. If someone is both rich and not strong then alice is either not patient or strong. If alice is not brave or not calm then fred is both not wise and brave. Everyone who is not generous is not rich and vice versa. Everyone who is humble or not strong is calm or not kind. Everyone who is not rich is strong or not kind. If john is either tall or strong then someone is tall or strong. Everyone who is not tall or patient is humble or not creative and vice versa. If someone is either strong or humble then lucy is both not creative and not brave. If fred is calm then someone is both not humble and not calm. Fred is both not old and not creative. Someone is both not brave and old. Someone is both not tall and not patient. Alice is both not brave and rich. Paul is either calm or generous. Someone is not tall. Someone is both patient and not creative. Someone is either not creative or creative. | Alice is strong. | contradiction | (![X]:((~quiet(X)&~humble(X))<=>(funny(X)|humble(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>((~strong(fred)&quiet(fred))))&
(((kind(fred)&~rich(fred)))<=>((humble(alice)<~>strong(alice))))&
(((strong(alice)&tall(alice)))=>(?[X]:((~calm(X)|quiet(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(quiet(X)|~curious(X))))&
(![X]:((~rich(X)<~>~kind(X))=>(rich(X)|~patient(X))))&
((?[X]:((rich(X)&~strong(X))))=>((~patient(alice)<~>strong(alice))))&
(((~brave(alice)|~calm(alice)))=>((~wise(fred)&brave(fred))))&
(![X]:(~generous(X)<=>~rich(X)))&
(![X]:((humble(X)|~strong(X))=>(calm(X)|~kind(X))))&
(![X]:(~rich(X)=>(strong(X)|~kind(X))))&
(((tall(john)<~>strong(john)))=>(?[X]:((tall(X)|strong(X)))))&
(![X]:((~tall(X)|patient(X))<=>(humble(X)|~creative(X))))&
((?[X]:((strong(X)<~>humble(X))))=>((~creative(lucy)&~brave(lucy))))&
((calm(fred))=>(?[X]:((~humble(X)&~calm(X)))))&
((~old(fred)&~creative(fred)))&
(?[X]:((~brave(X)&old(X))))&
(?[X]:((~tall(X)&~patient(X))))&
((~brave(alice)&rich(alice)))&
((calm(paul)<~>generous(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((~creative(X)<~>creative(X)))) | strong(alice) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7417076372349330988540758
% SZS output start Proof for 7417076372349330988540758
1. ! [X0] : ((~humble(X0) & ~quiet(X0)) <=> (humble(X0) | funny(X0))) [input p0]
2. ? [X0] : (generous(X0) | ~quiet(X0)) <=> (quiet(fred) & ~strong(fred)) [input p1]
3. (~rich(fred) & kind(fred)) <=> (humble(alice) <~> strong(alice)) [input p2]
9. ! [X0] : (~generous(X0) <=> ~rich(X0)) [input p8]
11. ! [X0] : (~rich(X0) => (~kind(X0) | strong(X0))) [input p10]
19. rich(alice) & ~brave(alice) [input p18]
24. strong(alice) [input hypothesis]
34. ! [X0] : ((~kind(X0) | strong(X0)) | rich(X0)) [ennf transformation 11]
35. ! [X0] : (~kind(X0) | strong(X0) | rich(X0)) [flattening 34]
39. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & ((humble(X0) | funny(X0)) | (humble(X0) | quiet(X0)))) [nnf transformation 1]
40. ! [X0] : (((~humble(X0) & ~quiet(X0)) | (~humble(X0) & ~funny(X0))) & (humble(X0) | funny(X0) | humble(X0) | quiet(X0))) [flattening 39]
41. (? [X0] : (generous(X0) | ~quiet(X0)) | (~quiet(fred) | strong(fred))) & ((quiet(fred) & ~strong(fred)) | ! [X0] : (~generous(X0) & quiet(X0))) [nnf transformation 2]
42. (? [X0] : (generous(X0) | ~quiet(X0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X0] : (~generous(X0) & quiet(X0))) [flattening 41]
43. (? [X0] : (generous(X0) | ~quiet(X0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X1] : (~generous(X1) & quiet(X1))) [rectify 42]
44. ? [X0] : (generous(X0) | ~quiet(X0)) => (generous(sK0) | ~quiet(sK0)) [choice axiom]
45. ((generous(sK0) | ~quiet(sK0)) | ~quiet(fred) | strong(fred)) & ((quiet(fred) & ~strong(fred)) | ! [X1] : (~generous(X1) & quiet(X1))) [skolemisation 43,44]
46. ((~rich(fred) & kind(fred)) | ((humble(alice) | ~strong(alice)) & (strong(alice) | ~humble(alice)))) & (((~strong(alice) | ~humble(alice)) & (strong(alice) | humble(alice))) | (rich(fred) | ~kind(fred))) [nnf transformation 3]
47. ((~rich(fred) & kind(fred)) | ((humble(alice) | ~strong(alice)) & (strong(alice) | ~humble(alice)))) & (((~strong(alice) | ~humble(alice)) & (strong(alice) | humble(alice))) | rich(fred) | ~kind(fred)) [flattening 46]
54. ! [X0] : ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))) [nnf transformation 9]
79. ~humble(X0) | ~humble(X0) [cnf transformation 40]
81. ~strong(fred) | ~generous(X1) [cnf transformation 45]
88. kind(fred) | humble(alice) | ~strong(alice) [cnf transformation 47]
90. ~rich(fred) | humble(alice) | ~strong(alice) [cnf transformation 47]
104. ~rich(X0) | generous(X0) [cnf transformation 54]
108. ~kind(X0) | strong(X0) | rich(X0) [cnf transformation 35]
128. rich(alice) [cnf transformation 19]
136. strong(alice) [cnf transformation 24]
139. ~humble(X0) [duplicate literal removal 79]
142. 1 <=> strong(fred) [avatar definition]
159. 5 <=> ! [X1] : ~generous(X1) [avatar definition]
160. ~generous(X1) <- (5) [avatar component clause 159]
166. 5 | ~1 [avatar split clause 81,142,159]
168. ~rich(fred) | ~strong(alice) [subsumption resolution 90,139]
170. 7 <=> strong(alice) [avatar definition]
174. 8 <=> rich(fred) [avatar definition]
176. ~rich(fred) <- (~8) [avatar component clause 174]
177. ~7 | ~8 [avatar split clause 168,174,170]
178. kind(fred) | ~strong(alice) [subsumption resolution 88,139]
180. 9 <=> kind(fred) [avatar definition]
182. kind(fred) <- (9) [avatar component clause 180]
183. ~7 | 9 [avatar split clause 178,180,170]
278. 7 [avatar split clause 136,170]
279. generous(alice) [resolution 104,128]
287. strong(fred) | rich(fred) <- (9) [resolution 108,182]
291. strong(fred) <- (~8, 9) [subsumption resolution 287,176]
292. 1 | 8 | ~9 [avatar split clause 291,180,174,142]
293. $false <- (5) [resolution 160,279]
294. ~5 [avatar contradiction clause 293]
295. $false [avatar sat refutation 166,177,183,278,292,294]
% SZS output end Proof for 7417076372349330988540758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is humble.
If paul is funny or generous then paul is not wise or not patient.
Everyone who is both not wise and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Everyone who is either not calm or not curious is strong or not kind.
If mary is not curious or not rich then john is not calm and vice versa.
If someone is either not rich or brave then alice is not calm and vice versa.
Everyone who is both creative and strong is either not patient or not old and vice versa.
Lucy is both strong and not calm.
Someone is either not patient or creative.
Someone is creative or calm.
Fred is tall.
Someone is generous or funny.
Lucy is rich.
Someone is both not patient and strong.
Someone is wise or funny. | Mary is funny. | entailment | (![X]:(~creative(X)=>humble(X)))&
(((funny(paul)|generous(paul)))=>((~wise(paul)|~patient(paul))))&
(![X]:((~wise(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
(![X]:((~calm(X)<~>~curious(X))=>(strong(X)|~kind(X))))&
(((~curious(mary)|~rich(mary)))<=>(~calm(john)))&
((?[X]:((~rich(X)<~>brave(X))))<=>(~calm(alice)))&
(![X]:((creative(X)&strong(X))<=>(~patient(X)<~>~old(X))))&
((strong(lucy)&~calm(lucy)))&
(?[X]:((~patient(X)<~>creative(X))))&
(?[X]:((creative(X)|calm(X))))&
(tall(fred))&
(?[X]:((generous(X)|funny(X))))&
(rich(lucy))&
(?[X]:((~patient(X)&strong(X))))&
(?[X]:((wise(X)|funny(X)))) | funny(mary) | [
"p2",
"p4",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3853081659266664673725275
% SZS output start Proof for 3853081659266664673725275
3. ! [X0] : ((creative(X0) & ~wise(X0)) <=> ~wise(X0)) [input p2]
5. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p4]
8. (curious(mary) | ~creative(mary)) <=> (wise(paul) | tall(paul)) [input p7]
9. ! [X0] : ((~funny(X0) <~> quiet(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p9]
12. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p11]
25. ~funny(mary) [input hypothesis]
29. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 10]
33. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) | wise(X0)))) [nnf transformation 3]
34. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | ~creative(X0) | wise(X0))) [flattening 33]
36. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 5]
37. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 36]
44. ((curious(mary) | ~creative(mary)) | (~wise(paul) & ~tall(paul))) & ((wise(paul) | tall(paul)) | (~curious(mary) & creative(mary))) [nnf transformation 8]
45. (curious(mary) | ~creative(mary) | (~wise(paul) & ~tall(paul))) & (wise(paul) | tall(paul) | (~curious(mary) & creative(mary))) [flattening 44]
46. ! [X0] : ((((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0))))) [nnf transformation 9]
47. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 12]
73. wise(X0) | creative(X0) [cnf transformation 34]
76. ~old(X0) | tall(X0) [cnf transformation 37]
77. ~old(X0) | ~curious(X0) [cnf transformation 37]
90. curious(mary) | ~creative(mary) | ~tall(paul) [cnf transformation 45]
92. ~wise(X0) | quiet(X0) | quiet(X0) | funny(X0) [cnf transformation 46]
98. ~quiet(X0) | funny(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 46]
100. tall(X0) | old(X0) [cnf transformation 29]
103. old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 47]
133. ~funny(mary) [cnf transformation 25]
134. ~wise(X0) | quiet(X0) | funny(X0) [duplicate literal removal 92]
137. ~quiet(X0) | funny(X0) | ~wise(X0) [duplicate literal removal 98]
170. 8 <=> creative(mary) [avatar definition]
171. creative(mary) <- (8) [avatar component clause 170]
174. 9 <=> curious(mary) [avatar definition]
176. curious(mary) <- (9) [avatar component clause 174]
179. 10 <=> tall(paul) [avatar definition]
181. ~tall(paul) <- (~10) [avatar component clause 179]
182. ~10 | ~8 | 9 [avatar split clause 90,174,170,179]
186. ~wise(X0) | funny(X0) [subsumption resolution 134,137]
187. tall(X0) [subsumption resolution 100,76]
189. ~curious(X0) | ~creative(X0) [subsumption resolution 103,77]
263. funny(X0) | creative(X0) [resolution 186,73]
266. $false <- (~10) [subsumption resolution 181,187]
267. 10 [avatar contradiction clause 266]
277. creative(mary) [resolution 263,133]
281. 8 [avatar split clause 277,170]
282. ~creative(mary) <- (9) [resolution 176,189]
283. $false <- (8, 9) [subsumption resolution 282,171]
284. ~8 | ~9 [avatar contradiction clause 283]
285. $false [avatar sat refutation 182,267,281,284]
% SZS output end Proof for 3853081659266664673725275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not strong or not rich then alice is both generous and happy and vice versa. Everyone who is not brave or funny is both not patient and wise and vice versa. Everyone who is either quiet or not creative is quiet and vice versa. If someone is curious then mary is old. If someone is either quiet or rich then fred is not quiet or not rich. If susan is both not strong and not humble then mary is either not humble or kind and vice versa. If someone is quiet then fred is either not tall or not generous. Everyone who is either calm or funny is both strong and not brave. If someone is kind then someone is either patient or happy. If someone is both not happy and funny then mary is brave or not generous and vice versa. Everyone who is not rich or generous is either humble or not quiet and vice versa. Everyone who is not quiet or creative is both brave and quiet. Everyone who is not brave is both not quiet and not patient and vice versa. Everyone who is old or wise is old and vice versa. If john is both old and not quiet then someone is either not creative or not rich and vice versa. If mary is either quiet or strong then alice is happy or not creative and vice versa. Mary is wise or not creative. John is not calm or strong. Lucy is not funny. Paul is either funny or old. Lucy is either funny or tall. Susan is both old and wise. | Alice is not funny. | neutral | (((~strong(fred)|~rich(fred)))<=>((generous(alice)&happy(alice))))&
(![X]:((~brave(X)|funny(X))<=>(~patient(X)&wise(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>quiet(X)))&
((?[X]:(curious(X)))=>(old(mary)))&
((?[X]:((quiet(X)<~>rich(X))))=>((~quiet(fred)|~rich(fred))))&
(((~strong(susan)&~humble(susan)))<=>((~humble(mary)<~>kind(mary))))&
((?[X]:(quiet(X)))=>((~tall(fred)<~>~generous(fred))))&
(![X]:((calm(X)<~>funny(X))=>(strong(X)&~brave(X))))&
((?[X]:(kind(X)))=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((~happy(X)&funny(X))))<=>((brave(mary)|~generous(mary))))&
(![X]:((~rich(X)|generous(X))<=>(humble(X)<~>~quiet(X))))&
(![X]:((~quiet(X)|creative(X))=>(brave(X)&quiet(X))))&
(![X]:(~brave(X)<=>(~quiet(X)&~patient(X))))&
(![X]:((old(X)|wise(X))<=>old(X)))&
(((old(john)&~quiet(john)))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(((quiet(mary)<~>strong(mary)))<=>((happy(alice)|~creative(alice))))&
((wise(mary)|~creative(mary)))&
((~calm(john)|strong(john)))&
(~funny(lucy))&
((funny(paul)<~>old(paul)))&
((funny(lucy)<~>tall(lucy)))&
((old(susan)&wise(susan))) | ~funny(alice) | [] | null | 0 |
Everyone who is either happy or not curious is both patient and funny.
Everyone who is either not creative or quiet is either wise or not humble.
If mary is both not curious and humble then fred is strong and vice versa.
Everyone who is both not funny and wise is wise or tall and vice versa.
Everyone who is either rich or funny is not creative and vice versa.
If someone is generous then paul is either old or not patient and vice versa.
Everyone who is not generous is both curious and not patient and vice versa.
Everyone who is both calm and tall is funny or curious and vice versa.
If someone is both not wise and strong then someone is either not strong or generous and vice versa.
Everyone who is either not patient or quiet is not curious or creative.
Everyone who is either calm or humble is rich and vice versa.
Everyone who is not brave or calm is rich.
Everyone who is both patient and rich is old.
Everyone who is not patient or not creative is brave or generous.
Everyone who is both not rich and not happy is both brave and humble.
Everyone who is wise is both tall and not wise and vice versa.
Someone is old.
Paul is both not curious and not tall.
Mary is creative or happy.
Fred is either quiet or not strong.
Someone is not strong.
Someone is generous. | Mary is strong. | neutral | (![X]:((happy(X)<~>~curious(X))=>(patient(X)&funny(X))))&
(![X]:((~creative(X)<~>quiet(X))=>(wise(X)<~>~humble(X))))&
(((~curious(mary)&humble(mary)))<=>(strong(fred)))&
(![X]:((~funny(X)&wise(X))<=>(wise(X)|tall(X))))&
(![X]:((rich(X)<~>funny(X))<=>~creative(X)))&
((?[X]:(generous(X)))<=>((old(paul)<~>~patient(paul))))&
(![X]:(~generous(X)<=>(curious(X)&~patient(X))))&
(![X]:((calm(X)&tall(X))<=>(funny(X)|curious(X))))&
((?[X]:((~wise(X)&strong(X))))<=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:((~patient(X)<~>quiet(X))=>(~curious(X)|creative(X))))&
(![X]:((calm(X)<~>humble(X))<=>rich(X)))&
(![X]:((~brave(X)|calm(X))=>rich(X)))&
(![X]:((patient(X)&rich(X))=>old(X)))&
(![X]:((~patient(X)|~creative(X))=>(brave(X)|generous(X))))&
(![X]:((~rich(X)&~happy(X))=>(brave(X)&humble(X))))&
(![X]:(wise(X)<=>(tall(X)&~wise(X))))&
(?[X]:(old(X)))&
((~curious(paul)&~tall(paul)))&
((creative(mary)|happy(mary)))&
((quiet(fred)<~>~strong(fred)))&
(?[X]:(~strong(X)))&
(?[X]:(generous(X))) | strong(mary) | [] | null | 0 |
If someone is not humble or humble then someone is both not quiet and not kind. Everyone who is generous or not old is funny or rich. Everyone who is wise or happy is not rich or wise and vice versa. If someone is rich then lucy is calm and vice versa. If mary is not humble or not kind then lucy is both generous and not brave. Everyone who is tall or kind is tall. If lucy is not quiet then someone is patient and vice versa. If someone is humble then someone is strong or not calm and vice versa. Everyone who is not patient or rich is either not generous or calm. Everyone who is both calm and humble is wise. Everyone who is either strong or not happy is not generous or patient. Everyone who is either not calm or calm is not kind or patient. Everyone who is both calm and patient is kind. If susan is either happy or generous then mary is either not strong or not calm and vice versa. Everyone who is not funny or not brave is not funny and vice versa. If lucy is calm or creative then john is not kind and vice versa. Someone is not tall. Paul is either funny or not patient. Someone is strong. Someone is funny or kind. Paul is both not calm and brave. Fred is rich or not wise. Someone is tall. Mary is not curious or not generous. | Mary is not kind. | neutral | ((?[X]:((~humble(X)|humble(X))))=>(?[X]:((~quiet(X)&~kind(X)))))&
(![X]:((generous(X)|~old(X))=>(funny(X)|rich(X))))&
(![X]:((wise(X)|happy(X))<=>(~rich(X)|wise(X))))&
((?[X]:(rich(X)))<=>(calm(lucy)))&
(((~humble(mary)|~kind(mary)))=>((generous(lucy)&~brave(lucy))))&
(![X]:((tall(X)|kind(X))=>tall(X)))&
((~quiet(lucy))<=>(?[X]:(patient(X))))&
((?[X]:(humble(X)))<=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((~patient(X)|rich(X))=>(~generous(X)<~>calm(X))))&
(![X]:((calm(X)&humble(X))=>wise(X)))&
(![X]:((strong(X)<~>~happy(X))=>(~generous(X)|patient(X))))&
(![X]:((~calm(X)<~>calm(X))=>(~kind(X)|patient(X))))&
(![X]:((calm(X)&patient(X))=>kind(X)))&
(((happy(susan)<~>generous(susan)))<=>((~strong(mary)<~>~calm(mary))))&
(![X]:((~funny(X)|~brave(X))<=>~funny(X)))&
(((calm(lucy)|creative(lucy)))<=>(~kind(john)))&
(?[X]:(~tall(X)))&
((funny(paul)<~>~patient(paul)))&
(?[X]:(strong(X)))&
(?[X]:((funny(X)|kind(X))))&
((~calm(paul)&brave(paul)))&
((rich(fred)|~wise(fred)))&
(?[X]:(tall(X)))&
((~curious(mary)|~generous(mary))) | ~kind(mary) | [] | null | 0 |
Everyone who is either wise or happy is either quiet or creative and vice versa.
If susan is not creative then someone is tall.
Everyone who is not kind is wise or not kind.
Everyone who is either humble or not creative is not brave or not rich.
If paul is either not creative or brave then susan is not curious.
Everyone who is either not generous or calm is both not kind and calm.
Everyone who is both quiet and calm is either not brave or brave and vice versa.
If someone is both patient and not generous then someone is both not wise and tall.
If alice is funny then mary is not brave or rich.
If someone is either calm or not funny then someone is kind or curious and vice versa.
Everyone who is kind is happy or not old.
Everyone who is not curious is either generous or not quiet.
Everyone who is both quiet and strong is not tall or creative.
If lucy is not patient then fred is tall or not generous.
Everyone who is not patient or wise is both not tall and tall and vice versa.
Susan is not humble.
Mary is either not happy or calm.
Paul is both kind and not generous.
Someone is either tall or old.
Someone is brave or creative.
Someone is both not wise and generous. | Susan is not tall. | neutral | (![X]:((wise(X)<~>happy(X))<=>(quiet(X)<~>creative(X))))&
((~creative(susan))=>(?[X]:(tall(X))))&
(![X]:(~kind(X)=>(wise(X)|~kind(X))))&
(![X]:((humble(X)<~>~creative(X))=>(~brave(X)|~rich(X))))&
(((~creative(paul)<~>brave(paul)))=>(~curious(susan)))&
(![X]:((~generous(X)<~>calm(X))=>(~kind(X)&calm(X))))&
(![X]:((quiet(X)&calm(X))<=>(~brave(X)<~>brave(X))))&
((?[X]:((patient(X)&~generous(X))))=>(?[X]:((~wise(X)&tall(X)))))&
((funny(alice))=>((~brave(mary)|rich(mary))))&
((?[X]:((calm(X)<~>~funny(X))))<=>(?[X]:((kind(X)|curious(X)))))&
(![X]:(kind(X)=>(happy(X)|~old(X))))&
(![X]:(~curious(X)=>(generous(X)<~>~quiet(X))))&
(![X]:((quiet(X)&strong(X))=>(~tall(X)|creative(X))))&
((~patient(lucy))=>((tall(fred)|~generous(fred))))&
(![X]:((~patient(X)|wise(X))<=>(~tall(X)&tall(X))))&
(~humble(susan))&
((~happy(mary)<~>calm(mary)))&
((kind(paul)&~generous(paul)))&
(?[X]:((tall(X)<~>old(X))))&
(?[X]:((brave(X)|creative(X))))&
(?[X]:((~wise(X)&generous(X)))) | ~tall(susan) | [] | null | 0 |
If paul is both creative and wise then someone is either wise or not humble and vice versa.
Everyone who is both patient and not old is rich or not patient.
Everyone who is quiet or not generous is either not humble or tall.
If someone is either curious or funny then fred is quiet.
If lucy is both not tall and not humble then someone is calm or not curious and vice versa.
If someone is both funny and kind then someone is either humble or not wise.
Everyone who is not tall is not generous or brave and vice versa.
Everyone who is not generous or not brave is not tall.
If lucy is not quiet or not tall then someone is not generous.
Everyone who is wise is not strong.
If someone is not calm or not old then someone is humble.
Everyone who is creative is both brave and not old and vice versa.
Everyone who is either not rich or not tall is creative.
Everyone who is old or not rich is old or not patient and vice versa.
If mary is both tall and not rich then alice is not funny or not rich and vice versa.
Someone is either funny or wise.
Fred is both not generous and not curious.
Someone is patient.
Someone is old.
Someone is not happy. | Mary is not funny. | neutral | (((creative(paul)&wise(paul)))<=>(?[X]:((wise(X)<~>~humble(X)))))&
(![X]:((patient(X)&~old(X))=>(rich(X)|~patient(X))))&
(![X]:((quiet(X)|~generous(X))=>(~humble(X)<~>tall(X))))&
((?[X]:((curious(X)<~>funny(X))))=>(quiet(fred)))&
(((~tall(lucy)&~humble(lucy)))<=>(?[X]:((calm(X)|~curious(X)))))&
((?[X]:((funny(X)&kind(X))))=>(?[X]:((humble(X)<~>~wise(X)))))&
(![X]:(~tall(X)<=>(~generous(X)|brave(X))))&
(![X]:((~generous(X)|~brave(X))=>~tall(X)))&
(((~quiet(lucy)|~tall(lucy)))=>(?[X]:(~generous(X))))&
(![X]:(wise(X)=>~strong(X)))&
((?[X]:((~calm(X)|~old(X))))=>(?[X]:(humble(X))))&
(![X]:(creative(X)<=>(brave(X)&~old(X))))&
(![X]:((~rich(X)<~>~tall(X))=>creative(X)))&
(![X]:((old(X)|~rich(X))<=>(old(X)|~patient(X))))&
(((tall(mary)&~rich(mary)))<=>((~funny(alice)|~rich(alice))))&
(?[X]:((funny(X)<~>wise(X))))&
((~generous(fred)&~curious(fred)))&
(?[X]:(patient(X)))&
(?[X]:(old(X)))&
(?[X]:(~happy(X))) | ~funny(mary) | [] | null | 0 |
Everyone who is both generous and not happy is not patient and vice versa.
If someone is either old or kind then fred is both not humble and not old.
Everyone who is old or kind is both not wise and tall.
Everyone who is either brave or strong is both rich and funny and vice versa.
Everyone who is not generous or brave is both not strong and not funny and vice versa.
If fred is not generous or not old then paul is both brave and strong and vice versa.
If someone is either calm or not calm then someone is humble and vice versa.
If someone is not strong then someone is not strong or not wise and vice versa.
Everyone who is both not funny and not old is not humble.
Everyone who is happy is both tall and happy and vice versa.
Everyone who is both creative and not creative is rich.
Everyone who is either not humble or not happy is not brave or not creative and vice versa.
If someone is both not curious and not humble then fred is not kind and vice versa.
If someone is either not brave or quiet then someone is calm.
Everyone who is humble is not wise.
Everyone who is quiet or wise is wise and vice versa.
Alice is both kind and not wise.
Fred is either generous or not happy.
Someone is not kind or curious.
Someone is happy or not strong.
Someone is not curious or not quiet.
Someone is both funny and not curious. | Paul is curious. | neutral | (![X]:((generous(X)&~happy(X))<=>~patient(X)))&
((?[X]:((old(X)<~>kind(X))))=>((~humble(fred)&~old(fred))))&
(![X]:((old(X)|kind(X))=>(~wise(X)&tall(X))))&
(![X]:((brave(X)<~>strong(X))<=>(rich(X)&funny(X))))&
(![X]:((~generous(X)|brave(X))<=>(~strong(X)&~funny(X))))&
(((~generous(fred)|~old(fred)))<=>((brave(paul)&strong(paul))))&
((?[X]:((calm(X)<~>~calm(X))))<=>(?[X]:(humble(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((~strong(X)|~wise(X)))))&
(![X]:((~funny(X)&~old(X))=>~humble(X)))&
(![X]:(happy(X)<=>(tall(X)&happy(X))))&
(![X]:((creative(X)&~creative(X))=>rich(X)))&
(![X]:((~humble(X)<~>~happy(X))<=>(~brave(X)|~creative(X))))&
((?[X]:((~curious(X)&~humble(X))))<=>(~kind(fred)))&
((?[X]:((~brave(X)<~>quiet(X))))=>(?[X]:(calm(X))))&
(![X]:(humble(X)=>~wise(X)))&
(![X]:((quiet(X)|wise(X))<=>wise(X)))&
((kind(alice)&~wise(alice)))&
((generous(fred)<~>~happy(fred)))&
(?[X]:((~kind(X)|curious(X))))&
(?[X]:((happy(X)|~strong(X))))&
(?[X]:((~curious(X)|~quiet(X))))&
(?[X]:((funny(X)&~curious(X)))) | curious(paul) | [] | null | 0 |
If someone is either happy or not creative then someone is either not humble or not strong.
If someone is calm or old then someone is not wise or wise and vice versa.
Everyone who is not funny or rich is both not calm and tall.
Everyone who is not old is kind and vice versa.
If john is not strong then someone is creative or not patient and vice versa.
If paul is either not curious or not rich then lucy is both not kind and humble and vice versa.
If someone is not humble then john is not funny and vice versa.
Everyone who is not humble is either not strong or not humble and vice versa.
Everyone who is either generous or not funny is strong and vice versa.
Everyone who is either not quiet or strong is both not calm and not old.
If someone is either not old or not generous then john is both brave and not generous.
If lucy is not brave or tall then someone is not strong or not rich.
If john is both not quiet and curious then alice is both humble and generous and vice versa.
Everyone who is calm is both calm and wise.
Everyone who is either not calm or creative is both strong and not patient and vice versa.
If lucy is both not quiet and old then someone is not funny or wise and vice versa.
Someone is either humble or not generous.
Alice is both funny and not kind.
John is old or patient.
Mary is rich or wise. | Mary is funny. | entailment | ((?[X]:((happy(X)<~>~creative(X))))=>(?[X]:((~humble(X)<~>~strong(X)))))&
((?[X]:((calm(X)|old(X))))<=>(?[X]:((~wise(X)|wise(X)))))&
(![X]:((~funny(X)|rich(X))=>(~calm(X)&tall(X))))&
(![X]:(~old(X)<=>kind(X)))&
((~strong(john))<=>(?[X]:((creative(X)|~patient(X)))))&
(((~curious(paul)<~>~rich(paul)))<=>((~kind(lucy)&humble(lucy))))&
((?[X]:(~humble(X)))<=>(~funny(john)))&
(![X]:(~humble(X)<=>(~strong(X)<~>~humble(X))))&
(![X]:((generous(X)<~>~funny(X))<=>strong(X)))&
(![X]:((~quiet(X)<~>strong(X))=>(~calm(X)&~old(X))))&
((?[X]:((~old(X)<~>~generous(X))))=>((brave(john)&~generous(john))))&
(((~brave(lucy)|tall(lucy)))=>(?[X]:((~strong(X)|~rich(X)))))&
(((~quiet(john)&curious(john)))<=>((humble(alice)&generous(alice))))&
(![X]:(calm(X)=>(calm(X)&wise(X))))&
(![X]:((~calm(X)<~>creative(X))<=>(strong(X)&~patient(X))))&
(((~quiet(lucy)&old(lucy)))<=>(?[X]:((~funny(X)|wise(X)))))&
(?[X]:((humble(X)<~>~generous(X))))&
((funny(alice)&~kind(alice)))&
((old(john)|patient(john)))&
((rich(mary)|wise(mary))) | funny(mary) | [
"p2",
"p4",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6940740985265638747729845
% SZS output start Proof for 6940740985265638747729845
3. ! [X0] : ((rich(X0) | ~funny(X0)) => (tall(X0) & ~calm(X0))) [input p2]
5. ~strong(john) <=> ? [X0] : (~patient(X0) | creative(X0)) [input p4]
8. ! [X0] : (~humble(X0) <=> (~strong(X0) <~> ~humble(X0))) [input p7]
15. ! [X0] : ((~calm(X0) <~> creative(X0)) <=> (~patient(X0) & strong(X0))) [input p14]
21. ~funny(mary) [input hypothesis]
27. ! [X0] : ((tall(X0) & ~calm(X0)) | (~rich(X0) & funny(X0))) [ennf transformation 3]
42. (~strong(john) | ! [X0] : (patient(X0) & ~creative(X0))) & (? [X0] : (~patient(X0) | creative(X0)) | strong(john)) [nnf transformation 5]
43. (~strong(john) | ! [X0] : (patient(X0) & ~creative(X0))) & (? [X1] : (~patient(X1) | creative(X1)) | strong(john)) [rectify 42]
44. ? [X1] : (~patient(X1) | creative(X1)) => (~patient(sK3) | creative(sK3)) [choice axiom]
45. (~strong(john) | ! [X0] : (patient(X0) & ~creative(X0))) & ((~patient(sK3) | creative(sK3)) | strong(john)) [skolemisation 43,44]
52. ! [X0] : ((~humble(X0) | ((~strong(X0) | humble(X0)) & (~humble(X0) | strong(X0)))) & (((humble(X0) | strong(X0)) & (~humble(X0) | ~strong(X0))) | humble(X0))) [nnf transformation 8]
60. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [flattening 60]
78. ~calm(X0) | funny(X0) [cnf transformation 27]
85. ~strong(john) | ~creative(X0) [cnf transformation 45]
86. ~strong(john) | patient(X0) [cnf transformation 45]
96. humble(X0) | strong(X0) | humble(X0) [cnf transformation 52]
97. ~humble(X0) | ~humble(X0) | strong(X0) [cnf transformation 52]
118. ~patient(X0) | creative(X0) | calm(X0) [cnf transformation 61]
133. ~funny(mary) [cnf transformation 21]
134. humble(X0) | strong(X0) [duplicate literal removal 96]
135. ~humble(X0) | strong(X0) [duplicate literal removal 97]
171. 9 <=> ! [X0] : patient(X0) [avatar definition]
172. patient(X0) <- (9) [avatar component clause 171]
174. 10 <=> strong(john) [avatar definition]
176. ~strong(john) <- (~10) [avatar component clause 174]
177. 9 | ~10 [avatar split clause 86,174,171]
179. 11 <=> ! [X0] : ~creative(X0) [avatar definition]
180. ~creative(X0) <- (11) [avatar component clause 179]
181. 11 | ~10 [avatar split clause 85,174,179]
226. strong(X0) [subsumption resolution 134,135]
281. 31 <=> ! [X0] : funny(X0) [avatar definition]
282. funny(X0) <- (31) [avatar component clause 281]
328. $false <- (~10) [subsumption resolution 176,226]
329. 10 [avatar contradiction clause 328]
349. creative(X0) | calm(X0) <- (9) [resolution 118,172]
350. calm(X0) <- (9, 11) [subsumption resolution 349,180]
353. funny(X1) <- (9, 11) [resolution 350,78]
357. 31 | ~9 | ~11 [avatar split clause 353,179,171,281]
360. $false <- (31) [resolution 282,133]
363. ~31 [avatar contradiction clause 360]
365. $false [avatar sat refutation 177,181,329,357,363]
% SZS output end Proof for 6940740985265638747729845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not tall and tall then alice is happy or generous and vice versa. If someone is both not curious and patient then someone is both old and not generous and vice versa. If john is both creative and kind then someone is not wise. If someone is strong or wise then john is either not humble or funny. Everyone who is either humble or kind is either not curious or not humble and vice versa. Everyone who is both not curious and not brave is rich. Everyone who is calm or not quiet is creative or not old and vice versa. If paul is wise then someone is generous. Everyone who is quiet is both rich and wise. Everyone who is both curious and old is brave and vice versa. Everyone who is brave or not strong is not curious. Everyone who is either not funny or not quiet is not generous. Everyone who is both not patient and calm is either strong or calm and vice versa. Everyone who is wise is not strong. If someone is either tall or not humble then someone is both not funny and not happy and vice versa. Everyone who is rich is kind or not patient and vice versa. Susan is funny. Fred is curious. Fred is not old. Someone is both not kind and not tall. Someone is not quiet or not old. Someone is either not quiet or not humble. Someone is generous or quiet. Alice is not wise. | Alice is old. | contradiction | ((?[X]:((~tall(X)&tall(X))))<=>((happy(alice)|generous(alice))))&
((?[X]:((~curious(X)&patient(X))))<=>(?[X]:((old(X)&~generous(X)))))&
(((creative(john)&kind(john)))=>(?[X]:(~wise(X))))&
((?[X]:((strong(X)|wise(X))))=>((~humble(john)<~>funny(john))))&
(![X]:((humble(X)<~>kind(X))<=>(~curious(X)<~>~humble(X))))&
(![X]:((~curious(X)&~brave(X))=>rich(X)))&
(![X]:((calm(X)|~quiet(X))<=>(creative(X)|~old(X))))&
((wise(paul))=>(?[X]:(generous(X))))&
(![X]:(quiet(X)=>(rich(X)&wise(X))))&
(![X]:((curious(X)&old(X))<=>brave(X)))&
(![X]:((brave(X)|~strong(X))=>~curious(X)))&
(![X]:((~funny(X)<~>~quiet(X))=>~generous(X)))&
(![X]:((~patient(X)&calm(X))<=>(strong(X)<~>calm(X))))&
(![X]:(wise(X)=>~strong(X)))&
((?[X]:((tall(X)<~>~humble(X))))<=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(rich(X)<=>(kind(X)|~patient(X))))&
(funny(susan))&
(curious(fred))&
(~old(fred))&
(?[X]:((~kind(X)&~tall(X))))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((generous(X)|quiet(X))))&
(~wise(alice)) | old(alice) | [
"p0",
"p1",
"p4",
"p5",
"p9",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 426180066953476364644456
% SZS output start Proof for 426180066953476364644456
1. ? [X0] : (tall(X0) & ~tall(X0)) <=> (generous(alice) | happy(alice)) [input p0]
2. ? [X0] : (patient(X0) & ~curious(X0)) <=> ? [X0] : (~generous(X0) & old(X0)) [input p1]
5. ! [X0] : ((humble(X0) <~> kind(X0)) <=> (~curious(X0) <~> ~humble(X0))) [input p4]
6. ! [X0] : ((~brave(X0) & ~curious(X0)) => rich(X0)) [input p5]
10. ! [X0] : ((old(X0) & curious(X0)) <=> brave(X0)) [input p9]
11. ! [X0] : ((~strong(X0) | brave(X0)) => ~curious(X0)) [input p10]
16. ! [X0] : (rich(X0) <=> (~patient(X0) | kind(X0))) [input p15]
25. old(alice) [input hypothesis]
26. ? [X0] : (patient(X0) & ~curious(X0)) <=> ? [X1] : (~generous(X1) & old(X1)) [rectify 2]
28. ! [X0] : (rich(X0) => (~patient(X0) | kind(X0))) [unused predicate definition removal 16]
32. ! [X0] : (rich(X0) | (brave(X0) | curious(X0))) [ennf transformation 6]
33. ! [X0] : (rich(X0) | brave(X0) | curious(X0)) [flattening 32]
36. ! [X0] : (~curious(X0) | (strong(X0) & ~brave(X0))) [ennf transformation 11]
39. ! [X0] : ((~patient(X0) | kind(X0)) | ~rich(X0)) [ennf transformation 28]
40. ! [X0] : (~patient(X0) | kind(X0) | ~rich(X0)) [flattening 39]
41. (? [X0] : (tall(X0) & ~tall(X0)) | (~generous(alice) & ~happy(alice))) & ((generous(alice) | happy(alice)) | ! [X0] : (~tall(X0) | tall(X0))) [nnf transformation 1]
42. (? [X0] : (tall(X0) & ~tall(X0)) | (~generous(alice) & ~happy(alice))) & (generous(alice) | happy(alice) | ! [X0] : (~tall(X0) | tall(X0))) [flattening 41]
43. (? [X0] : (tall(X0) & ~tall(X0)) | (~generous(alice) & ~happy(alice))) & (generous(alice) | happy(alice) | ! [X1] : (~tall(X1) | tall(X1))) [rectify 42]
44. ? [X0] : (tall(X0) & ~tall(X0)) => (tall(sK0) & ~tall(sK0)) [choice axiom]
45. ((tall(sK0) & ~tall(sK0)) | (~generous(alice) & ~happy(alice))) & (generous(alice) | happy(alice) | ! [X1] : (~tall(X1) | tall(X1))) [skolemisation 43,44]
46. (? [X0] : (patient(X0) & ~curious(X0)) | ! [X1] : (generous(X1) | ~old(X1))) & (? [X1] : (~generous(X1) & old(X1)) | ! [X0] : (~patient(X0) | curious(X0))) [nnf transformation 26]
47. (? [X0] : (patient(X0) & ~curious(X0)) | ! [X1] : (generous(X1) | ~old(X1))) & (? [X2] : (~generous(X2) & old(X2)) | ! [X3] : (~patient(X3) | curious(X3))) [rectify 46]
48. ? [X0] : (patient(X0) & ~curious(X0)) => (patient(sK1) & ~curious(sK1)) [choice axiom]
49. ? [X2] : (~generous(X2) & old(X2)) => (~generous(sK2) & old(sK2)) [choice axiom]
50. ((patient(sK1) & ~curious(sK1)) | ! [X1] : (generous(X1) | ~old(X1))) & ((~generous(sK2) & old(sK2)) | ! [X3] : (~patient(X3) | curious(X3))) [skolemisation 47,49,48]
54. ! [X0] : ((((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ((~curious(X0) | humble(X0)) & (~humble(X0) | curious(X0)))) & (((humble(X0) | curious(X0)) & (~humble(X0) | ~curious(X0))) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0))))) [nnf transformation 5]
59. ! [X0] : (((old(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | (~old(X0) | ~curious(X0)))) [nnf transformation 10]
60. ! [X0] : (((old(X0) & curious(X0)) | ~brave(X0)) & (brave(X0) | ~old(X0) | ~curious(X0))) [flattening 59]
80. ~tall(sK0) | ~generous(alice) [cnf transformation 45]
82. tall(sK0) | ~generous(alice) [cnf transformation 45]
85. ~curious(sK1) | generous(X1) | ~old(X1) [cnf transformation 50]
86. patient(sK1) | generous(X1) | ~old(X1) [cnf transformation 50]
92. ~humble(X0) | ~curious(X0) | kind(X0) | ~humble(X0) [cnf transformation 54]
95. humble(X0) | curious(X0) | humble(X0) | ~kind(X0) [cnf transformation 54]
97. kind(X0) | humble(X0) | ~curious(X0) | humble(X0) [cnf transformation 54]
98. ~kind(X0) | ~humble(X0) | ~humble(X0) | curious(X0) [cnf transformation 54]
100. rich(X0) | brave(X0) | curious(X0) [cnf transformation 33]
109. ~brave(X0) | curious(X0) [cnf transformation 60]
111. ~curious(X0) | ~brave(X0) [cnf transformation 36]
128. ~rich(X0) | kind(X0) | ~patient(X0) [cnf transformation 40]
139. old(alice) [cnf transformation 25]
142. ~humble(X0) | ~curious(X0) | kind(X0) [duplicate literal removal 92]
143. humble(X0) | curious(X0) | ~kind(X0) [duplicate literal removal 95]
144. ~curious(X0) | humble(X0) | kind(X0) [duplicate literal removal 97]
145. ~humble(X0) | ~kind(X0) | curious(X0) [duplicate literal removal 98]
147. 1 <=> generous(alice) [avatar definition]
149. ~generous(alice) <- (~1) [avatar component clause 147]
151. 2 <=> tall(sK0) [avatar definition]
154. ~1 | 2 [avatar split clause 82,151,147]
160. ~1 | ~2 [avatar split clause 80,151,147]
163. 4 <=> ! [X1] : (generous(X1) | ~old(X1)) [avatar definition]
164. ~old(X1) | generous(X1) <- (4) [avatar component clause 163]
166. 5 <=> patient(sK1) [avatar definition]
168. patient(sK1) <- (5) [avatar component clause 166]
169. 4 | 5 [avatar split clause 86,166,163]
171. 6 <=> curious(sK1) [avatar definition]
173. ~curious(sK1) <- (~6) [avatar component clause 171]
174. 4 | ~6 [avatar split clause 85,171,163]
219. ~kind(X0) | curious(X0) [subsumption resolution 143,145]
220. ~curious(X0) | kind(X0) [subsumption resolution 142,144]
230. ~brave(X0) [subsumption resolution 111,109]
296. generous(alice) <- (4) [resolution 164,139]
297. $false <- (~1, 4) [subsumption resolution 296,149]
298. 1 | ~4 [avatar contradiction clause 297]
371. kind(X0) | ~patient(X0) | brave(X0) | curious(X0) [resolution 128,100]
372. kind(X0) | ~patient(X0) | curious(X0) [subsumption resolution 371,230]
373. ~patient(X0) | kind(X0) [subsumption resolution 372,220]
376. kind(sK1) <- (5) [resolution 373,168]
379. curious(sK1) <- (5) [resolution 376,219]
380. $false <- (5, ~6) [subsumption resolution 379,173]
381. ~5 | 6 [avatar contradiction clause 380]
382. $false [avatar sat refutation 154,160,169,174,298,381]
% SZS output end Proof for 426180066953476364644456
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either wise or not happy is happy or not kind.
If someone is both not patient and generous then someone is either generous or not kind.
Everyone who is not creative is wise or not kind.
Everyone who is both patient and funny is not kind or brave and vice versa.
Everyone who is not quiet is either not wise or brave and vice versa.
Everyone who is either quiet or not old is either curious or not kind.
If alice is both wise and not generous then alice is tall and vice versa.
If lucy is both kind and not quiet then paul is either creative or curious and vice versa.
Everyone who is not humble or not happy is creative or patient.
If someone is humble then fred is either creative or wise and vice versa.
If susan is not rich or not wise then fred is not quiet or not brave.
Everyone who is both happy and not wise is both generous and not calm.
Everyone who is not kind or kind is either not humble or generous and vice versa.
Everyone who is not funny or strong is either not brave or not quiet and vice versa.
Everyone who is either tall or not rich is either wise or old and vice versa.
If lucy is either not creative or happy then someone is both not rich and not tall.
Someone is either creative or not calm.
Fred is either not kind or not brave.
Fred is both not tall and not curious.
Paul is tall.
Someone is either strong or creative.
Lucy is both quiet and wise.
Someone is either not old or not quiet.
Paul is both happy and not quiet. | Fred is tall. | contradiction | (![X]:((wise(X)<~>~happy(X))=>(happy(X)|~kind(X))))&
((?[X]:((~patient(X)&generous(X))))=>(?[X]:((generous(X)<~>~kind(X)))))&
(![X]:(~creative(X)=>(wise(X)|~kind(X))))&
(![X]:((patient(X)&funny(X))<=>(~kind(X)|brave(X))))&
(![X]:(~quiet(X)<=>(~wise(X)<~>brave(X))))&
(![X]:((quiet(X)<~>~old(X))=>(curious(X)<~>~kind(X))))&
(((wise(alice)&~generous(alice)))<=>(tall(alice)))&
(((kind(lucy)&~quiet(lucy)))<=>((creative(paul)<~>curious(paul))))&
(![X]:((~humble(X)|~happy(X))=>(creative(X)|patient(X))))&
((?[X]:(humble(X)))<=>((creative(fred)<~>wise(fred))))&
(((~rich(susan)|~wise(susan)))=>((~quiet(fred)|~brave(fred))))&
(![X]:((happy(X)&~wise(X))=>(generous(X)&~calm(X))))&
(![X]:((~kind(X)|kind(X))<=>(~humble(X)<~>generous(X))))&
(![X]:((~funny(X)|strong(X))<=>(~brave(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>~rich(X))<=>(wise(X)<~>old(X))))&
(((~creative(lucy)<~>happy(lucy)))=>(?[X]:((~rich(X)&~tall(X)))))&
(?[X]:((creative(X)<~>~calm(X))))&
((~kind(fred)<~>~brave(fred)))&
((~tall(fred)&~curious(fred)))&
(tall(paul))&
(?[X]:((strong(X)<~>creative(X))))&
((quiet(lucy)&wise(lucy)))&
(?[X]:((~old(X)<~>~quiet(X))))&
((happy(paul)&~quiet(paul))) | tall(fred) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2195558895901844084627160
% SZS output start Proof for 2195558895901844084627160
19. ~curious(fred) & ~tall(fred) [input p18]
25. tall(fred) [input hypothesis]
140. ~tall(fred) [cnf transformation 19]
151. tall(fred) [cnf transformation 25]
301. $false [subsumption resolution 151,140]
% SZS output end Proof for 2195558895901844084627160
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not strong is not quiet or tall.
Everyone who is not generous or not quiet is both humble and curious and vice versa.
If mary is both rich and kind then someone is either not quiet or not generous and vice versa.
Everyone who is curious is not happy.
Everyone who is both not curious and wise is both not kind and happy.
If john is both not old and not calm then john is not tall or not generous and vice versa.
If someone is not kind then john is either not quiet or happy and vice versa.
Everyone who is both strong and patient is happy or wise.
Everyone who is both not curious and curious is generous or creative and vice versa.
Everyone who is both calm and not brave is rich.
Everyone who is not brave or not creative is not patient.
If lucy is not strong or tall then someone is either not creative or not patient and vice versa.
If paul is happy or not strong then someone is both not calm and curious and vice versa.
Everyone who is wise is not humble or generous.
Everyone who is both funny and tall is not strong.
Everyone who is calm is both curious and generous.
Lucy is either quiet or humble.
Fred is not kind.
Alice is not kind.
John is either funny or patient.
Mary is either quiet or funny. | John is rich. | neutral | (![X]:((~happy(X)&~strong(X))=>(~quiet(X)|tall(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(humble(X)&curious(X))))&
(((rich(mary)&kind(mary)))<=>(?[X]:((~quiet(X)<~>~generous(X)))))&
(![X]:(curious(X)=>~happy(X)))&
(![X]:((~curious(X)&wise(X))=>(~kind(X)&happy(X))))&
(((~old(john)&~calm(john)))<=>((~tall(john)|~generous(john))))&
((?[X]:(~kind(X)))<=>((~quiet(john)<~>happy(john))))&
(![X]:((strong(X)&patient(X))=>(happy(X)|wise(X))))&
(![X]:((~curious(X)&curious(X))<=>(generous(X)|creative(X))))&
(![X]:((calm(X)&~brave(X))=>rich(X)))&
(![X]:((~brave(X)|~creative(X))=>~patient(X)))&
(((~strong(lucy)|tall(lucy)))<=>(?[X]:((~creative(X)<~>~patient(X)))))&
(((happy(paul)|~strong(paul)))<=>(?[X]:((~calm(X)&curious(X)))))&
(![X]:(wise(X)=>(~humble(X)|generous(X))))&
(![X]:((funny(X)&tall(X))=>~strong(X)))&
(![X]:(calm(X)=>(curious(X)&generous(X))))&
((quiet(lucy)<~>humble(lucy)))&
(~kind(fred))&
(~kind(alice))&
((funny(john)<~>patient(john)))&
((quiet(mary)<~>funny(mary))) | rich(john) | [] | null | 0 |
If paul is both quiet and rich then john is both not humble and not wise.
Everyone who is not patient is kind or not humble.
Everyone who is curious is either not old or old and vice versa.
If alice is either not happy or generous then someone is humble or not brave and vice versa.
If fred is not patient then someone is either strong or not strong and vice versa.
Everyone who is both not curious and quiet is either happy or not tall and vice versa.
Everyone who is wise or happy is not creative.
If paul is wise or not creative then mary is tall and vice versa.
If someone is brave or tall then someone is old and vice versa.
If lucy is either not happy or rich then someone is not patient.
Everyone who is both kind and not funny is either not happy or brave.
If john is happy then someone is not wise and vice versa.
If paul is brave then paul is creative.
If someone is both not tall and not happy then john is patient and vice versa.
If alice is rich then someone is not patient or not calm and vice versa.
If paul is both not curious and not patient then mary is rich or calm and vice versa.
Someone is either funny or not patient.
Alice is humble or quiet.
Someone is not funny.
Someone is either not humble or quiet.
Someone is either not calm or creative.
Susan is tall.
John is either not strong or quiet.
Mary is old. | John is patient. | contradiction | (((quiet(paul)&rich(paul)))=>((~humble(john)&~wise(john))))&
(![X]:(~patient(X)=>(kind(X)|~humble(X))))&
(![X]:(curious(X)<=>(~old(X)<~>old(X))))&
(((~happy(alice)<~>generous(alice)))<=>(?[X]:((humble(X)|~brave(X)))))&
((~patient(fred))<=>(?[X]:((strong(X)<~>~strong(X)))))&
(![X]:((~curious(X)&quiet(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((wise(X)|happy(X))=>~creative(X)))&
(((wise(paul)|~creative(paul)))<=>(tall(mary)))&
((?[X]:((brave(X)|tall(X))))<=>(?[X]:(old(X))))&
(((~happy(lucy)<~>rich(lucy)))=>(?[X]:(~patient(X))))&
(![X]:((kind(X)&~funny(X))=>(~happy(X)<~>brave(X))))&
((happy(john))<=>(?[X]:(~wise(X))))&
((brave(paul))=>(creative(paul)))&
((?[X]:((~tall(X)&~happy(X))))<=>(patient(john)))&
((rich(alice))<=>(?[X]:((~patient(X)|~calm(X)))))&
(((~curious(paul)&~patient(paul)))<=>((rich(mary)|calm(mary))))&
(?[X]:((funny(X)<~>~patient(X))))&
((humble(alice)|quiet(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~calm(X)<~>creative(X))))&
(tall(susan))&
((~strong(john)<~>quiet(john)))&
(old(mary)) | patient(john) | [
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8943045748690186657420470
% SZS output start Proof for 8943045748690186657420470
3. ! [X0] : (curious(X0) <=> (~old(X0) <~> old(X0))) [input p2]
6. ! [X0] : ((quiet(X0) & ~curious(X0)) <=> (happy(X0) <~> ~tall(X0))) [input p5]
14. ? [X0] : (~happy(X0) & ~tall(X0)) <=> patient(john) [input p13]
25. patient(john) [input hypothesis]
36. ! [X0] : ((curious(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) & (((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | ~curious(X0))) [nnf transformation 3]
45. ! [X0] : (((quiet(X0) & ~curious(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (~quiet(X0) | curious(X0)))) [nnf transformation 6]
46. ! [X0] : (((quiet(X0) & ~curious(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ~quiet(X0) | curious(X0))) [flattening 45]
62. (? [X0] : (~happy(X0) & ~tall(X0)) | ~patient(john)) & (patient(john) | ! [X0] : (happy(X0) | tall(X0))) [nnf transformation 14]
63. (? [X0] : (~happy(X0) & ~tall(X0)) | ~patient(john)) & (patient(john) | ! [X1] : (happy(X1) | tall(X1))) [rectify 62]
64. ? [X0] : (~happy(X0) & ~tall(X0)) => (~happy(sK6) & ~tall(sK6)) [choice axiom]
65. ((~happy(sK6) & ~tall(sK6)) | ~patient(john)) & (patient(john) | ! [X1] : (happy(X1) | tall(X1))) [skolemisation 63,64]
89. curious(X0) | old(X0) | old(X0) [cnf transformation 36]
90. curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 36]
104. ~curious(X0) | happy(X0) | tall(X0) [cnf transformation 46]
123. ~tall(sK6) | ~patient(john) [cnf transformation 65]
124. ~happy(sK6) | ~patient(john) [cnf transformation 65]
145. patient(john) [cnf transformation 25]
148. curious(X0) | old(X0) [duplicate literal removal 89]
149. ~old(X0) | curious(X0) [duplicate literal removal 90]
168. curious(X0) [subsumption resolution 148,149]
209. tall(X0) | happy(X0) [subsumption resolution 104,168]
284. 30 <=> patient(john) [avatar definition]
288. 31 <=> happy(sK6) [avatar definition]
290. ~happy(sK6) <- (~31) [avatar component clause 288]
291. ~30 | ~31 [avatar split clause 124,288,284]
293. 32 <=> tall(sK6) [avatar definition]
295. ~tall(sK6) <- (~32) [avatar component clause 293]
296. ~30 | ~32 [avatar split clause 123,293,284]
385. 30 [avatar split clause 145,284]
392. happy(sK6) <- (~32) [resolution 209,295]
393. $false <- (~31, ~32) [subsumption resolution 392,290]
394. 31 | 32 [avatar contradiction clause 393]
395. $false [avatar sat refutation 291,296,385,394]
% SZS output end Proof for 8943045748690186657420470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is not rich.
Everyone who is not strong or not funny is both old and not rich and vice versa.
Everyone who is both not wise and not creative is either not creative or calm.
Everyone who is either not old or not funny is both brave and creative and vice versa.
Everyone who is both not calm and not creative is either funny or not creative.
Everyone who is either not rich or not brave is either not tall or brave.
If alice is happy or not brave then fred is either wise or creative.
Everyone who is both not creative and not patient is tall and vice versa.
Everyone who is either not happy or not patient is both not calm and not brave.
Everyone who is either not generous or humble is patient and vice versa.
If fred is both kind and curious then someone is not humble.
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 humble or humble.
If alice is either curious or generous then someone is not patient and vice versa.
If someone is either not generous or not calm then someone is not patient or not brave.
Everyone who is either kind or humble is either tall or not funny.
John is not creative.
Fred is not brave.
Mary is either not tall or humble.
Someone is either curious or not humble.
Someone is curious.
Susan is wise. | Alice is calm. | entailment | ((?[X]:(~generous(X)))=>(?[X]:(~rich(X))))&
(![X]:((~strong(X)|~funny(X))<=>(old(X)&~rich(X))))&
(![X]:((~wise(X)&~creative(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(brave(X)&creative(X))))&
(![X]:((~calm(X)&~creative(X))=>(funny(X)<~>~creative(X))))&
(![X]:((~rich(X)<~>~brave(X))=>(~tall(X)<~>brave(X))))&
(((happy(alice)|~brave(alice)))=>((wise(fred)<~>creative(fred))))&
(![X]:((~creative(X)&~patient(X))<=>tall(X)))&
(![X]:((~happy(X)<~>~patient(X))=>(~calm(X)&~brave(X))))&
(![X]:((~generous(X)<~>humble(X))<=>patient(X)))&
(((kind(fred)&curious(fred)))=>(?[X]:(~humble(X))))&
(![X]:(~tall(X)<=>(~funny(X)&~humble(X))))&
(![X]:((curious(X)&~funny(X))=>(~humble(X)|humble(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((~patient(X)|~brave(X)))))&
(![X]:((kind(X)<~>humble(X))=>(tall(X)<~>~funny(X))))&
(~creative(john))&
(~brave(fred))&
((~tall(mary)<~>humble(mary)))&
(?[X]:((curious(X)<~>~humble(X))))&
(?[X]:(curious(X)))&
(wise(susan)) | calm(alice) | [
"p1",
"p3",
"p4",
"p5",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6674854164577528543854224
% SZS output start Proof for 6674854164577528543854224
2. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> (~rich(X0) & old(X0))) [input p1]
4. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> (creative(X0) & brave(X0))) [input p3]
5. ! [X0] : ((~creative(X0) & ~calm(X0)) => (funny(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : ((~rich(X0) <~> ~brave(X0)) => (~tall(X0) <~> brave(X0))) [input p5]
8. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> tall(X0)) [input p7]
12. ! [X0] : (~tall(X0) <=> (~humble(X0) & ~funny(X0))) [input p11]
23. ~calm(alice) [input hypothesis]
29. ! [X0] : ((funny(X0) <~> ~creative(X0)) | (creative(X0) | calm(X0))) [ennf transformation 5]
30. ! [X0] : ((funny(X0) <~> ~creative(X0)) | creative(X0) | calm(X0)) [flattening 29]
31. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~rich(X0) <=> ~brave(X0))) [ennf transformation 6]
43. ! [X0] : (((~funny(X0) | ~strong(X0)) | (rich(X0) | ~old(X0))) & ((~rich(X0) & old(X0)) | (funny(X0) & strong(X0)))) [nnf transformation 2]
44. ! [X0] : ((~funny(X0) | ~strong(X0) | rich(X0) | ~old(X0)) & ((~rich(X0) & old(X0)) | (funny(X0) & strong(X0)))) [flattening 43]
46. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 4]
47. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [flattening 46]
48. ! [X0] : (((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | creative(X0) | calm(X0)) [nnf transformation 30]
49. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | ((~rich(X0) | brave(X0)) & (~brave(X0) | rich(X0)))) [nnf transformation 31]
51. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | (patient(X0) | creative(X0)))) [nnf transformation 8]
52. ! [X0] : (((~patient(X0) & ~creative(X0)) | ~tall(X0)) & (tall(X0) | patient(X0) | creative(X0))) [flattening 51]
57. ! [X0] : ((~tall(X0) | (humble(X0) | funny(X0))) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [nnf transformation 12]
58. ! [X0] : ((~tall(X0) | humble(X0) | funny(X0)) & ((~humble(X0) & ~funny(X0)) | tall(X0))) [flattening 57]
76. old(X0) | funny(X0) [cnf transformation 44]
78. ~rich(X0) | funny(X0) [cnf transformation 44]
83. brave(X0) | ~old(X0) | funny(X0) [cnf transformation 47]
85. creative(X0) | ~old(X0) | funny(X0) [cnf transformation 47]
89. creative(X0) | ~funny(X0) | creative(X0) | calm(X0) [cnf transformation 48]
92. ~brave(X0) | tall(X0) | ~brave(X0) | rich(X0) [cnf transformation 49]
99. ~tall(X0) | ~creative(X0) [cnf transformation 52]
110. ~funny(X0) | tall(X0) [cnf transformation 58]
132. ~calm(alice) [cnf transformation 23]
134. ~brave(X0) | tall(X0) | rich(X0) [duplicate literal removal 92]
135. creative(X0) | ~funny(X0) | calm(X0) [duplicate literal removal 89]
145. creative(X0) | funny(X0) [subsumption resolution 85,76]
147. brave(X0) | funny(X0) [subsumption resolution 83,76]
149. calm(X0) | creative(X0) [subsumption resolution 135,145]
246. creative(alice) [resolution 149,132]
384. tall(X1) | rich(X1) | funny(X1) [resolution 134,147]
395. tall(X1) | funny(X1) [subsumption resolution 384,78]
396. tall(X1) [subsumption resolution 395,110]
400. ~creative(X2) [resolution 396,99]
526. $false [resolution 400,246]
% SZS output end Proof for 6674854164577528543854224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then fred is both patient and not creative and vice versa.
Everyone who is humble or not wise is either kind or not curious and vice versa.
Everyone who is not funny or not calm is funny.
If lucy is both not creative and not kind then someone is either old or humble and vice versa.
If john is both rich and not funny then fred is humble or not tall and vice versa.
If someone is both not strong and humble then fred is old or humble and vice versa.
If paul is either strong or not strong then alice is both tall and curious.
Everyone who is not strong is kind.
If someone is either not strong or humble then john is not funny and vice versa.
Everyone who is not calm is creative or kind and vice versa.
Everyone who is not generous or generous is either rich or generous and vice versa.
Everyone who is wise or quiet is not kind and vice versa.
If susan is not brave or old then mary is not rich or patient.
Everyone who is not strong is not calm or rich.
Everyone who is not wise is both not rich and not calm and vice versa.
Everyone who is not calm is patient or strong.
John is both old and not wise.
John is old.
Mary is either tall or not strong.
Someone is either not patient or wise.
Fred is not patient or strong. | Fred is not humble. | entailment | ((?[X]:(wise(X)))<=>((patient(fred)&~creative(fred))))&
(![X]:((humble(X)|~wise(X))<=>(kind(X)<~>~curious(X))))&
(![X]:((~funny(X)|~calm(X))=>funny(X)))&
(((~creative(lucy)&~kind(lucy)))<=>(?[X]:((old(X)<~>humble(X)))))&
(((rich(john)&~funny(john)))<=>((humble(fred)|~tall(fred))))&
((?[X]:((~strong(X)&humble(X))))<=>((old(fred)|humble(fred))))&
(((strong(paul)<~>~strong(paul)))=>((tall(alice)&curious(alice))))&
(![X]:(~strong(X)=>kind(X)))&
((?[X]:((~strong(X)<~>humble(X))))<=>(~funny(john)))&
(![X]:(~calm(X)<=>(creative(X)|kind(X))))&
(![X]:((~generous(X)|generous(X))<=>(rich(X)<~>generous(X))))&
(![X]:((wise(X)|quiet(X))<=>~kind(X)))&
(((~brave(susan)|old(susan)))=>((~rich(mary)|patient(mary))))&
(![X]:(~strong(X)=>(~calm(X)|rich(X))))&
(![X]:(~wise(X)<=>(~rich(X)&~calm(X))))&
(![X]:(~calm(X)=>(patient(X)|strong(X))))&
((old(john)&~wise(john)))&
(old(john))&
((tall(mary)<~>~strong(mary)))&
(?[X]:((~patient(X)<~>wise(X))))&
((~patient(fred)|strong(fred))) | ~humble(fred) | [
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 7710049986723612820435909
% SZS output start Proof for 7710049986723612820435909
3. ! [X0] : ((~calm(X0) | ~funny(X0)) => funny(X0)) [input p2]
5. (~funny(john) & rich(john)) <=> (~tall(fred) | humble(fred)) [input p4]
22. humble(fred) [input hypothesis]
24. ! [X0] : (funny(X0) | (calm(X0) & funny(X0))) [ennf transformation 3]
45. ((~funny(john) & rich(john)) | (tall(fred) & ~humble(fred))) & ((~tall(fred) | humble(fred)) | (funny(john) | ~rich(john))) [nnf transformation 5]
46. ((~funny(john) & rich(john)) | (tall(fred) & ~humble(fred))) & (~tall(fred) | humble(fred) | funny(john) | ~rich(john)) [flattening 45]
78. funny(X0) | funny(X0) [cnf transformation 24]
89. ~funny(john) | ~humble(fred) [cnf transformation 46]
131. humble(fred) [cnf transformation 22]
140. funny(X0) [duplicate literal removal 78]
188. ~humble(fred) [subsumption resolution 89,140]
264. $false [subsumption resolution 131,188]
% SZS output end Proof for 7710049986723612820435909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or humble then alice is not rich. Everyone who is both not rich and not strong is either kind or not tall. Everyone who is both not old and not generous is both strong and tall. Everyone who is not strong is not rich. Everyone who is old is both brave and creative and vice versa. Everyone who is strong or creative is both not wise and old. Everyone who is either curious or not curious is either calm or not curious and vice versa. Everyone who is either happy or wise is kind or funny and vice versa. Everyone who is both calm and happy is either curious or not funny. If someone is happy then someone is not brave or not curious. If fred is either not creative or not patient then mary is kind and vice versa. Everyone who is brave is not old or not kind. If fred is both strong and generous then alice is both strong and not humble. Everyone who is happy or wise is not rich or humble. Everyone who is not calm is not old and vice versa. Everyone who is either not brave or kind is both kind and strong. Fred is both creative and not patient. Someone is not curious or creative. Paul is both not quiet and funny. Alice is brave or not old. Someone is patient. Someone is not strong or not funny. Mary is both not wise and not quiet. Someone is funny. | Mary is tall. | entailment | ((?[X]:((~generous(X)<~>humble(X))))=>(~rich(alice)))&
(![X]:((~rich(X)&~strong(X))=>(kind(X)<~>~tall(X))))&
(![X]:((~old(X)&~generous(X))=>(strong(X)&tall(X))))&
(![X]:(~strong(X)=>~rich(X)))&
(![X]:(old(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)|creative(X))=>(~wise(X)&old(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(calm(X)<~>~curious(X))))&
(![X]:((happy(X)<~>wise(X))<=>(kind(X)|funny(X))))&
(![X]:((calm(X)&happy(X))=>(curious(X)<~>~funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((~brave(X)|~curious(X)))))&
(((~creative(fred)<~>~patient(fred)))<=>(kind(mary)))&
(![X]:(brave(X)=>(~old(X)|~kind(X))))&
(((strong(fred)&generous(fred)))=>((strong(alice)&~humble(alice))))&
(![X]:((happy(X)|wise(X))=>(~rich(X)|humble(X))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:((~brave(X)<~>kind(X))=>(kind(X)&strong(X))))&
((creative(fred)&~patient(fred)))&
(?[X]:((~curious(X)|creative(X))))&
((~quiet(paul)&funny(paul)))&
((brave(alice)|~old(alice)))&
(?[X]:(patient(X)))&
(?[X]:((~strong(X)|~funny(X))))&
((~wise(mary)&~quiet(mary)))&
(?[X]:(funny(X))) | tall(mary) | [
"p1",
"p3",
"p4",
"p5",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 521804549126080536607268
% SZS output start Proof for 521804549126080536607268
2. ! [X0] : ((~strong(X0) & ~rich(X0)) => (kind(X0) <~> ~tall(X0))) [input p1]
4. ! [X0] : (~strong(X0) => ~rich(X0)) [input p3]
5. ! [X0] : (old(X0) <=> (creative(X0) & brave(X0))) [input p4]
6. ! [X0] : ((creative(X0) | strong(X0)) => (old(X0) & ~wise(X0))) [input p5]
11. (~creative(fred) <~> ~patient(fred)) <=> kind(mary) [input p10]
12. ! [X0] : (brave(X0) => (~kind(X0) | ~old(X0))) [input p11]
17. ~patient(fred) & creative(fred) [input p16]
25. ~tall(mary) [input hypothesis]
30. ! [X0] : ((kind(X0) <~> ~tall(X0)) | (strong(X0) | rich(X0))) [ennf transformation 2]
31. ! [X0] : ((kind(X0) <~> ~tall(X0)) | strong(X0) | rich(X0)) [flattening 30]
34. ! [X0] : (~rich(X0) | strong(X0)) [ennf transformation 4]
35. ! [X0] : ((old(X0) & ~wise(X0)) | (~creative(X0) & ~strong(X0))) [ennf transformation 6]
39. ! [X0] : ((~kind(X0) | ~old(X0)) | ~brave(X0)) [ennf transformation 12]
40. ! [X0] : (~kind(X0) | ~old(X0) | ~brave(X0)) [flattening 39]
47. ! [X0] : (((tall(X0) | ~kind(X0)) & (~tall(X0) | kind(X0))) | strong(X0) | rich(X0)) [nnf transformation 31]
48. ! [X0] : ((old(X0) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | ~old(X0))) [nnf transformation 5]
49. ! [X0] : ((old(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | ~old(X0))) [flattening 48]
57. (((patient(fred) | creative(fred)) & (~patient(fred) | ~creative(fred))) | ~kind(mary)) & (kind(mary) | ((~creative(fred) | patient(fred)) & (~patient(fred) | creative(fred)))) [nnf transformation 11]
71. ~kind(X0) | tall(X0) | strong(X0) | rich(X0) [cnf transformation 47]
74. ~rich(X0) | strong(X0) [cnf transformation 34]
75. ~old(X0) | brave(X0) [cnf transformation 49]
80. ~strong(X0) | old(X0) [cnf transformation 35]
100. kind(mary) | ~creative(fred) | patient(fred) [cnf transformation 57]
103. ~kind(X0) | ~old(X0) | ~brave(X0) [cnf transformation 40]
114. creative(fred) [cnf transformation 17]
115. ~patient(fred) [cnf transformation 17]
123. ~tall(mary) [cnf transformation 25]
159. 7 <=> kind(mary) [avatar definition]
160. kind(mary) <- (7) [avatar component clause 159]
163. 8 <=> creative(fred) [avatar definition]
167. 9 <=> patient(fred) [avatar definition]
172. 9 | ~8 | 7 [avatar split clause 100,159,163,167]
174. ~old(X0) | ~kind(X0) [subsumption resolution 103,75]
193. ~9 [avatar split clause 115,167]
194. 8 [avatar split clause 114,163]
328. tall(mary) | strong(mary) | rich(mary) <- (7) [resolution 71,160]
329. strong(mary) | rich(mary) <- (7) [subsumption resolution 328,123]
358. 35 <=> strong(mary) [avatar definition]
360. strong(mary) <- (35) [avatar component clause 358]
363. strong(mary) <- (7) [subsumption resolution 329,74]
364. 35 | ~7 [avatar split clause 363,159,358]
461. old(mary) <- (35) [resolution 360,80]
502. ~kind(mary) <- (35) [resolution 461,174]
506. $false <- (7, 35) [subsumption resolution 502,160]
507. ~7 | ~35 [avatar contradiction clause 506]
510. $false [avatar sat refutation 172,193,194,364,507]
% SZS output end Proof for 521804549126080536607268
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or patient then someone is not rich or not happy.
If someone is patient then fred is both not humble and brave.
Everyone who is tall or wise is not generous.
If fred is both brave and creative then alice is either strong or not kind and vice versa.
Everyone who is either not quiet or not calm is both generous and not strong and vice versa.
Everyone who is generous is both kind and not kind and vice versa.
Everyone who is both tall and not creative is either rich or old.
Everyone who is both not curious and rich is not wise or creative.
Everyone who is both kind and not old is not tall or not calm and vice versa.
If fred is either kind or calm then alice is not kind or not tall.
Everyone who is both creative and not curious is happy or rich and vice versa.
If someone is both not kind and tall then someone is not kind and vice versa.
Everyone who is either quiet or not old is either rich or generous and vice versa.
If someone is either not rich or generous then mary is patient and vice versa.
If john is calm then john is either not rich or kind.
If someone is not happy then john is both not happy and not generous and vice versa.
Someone is not old or rich.
Someone is not tall.
Someone is both happy and humble.
Susan is not funny.
Someone is creative.
Fred is both curious and not tall.
Mary is both not brave and not rich.
Someone is either tall or not quiet. | Mary is quiet. | entailment | ((?[X]:((~funny(X)<~>patient(X))))=>(?[X]:((~rich(X)|~happy(X)))))&
((?[X]:(patient(X)))=>((~humble(fred)&brave(fred))))&
(![X]:((tall(X)|wise(X))=>~generous(X)))&
(((brave(fred)&creative(fred)))<=>((strong(alice)<~>~kind(alice))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(generous(X)&~strong(X))))&
(![X]:(generous(X)<=>(kind(X)&~kind(X))))&
(![X]:((tall(X)&~creative(X))=>(rich(X)<~>old(X))))&
(![X]:((~curious(X)&rich(X))=>(~wise(X)|creative(X))))&
(![X]:((kind(X)&~old(X))<=>(~tall(X)|~calm(X))))&
(((kind(fred)<~>calm(fred)))=>((~kind(alice)|~tall(alice))))&
(![X]:((creative(X)&~curious(X))<=>(happy(X)|rich(X))))&
((?[X]:((~kind(X)&tall(X))))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)<~>~old(X))<=>(rich(X)<~>generous(X))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(patient(mary)))&
((calm(john))=>((~rich(john)<~>kind(john))))&
((?[X]:(~happy(X)))<=>((~happy(john)&~generous(john))))&
(?[X]:((~old(X)|rich(X))))&
(?[X]:(~tall(X)))&
(?[X]:((happy(X)&humble(X))))&
(~funny(susan))&
(?[X]:(creative(X)))&
((curious(fred)&~tall(fred)))&
((~brave(mary)&~rich(mary)))&
(?[X]:((tall(X)<~>~quiet(X)))) | quiet(mary) | [
"p4",
"p5",
"p8",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1110375853900230800518917
% SZS output start Proof for 1110375853900230800518917
5. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) <=> (~strong(X0) & generous(X0))) [input p4]
6. ! [X0] : (generous(X0) <=> (~kind(X0) & kind(X0))) [input p5]
9. ! [X0] : ((~old(X0) & kind(X0)) <=> (~calm(X0) | ~tall(X0))) [input p8]
13. ! [X0] : ((quiet(X0) <~> ~old(X0)) <=> (rich(X0) <~> generous(X0))) [input p12]
23. ~rich(mary) & ~brave(mary) [input p22]
25. ~quiet(mary) [input hypothesis]
44. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | (strong(X0) | ~generous(X0))) & ((~strong(X0) & generous(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [nnf transformation 5]
45. ! [X0] : ((((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | strong(X0) | ~generous(X0)) & ((~strong(X0) & generous(X0)) | ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))))) [flattening 44]
46. ! [X0] : ((generous(X0) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | ~generous(X0))) [nnf transformation 6]
47. ! [X0] : ((generous(X0) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | ~generous(X0))) [flattening 46]
49. ! [X0] : (((~old(X0) & kind(X0)) | (calm(X0) & tall(X0))) & ((~calm(X0) | ~tall(X0)) | (old(X0) | ~kind(X0)))) [nnf transformation 9]
50. ! [X0] : (((~old(X0) & kind(X0)) | (calm(X0) & tall(X0))) & (~calm(X0) | ~tall(X0) | old(X0) | ~kind(X0))) [flattening 49]
59. ! [X0] : ((((old(X0) | ~quiet(X0)) & (~old(X0) | quiet(X0))) | ((rich(X0) | ~generous(X0)) & (generous(X0) | ~rich(X0)))) & (((~generous(X0) | ~rich(X0)) & (generous(X0) | rich(X0))) | ((quiet(X0) | old(X0)) & (~old(X0) | ~quiet(X0))))) [nnf transformation 13]
92. ~calm(X0) | generous(X0) | quiet(X0) [cnf transformation 45]
98. kind(X0) | ~generous(X0) [cnf transformation 47]
99. ~kind(X0) | ~generous(X0) [cnf transformation 47]
107. ~old(X0) | calm(X0) [cnf transformation 50]
119. generous(X0) | rich(X0) | quiet(X0) | old(X0) [cnf transformation 59]
144. ~rich(mary) [cnf transformation 23]
147. ~quiet(mary) [cnf transformation 25]
195. ~generous(X0) [subsumption resolution 98,99]
233. old(X0) | quiet(X0) | rich(X0) [subsumption resolution 119,195]
322. calm(X1) | rich(X1) | quiet(X1) [resolution 233,107]
334. rich(X1) | quiet(X1) | generous(X1) | quiet(X1) [resolution 322,92]
335. rich(X1) | quiet(X1) | generous(X1) [duplicate literal removal 334]
337. quiet(X1) | rich(X1) [subsumption resolution 335,195]
340. rich(mary) [resolution 337,147]
345. $false [subsumption resolution 340,144]
% SZS output end Proof for 1110375853900230800518917
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
If someone is funny or generous then mary is tall or not patient.
If someone is either humble or tall then alice is quiet and vice versa.
If alice is both not old and rich then someone is both patient and not quiet.
Everyone who is either rich or not humble is not calm and vice versa.
Everyone who is both humble and not curious is either humble or not calm.
If alice is either not funny or patient then someone is both brave and wise.
If mary is not patient then someone is tall and vice versa.
If fred is both kind and not curious then alice is both not quiet and creative and vice versa.
Everyone who is either not wise or not strong is not humble or tall.
Everyone who is curious or not humble is both not funny and old.
Everyone who is both not patient and not quiet is both strong and brave.
Everyone who is either rich or quiet is brave or kind and vice versa.
Everyone who is quiet or happy is both not old and rich and vice versa.
Paul is both calm and kind.
John is both not kind and curious.
Someone is calm.
Mary is either not humble or not brave.
Someone is either happy or wise.
Someone is not rich. | Mary is not creative. | neutral | (![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((funny(X)|generous(X))))=>((tall(mary)|~patient(mary))))&
((?[X]:((humble(X)<~>tall(X))))<=>(quiet(alice)))&
(((~old(alice)&rich(alice)))=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~humble(X))<=>~calm(X)))&
(![X]:((humble(X)&~curious(X))=>(humble(X)<~>~calm(X))))&
(((~funny(alice)<~>patient(alice)))=>(?[X]:((brave(X)&wise(X)))))&
((~patient(mary))<=>(?[X]:(tall(X))))&
(((kind(fred)&~curious(fred)))<=>((~quiet(alice)&creative(alice))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)|tall(X))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)&old(X))))&
(![X]:((~patient(X)&~quiet(X))=>(strong(X)&brave(X))))&
(![X]:((rich(X)<~>quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((quiet(X)|happy(X))<=>(~old(X)&rich(X))))&
((calm(paul)&kind(paul)))&
((~kind(john)&curious(john)))&
(?[X]:(calm(X)))&
((~humble(mary)<~>~brave(mary)))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:(~rich(X))) | ~creative(mary) | [] | null | 0 |
If someone is both happy and funny then susan is kind and vice versa. If susan is not tall then john is both curious and calm and vice versa. Everyone who is both kind and not creative is either generous or humble and vice versa. Everyone who is not creative is both not curious and wise and vice versa. Everyone who is not rich or not generous is happy or not happy and vice versa. Everyone who is either wise or old is either not old or generous. If fred is curious then someone is rich. If mary is both not strong and creative then someone is either not generous or humble and vice versa. If someone is not strong or not old then someone is either not curious or creative and vice versa. If someone is wise then someone is not happy or patient and vice versa. Everyone who is not patient or funny is not patient. Everyone who is not wise is not quiet or not rich. Everyone who is either old or calm is quiet and vice versa. Everyone who is creative or not creative is not tall and vice versa. If fred is not brave then someone is either not tall or brave. Everyone who is curious or not rich is not humble or not tall. Someone is calm. Paul is not generous or brave. Alice is happy. Someone is curious or not tall. Alice is not old. Lucy is either happy or not creative. Someone is creative. | Lucy is strong. | neutral | ((?[X]:((happy(X)&funny(X))))<=>(kind(susan)))&
((~tall(susan))<=>((curious(john)&calm(john))))&
(![X]:((kind(X)&~creative(X))<=>(generous(X)<~>humble(X))))&
(![X]:(~creative(X)<=>(~curious(X)&wise(X))))&
(![X]:((~rich(X)|~generous(X))<=>(happy(X)|~happy(X))))&
(![X]:((wise(X)<~>old(X))=>(~old(X)<~>generous(X))))&
((curious(fred))=>(?[X]:(rich(X))))&
(((~strong(mary)&creative(mary)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
((?[X]:((~strong(X)|~old(X))))<=>(?[X]:((~curious(X)<~>creative(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~patient(X)|funny(X))=>~patient(X)))&
(![X]:(~wise(X)=>(~quiet(X)|~rich(X))))&
(![X]:((old(X)<~>calm(X))<=>quiet(X)))&
(![X]:((creative(X)|~creative(X))<=>~tall(X)))&
((~brave(fred))=>(?[X]:((~tall(X)<~>brave(X)))))&
(![X]:((curious(X)|~rich(X))=>(~humble(X)|~tall(X))))&
(?[X]:(calm(X)))&
((~generous(paul)|brave(paul)))&
(happy(alice))&
(?[X]:((curious(X)|~tall(X))))&
(~old(alice))&
((happy(lucy)<~>~creative(lucy)))&
(?[X]:(creative(X))) | strong(lucy) | [] | null | 0 |
If paul is not wise or tall then susan is either not patient or kind.
Everyone who is not tall is rich or tall and vice versa.
If someone is rich then someone is not calm or rich and vice versa.
Everyone who is creative or not curious is either not kind or wise and vice versa.
If someone is not brave or not quiet then someone is not humble or not strong.
If alice is either kind or not creative then someone is tall.
Everyone who is tall is not quiet.
Everyone who is both not humble and not patient is both calm and generous and vice versa.
If someone is both not tall and not calm then john is not wise or calm.
If someone is both not tall and creative then mary is both tall and not quiet and vice versa.
If susan is both not curious and not kind then susan is not curious or not generous.
Everyone who is both not humble and not creative is both not humble and patient and vice versa.
Everyone who is both wise and not curious is either not tall or not strong and vice versa.
If someone is either not rich or creative then someone is either not strong or quiet and vice versa.
Everyone who is either happy or strong is either not curious or brave and vice versa.
Everyone who is either not quiet or rich is both not patient and not curious and vice versa.
Lucy is not strong.
Someone is not patient or not strong.
Alice is not curious or strong.
John is happy.
Someone is curious or happy.
Someone is not calm.
Someone is old. | Susan is not strong. | neutral | (((~wise(paul)|tall(paul)))=>((~patient(susan)<~>kind(susan))))&
(![X]:(~tall(X)<=>(rich(X)|tall(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:((creative(X)|~curious(X))<=>(~kind(X)<~>wise(X))))&
((?[X]:((~brave(X)|~quiet(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(((kind(alice)<~>~creative(alice)))=>(?[X]:(tall(X))))&
(![X]:(tall(X)=>~quiet(X)))&
(![X]:((~humble(X)&~patient(X))<=>(calm(X)&generous(X))))&
((?[X]:((~tall(X)&~calm(X))))=>((~wise(john)|calm(john))))&
((?[X]:((~tall(X)&creative(X))))<=>((tall(mary)&~quiet(mary))))&
(((~curious(susan)&~kind(susan)))=>((~curious(susan)|~generous(susan))))&
(![X]:((~humble(X)&~creative(X))<=>(~humble(X)&patient(X))))&
(![X]:((wise(X)&~curious(X))<=>(~tall(X)<~>~strong(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>strong(X))<=>(~curious(X)<~>brave(X))))&
(![X]:((~quiet(X)<~>rich(X))<=>(~patient(X)&~curious(X))))&
(~strong(lucy))&
(?[X]:((~patient(X)|~strong(X))))&
((~curious(alice)|strong(alice)))&
(happy(john))&
(?[X]:((curious(X)|happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:(old(X))) | ~strong(susan) | [] | null | 0 |
Everyone who is either not old or old is not brave or not rich. If john is not humble then mary is either not humble or humble. If someone is both rich and quiet then someone is either wise or not happy and vice versa. Everyone who is not creative or not patient is both humble and not brave and vice versa. If mary is not kind then mary is either not wise or not generous and vice versa. Everyone who is either not creative or strong is either not creative or not brave and vice versa. Everyone who is not happy is both curious and tall. Everyone who is not rich is old or kind and vice versa. If someone is not old or humble then mary is either brave or not brave and vice versa. Everyone who is calm or not brave is both not calm and rich. Everyone who is rich is either generous or not rich. Everyone who is rich is either creative or generous. If paul is either not strong or brave then john is funny or not patient and vice versa. If mary is not humble or tall then susan is not curious and vice versa. Everyone who is not quiet or not rich is either not happy or funny and vice versa. If lucy is either patient or curious then someone is both wise and brave and vice versa. Someone is both not rich and not tall. Someone is either not wise or generous. Someone is strong or not wise. Mary is either quiet or patient. Someone is either not creative or old. Someone is either not funny or not old. Someone is not generous. | John is not patient. | contradiction | (![X]:((~old(X)<~>old(X))=>(~brave(X)|~rich(X))))&
((~humble(john))=>((~humble(mary)<~>humble(mary))))&
((?[X]:((rich(X)&quiet(X))))<=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((~creative(X)|~patient(X))<=>(humble(X)&~brave(X))))&
((~kind(mary))<=>((~wise(mary)<~>~generous(mary))))&
(![X]:((~creative(X)<~>strong(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~happy(X)=>(curious(X)&tall(X))))&
(![X]:(~rich(X)<=>(old(X)|kind(X))))&
((?[X]:((~old(X)|humble(X))))<=>((brave(mary)<~>~brave(mary))))&
(![X]:((calm(X)|~brave(X))=>(~calm(X)&rich(X))))&
(![X]:(rich(X)=>(generous(X)<~>~rich(X))))&
(![X]:(rich(X)=>(creative(X)<~>generous(X))))&
(((~strong(paul)<~>brave(paul)))<=>((funny(john)|~patient(john))))&
(((~humble(mary)|tall(mary)))<=>(~curious(susan)))&
(![X]:((~quiet(X)|~rich(X))<=>(~happy(X)<~>funny(X))))&
(((patient(lucy)<~>curious(lucy)))<=>(?[X]:((wise(X)&brave(X)))))&
(?[X]:((~rich(X)&~tall(X))))&
(?[X]:((~wise(X)<~>generous(X))))&
(?[X]:((strong(X)|~wise(X))))&
((quiet(mary)<~>patient(mary)))&
(?[X]:((~creative(X)<~>old(X))))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:(~generous(X))) | ~patient(john) | [
"p3",
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3910050573092107321534356
% SZS output start Proof for 3910050573092107321534356
4. ! [X0] : ((~patient(X0) | ~creative(X0)) <=> (~brave(X0) & humble(X0))) [input p3]
6. ! [X0] : ((~creative(X0) <~> strong(X0)) <=> (~creative(X0) <~> ~brave(X0))) [input p5]
13. (~strong(paul) <~> brave(paul)) <=> (~patient(john) | funny(john)) [input p12]
24. ~patient(john) [input hypothesis]
41. ! [X0] : (((~patient(X0) | ~creative(X0)) | (brave(X0) | ~humble(X0))) & ((~brave(X0) & humble(X0)) | (patient(X0) & creative(X0)))) [nnf transformation 4]
42. ! [X0] : ((~patient(X0) | ~creative(X0) | brave(X0) | ~humble(X0)) & ((~brave(X0) & humble(X0)) | (patient(X0) & creative(X0)))) [flattening 41]
44. ! [X0] : ((((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((~creative(X0) | ~strong(X0)) & (strong(X0) | creative(X0))))) [nnf transformation 6]
53. (((~brave(paul) | strong(paul)) & (brave(paul) | ~strong(paul))) | (patient(john) & ~funny(john))) & ((~patient(john) | funny(john)) | ((~strong(paul) | ~brave(paul)) & (brave(paul) | strong(paul)))) [nnf transformation 13]
54. (((~brave(paul) | strong(paul)) & (brave(paul) | ~strong(paul))) | (patient(john) & ~funny(john))) & (~patient(john) | funny(john) | ((~strong(paul) | ~brave(paul)) & (brave(paul) | strong(paul)))) [flattening 53]
91. ~brave(X0) | creative(X0) [cnf transformation 42]
99. ~brave(X0) | ~creative(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 44]
100. brave(X0) | creative(X0) | strong(X0) | creative(X0) [cnf transformation 44]
103. strong(X0) | ~creative(X0) | ~creative(X0) | brave(X0) [cnf transformation 44]
125. brave(paul) | ~strong(paul) | patient(john) [cnf transformation 54]
127. ~brave(paul) | strong(paul) | patient(john) [cnf transformation 54]
155. ~patient(john) [cnf transformation 24]
159. ~brave(X0) | ~creative(X0) | ~strong(X0) [duplicate literal removal 99]
160. brave(X0) | creative(X0) | strong(X0) [duplicate literal removal 100]
161. strong(X0) | ~creative(X0) | brave(X0) [duplicate literal removal 103]
213. brave(X0) | strong(X0) [subsumption resolution 160,161]
214. ~brave(X0) | ~strong(X0) [subsumption resolution 159,91]
230. strong(paul) | patient(john) [subsumption resolution 127,213]
232. 14 <=> patient(john) [avatar definition]
236. 15 <=> strong(paul) [avatar definition]
239. 14 | 15 [avatar split clause 230,236,232]
246. ~strong(paul) | patient(john) [subsumption resolution 125,214]
247. 14 | ~15 [avatar split clause 246,236,232]
339. ~14 [avatar split clause 155,232]
340. $false [avatar sat refutation 239,247,339]
% SZS output end Proof for 3910050573092107321534356
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or not kind then alice is both generous and brave. If john is patient then someone is quiet or curious. Everyone who is both not rich and brave is both not funny and happy and vice versa. Everyone who is not tall or not curious is both strong and not patient. Everyone who is brave or not wise is both rich and not patient. If lucy is either not old or not happy then susan is either humble or not curious and vice versa. Everyone who is brave or not rich is both not strong and humble and vice versa. If someone is either not quiet or old then someone is not patient or wise and vice versa. If someone is both not calm and rich then someone is either not creative or curious and vice versa. Everyone who is both happy and quiet is both not wise and humble. If someone is not humble or calm then lucy is both not generous and not old and vice versa. Everyone who is both not strong and happy is not humble or not patient. Everyone who is not strong or not curious is not brave. If mary is kind then john is old or not happy. If lucy is either not strong or curious then someone is either kind or old and vice versa. If someone is either not happy or old then paul is calm and vice versa. Someone is both not humble and rich. John is both funny and not calm. Paul is either kind or not kind. Mary is not calm. Someone is both not quiet and not humble. Mary is both generous and not brave. John is not kind or not wise. Someone is not generous or patient. | Mary is calm. | contradiction | ((?[X]:((~generous(X)<~>~kind(X))))=>((generous(alice)&brave(alice))))&
((patient(john))=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~rich(X)&brave(X))<=>(~funny(X)&happy(X))))&
(![X]:((~tall(X)|~curious(X))=>(strong(X)&~patient(X))))&
(![X]:((brave(X)|~wise(X))=>(rich(X)&~patient(X))))&
(((~old(lucy)<~>~happy(lucy)))<=>((humble(susan)<~>~curious(susan))))&
(![X]:((brave(X)|~rich(X))<=>(~strong(X)&humble(X))))&
((?[X]:((~quiet(X)<~>old(X))))<=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((~calm(X)&rich(X))))<=>(?[X]:((~creative(X)<~>curious(X)))))&
(![X]:((happy(X)&quiet(X))=>(~wise(X)&humble(X))))&
((?[X]:((~humble(X)|calm(X))))<=>((~generous(lucy)&~old(lucy))))&
(![X]:((~strong(X)&happy(X))=>(~humble(X)|~patient(X))))&
(![X]:((~strong(X)|~curious(X))=>~brave(X)))&
((kind(mary))=>((old(john)|~happy(john))))&
(((~strong(lucy)<~>curious(lucy)))<=>(?[X]:((kind(X)<~>old(X)))))&
((?[X]:((~happy(X)<~>old(X))))<=>(calm(paul)))&
(?[X]:((~humble(X)&rich(X))))&
((funny(john)&~calm(john)))&
((kind(paul)<~>~kind(paul)))&
(~calm(mary))&
(?[X]:((~quiet(X)&~humble(X))))&
((generous(mary)&~brave(mary)))&
((~kind(john)|~wise(john)))&
(?[X]:((~generous(X)|patient(X)))) | calm(mary) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2453554831250626029173879
% SZS output start Proof for 2453554831250626029173879
20. ~calm(mary) [input p19]
25. calm(mary) [input hypothesis]
147. ~calm(mary) [cnf transformation 20]
154. calm(mary) [cnf transformation 25]
368. $false [subsumption resolution 154,147]
% SZS output end Proof for 2453554831250626029173879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or generous is patient.
If someone is not patient then fred is both not old and not tall and vice versa.
Everyone who is either old or generous is both creative and brave.
Everyone who is both quiet and curious is not patient or not brave.
Everyone who is not quiet or not creative is either curious or not rich.
If susan is both not humble and not old then mary is not happy and vice versa.
Everyone who is both not funny and not old is humble and vice versa.
If mary is either not strong or happy then someone is both not quiet and not humble and vice versa.
Everyone who is both happy and not patient is not generous or not patient and vice versa.
Everyone who is both not creative and not patient is not happy or strong and vice versa.
Everyone who is either not tall or rich is either patient or old and vice versa.
Everyone who is both curious and patient is not happy or funny and vice versa.
Everyone who is happy or not generous is not creative and vice versa.
If mary is creative then someone is either rich or not humble and vice versa.
If mary is both not curious and creative then lucy is either not generous or not kind.
If someone is not funny or not creative then someone is either tall or old.
Someone is not generous or not calm.
Paul is old or funny.
Someone is either wise or not strong.
Fred is both happy and kind.
Someone is not brave or wise.
Fred is either not wise or curious. | Mary is tall. | contradiction | (![X]:((~old(X)|generous(X))=>patient(X)))&
((?[X]:(~patient(X)))<=>((~old(fred)&~tall(fred))))&
(![X]:((old(X)<~>generous(X))=>(creative(X)&brave(X))))&
(![X]:((quiet(X)&curious(X))=>(~patient(X)|~brave(X))))&
(![X]:((~quiet(X)|~creative(X))=>(curious(X)<~>~rich(X))))&
(((~humble(susan)&~old(susan)))<=>(~happy(mary)))&
(![X]:((~funny(X)&~old(X))<=>humble(X)))&
(((~strong(mary)<~>happy(mary)))<=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:((happy(X)&~patient(X))<=>(~generous(X)|~patient(X))))&
(![X]:((~creative(X)&~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(patient(X)<~>old(X))))&
(![X]:((curious(X)&patient(X))<=>(~happy(X)|funny(X))))&
(![X]:((happy(X)|~generous(X))<=>~creative(X)))&
((creative(mary))<=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~curious(mary)&creative(mary)))=>((~generous(lucy)<~>~kind(lucy))))&
((?[X]:((~funny(X)|~creative(X))))=>(?[X]:((tall(X)<~>old(X)))))&
(?[X]:((~generous(X)|~calm(X))))&
((old(paul)|funny(paul)))&
(?[X]:((wise(X)<~>~strong(X))))&
((happy(fred)&kind(fred)))&
(?[X]:((~brave(X)|wise(X))))&
((~wise(fred)<~>curious(fred))) | tall(mary) | [
"p0",
"p1",
"p2",
"p6",
"p8",
"p9",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2670435618077376510894432
% SZS output start Proof for 2670435618077376510894432
1. ! [X0] : ((generous(X0) | ~old(X0)) => patient(X0)) [input p0]
2. ? [X0] : ~patient(X0) <=> (~tall(fred) & ~old(fred)) [input p1]
3. ! [X0] : ((old(X0) <~> generous(X0)) => (brave(X0) & creative(X0))) [input p2]
7. ! [X0] : ((~old(X0) & ~funny(X0)) <=> humble(X0)) [input p6]
9. ! [X0] : ((~patient(X0) & happy(X0)) <=> (~patient(X0) | ~generous(X0))) [input p8]
10. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (strong(X0) | ~happy(X0))) [input p9]
11. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> (patient(X0) <~> old(X0))) [input p10]
13. ! [X0] : ((~generous(X0) | happy(X0)) <=> ~creative(X0)) [input p12]
14. creative(mary) <=> ? [X0] : (rich(X0) <~> ~humble(X0)) [input p13]
23. tall(mary) [input hypothesis]
26. ! [X0] : (patient(X0) | (~generous(X0) & old(X0))) [ennf transformation 1]
27. ! [X0] : ((brave(X0) & creative(X0)) | (old(X0) <=> generous(X0))) [ennf transformation 3]
34. (? [X0] : ~patient(X0) | (tall(fred) | old(fred))) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [nnf transformation 2]
35. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X0] : patient(X0)) [flattening 34]
36. (? [X0] : ~patient(X0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [rectify 35]
37. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
38. (~patient(sK0) | tall(fred) | old(fred)) & ((~tall(fred) & ~old(fred)) | ! [X1] : patient(X1)) [skolemisation 36,37]
39. ! [X0] : ((brave(X0) & creative(X0)) | ((old(X0) | ~generous(X0)) & (generous(X0) | ~old(X0)))) [nnf transformation 27]
43. ! [X0] : (((~old(X0) & ~funny(X0)) | ~humble(X0)) & (humble(X0) | (old(X0) | funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((~old(X0) & ~funny(X0)) | ~humble(X0)) & (humble(X0) | old(X0) | funny(X0))) [flattening 43]
49. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & ((~patient(X0) | ~generous(X0)) | (patient(X0) | ~happy(X0)))) [nnf transformation 9]
50. ! [X0] : (((~patient(X0) & happy(X0)) | (patient(X0) & generous(X0))) & (~patient(X0) | ~generous(X0) | patient(X0) | ~happy(X0))) [flattening 49]
51. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | (patient(X0) | creative(X0)))) [nnf transformation 10]
52. ! [X0] : (((~patient(X0) & ~creative(X0)) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | patient(X0) | creative(X0))) [flattening 51]
53. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 11]
56. ! [X0] : (((~generous(X0) | happy(X0)) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [nnf transformation 13]
57. ! [X0] : ((~generous(X0) | happy(X0) | creative(X0)) & (~creative(X0) | (generous(X0) & ~happy(X0)))) [flattening 56]
58. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X0] : ((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | ~creative(mary)) [nnf transformation 14]
59. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) | ~creative(mary)) [rectify 58]
60. ? [X1] : ((humble(X1) | ~rich(X1)) & (~humble(X1) | rich(X1))) => ((humble(sK2) | ~rich(sK2)) & (~humble(sK2) | rich(sK2))) [choice axiom]
61. (creative(mary) | ! [X0] : ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0)))) & (((humble(sK2) | ~rich(sK2)) & (~humble(sK2) | rich(sK2))) | ~creative(mary)) [skolemisation 59,60]
73. patient(X0) | old(X0) [cnf transformation 26]
74. ~generous(X0) | patient(X0) [cnf transformation 26]
75. ~old(fred) | patient(X1) [cnf transformation 38]
76. ~tall(fred) | patient(X1) [cnf transformation 38]
77. ~patient(sK0) | tall(fred) | old(fred) [cnf transformation 38]
78. ~old(X0) | generous(X0) | creative(X0) [cnf transformation 39]
79. ~generous(X0) | old(X0) | creative(X0) [cnf transformation 39]
92. ~humble(X0) | ~old(X0) [cnf transformation 44]
101. happy(X0) | patient(X0) [cnf transformation 50]
102. ~patient(X0) | generous(X0) [cnf transformation 50]
107. ~patient(X0) | happy(X0) [cnf transformation 52]
112. ~rich(X0) | ~patient(X0) | ~tall(X0) | ~old(X0) [cnf transformation 53]
122. ~creative(X0) | ~happy(X0) [cnf transformation 57]
128. creative(mary) | rich(X0) | humble(X0) [cnf transformation 61]
143. tall(mary) [cnf transformation 23]
145. 1 <=> old(fred) [avatar definition]
149. 2 <=> tall(fred) [avatar definition]
153. 3 <=> patient(sK0) [avatar definition]
155. ~patient(sK0) <- (~3) [avatar component clause 153]
156. 1 | 2 | ~3 [avatar split clause 77,153,149,145]
158. 4 <=> ! [X1] : patient(X1) [avatar definition]
159. patient(X1) <- (4) [avatar component clause 158]
160. 4 | ~2 [avatar split clause 76,149,158]
161. 4 | ~1 [avatar split clause 75,145,158]
198. happy(X0) [subsumption resolution 107,101]
205. ~creative(X0) [subsumption resolution 122,198]
206. humble(X0) | rich(X0) [subsumption resolution 128,205]
265. old(sK0) <- (~3) [resolution 73,155]
275. ~old(X0) | rich(X0) [resolution 206,92]
280. generous(sK0) | creative(sK0) <- (~3) [resolution 78,265]
282. generous(sK0) <- (~3) [subsumption resolution 280,205]
307. patient(sK0) <- (~3) [resolution 282,74]
308. $false <- (~3) [subsumption resolution 307,155]
309. 3 [avatar contradiction clause 308]
310. generous(X0) <- (4) [resolution 159,102]
312. old(X1) | creative(X1) <- (4) [resolution 310,79]
314. old(X1) <- (4) [subsumption resolution 312,205]
386. rich(X0) <- (4) [resolution 275,314]
404. ~patient(X1) | ~tall(X1) | ~old(X1) <- (4) [resolution 386,112]
409. ~tall(X1) | ~old(X1) <- (4) [subsumption resolution 404,159]
410. ~tall(X1) <- (4) [subsumption resolution 409,314]
425. $false <- (4) [resolution 410,143]
426. ~4 [avatar contradiction clause 425]
427. $false [avatar sat refutation 156,160,161,309,426]
% SZS output end Proof for 2670435618077376510894432
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is calm or funny then someone is not patient and vice versa.
If susan is not happy or not funny then susan is calm.
Everyone who is old or not calm is not funny.
Everyone who is both wise and creative is old or not brave.
Everyone who is tall or not strong is either not calm or old.
If alice is brave then someone is not calm and vice versa.
If fred is not strong or patient then someone is either not old or not happy.
If john is both tall and not strong then alice is calm or quiet and vice versa.
If someone is quiet or tall then someone is funny.
If john is both not brave and humble then lucy is either not kind or not humble.
If someone is wise then lucy is both happy and not patient and vice versa.
Everyone who is not quiet is either not funny or tall.
If someone is humble or generous then someone is either rich or not creative.
If paul is not rich or not quiet then someone is not happy and vice versa.
If someone is wise or not rich then susan is not funny and vice versa.
If someone is either strong or not patient then someone is both not curious and not creative.
John is either not funny or tall.
Someone is calm.
Someone is either tall or quiet.
Someone is not curious.
Someone is both brave and not humble.
John is both kind and creative.
Someone is both funny and not humble.
Someone is both tall and not kind. | Alice is not brave. | contradiction | (((calm(lucy)|funny(lucy)))<=>(?[X]:(~patient(X))))&
(((~happy(susan)|~funny(susan)))=>(calm(susan)))&
(![X]:((old(X)|~calm(X))=>~funny(X)))&
(![X]:((wise(X)&creative(X))=>(old(X)|~brave(X))))&
(![X]:((tall(X)|~strong(X))=>(~calm(X)<~>old(X))))&
((brave(alice))<=>(?[X]:(~calm(X))))&
(((~strong(fred)|patient(fred)))=>(?[X]:((~old(X)<~>~happy(X)))))&
(((tall(john)&~strong(john)))<=>((calm(alice)|quiet(alice))))&
((?[X]:((quiet(X)|tall(X))))=>(?[X]:(funny(X))))&
(((~brave(john)&humble(john)))=>((~kind(lucy)<~>~humble(lucy))))&
((?[X]:(wise(X)))<=>((happy(lucy)&~patient(lucy))))&
(![X]:(~quiet(X)=>(~funny(X)<~>tall(X))))&
((?[X]:((humble(X)|generous(X))))=>(?[X]:((rich(X)<~>~creative(X)))))&
(((~rich(paul)|~quiet(paul)))<=>(?[X]:(~happy(X))))&
((?[X]:((wise(X)|~rich(X))))<=>(~funny(susan)))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~curious(X)&~creative(X)))))&
((~funny(john)<~>tall(john)))&
(?[X]:(calm(X)))&
(?[X]:((tall(X)<~>quiet(X))))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)&~humble(X))))&
((kind(john)&creative(john)))&
(?[X]:((funny(X)&~humble(X))))&
(?[X]:((tall(X)&~kind(X)))) | ~brave(alice) | [
"p2",
"p4",
"p5",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3860491018967215803288770
% SZS output start Proof for 3860491018967215803288770
3. ! [X0] : ((~calm(X0) | old(X0)) => ~funny(X0)) [input p2]
5. ! [X0] : ((~strong(X0) | tall(X0)) => (~calm(X0) <~> old(X0))) [input p4]
6. brave(alice) <=> ? [X0] : ~calm(X0) [input p5]
8. (~strong(john) & tall(john)) <=> (quiet(alice) | calm(alice)) [input p7]
17. ~funny(john) <~> tall(john) [input p16]
25. ~brave(alice) [input hypothesis]
33. ! [X0] : (~funny(X0) | (calm(X0) & ~old(X0))) [ennf transformation 3]
36. ! [X0] : ((~calm(X0) <~> old(X0)) | (strong(X0) & ~tall(X0))) [ennf transformation 5]
49. ! [X0] : (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | (strong(X0) & ~tall(X0))) [nnf transformation 36]
50. (brave(alice) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ~brave(alice)) [nnf transformation 6]
51. (brave(alice) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ~brave(alice)) [rectify 50]
52. ? [X1] : ~calm(X1) => ~calm(sK1) [choice axiom]
53. (brave(alice) | ! [X0] : calm(X0)) & (~calm(sK1) | ~brave(alice)) [skolemisation 51,52]
57. ((~strong(john) & tall(john)) | (~quiet(alice) & ~calm(alice))) & ((quiet(alice) | calm(alice)) | (strong(john) | ~tall(john))) [nnf transformation 8]
58. ((~strong(john) & tall(john)) | (~quiet(alice) & ~calm(alice))) & (quiet(alice) | calm(alice) | strong(john) | ~tall(john)) [flattening 57]
86. (~tall(john) | funny(john)) & (tall(john) | ~funny(john)) [nnf transformation 17]
103. ~old(X0) | ~funny(X0) [cnf transformation 33]
106. ~tall(X0) | ~calm(X0) | old(X0) [cnf transformation 49]
111. brave(alice) | calm(X0) [cnf transformation 53]
117. tall(john) | ~calm(alice) [cnf transformation 58]
141. ~tall(john) | funny(john) [cnf transformation 86]
153. ~brave(alice) [cnf transformation 25]
187. 8 <=> ! [X0] : calm(X0) [avatar definition]
188. calm(X0) <- (8) [avatar component clause 187]
190. 9 <=> brave(alice) [avatar definition]
193. 8 | 9 [avatar split clause 111,190,187]
229. 17 <=> calm(alice) [avatar definition]
231. ~calm(alice) <- (~17) [avatar component clause 229]
234. 18 <=> tall(john) [avatar definition]
236. tall(john) <- (18) [avatar component clause 234]
238. ~17 | 18 [avatar split clause 117,234,229]
346. 43 <=> funny(john) [avatar definition]
348. funny(john) <- (43) [avatar component clause 346]
349. 43 | ~18 [avatar split clause 141,234,346]
361. ~9 [avatar split clause 153,190]
362. $false <- (8, ~17) [resolution 231,188]
363. ~8 | 17 [avatar contradiction clause 362]
369. ~calm(john) | old(john) <- (18) [resolution 106,236]
372. old(john) <- (8, 18) [subsumption resolution 369,188]
389. ~funny(john) <- (8, 18) [resolution 372,103]
390. $false <- (8, 18, 43) [subsumption resolution 389,348]
391. ~8 | ~18 | ~43 [avatar contradiction clause 390]
392. $false [avatar sat refutation 193,238,349,361,363,391]
% SZS output end Proof for 3860491018967215803288770
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind is both not funny and strong. Everyone who is either not curious or not creative is either not curious or wise. Everyone who is not strong is either not tall or not wise and vice versa. If someone is not wise or not old then paul is quiet or brave. If someone is old or curious then mary is either not calm or old and vice versa. If susan is either not kind or calm then someone is tall or brave and vice versa. If susan is either curious or not patient then mary is both strong and not curious. Everyone who is both not patient and not strong is either generous or not brave and vice versa. Everyone who is either not humble or not curious is wise. Everyone who is old or happy is not old. Everyone who is not humble is old or not old. If someone is humble then mary is both rich and kind and vice versa. If someone is either not happy or not brave then someone is both not quiet and happy and vice versa. If someone is either kind or tall then alice is not funny. Everyone who is not strong is generous. If susan is both not calm and calm then someone is strong and vice versa. Alice is both calm and not patient. Someone is patient or tall. Mary is both funny and not calm. Someone is not brave. Someone is creative or generous. Fred is not brave. Someone is either not kind or creative. | Mary is not generous. | contradiction | (![X]:(kind(X)=>(~funny(X)&strong(X))))&
(![X]:((~curious(X)<~>~creative(X))=>(~curious(X)<~>wise(X))))&
(![X]:(~strong(X)<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~wise(X)|~old(X))))=>((quiet(paul)|brave(paul))))&
((?[X]:((old(X)|curious(X))))<=>((~calm(mary)<~>old(mary))))&
(((~kind(susan)<~>calm(susan)))<=>(?[X]:((tall(X)|brave(X)))))&
(((curious(susan)<~>~patient(susan)))=>((strong(mary)&~curious(mary))))&
(![X]:((~patient(X)&~strong(X))<=>(generous(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
(![X]:(~strong(X)=>generous(X)))&
(((~calm(susan)&calm(susan)))<=>(?[X]:(strong(X))))&
((calm(alice)&~patient(alice)))&
(?[X]:((patient(X)|tall(X))))&
((funny(mary)&~calm(mary)))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X)))) | ~generous(mary) | [
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5952608163679191903125021
% SZS output start Proof for 5952608163679191903125021
15. ! [X0] : (~strong(X0) => generous(X0)) [input p14]
16. (calm(susan) & ~calm(susan)) <=> ? [X0] : strong(X0) [input p15]
24. ~generous(mary) [input hypothesis]
36. ! [X0] : (generous(X0) | strong(X0)) [ennf transformation 15]
62. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | (~calm(susan) | calm(susan))) [nnf transformation 16]
63. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | ~calm(susan) | calm(susan)) [flattening 62]
64. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | ~calm(susan) | calm(susan)) [rectify 63]
65. ? [X1] : strong(X1) => strong(sK5) [choice axiom]
66. ((calm(susan) & ~calm(susan)) | ! [X0] : ~strong(X0)) & (strong(sK5) | ~calm(susan) | calm(susan)) [skolemisation 64,65]
126. generous(X0) | strong(X0) [cnf transformation 36]
128. ~calm(susan) | ~strong(X0) [cnf transformation 66]
129. calm(susan) | ~strong(X0) [cnf transformation 66]
140. ~generous(mary) [cnf transformation 24]
196. 13 <=> calm(susan) [avatar definition]
299. 35 <=> ! [X0] : ~strong(X0) [avatar definition]
300. ~strong(X0) <- (35) [avatar component clause 299]
301. 35 | 13 [avatar split clause 129,196,299]
302. 35 | ~13 [avatar split clause 128,196,299]
345. strong(mary) [resolution 126,140]
346. $false <- (35) [subsumption resolution 345,300]
347. ~35 [avatar contradiction clause 346]
348. $false [avatar sat refutation 301,302,347]
% SZS output end Proof for 5952608163679191903125021
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and generous is funny and vice versa.
Everyone who is rich is not funny or humble and vice versa.
If mary is both not generous and not kind then paul is not calm or curious and vice versa.
If john is both not strong and not creative then someone is either creative or not funny and vice versa.
Everyone who is happy is both patient and calm and vice versa.
If someone is both not curious and not tall then mary is happy or tall and vice versa.
If john is humble or kind then someone is both kind and tall and vice versa.
Everyone who is not humble is not old and vice versa.
If someone is both humble and brave then susan is funny and vice versa.
Everyone who is not generous or not tall is not humble.
Everyone who is either not tall or rich is both happy and patient and vice versa.
If someone is both not strong and not brave then alice is tall or not funny and vice versa.
If someone is either not tall or funny then someone is both happy and funny.
Everyone who is rich is wise and vice versa.
If mary is either generous or not wise then someone is patient.
Everyone who is not creative or not humble is brave or not happy.
Someone is not kind or happy.
Mary is both tall and old.
Someone is both not curious and old.
Alice is both not quiet and kind.
Fred is both not generous and not funny.
Lucy is either creative or not creative.
Paul is either generous or humble.
Someone is rich. | Mary is not wise. | contradiction | (![X]:((~creative(X)&generous(X))<=>funny(X)))&
(![X]:(rich(X)<=>(~funny(X)|humble(X))))&
(((~generous(mary)&~kind(mary)))<=>((~calm(paul)|curious(paul))))&
(((~strong(john)&~creative(john)))<=>(?[X]:((creative(X)<~>~funny(X)))))&
(![X]:(happy(X)<=>(patient(X)&calm(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>((happy(mary)|tall(mary))))&
(((humble(john)|kind(john)))<=>(?[X]:((kind(X)&tall(X)))))&
(![X]:(~humble(X)<=>~old(X)))&
((?[X]:((humble(X)&brave(X))))<=>(funny(susan)))&
(![X]:((~generous(X)|~tall(X))=>~humble(X)))&
(![X]:((~tall(X)<~>rich(X))<=>(happy(X)&patient(X))))&
((?[X]:((~strong(X)&~brave(X))))<=>((tall(alice)|~funny(alice))))&
((?[X]:((~tall(X)<~>funny(X))))=>(?[X]:((happy(X)&funny(X)))))&
(![X]:(rich(X)<=>wise(X)))&
(((generous(mary)<~>~wise(mary)))=>(?[X]:(patient(X))))&
(![X]:((~creative(X)|~humble(X))=>(brave(X)|~happy(X))))&
(?[X]:((~kind(X)|happy(X))))&
((tall(mary)&old(mary)))&
(?[X]:((~curious(X)&old(X))))&
((~quiet(alice)&kind(alice)))&
((~generous(fred)&~funny(fred)))&
((creative(lucy)<~>~creative(lucy)))&
((generous(paul)<~>humble(paul)))&
(?[X]:(rich(X))) | ~wise(mary) | [
"p1",
"p7",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1043540289490756926920058
% SZS output start Proof for 1043540289490756926920058
2. ! [X0] : (rich(X0) <=> (humble(X0) | ~funny(X0))) [input p1]
8. ! [X0] : (~humble(X0) <=> ~old(X0)) [input p7]
14. ! [X0] : (rich(X0) <=> wise(X0)) [input p13]
18. old(mary) & tall(mary) [input p17]
25. ~wise(mary) [input hypothesis]
35. ! [X0] : ((rich(X0) | (~humble(X0) & funny(X0))) & ((humble(X0) | ~funny(X0)) | ~rich(X0))) [nnf transformation 2]
36. ! [X0] : ((rich(X0) | (~humble(X0) & funny(X0))) & (humble(X0) | ~funny(X0) | ~rich(X0))) [flattening 35]
56. ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 8]
72. ! [X0] : ((rich(X0) | ~wise(X0)) & (wise(X0) | ~rich(X0))) [nnf transformation 14]
89. ~humble(X0) | rich(X0) [cnf transformation 36]
114. ~old(X0) | humble(X0) [cnf transformation 56]
136. ~rich(X0) | wise(X0) [cnf transformation 72]
144. old(mary) [cnf transformation 18]
155. ~wise(mary) [cnf transformation 25]
313. 33 <=> wise(mary) [avatar definition]
314. ~wise(mary) <- (~33) [avatar component clause 313]
334. ~33 [avatar split clause 155,313]
338. humble(mary) [resolution 114,144]
342. rich(mary) [resolution 338,89]
453. wise(mary) [resolution 342,136]
454. $false <- (~33) [subsumption resolution 453,314]
455. 33 [avatar contradiction clause 454]
456. $false [avatar sat refutation 334,455]
% SZS output end Proof for 1043540289490756926920058
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both creative and generous then someone is not strong.
Everyone who is both quiet and old is either creative or not kind and vice versa.
If someone is not old or patient then someone is both not rich and brave and vice versa.
If someone is rich then someone is either generous or humble.
Everyone who is either not calm or not humble is rich or curious and vice versa.
Everyone who is both not brave and patient is either not happy or quiet.
Everyone who is not rich or not calm is both not rich and creative.
If fred is happy or rich then fred is either generous or kind.
If john is not happy then susan is kind.
If paul is tall then paul is either humble or generous.
If mary is not kind or kind then mary is both not tall and not happy.
Everyone who is strong or funny is either strong or generous.
Everyone who is both not quiet and humble is old or wise.
Everyone who is not generous or happy is not happy or not tall.
Everyone who is either humble or quiet is both not creative and funny.
If someone is not old then lucy is both kind and not quiet and vice versa.
Someone is tall.
Someone is curious.
Someone is not generous or brave.
John is not humble or not creative.
Someone is both kind and humble.
Someone is either not old or not rich.
Someone is both kind and curious.
John is both patient and not curious. | John is humble. | contradiction | (((creative(alice)&generous(alice)))=>(?[X]:(~strong(X))))&
(![X]:((quiet(X)&old(X))<=>(creative(X)<~>~kind(X))))&
((?[X]:((~old(X)|patient(X))))<=>(?[X]:((~rich(X)&brave(X)))))&
((?[X]:(rich(X)))=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:((~calm(X)<~>~humble(X))<=>(rich(X)|curious(X))))&
(![X]:((~brave(X)&patient(X))=>(~happy(X)<~>quiet(X))))&
(![X]:((~rich(X)|~calm(X))=>(~rich(X)&creative(X))))&
(((happy(fred)|rich(fred)))=>((generous(fred)<~>kind(fred))))&
((~happy(john))=>(kind(susan)))&
((tall(paul))=>((humble(paul)<~>generous(paul))))&
(((~kind(mary)|kind(mary)))=>((~tall(mary)&~happy(mary))))&
(![X]:((strong(X)|funny(X))=>(strong(X)<~>generous(X))))&
(![X]:((~quiet(X)&humble(X))=>(old(X)|wise(X))))&
(![X]:((~generous(X)|happy(X))=>(~happy(X)|~tall(X))))&
(![X]:((humble(X)<~>quiet(X))=>(~creative(X)&funny(X))))&
((?[X]:(~old(X)))<=>((kind(lucy)&~quiet(lucy))))&
(?[X]:(tall(X)))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|brave(X))))&
((~humble(john)|~creative(john)))&
(?[X]:((kind(X)&humble(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((kind(X)&curious(X))))&
((patient(john)&~curious(john))) | humble(john) | [
"p4",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5229735982764975827280676
% SZS output start Proof for 5229735982764975827280676
5. ! [X0] : ((~calm(X0) <~> ~humble(X0)) <=> (curious(X0) | rich(X0))) [input p4]
7. ! [X0] : ((~calm(X0) | ~rich(X0)) => (creative(X0) & ~rich(X0))) [input p6]
20. ~creative(john) | ~humble(john) [input p19]
25. humble(john) [input hypothesis]
34. ! [X0] : ((creative(X0) & ~rich(X0)) | (calm(X0) & rich(X0))) [ennf transformation 7]
56. ! [X0] : ((((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))))) [nnf transformation 5]
57. ! [X0] : ((((humble(X0) | calm(X0)) & (~humble(X0) | ~calm(X0))) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | ((~calm(X0) | humble(X0)) & (~humble(X0) | calm(X0))))) [flattening 56]
97. ~calm(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 57]
105. rich(X0) | creative(X0) [cnf transformation 34]
106. calm(X0) | creative(X0) [cnf transformation 34]
134. ~creative(john) | ~humble(john) [cnf transformation 20]
143. humble(john) [cnf transformation 25]
286. 31 <=> humble(john) [avatar definition]
287. humble(john) <- (31) [avatar component clause 286]
290. 32 <=> creative(john) [avatar definition]
292. ~creative(john) <- (~32) [avatar component clause 290]
293. ~31 | ~32 [avatar split clause 134,290,286]
304. 31 [avatar split clause 143,286]
366. ~humble(X0) | ~rich(X0) | creative(X0) [resolution 97,106]
367. ~humble(X0) | creative(X0) [subsumption resolution 366,105]
555. creative(john) <- (31) [resolution 367,287]
558. $false <- (31, ~32) [subsumption resolution 555,292]
559. ~31 | 32 [avatar contradiction clause 558]
560. $false [avatar sat refutation 293,304,559]
% SZS output end Proof for 5229735982764975827280676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not generous is old and vice versa. If someone is both wise and not calm then susan is calm and vice versa. Everyone who is both not generous and humble is either not calm or not rich. If john is both funny and not calm then lucy is not strong. If someone is both brave and not patient then someone is both tall and not patient. Everyone who is both not creative and quiet is either not tall or not happy. If someone is creative or not patient then someone is either brave or not old. If someone is curious or not generous then alice is strong. If someone is both not quiet and not rich then someone is both not creative and not quiet. If john is calm or creative then someone is both old and not humble and vice versa. Everyone who is not old or old is both not generous and not funny. Everyone who is both wise and not happy is not happy and vice versa. Everyone who is brave or not curious is not brave or not curious and vice versa. Everyone who is generous or not generous is either old or not old. Everyone who is both not brave and not tall is not humble or old and vice versa. If someone is tall then someone is strong or old. Alice is either not happy or not funny. John is calm. Someone is tall or quiet. Someone is either not quiet or not calm. | Alice is not rich. | neutral | (![X]:((happy(X)|~generous(X))<=>old(X)))&
((?[X]:((wise(X)&~calm(X))))<=>(calm(susan)))&
(![X]:((~generous(X)&humble(X))=>(~calm(X)<~>~rich(X))))&
(((funny(john)&~calm(john)))=>(~strong(lucy)))&
((?[X]:((brave(X)&~patient(X))))=>(?[X]:((tall(X)&~patient(X)))))&
(![X]:((~creative(X)&quiet(X))=>(~tall(X)<~>~happy(X))))&
((?[X]:((creative(X)|~patient(X))))=>(?[X]:((brave(X)<~>~old(X)))))&
((?[X]:((curious(X)|~generous(X))))=>(strong(alice)))&
((?[X]:((~quiet(X)&~rich(X))))=>(?[X]:((~creative(X)&~quiet(X)))))&
(((calm(john)|creative(john)))<=>(?[X]:((old(X)&~humble(X)))))&
(![X]:((~old(X)|old(X))=>(~generous(X)&~funny(X))))&
(![X]:((wise(X)&~happy(X))<=>~happy(X)))&
(![X]:((brave(X)|~curious(X))<=>(~brave(X)|~curious(X))))&
(![X]:((generous(X)|~generous(X))=>(old(X)<~>~old(X))))&
(![X]:((~brave(X)&~tall(X))<=>(~humble(X)|old(X))))&
((?[X]:(tall(X)))=>(?[X]:((strong(X)|old(X)))))&
((~happy(alice)<~>~funny(alice)))&
(calm(john))&
(?[X]:((tall(X)|quiet(X))))&
(?[X]:((~quiet(X)<~>~calm(X)))) | ~rich(alice) | [] | null | 0 |
Everyone who is both rich and not curious is not calm or not happy and vice versa.
If someone is either not strong or not brave then lucy is either not funny or brave.
Everyone who is both happy and not strong is both not humble and not strong.
Everyone who is either not wise or not generous is not rich.
Everyone who is patient is not calm or humble.
Everyone who is both not brave and creative is both funny and humble.
If someone is both not humble and creative then someone is not quiet or patient.
Everyone who is calm is both happy and tall.
Everyone who is either wise or kind is quiet and vice versa.
Everyone who is both not old and rich is either quiet or calm.
Everyone who is either calm or happy is humble or wise and vice versa.
Everyone who is either not generous or not calm is not brave or not funny and vice versa.
Everyone who is happy or not curious is not happy and vice versa.
If paul is not tall then john is tall and vice versa.
If fred is wise or not kind then someone is not kind or not funny and vice versa.
Everyone who is happy is not old or not brave and vice versa.
Someone is both patient and not creative.
Fred is not tall.
Lucy is either creative or happy.
Someone is either not happy or calm.
Someone is kind or not brave.
Someone is brave. | Lucy is not humble. | entailment | (![X]:((rich(X)&~curious(X))<=>(~calm(X)|~happy(X))))&
((?[X]:((~strong(X)<~>~brave(X))))=>((~funny(lucy)<~>brave(lucy))))&
(![X]:((happy(X)&~strong(X))=>(~humble(X)&~strong(X))))&
(![X]:((~wise(X)<~>~generous(X))=>~rich(X)))&
(![X]:(patient(X)=>(~calm(X)|humble(X))))&
(![X]:((~brave(X)&creative(X))=>(funny(X)&humble(X))))&
((?[X]:((~humble(X)&creative(X))))=>(?[X]:((~quiet(X)|patient(X)))))&
(![X]:(calm(X)=>(happy(X)&tall(X))))&
(![X]:((wise(X)<~>kind(X))<=>quiet(X)))&
(![X]:((~old(X)&rich(X))=>(quiet(X)<~>calm(X))))&
(![X]:((calm(X)<~>happy(X))<=>(humble(X)|wise(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~brave(X)|~funny(X))))&
(![X]:((happy(X)|~curious(X))<=>~happy(X)))&
((~tall(paul))<=>(tall(john)))&
(((wise(fred)|~kind(fred)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(happy(X)<=>(~old(X)|~brave(X))))&
(?[X]:((patient(X)&~creative(X))))&
(~tall(fred))&
((creative(lucy)<~>happy(lucy)))&
(?[X]:((~happy(X)<~>calm(X))))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:(brave(X))) | ~humble(lucy) | [
"p7",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7934344941850427014435912
% SZS output start Proof for 7934344941850427014435912
8. ! [X0] : (calm(X0) => (tall(X0) & happy(X0))) [input p7]
11. ! [X0] : ((calm(X0) <~> happy(X0)) <=> (wise(X0) | humble(X0))) [input p10]
13. ! [X0] : ((~curious(X0) | happy(X0)) <=> ~happy(X0)) [input p12]
23. humble(lucy) [input hypothesis]
34. ! [X0] : ((tall(X0) & happy(X0)) | ~calm(X0)) [ennf transformation 8]
46. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [nnf transformation 11]
47. ! [X0] : ((((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0))))) [flattening 46]
50. ! [X0] : (((~curious(X0) | happy(X0)) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [nnf transformation 13]
51. ! [X0] : ((~curious(X0) | happy(X0) | happy(X0)) & (~happy(X0) | (curious(X0) & ~happy(X0)))) [flattening 50]
87. ~calm(X0) | happy(X0) [cnf transformation 34]
97. happy(X0) | calm(X0) | ~humble(X0) [cnf transformation 47]
99. ~happy(X0) | ~calm(X0) | ~humble(X0) [cnf transformation 47]
107. ~happy(X0) | ~happy(X0) [cnf transformation 51]
128. humble(lucy) [cnf transformation 23]
129. ~happy(X0) [duplicate literal removal 107]
163. ~humble(X0) | ~calm(X0) [subsumption resolution 99,87]
165. ~humble(X0) | happy(X0) [subsumption resolution 97,163]
215. happy(lucy) [resolution 165,128]
216. $false [subsumption resolution 215,129]
% SZS output end Proof for 7934344941850427014435912
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is either quiet or not patient and vice versa.
Everyone who is tall is both not tall and generous and vice versa.
If mary is not strong then susan is both creative and not tall and vice versa.
If mary is both not tall and not quiet then susan is either wise or strong and vice versa.
If lucy is either funny or calm then lucy is both curious and tall and vice versa.
If mary is either not calm or kind then someone is either tall or calm.
Everyone who is either brave or not curious is tall.
If someone is strong or rich then paul is either not patient or not happy and vice versa.
Everyone who is not funny is either humble or patient and vice versa.
Everyone who is both not strong and humble is not quiet or not old.
If someone is both not curious and curious then lucy is happy or tall and vice versa.
If someone is both not generous and calm then paul is humble.
If lucy is not humble then someone is either calm or not generous.
Everyone who is not quiet is both generous and rich and vice versa.
If someone is not tall or calm then paul is either not rich or humble and vice versa.
Alice is both not strong and not brave.
John is curious.
Someone is not old.
Someone is not tall or quiet.
Someone is not brave or funny.
Alice is either wise or strong.
Fred is rich.
Someone is either rich or not kind. | Alice is patient. | entailment | (![X]:(~generous(X)<=>(quiet(X)<~>~patient(X))))&
(![X]:(tall(X)<=>(~tall(X)&generous(X))))&
((~strong(mary))<=>((creative(susan)&~tall(susan))))&
(((~tall(mary)&~quiet(mary)))<=>((wise(susan)<~>strong(susan))))&
(((funny(lucy)<~>calm(lucy)))<=>((curious(lucy)&tall(lucy))))&
(((~calm(mary)<~>kind(mary)))=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((brave(X)<~>~curious(X))=>tall(X)))&
((?[X]:((strong(X)|rich(X))))<=>((~patient(paul)<~>~happy(paul))))&
(![X]:(~funny(X)<=>(humble(X)<~>patient(X))))&
(![X]:((~strong(X)&humble(X))=>(~quiet(X)|~old(X))))&
((?[X]:((~curious(X)&curious(X))))<=>((happy(lucy)|tall(lucy))))&
((?[X]:((~generous(X)&calm(X))))=>(humble(paul)))&
((~humble(lucy))=>(?[X]:((calm(X)<~>~generous(X)))))&
(![X]:(~quiet(X)<=>(generous(X)&rich(X))))&
((?[X]:((~tall(X)|calm(X))))<=>((~rich(paul)<~>humble(paul))))&
((~strong(alice)&~brave(alice)))&
(curious(john))&
(?[X]:(~old(X)))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:((~brave(X)|funny(X))))&
((wise(alice)<~>strong(alice)))&
(rich(fred))&
(?[X]:((rich(X)<~>~kind(X)))) | patient(alice) | [
"p0",
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3008824246731613096754409
% SZS output start Proof for 3008824246731613096754409
1. ! [X0] : (~generous(X0) <=> (quiet(X0) <~> ~patient(X0))) [input p0]
2. ! [X0] : (tall(X0) <=> (generous(X0) & ~tall(X0))) [input p1]
14. ! [X0] : (~quiet(X0) <=> (rich(X0) & generous(X0))) [input p13]
24. ~patient(alice) [input hypothesis]
31. ! [X0] : ((~generous(X0) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) & (((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | generous(X0))) [nnf transformation 1]
32. ! [X0] : ((tall(X0) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ~tall(X0))) [nnf transformation 2]
33. ! [X0] : ((tall(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ~tall(X0))) [flattening 32]
57. ! [X0] : ((~quiet(X0) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | quiet(X0))) [nnf transformation 14]
58. ! [X0] : ((~quiet(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | quiet(X0))) [flattening 57]
72. ~quiet(X0) | patient(X0) | generous(X0) [cnf transformation 31]
75. ~tall(X0) | ~tall(X0) [cnf transformation 33]
77. tall(X0) | ~generous(X0) | tall(X0) [cnf transformation 33]
117. quiet(X0) | generous(X0) [cnf transformation 58]
136. ~patient(alice) [cnf transformation 24]
137. ~tall(X0) [duplicate literal removal 75]
138. ~generous(X0) | tall(X0) [duplicate literal removal 77]
306. patient(X0) | generous(X0) | generous(X0) [resolution 72,117]
310. patient(X0) | generous(X0) [duplicate literal removal 306]
311. generous(alice) [resolution 310,136]
317. tall(alice) [resolution 311,138]
319. $false [subsumption resolution 317,137]
% SZS output end Proof for 3008824246731613096754409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not old is either not curious or not rich and vice versa.
If someone is both not calm and not humble then lucy is both not funny and not curious.
Everyone who is either not strong or patient is calm or patient.
Everyone who is either not kind or not quiet is not strong.
If someone is either not quiet or old then lucy is not quiet or tall and vice versa.
Everyone who is either not tall or not calm is either brave or not calm.
If someone is not kind then fred is either not wise or not humble and vice versa.
If john is generous or not brave then someone is wise.
If someone is both generous and not quiet then susan is not kind or strong.
Everyone who is both strong and not kind is either quiet or not wise.
Everyone who is both humble and quiet is both not kind and not rich.
If someone is not patient or rich then someone is not rich or not quiet.
Everyone who is either patient or not happy is generous and vice versa.
Everyone who is tall is either quiet or curious.
Everyone who is either not old or kind is funny or not rich.
Everyone who is either not brave or funny is not happy and vice versa.
Fred is strong.
Susan is either quiet or not curious.
Fred is either not humble or not brave.
Someone is strong or rich.
Susan is funny or happy.
Someone is both tall and not rich.
Alice is generous.
Fred is not happy or not curious. | Lucy is not calm. | neutral | (![X]:((happy(X)&~old(X))<=>(~curious(X)<~>~rich(X))))&
((?[X]:((~calm(X)&~humble(X))))=>((~funny(lucy)&~curious(lucy))))&
(![X]:((~strong(X)<~>patient(X))=>(calm(X)|patient(X))))&
(![X]:((~kind(X)<~>~quiet(X))=>~strong(X)))&
((?[X]:((~quiet(X)<~>old(X))))<=>((~quiet(lucy)|tall(lucy))))&
(![X]:((~tall(X)<~>~calm(X))=>(brave(X)<~>~calm(X))))&
((?[X]:(~kind(X)))<=>((~wise(fred)<~>~humble(fred))))&
(((generous(john)|~brave(john)))=>(?[X]:(wise(X))))&
((?[X]:((generous(X)&~quiet(X))))=>((~kind(susan)|strong(susan))))&
(![X]:((strong(X)&~kind(X))=>(quiet(X)<~>~wise(X))))&
(![X]:((humble(X)&quiet(X))=>(~kind(X)&~rich(X))))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>generous(X)))&
(![X]:(tall(X)=>(quiet(X)<~>curious(X))))&
(![X]:((~old(X)<~>kind(X))=>(funny(X)|~rich(X))))&
(![X]:((~brave(X)<~>funny(X))<=>~happy(X)))&
(strong(fred))&
((quiet(susan)<~>~curious(susan)))&
((~humble(fred)<~>~brave(fred)))&
(?[X]:((strong(X)|rich(X))))&
((funny(susan)|happy(susan)))&
(?[X]:((tall(X)&~rich(X))))&
(generous(alice))&
((~happy(fred)|~curious(fred))) | ~calm(lucy) | [] | null | 0 |
Everyone who is both brave and not calm is either happy or not wise and vice versa.
Everyone who is strong is either not generous or not kind.
If someone is not funny then mary is either wise or not creative and vice versa.
Everyone who is funny is curious or not kind.
Everyone who is both not old and kind is quiet and vice versa.
Everyone who is humble or not wise is kind and vice versa.
If lucy is not calm or not tall then someone is either funny or old.
Everyone who is both not generous and not brave is happy.
Everyone who is quiet or not calm is kind and vice versa.
Everyone who is brave or creative is not happy and vice versa.
Everyone who is brave is both calm and strong.
Everyone who is either patient or not kind is curious or humble.
Everyone who is either quiet or calm is both not patient and not creative and vice versa.
Everyone who is happy or not kind is happy or not creative.
Everyone who is both not happy and not wise is both wise and kind.
Everyone who is creative is patient and vice versa.
Alice is brave.
Paul is not funny.
Susan is both rich and tall.
John is both not humble and not quiet.
Fred is both not quiet and not creative.
Fred is either not calm or not old.
Someone is patient or not old.
Someone is not humble. | Mary is wise. | neutral | (![X]:((brave(X)&~calm(X))<=>(happy(X)<~>~wise(X))))&
(![X]:(strong(X)=>(~generous(X)<~>~kind(X))))&
((?[X]:(~funny(X)))<=>((wise(mary)<~>~creative(mary))))&
(![X]:(funny(X)=>(curious(X)|~kind(X))))&
(![X]:((~old(X)&kind(X))<=>quiet(X)))&
(![X]:((humble(X)|~wise(X))<=>kind(X)))&
(((~calm(lucy)|~tall(lucy)))=>(?[X]:((funny(X)<~>old(X)))))&
(![X]:((~generous(X)&~brave(X))=>happy(X)))&
(![X]:((quiet(X)|~calm(X))<=>kind(X)))&
(![X]:((brave(X)|creative(X))<=>~happy(X)))&
(![X]:(brave(X)=>(calm(X)&strong(X))))&
(![X]:((patient(X)<~>~kind(X))=>(curious(X)|humble(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(~patient(X)&~creative(X))))&
(![X]:((happy(X)|~kind(X))=>(happy(X)|~creative(X))))&
(![X]:((~happy(X)&~wise(X))=>(wise(X)&kind(X))))&
(![X]:(creative(X)<=>patient(X)))&
(brave(alice))&
(~funny(paul))&
((rich(susan)&tall(susan)))&
((~humble(john)&~quiet(john)))&
((~quiet(fred)&~creative(fred)))&
((~calm(fred)<~>~old(fred)))&
(?[X]:((patient(X)|~old(X))))&
(?[X]:(~humble(X))) | wise(mary) | [] | null | 0 |
If paul is kind then someone is calm or funny.
Everyone who is either funny or calm is not old or happy and vice versa.
If someone is both not rich and not patient then someone is both not wise and brave and vice versa.
If someone is not quiet then fred is not wise or tall.
Everyone who is curious or not strong is both kind and happy.
Everyone who is both not wise and wise is curious and vice versa.
Everyone who is not old is not creative or not patient.
If lucy is both old and not wise then someone is not happy and vice versa.
Everyone who is both brave and not patient is patient or not kind and vice versa.
Everyone who is either brave or not wise is either not old or not funny.
If susan is either curious or not tall then someone is rich and vice versa.
Everyone who is either brave or patient is brave or not rich and vice versa.
If someone is not curious then lucy is either funny or not happy.
Everyone who is not brave is either patient or curious and vice versa.
Everyone who is both not patient and funny is not calm or brave and vice versa.
Everyone who is humble is not happy or not tall.
Paul is not rich.
Someone is happy.
Paul is either curious or not happy.
Someone is either creative or not creative.
Someone is not wise.
Fred is rich or curious.
John is not creative. | Susan is curious. | contradiction | ((kind(paul))=>(?[X]:((calm(X)|funny(X)))))&
(![X]:((funny(X)<~>calm(X))<=>(~old(X)|happy(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
((?[X]:(~quiet(X)))=>((~wise(fred)|tall(fred))))&
(![X]:((curious(X)|~strong(X))=>(kind(X)&happy(X))))&
(![X]:((~wise(X)&wise(X))<=>curious(X)))&
(![X]:(~old(X)=>(~creative(X)|~patient(X))))&
(((old(lucy)&~wise(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((brave(X)&~patient(X))<=>(patient(X)|~kind(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~old(X)<~>~funny(X))))&
(((curious(susan)<~>~tall(susan)))<=>(?[X]:(rich(X))))&
(![X]:((brave(X)<~>patient(X))<=>(brave(X)|~rich(X))))&
((?[X]:(~curious(X)))=>((funny(lucy)<~>~happy(lucy))))&
(![X]:(~brave(X)<=>(patient(X)<~>curious(X))))&
(![X]:((~patient(X)&funny(X))<=>(~calm(X)|brave(X))))&
(![X]:(humble(X)=>(~happy(X)|~tall(X))))&
(~rich(paul))&
(?[X]:(happy(X)))&
((curious(paul)<~>~happy(paul)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:(~wise(X)))&
((rich(fred)|curious(fred)))&
(~creative(john)) | curious(susan) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 3199485158114532866551879
% SZS output start Proof for 3199485158114532866551879
6. ! [X0] : ((wise(X0) & ~wise(X0)) <=> curious(X0)) [input p5]
24. curious(susan) [input hypothesis]
44. ! [X0] : (((wise(X0) & ~wise(X0)) | ~curious(X0)) & (curious(X0) | (~wise(X0) | wise(X0)))) [nnf transformation 6]
45. ! [X0] : (((wise(X0) & ~wise(X0)) | ~curious(X0)) & (curious(X0) | ~wise(X0) | wise(X0))) [flattening 44]
86. ~wise(X0) | ~curious(X0) [cnf transformation 45]
87. wise(X0) | ~curious(X0) [cnf transformation 45]
131. curious(susan) [cnf transformation 24]
175. ~curious(X0) [subsumption resolution 86,87]
228. $false [subsumption resolution 131,175]
% SZS output end Proof for 3199485158114532866551879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and happy is not brave or not wise.
If susan is both not patient and creative then someone is not curious and vice versa.
If alice is not strong or not old then someone is either not kind or creative.
If alice is either happy or humble then someone is not generous.
If susan is either not happy or humble then someone is both humble and not funny.
Everyone who is both not happy and calm is humble or kind.
If someone is both not patient and not old then someone is either not humble or brave.
If someone is either not strong or strong then someone is not patient or not strong and vice versa.
If someone is both not calm and quiet then someone is not happy and vice versa.
Everyone who is wise is both creative and rich and vice versa.
If someone is either rich or generous then fred is either humble or brave.
Everyone who is not tall or not patient is both not kind and not humble.
Everyone who is either not patient or not tall is either not happy or old and vice versa.
Everyone who is both generous and not happy is old or not rich and vice versa.
Everyone who is not brave or patient is both funny and rich and vice versa.
Everyone who is both strong and not patient is either wise or not funny and vice versa.
Fred is either not patient or not happy.
Mary is not kind or happy.
Alice is either creative or happy.
Someone is either not wise or not kind.
Mary is not calm or tall.
Someone is quiet or not generous.
Someone is not old or not humble.
Alice is either not calm or calm. | Alice is calm. | neutral | (![X]:((~strong(X)&happy(X))=>(~brave(X)|~wise(X))))&
(((~patient(susan)&creative(susan)))<=>(?[X]:(~curious(X))))&
(((~strong(alice)|~old(alice)))=>(?[X]:((~kind(X)<~>creative(X)))))&
(((happy(alice)<~>humble(alice)))=>(?[X]:(~generous(X))))&
(((~happy(susan)<~>humble(susan)))=>(?[X]:((humble(X)&~funny(X)))))&
(![X]:((~happy(X)&calm(X))=>(humble(X)|kind(X))))&
((?[X]:((~patient(X)&~old(X))))=>(?[X]:((~humble(X)<~>brave(X)))))&
((?[X]:((~strong(X)<~>strong(X))))<=>(?[X]:((~patient(X)|~strong(X)))))&
((?[X]:((~calm(X)&quiet(X))))<=>(?[X]:(~happy(X))))&
(![X]:(wise(X)<=>(creative(X)&rich(X))))&
((?[X]:((rich(X)<~>generous(X))))=>((humble(fred)<~>brave(fred))))&
(![X]:((~tall(X)|~patient(X))=>(~kind(X)&~humble(X))))&
(![X]:((~patient(X)<~>~tall(X))<=>(~happy(X)<~>old(X))))&
(![X]:((generous(X)&~happy(X))<=>(old(X)|~rich(X))))&
(![X]:((~brave(X)|patient(X))<=>(funny(X)&rich(X))))&
(![X]:((strong(X)&~patient(X))<=>(wise(X)<~>~funny(X))))&
((~patient(fred)<~>~happy(fred)))&
((~kind(mary)|happy(mary)))&
((creative(alice)<~>happy(alice)))&
(?[X]:((~wise(X)<~>~kind(X))))&
((~calm(mary)|tall(mary)))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:((~old(X)|~humble(X))))&
((~calm(alice)<~>calm(alice))) | calm(alice) | [] | null | 0 |
If someone is humble then someone is either not patient or not rich and vice versa. If alice is brave or funny then someone is either not quiet or not funny and vice versa. Everyone who is both funny and brave is not curious or calm and vice versa. Everyone who is either strong or not happy is both tall and generous. Everyone who is either wise or tall is not brave or calm and vice versa. If alice is calm then someone is both not curious and brave and vice versa. Everyone who is calm is either rich or calm. Everyone who is both brave and curious is either old or not patient and vice versa. Everyone who is calm is old or not happy. If john is both quiet and funny then john is both creative and happy and vice versa. Everyone who is either tall or happy is curious and vice versa. If someone is both not funny and generous then someone is not quiet or curious. If someone is old then someone is either not humble or not funny and vice versa. Everyone who is humble is not patient or not kind. If fred is both happy and not calm then john is not wise or quiet and vice versa. Everyone who is happy or calm is not calm. Mary is both quiet and not humble. Lucy is either not generous or strong. Someone is tall or not strong. Someone is not humble. Someone is not happy or not funny. Someone is both humble and not funny. Someone is both happy and not patient. | Mary is patient. | neutral | ((?[X]:(humble(X)))<=>(?[X]:((~patient(X)<~>~rich(X)))))&
(((brave(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
(![X]:((funny(X)&brave(X))<=>(~curious(X)|calm(X))))&
(![X]:((strong(X)<~>~happy(X))=>(tall(X)&generous(X))))&
(![X]:((wise(X)<~>tall(X))<=>(~brave(X)|calm(X))))&
((calm(alice))<=>(?[X]:((~curious(X)&brave(X)))))&
(![X]:(calm(X)=>(rich(X)<~>calm(X))))&
(![X]:((brave(X)&curious(X))<=>(old(X)<~>~patient(X))))&
(![X]:(calm(X)=>(old(X)|~happy(X))))&
(((quiet(john)&funny(john)))<=>((creative(john)&happy(john))))&
(![X]:((tall(X)<~>happy(X))<=>curious(X)))&
((?[X]:((~funny(X)&generous(X))))=>(?[X]:((~quiet(X)|curious(X)))))&
((?[X]:(old(X)))<=>(?[X]:((~humble(X)<~>~funny(X)))))&
(![X]:(humble(X)=>(~patient(X)|~kind(X))))&
(((happy(fred)&~calm(fred)))<=>((~wise(john)|quiet(john))))&
(![X]:((happy(X)|calm(X))=>~calm(X)))&
((quiet(mary)&~humble(mary)))&
((~generous(lucy)<~>strong(lucy)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|~funny(X))))&
(?[X]:((humble(X)&~funny(X))))&
(?[X]:((happy(X)&~patient(X)))) | patient(mary) | [] | null | 0 |
Everyone who is both kind and calm is both not tall and calm.
If someone is either funny or happy then paul is either not tall or not humble.
If someone is either not calm or wise then john is calm or wise and vice versa.
If someone is not creative or not quiet then mary is both not generous and patient.
If someone is not patient or not old then someone is both not wise and not kind and vice versa.
Everyone who is humble is both humble and not strong.
Everyone who is tall is not funny.
Everyone who is either generous or wise is quiet or not kind and vice versa.
Everyone who is strong is humble and vice versa.
Everyone who is both quiet and not patient is either brave or old and vice versa.
Everyone who is not generous is quiet or creative and vice versa.
If someone is both happy and not tall then someone is either old or creative and vice versa.
Everyone who is either quiet or not patient is not wise.
If someone is not funny then someone is both not kind and strong and vice versa.
If someone is not generous or creative then alice is not kind or happy and vice versa.
If someone is rich then susan is both funny and kind.
Lucy is kind or not strong.
Lucy is not tall or kind.
Someone is either not funny or not brave.
Someone is rich.
Someone is not patient or not tall.
Mary is quiet or kind.
Mary is generous or calm. | Mary is happy. | entailment | (![X]:((kind(X)&calm(X))=>(~tall(X)&calm(X))))&
((?[X]:((funny(X)<~>happy(X))))=>((~tall(paul)<~>~humble(paul))))&
((?[X]:((~calm(X)<~>wise(X))))<=>((calm(john)|wise(john))))&
((?[X]:((~creative(X)|~quiet(X))))=>((~generous(mary)&patient(mary))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~wise(X)&~kind(X)))))&
(![X]:(humble(X)=>(humble(X)&~strong(X))))&
(![X]:(tall(X)=>~funny(X)))&
(![X]:((generous(X)<~>wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((quiet(X)&~patient(X))<=>(brave(X)<~>old(X))))&
(![X]:(~generous(X)<=>(quiet(X)|creative(X))))&
((?[X]:((happy(X)&~tall(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((quiet(X)<~>~patient(X))=>~wise(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~kind(X)&strong(X)))))&
((?[X]:((~generous(X)|creative(X))))<=>((~kind(alice)|happy(alice))))&
((?[X]:(rich(X)))=>((funny(susan)&kind(susan))))&
((kind(lucy)|~strong(lucy)))&
((~tall(lucy)|kind(lucy)))&
(?[X]:((~funny(X)<~>~brave(X))))&
(?[X]:(rich(X)))&
(?[X]:((~patient(X)|~tall(X))))&
((quiet(mary)|kind(mary)))&
((generous(mary)|calm(mary))) | happy(mary) | [
"p1",
"p5",
"p6",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 422444286307479868815195
% SZS output start Proof for 422444286307479868815195
2. ? [X0] : (funny(X0) <~> happy(X0)) => (~tall(paul) <~> ~humble(paul)) [input p1]
6. ! [X0] : (humble(X0) => (~strong(X0) & humble(X0))) [input p5]
7. ! [X0] : (tall(X0) => ~funny(X0)) [input p6]
9. ! [X0] : (strong(X0) <=> humble(X0)) [input p8]
14. ? [X0] : ~funny(X0) <=> ? [X0] : (strong(X0) & ~kind(X0)) [input p13]
24. ~happy(mary) [input hypothesis]
27. ? [X0] : ~funny(X0) <=> ? [X1] : (strong(X1) & ~kind(X1)) [rectify 14]
30. (~tall(paul) <~> ~humble(paul)) | ! [X0] : (funny(X0) <=> happy(X0)) [ennf transformation 2]
32. ! [X0] : ((~strong(X0) & humble(X0)) | ~humble(X0)) [ennf transformation 6]
33. ! [X0] : (~funny(X0) | ~tall(X0)) [ennf transformation 7]
36. ((humble(paul) | tall(paul)) & (~humble(paul) | ~tall(paul))) | ! [X0] : ((funny(X0) | ~happy(X0)) & (happy(X0) | ~funny(X0))) [nnf transformation 30]
49. ! [X0] : ((strong(X0) | ~humble(X0)) & (humble(X0) | ~strong(X0))) [nnf transformation 9]
60. (? [X0] : ~funny(X0) | ! [X1] : (~strong(X1) | kind(X1))) & (? [X1] : (strong(X1) & ~kind(X1)) | ! [X0] : funny(X0)) [nnf transformation 27]
61. (? [X0] : ~funny(X0) | ! [X1] : (~strong(X1) | kind(X1))) & (? [X2] : (strong(X2) & ~kind(X2)) | ! [X3] : funny(X3)) [rectify 60]
62. ? [X0] : ~funny(X0) => ~funny(sK5) [choice axiom]
63. ? [X2] : (strong(X2) & ~kind(X2)) => (strong(sK6) & ~kind(sK6)) [choice axiom]
64. (~funny(sK5) | ! [X1] : (~strong(X1) | kind(X1))) & ((strong(sK6) & ~kind(sK6)) | ! [X3] : funny(X3)) [skolemisation 61,63,62]
81. humble(paul) | tall(paul) | happy(X0) | ~funny(X0) [cnf transformation 36]
99. ~strong(X0) | ~humble(X0) [cnf transformation 32]
100. ~funny(X0) | ~tall(X0) [cnf transformation 33]
107. humble(X0) | ~strong(X0) [cnf transformation 49]
108. strong(X0) | ~humble(X0) [cnf transformation 49]
127. strong(sK6) | funny(X3) [cnf transformation 64]
143. ~happy(mary) [cnf transformation 24]
148. 2 <=> tall(paul) [avatar definition]
150. tall(paul) <- (2) [avatar component clause 148]
152. 3 <=> humble(paul) [avatar definition]
154. humble(paul) <- (3) [avatar component clause 152]
157. 4 <=> ! [X0] : (happy(X0) | ~funny(X0)) [avatar definition]
158. happy(X0) | ~funny(X0) <- (4) [avatar component clause 157]
159. 4 | 2 | 3 [avatar split clause 81,152,148,157]
238. ~humble(X0) [subsumption resolution 108,99]
239. ~strong(X0) [subsumption resolution 107,238]
271. funny(X3) [subsumption resolution 127,239]
339. ~tall(X0) [resolution 100,271]
347. $false <- (2) [resolution 339,150]
348. ~2 [avatar contradiction clause 347]
349. happy(X0) <- (4) [subsumption resolution 158,271]
350. $false <- (4) [resolution 349,143]
351. ~4 [avatar contradiction clause 350]
352. $false <- (3) [subsumption resolution 154,238]
353. ~3 [avatar contradiction clause 352]
354. $false [avatar sat refutation 159,348,351,353]
% SZS output end Proof for 422444286307479868815195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either brave or not kind. If someone is humble or wise then someone is either tall or brave and vice versa. If fred is not calm then someone is not humble or not funny and vice versa. Everyone who is both not brave and not rich is not old and vice versa. Everyone who is either quiet or strong is not strong or not humble and vice versa. Everyone who is not wise is both funny and old and vice versa. Everyone who is either tall or not tall is not brave. Everyone who is either generous or not rich is either not strong or brave and vice versa. Everyone who is not quiet or curious is generous. If fred is both wise and not brave then paul is curious. If alice is either not wise or not calm then someone is either wise or creative. If someone is creative then alice is humble or not patient. Everyone who is generous or not creative is either not funny or not rich and vice versa. If paul is both patient and not old then mary is funny. Everyone who is either curious or not calm is not tall and vice versa. John is either not strong or not happy. Someone is not brave. Someone is either brave or not kind. John is not wise. Someone is patient. Susan is not curious or calm. Lucy is not creative. | Lucy is not rich. | neutral | (![X]:(~brave(X)=>(brave(X)<~>~kind(X))))&
((?[X]:((humble(X)|wise(X))))<=>(?[X]:((tall(X)<~>brave(X)))))&
((~calm(fred))<=>(?[X]:((~humble(X)|~funny(X)))))&
(![X]:((~brave(X)&~rich(X))<=>~old(X)))&
(![X]:((quiet(X)<~>strong(X))<=>(~strong(X)|~humble(X))))&
(![X]:(~wise(X)<=>(funny(X)&old(X))))&
(![X]:((tall(X)<~>~tall(X))=>~brave(X)))&
(![X]:((generous(X)<~>~rich(X))<=>(~strong(X)<~>brave(X))))&
(![X]:((~quiet(X)|curious(X))=>generous(X)))&
(((wise(fred)&~brave(fred)))=>(curious(paul)))&
(((~wise(alice)<~>~calm(alice)))=>(?[X]:((wise(X)<~>creative(X)))))&
((?[X]:(creative(X)))=>((humble(alice)|~patient(alice))))&
(![X]:((generous(X)|~creative(X))<=>(~funny(X)<~>~rich(X))))&
(((patient(paul)&~old(paul)))=>(funny(mary)))&
(![X]:((curious(X)<~>~calm(X))<=>~tall(X)))&
((~strong(john)<~>~happy(john)))&
(?[X]:(~brave(X)))&
(?[X]:((brave(X)<~>~kind(X))))&
(~wise(john))&
(?[X]:(patient(X)))&
((~curious(susan)|calm(susan)))&
(~creative(lucy)) | ~rich(lucy) | [] | null | 0 |
If fred is wise or not kind then someone is not kind or not funny and vice versa.
Everyone who is happy is not old or not brave and vice versa.
Everyone who is either not tall or not funny is not tall and vice versa.
If someone is kind then someone is quiet.
If susan is either old or not creative then someone is humble or not kind.
Everyone who is both not tall and not quiet is either humble or not happy and vice versa.
Everyone who is both generous and not funny is old and vice versa.
Everyone who is not humble or kind is not patient.
If someone is both not creative and not generous then lucy is not humble.
Everyone who is not calm is both funny and old.
Everyone who is not happy is not kind.
Everyone who is both not wise and not generous is both not curious and creative.
Everyone who is funny or rich is not brave.
If paul is not generous or not curious then someone is not calm.
Everyone who is brave is not wise or not patient and vice versa.
Susan is generous or not calm.
Someone is wise or not humble.
John is not creative.
Someone is happy or not humble.
Alice is happy or not creative. | Paul is generous. | entailment | (((wise(fred)|~kind(fred)))<=>(?[X]:((~kind(X)|~funny(X)))))&
(![X]:(happy(X)<=>(~old(X)|~brave(X))))&
(![X]:((~tall(X)<~>~funny(X))<=>~tall(X)))&
((?[X]:(kind(X)))=>(?[X]:(quiet(X))))&
(((old(susan)<~>~creative(susan)))=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>(humble(X)<~>~happy(X))))&
(![X]:((generous(X)&~funny(X))<=>old(X)))&
(![X]:((~humble(X)|kind(X))=>~patient(X)))&
((?[X]:((~creative(X)&~generous(X))))=>(~humble(lucy)))&
(![X]:(~calm(X)=>(funny(X)&old(X))))&
(![X]:(~happy(X)=>~kind(X)))&
(![X]:((~wise(X)&~generous(X))=>(~curious(X)&creative(X))))&
(![X]:((funny(X)|rich(X))=>~brave(X)))&
(((~generous(paul)|~curious(paul)))=>(?[X]:(~calm(X))))&
(![X]:(brave(X)<=>(~wise(X)|~patient(X))))&
((generous(susan)|~calm(susan)))&
(?[X]:((wise(X)|~humble(X))))&
(~creative(john))&
(?[X]:((happy(X)|~humble(X))))&
((happy(alice)|~creative(alice))) | generous(paul) | [
"p2",
"p6",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6448395828851566552746507
% SZS output start Proof for 6448395828851566552746507
3. ! [X0] : ((~tall(X0) <~> ~funny(X0)) <=> ~tall(X0)) [input p2]
7. ! [X0] : ((~funny(X0) & generous(X0)) <=> old(X0)) [input p6]
10. ! [X0] : (~calm(X0) => (old(X0) & funny(X0))) [input p9]
14. (~curious(paul) | ~generous(paul)) => ? [X0] : ~calm(X0) [input p13]
21. ~generous(paul) [input hypothesis]
28. ! [X0] : ((old(X0) & funny(X0)) | calm(X0)) [ennf transformation 10]
33. ? [X0] : ~calm(X0) | (curious(paul) & generous(paul)) [ennf transformation 14]
41. ! [X0] : ((((funny(X0) | tall(X0)) & (~funny(X0) | ~tall(X0))) | tall(X0)) & (~tall(X0) | ((~tall(X0) | funny(X0)) & (~funny(X0) | tall(X0))))) [nnf transformation 3]
50. ! [X0] : (((~funny(X0) & generous(X0)) | ~old(X0)) & (old(X0) | (funny(X0) | ~generous(X0)))) [nnf transformation 7]
51. ! [X0] : (((~funny(X0) & generous(X0)) | ~old(X0)) & (old(X0) | funny(X0) | ~generous(X0))) [flattening 50]
52. ? [X0] : ~calm(X0) => ~calm(sK3) [choice axiom]
53. ~calm(sK3) | (curious(paul) & generous(paul)) [skolemisation 33,52]
68. ~tall(X0) | ~tall(X0) | funny(X0) [cnf transformation 41]
70. funny(X0) | tall(X0) | tall(X0) [cnf transformation 41]
82. ~old(X0) | ~funny(X0) [cnf transformation 51]
87. calm(X0) | old(X0) [cnf transformation 28]
92. ~calm(sK3) | generous(paul) [cnf transformation 53]
102. ~generous(paul) [cnf transformation 21]
103. ~tall(X0) | funny(X0) [duplicate literal removal 68]
104. funny(X0) | tall(X0) [duplicate literal removal 70]
106. 1 <=> ! [X0] : funny(X0) [avatar definition]
107. funny(X0) <- (1) [avatar component clause 106]
131. funny(X0) [subsumption resolution 103,104]
132. 1 [avatar split clause 131,106]
172. 16 <=> calm(sK3) [avatar definition]
174. ~calm(sK3) <- (~16) [avatar component clause 172]
177. 17 <=> generous(paul) [avatar definition]
180. 17 | ~16 [avatar split clause 92,172,177]
217. ~17 [avatar split clause 102,177]
225. old(sK3) <- (~16) [resolution 87,174]
234. ~funny(sK3) <- (~16) [resolution 225,82]
236. $false <- (1, ~16) [subsumption resolution 234,107]
237. ~1 | 16 [avatar contradiction clause 236]
238. $false [avatar sat refutation 132,180,217,237]
% SZS output end Proof for 6448395828851566552746507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is both not tall and quiet and vice versa. Everyone who is not generous is both not wise and not patient. If someone is not creative or not funny then paul is tall and vice versa. If susan is either old or not quiet then someone is old and vice versa. Everyone who is either not kind or curious is wise or calm. Everyone who is strong or funny is brave. Everyone who is not patient is either humble or not wise. Everyone who is both not creative and creative is patient or not curious and vice versa. Everyone who is either happy or not wise is funny or creative and vice versa. If susan is happy then mary is both not wise and funny and vice versa. Everyone who is not calm or rich is either kind or happy and vice versa. Everyone who is not tall is not rich and vice versa. If someone is both not humble and not kind then fred is not humble and vice versa. Everyone who is either not happy or not funny is both humble and patient. Everyone who is either not patient or not generous is not rich or old. If susan is not kind or not creative then someone is either not happy or not creative and vice versa. Someone is creative. Someone is both curious and not calm. Someone is not generous or not rich. Someone is not quiet or calm. Paul is either kind or not brave. Mary is quiet. Someone is either not old or not curious. | Fred is patient. | contradiction | (![X]:(~curious(X)<=>(~tall(X)&quiet(X))))&
(![X]:(~generous(X)=>(~wise(X)&~patient(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(tall(paul)))&
(((old(susan)<~>~quiet(susan)))<=>(?[X]:(old(X))))&
(![X]:((~kind(X)<~>curious(X))=>(wise(X)|calm(X))))&
(![X]:((strong(X)|funny(X))=>brave(X)))&
(![X]:(~patient(X)=>(humble(X)<~>~wise(X))))&
(![X]:((~creative(X)&creative(X))<=>(patient(X)|~curious(X))))&
(![X]:((happy(X)<~>~wise(X))<=>(funny(X)|creative(X))))&
((happy(susan))<=>((~wise(mary)&funny(mary))))&
(![X]:((~calm(X)|rich(X))<=>(kind(X)<~>happy(X))))&
(![X]:(~tall(X)<=>~rich(X)))&
((?[X]:((~humble(X)&~kind(X))))<=>(~humble(fred)))&
(![X]:((~happy(X)<~>~funny(X))=>(humble(X)&patient(X))))&
(![X]:((~patient(X)<~>~generous(X))=>(~rich(X)|old(X))))&
(((~kind(susan)|~creative(susan)))<=>(?[X]:((~happy(X)<~>~creative(X)))))&
(?[X]:(creative(X)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((~generous(X)|~rich(X))))&
(?[X]:((~quiet(X)|calm(X))))&
((kind(paul)<~>~brave(paul)))&
(quiet(mary))&
(?[X]:((~old(X)<~>~curious(X)))) | patient(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4495183745178537178121571
% SZS output start Proof for 4495183745178537178121571
8. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (~curious(X0) | patient(X0))) [input p7]
24. patient(fred) [input hypothesis]
46. ! [X0] : (((creative(X0) & ~creative(X0)) | (curious(X0) & ~patient(X0))) & ((~curious(X0) | patient(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 8]
47. ! [X0] : (((creative(X0) & ~creative(X0)) | (curious(X0) & ~patient(X0))) & (~curious(X0) | patient(X0) | ~creative(X0) | creative(X0))) [flattening 46]
96. ~creative(X0) | ~patient(X0) [cnf transformation 47]
98. creative(X0) | ~patient(X0) [cnf transformation 47]
142. patient(fred) [cnf transformation 24]
184. ~patient(X0) [subsumption resolution 96,98]
278. $false [subsumption resolution 142,184]
% SZS output end Proof for 4495183745178537178121571
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet then alice is either rich or not patient. Everyone who is creative or funny is either not brave or not humble and vice versa. If someone is both creative and happy then someone is either happy or not humble and vice versa. Everyone who is curious or tall is brave. Everyone who is creative or not funny is not creative and vice versa. If someone is not funny or not strong then someone is either not funny or creative. Everyone who is not generous or not curious is humble and vice versa. Everyone who is either calm or not happy is both humble and not kind. If john is either not old or not brave then someone is not happy or rich and vice versa. Everyone who is not wise or tall is either not generous or not strong and vice versa. If mary is both not curious and generous then someone is not creative and vice versa. Everyone who is either not curious or not funny is either not calm or humble. Everyone who is both wise and calm is not brave. Everyone who is patient is both generous and not humble. If fred is both tall and brave then someone is either wise or not strong and vice versa. If susan is either not calm or curious then someone is either not funny or not rich. Someone is kind. Someone is not happy. Someone is either rich or happy. Paul is not strong or curious. Someone is generous or humble. | Fred is funny. | contradiction | ((?[X]:(~quiet(X)))=>((rich(alice)<~>~patient(alice))))&
(![X]:((creative(X)|funny(X))<=>(~brave(X)<~>~humble(X))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:((curious(X)|tall(X))=>brave(X)))&
(![X]:((creative(X)|~funny(X))<=>~creative(X)))&
((?[X]:((~funny(X)|~strong(X))))=>(?[X]:((~funny(X)<~>creative(X)))))&
(![X]:((~generous(X)|~curious(X))<=>humble(X)))&
(![X]:((calm(X)<~>~happy(X))=>(humble(X)&~kind(X))))&
(((~old(john)<~>~brave(john)))<=>(?[X]:((~happy(X)|rich(X)))))&
(![X]:((~wise(X)|tall(X))<=>(~generous(X)<~>~strong(X))))&
(((~curious(mary)&generous(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)<~>~funny(X))=>(~calm(X)<~>humble(X))))&
(![X]:((wise(X)&calm(X))=>~brave(X)))&
(![X]:(patient(X)=>(generous(X)&~humble(X))))&
(((tall(fred)&brave(fred)))<=>(?[X]:((wise(X)<~>~strong(X)))))&
(((~calm(susan)<~>curious(susan)))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(?[X]:(kind(X)))&
(?[X]:(~happy(X)))&
(?[X]:((rich(X)<~>happy(X))))&
((~strong(paul)|curious(paul)))&
(?[X]:((generous(X)|humble(X)))) | funny(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 768749335508856539296691
% SZS output start Proof for 768749335508856539296691
5. ! [X0] : ((~funny(X0) | creative(X0)) <=> ~creative(X0)) [input p4]
22. funny(fred) [input hypothesis]
41. ! [X0] : (((~funny(X0) | creative(X0)) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [nnf transformation 5]
42. ! [X0] : ((~funny(X0) | creative(X0) | creative(X0)) & (~creative(X0) | (funny(X0) & ~creative(X0)))) [flattening 41]
93. ~creative(X0) | ~creative(X0) [cnf transformation 42]
95. ~funny(X0) | creative(X0) | creative(X0) [cnf transformation 42]
143. funny(fred) [cnf transformation 22]
144. ~creative(X0) [duplicate literal removal 93]
145. ~funny(X0) | creative(X0) [duplicate literal removal 95]
283. creative(fred) [resolution 145,143]
284. $false [subsumption resolution 283,144]
% SZS output end Proof for 768749335508856539296691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or strong is both kind and old and vice versa.
Everyone who is not old is tall or not generous.
Everyone who is not rich is rich or not creative.
Everyone who is both not wise and funny is not quiet.
If someone is not quiet or brave then someone is not old and vice versa.
If paul is calm or not strong then alice is either not creative or patient.
Everyone who is old or not humble is not kind or not rich.
If alice is either curious or happy then someone is both creative and not kind and vice versa.
If someone is both not humble and kind then someone is not humble or funny.
Everyone who is not generous or not calm is strong.
Everyone who is either not happy or not strong is wise or not tall and vice versa.
Everyone who is strong is either not kind or creative.
Everyone who is either old or quiet is either not creative or calm and vice versa.
If paul is either not generous or not creative then someone is either not generous or rich.
Everyone who is tall or not funny is both not kind and generous and vice versa.
Someone is not rich.
Someone is either wise or not old.
John is both calm and not brave.
Someone is not brave.
Alice is either not quiet or not happy.
Lucy is both happy and generous.
John is not strong or patient. | Alice is not calm. | contradiction | (![X]:((~calm(X)|strong(X))<=>(kind(X)&old(X))))&
(![X]:(~old(X)=>(tall(X)|~generous(X))))&
(![X]:(~rich(X)=>(rich(X)|~creative(X))))&
(![X]:((~wise(X)&funny(X))=>~quiet(X)))&
((?[X]:((~quiet(X)|brave(X))))<=>(?[X]:(~old(X))))&
(((calm(paul)|~strong(paul)))=>((~creative(alice)<~>patient(alice))))&
(![X]:((old(X)|~humble(X))=>(~kind(X)|~rich(X))))&
(((curious(alice)<~>happy(alice)))<=>(?[X]:((creative(X)&~kind(X)))))&
((?[X]:((~humble(X)&kind(X))))=>(?[X]:((~humble(X)|funny(X)))))&
(![X]:((~generous(X)|~calm(X))=>strong(X)))&
(![X]:((~happy(X)<~>~strong(X))<=>(wise(X)|~tall(X))))&
(![X]:(strong(X)=>(~kind(X)<~>creative(X))))&
(![X]:((old(X)<~>quiet(X))<=>(~creative(X)<~>calm(X))))&
(((~generous(paul)<~>~creative(paul)))=>(?[X]:((~generous(X)<~>rich(X)))))&
(![X]:((tall(X)|~funny(X))<=>(~kind(X)&generous(X))))&
(?[X]:(~rich(X)))&
(?[X]:((wise(X)<~>~old(X))))&
((calm(john)&~brave(john)))&
(?[X]:(~brave(X)))&
((~quiet(alice)<~>~happy(alice)))&
((happy(lucy)&generous(lucy)))&
((~strong(john)|patient(john))) | ~calm(alice) | [
"p0",
"p2",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 394009080443316431080593
% SZS output start Proof for 394009080443316431080593
1. ! [X0] : ((strong(X0) | ~calm(X0)) <=> (old(X0) & kind(X0))) [input p0]
3. ! [X0] : (~rich(X0) => (~creative(X0) | rich(X0))) [input p2]
7. ! [X0] : ((~humble(X0) | old(X0)) => (~rich(X0) | ~kind(X0))) [input p6]
10. ! [X0] : ((~calm(X0) | ~generous(X0)) => strong(X0)) [input p9]
12. ! [X0] : (strong(X0) => (~kind(X0) <~> creative(X0))) [input p11]
23. ~calm(alice) [input hypothesis]
28. ! [X0] : ((~creative(X0) | rich(X0)) | rich(X0)) [ennf transformation 3]
29. ! [X0] : (~creative(X0) | rich(X0) | rich(X0)) [flattening 28]
33. ! [X0] : ((~rich(X0) | ~kind(X0)) | (humble(X0) & ~old(X0))) [ennf transformation 7]
34. ! [X0] : (~rich(X0) | ~kind(X0) | (humble(X0) & ~old(X0))) [flattening 33]
36. ! [X0] : (strong(X0) | (calm(X0) & generous(X0))) [ennf transformation 10]
37. ! [X0] : ((~kind(X0) <~> creative(X0)) | ~strong(X0)) [ennf transformation 12]
39. ! [X0] : (((strong(X0) | ~calm(X0)) | (~old(X0) | ~kind(X0))) & ((old(X0) & kind(X0)) | (~strong(X0) & calm(X0)))) [nnf transformation 1]
40. ! [X0] : ((strong(X0) | ~calm(X0) | ~old(X0) | ~kind(X0)) & ((old(X0) & kind(X0)) | (~strong(X0) & calm(X0)))) [flattening 39]
56. ! [X0] : (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | ~strong(X0)) [nnf transformation 37]
72. ~strong(X0) | kind(X0) [cnf transformation 40]
74. ~strong(X0) | old(X0) [cnf transformation 40]
77. ~creative(X0) | rich(X0) | rich(X0) [cnf transformation 29]
86. ~rich(X0) | ~kind(X0) | ~old(X0) [cnf transformation 34]
96. strong(X0) | calm(X0) [cnf transformation 36]
103. creative(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 56]
133. ~calm(alice) [cnf transformation 23]
134. ~creative(X0) | rich(X0) [duplicate literal removal 77]
164. 8 <=> creative(alice) [avatar definition]
166. creative(alice) <- (8) [avatar component clause 164]
216. ~strong(X0) | creative(X0) [subsumption resolution 103,72]
338. 35 <=> strong(alice) [avatar definition]
339. strong(alice) <- (35) [avatar component clause 338]
340. ~strong(alice) <- (~35) [avatar component clause 338]
346. calm(alice) <- (~35) [resolution 340,96]
347. $false <- (~35) [subsumption resolution 346,133]
348. 35 [avatar contradiction clause 347]
360. creative(alice) <- (35) [resolution 339,216]
361. old(alice) <- (35) [resolution 339,74]
362. kind(alice) <- (35) [resolution 339,72]
365. 8 | ~35 [avatar split clause 360,338,164]
366. rich(alice) <- (8) [resolution 166,134]
392. ~kind(alice) | ~old(alice) <- (8) [resolution 366,86]
394. ~old(alice) <- (8, 35) [subsumption resolution 392,362]
395. $false <- (8, 35) [subsumption resolution 394,361]
396. ~8 | ~35 [avatar contradiction clause 395]
397. $false [avatar sat refutation 348,365,396]
% SZS output end Proof for 394009080443316431080593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either tall or not curious then susan is not happy or kind.
Everyone who is generous is tall and vice versa.
If fred is not brave then someone is either creative or not happy and vice versa.
If paul is both not strong and not old then someone is not tall or not brave and vice versa.
Everyone who is not rich is strong and vice versa.
If alice is both not creative and not wise then alice is not rich or humble and vice versa.
If someone is calm or happy then fred is either not wise or not generous.
Everyone who is both not wise and not kind is quiet and vice versa.
If fred is not wise or not humble then alice is either strong or patient.
Everyone who is both not patient and tall is both not curious and not calm.
If someone is not happy then paul is both rich and not happy.
If someone is either not brave or not strong then someone is rich or quiet.
Everyone who is both not quiet and strong is not brave or creative and vice versa.
Everyone who is brave or not quiet is not wise.
Everyone who is either happy or not brave is both not curious and quiet.
If someone is not brave then alice is both not happy and wise and vice versa.
Fred is rich or not generous.
Someone is generous.
Lucy is not curious or not tall.
Someone is either creative or not creative.
Someone is not kind or not generous. | Paul is kind. | contradiction | (((tall(susan)<~>~curious(susan)))=>((~happy(susan)|kind(susan))))&
(![X]:(generous(X)<=>tall(X)))&
((~brave(fred))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(((~strong(paul)&~old(paul)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:(~rich(X)<=>strong(X)))&
(((~creative(alice)&~wise(alice)))<=>((~rich(alice)|humble(alice))))&
((?[X]:((calm(X)|happy(X))))=>((~wise(fred)<~>~generous(fred))))&
(![X]:((~wise(X)&~kind(X))<=>quiet(X)))&
(((~wise(fred)|~humble(fred)))=>((strong(alice)<~>patient(alice))))&
(![X]:((~patient(X)&tall(X))=>(~curious(X)&~calm(X))))&
((?[X]:(~happy(X)))=>((rich(paul)&~happy(paul))))&
((?[X]:((~brave(X)<~>~strong(X))))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~quiet(X)&strong(X))<=>(~brave(X)|creative(X))))&
(![X]:((brave(X)|~quiet(X))=>~wise(X)))&
(![X]:((happy(X)<~>~brave(X))=>(~curious(X)&quiet(X))))&
((?[X]:(~brave(X)))<=>((~happy(alice)&wise(alice))))&
((rich(fred)|~generous(fred)))&
(?[X]:(generous(X)))&
((~curious(lucy)|~tall(lucy)))&
(?[X]:((creative(X)<~>~creative(X))))&
(?[X]:((~kind(X)|~generous(X)))) | kind(paul) | [
"p2",
"p4",
"p7",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5364558872225159467650622
% SZS output start Proof for 5364558872225159467650622
3. ~brave(fred) <=> ? [X0] : (creative(X0) <~> ~happy(X0)) [input p2]
5. ! [X0] : (~rich(X0) <=> strong(X0)) [input p4]
8. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> quiet(X0)) [input p7]
11. ? [X0] : ~happy(X0) => (~happy(paul) & rich(paul)) [input p10]
13. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> (creative(X0) | ~brave(X0))) [input p12]
14. ! [X0] : ((~quiet(X0) | brave(X0)) => ~wise(X0)) [input p13]
15. ! [X0] : ((happy(X0) <~> ~brave(X0)) => (quiet(X0) & ~curious(X0))) [input p14]
16. ? [X0] : ~brave(X0) <=> (wise(alice) & ~happy(alice)) [input p15]
22. kind(paul) [input hypothesis]
32. (~happy(paul) & rich(paul)) | ! [X0] : happy(X0) [ennf transformation 11]
34. ! [X0] : (~wise(X0) | (quiet(X0) & ~brave(X0))) [ennf transformation 14]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | (happy(X0) <=> ~brave(X0))) [ennf transformation 15]
38. (~brave(fred) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | brave(fred)) [nnf transformation 3]
39. (~brave(fred) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) | brave(fred)) [rectify 38]
40. ? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) => ((happy(sK0) | ~creative(sK0)) & (~happy(sK0) | creative(sK0))) [choice axiom]
41. (~brave(fred) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(sK0) | ~creative(sK0)) & (~happy(sK0) | creative(sK0))) | brave(fred)) [skolemisation 39,40]
47. ! [X0] : ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0))) [nnf transformation 5]
51. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | (kind(X0) | wise(X0)))) [nnf transformation 8]
52. ! [X0] : (((~kind(X0) & ~wise(X0)) | ~quiet(X0)) & (quiet(X0) | kind(X0) | wise(X0))) [flattening 51]
58. ! [X0] : (((strong(X0) & ~quiet(X0)) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | (~strong(X0) | quiet(X0)))) [nnf transformation 13]
59. ! [X0] : (((strong(X0) & ~quiet(X0)) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | ~strong(X0) | quiet(X0))) [flattening 58]
60. ! [X0] : ((quiet(X0) & ~curious(X0)) | ((happy(X0) | brave(X0)) & (~brave(X0) | ~happy(X0)))) [nnf transformation 35]
61. (? [X0] : ~brave(X0) | (~wise(alice) | happy(alice))) & ((wise(alice) & ~happy(alice)) | ! [X0] : brave(X0)) [nnf transformation 16]
62. (? [X0] : ~brave(X0) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X0] : brave(X0)) [flattening 61]
63. (? [X0] : ~brave(X0) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X1] : brave(X1)) [rectify 62]
64. ? [X0] : ~brave(X0) => ~brave(sK3) [choice axiom]
65. (~brave(sK3) | ~wise(alice) | happy(alice)) & ((wise(alice) & ~happy(alice)) | ! [X1] : brave(X1)) [skolemisation 63,64]
80. ~brave(fred) | creative(X0) | happy(X0) [cnf transformation 41]
87. ~rich(X0) | ~strong(X0) [cnf transformation 47]
96. ~quiet(X0) | ~wise(X0) [cnf transformation 52]
97. ~quiet(X0) | ~kind(X0) [cnf transformation 52]
103. rich(paul) | happy(X0) [cnf transformation 32]
104. ~happy(paul) | happy(X0) [cnf transformation 32]
111. ~creative(X0) | strong(X0) [cnf transformation 59]
113. ~wise(X0) | quiet(X0) [cnf transformation 34]
116. ~brave(X0) | quiet(X0) | ~happy(X0) [cnf transformation 60]
119. wise(alice) | brave(X1) [cnf transformation 65]
127. kind(paul) [cnf transformation 22]
147. 5 <=> ! [X0] : (creative(X0) | happy(X0)) [avatar definition]
148. creative(X0) | happy(X0) <- (5) [avatar component clause 147]
150. 6 <=> brave(fred) [avatar definition]
152. ~brave(fred) <- (~6) [avatar component clause 150]
153. 5 | ~6 [avatar split clause 80,150,147]
169. 10 <=> ! [X0] : brave(X0) [avatar definition]
170. brave(X0) <- (10) [avatar component clause 169]
181. 13 <=> strong(paul) [avatar definition]
183. ~strong(paul) <- (~13) [avatar component clause 181]
246. 26 <=> ! [X0] : happy(X0) [avatar definition]
247. happy(X0) <- (26) [avatar component clause 246]
249. 27 <=> happy(paul) [avatar definition]
251. ~happy(paul) <- (~27) [avatar component clause 249]
252. 26 | ~27 [avatar split clause 104,249,246]
254. 28 <=> rich(paul) [avatar definition]
256. rich(paul) <- (28) [avatar component clause 254]
257. 26 | 28 [avatar split clause 103,254,246]
274. ~wise(X0) [subsumption resolution 113,96]
276. brave(X1) [subsumption resolution 119,274]
277. 10 [avatar split clause 276,169]
310. $false <- (~6, 10) [subsumption resolution 152,170]
311. 6 | ~10 [avatar contradiction clause 310]
324. ~strong(paul) <- (28) [resolution 87,256]
331. strong(X0) | happy(X0) <- (5) [resolution 148,111]
362. happy(paul) <- (5, ~13) [resolution 331,183]
365. $false <- (5, ~13, ~27) [subsumption resolution 362,251]
366. ~5 | 13 | 27 [avatar contradiction clause 365]
367. ~13 | ~28 [avatar split clause 324,254,181]
383. quiet(X1) | ~happy(X1) <- (10) [resolution 116,170]
384. quiet(X1) <- (10, 26) [subsumption resolution 383,247]
387. ~kind(X2) <- (10, 26) [resolution 384,97]
395. $false <- (10, 26) [resolution 387,127]
398. ~10 | ~26 [avatar contradiction clause 395]
399. $false [avatar sat refutation 153,252,257,277,311,366,367,398]
% SZS output end Proof for 5364558872225159467650622
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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