premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not brave is either generous or not kind and vice versa. Everyone who is either not kind or not curious is both humble and not rich and vice versa. If someone is strong or happy then someone is wise or not tall and vice versa. If someone is funny or not wise then paul is kind or not strong and vice versa. If fred is not patient then mary is either not patient or strong. Everyone who is humble is both funny and humble. If someone is either not quiet or not kind then someone is not old or not wise and vice versa. Everyone who is either not creative or not funny is not kind. If someone is old then someone is not curious and vice versa. Everyone who is wise is either rich or old. If someone is both patient and not curious then fred is not funny or old and vice versa. If paul is both not kind and not calm then lucy is either not creative or not patient. If someone is both not curious and calm then fred is not happy or strong. Everyone who is generous is either brave or not patient and vice versa. Everyone who is both creative and not patient is either wise or not curious and vice versa. If someone is either not brave or not funny then john is both strong and not quiet and vice versa. Someone is rich or old. Someone is both wise and not kind. Mary is kind. Someone is both not curious and not patient. Someone is not strong or creative. Someone is not kind or not happy. Susan is either brave or not humble. Someone is not wise or kind. | Mary is patient. | contradiction | (![X]:(~brave(X)<=>(generous(X)<~>~kind(X))))&
(![X]:((~kind(X)<~>~curious(X))<=>(humble(X)&~rich(X))))&
((?[X]:((strong(X)|happy(X))))<=>(?[X]:((wise(X)|~tall(X)))))&
((?[X]:((funny(X)|~wise(X))))<=>((kind(paul)|~strong(paul))))&
((~patient(fred))=>((~patient(mary)<~>strong(mary))))&
(![X]:(humble(X)=>(funny(X)&humble(X))))&
((?[X]:((~quiet(X)<~>~kind(X))))<=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:((~creative(X)<~>~funny(X))=>~kind(X)))&
((?[X]:(old(X)))<=>(?[X]:(~curious(X))))&
(![X]:(wise(X)=>(rich(X)<~>old(X))))&
((?[X]:((patient(X)&~curious(X))))<=>((~funny(fred)|old(fred))))&
(((~kind(paul)&~calm(paul)))=>((~creative(lucy)<~>~patient(lucy))))&
((?[X]:((~curious(X)&calm(X))))=>((~happy(fred)|strong(fred))))&
(![X]:(generous(X)<=>(brave(X)<~>~patient(X))))&
(![X]:((creative(X)&~patient(X))<=>(wise(X)<~>~curious(X))))&
((?[X]:((~brave(X)<~>~funny(X))))<=>((strong(john)&~quiet(john))))&
(?[X]:((rich(X)|old(X))))&
(?[X]:((wise(X)&~kind(X))))&
(kind(mary))&
(?[X]:((~curious(X)&~patient(X))))&
(?[X]:((~strong(X)|creative(X))))&
(?[X]:((~kind(X)|~happy(X))))&
((brave(susan)<~>~humble(susan)))&
(?[X]:((~wise(X)|kind(X)))) | patient(mary) | [
"p0",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8119812719720565715625194
% SZS output start Proof for 8119812719720565715625194
1. ! [X0] : (~brave(X0) <=> (generous(X0) <~> ~kind(X0))) [input p0]
14. ! [X0] : (generous(X0) <=> (brave(X0) <~> ~patient(X0))) [input p13]
19. kind(mary) [input p18]
25. patient(mary) [input hypothesis]
37. ! [X0] : ((~brave(X0) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0)))) & (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | brave(X0))) [nnf transformation 1]
69. ! [X0] : ((generous(X0) | ((brave(X0) | patient(X0)) & (~patient(X0) | ~brave(X0)))) & (((patient(X0) | ~brave(X0)) & (~patient(X0) | brave(X0))) | ~generous(X0))) [nnf transformation 14]
90. ~kind(X0) | generous(X0) | brave(X0) [cnf transformation 37]
92. ~kind(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 37]
132. ~patient(X0) | brave(X0) | ~generous(X0) [cnf transformation 69]
134. ~patient(X0) | generous(X0) | ~brave(X0) [cnf transformation 69]
151. kind(mary) [cnf transformation 19]
159. patient(mary) [cnf transformation 25]
223. 16 <=> patient(mary) [avatar definition]
225. patient(mary) <- (16) [avatar component clause 223]
403. 16 [avatar split clause 159,223]
406. generous(mary) | brave(mary) [resolution 90,151]
409. 56 <=> brave(mary) [avatar definition]
411. brave(mary) <- (56) [avatar component clause 409]
413. 57 <=> generous(mary) [avatar definition]
414. ~generous(mary) <- (~57) [avatar component clause 413]
416. 56 | 57 [avatar split clause 406,413,409]
427. ~brave(mary) | ~generous(mary) [resolution 92,151]
514. brave(mary) | ~generous(mary) <- (16) [resolution 132,225]
537. ~57 | 56 | ~16 [avatar split clause 514,223,409,413]
538. ~57 | ~56 [avatar split clause 427,409,413]
543. generous(mary) | ~brave(mary) <- (16) [resolution 134,225]
547. ~brave(mary) <- (16, ~57) [subsumption resolution 543,414]
548. $false <- (16, 56, ~57) [subsumption resolution 547,411]
549. ~16 | ~56 | 57 [avatar contradiction clause 548]
552. $false [avatar sat refutation 403,416,537,538,549]
% SZS output end Proof for 8119812719720565715625194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not brave and old is either not quiet or not creative and vice versa.
Everyone who is creative or not generous is both not curious and not creative and vice versa.
If lucy is either not rich or curious then john is funny.
Everyone who is not tall is both strong and not old and vice versa.
If susan is both not funny and wise then john is either not happy or brave.
Everyone who is both humble and not strong is either not old or not creative and vice versa.
Everyone who is either brave or not tall is both not brave and not humble.
If john is either old or not kind then someone is either strong or brave.
If mary is both not kind and curious then someone is tall or not brave and vice versa.
Everyone who is either strong or not patient is either tall or wise and vice versa.
Everyone who is not brave is not wise or funny and vice versa.
If paul is both not calm and curious then fred is quiet or not strong.
Everyone who is not wise is not kind.
Everyone who is not funny or not humble is curious or not old.
Everyone who is both not funny and not old is both not funny and not tall and vice versa.
Everyone who is not humble is not old and vice versa.
Fred is not generous or not quiet.
Someone is both patient and not creative.
Someone is old or not humble.
Lucy is either not rich or humble.
Someone is both not creative and calm.
Someone is both patient and not happy.
Fred is either kind or wise.
Someone is either not tall or not generous. | Mary is not calm. | neutral | (![X]:((~brave(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((creative(X)|~generous(X))<=>(~curious(X)&~creative(X))))&
(((~rich(lucy)<~>curious(lucy)))=>(funny(john)))&
(![X]:(~tall(X)<=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
((~generous(fred)|~quiet(fred)))&
(?[X]:((patient(X)&~creative(X))))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X)))) | ~calm(mary) | [] | null | 0 |
If someone is both rich and kind then someone is both tall and kind and vice versa.
If mary is generous or curious then someone is either not strong or not kind.
Everyone who is humble or not old is happy or not wise.
Everyone who is tall is not curious.
If someone is either not humble or humble then someone is both patient and not kind.
Everyone who is not kind is not quiet.
If alice is either not strong or not wise then mary is either patient or not curious and vice versa.
Everyone who is not creative or not curious is curious or generous and vice versa.
Everyone who is both not wise and not kind is not generous or not rich.
If someone is both not humble and not curious then mary is either not generous or curious.
Everyone who is both funny and not happy is rich or calm and vice versa.
Everyone who is either not old or not patient is not happy or strong and vice versa.
Everyone who is both funny and not generous is calm.
Everyone who is either kind or old is not calm and vice versa.
If someone is humble then susan is both funny and not wise.
Everyone who is brave or creative is either not generous or quiet.
Susan is not creative or rich.
Lucy is quiet or not funny.
Fred is both funny and not happy.
Someone is either not rich or calm.
Alice is both patient and old.
Someone is creative.
Alice is tall.
Someone is both not patient and creative. | Alice is not kind. | entailment | ((?[X]:((rich(X)&kind(X))))<=>(?[X]:((tall(X)&kind(X)))))&
(((generous(mary)|curious(mary)))=>(?[X]:((~strong(X)<~>~kind(X)))))&
(![X]:((humble(X)|~old(X))=>(happy(X)|~wise(X))))&
(![X]:(tall(X)=>~curious(X)))&
((?[X]:((~humble(X)<~>humble(X))))=>(?[X]:((patient(X)&~kind(X)))))&
(![X]:(~kind(X)=>~quiet(X)))&
(((~strong(alice)<~>~wise(alice)))<=>((patient(mary)<~>~curious(mary))))&
(![X]:((~creative(X)|~curious(X))<=>(curious(X)|generous(X))))&
(![X]:((~wise(X)&~kind(X))=>(~generous(X)|~rich(X))))&
((?[X]:((~humble(X)&~curious(X))))=>((~generous(mary)<~>curious(mary))))&
(![X]:((funny(X)&~happy(X))<=>(rich(X)|calm(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(~happy(X)|strong(X))))&
(![X]:((funny(X)&~generous(X))=>calm(X)))&
(![X]:((kind(X)<~>old(X))<=>~calm(X)))&
((?[X]:(humble(X)))=>((funny(susan)&~wise(susan))))&
(![X]:((brave(X)|creative(X))=>(~generous(X)<~>quiet(X))))&
((~creative(susan)|rich(susan)))&
((quiet(lucy)|~funny(lucy)))&
((funny(fred)&~happy(fred)))&
(?[X]:((~rich(X)<~>calm(X))))&
((patient(alice)&old(alice)))&
(?[X]:(creative(X)))&
(tall(alice))&
(?[X]:((~patient(X)&creative(X)))) | ~kind(alice) | [
"p10",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7962598530656132781836866
% SZS output start Proof for 7962598530656132781836866
11. ! [X0] : ((~happy(X0) & funny(X0)) <=> (calm(X0) | rich(X0))) [input p10]
12. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (strong(X0) | ~happy(X0))) [input p11]
14. ! [X0] : ((kind(X0) <~> old(X0)) <=> ~calm(X0)) [input p13]
21. old(alice) & patient(alice) [input p20]
25. kind(alice) [input hypothesis]
58. ! [X0] : (((~happy(X0) & funny(X0)) | (~calm(X0) & ~rich(X0))) & ((calm(X0) | rich(X0)) | (happy(X0) | ~funny(X0)))) [nnf transformation 11]
59. ! [X0] : (((~happy(X0) & funny(X0)) | (~calm(X0) & ~rich(X0))) & (calm(X0) | rich(X0) | happy(X0) | ~funny(X0))) [flattening 58]
60. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~strong(X0) & happy(X0))) & ((strong(X0) | ~happy(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 12]
61. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~strong(X0) & happy(X0))) & (strong(X0) | ~happy(X0) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 60]
62. ! [X0] : ((((~old(X0) | ~kind(X0)) & (old(X0) | kind(X0))) | calm(X0)) & (~calm(X0) | ((kind(X0) | ~old(X0)) & (old(X0) | ~kind(X0))))) [nnf transformation 14]
106. ~calm(X0) | ~happy(X0) [cnf transformation 59]
109. ~patient(X0) | ~old(X0) | happy(X0) [cnf transformation 61]
117. ~old(X0) | ~kind(X0) | calm(X0) [cnf transformation 62]
128. patient(alice) [cnf transformation 21]
129. old(alice) [cnf transformation 21]
134. kind(alice) [cnf transformation 25]
288. ~old(alice) | happy(alice) [resolution 109,128]
290. happy(alice) [subsumption resolution 288,129]
396. ~kind(alice) | calm(alice) [resolution 117,129]
397. calm(alice) [subsumption resolution 396,134]
423. ~happy(alice) [resolution 397,106]
425. $false [subsumption resolution 423,290]
% SZS output end Proof for 7962598530656132781836866
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both patient and generous then someone is either old or patient and vice versa.
Everyone who is not humble is either not wise or not humble and vice versa.
Everyone who is generous or not funny is strong and vice versa.
Everyone who is either not generous or not rich is not calm or patient and vice versa.
Everyone who is either not tall or creative is either not rich or humble and vice versa.
If someone is both not generous and not creative then someone is funny.
Everyone who is creative is not wise.
Everyone who is not old is both creative and generous.
Everyone who is not curious or generous is both not tall and wise.
Everyone who is patient is either not old or wise and vice versa.
If john is funny or curious then someone is either brave or not tall.
Everyone who is either not happy or tall is both patient and funny and vice versa.
If someone is not quiet or not strong then susan is either not calm or kind and vice versa.
If lucy is funny then someone is both funny and not humble.
Everyone who is happy or not patient is either not rich or not brave.
Paul is brave.
Someone is either kind or happy.
Someone is either not wise or not quiet.
Someone is quiet.
Paul is not tall.
Lucy is humble or not kind. | Paul is curious. | neutral | ((?[X]:((patient(X)&generous(X))))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(~humble(X)<=>(~wise(X)<~>~humble(X))))&
(![X]:((generous(X)|~funny(X))<=>strong(X)))&
(![X]:((~generous(X)<~>~rich(X))<=>(~calm(X)|patient(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(~rich(X)<~>humble(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:(funny(X))))&
(![X]:(creative(X)=>~wise(X)))&
(![X]:(~old(X)=>(creative(X)&generous(X))))&
(![X]:((~curious(X)|generous(X))=>(~tall(X)&wise(X))))&
(![X]:(patient(X)<=>(~old(X)<~>wise(X))))&
(((funny(john)|curious(john)))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(patient(X)&funny(X))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((~calm(susan)<~>kind(susan))))&
((funny(lucy))=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:((happy(X)|~patient(X))=>(~rich(X)<~>~brave(X))))&
(brave(paul))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~wise(X)<~>~quiet(X))))&
(?[X]:(quiet(X)))&
(~tall(paul))&
((humble(lucy)|~kind(lucy))) | curious(paul) | [] | null | 0 |
Everyone who is either not quiet or tall is both happy and not kind and vice versa. Everyone who is old is both kind and not curious and vice versa. If someone is not strong then someone is not wise or not humble. Everyone who is both not quiet and not wise is wise or not generous and vice versa. Everyone who is both not wise and not kind is funny or creative and vice versa. Everyone who is either not rich or not tall is not wise and vice versa. Everyone who is both funny and not generous is not old or not calm and vice versa. If someone is not rich then someone is not happy and vice versa. Everyone who is both wise and not creative is not old and vice versa. If someone is both calm and not strong then someone is both happy and generous and vice versa. If lucy is happy then someone is wise or funny. If someone is both curious and not quiet then someone is either not wise or strong and vice versa. If someone is not strong or not funny then lucy is not quiet or not generous and vice versa. If alice is both strong and not rich then someone is not creative and vice versa. Susan is either not tall or patient. Someone is happy. Someone is not happy. Someone is either not old or kind. John is not happy. | Lucy is not calm. | contradiction | (![X]:((~quiet(X)<~>tall(X))<=>(happy(X)&~kind(X))))&
(![X]:(old(X)<=>(kind(X)&~curious(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((~quiet(X)&~wise(X))<=>(wise(X)|~generous(X))))&
(![X]:((~wise(X)&~kind(X))<=>(funny(X)|creative(X))))&
(![X]:((~rich(X)<~>~tall(X))<=>~wise(X)))&
(![X]:((funny(X)&~generous(X))<=>(~old(X)|~calm(X))))&
((?[X]:(~rich(X)))<=>(?[X]:(~happy(X))))&
(![X]:((wise(X)&~creative(X))<=>~old(X)))&
((?[X]:((calm(X)&~strong(X))))<=>(?[X]:((happy(X)&generous(X)))))&
((happy(lucy))=>(?[X]:((wise(X)|funny(X)))))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:((~wise(X)<~>strong(X)))))&
((?[X]:((~strong(X)|~funny(X))))<=>((~quiet(lucy)|~generous(lucy))))&
(((strong(alice)&~rich(alice)))<=>(?[X]:(~creative(X))))&
((~tall(susan)<~>patient(susan)))&
(?[X]:(happy(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~old(X)<~>kind(X))))&
(~happy(john)) | ~calm(lucy) | [
"p1",
"p3",
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 852091566055787379774019
% SZS output start Proof for 852091566055787379774019
2. ! [X0] : (old(X0) <=> (~curious(X0) & kind(X0))) [input p1]
4. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (~generous(X0) | wise(X0))) [input p3]
5. ! [X0] : ((~kind(X0) & ~wise(X0)) <=> (creative(X0) | funny(X0))) [input p4]
7. ! [X0] : ((~generous(X0) & funny(X0)) <=> (~calm(X0) | ~old(X0))) [input p6]
9. ! [X0] : ((~creative(X0) & wise(X0)) <=> ~old(X0)) [input p8]
20. ~calm(lucy) [input hypothesis]
29. ! [X0] : ((old(X0) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | ~old(X0))) [nnf transformation 2]
30. ! [X0] : ((old(X0) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | ~old(X0))) [flattening 29]
31. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (generous(X0) & ~wise(X0))) & ((~generous(X0) | wise(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 4]
32. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (generous(X0) & ~wise(X0))) & (~generous(X0) | wise(X0) | wise(X0) | quiet(X0))) [flattening 31]
33. ! [X0] : (((~kind(X0) & ~wise(X0)) | (~creative(X0) & ~funny(X0))) & ((creative(X0) | funny(X0)) | (kind(X0) | wise(X0)))) [nnf transformation 5]
34. ! [X0] : (((~kind(X0) & ~wise(X0)) | (~creative(X0) & ~funny(X0))) & (creative(X0) | funny(X0) | kind(X0) | wise(X0))) [flattening 33]
36. ! [X0] : (((~generous(X0) & funny(X0)) | (calm(X0) & old(X0))) & ((~calm(X0) | ~old(X0)) | (generous(X0) | ~funny(X0)))) [nnf transformation 7]
37. ! [X0] : (((~generous(X0) & funny(X0)) | (calm(X0) & old(X0))) & (~calm(X0) | ~old(X0) | generous(X0) | ~funny(X0))) [flattening 36]
43. ! [X0] : (((~creative(X0) & wise(X0)) | old(X0)) & (~old(X0) | (creative(X0) | ~wise(X0)))) [nnf transformation 9]
44. ! [X0] : (((~creative(X0) & wise(X0)) | old(X0)) & (~old(X0) | creative(X0) | ~wise(X0))) [flattening 43]
81. ~old(X0) | kind(X0) [cnf transformation 30]
87. ~wise(X0) | ~wise(X0) [cnf transformation 32]
92. ~funny(X0) | ~kind(X0) [cnf transformation 34]
100. calm(X0) | funny(X0) [cnf transformation 37]
106. wise(X0) | old(X0) [cnf transformation 44]
133. ~calm(lucy) [cnf transformation 20]
135. ~wise(X0) [duplicate literal removal 87]
156. old(X0) [subsumption resolution 106,135]
274. kind(X0) [resolution 81,156]
282. funny(lucy) [resolution 100,133]
283. ~kind(lucy) [resolution 282,92]
284. $false [subsumption resolution 283,274]
% SZS output end Proof for 852091566055787379774019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then someone is not humble.
Everyone who is either not humble or not kind is not generous or quiet.
Everyone who is both happy and funny is not kind.
If fred is not creative then paul is both not strong and not funny and vice versa.
Everyone who is either not wise or rich is patient and vice versa.
If someone is strong then someone is either not humble or wise and vice versa.
If john is wise then someone is not calm and vice versa.
If someone is brave then paul is not wise or not tall.
Everyone who is both kind and not wise is not patient or not funny and vice versa.
If fred is not kind or humble then someone is not creative or old.
Everyone who is rich or not strong is both not quiet and not kind.
Everyone who is either not humble or not patient is both strong and not patient.
Everyone who is both curious and generous is either happy or rich.
If john is brave then mary is either not happy or wise.
If someone is both brave and not happy then lucy is not strong.
Everyone who is either calm or not creative is not generous or not funny.
John is both generous and quiet.
Mary is not quiet or happy.
Someone is kind or not patient.
Alice is either quiet or wise.
Fred is either strong or wise.
Lucy is either patient or not curious.
Susan is both rich and not brave.
Someone is brave or not humble. | Susan is humble. | entailment | ((strong(lucy))=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)<~>~kind(X))=>(~generous(X)|quiet(X))))&
(![X]:((happy(X)&funny(X))=>~kind(X)))&
((~creative(fred))<=>((~strong(paul)&~funny(paul))))&
(![X]:((~wise(X)<~>rich(X))<=>patient(X)))&
((?[X]:(strong(X)))<=>(?[X]:((~humble(X)<~>wise(X)))))&
((wise(john))<=>(?[X]:(~calm(X))))&
((?[X]:(brave(X)))=>((~wise(paul)|~tall(paul))))&
(![X]:((kind(X)&~wise(X))<=>(~patient(X)|~funny(X))))&
(((~kind(fred)|humble(fred)))=>(?[X]:((~creative(X)|old(X)))))&
(![X]:((rich(X)|~strong(X))=>(~quiet(X)&~kind(X))))&
(![X]:((~humble(X)<~>~patient(X))=>(strong(X)&~patient(X))))&
(![X]:((curious(X)&generous(X))=>(happy(X)<~>rich(X))))&
((brave(john))=>((~happy(mary)<~>wise(mary))))&
((?[X]:((brave(X)&~happy(X))))=>(~strong(lucy)))&
(![X]:((calm(X)<~>~creative(X))=>(~generous(X)|~funny(X))))&
((generous(john)&quiet(john)))&
((~quiet(mary)|happy(mary)))&
(?[X]:((kind(X)|~patient(X))))&
((quiet(alice)<~>wise(alice)))&
((strong(fred)<~>wise(fred)))&
((patient(lucy)<~>~curious(lucy)))&
((rich(susan)&~brave(susan)))&
(?[X]:((brave(X)|~humble(X)))) | humble(susan) | [
"p8",
"p10",
"p11",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4376861748327372979846855
% SZS output start Proof for 4376861748327372979846855
9. ! [X0] : ((~wise(X0) & kind(X0)) <=> (~funny(X0) | ~patient(X0))) [input p8]
11. ! [X0] : ((~strong(X0) | rich(X0)) => (~kind(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : ((~humble(X0) <~> ~patient(X0)) => (~patient(X0) & strong(X0))) [input p11]
23. ~brave(susan) & rich(susan) [input p22]
25. ~humble(susan) [input hypothesis]
34. ! [X0] : ((~kind(X0) & ~quiet(X0)) | (strong(X0) & ~rich(X0))) [ennf transformation 11]
35. ! [X0] : ((~patient(X0) & strong(X0)) | (~humble(X0) <=> ~patient(X0))) [ennf transformation 12]
57. ! [X0] : (((~wise(X0) & kind(X0)) | (funny(X0) & patient(X0))) & ((~funny(X0) | ~patient(X0)) | (wise(X0) | ~kind(X0)))) [nnf transformation 9]
58. ! [X0] : (((~wise(X0) & kind(X0)) | (funny(X0) & patient(X0))) & (~funny(X0) | ~patient(X0) | wise(X0) | ~kind(X0))) [flattening 57]
59. ! [X0] : ((~patient(X0) & strong(X0)) | ((~humble(X0) | patient(X0)) & (~patient(X0) | humble(X0)))) [nnf transformation 35]
88. patient(X0) | kind(X0) [cnf transformation 58]
94. ~rich(X0) | ~kind(X0) [cnf transformation 34]
98. ~patient(X0) | ~patient(X0) | humble(X0) [cnf transformation 59]
117. rich(susan) [cnf transformation 23]
120. ~humble(susan) [cnf transformation 25]
121. ~patient(X0) | humble(X0) [duplicate literal removal 98]
256. ~kind(susan) [resolution 94,117]
264. kind(X0) | humble(X0) [resolution 121,88]
320. humble(susan) [resolution 264,256]
322. $false [subsumption resolution 320,120]
% SZS output end Proof for 4376861748327372979846855
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or curious is not strong or brave and vice versa.
If someone is patient then susan is tall.
Everyone who is not curious is rich and vice versa.
If someone is kind or not happy then john is either funny or not quiet and vice versa.
Everyone who is either not generous or not rich is not quiet or not kind and vice versa.
Everyone who is humble or generous is not humble or not funny and vice versa.
If someone is both not creative and patient then susan is not creative and vice versa.
If someone is both not rich and calm then someone is not creative or curious.
Everyone who is old is either curious or tall and vice versa.
If susan is both strong and patient then someone is either not quiet or not tall and vice versa.
Everyone who is either quiet or not calm is both humble and not quiet and vice versa.
Everyone who is humble is wise or not curious.
Everyone who is curious is either not old or brave and vice versa.
If someone is not brave then someone is old and vice versa.
If someone is not kind or curious then paul is either not funny or tall and vice versa.
If someone is happy or not quiet then alice is both not humble and rich and vice versa.
Susan is both tall and not funny.
Alice is both not curious and patient.
Lucy is both not funny and not calm.
Mary is not brave or not kind.
Lucy is either not curious or kind.
Mary is both kind and patient.
John is not funny or not strong.
Fred is patient. | Alice is not quiet. | contradiction | (![X]:((kind(X)<~>curious(X))<=>(~strong(X)|brave(X))))&
((?[X]:(patient(X)))=>(tall(susan)))&
(![X]:(~curious(X)<=>rich(X)))&
((?[X]:((kind(X)|~happy(X))))<=>((funny(john)<~>~quiet(john))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~quiet(X)|~kind(X))))&
(![X]:((humble(X)|generous(X))<=>(~humble(X)|~funny(X))))&
((?[X]:((~creative(X)&patient(X))))<=>(~creative(susan)))&
((?[X]:((~rich(X)&calm(X))))=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:(old(X)<=>(curious(X)<~>tall(X))))&
(((strong(susan)&patient(susan)))<=>(?[X]:((~quiet(X)<~>~tall(X)))))&
(![X]:((quiet(X)<~>~calm(X))<=>(humble(X)&~quiet(X))))&
(![X]:(humble(X)=>(wise(X)|~curious(X))))&
(![X]:(curious(X)<=>(~old(X)<~>brave(X))))&
((?[X]:(~brave(X)))<=>(?[X]:(old(X))))&
((?[X]:((~kind(X)|curious(X))))<=>((~funny(paul)<~>tall(paul))))&
((?[X]:((happy(X)|~quiet(X))))<=>((~humble(alice)&rich(alice))))&
((tall(susan)&~funny(susan)))&
((~curious(alice)&patient(alice)))&
((~funny(lucy)&~calm(lucy)))&
((~brave(mary)|~kind(mary)))&
((~curious(lucy)<~>kind(lucy)))&
((kind(mary)&patient(mary)))&
((~funny(john)|~strong(john)))&
(patient(fred)) | ~quiet(alice) | [
"p2",
"p4",
"p5",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6371942749172940648736046
% SZS output start Proof for 6371942749172940648736046
3. ! [X0] : (~curious(X0) <=> rich(X0)) [input p2]
5. ! [X0] : ((~generous(X0) <~> ~rich(X0)) <=> (~kind(X0) | ~quiet(X0))) [input p4]
6. ! [X0] : ((generous(X0) | humble(X0)) <=> (~funny(X0) | ~humble(X0))) [input p5]
16. ? [X0] : (~quiet(X0) | happy(X0)) <=> (rich(alice) & ~humble(alice)) [input p15]
18. patient(alice) & ~curious(alice) [input p17]
25. ~quiet(alice) [input hypothesis]
33. ! [X0] : ((~curious(X0) | ~rich(X0)) & (rich(X0) | curious(X0))) [nnf transformation 3]
38. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | (kind(X0) & quiet(X0))) & ((~kind(X0) | ~quiet(X0)) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [nnf transformation 5]
39. ! [X0] : ((((rich(X0) | generous(X0)) & (~rich(X0) | ~generous(X0))) | (kind(X0) & quiet(X0))) & (~kind(X0) | ~quiet(X0) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0))))) [flattening 38]
40. ! [X0] : (((generous(X0) | humble(X0)) | (funny(X0) & humble(X0))) & ((~funny(X0) | ~humble(X0)) | (~generous(X0) & ~humble(X0)))) [nnf transformation 6]
41. ! [X0] : ((generous(X0) | humble(X0) | (funny(X0) & humble(X0))) & (~funny(X0) | ~humble(X0) | (~generous(X0) & ~humble(X0)))) [flattening 40]
67. (? [X0] : (~quiet(X0) | happy(X0)) | (~rich(alice) | humble(alice))) & ((rich(alice) & ~humble(alice)) | ! [X0] : (quiet(X0) & ~happy(X0))) [nnf transformation 16]
68. (? [X0] : (~quiet(X0) | happy(X0)) | ~rich(alice) | humble(alice)) & ((rich(alice) & ~humble(alice)) | ! [X0] : (quiet(X0) & ~happy(X0))) [flattening 67]
69. (? [X0] : (~quiet(X0) | happy(X0)) | ~rich(alice) | humble(alice)) & ((rich(alice) & ~humble(alice)) | ! [X1] : (quiet(X1) & ~happy(X1))) [rectify 68]
70. ? [X0] : (~quiet(X0) | happy(X0)) => (~quiet(sK7) | happy(sK7)) [choice axiom]
71. ((~quiet(sK7) | happy(sK7)) | ~rich(alice) | humble(alice)) & ((rich(alice) & ~humble(alice)) | ! [X1] : (quiet(X1) & ~happy(X1))) [skolemisation 69,70]
80. rich(X0) | curious(X0) [cnf transformation 33]
90. ~generous(X0) | ~rich(X0) | quiet(X0) [cnf transformation 39]
96. generous(X0) | humble(X0) | humble(X0) [cnf transformation 41]
131. ~humble(alice) | quiet(X1) [cnf transformation 71]
137. ~curious(alice) [cnf transformation 18]
148. ~quiet(alice) [cnf transformation 25]
152. humble(X0) | generous(X0) [duplicate literal removal 96]
292. 32 <=> humble(alice) [avatar definition]
293. ~humble(alice) <- (~32) [avatar component clause 292]
296. 33 <=> rich(alice) [avatar definition]
298. ~rich(alice) <- (~33) [avatar component clause 296]
309. 36 <=> ! [X1] : quiet(X1) [avatar definition]
310. quiet(X1) <- (36) [avatar component clause 309]
316. 36 | ~32 [avatar split clause 131,292,309]
352. generous(alice) <- (~32) [resolution 152,293]
356. ~rich(alice) | quiet(alice) <- (~32) [resolution 90,352]
360. ~rich(alice) <- (~32) [subsumption resolution 356,148]
361. ~33 | 32 [avatar split clause 360,292,296]
362. curious(alice) <- (~33) [resolution 298,80]
363. $false <- (~33) [subsumption resolution 362,137]
364. 33 [avatar contradiction clause 363]
369. $false <- (36) [resolution 310,148]
372. ~36 [avatar contradiction clause 369]
374. $false [avatar sat refutation 316,361,364,372]
% SZS output end Proof for 6371942749172940648736046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is humble or generous then fred is not brave.
Everyone who is both strong and not curious is both funny and rich and vice versa.
Everyone who is both patient and curious is both not creative and not old.
If susan is either not quiet or creative then lucy is either rich or curious and vice versa.
If someone is calm or not generous then lucy is rich or happy and vice versa.
Everyone who is not creative or not tall is both not generous and quiet and vice versa.
If someone is either not wise or not strong then someone is not humble.
Everyone who is old or quiet is not humble.
If someone is not calm then someone is creative or not strong.
Everyone who is both strong and quiet is both not calm and not strong and vice versa.
Everyone who is both not tall and wise is both not happy and not wise.
Everyone who is generous is both not quiet and not calm and vice versa.
Everyone who is both wise and strong is both funny and not wise and vice versa.
If someone is not rich or wise then lucy is both brave and creative and vice versa.
If someone is kind then mary is not old or humble.
Everyone who is either not wise or not humble is both not humble and brave.
Someone is either quiet or calm.
Lucy is either tall or rich.
Lucy is either not old or generous.
Someone is not wise or not old.
Someone is happy or not kind.
Someone is not kind or rich.
Mary is both kind and strong. | Fred is not wise. | neutral | (((humble(lucy)|generous(lucy)))=>(~brave(fred)))&
(![X]:((strong(X)&~curious(X))<=>(funny(X)&rich(X))))&
(![X]:((patient(X)&curious(X))=>(~creative(X)&~old(X))))&
(((~quiet(susan)<~>creative(susan)))<=>((rich(lucy)<~>curious(lucy))))&
((?[X]:((calm(X)|~generous(X))))<=>((rich(lucy)|happy(lucy))))&
(![X]:((~creative(X)|~tall(X))<=>(~generous(X)&quiet(X))))&
((?[X]:((~wise(X)<~>~strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((old(X)|quiet(X))=>~humble(X)))&
((?[X]:(~calm(X)))=>(?[X]:((creative(X)|~strong(X)))))&
(![X]:((strong(X)&quiet(X))<=>(~calm(X)&~strong(X))))&
(![X]:((~tall(X)&wise(X))=>(~happy(X)&~wise(X))))&
(![X]:(generous(X)<=>(~quiet(X)&~calm(X))))&
(![X]:((wise(X)&strong(X))<=>(funny(X)&~wise(X))))&
((?[X]:((~rich(X)|wise(X))))<=>((brave(lucy)&creative(lucy))))&
((?[X]:(kind(X)))=>((~old(mary)|humble(mary))))&
(![X]:((~wise(X)<~>~humble(X))=>(~humble(X)&brave(X))))&
(?[X]:((quiet(X)<~>calm(X))))&
((tall(lucy)<~>rich(lucy)))&
((~old(lucy)<~>generous(lucy)))&
(?[X]:((~wise(X)|~old(X))))&
(?[X]:((happy(X)|~kind(X))))&
(?[X]:((~kind(X)|rich(X))))&
((kind(mary)&strong(mary))) | ~wise(fred) | [] | null | 0 |
Everyone who is not generous is not calm or old.
If fred is both rich and funny then someone is wise or curious and vice versa.
Everyone who is not generous or curious is happy and vice versa.
If someone is both not old and strong then alice is either quiet or generous and vice versa.
If someone is wise then john is strong or wise.
Everyone who is humble is not tall or not patient and vice versa.
If someone is not calm or quiet then someone is either patient or rich.
If susan is brave then mary is not quiet or creative and vice versa.
Everyone who is curious or not quiet is happy and vice versa.
Everyone who is rich is either humble or not creative and vice versa.
Everyone who is not creative is either not strong or calm.
If john is both wise and not curious then fred is both happy and not tall.
Everyone who is both not creative and not strong is both happy and not quiet.
Everyone who is both tall and not patient is quiet and vice versa.
Everyone who is not tall is not kind or patient and vice versa.
If paul is not curious or old then lucy is either funny or not tall and vice versa.
Lucy is not strong.
Someone is both calm and funny.
Paul is either not wise or not generous.
Paul is either not patient or tall.
Lucy is either strong or not quiet.
Someone is not old or not generous.
Paul is humble. | Fred is funny. | entailment | (![X]:(~generous(X)=>(~calm(X)|old(X))))&
(((rich(fred)&funny(fred)))<=>(?[X]:((wise(X)|curious(X)))))&
(![X]:((~generous(X)|curious(X))<=>happy(X)))&
((?[X]:((~old(X)&strong(X))))<=>((quiet(alice)<~>generous(alice))))&
((?[X]:(wise(X)))=>((strong(john)|wise(john))))&
(![X]:(humble(X)<=>(~tall(X)|~patient(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((patient(X)<~>rich(X)))))&
((brave(susan))<=>((~quiet(mary)|creative(mary))))&
(![X]:((curious(X)|~quiet(X))<=>happy(X)))&
(![X]:(rich(X)<=>(humble(X)<~>~creative(X))))&
(![X]:(~creative(X)=>(~strong(X)<~>calm(X))))&
(((wise(john)&~curious(john)))=>((happy(fred)&~tall(fred))))&
(![X]:((~creative(X)&~strong(X))=>(happy(X)&~quiet(X))))&
(![X]:((tall(X)&~patient(X))<=>quiet(X)))&
(![X]:(~tall(X)<=>(~kind(X)|patient(X))))&
(((~curious(paul)|old(paul)))<=>((funny(lucy)<~>~tall(lucy))))&
(~strong(lucy))&
(?[X]:((calm(X)&funny(X))))&
((~wise(paul)<~>~generous(paul)))&
((~patient(paul)<~>tall(paul)))&
((strong(lucy)<~>~quiet(lucy)))&
(?[X]:((~old(X)|~generous(X))))&
(humble(paul)) | funny(fred) | [
"p1",
"p2",
"p8",
"p13",
"p14",
"p18",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4697640477806923850523986
% SZS output start Proof for 4697640477806923850523986
2. (funny(fred) & rich(fred)) <=> ? [X0] : (curious(X0) | wise(X0)) [input p1]
3. ! [X0] : ((curious(X0) | ~generous(X0)) <=> happy(X0)) [input p2]
9. ! [X0] : ((~quiet(X0) | curious(X0)) <=> happy(X0)) [input p8]
14. ! [X0] : ((~patient(X0) & tall(X0)) <=> quiet(X0)) [input p13]
15. ! [X0] : (~tall(X0) <=> (patient(X0) | ~kind(X0))) [input p14]
19. ~wise(paul) <~> ~generous(paul) [input p18]
20. ~patient(paul) <~> tall(paul) [input p19]
24. ~funny(fred) [input hypothesis]
36. ((funny(fred) & rich(fred)) | ! [X0] : (~curious(X0) & ~wise(X0))) & (? [X0] : (curious(X0) | wise(X0)) | (~funny(fred) | ~rich(fred))) [nnf transformation 2]
37. ((funny(fred) & rich(fred)) | ! [X0] : (~curious(X0) & ~wise(X0))) & (? [X0] : (curious(X0) | wise(X0)) | ~funny(fred) | ~rich(fred)) [flattening 36]
38. ((funny(fred) & rich(fred)) | ! [X0] : (~curious(X0) & ~wise(X0))) & (? [X1] : (curious(X1) | wise(X1)) | ~funny(fred) | ~rich(fred)) [rectify 37]
39. ? [X1] : (curious(X1) | wise(X1)) => (curious(sK0) | wise(sK0)) [choice axiom]
40. ((funny(fred) & rich(fred)) | ! [X0] : (~curious(X0) & ~wise(X0))) & ((curious(sK0) | wise(sK0)) | ~funny(fred) | ~rich(fred)) [skolemisation 38,39]
41. ! [X0] : (((curious(X0) | ~generous(X0)) | ~happy(X0)) & (happy(X0) | (~curious(X0) & generous(X0)))) [nnf transformation 3]
42. ! [X0] : ((curious(X0) | ~generous(X0) | ~happy(X0)) & (happy(X0) | (~curious(X0) & generous(X0)))) [flattening 41]
55. ! [X0] : (((~quiet(X0) | curious(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) & ~curious(X0)))) [nnf transformation 9]
56. ! [X0] : ((~quiet(X0) | curious(X0) | ~happy(X0)) & (happy(X0) | (quiet(X0) & ~curious(X0)))) [flattening 55]
59. ! [X0] : (((~patient(X0) & tall(X0)) | ~quiet(X0)) & (quiet(X0) | (patient(X0) | ~tall(X0)))) [nnf transformation 14]
60. ! [X0] : (((~patient(X0) & tall(X0)) | ~quiet(X0)) & (quiet(X0) | patient(X0) | ~tall(X0))) [flattening 59]
61. ! [X0] : ((~tall(X0) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | tall(X0))) [nnf transformation 15]
62. ! [X0] : ((~tall(X0) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | tall(X0))) [flattening 61]
67. (generous(paul) | wise(paul)) & (~generous(paul) | ~wise(paul)) [nnf transformation 19]
68. (~tall(paul) | patient(paul)) & (tall(paul) | ~patient(paul)) [nnf transformation 20]
76. funny(fred) | ~wise(X0) [cnf transformation 40]
77. funny(fred) | ~curious(X0) [cnf transformation 40]
80. ~happy(X0) | ~generous(X0) | curious(X0) [cnf transformation 42]
99. quiet(X0) | happy(X0) [cnf transformation 56]
112. ~quiet(X0) | tall(X0) [cnf transformation 60]
116. ~patient(X0) | ~tall(X0) [cnf transformation 62]
127. generous(paul) | wise(paul) [cnf transformation 67]
129. ~tall(paul) | patient(paul) [cnf transformation 68]
134. ~funny(fred) [cnf transformation 24]
136. 1 <=> ! [X0] : ~curious(X0) [avatar definition]
137. ~curious(X0) <- (1) [avatar component clause 136]
139. 2 <=> funny(fred) [avatar definition]
142. 1 | 2 [avatar split clause 77,139,136]
144. 3 <=> ! [X0] : ~wise(X0) [avatar definition]
145. ~wise(X0) <- (3) [avatar component clause 144]
146. 3 | 2 [avatar split clause 76,139,144]
266. 28 <=> wise(paul) [avatar definition]
268. wise(paul) <- (28) [avatar component clause 266]
270. 29 <=> generous(paul) [avatar definition]
272. generous(paul) <- (29) [avatar component clause 270]
273. 28 | 29 [avatar split clause 127,270,266]
275. ~tall(paul) [subsumption resolution 129,116]
287. ~2 [avatar split clause 134,139]
288. $false <- (3, 28) [resolution 268,145]
289. ~3 | ~28 [avatar contradiction clause 288]
296. tall(X0) | happy(X0) [resolution 112,99]
410. happy(paul) [resolution 296,275]
420. ~generous(paul) | curious(paul) [resolution 410,80]
421. curious(paul) <- (29) [subsumption resolution 420,272]
424. $false <- (1, 29) [subsumption resolution 421,137]
425. ~1 | ~29 [avatar contradiction clause 424]
428. $false [avatar sat refutation 142,146,273,287,289,425]
% SZS output end Proof for 4697640477806923850523986
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and happy is not tall.
If someone is not happy or creative then fred is generous.
If someone is either tall or not brave then lucy is not calm and vice versa.
Everyone who is not generous is wise or not funny and vice versa.
If lucy is either not rich or not happy then someone is calm or not happy.
Everyone who is either not calm or generous is quiet and vice versa.
Everyone who is not patient or not happy is not humble or not curious.
If mary is either happy or humble then someone is not tall.
If someone is generous then alice is both not generous and not wise.
If john is patient or wise then someone is not quiet or not generous and vice versa.
If fred is either not patient or not creative then someone is old.
Everyone who is both not patient and not creative is both not wise and brave and vice versa.
Everyone who is not rich or not wise is either wise or generous and vice versa.
If paul is both rich and not strong then alice is both not strong and quiet.
Everyone who is not old or not brave is happy or rich and vice versa.
Alice is curious or not humble.
Someone is both not calm and happy.
Paul is either curious or generous.
Someone is both patient and not calm.
Mary is either not generous or not curious.
John is not tall or rich.
Someone is either rich or wise.
Someone is either not brave or not quiet. | Lucy is calm. | contradiction | (![X]:((~creative(X)&happy(X))=>~tall(X)))&
((?[X]:((~happy(X)|creative(X))))=>(generous(fred)))&
((?[X]:((tall(X)<~>~brave(X))))<=>(~calm(lucy)))&
(![X]:(~generous(X)<=>(wise(X)|~funny(X))))&
(((~rich(lucy)<~>~happy(lucy)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>quiet(X)))&
(![X]:((~patient(X)|~happy(X))=>(~humble(X)|~curious(X))))&
(((happy(mary)<~>humble(mary)))=>(?[X]:(~tall(X))))&
((?[X]:(generous(X)))=>((~generous(alice)&~wise(alice))))&
(((patient(john)|wise(john)))<=>(?[X]:((~quiet(X)|~generous(X)))))&
(((~patient(fred)<~>~creative(fred)))=>(?[X]:(old(X))))&
(![X]:((~patient(X)&~creative(X))<=>(~wise(X)&brave(X))))&
(![X]:((~rich(X)|~wise(X))<=>(wise(X)<~>generous(X))))&
(((rich(paul)&~strong(paul)))=>((~strong(alice)&quiet(alice))))&
(![X]:((~old(X)|~brave(X))<=>(happy(X)|rich(X))))&
((curious(alice)|~humble(alice)))&
(?[X]:((~calm(X)&happy(X))))&
((curious(paul)<~>generous(paul)))&
(?[X]:((patient(X)&~calm(X))))&
((~generous(mary)<~>~curious(mary)))&
((~tall(john)|rich(john)))&
(?[X]:((rich(X)<~>wise(X))))&
(?[X]:((~brave(X)<~>~quiet(X)))) | calm(lucy) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7643964919733105748465585
% SZS output start Proof for 7643964919733105748465585
1. ! [X0] : ((happy(X0) & ~creative(X0)) => ~tall(X0)) [input p0]
2. ? [X0] : (creative(X0) | ~happy(X0)) => generous(fred) [input p1]
3. ? [X0] : (tall(X0) <~> ~brave(X0)) <=> ~calm(lucy) [input p2]
9. ? [X0] : generous(X0) => (~wise(alice) & ~generous(alice)) [input p8]
11. (~patient(fred) <~> ~creative(fred)) => ? [X0] : old(X0) [input p10]
12. ! [X0] : ((~creative(X0) & ~patient(X0)) <=> (brave(X0) & ~wise(X0))) [input p11]
13. ! [X0] : ((~wise(X0) | ~rich(X0)) <=> (wise(X0) <~> generous(X0))) [input p12]
15. ! [X0] : ((~brave(X0) | ~old(X0)) <=> (rich(X0) | happy(X0))) [input p14]
24. calm(lucy) [input hypothesis]
25. ! [X0] : (~tall(X0) | (~happy(X0) | creative(X0))) [ennf transformation 1]
26. ! [X0] : (~tall(X0) | ~happy(X0) | creative(X0)) [flattening 25]
27. generous(fred) | ! [X0] : (~creative(X0) & happy(X0)) [ennf transformation 2]
32. (~wise(alice) & ~generous(alice)) | ! [X0] : ~generous(X0) [ennf transformation 9]
33. ? [X0] : old(X0) | (~patient(fred) <=> ~creative(fred)) [ennf transformation 11]
36. (? [X0] : ((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | calm(lucy)) & (~calm(lucy) | ! [X0] : ((tall(X0) | brave(X0)) & (~brave(X0) | ~tall(X0)))) [nnf transformation 3]
37. (? [X0] : ((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) | calm(lucy)) & (~calm(lucy) | ! [X1] : ((tall(X1) | brave(X1)) & (~brave(X1) | ~tall(X1)))) [rectify 36]
38. ? [X0] : ((brave(X0) | ~tall(X0)) & (~brave(X0) | tall(X0))) => ((brave(sK0) | ~tall(sK0)) & (~brave(sK0) | tall(sK0))) [choice axiom]
39. (((brave(sK0) | ~tall(sK0)) & (~brave(sK0) | tall(sK0))) | calm(lucy)) & (~calm(lucy) | ! [X1] : ((tall(X1) | brave(X1)) & (~brave(X1) | ~tall(X1)))) [skolemisation 37,38]
54. ? [X0] : old(X0) | ((~patient(fred) | creative(fred)) & (~creative(fred) | patient(fred))) [nnf transformation 33]
55. ? [X0] : old(X0) => old(sK4) [choice axiom]
56. old(sK4) | ((~patient(fred) | creative(fred)) & (~creative(fred) | patient(fred))) [skolemisation 54,55]
57. ! [X0] : (((~creative(X0) & ~patient(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (creative(X0) | patient(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | creative(X0) | patient(X0))) [flattening 57]
59. ! [X0] : (((~wise(X0) | ~rich(X0)) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | (wise(X0) & rich(X0)))) [nnf transformation 13]
60. ! [X0] : ((~wise(X0) | ~rich(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) & (((~generous(X0) | ~wise(X0)) & (generous(X0) | wise(X0))) | (wise(X0) & rich(X0)))) [flattening 59]
61. ! [X0] : (((~brave(X0) | ~old(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (brave(X0) & old(X0)))) [nnf transformation 15]
62. ! [X0] : ((~brave(X0) | ~old(X0) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | (brave(X0) & old(X0)))) [flattening 61]
75. ~tall(X0) | ~happy(X0) | creative(X0) [cnf transformation 26]
76. generous(fred) | happy(X0) [cnf transformation 27]
77. generous(fred) | ~creative(X0) [cnf transformation 27]
79. ~calm(lucy) | tall(X1) | brave(X1) [cnf transformation 39]
95. ~generous(alice) | ~generous(X0) [cnf transformation 32]
96. ~wise(alice) | ~generous(X0) [cnf transformation 32]
102. old(sK4) | ~patient(fred) | creative(fred) [cnf transformation 56]
103. ~wise(X0) | creative(X0) | patient(X0) [cnf transformation 58]
108. generous(X0) | wise(X0) | wise(X0) [cnf transformation 60]
117. ~old(X0) | ~brave(X0) | ~happy(X0) [cnf transformation 62]
133. calm(lucy) [cnf transformation 24]
134. wise(X0) | generous(X0) [duplicate literal removal 108]
137. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
138. ~creative(X0) <- (1) [avatar component clause 137]
140. 2 <=> generous(fred) [avatar definition]
142. generous(fred) <- (2) [avatar component clause 140]
143. 1 | 2 [avatar split clause 77,140,137]
145. 3 <=> ! [X0] : happy(X0) [avatar definition]
146. happy(X0) <- (3) [avatar component clause 145]
147. 3 | 2 [avatar split clause 76,140,145]
149. 4 <=> calm(lucy) [avatar definition]
163. 7 <=> ! [X1] : (tall(X1) | brave(X1)) [avatar definition]
164. brave(X1) | tall(X1) <- (7) [avatar component clause 163]
165. 7 | ~4 [avatar split clause 79,149,163]
203. 16 <=> ! [X0] : ~generous(X0) [avatar definition]
204. ~generous(X0) <- (16) [avatar component clause 203]
206. 17 <=> wise(alice) [avatar definition]
208. ~wise(alice) <- (~17) [avatar component clause 206]
209. 16 | ~17 [avatar split clause 96,206,203]
211. 18 <=> generous(alice) [avatar definition]
213. ~generous(alice) <- (~18) [avatar component clause 211]
214. 16 | ~18 [avatar split clause 95,211,203]
242. 25 <=> creative(fred) [avatar definition]
244. creative(fred) <- (25) [avatar component clause 242]
246. 26 <=> patient(fred) [avatar definition]
248. ~patient(fred) <- (~26) [avatar component clause 246]
250. 27 <=> old(sK4) [avatar definition]
252. old(sK4) <- (27) [avatar component clause 250]
253. 25 | ~26 | 27 [avatar split clause 102,250,246,242]
331. 4 [avatar split clause 133,149]
334. generous(alice) <- (~17) [resolution 134,208]
336. $false <- (~17, ~18) [subsumption resolution 334,213]
337. 17 | 18 [avatar contradiction clause 336]
338. $false <- (2, 16) [resolution 204,142]
341. ~2 | ~16 [avatar contradiction clause 338]
391. creative(X0) | patient(X0) | generous(X0) [resolution 103,134]
394. patient(X0) | generous(X0) <- (1) [subsumption resolution 391,138]
395. patient(X0) <- (1, 16) [subsumption resolution 394,204]
398. $false <- (1, 16, ~26) [resolution 395,248]
399. ~1 | ~16 | 26 [avatar contradiction clause 398]
400. $false <- (1, 25) [subsumption resolution 244,138]
401. ~1 | ~25 [avatar contradiction clause 400]
447. ~brave(sK4) | ~happy(sK4) <- (27) [resolution 117,252]
449. ~brave(sK4) <- (3, 27) [subsumption resolution 447,146]
456. tall(sK4) <- (3, 7, 27) [resolution 449,164]
457. ~happy(sK4) | creative(sK4) <- (3, 7, 27) [resolution 456,75]
458. creative(sK4) <- (3, 7, 27) [subsumption resolution 457,146]
459. $false <- (1, 3, 7, 27) [subsumption resolution 458,138]
460. ~1 | ~3 | ~7 | ~27 [avatar contradiction clause 459]
461. $false [avatar sat refutation 143,147,165,209,214,253,331,337,341,399,401,460]
% SZS output end Proof for 7643964919733105748465585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not brave is not kind or not happy and vice versa.
If someone is either patient or not tall then someone is not happy or not old and vice versa.
Everyone who is wise is tall or not quiet and vice versa.
Everyone who is both not rich and calm is not strong or old and vice versa.
Everyone who is both brave and wise is not kind or funny and vice versa.
If alice is not calm then fred is both not wise and curious.
Everyone who is not kind or not curious is either not kind or tall.
If someone is creative then someone is rich or wise and vice versa.
Everyone who is either curious or funny is not humble.
Everyone who is both not happy and calm is curious.
If someone is either happy or brave then someone is either funny or creative.
If someone is rich then mary is rich.
If susan is either humble or not happy then someone is either funny or tall and vice versa.
If alice is either not happy or not brave then someone is not quiet or tall.
Everyone who is either not brave or not creative is patient and vice versa.
Everyone who is either generous or rich is either brave or generous and vice versa.
Alice is either not tall or not funny.
Someone is strong or not curious.
Paul is either not brave or not funny.
Someone is not strong or happy.
Someone is both not humble and funny.
Fred is both not calm and tall.
Lucy is old or not calm.
Someone is rich. | Paul is not old. | entailment | (![X]:((~calm(X)<~>~brave(X))<=>(~kind(X)|~happy(X))))&
((?[X]:((patient(X)<~>~tall(X))))<=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:(wise(X)<=>(tall(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~strong(X)|old(X))))&
(![X]:((brave(X)&wise(X))<=>(~kind(X)|funny(X))))&
((~calm(alice))=>((~wise(fred)&curious(fred))))&
(![X]:((~kind(X)|~curious(X))=>(~kind(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((curious(X)<~>funny(X))=>~humble(X)))&
(![X]:((~happy(X)&calm(X))=>curious(X)))&
((?[X]:((happy(X)<~>brave(X))))=>(?[X]:((funny(X)<~>creative(X)))))&
((?[X]:(rich(X)))=>(rich(mary)))&
(((humble(susan)<~>~happy(susan)))<=>(?[X]:((funny(X)<~>tall(X)))))&
(((~happy(alice)<~>~brave(alice)))=>(?[X]:((~quiet(X)|tall(X)))))&
(![X]:((~brave(X)<~>~creative(X))<=>patient(X)))&
(![X]:((generous(X)<~>rich(X))<=>(brave(X)<~>generous(X))))&
((~tall(alice)<~>~funny(alice)))&
(?[X]:((strong(X)|~curious(X))))&
((~brave(paul)<~>~funny(paul)))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((~humble(X)&funny(X))))&
((~calm(fred)&tall(fred)))&
((old(lucy)|~calm(lucy)))&
(?[X]:(rich(X))) | ~old(paul) | [
"p3",
"p4",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 728317281546917676950128
% SZS output start Proof for 728317281546917676950128
4. ! [X0] : ((calm(X0) & ~rich(X0)) <=> (old(X0) | ~strong(X0))) [input p3]
5. ! [X0] : ((wise(X0) & brave(X0)) <=> (funny(X0) | ~kind(X0))) [input p4]
16. ! [X0] : ((generous(X0) <~> rich(X0)) <=> (brave(X0) <~> generous(X0))) [input p15]
19. ~brave(paul) <~> ~funny(paul) [input p18]
25. old(paul) [input hypothesis]
46. ! [X0] : (((calm(X0) & ~rich(X0)) | (~old(X0) & strong(X0))) & ((old(X0) | ~strong(X0)) | (~calm(X0) | rich(X0)))) [nnf transformation 4]
47. ! [X0] : (((calm(X0) & ~rich(X0)) | (~old(X0) & strong(X0))) & (old(X0) | ~strong(X0) | ~calm(X0) | rich(X0))) [flattening 46]
48. ! [X0] : (((wise(X0) & brave(X0)) | (~funny(X0) & kind(X0))) & ((funny(X0) | ~kind(X0)) | (~wise(X0) | ~brave(X0)))) [nnf transformation 5]
49. ! [X0] : (((wise(X0) & brave(X0)) | (~funny(X0) & kind(X0))) & (funny(X0) | ~kind(X0) | ~wise(X0) | ~brave(X0))) [flattening 48]
69. ! [X0] : ((((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | ((brave(X0) | ~generous(X0)) & (generous(X0) | ~brave(X0)))) & (((~generous(X0) | ~brave(X0)) & (generous(X0) | brave(X0))) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0))))) [nnf transformation 16]
73. (funny(paul) | brave(paul)) & (~funny(paul) | ~brave(paul)) [nnf transformation 19]
97. ~rich(X0) | ~old(X0) [cnf transformation 47]
102. ~funny(X0) | brave(X0) [cnf transformation 49]
138. ~generous(X0) | ~brave(X0) | rich(X0) | ~generous(X0) [cnf transformation 69]
140. rich(X0) | generous(X0) | generous(X0) | ~brave(X0) [cnf transformation 69]
148. funny(paul) | brave(paul) [cnf transformation 73]
156. old(paul) [cnf transformation 25]
158. ~generous(X0) | ~brave(X0) | rich(X0) [duplicate literal removal 138]
159. rich(X0) | generous(X0) | ~brave(X0) [duplicate literal removal 140]
305. ~brave(X0) | rich(X0) [subsumption resolution 158,159]
326. brave(paul) [subsumption resolution 148,102]
393. rich(paul) [resolution 305,326]
476. ~old(paul) [resolution 393,97]
478. $false [subsumption resolution 476,156]
% SZS output end Proof for 728317281546917676950128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not quiet or kind then someone is humble or creative and vice versa.
Everyone who is happy is either not rich or not patient.
Everyone who is both not rich and not tall is not wise.
If someone is both strong and humble then someone is either not humble or rich.
Everyone who is either not curious or strong is not curious or old.
Everyone who is not curious is not patient or brave and vice versa.
Everyone who is not brave is both not wise and not strong.
If someone is curious then someone is rich.
If someone is both not quiet and not strong then someone is both strong and curious and vice versa.
Everyone who is both tall and not generous is funny and vice versa.
Everyone who is either quiet or not kind is not curious and vice versa.
Everyone who is both curious and not happy is both tall and brave.
If paul is both not kind and not strong then someone is patient or strong and vice versa.
Everyone who is curious or not old is either not strong or funny and vice versa.
If someone is either strong or not brave then susan is both generous and calm and vice versa.
If someone is not kind or not patient then someone is patient or funny and vice versa.
Alice is not generous.
Someone is both not strong and not funny.
Alice is both curious and not old.
Someone is either patient or creative.
John is either not wise or rich.
Someone is both generous and rich.
Paul is either tall or not old. | Susan is not humble. | neutral | ((?[X]:((~quiet(X)<~>kind(X))))<=>(?[X]:((humble(X)|creative(X)))))&
(![X]:(happy(X)=>(~rich(X)<~>~patient(X))))&
(![X]:((~rich(X)&~tall(X))=>~wise(X)))&
((?[X]:((strong(X)&humble(X))))=>(?[X]:((~humble(X)<~>rich(X)))))&
(![X]:((~curious(X)<~>strong(X))=>(~curious(X)|old(X))))&
(![X]:(~curious(X)<=>(~patient(X)|brave(X))))&
(![X]:(~brave(X)=>(~wise(X)&~strong(X))))&
((?[X]:(curious(X)))=>(?[X]:(rich(X))))&
((?[X]:((~quiet(X)&~strong(X))))<=>(?[X]:((strong(X)&curious(X)))))&
(![X]:((tall(X)&~generous(X))<=>funny(X)))&
(![X]:((quiet(X)<~>~kind(X))<=>~curious(X)))&
(![X]:((curious(X)&~happy(X))=>(tall(X)&brave(X))))&
(((~kind(paul)&~strong(paul)))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((curious(X)|~old(X))<=>(~strong(X)<~>funny(X))))&
((?[X]:((strong(X)<~>~brave(X))))<=>((generous(susan)&calm(susan))))&
((?[X]:((~kind(X)|~patient(X))))<=>(?[X]:((patient(X)|funny(X)))))&
(~generous(alice))&
(?[X]:((~strong(X)&~funny(X))))&
((curious(alice)&~old(alice)))&
(?[X]:((patient(X)<~>creative(X))))&
((~wise(john)<~>rich(john)))&
(?[X]:((generous(X)&rich(X))))&
((tall(paul)<~>~old(paul))) | ~humble(susan) | [] | null | 0 |
If someone is both not wise and not old then someone is creative or brave.
Everyone who is not tall or not creative is both curious and not patient.
If someone is both not tall and not patient then fred is either not wise or humble and vice versa.
If someone is not patient then john is not humble and vice versa.
If fred is either tall or not curious then someone is either not curious or kind and vice versa.
If someone is not quiet or not strong then someone is happy or not kind.
Everyone who is not wise or old is both quiet and old and vice versa.
Everyone who is rich is not patient and vice versa.
Everyone who is not curious is either wise or not quiet and vice versa.
Everyone who is not strong is patient and vice versa.
Everyone who is not old is wise or kind and vice versa.
If someone is either not creative or tall then someone is old and vice versa.
If mary is both kind and generous then someone is both patient and tall and vice versa.
Everyone who is kind is not tall or not creative and vice versa.
If alice is not creative or not old then paul is not creative or curious and vice versa.
Everyone who is creative is either happy or not tall and vice versa.
Susan is brave.
John is not wise or not patient.
Someone is either not patient or tall.
Mary is both brave and not kind.
Mary is both not old and calm.
Someone is not quiet or not brave. | Mary is calm. | entailment | ((?[X]:((~wise(X)&~old(X))))=>(?[X]:((creative(X)|brave(X)))))&
(![X]:((~tall(X)|~creative(X))=>(curious(X)&~patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>((~wise(fred)<~>humble(fred))))&
((?[X]:(~patient(X)))<=>(~humble(john)))&
(((tall(fred)<~>~curious(fred)))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:((happy(X)|~kind(X)))))&
(![X]:((~wise(X)|old(X))<=>(quiet(X)&old(X))))&
(![X]:(rich(X)<=>~patient(X)))&
(![X]:(~curious(X)<=>(wise(X)<~>~quiet(X))))&
(![X]:(~strong(X)<=>patient(X)))&
(![X]:(~old(X)<=>(wise(X)|kind(X))))&
((?[X]:((~creative(X)<~>tall(X))))<=>(?[X]:(old(X))))&
(((kind(mary)&generous(mary)))<=>(?[X]:((patient(X)&tall(X)))))&
(![X]:(kind(X)<=>(~tall(X)|~creative(X))))&
(((~creative(alice)|~old(alice)))<=>((~creative(paul)|curious(paul))))&
(![X]:(creative(X)<=>(happy(X)<~>~tall(X))))&
(brave(susan))&
((~wise(john)|~patient(john)))&
(?[X]:((~patient(X)<~>tall(X))))&
((brave(mary)&~kind(mary)))&
((~old(mary)&calm(mary)))&
(?[X]:((~quiet(X)|~brave(X)))) | calm(mary) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4724424003461535057303204
% SZS output start Proof for 4724424003461535057303204
21. calm(mary) & ~old(mary) [input p20]
23. ~calm(mary) [input hypothesis]
137. calm(mary) [cnf transformation 21]
139. ~calm(mary) [cnf transformation 23]
343. $false [subsumption resolution 139,137]
% SZS output end Proof for 4724424003461535057303204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is patient.
If someone is tall then someone is kind and vice versa.
Everyone who is humble or rich is either not strong or not happy.
Everyone who is either not generous or not creative is strong or wise and vice versa.
Everyone who is curious is not wise and vice versa.
Everyone who is both not old and kind is both rich and curious.
If someone is not old then alice is either not curious or wise.
If someone is wise or not rich then someone is both not quiet and not patient.
Everyone who is either curious or not generous is patient.
If john is either not wise or not patient then someone is quiet or not happy.
Everyone who is both funny and not curious is creative or not happy and vice versa.
If lucy is calm or not humble then someone is both not brave and not kind.
Everyone who is both not tall and brave is both rich and wise and vice versa.
Everyone who is either not brave or not quiet is both not curious and not happy.
Susan is generous or not quiet.
Paul is not happy or happy.
Someone is both not calm and patient.
Paul is not calm or kind.
Someone is not brave.
Lucy is not tall or creative. | Susan is generous. | contradiction | (![X]:((~creative(X)<~>~old(X))=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:(kind(X))))&
(![X]:((humble(X)|rich(X))=>(~strong(X)<~>~happy(X))))&
(![X]:((~generous(X)<~>~creative(X))<=>(strong(X)|wise(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~old(X)&kind(X))=>(rich(X)&curious(X))))&
((?[X]:(~old(X)))=>((~curious(alice)<~>wise(alice))))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((curious(X)<~>~generous(X))=>patient(X)))&
(((~wise(john)<~>~patient(john)))=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((funny(X)&~curious(X))<=>(creative(X)|~happy(X))))&
(((calm(lucy)|~humble(lucy)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~tall(X)&brave(X))<=>(rich(X)&wise(X))))&
(![X]:((~brave(X)<~>~quiet(X))=>(~curious(X)&~happy(X))))&
((generous(susan)|~quiet(susan)))&
((~happy(paul)|happy(paul)))&
(?[X]:((~calm(X)&patient(X))))&
((~calm(paul)|kind(paul)))&
(?[X]:(~brave(X)))&
((~tall(lucy)|creative(lucy))) | generous(susan) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7268853407403656166902825
% SZS output start Proof for 7268853407403656166902825
1. ! [X0] : ((~creative(X0) <~> ~old(X0)) => patient(X0)) [input p0]
3. ! [X0] : ((rich(X0) | humble(X0)) => (~strong(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : ((~generous(X0) <~> ~creative(X0)) <=> (wise(X0) | strong(X0))) [input p3]
5. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p4]
7. ? [X0] : ~old(X0) => (~curious(alice) <~> wise(alice)) [input p6]
8. ? [X0] : (~rich(X0) | wise(X0)) => ? [X0] : (~patient(X0) & ~quiet(X0)) [input p7]
9. ! [X0] : ((curious(X0) <~> ~generous(X0)) => patient(X0)) [input p8]
11. ! [X0] : ((~curious(X0) & funny(X0)) <=> (~happy(X0) | creative(X0))) [input p10]
21. generous(susan) [input hypothesis]
23. ? [X0] : (~rich(X0) | wise(X0)) => ? [X1] : (~patient(X1) & ~quiet(X1)) [rectify 8]
27. ! [X0] : (patient(X0) | (~creative(X0) <=> ~old(X0))) [ennf transformation 1]
28. ! [X0] : ((~strong(X0) <~> ~happy(X0)) | (~rich(X0) & ~humble(X0))) [ennf transformation 3]
31. (~curious(alice) <~> wise(alice)) | ! [X0] : old(X0) [ennf transformation 7]
32. ? [X1] : (~patient(X1) & ~quiet(X1)) | ! [X0] : (rich(X0) & ~wise(X0)) [ennf transformation 23]
33. ! [X0] : (patient(X0) | (curious(X0) <=> ~generous(X0))) [ennf transformation 9]
37. ! [X0] : (patient(X0) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 27]
43. ! [X0] : (((happy(X0) | strong(X0)) & (~happy(X0) | ~strong(X0))) | (~rich(X0) & ~humble(X0))) [nnf transformation 28]
44. ! [X0] : ((((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))))) [nnf transformation 4]
45. ! [X0] : ((((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))))) [flattening 44]
46. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 5]
47. ((~wise(alice) | curious(alice)) & (wise(alice) | ~curious(alice))) | ! [X0] : old(X0) [nnf transformation 31]
48. ? [X0] : (~patient(X0) & ~quiet(X0)) | ! [X1] : (rich(X1) & ~wise(X1)) [rectify 32]
49. ? [X0] : (~patient(X0) & ~quiet(X0)) => (~patient(sK2) & ~quiet(sK2)) [choice axiom]
50. (~patient(sK2) & ~quiet(sK2)) | ! [X1] : (rich(X1) & ~wise(X1)) [skolemisation 48,49]
51. ! [X0] : (patient(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 33]
55. ! [X0] : (((~curious(X0) & funny(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (curious(X0) | ~funny(X0)))) [nnf transformation 11]
56. ! [X0] : (((~curious(X0) & funny(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | curious(X0) | ~funny(X0))) [flattening 55]
66. ~old(X0) | patient(X0) | creative(X0) [cnf transformation 37]
71. ~happy(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 43]
75. ~generous(X0) | strong(X0) | wise(X0) | creative(X0) [cnf transformation 45]
77. ~wise(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 45]
80. ~curious(X0) | ~wise(X0) [cnf transformation 46]
81. curious(X0) | wise(X0) [cnf transformation 46]
84. wise(alice) | ~curious(alice) | old(X0) [cnf transformation 47]
85. ~wise(alice) | curious(alice) | old(X0) [cnf transformation 47]
88. ~patient(sK2) | ~wise(X1) [cnf transformation 50]
89. ~patient(sK2) | rich(X1) [cnf transformation 50]
91. curious(X0) | patient(X0) | generous(X0) [cnf transformation 51]
97. ~curious(X0) | ~creative(X0) [cnf transformation 56]
98. ~curious(X0) | happy(X0) [cnf transformation 56]
114. generous(susan) [cnf transformation 21]
131. curious(alice) | old(X0) [subsumption resolution 85,81]
133. 5 <=> ! [X0] : old(X0) [avatar definition]
134. old(X0) <- (5) [avatar component clause 133]
136. 6 <=> curious(alice) [avatar definition]
139. 5 | 6 [avatar split clause 131,136,133]
140. ~curious(alice) | old(X0) [subsumption resolution 84,80]
141. 5 | ~6 [avatar split clause 140,136,133]
143. 7 <=> ! [X1] : rich(X1) [avatar definition]
144. rich(X1) <- (7) [avatar component clause 143]
146. 8 <=> patient(sK2) [avatar definition]
148. ~patient(sK2) <- (~8) [avatar component clause 146]
149. 7 | ~8 [avatar split clause 89,146,143]
151. 9 <=> ! [X1] : ~wise(X1) [avatar definition]
152. ~wise(X1) <- (9) [avatar component clause 151]
153. 9 | ~8 [avatar split clause 88,146,151]
193. 18 <=> generous(susan) [avatar definition]
195. generous(susan) <- (18) [avatar component clause 193]
210. 18 [avatar split clause 114,193]
214. ~creative(X0) | wise(X0) [resolution 97,81]
215. wise(X0) | happy(X0) [resolution 98,81]
216. patient(X0) | creative(X0) <- (5) [resolution 66,134]
217. creative(sK2) <- (5, ~8) [resolution 216,148]
219. wise(sK2) <- (5, ~8) [resolution 217,214]
223. 22 <=> strong(susan) [avatar definition]
224. strong(susan) <- (22) [avatar component clause 223]
225. ~strong(susan) <- (~22) [avatar component clause 223]
227. 23 <=> creative(susan) [avatar definition]
228. creative(susan) <- (23) [avatar component clause 227]
232. ~generous(sK2) | ~creative(sK2) <- (5, ~8) [resolution 77,219]
233. ~generous(sK2) <- (5, ~8) [subsumption resolution 232,217]
239. patient(X2) | generous(X2) | ~creative(X2) [resolution 91,97]
242. generous(X2) | patient(X2) <- (5) [subsumption resolution 239,216]
244. patient(sK2) <- (5, ~8) [resolution 242,233]
246. $false <- (5, ~8) [subsumption resolution 244,148]
247. ~5 | 8 [avatar contradiction clause 246]
249. happy(X0) <- (9) [resolution 152,215]
251. ~strong(X0) | ~rich(X0) <- (9) [resolution 249,71]
254. ~strong(X0) <- (7, 9) [subsumption resolution 251,144]
298. strong(susan) | wise(susan) | creative(susan) <- (18) [resolution 75,195]
300. wise(susan) | creative(susan) <- (18, ~22) [subsumption resolution 298,225]
301. creative(susan) <- (9, 18, ~22) [subsumption resolution 300,152]
302. 23 | ~9 | ~18 | 22 [avatar split clause 301,223,193,151,227]
306. $false <- (7, 9, 22) [subsumption resolution 224,254]
307. ~7 | ~9 | ~22 [avatar contradiction clause 306]
310. wise(susan) <- (23) [resolution 228,214]
312. $false <- (9, 23) [subsumption resolution 310,152]
313. ~9 | ~23 [avatar contradiction clause 312]
314. $false [avatar sat refutation 139,141,149,153,210,247,302,307,313]
% SZS output end Proof for 7268853407403656166902825
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not strong is either not curious or wise and vice versa. If someone is either happy or not kind then someone is patient or strong and vice versa. Everyone who is either humble or old is both not funny and humble and vice versa. Everyone who is not quiet is funny and vice versa. Everyone who is not kind is brave and vice versa. Everyone who is either not generous or calm is quiet or rich. Everyone who is not rich or not kind is calm or not rich and vice versa. If someone is either creative or calm then mary is either not funny or generous. If john is not happy or kind then someone is both patient and quiet and vice versa. If someone is either creative or wise then mary is either not humble or not tall. Everyone who is both funny and not strong is both not generous and creative and vice versa. Everyone who is not humble or not old is humble. If someone is not old or brave then someone is not old or patient and vice versa. Everyone who is both rich and not old is generous or creative and vice versa. If lucy is either quiet or not old then someone is either curious or quiet. If someone is both creative and old then someone is calm or brave. Mary is not calm. Someone is old or funny. John is both brave and tall. Someone is both rich and not kind. Paul is either generous or not old. Someone is not happy. Susan is not patient or not humble. | Mary is not creative. | entailment | (![X]:((humble(X)|~strong(X))<=>(~curious(X)<~>wise(X))))&
((?[X]:((happy(X)<~>~kind(X))))<=>(?[X]:((patient(X)|strong(X)))))&
(![X]:((humble(X)<~>old(X))<=>(~funny(X)&humble(X))))&
(![X]:(~quiet(X)<=>funny(X)))&
(![X]:(~kind(X)<=>brave(X)))&
(![X]:((~generous(X)<~>calm(X))=>(quiet(X)|rich(X))))&
(![X]:((~rich(X)|~kind(X))<=>(calm(X)|~rich(X))))&
((?[X]:((creative(X)<~>calm(X))))=>((~funny(mary)<~>generous(mary))))&
(((~happy(john)|kind(john)))<=>(?[X]:((patient(X)&quiet(X)))))&
((?[X]:((creative(X)<~>wise(X))))=>((~humble(mary)<~>~tall(mary))))&
(![X]:((funny(X)&~strong(X))<=>(~generous(X)&creative(X))))&
(![X]:((~humble(X)|~old(X))=>humble(X)))&
((?[X]:((~old(X)|brave(X))))<=>(?[X]:((~old(X)|patient(X)))))&
(![X]:((rich(X)&~old(X))<=>(generous(X)|creative(X))))&
(((quiet(lucy)<~>~old(lucy)))=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:((creative(X)&old(X))))=>(?[X]:((calm(X)|brave(X)))))&
(~calm(mary))&
(?[X]:((old(X)|funny(X))))&
((brave(john)&tall(john)))&
(?[X]:((rich(X)&~kind(X))))&
((generous(paul)<~>~old(paul)))&
(?[X]:(~happy(X)))&
((~patient(susan)|~humble(susan))) | ~creative(mary) | [
"p2",
"p7",
"p10",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2359456585885242904761025
% SZS output start Proof for 2359456585885242904761025
3. ! [X0] : ((humble(X0) <~> old(X0)) <=> (humble(X0) & ~funny(X0))) [input p2]
8. ? [X0] : (creative(X0) <~> calm(X0)) => (~funny(mary) <~> generous(mary)) [input p7]
11. ! [X0] : ((~strong(X0) & funny(X0)) <=> (creative(X0) & ~generous(X0))) [input p10]
12. ! [X0] : ((~old(X0) | ~humble(X0)) => humble(X0)) [input p11]
14. ! [X0] : ((~old(X0) & rich(X0)) <=> (creative(X0) | generous(X0))) [input p13]
17. ~calm(mary) [input p16]
24. creative(mary) [input hypothesis]
30. (~funny(mary) <~> generous(mary)) | ! [X0] : (creative(X0) <=> calm(X0)) [ennf transformation 8]
32. ! [X0] : (humble(X0) | (old(X0) & humble(X0))) [ennf transformation 12]
42. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~humble(X0) | funny(X0))) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 3]
43. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ~humble(X0) | funny(X0)) & ((humble(X0) & ~funny(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 42]
49. ((~generous(mary) | funny(mary)) & (generous(mary) | ~funny(mary))) | ! [X0] : ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0))) [nnf transformation 30]
56. ! [X0] : (((~strong(X0) & funny(X0)) | (~creative(X0) | generous(X0))) & ((creative(X0) & ~generous(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 11]
57. ! [X0] : (((~strong(X0) & funny(X0)) | ~creative(X0) | generous(X0)) & ((creative(X0) & ~generous(X0)) | strong(X0) | ~funny(X0))) [flattening 56]
63. ! [X0] : (((~old(X0) & rich(X0)) | (~creative(X0) & ~generous(X0))) & ((creative(X0) | generous(X0)) | (old(X0) | ~rich(X0)))) [nnf transformation 14]
64. ! [X0] : (((~old(X0) & rich(X0)) | (~creative(X0) & ~generous(X0))) & (creative(X0) | generous(X0) | old(X0) | ~rich(X0))) [flattening 63]
90. ~funny(X0) | old(X0) | ~humble(X0) [cnf transformation 43]
93. humble(X0) | humble(X0) | ~old(X0) [cnf transformation 43]
108. ~generous(mary) | funny(mary) | calm(X0) | ~creative(X0) [cnf transformation 49]
121. ~creative(X0) | funny(X0) | generous(X0) [cnf transformation 57]
124. humble(X0) | old(X0) [cnf transformation 32]
133. ~creative(X0) | ~old(X0) [cnf transformation 64]
139. ~calm(mary) [cnf transformation 17]
149. creative(mary) [cnf transformation 24]
151. ~old(X0) | humble(X0) [duplicate literal removal 93]
191. 10 <=> funny(mary) [avatar definition]
193. funny(mary) <- (10) [avatar component clause 191]
195. 11 <=> generous(mary) [avatar definition]
200. 12 <=> ! [X0] : (calm(X0) | ~creative(X0)) [avatar definition]
201. ~creative(X0) | calm(X0) <- (12) [avatar component clause 200]
202. 12 | 10 | ~11 [avatar split clause 108,195,191,200]
247. humble(X0) [subsumption resolution 124,151]
311. ~old(mary) [resolution 133,149]
344. funny(mary) | generous(mary) [resolution 121,149]
351. old(mary) | ~humble(mary) <- (10) [resolution 193,90]
352. ~humble(mary) <- (10) [subsumption resolution 351,311]
353. $false <- (10) [subsumption resolution 352,247]
354. ~10 [avatar contradiction clause 353]
355. 11 | 10 [avatar split clause 344,191,195]
360. calm(mary) <- (12) [resolution 201,149]
361. $false <- (12) [subsumption resolution 360,139]
362. ~12 [avatar contradiction clause 361]
363. $false [avatar sat refutation 202,354,355,362]
% SZS output end Proof for 2359456585885242904761025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong or not old then someone is either not creative or brave.
Everyone who is not happy is both rich and happy and vice versa.
Everyone who is either not tall or old is not rich and vice versa.
If fred is either not humble or strong then someone is patient or not creative and vice versa.
If lucy is quiet or not quiet then someone is not happy or not kind.
If someone is not old then someone is both creative and not patient.
If someone is both calm and not kind then paul is both humble and brave.
Everyone who is both not rich and not tall is both not strong and rich and vice versa.
If someone is either not curious or not rich then susan is either not happy or not old.
Everyone who is either old or wise is not strong.
If someone is calm or not calm then someone is kind or rich and vice versa.
Everyone who is rich or not humble is quiet or not happy and vice versa.
If fred is not kind then someone is either curious or not patient and vice versa.
If susan is either rich or curious then someone is old or not happy.
If someone is either not old or not kind then john is not brave.
If paul is not curious or old then someone is both not kind and quiet.
Someone is either not happy or not quiet.
Fred is tall or generous.
Mary is both not brave and quiet.
Lucy is either rich or strong.
Someone is strong or creative.
Mary is strong.
Fred is humble.
Someone is either creative or brave. | John is not curious. | entailment | ((?[X]:((strong(X)|~old(X))))=>(?[X]:((~creative(X)<~>brave(X)))))&
(![X]:(~happy(X)<=>(rich(X)&happy(X))))&
(![X]:((~tall(X)<~>old(X))<=>~rich(X)))&
(((~humble(fred)<~>strong(fred)))<=>(?[X]:((patient(X)|~creative(X)))))&
(((quiet(lucy)|~quiet(lucy)))=>(?[X]:((~happy(X)|~kind(X)))))&
((?[X]:(~old(X)))=>(?[X]:((creative(X)&~patient(X)))))&
((?[X]:((calm(X)&~kind(X))))=>((humble(paul)&brave(paul))))&
(![X]:((~rich(X)&~tall(X))<=>(~strong(X)&rich(X))))&
((?[X]:((~curious(X)<~>~rich(X))))=>((~happy(susan)<~>~old(susan))))&
(![X]:((old(X)<~>wise(X))=>~strong(X)))&
((?[X]:((calm(X)|~calm(X))))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((rich(X)|~humble(X))<=>(quiet(X)|~happy(X))))&
((~kind(fred))<=>(?[X]:((curious(X)<~>~patient(X)))))&
(((rich(susan)<~>curious(susan)))=>(?[X]:((old(X)|~happy(X)))))&
((?[X]:((~old(X)<~>~kind(X))))=>(~brave(john)))&
(((~curious(paul)|old(paul)))=>(?[X]:((~kind(X)&quiet(X)))))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((tall(fred)|generous(fred)))&
((~brave(mary)&quiet(mary)))&
((rich(lucy)<~>strong(lucy)))&
(?[X]:((strong(X)|creative(X))))&
(strong(mary))&
(humble(fred))&
(?[X]:((creative(X)<~>brave(X)))) | ~curious(john) | [
"p1",
"p2",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 2729067431759015680932042
% SZS output start Proof for 2729067431759015680932042
2. ! [X0] : (~happy(X0) <=> (happy(X0) & rich(X0))) [input p1]
3. ! [X0] : ((~tall(X0) <~> old(X0)) <=> ~rich(X0)) [input p2]
8. ! [X0] : ((~tall(X0) & ~rich(X0)) <=> (rich(X0) & ~strong(X0))) [input p7]
9. ? [X0] : (~curious(X0) <~> ~rich(X0)) => (~happy(susan) <~> ~old(susan)) [input p8]
25. curious(john) [input hypothesis]
34. (~happy(susan) <~> ~old(susan)) | ! [X0] : (~curious(X0) <=> ~rich(X0)) [ennf transformation 9]
43. ! [X0] : ((~happy(X0) | (~happy(X0) | ~rich(X0))) & ((happy(X0) & rich(X0)) | happy(X0))) [nnf transformation 2]
44. ! [X0] : ((~happy(X0) | ~happy(X0) | ~rich(X0)) & ((happy(X0) & rich(X0)) | happy(X0))) [flattening 43]
45. ! [X0] : ((((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | rich(X0)) & (~rich(X0) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0))))) [nnf transformation 3]
55. ! [X0] : (((~tall(X0) & ~rich(X0)) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | (tall(X0) | rich(X0)))) [nnf transformation 8]
56. ! [X0] : (((~tall(X0) & ~rich(X0)) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | tall(X0) | rich(X0))) [flattening 55]
57. ((old(susan) | happy(susan)) & (~old(susan) | ~happy(susan))) | ! [X0] : ((~curious(X0) | rich(X0)) & (~rich(X0) | curious(X0))) [nnf transformation 34]
90. happy(X0) | happy(X0) [cnf transformation 44]
91. ~happy(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 44]
94. ~tall(X0) | old(X0) | rich(X0) [cnf transformation 45]
109. rich(X0) | tall(X0) | rich(X0) [cnf transformation 56]
113. ~old(susan) | ~happy(susan) | ~curious(X0) | rich(X0) [cnf transformation 57]
149. curious(john) [cnf transformation 25]
150. tall(X0) | rich(X0) [duplicate literal removal 109]
152. happy(X0) [duplicate literal removal 90]
153. ~rich(X0) | ~happy(X0) [duplicate literal removal 91]
155. 1 <=> ! [X1] : old(X1) [avatar definition]
156. old(X1) <- (1) [avatar component clause 155]
235. ~old(susan) | ~curious(X0) | rich(X0) [subsumption resolution 113,152]
237. 18 <=> ! [X0] : (~curious(X0) | rich(X0)) [avatar definition]
238. ~curious(X0) | rich(X0) <- (18) [avatar component clause 237]
240. 19 <=> old(susan) [avatar definition]
242. ~old(susan) <- (~19) [avatar component clause 240]
243. 18 | ~19 [avatar split clause 235,240,237]
361. old(X0) | rich(X0) | rich(X0) [resolution 94,150]
362. rich(X0) | old(X0) [duplicate literal removal 361]
366. old(X1) | ~happy(X1) [resolution 362,153]
371. old(X1) [subsumption resolution 366,152]
372. 1 [avatar split clause 371,155]
378. rich(john) <- (18) [resolution 238,149]
380. ~happy(john) <- (18) [resolution 378,153]
382. $false <- (18) [subsumption resolution 380,152]
383. ~18 [avatar contradiction clause 382]
384. $false <- (1, ~19) [subsumption resolution 242,156]
385. ~1 | 19 [avatar contradiction clause 384]
386. $false [avatar sat refutation 243,372,383,385]
% SZS output end Proof for 2729067431759015680932042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and not funny is not funny. Everyone who is either not wise or not old is wise or patient. Everyone who is both not generous and rich is creative and vice versa. If someone is either calm or quiet then susan is both not curious and not generous and vice versa. If someone is both rich and funny then someone is both curious and not creative. If alice is not patient then someone is not creative. If john is both not curious and creative then someone is not rich and vice versa. If someone is either not kind or not calm then someone is not old or not brave. If someone is both brave and generous then someone is either patient or not humble and vice versa. Everyone who is funny is either humble or happy. Everyone who is both generous and not tall is not patient. If susan is calm then someone is kind or calm. If someone is either not calm or calm then someone is both kind and not creative and vice versa. If susan is both old and not happy then someone is either not calm or happy and vice versa. Everyone who is happy is both not tall and not patient and vice versa. Everyone who is quiet is either curious or not quiet and vice versa. Someone is both tall and not strong. Fred is not curious or humble. Someone is either tall or curious. Susan is both not generous and not brave. Alice is kind or creative. Someone is not curious or not tall. Fred is either not generous or not creative. | Susan is happy. | neutral | (![X]:((~wise(X)&~funny(X))=>~funny(X)))&
(![X]:((~wise(X)<~>~old(X))=>(wise(X)|patient(X))))&
(![X]:((~generous(X)&rich(X))<=>creative(X)))&
((?[X]:((calm(X)<~>quiet(X))))<=>((~curious(susan)&~generous(susan))))&
((?[X]:((rich(X)&funny(X))))=>(?[X]:((curious(X)&~creative(X)))))&
((~patient(alice))=>(?[X]:(~creative(X))))&
(((~curious(john)&creative(john)))<=>(?[X]:(~rich(X))))&
((?[X]:((~kind(X)<~>~calm(X))))=>(?[X]:((~old(X)|~brave(X)))))&
((?[X]:((brave(X)&generous(X))))<=>(?[X]:((patient(X)<~>~humble(X)))))&
(![X]:(funny(X)=>(humble(X)<~>happy(X))))&
(![X]:((generous(X)&~tall(X))=>~patient(X)))&
((calm(susan))=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:((~calm(X)<~>calm(X))))<=>(?[X]:((kind(X)&~creative(X)))))&
(((old(susan)&~happy(susan)))<=>(?[X]:((~calm(X)<~>happy(X)))))&
(![X]:(happy(X)<=>(~tall(X)&~patient(X))))&
(![X]:(quiet(X)<=>(curious(X)<~>~quiet(X))))&
(?[X]:((tall(X)&~strong(X))))&
((~curious(fred)|humble(fred)))&
(?[X]:((tall(X)<~>curious(X))))&
((~generous(susan)&~brave(susan)))&
((kind(alice)|creative(alice)))&
(?[X]:((~curious(X)|~tall(X))))&
((~generous(fred)<~>~creative(fred))) | happy(susan) | [] | null | 0 |
Everyone who is tall or rich is either not patient or not humble and vice versa.
Everyone who is either not patient or strong is happy and vice versa.
Everyone who is both generous and quiet is not brave or not rich.
Everyone who is not kind or old is tall.
If someone is either not quiet or not strong then someone is both happy and not happy and vice versa.
If lucy is creative or curious then someone is both not generous and happy and vice versa.
Everyone who is both creative and rich is not rich or creative and vice versa.
If someone is not creative or not old then fred is funny.
Everyone who is both calm and funny is either not funny or creative and vice versa.
If someone is curious or humble then lucy is brave or not wise and vice versa.
Everyone who is quiet or not humble is either kind or calm.
If susan is either old or not patient then fred is either quiet or not funny and vice versa.
Everyone who is either old or not humble is not quiet or quiet.
Everyone who is humble is both calm and tall and vice versa.
If someone is quiet then susan is not strong or not happy and vice versa.
If alice is strong then mary is either not patient or not quiet.
Susan is not rich or funny.
Susan is either funny or not quiet.
Someone is either rich or not generous.
Mary is either strong or not patient.
Someone is both generous and funny.
Someone is both happy and not humble.
Someone is both humble and kind. | Alice is quiet. | contradiction | (![X]:((tall(X)|rich(X))<=>(~patient(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>strong(X))<=>happy(X)))&
(![X]:((generous(X)&quiet(X))=>(~brave(X)|~rich(X))))&
(![X]:((~kind(X)|old(X))=>tall(X)))&
((?[X]:((~quiet(X)<~>~strong(X))))<=>(?[X]:((happy(X)&~happy(X)))))&
(((creative(lucy)|curious(lucy)))<=>(?[X]:((~generous(X)&happy(X)))))&
(![X]:((creative(X)&rich(X))<=>(~rich(X)|creative(X))))&
((?[X]:((~creative(X)|~old(X))))=>(funny(fred)))&
(![X]:((calm(X)&funny(X))<=>(~funny(X)<~>creative(X))))&
((?[X]:((curious(X)|humble(X))))<=>((brave(lucy)|~wise(lucy))))&
(![X]:((quiet(X)|~humble(X))=>(kind(X)<~>calm(X))))&
(((old(susan)<~>~patient(susan)))<=>((quiet(fred)<~>~funny(fred))))&
(![X]:((old(X)<~>~humble(X))=>(~quiet(X)|quiet(X))))&
(![X]:(humble(X)<=>(calm(X)&tall(X))))&
((?[X]:(quiet(X)))<=>((~strong(susan)|~happy(susan))))&
((strong(alice))=>((~patient(mary)<~>~quiet(mary))))&
((~rich(susan)|funny(susan)))&
((funny(susan)<~>~quiet(susan)))&
(?[X]:((rich(X)<~>~generous(X))))&
((strong(mary)<~>~patient(mary)))&
(?[X]:((generous(X)&funny(X))))&
(?[X]:((happy(X)&~humble(X))))&
(?[X]:((humble(X)&kind(X)))) | quiet(alice) | [
"p4",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3477704344588297872476019
% SZS output start Proof for 3477704344588297872476019
5. ? [X0] : (~quiet(X0) <~> ~strong(X0)) <=> ? [X0] : (~happy(X0) & happy(X0)) [input p4]
16. strong(alice) => (~patient(mary) <~> ~quiet(mary)) [input p15]
20. strong(mary) <~> ~patient(mary) [input p19]
24. quiet(alice) [input hypothesis]
25. ? [X0] : (~quiet(X0) <~> ~strong(X0)) <=> ? [X1] : (~happy(X1) & happy(X1)) [rectify 5]
33. (~patient(mary) <~> ~quiet(mary)) | ~strong(alice) [ennf transformation 16]
37. (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X1] : (~happy(X1) & happy(X1)) | ! [X0] : ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) [nnf transformation 25]
38. (? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | ~happy(X1))) & (? [X2] : (~happy(X2) & happy(X2)) | ! [X3] : ((~quiet(X3) | strong(X3)) & (~strong(X3) | quiet(X3)))) [rectify 37]
39. ? [X0] : ((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) => ((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) [choice axiom]
40. ? [X2] : (~happy(X2) & happy(X2)) => (~happy(sK1) & happy(sK1)) [choice axiom]
41. (((strong(sK0) | quiet(sK0)) & (~strong(sK0) | ~quiet(sK0))) | ! [X1] : (happy(X1) | ~happy(X1))) & ((~happy(sK1) & happy(sK1)) | ! [X3] : ((~quiet(X3) | strong(X3)) & (~strong(X3) | quiet(X3)))) [skolemisation 38,40,39]
66. ((quiet(mary) | patient(mary)) & (~quiet(mary) | ~patient(mary))) | ~strong(alice) [nnf transformation 33]
71. (patient(mary) | ~strong(mary)) & (~patient(mary) | strong(mary)) [nnf transformation 20]
91. happy(sK1) | ~strong(X3) | quiet(X3) [cnf transformation 41]
92. happy(sK1) | ~quiet(X3) | strong(X3) [cnf transformation 41]
93. ~happy(sK1) | ~strong(X3) | quiet(X3) [cnf transformation 41]
94. ~happy(sK1) | ~quiet(X3) | strong(X3) [cnf transformation 41]
139. ~quiet(mary) | ~patient(mary) | ~strong(alice) [cnf transformation 66]
140. quiet(mary) | patient(mary) | ~strong(alice) [cnf transformation 66]
146. ~patient(mary) | strong(mary) [cnf transformation 71]
147. patient(mary) | ~strong(mary) [cnf transformation 71]
154. quiet(alice) [cnf transformation 24]
160. 1 <=> ! [X3] : (~quiet(X3) | strong(X3)) [avatar definition]
161. ~quiet(X3) | strong(X3) <- (1) [avatar component clause 160]
163. 2 <=> happy(sK1) [avatar definition]
166. 1 | ~2 [avatar split clause 94,163,160]
168. 3 <=> ! [X3] : (~strong(X3) | quiet(X3)) [avatar definition]
169. ~strong(X3) | quiet(X3) <- (3) [avatar component clause 168]
170. 3 | ~2 [avatar split clause 93,163,168]
171. 1 | 2 [avatar split clause 92,163,160]
172. 3 | 2 [avatar split clause 91,163,168]
275. 25 <=> strong(alice) [avatar definition]
279. 26 <=> patient(mary) [avatar definition]
283. 27 <=> quiet(mary) [avatar definition]
284. ~quiet(mary) <- (~27) [avatar component clause 283]
285. quiet(mary) <- (27) [avatar component clause 283]
286. ~25 | 26 | 27 [avatar split clause 140,283,279,275]
287. ~25 | ~26 | ~27 [avatar split clause 139,283,279,275]
292. 28 <=> strong(mary) [avatar definition]
293. strong(mary) <- (28) [avatar component clause 292]
294. ~strong(mary) <- (~28) [avatar component clause 292]
295. ~28 | 26 [avatar split clause 147,279,292]
296. 28 | ~26 [avatar split clause 146,279,292]
310. strong(alice) <- (1) [resolution 161,154]
315. 25 | ~1 [avatar split clause 310,160,275]
316. strong(mary) <- (1, 27) [resolution 285,161]
317. $false <- (1, 27, ~28) [subsumption resolution 316,294]
318. ~1 | ~27 | 28 [avatar contradiction clause 317]
322. quiet(mary) <- (3, 28) [resolution 169,293]
323. $false <- (3, ~27, 28) [subsumption resolution 322,284]
324. ~3 | 27 | ~28 [avatar contradiction clause 323]
325. $false [avatar sat refutation 166,170,171,172,286,287,295,296,315,318,324]
% SZS output end Proof for 3477704344588297872476019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both generous and patient then alice is quiet or not calm and vice versa.
Everyone who is both not kind and brave is either humble or quiet and vice versa.
If someone is strong then lucy is both old and calm.
Everyone who is funny is both brave and tall and vice versa.
Everyone who is not patient is both old and funny.
If fred is not happy or wise then someone is both patient and not creative.
If someone is either kind or tall then mary is not happy or humble and vice versa.
Everyone who is either old or not patient is not patient.
If someone is happy or not kind then fred is not brave or not quiet and vice versa.
Everyone who is not curious is both wise and not calm.
Everyone who is both tall and funny is not strong and vice versa.
Everyone who is either brave or not quiet is not old.
Everyone who is both brave and not kind is quiet and vice versa.
Everyone who is not old or creative is strong and vice versa.
If fred is quiet then paul is either not happy or humble.
Everyone who is rich or calm is both brave and old and vice versa.
Susan is not rich or not kind.
Someone is either not creative or funny.
Someone is happy or funny.
Paul is both patient and not happy.
Someone is either not kind or not generous.
Someone is either old or calm. | Paul is not strong. | contradiction | (((generous(mary)&patient(mary)))<=>((quiet(alice)|~calm(alice))))&
(![X]:((~kind(X)&brave(X))<=>(humble(X)<~>quiet(X))))&
((?[X]:(strong(X)))=>((old(lucy)&calm(lucy))))&
(![X]:(funny(X)<=>(brave(X)&tall(X))))&
(![X]:(~patient(X)=>(old(X)&funny(X))))&
(((~happy(fred)|wise(fred)))=>(?[X]:((patient(X)&~creative(X)))))&
((?[X]:((kind(X)<~>tall(X))))<=>((~happy(mary)|humble(mary))))&
(![X]:((old(X)<~>~patient(X))=>~patient(X)))&
((?[X]:((happy(X)|~kind(X))))<=>((~brave(fred)|~quiet(fred))))&
(![X]:(~curious(X)=>(wise(X)&~calm(X))))&
(![X]:((tall(X)&funny(X))<=>~strong(X)))&
(![X]:((brave(X)<~>~quiet(X))=>~old(X)))&
(![X]:((brave(X)&~kind(X))<=>quiet(X)))&
(![X]:((~old(X)|creative(X))<=>strong(X)))&
((quiet(fred))=>((~happy(paul)<~>humble(paul))))&
(![X]:((rich(X)|calm(X))<=>(brave(X)&old(X))))&
((~rich(susan)|~kind(susan)))&
(?[X]:((~creative(X)<~>funny(X))))&
(?[X]:((happy(X)|funny(X))))&
((patient(paul)&~happy(paul)))&
(?[X]:((~kind(X)<~>~generous(X))))&
(?[X]:((old(X)<~>calm(X)))) | ~strong(paul) | [
"p7",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 432588778689656837884093
% SZS output start Proof for 432588778689656837884093
8. ! [X0] : ((old(X0) <~> ~patient(X0)) => ~patient(X0)) [input p7]
14. ! [X0] : ((creative(X0) | ~old(X0)) <=> strong(X0)) [input p13]
20. ~happy(paul) & patient(paul) [input p19]
23. ~strong(paul) [input hypothesis]
29. ! [X0] : (~patient(X0) | (old(X0) <=> ~patient(X0))) [ennf transformation 8]
45. ! [X0] : (~patient(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) [nnf transformation 29]
56. ! [X0] : (((creative(X0) | ~old(X0)) | ~strong(X0)) & (strong(X0) | (~creative(X0) & old(X0)))) [nnf transformation 14]
57. ! [X0] : ((creative(X0) | ~old(X0) | ~strong(X0)) & (strong(X0) | (~creative(X0) & old(X0)))) [flattening 56]
98. ~patient(X0) | ~patient(X0) | ~old(X0) [cnf transformation 45]
112. old(X0) | strong(X0) [cnf transformation 57]
126. patient(paul) [cnf transformation 20]
132. ~strong(paul) [cnf transformation 23]
133. ~old(X0) | ~patient(X0) [duplicate literal removal 98]
302. ~patient(X0) | strong(X0) [resolution 133,112]
382. strong(paul) [resolution 302,126]
385. $false [subsumption resolution 382,132]
% SZS output end Proof for 432588778689656837884093
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not brave then someone is both not strong and not humble and vice versa. If someone is either kind or generous then mary is curious or tall. Everyone who is either not brave or not patient is either curious or quiet. Everyone who is either happy or not quiet is both not humble and generous and vice versa. Everyone who is curious or not kind is not tall or not brave. Everyone who is either not wise or not quiet is brave. Everyone who is both generous and strong is both humble and not curious and vice versa. Everyone who is either creative or kind is either not wise or not happy and vice versa. Everyone who is funny or not rich is both not humble and humble and vice versa. If paul is not kind then john is not creative or quiet and vice versa. If fred is not wise then mary is both not brave and happy. Everyone who is not strong or rich is both not kind and not tall and vice versa. If susan is both brave and patient then susan is tall or not strong and vice versa. If alice is happy or not funny then lucy is both not kind and humble. Everyone who is both creative and wise is not calm and vice versa. If someone is either humble or not happy then someone is funny or not patient. Someone is not quiet. Alice is either strong or quiet. Someone is both not generous and not wise. Someone is either not curious or curious. John is old. Mary is wise. | Susan is old. | neutral | ((?[X]:((~old(X)|~brave(X))))<=>(?[X]:((~strong(X)&~humble(X)))))&
((?[X]:((kind(X)<~>generous(X))))=>((curious(mary)|tall(mary))))&
(![X]:((~brave(X)<~>~patient(X))=>(curious(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~quiet(X))<=>(~humble(X)&generous(X))))&
(![X]:((curious(X)|~kind(X))=>(~tall(X)|~brave(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>brave(X)))&
(![X]:((generous(X)&strong(X))<=>(humble(X)&~curious(X))))&
(![X]:((creative(X)<~>kind(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((funny(X)|~rich(X))<=>(~humble(X)&humble(X))))&
((~kind(paul))<=>((~creative(john)|quiet(john))))&
((~wise(fred))=>((~brave(mary)&happy(mary))))&
(![X]:((~strong(X)|rich(X))<=>(~kind(X)&~tall(X))))&
(((brave(susan)&patient(susan)))<=>((tall(susan)|~strong(susan))))&
(((happy(alice)|~funny(alice)))=>((~kind(lucy)&humble(lucy))))&
(![X]:((creative(X)&wise(X))<=>~calm(X)))&
((?[X]:((humble(X)<~>~happy(X))))=>(?[X]:((funny(X)|~patient(X)))))&
(?[X]:(~quiet(X)))&
((strong(alice)<~>quiet(alice)))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:((~curious(X)<~>curious(X))))&
(old(john))&
(wise(mary)) | old(susan) | [] | null | 0 |
Everyone who is wise is either not funny or not curious.
Everyone who is both tall and curious is not humble.
If someone is either curious or old then someone is both not humble and not happy.
Everyone who is curious or not kind is not wise or not tall.
Everyone who is both not patient and rich is both quiet and not generous.
Everyone who is funny or calm is not brave and vice versa.
Everyone who is not generous is kind or not kind and vice versa.
If alice is either not funny or not strong then someone is not strong or not curious.
Everyone who is either creative or not curious is strong and vice versa.
If john is both humble and rich then someone is both calm and brave.
If fred is funny or not creative then someone is kind or not wise and vice versa.
If someone is quiet then paul is not creative or not wise.
If someone is not brave or not funny then fred is both brave and not creative and vice versa.
If someone is quiet then someone is creative and vice versa.
Everyone who is both creative and not rich is both not happy and not wise and vice versa.
Lucy is either not happy or not strong.
Mary is humble.
Paul is strong or curious.
Someone is tall.
Susan is either not curious or funny. | Fred is not curious. | neutral | (![X]:(wise(X)=>(~funny(X)<~>~curious(X))))&
(![X]:((tall(X)&curious(X))=>~humble(X)))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~humble(X)&~happy(X)))))&
(![X]:((curious(X)|~kind(X))=>(~wise(X)|~tall(X))))&
(![X]:((~patient(X)&rich(X))=>(quiet(X)&~generous(X))))&
(![X]:((funny(X)|calm(X))<=>~brave(X)))&
(![X]:(~generous(X)<=>(kind(X)|~kind(X))))&
(((~funny(alice)<~>~strong(alice)))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((creative(X)<~>~curious(X))<=>strong(X)))&
(((humble(john)&rich(john)))=>(?[X]:((calm(X)&brave(X)))))&
(((funny(fred)|~creative(fred)))<=>(?[X]:((kind(X)|~wise(X)))))&
((?[X]:(quiet(X)))=>((~creative(paul)|~wise(paul))))&
((?[X]:((~brave(X)|~funny(X))))<=>((brave(fred)&~creative(fred))))&
((?[X]:(quiet(X)))<=>(?[X]:(creative(X))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&~wise(X))))&
((~happy(lucy)<~>~strong(lucy)))&
(humble(mary))&
((strong(paul)|curious(paul)))&
(?[X]:(tall(X)))&
((~curious(susan)<~>funny(susan))) | ~curious(fred) | [] | null | 0 |
If someone is both not kind and funny then paul is both not calm and old.
Everyone who is not rich is not strong or creative.
Everyone who is not creative is both rich and not creative and vice versa.
Everyone who is either not generous or kind is generous or not kind.
Everyone who is both not tall and strong is not calm and vice versa.
If someone is both not patient and quiet then paul is quiet or creative and vice versa.
Everyone who is wise or happy is either patient or not calm and vice versa.
If susan is both not patient and not generous then paul is either not happy or curious.
If someone is either funny or not creative then someone is not brave and vice versa.
Everyone who is not tall or brave is both not strong and not calm and vice versa.
If susan is either quiet or not humble then paul is not strong or wise.
If someone is rich then someone is humble or not creative and vice versa.
Everyone who is either not humble or not funny is either wise or not calm and vice versa.
Everyone who is either not creative or not curious is creative.
Everyone who is either not wise or humble is kind.
Everyone who is both calm and not tall is both not humble and curious.
Someone is both not rich and not wise.
Someone is not strong.
Someone is both kind and not creative.
Someone is not brave.
Someone is not quiet or brave.
John is both patient and not rich. | Paul is not kind. | contradiction | ((?[X]:((~kind(X)&funny(X))))=>((~calm(paul)&old(paul))))&
(![X]:(~rich(X)=>(~strong(X)|creative(X))))&
(![X]:(~creative(X)<=>(rich(X)&~creative(X))))&
(![X]:((~generous(X)<~>kind(X))=>(generous(X)|~kind(X))))&
(![X]:((~tall(X)&strong(X))<=>~calm(X)))&
((?[X]:((~patient(X)&quiet(X))))<=>((quiet(paul)|creative(paul))))&
(![X]:((wise(X)|happy(X))<=>(patient(X)<~>~calm(X))))&
(((~patient(susan)&~generous(susan)))=>((~happy(paul)<~>curious(paul))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~tall(X)|brave(X))<=>(~strong(X)&~calm(X))))&
(((quiet(susan)<~>~humble(susan)))=>((~strong(paul)|wise(paul))))&
((?[X]:(rich(X)))<=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((~humble(X)<~>~funny(X))<=>(wise(X)<~>~calm(X))))&
(![X]:((~creative(X)<~>~curious(X))=>creative(X)))&
(![X]:((~wise(X)<~>humble(X))=>kind(X)))&
(![X]:((calm(X)&~tall(X))=>(~humble(X)&curious(X))))&
(?[X]:((~rich(X)&~wise(X))))&
(?[X]:(~strong(X)))&
(?[X]:((kind(X)&~creative(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~quiet(X)|brave(X))))&
((patient(john)&~rich(john))) | ~kind(paul) | [
"p0",
"p4",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2298471193566674233370936
% SZS output start Proof for 2298471193566674233370936
1. ? [X0] : (funny(X0) & ~kind(X0)) => (old(paul) & ~calm(paul)) [input p0]
5. ! [X0] : ((strong(X0) & ~tall(X0)) <=> ~calm(X0)) [input p4]
10. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (~calm(X0) & ~strong(X0))) [input p9]
13. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> (wise(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : ((~wise(X0) <~> humble(X0)) => kind(X0)) [input p14]
23. ~kind(paul) [input hypothesis]
26. ? [X0] : (funny(X0) & ~kind(X0)) => ~calm(paul) [pure predicate removal 1]
27. ~calm(paul) | ! [X0] : (~funny(X0) | kind(X0)) [ennf transformation 26]
37. ! [X0] : (kind(X0) | (~wise(X0) <=> humble(X0))) [ennf transformation 15]
43. ! [X0] : (((strong(X0) & ~tall(X0)) | calm(X0)) & (~calm(X0) | (~strong(X0) | tall(X0)))) [nnf transformation 5]
44. ! [X0] : (((strong(X0) & ~tall(X0)) | calm(X0)) & (~calm(X0) | ~strong(X0) | tall(X0))) [flattening 43]
58. ! [X0] : (((brave(X0) | ~tall(X0)) | (calm(X0) | strong(X0))) & ((~calm(X0) & ~strong(X0)) | (~brave(X0) & tall(X0)))) [nnf transformation 10]
59. ! [X0] : ((brave(X0) | ~tall(X0) | calm(X0) | strong(X0)) & ((~calm(X0) & ~strong(X0)) | (~brave(X0) & tall(X0)))) [flattening 58]
66. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0)))) & (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 13]
68. ! [X0] : (kind(X0) | ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0)))) [nnf transformation 37]
79. ~calm(paul) | ~funny(X0) | kind(X0) [cnf transformation 27]
87. ~tall(X0) | calm(X0) [cnf transformation 44]
88. strong(X0) | calm(X0) [cnf transformation 44]
106. ~strong(X0) | tall(X0) [cnf transformation 59]
117. ~humble(X0) | wise(X0) | ~calm(X0) | funny(X0) [cnf transformation 66]
122. ~wise(X0) | humble(X0) | ~calm(X0) | funny(X0) [cnf transformation 66]
126. humble(X0) | kind(X0) | wise(X0) [cnf transformation 68]
127. ~humble(X0) | ~wise(X0) | kind(X0) [cnf transformation 68]
139. ~kind(paul) [cnf transformation 23]
144. 1 <=> ! [X0] : (~funny(X0) | kind(X0)) [avatar definition]
145. ~funny(X0) | kind(X0) <- (1) [avatar component clause 144]
147. 2 <=> calm(paul) [avatar definition]
149. ~calm(paul) <- (~2) [avatar component clause 147]
150. 1 | ~2 [avatar split clause 79,147,144]
276. tall(X0) | calm(X0) [resolution 106,88]
278. calm(X0) [subsumption resolution 276,87]
281. $false <- (~2) [resolution 278,149]
283. 2 [avatar contradiction clause 281]
336. wise(X0) | ~calm(X0) | funny(X0) | kind(X0) | wise(X0) [resolution 117,126]
337. wise(X0) | ~calm(X0) | funny(X0) | kind(X0) [duplicate literal removal 336]
340. wise(X0) | funny(X0) | kind(X0) [subsumption resolution 337,278]
341. wise(X0) | kind(X0) <- (1) [subsumption resolution 340,145]
358. humble(X0) | ~calm(X0) | funny(X0) | kind(X0) <- (1) [resolution 122,341]
359. humble(X0) | funny(X0) | kind(X0) <- (1) [subsumption resolution 358,278]
360. humble(X0) | kind(X0) <- (1) [subsumption resolution 359,145]
374. kind(X4) | ~wise(X4) | kind(X4) <- (1) [resolution 360,127]
376. kind(X4) | ~wise(X4) <- (1) [duplicate literal removal 374]
377. kind(X4) <- (1) [subsumption resolution 376,341]
378. $false <- (1) [resolution 377,139]
379. ~1 [avatar contradiction clause 378]
380. $false [avatar sat refutation 150,283,379]
% SZS output end Proof for 2298471193566674233370936
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not rich is either not generous or old and vice versa. If mary is kind or not strong then someone is not creative. If paul is either creative or tall then alice is both kind and not kind and vice versa. Everyone who is not happy or curious is kind or not curious. Everyone who is both quiet and brave is either patient or not old. If someone is either patient or not quiet then susan is patient. Everyone who is funny is either humble or not generous. If someone is not old then someone is not wise and vice versa. Everyone who is kind or not creative is not generous and vice versa. If someone is curious then someone is either humble or kind and vice versa. If paul is both curious and kind then someone is not calm and vice versa. Everyone who is calm or not tall is both funny and not brave and vice versa. Everyone who is not quiet or not old is both not calm and kind. Everyone who is either not creative or tall is both not happy and calm. Everyone who is kind is wise. If susan is either strong or not generous then someone is not rich or funny and vice versa. John is creative. Someone is strong. Mary is both patient and funny. Someone is not humble or not creative. Susan is strong. Alice is happy or not creative. Someone is not tall. Someone is brave. | Paul is humble. | contradiction | (![X]:((~strong(X)<~>~rich(X))<=>(~generous(X)<~>old(X))))&
(((kind(mary)|~strong(mary)))=>(?[X]:(~creative(X))))&
(((creative(paul)<~>tall(paul)))<=>((kind(alice)&~kind(alice))))&
(![X]:((~happy(X)|curious(X))=>(kind(X)|~curious(X))))&
(![X]:((quiet(X)&brave(X))=>(patient(X)<~>~old(X))))&
((?[X]:((patient(X)<~>~quiet(X))))=>(patient(susan)))&
(![X]:(funny(X)=>(humble(X)<~>~generous(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~wise(X))))&
(![X]:((kind(X)|~creative(X))<=>~generous(X)))&
((?[X]:(curious(X)))<=>(?[X]:((humble(X)<~>kind(X)))))&
(((curious(paul)&kind(paul)))<=>(?[X]:(~calm(X))))&
(![X]:((calm(X)|~tall(X))<=>(funny(X)&~brave(X))))&
(![X]:((~quiet(X)|~old(X))=>(~calm(X)&kind(X))))&
(![X]:((~creative(X)<~>tall(X))=>(~happy(X)&calm(X))))&
(![X]:(kind(X)=>wise(X)))&
(((strong(susan)<~>~generous(susan)))<=>(?[X]:((~rich(X)|funny(X)))))&
(creative(john))&
(?[X]:(strong(X)))&
((patient(mary)&funny(mary)))&
(?[X]:((~humble(X)|~creative(X))))&
(strong(susan))&
((happy(alice)|~creative(alice)))&
(?[X]:(~tall(X)))&
(?[X]:(brave(X))) | humble(paul) | [
"p2",
"p6",
"p8",
"p10",
"p11",
"p13",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1152729468830599306171302
% SZS output start Proof for 1152729468830599306171302
3. (creative(paul) <~> tall(paul)) <=> (~kind(alice) & kind(alice)) [input p2]
7. ! [X0] : (funny(X0) => (humble(X0) <~> ~generous(X0))) [input p6]
9. ! [X0] : ((~creative(X0) | kind(X0)) <=> ~generous(X0)) [input p8]
11. (kind(paul) & curious(paul)) <=> ? [X0] : ~calm(X0) [input p10]
12. ! [X0] : ((~tall(X0) | calm(X0)) <=> (~brave(X0) & funny(X0))) [input p11]
14. ! [X0] : ((~creative(X0) <~> tall(X0)) => (calm(X0) & ~happy(X0))) [input p13]
24. ? [X0] : brave(X0) [input p23]
25. humble(paul) [input hypothesis]
34. ! [X0] : ((humble(X0) <~> ~generous(X0)) | ~funny(X0)) [ennf transformation 7]
36. ! [X0] : ((calm(X0) & ~happy(X0)) | (~creative(X0) <=> tall(X0))) [ennf transformation 14]
41. (((~tall(paul) | ~creative(paul)) & (tall(paul) | creative(paul))) | (kind(alice) | ~kind(alice))) & ((~kind(alice) & kind(alice)) | ((creative(paul) | ~tall(paul)) & (tall(paul) | ~creative(paul)))) [nnf transformation 3]
42. (((~tall(paul) | ~creative(paul)) & (tall(paul) | creative(paul))) | kind(alice) | ~kind(alice)) & ((~kind(alice) & kind(alice)) | ((creative(paul) | ~tall(paul)) & (tall(paul) | ~creative(paul)))) [flattening 41]
45. ! [X0] : (((generous(X0) | ~humble(X0)) & (~generous(X0) | humble(X0))) | ~funny(X0)) [nnf transformation 34]
51. ! [X0] : (((~creative(X0) | kind(X0)) | generous(X0)) & (~generous(X0) | (creative(X0) & ~kind(X0)))) [nnf transformation 9]
52. ! [X0] : ((~creative(X0) | kind(X0) | generous(X0)) & (~generous(X0) | (creative(X0) & ~kind(X0)))) [flattening 51]
58. ((kind(paul) & curious(paul)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | (~kind(paul) | ~curious(paul))) [nnf transformation 11]
59. ((kind(paul) & curious(paul)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | ~kind(paul) | ~curious(paul)) [flattening 58]
60. ((kind(paul) & curious(paul)) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | ~kind(paul) | ~curious(paul)) [rectify 59]
61. ? [X1] : ~calm(X1) => ~calm(sK5) [choice axiom]
62. ((kind(paul) & curious(paul)) | ! [X0] : calm(X0)) & (~calm(sK5) | ~kind(paul) | ~curious(paul)) [skolemisation 60,61]
63. ! [X0] : (((~tall(X0) | calm(X0)) | (brave(X0) | ~funny(X0))) & ((~brave(X0) & funny(X0)) | (tall(X0) & ~calm(X0)))) [nnf transformation 12]
64. ! [X0] : ((~tall(X0) | calm(X0) | brave(X0) | ~funny(X0)) & ((~brave(X0) & funny(X0)) | (tall(X0) & ~calm(X0)))) [flattening 63]
65. ! [X0] : ((calm(X0) & ~happy(X0)) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0)))) [nnf transformation 36]
76. ? [X0] : brave(X0) => brave(sK10) [choice axiom]
77. brave(sK10) [skolemisation 24,76]
89. kind(alice) | creative(paul) | ~tall(paul) [cnf transformation 42]
91. ~kind(alice) | creative(paul) | ~tall(paul) [cnf transformation 42]
101. ~humble(X0) | generous(X0) | ~funny(X0) [cnf transformation 45]
104. ~kind(X0) | ~generous(X0) [cnf transformation 52]
113. kind(paul) | calm(X0) [cnf transformation 62]
114. ~calm(X0) | funny(X0) [cnf transformation 64]
115. funny(X0) | tall(X0) [cnf transformation 64]
116. ~calm(X0) | ~brave(X0) [cnf transformation 64]
126. ~tall(X0) | ~creative(X0) | calm(X0) [cnf transformation 65]
142. brave(sK10) [cnf transformation 77]
143. humble(paul) [cnf transformation 25]
160. 4 <=> tall(paul) [avatar definition]
161. tall(paul) <- (4) [avatar component clause 160]
164. 5 <=> creative(paul) [avatar definition]
166. creative(paul) <- (5) [avatar component clause 164]
168. 6 <=> kind(alice) [avatar definition]
171. ~4 | 5 | ~6 [avatar split clause 91,168,164,160]
173. ~4 | 5 | 6 [avatar split clause 89,168,164,160]
229. 20 <=> ! [X0] : calm(X0) [avatar definition]
230. calm(X0) <- (20) [avatar component clause 229]
232. 21 <=> kind(paul) [avatar definition]
234. kind(paul) <- (21) [avatar component clause 232]
235. 20 | 21 [avatar split clause 113,232,229]
298. ~brave(X0) <- (20) [resolution 116,230]
299. $false <- (20) [resolution 298,142]
300. ~20 [avatar contradiction clause 299]
303. ~generous(paul) <- (21) [resolution 234,104]
331. generous(paul) | ~funny(paul) [resolution 101,143]
333. ~funny(paul) <- (21) [subsumption resolution 331,303]
354. tall(paul) <- (21) [resolution 333,115]
357. 4 | ~21 [avatar split clause 354,232,160]
386. ~creative(paul) | calm(paul) <- (4) [resolution 126,161]
396. calm(paul) <- (4, 5) [subsumption resolution 386,166]
450. funny(paul) <- (4, 5) [resolution 396,114]
451. $false <- (4, 5, 21) [subsumption resolution 450,333]
452. ~4 | ~5 | ~21 [avatar contradiction clause 451]
453. $false [avatar sat refutation 171,173,235,300,357,452]
% SZS output end Proof for 1152729468830599306171302
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not curious is both brave and not brave.
Everyone who is not old or not wise is both wise and happy and vice versa.
Everyone who is either rich or not humble is both calm and wise and vice versa.
Everyone who is not happy is strong and vice versa.
If lucy is both generous and not calm then someone is not wise and vice versa.
If mary is not wise or not strong then someone is both not kind and creative and vice versa.
Everyone who is not brave is both happy and humble.
If someone is not strong or not funny then lucy is tall and vice versa.
If john is either not creative or not happy then mary is humble or kind and vice versa.
If alice is both not tall and brave then alice is wise or not generous.
Everyone who is either not strong or not humble is patient or generous and vice versa.
Everyone who is not rich or tall is not patient and vice versa.
Everyone who is not generous or not patient is old and vice versa.
If lucy is both not wise and happy then john is not creative or not kind and vice versa.
Everyone who is both curious and wise is both not quiet and not calm and vice versa.
Everyone who is generous or not happy is either generous or not patient.
Susan is not happy or kind.
Someone is quiet.
Someone is both not patient and not kind.
Lucy is both old and funny. | Alice is not funny. | neutral | (![X]:((happy(X)&~curious(X))=>(brave(X)&~brave(X))))&
(![X]:((~old(X)|~wise(X))<=>(wise(X)&happy(X))))&
(![X]:((rich(X)<~>~humble(X))<=>(calm(X)&wise(X))))&
(![X]:(~happy(X)<=>strong(X)))&
(((generous(lucy)&~calm(lucy)))<=>(?[X]:(~wise(X))))&
(((~wise(mary)|~strong(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:(~brave(X)=>(happy(X)&humble(X))))&
((?[X]:((~strong(X)|~funny(X))))<=>(tall(lucy)))&
(((~creative(john)<~>~happy(john)))<=>((humble(mary)|kind(mary))))&
(((~tall(alice)&brave(alice)))=>((wise(alice)|~generous(alice))))&
(![X]:((~strong(X)<~>~humble(X))<=>(patient(X)|generous(X))))&
(![X]:((~rich(X)|tall(X))<=>~patient(X)))&
(![X]:((~generous(X)|~patient(X))<=>old(X)))&
(((~wise(lucy)&happy(lucy)))<=>((~creative(john)|~kind(john))))&
(![X]:((curious(X)&wise(X))<=>(~quiet(X)&~calm(X))))&
(![X]:((generous(X)|~happy(X))=>(generous(X)<~>~patient(X))))&
((~happy(susan)|kind(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((~patient(X)&~kind(X))))&
((old(lucy)&funny(lucy))) | ~funny(alice) | [] | null | 0 |
Everyone who is either not strong or old is both strong and not tall. Everyone who is patient or not calm is both not wise and old. If john is funny or curious then lucy is either generous or tall. If someone is not patient then someone is not generous. If someone is kind then someone is either not happy or not strong. Everyone who is either old or not humble is both not curious and not patient and vice versa. If lucy is both curious and creative then someone is either not rich or not generous. If mary is rich then mary is both generous and not calm. Everyone who is curious or calm is not wise. Everyone who is both strong and not wise is patient or wise and vice versa. If someone is rich then someone is both not funny and not calm and vice versa. Everyone who is curious or not wise is creative or tall. Everyone who is both not kind and not calm is both strong and not quiet. Everyone who is rich is not patient or happy and vice versa. If someone is both curious and not old then alice is calm or not brave and vice versa. Everyone who is brave is either not brave or not generous and vice versa. Fred is not curious or not kind. Someone is both not rich and not happy. Someone is either not happy or not tall. Someone is not calm or tall. Someone is strong. Alice is not humble. | Mary is tall. | contradiction | (![X]:((~strong(X)<~>old(X))=>(strong(X)&~tall(X))))&
(![X]:((patient(X)|~calm(X))=>(~wise(X)&old(X))))&
(((funny(john)|curious(john)))=>((generous(lucy)<~>tall(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:(~generous(X))))&
((?[X]:(kind(X)))=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((old(X)<~>~humble(X))<=>(~curious(X)&~patient(X))))&
(((curious(lucy)&creative(lucy)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
((rich(mary))=>((generous(mary)&~calm(mary))))&
(![X]:((curious(X)|calm(X))=>~wise(X)))&
(![X]:((strong(X)&~wise(X))<=>(patient(X)|wise(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~funny(X)&~calm(X)))))&
(![X]:((curious(X)|~wise(X))=>(creative(X)|tall(X))))&
(![X]:((~kind(X)&~calm(X))=>(strong(X)&~quiet(X))))&
(![X]:(rich(X)<=>(~patient(X)|happy(X))))&
((?[X]:((curious(X)&~old(X))))<=>((calm(alice)|~brave(alice))))&
(![X]:(brave(X)<=>(~brave(X)<~>~generous(X))))&
((~curious(fred)|~kind(fred)))&
(?[X]:((~rich(X)&~happy(X))))&
(?[X]:((~happy(X)<~>~tall(X))))&
(?[X]:((~calm(X)|tall(X))))&
(?[X]:(strong(X)))&
(~humble(alice)) | tall(mary) | [
"p0",
"p1",
"p7",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7063545107849088494853421
% SZS output start Proof for 7063545107849088494853421
1. ! [X0] : ((~strong(X0) <~> old(X0)) => (~tall(X0) & strong(X0))) [input p0]
2. ! [X0] : ((~calm(X0) | patient(X0)) => (old(X0) & ~wise(X0))) [input p1]
8. rich(mary) => (~calm(mary) & generous(mary)) [input p7]
10. ! [X0] : ((~wise(X0) & strong(X0)) <=> (wise(X0) | patient(X0))) [input p9]
14. ! [X0] : (rich(X0) <=> (happy(X0) | ~patient(X0))) [input p13]
16. ! [X0] : (brave(X0) <=> (~brave(X0) <~> ~generous(X0))) [input p15]
23. tall(mary) [input hypothesis]
28. ! [X0] : ((~tall(X0) & strong(X0)) | (~strong(X0) <=> old(X0))) [ennf transformation 1]
29. ! [X0] : ((old(X0) & ~wise(X0)) | (calm(X0) & ~patient(X0))) [ennf transformation 2]
35. (~calm(mary) & generous(mary)) | ~rich(mary) [ennf transformation 8]
41. ! [X0] : ((~tall(X0) & strong(X0)) | ((~strong(X0) | ~old(X0)) & (old(X0) | strong(X0)))) [nnf transformation 28]
55. ! [X0] : (((~wise(X0) & strong(X0)) | (~wise(X0) & ~patient(X0))) & ((wise(X0) | patient(X0)) | (wise(X0) | ~strong(X0)))) [nnf transformation 10]
56. ! [X0] : (((~wise(X0) & strong(X0)) | (~wise(X0) & ~patient(X0))) & (wise(X0) | patient(X0) | wise(X0) | ~strong(X0))) [flattening 55]
62. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ~rich(X0))) [nnf transformation 14]
63. ! [X0] : ((rich(X0) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ~rich(X0))) [flattening 62]
69. ! [X0] : ((brave(X0) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | ~brave(X0))) [nnf transformation 16]
82. ~tall(X0) | ~strong(X0) | ~old(X0) [cnf transformation 41]
85. ~patient(X0) | old(X0) [cnf transformation 29]
102. generous(mary) | ~rich(mary) [cnf transformation 35]
107. ~patient(X0) | strong(X0) [cnf transformation 56]
118. rich(X0) | patient(X0) [cnf transformation 63]
125. ~generous(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 69]
127. brave(X0) | ~generous(X0) | brave(X0) [cnf transformation 69]
137. tall(mary) [cnf transformation 23]
138. ~generous(X0) | ~brave(X0) [duplicate literal removal 125]
139. ~generous(X0) | brave(X0) [duplicate literal removal 127]
205. 14 <=> rich(mary) [avatar definition]
207. ~rich(mary) <- (~14) [avatar component clause 205]
214. 16 <=> generous(mary) [avatar definition]
216. generous(mary) <- (16) [avatar component clause 214]
217. ~14 | 16 [avatar split clause 102,214,205]
266. ~generous(X0) [subsumption resolution 138,139]
298. patient(mary) <- (~14) [resolution 118,207]
302. strong(mary) <- (~14) [resolution 298,107]
303. old(mary) <- (~14) [resolution 298,85]
315. ~strong(mary) | ~old(mary) [resolution 82,137]
316. ~old(mary) <- (~14) [subsumption resolution 315,302]
317. $false <- (~14) [subsumption resolution 316,303]
318. 14 [avatar contradiction clause 317]
328. $false <- (16) [subsumption resolution 216,266]
329. ~16 [avatar contradiction clause 328]
330. $false [avatar sat refutation 217,318,329]
% SZS output end Proof for 7063545107849088494853421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or rich then someone is not curious. Everyone who is old or not generous is either wise or funny and vice versa. If paul is quiet then someone is either creative or humble. Everyone who is not creative is not calm and vice versa. Everyone who is calm or not tall is both funny and wise. If someone is quiet then susan is both not creative and patient and vice versa. Everyone who is wise or not strong is either patient or funny. If someone is not happy or brave then paul is happy and vice versa. Everyone who is either kind or quiet is both not quiet and not strong and vice versa. If mary is wise or not rich then someone is either quiet or old. Everyone who is patient or humble is calm. If alice is both not humble and patient then john is either generous or tall and vice versa. Everyone who is either not quiet or not kind is either not strong or old. Everyone who is either strong or not funny is both not old and not calm. If paul is both kind and generous then someone is both not quiet and not funny. Everyone who is not wise is not strong and vice versa. Someone is either tall or not wise. Alice is both tall and generous. Paul is tall. Mary is happy or not rich. Lucy is not brave or old. Someone is either not strong or happy. | Lucy is brave. | contradiction | (((~happy(fred)|rich(fred)))=>(?[X]:(~curious(X))))&
(![X]:((old(X)|~generous(X))<=>(wise(X)<~>funny(X))))&
((quiet(paul))=>(?[X]:((creative(X)<~>humble(X)))))&
(![X]:(~creative(X)<=>~calm(X)))&
(![X]:((calm(X)|~tall(X))=>(funny(X)&wise(X))))&
((?[X]:(quiet(X)))<=>((~creative(susan)&patient(susan))))&
(![X]:((wise(X)|~strong(X))=>(patient(X)<~>funny(X))))&
((?[X]:((~happy(X)|brave(X))))<=>(happy(paul)))&
(![X]:((kind(X)<~>quiet(X))<=>(~quiet(X)&~strong(X))))&
(((wise(mary)|~rich(mary)))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:((patient(X)|humble(X))=>calm(X)))&
(((~humble(alice)&patient(alice)))<=>((generous(john)<~>tall(john))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~strong(X)<~>old(X))))&
(![X]:((strong(X)<~>~funny(X))=>(~old(X)&~calm(X))))&
(((kind(paul)&generous(paul)))=>(?[X]:((~quiet(X)&~funny(X)))))&
(![X]:(~wise(X)<=>~strong(X)))&
(?[X]:((tall(X)<~>~wise(X))))&
((tall(alice)&generous(alice)))&
(tall(paul))&
((happy(mary)|~rich(mary)))&
((~brave(lucy)|old(lucy)))&
(?[X]:((~strong(X)<~>happy(X)))) | brave(lucy) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 108905651963418853115848
% SZS output start Proof for 108905651963418853115848
2. ! [X0] : ((~generous(X0) | old(X0)) <=> (wise(X0) <~> funny(X0))) [input p1]
4. ! [X0] : (~creative(X0) <=> ~calm(X0)) [input p3]
5. ! [X0] : ((~tall(X0) | calm(X0)) => (wise(X0) & funny(X0))) [input p4]
6. ? [X0] : quiet(X0) <=> (patient(susan) & ~creative(susan)) [input p5]
7. ! [X0] : ((~strong(X0) | wise(X0)) => (patient(X0) <~> funny(X0))) [input p6]
9. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> (~strong(X0) & ~quiet(X0))) [input p8]
11. ! [X0] : ((humble(X0) | patient(X0)) => calm(X0)) [input p10]
13. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) => (~strong(X0) <~> old(X0))) [input p12]
16. ! [X0] : (~wise(X0) <=> ~strong(X0)) [input p15]
21. old(lucy) | ~brave(lucy) [input p20]
23. brave(lucy) [input hypothesis]
26. ! [X0] : ((wise(X0) & funny(X0)) | (tall(X0) & ~calm(X0))) [ennf transformation 5]
27. ! [X0] : ((patient(X0) <~> funny(X0)) | (strong(X0) & ~wise(X0))) [ennf transformation 7]
29. ! [X0] : (calm(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 11]
30. ! [X0] : ((~strong(X0) <~> old(X0)) | (~quiet(X0) <=> ~kind(X0))) [ennf transformation 13]
34. ! [X0] : (((~generous(X0) | old(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (generous(X0) & ~old(X0)))) [nnf transformation 2]
35. ! [X0] : ((~generous(X0) | old(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (generous(X0) & ~old(X0)))) [flattening 34]
39. ! [X0] : ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0))) [nnf transformation 4]
40. (? [X0] : quiet(X0) | (~patient(susan) | creative(susan))) & ((patient(susan) & ~creative(susan)) | ! [X0] : ~quiet(X0)) [nnf transformation 6]
41. (? [X0] : quiet(X0) | ~patient(susan) | creative(susan)) & ((patient(susan) & ~creative(susan)) | ! [X0] : ~quiet(X0)) [flattening 40]
42. (? [X0] : quiet(X0) | ~patient(susan) | creative(susan)) & ((patient(susan) & ~creative(susan)) | ! [X1] : ~quiet(X1)) [rectify 41]
43. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
44. (quiet(sK1) | ~patient(susan) | creative(susan)) & ((patient(susan) & ~creative(susan)) | ! [X1] : ~quiet(X1)) [skolemisation 42,43]
45. ! [X0] : (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (strong(X0) & ~wise(X0))) [nnf transformation 27]
50. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (strong(X0) | quiet(X0))) & ((~strong(X0) & ~quiet(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 9]
51. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | strong(X0) | quiet(X0)) & ((~strong(X0) & ~quiet(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [flattening 50]
57. ! [X0] : (((~old(X0) | strong(X0)) & (old(X0) | ~strong(X0))) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0)))) [nnf transformation 30]
61. ! [X0] : ((~wise(X0) | strong(X0)) & (~strong(X0) | wise(X0))) [nnf transformation 16]
70. ~funny(X0) | ~wise(X0) | ~old(X0) [cnf transformation 35]
76. ~calm(X0) | creative(X0) [cnf transformation 39]
78. ~calm(X0) | funny(X0) [cnf transformation 26]
82. ~creative(susan) | ~quiet(X1) [cnf transformation 44]
83. patient(susan) | ~quiet(X1) [cnf transformation 44]
85. ~wise(X0) | patient(X0) | funny(X0) [cnf transformation 45]
86. strong(X0) | patient(X0) | funny(X0) [cnf transformation 45]
94. ~kind(X0) | quiet(X0) | ~strong(X0) [cnf transformation 51]
96. quiet(X0) | kind(X0) | strong(X0) | quiet(X0) [cnf transformation 51]
102. ~patient(X0) | calm(X0) [cnf transformation 29]
112. ~old(X0) | strong(X0) | ~kind(X0) | quiet(X0) [cnf transformation 57]
120. ~strong(X0) | wise(X0) [cnf transformation 61]
128. old(lucy) | ~brave(lucy) [cnf transformation 21]
131. brave(lucy) [cnf transformation 23]
133. kind(X0) | quiet(X0) | strong(X0) [duplicate literal removal 96]
149. 4 <=> creative(susan) [avatar definition]
150. ~creative(susan) <- (~4) [avatar component clause 149]
153. 5 <=> patient(susan) [avatar definition]
154. patient(susan) <- (5) [avatar component clause 153]
162. 7 <=> ! [X1] : ~quiet(X1) [avatar definition]
163. ~quiet(X1) <- (7) [avatar component clause 162]
164. 7 | 5 [avatar split clause 83,153,162]
165. 7 | ~4 [avatar split clause 82,149,162]
229. ~kind(X0) | ~old(X0) | quiet(X0) [subsumption resolution 112,94]
257. 26 <=> brave(lucy) [avatar definition]
261. 27 <=> old(lucy) [avatar definition]
263. old(lucy) <- (27) [avatar component clause 261]
264. ~26 | 27 [avatar split clause 128,261,257]
275. 26 [avatar split clause 131,257]
278. calm(susan) <- (5) [resolution 102,154]
281. creative(susan) <- (5) [resolution 278,76]
282. $false <- (~4, 5) [subsumption resolution 281,150]
283. 4 | ~5 [avatar contradiction clause 282]
297. 30 <=> funny(lucy) [avatar definition]
298. ~funny(lucy) <- (~30) [avatar component clause 297]
299. funny(lucy) <- (30) [avatar component clause 297]
301. 31 <=> wise(lucy) [avatar definition]
316. ~wise(lucy) | ~old(lucy) <- (30) [resolution 70,299]
319. ~wise(lucy) <- (27, 30) [subsumption resolution 316,263]
320. ~31 | ~27 | ~30 [avatar split clause 319,297,261,301]
351. patient(X1) | funny(X1) | wise(X1) [resolution 86,120]
361. patient(X1) | funny(X1) [subsumption resolution 351,85]
420. ~old(X0) | quiet(X0) | quiet(X0) | strong(X0) [resolution 229,133]
421. ~old(X0) | quiet(X0) | strong(X0) [duplicate literal removal 420]
422. ~old(X0) | strong(X0) <- (7) [subsumption resolution 421,163]
434. funny(X2) | calm(X2) [resolution 361,102]
438. funny(X2) [subsumption resolution 434,78]
439. strong(lucy) <- (7, 27) [resolution 422,263]
450. wise(lucy) <- (7, 27) [resolution 439,120]
459. 31 | ~7 | ~27 [avatar split clause 450,261,162,301]
460. $false <- (~30) [subsumption resolution 298,438]
461. 30 [avatar contradiction clause 460]
462. $false [avatar sat refutation 164,165,264,275,283,320,459,461]
% SZS output end Proof for 108905651963418853115848
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not quiet is not funny.
Everyone who is both not happy and brave is curious and vice versa.
Everyone who is either calm or not brave is brave and vice versa.
Everyone who is either happy or tall is either not quiet or not tall.
Everyone who is both not funny and not brave is calm and vice versa.
Everyone who is brave or old is both not rich and curious and vice versa.
If mary is wise or not happy then someone is curious or kind.
If someone is either not patient or quiet then someone is not calm or creative and vice versa.
Everyone who is not wise or patient is either not patient or rich.
Everyone who is either not kind or not old is either not rich or quiet.
Everyone who is both old and not tall is not humble or not quiet and vice versa.
Everyone who is both not rich and calm is both not wise and not creative and vice versa.
If susan is both not rich and wise then someone is both tall and quiet and vice versa.
Everyone who is both happy and not strong is either creative or not generous and vice versa.
If someone is both curious and funny then alice is rich.
If someone is both funny and wise then someone is not kind.
Paul is not brave or strong.
Someone is either not creative or happy.
Mary is both not funny and humble.
Lucy is not wise.
Someone is wise.
Someone is humble. | Lucy is not old. | entailment | (![X]:((funny(X)|~quiet(X))=>~funny(X)))&
(![X]:((~happy(X)&brave(X))<=>curious(X)))&
(![X]:((calm(X)<~>~brave(X))<=>brave(X)))&
(![X]:((happy(X)<~>tall(X))=>(~quiet(X)<~>~tall(X))))&
(![X]:((~funny(X)&~brave(X))<=>calm(X)))&
(![X]:((brave(X)|old(X))<=>(~rich(X)&curious(X))))&
(((wise(mary)|~happy(mary)))=>(?[X]:((curious(X)|kind(X)))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(?[X]:((~calm(X)|creative(X)))))&
(![X]:((~wise(X)|patient(X))=>(~patient(X)<~>rich(X))))&
(![X]:((~kind(X)<~>~old(X))=>(~rich(X)<~>quiet(X))))&
(![X]:((old(X)&~tall(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&~creative(X))))&
(((~rich(susan)&wise(susan)))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((happy(X)&~strong(X))<=>(creative(X)<~>~generous(X))))&
((?[X]:((curious(X)&funny(X))))=>(rich(alice)))&
((?[X]:((funny(X)&wise(X))))=>(?[X]:(~kind(X))))&
((~brave(paul)|strong(paul)))&
(?[X]:((~creative(X)<~>happy(X))))&
((~funny(mary)&humble(mary)))&
(~wise(lucy))&
(?[X]:(wise(X)))&
(?[X]:(humble(X))) | ~old(lucy) | [
"p1",
"p2",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 671586077058769860829275
% SZS output start Proof for 671586077058769860829275
2. ! [X0] : ((brave(X0) & ~happy(X0)) <=> curious(X0)) [input p1]
3. ! [X0] : ((calm(X0) <~> ~brave(X0)) <=> brave(X0)) [input p2]
5. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> calm(X0)) [input p4]
6. ! [X0] : ((old(X0) | brave(X0)) <=> (curious(X0) & ~rich(X0))) [input p5]
23. old(lucy) [input hypothesis]
33. ! [X0] : (((brave(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | (~brave(X0) | happy(X0)))) [nnf transformation 2]
34. ! [X0] : (((brave(X0) & ~happy(X0)) | ~curious(X0)) & (curious(X0) | ~brave(X0) | happy(X0))) [flattening 33]
35. ! [X0] : ((((brave(X0) | ~calm(X0)) & (~brave(X0) | calm(X0))) | ~brave(X0)) & (brave(X0) | ((calm(X0) | brave(X0)) & (~brave(X0) | ~calm(X0))))) [nnf transformation 3]
37. ! [X0] : (((~brave(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | (brave(X0) | funny(X0)))) [nnf transformation 5]
38. ! [X0] : (((~brave(X0) & ~funny(X0)) | ~calm(X0)) & (calm(X0) | brave(X0) | funny(X0))) [flattening 37]
39. ! [X0] : (((old(X0) | brave(X0)) | (~curious(X0) | rich(X0))) & ((curious(X0) & ~rich(X0)) | (~old(X0) & ~brave(X0)))) [nnf transformation 6]
40. ! [X0] : ((old(X0) | brave(X0) | ~curious(X0) | rich(X0)) & ((curious(X0) & ~rich(X0)) | (~old(X0) & ~brave(X0)))) [flattening 39]
75. ~curious(X0) | brave(X0) [cnf transformation 34]
77. brave(X0) | calm(X0) | brave(X0) [cnf transformation 35]
78. ~brave(X0) | calm(X0) | ~brave(X0) [cnf transformation 35]
86. ~brave(X0) | ~calm(X0) [cnf transformation 38]
90. ~old(X0) | curious(X0) [cnf transformation 40]
137. old(lucy) [cnf transformation 23]
141. brave(X0) | calm(X0) [duplicate literal removal 77]
142. ~brave(X0) | calm(X0) [duplicate literal removal 78]
144. calm(X0) [subsumption resolution 141,142]
145. ~brave(X0) [subsumption resolution 86,144]
224. curious(lucy) [resolution 90,137]
225. brave(lucy) [resolution 224,75]
227. $false [subsumption resolution 225,145]
% SZS output end Proof for 671586077058769860829275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not tall or not old then someone is curious or not calm.
Everyone who is not patient or wise is patient or creative and vice versa.
If paul is not old or patient then someone is creative or brave and vice versa.
If alice is not rich or not generous then someone is patient and vice versa.
If someone is tall or not patient then lucy is tall or old.
Everyone who is either kind or wise is not strong or tall and vice versa.
Everyone who is patient or generous is not old or not tall.
If someone is either not tall or not wise then someone is both generous and not wise.
Everyone who is either not strong or not patient is either humble or not old.
Everyone who is both kind and rich is old or not brave and vice versa.
Everyone who is not patient or patient is both not patient and not calm and vice versa.
Everyone who is wise or not old is either not calm or not curious.
If susan is quiet then paul is either not patient or not kind and vice versa.
Everyone who is either strong or humble is calm.
Everyone who is calm is both patient and not wise.
Everyone who is both curious and not tall is tall.
Fred is not kind.
Someone is rich.
Susan is either not brave or happy.
John is either not brave or not patient.
Susan is either not brave or curious.
Someone is either kind or not strong. | Paul is tall. | entailment | (((~tall(alice)<~>~old(alice)))=>(?[X]:((curious(X)|~calm(X)))))&
(![X]:((~patient(X)|wise(X))<=>(patient(X)|creative(X))))&
(((~old(paul)|patient(paul)))<=>(?[X]:((creative(X)|brave(X)))))&
(((~rich(alice)|~generous(alice)))<=>(?[X]:(patient(X))))&
((?[X]:((tall(X)|~patient(X))))=>((tall(lucy)|old(lucy))))&
(![X]:((kind(X)<~>wise(X))<=>(~strong(X)|tall(X))))&
(![X]:((patient(X)|generous(X))=>(~old(X)|~tall(X))))&
((?[X]:((~tall(X)<~>~wise(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~strong(X)<~>~patient(X))=>(humble(X)<~>~old(X))))&
(![X]:((kind(X)&rich(X))<=>(old(X)|~brave(X))))&
(![X]:((~patient(X)|patient(X))<=>(~patient(X)&~calm(X))))&
(![X]:((wise(X)|~old(X))=>(~calm(X)<~>~curious(X))))&
((quiet(susan))<=>((~patient(paul)<~>~kind(paul))))&
(![X]:((strong(X)<~>humble(X))=>calm(X)))&
(![X]:(calm(X)=>(patient(X)&~wise(X))))&
(![X]:((curious(X)&~tall(X))=>tall(X)))&
(~kind(fred))&
(?[X]:(rich(X)))&
((~brave(susan)<~>happy(susan)))&
((~brave(john)<~>~patient(john)))&
((~brave(susan)<~>curious(susan)))&
(?[X]:((kind(X)<~>~strong(X)))) | tall(paul) | [
"p2",
"p10",
"p11",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3122943592877381082543641
% SZS output start Proof for 3122943592877381082543641
3. (patient(paul) | ~old(paul)) <=> ? [X0] : (brave(X0) | creative(X0)) [input p2]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~calm(X0) & ~patient(X0))) [input p10]
12. ! [X0] : ((~old(X0) | wise(X0)) => (~calm(X0) <~> ~curious(X0))) [input p11]
16. ! [X0] : ((~tall(X0) & curious(X0)) => tall(X0)) [input p15]
20. ~brave(john) <~> ~patient(john) [input p19]
23. ~tall(paul) [input hypothesis]
32. ! [X0] : ((~calm(X0) <~> ~curious(X0)) | (old(X0) & ~wise(X0))) [ennf transformation 12]
35. ! [X0] : (tall(X0) | (tall(X0) | ~curious(X0))) [ennf transformation 16]
36. ! [X0] : (tall(X0) | tall(X0) | ~curious(X0)) [flattening 35]
42. ((patient(paul) | ~old(paul)) | ! [X0] : (~brave(X0) & ~creative(X0))) & (? [X0] : (brave(X0) | creative(X0)) | (~patient(paul) & old(paul))) [nnf transformation 3]
43. (patient(paul) | ~old(paul) | ! [X0] : (~brave(X0) & ~creative(X0))) & (? [X0] : (brave(X0) | creative(X0)) | (~patient(paul) & old(paul))) [flattening 42]
44. (patient(paul) | ~old(paul) | ! [X0] : (~brave(X0) & ~creative(X0))) & (? [X1] : (brave(X1) | creative(X1)) | (~patient(paul) & old(paul))) [rectify 43]
45. ? [X1] : (brave(X1) | creative(X1)) => (brave(sK1) | creative(sK1)) [choice axiom]
46. (patient(paul) | ~old(paul) | ! [X0] : (~brave(X0) & ~creative(X0))) & ((brave(sK1) | creative(sK1)) | (~patient(paul) & old(paul))) [skolemisation 44,45]
61. ! [X0] : (((patient(X0) | ~patient(X0)) | (calm(X0) | patient(X0))) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
62. ! [X0] : ((patient(X0) | ~patient(X0) | calm(X0) | patient(X0)) & ((~calm(X0) & ~patient(X0)) | (~patient(X0) & patient(X0)))) [flattening 61]
63. ! [X0] : (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (old(X0) & ~wise(X0))) [nnf transformation 32]
69. (patient(john) | brave(john)) & (~patient(john) | ~brave(john)) [nnf transformation 20]
83. patient(paul) | ~old(paul) | ~brave(X0) [cnf transformation 46]
111. ~patient(X0) | ~patient(X0) [cnf transformation 62]
112. ~calm(X0) | patient(X0) [cnf transformation 62]
113. ~patient(X0) | ~calm(X0) [cnf transformation 62]
118. curious(X0) | calm(X0) | old(X0) [cnf transformation 63]
127. tall(X0) | tall(X0) | ~curious(X0) [cnf transformation 36]
133. patient(john) | brave(john) [cnf transformation 69]
138. ~tall(paul) [cnf transformation 23]
139. ~curious(X0) | tall(X0) [duplicate literal removal 127]
140. ~patient(X0) [duplicate literal removal 111]
163. 5 <=> ! [X0] : ~brave(X0) [avatar definition]
164. ~brave(X0) <- (5) [avatar component clause 163]
166. 6 <=> old(paul) [avatar definition]
168. ~old(paul) <- (~6) [avatar component clause 166]
170. 7 <=> patient(paul) [avatar definition]
172. patient(paul) <- (7) [avatar component clause 170]
173. 5 | ~6 | 7 [avatar split clause 83,170,166,163]
189. 11 <=> ! [X0] : ~patient(X0) [avatar definition]
190. ~patient(X0) <- (11) [avatar component clause 189]
240. ~calm(X0) [subsumption resolution 112,113]
241. 11 [avatar split clause 140,189]
242. curious(X0) | old(X0) [subsumption resolution 118,240]
269. 27 <=> brave(john) [avatar definition]
271. brave(john) <- (27) [avatar component clause 269]
273. 28 <=> patient(john) [avatar definition]
275. patient(john) <- (28) [avatar component clause 273]
276. 27 | 28 [avatar split clause 133,273,269]
294. $false <- (5, 27) [resolution 271,164]
295. ~5 | ~27 [avatar contradiction clause 294]
304. old(X0) | tall(X0) [resolution 242,139]
312. tall(paul) <- (~6) [resolution 304,168]
315. $false <- (~6) [subsumption resolution 312,138]
316. 6 [avatar contradiction clause 315]
317. $false <- (7, 11) [subsumption resolution 172,190]
318. ~7 | ~11 [avatar contradiction clause 317]
319. $false <- (11, 28) [subsumption resolution 275,190]
320. ~11 | ~28 [avatar contradiction clause 319]
321. $false [avatar sat refutation 173,241,276,295,316,318,320]
% SZS output end Proof for 3122943592877381082543641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and not wise is either not creative or funny and vice versa.
If someone is tall then lucy is not rich and vice versa.
Everyone who is both creative and not tall is not quiet or not generous.
If susan is both happy and not tall then alice is rich and vice versa.
If someone is not creative or not wise then lucy is both not curious and patient.
If paul is either not funny or not kind then paul is rich or not creative.
Everyone who is tall or not happy is either curious or wise and vice versa.
Everyone who is both not creative and wise is strong and vice versa.
Everyone who is not funny or not happy is both not rich and not strong and vice versa.
Everyone who is not patient or not quiet is old or calm and vice versa.
Everyone who is happy is both funny and not old.
Everyone who is humble is either strong or not patient.
Everyone who is either not happy or brave is not old or funny and vice versa.
Everyone who is either brave or not old is wise or kind and vice versa.
Everyone who is either funny or creative is both rich and humble and vice versa.
If mary is not generous or not rich then someone is wise.
Someone is not old or not generous.
Alice is not generous or not kind.
Someone is not humble. | Susan is not funny. | contradiction | (![X]:((~kind(X)&~wise(X))<=>(~creative(X)<~>funny(X))))&
((?[X]:(tall(X)))<=>(~rich(lucy)))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)|~generous(X))))&
(((happy(susan)&~tall(susan)))<=>(rich(alice)))&
((?[X]:((~creative(X)|~wise(X))))=>((~curious(lucy)&patient(lucy))))&
(((~funny(paul)<~>~kind(paul)))=>((rich(paul)|~creative(paul))))&
(![X]:((tall(X)|~happy(X))<=>(curious(X)<~>wise(X))))&
(![X]:((~creative(X)&wise(X))<=>strong(X)))&
(![X]:((~funny(X)|~happy(X))<=>(~rich(X)&~strong(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(old(X)|calm(X))))&
(![X]:(happy(X)=>(funny(X)&~old(X))))&
(![X]:(humble(X)=>(strong(X)<~>~patient(X))))&
(![X]:((~happy(X)<~>brave(X))<=>(~old(X)|funny(X))))&
(![X]:((brave(X)<~>~old(X))<=>(wise(X)|kind(X))))&
(![X]:((funny(X)<~>creative(X))<=>(rich(X)&humble(X))))&
(((~generous(mary)|~rich(mary)))=>(?[X]:(wise(X))))&
(?[X]:((~old(X)|~generous(X))))&
((~generous(alice)|~kind(alice)))&
(?[X]:(~humble(X))) | ~funny(susan) | [
"p0",
"p8",
"p10",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3441410066807061984971201
% SZS output start Proof for 3441410066807061984971201
1. ! [X0] : ((~wise(X0) & ~kind(X0)) <=> (~creative(X0) <~> funny(X0))) [input p0]
9. ! [X0] : ((~happy(X0) | ~funny(X0)) <=> (~strong(X0) & ~rich(X0))) [input p8]
11. ! [X0] : (happy(X0) => (~old(X0) & funny(X0))) [input p10]
13. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> (funny(X0) | ~old(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> ~old(X0)) <=> (kind(X0) | wise(X0))) [input p13]
15. ! [X0] : ((funny(X0) <~> creative(X0)) <=> (humble(X0) & rich(X0))) [input p14]
20. ~funny(susan) [input hypothesis]
26. ! [X0] : ((~old(X0) & funny(X0)) | ~happy(X0)) [ennf transformation 11]
29. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | (wise(X0) | kind(X0)))) [nnf transformation 1]
30. ! [X0] : (((~wise(X0) & ~kind(X0)) | ((~creative(X0) | ~funny(X0)) & (funny(X0) | creative(X0)))) & (((~funny(X0) | creative(X0)) & (funny(X0) | ~creative(X0))) | wise(X0) | kind(X0))) [flattening 29]
42. ! [X0] : (((~happy(X0) | ~funny(X0)) | (strong(X0) | rich(X0))) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [nnf transformation 9]
43. ! [X0] : ((~happy(X0) | ~funny(X0) | strong(X0) | rich(X0)) & ((~strong(X0) & ~rich(X0)) | (happy(X0) & funny(X0)))) [flattening 42]
47. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 13]
48. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [flattening 47]
49. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [nnf transformation 14]
50. ! [X0] : ((((old(X0) | ~brave(X0)) & (~old(X0) | brave(X0))) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0))))) [flattening 49]
51. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | (~humble(X0) | ~rich(X0))) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [nnf transformation 15]
52. ! [X0] : ((((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ~humble(X0) | ~rich(X0)) & ((humble(X0) & rich(X0)) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0))))) [flattening 51]
61. ~kind(X0) | funny(X0) | creative(X0) [cnf transformation 30]
63. ~wise(X0) | funny(X0) | creative(X0) [cnf transformation 30]
86. ~rich(X0) | funny(X0) [cnf transformation 43]
95. ~happy(X0) | funny(X0) [cnf transformation 26]
99. funny(X0) | ~old(X0) | brave(X0) | happy(X0) [cnf transformation 48]
102. brave(X0) | ~happy(X0) | ~funny(X0) [cnf transformation 48]
103. ~brave(X0) | happy(X0) | old(X0) [cnf transformation 48]
105. ~brave(X0) | wise(X0) | ~old(X0) | kind(X0) [cnf transformation 50]
106. brave(X0) | wise(X0) | kind(X0) | old(X0) [cnf transformation 50]
112. rich(X0) | funny(X0) | ~creative(X0) [cnf transformation 52]
122. ~funny(susan) [cnf transformation 20]
189. ~happy(X0) | brave(X0) [subsumption resolution 102,95]
190. ~old(X0) | funny(X0) | brave(X0) [subsumption resolution 99,189]
192. ~creative(X0) | funny(X0) [subsumption resolution 112,86]
404. wise(X4) | kind(X4) | old(X4) | happy(X4) | old(X4) [resolution 106,103]
405. old(X4) | kind(X4) | wise(X4) | happy(X4) [duplicate literal removal 404]
426. kind(X0) | wise(X0) | happy(X0) | funny(X0) | brave(X0) [resolution 405,190]
444. brave(X0) | wise(X0) | funny(X0) | kind(X0) [subsumption resolution 426,189]
648. wise(X0) | funny(X0) | kind(X0) | wise(X0) | ~old(X0) | kind(X0) [resolution 444,105]
653. ~old(X0) | funny(X0) | kind(X0) | wise(X0) [duplicate literal removal 648]
724. funny(X0) | kind(X0) | wise(X0) | kind(X0) | wise(X0) | happy(X0) [resolution 653,405]
725. funny(X0) | kind(X0) | wise(X0) | happy(X0) [duplicate literal removal 724]
726. funny(X0) | kind(X0) | wise(X0) [subsumption resolution 725,95]
749. kind(susan) | wise(susan) [resolution 726,122]
759. 54 <=> wise(susan) [avatar definition]
761. wise(susan) <- (54) [avatar component clause 759]
763. 55 <=> kind(susan) [avatar definition]
765. kind(susan) <- (55) [avatar component clause 763]
766. 54 | 55 [avatar split clause 749,763,759]
767. funny(susan) | creative(susan) <- (55) [resolution 765,61]
768. creative(susan) <- (55) [subsumption resolution 767,122]
775. funny(susan) <- (55) [resolution 768,192]
777. $false <- (55) [subsumption resolution 775,122]
778. ~55 [avatar contradiction clause 777]
780. funny(susan) | creative(susan) <- (54) [resolution 761,63]
782. 56 <=> creative(susan) [avatar definition]
784. creative(susan) <- (56) [avatar component clause 782]
790. creative(susan) <- (54) [subsumption resolution 780,122]
791. 56 | ~54 [avatar split clause 790,759,782]
794. funny(susan) <- (56) [resolution 784,192]
796. $false <- (56) [subsumption resolution 794,122]
797. ~56 [avatar contradiction clause 796]
798. $false [avatar sat refutation 766,778,791,797]
% SZS output end Proof for 3441410066807061984971201
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is curious or not curious then someone is not brave. If someone is both not rich and old then someone is not funny and vice versa. If someone is not strong or tall then fred is both not creative and not humble. If mary is not humble then someone is old or not brave and vice versa. If someone is either not rich or strong then fred is both not generous and curious. Everyone who is both not patient and tall is both not happy and curious and vice versa. Everyone who is either funny or not tall is both patient and generous and vice versa. Everyone who is either curious or not funny is both not patient and not happy. Everyone who is happy is either old or brave. If someone is both not kind and strong then john is both not generous and not creative and vice versa. Everyone who is creative is humble. If lucy is both tall and strong then someone is either not brave or not happy and vice versa. Everyone who is not old or not wise is both tall and brave and vice versa. Everyone who is not generous or not creative is both not wise and funny. Everyone who is both not generous and not curious is not calm and vice versa. If someone is either tall or curious then mary is tall. Someone is both not kind and not happy. Someone is both strong and wise. Someone is either not curious or not generous. Someone is either funny or not brave. Alice is not strong. Someone is creative or calm. Someone is not humble or not rich. | Susan is brave. | neutral | (((curious(susan)|~curious(susan)))=>(?[X]:(~brave(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:(~funny(X))))&
((?[X]:((~strong(X)|tall(X))))=>((~creative(fred)&~humble(fred))))&
((~humble(mary))<=>(?[X]:((old(X)|~brave(X)))))&
((?[X]:((~rich(X)<~>strong(X))))=>((~generous(fred)&curious(fred))))&
(![X]:((~patient(X)&tall(X))<=>(~happy(X)&curious(X))))&
(![X]:((funny(X)<~>~tall(X))<=>(patient(X)&generous(X))))&
(![X]:((curious(X)<~>~funny(X))=>(~patient(X)&~happy(X))))&
(![X]:(happy(X)=>(old(X)<~>brave(X))))&
((?[X]:((~kind(X)&strong(X))))<=>((~generous(john)&~creative(john))))&
(![X]:(creative(X)=>humble(X)))&
(((tall(lucy)&strong(lucy)))<=>(?[X]:((~brave(X)<~>~happy(X)))))&
(![X]:((~old(X)|~wise(X))<=>(tall(X)&brave(X))))&
(![X]:((~generous(X)|~creative(X))=>(~wise(X)&funny(X))))&
(![X]:((~generous(X)&~curious(X))<=>~calm(X)))&
((?[X]:((tall(X)<~>curious(X))))=>(tall(mary)))&
(?[X]:((~kind(X)&~happy(X))))&
(?[X]:((strong(X)&wise(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((funny(X)<~>~brave(X))))&
(~strong(alice))&
(?[X]:((creative(X)|calm(X))))&
(?[X]:((~humble(X)|~rich(X)))) | brave(susan) | [] | null | 0 |
If someone is humble or not generous then someone is rich or not wise.
If someone is both not creative and not curious then mary is brave.
If someone is both brave and wise then someone is either not rich or kind and vice versa.
Everyone who is either not old or not rich is not tall or calm and vice versa.
If someone is either not brave or not kind then someone is both not kind and kind and vice versa.
Everyone who is both generous and not old is both quiet and not tall and vice versa.
Everyone who is funny is not curious or not patient and vice versa.
Everyone who is not wise is either wise or not kind.
Everyone who is not quiet is either quiet or not humble.
Everyone who is either quiet or not humble is not patient.
Everyone who is either not calm or not funny is brave and vice versa.
If fred is both not brave and old then someone is not brave and vice versa.
Everyone who is not patient is old and vice versa.
Everyone who is both not strong and strong is not funny.
If alice is both strong and not funny then someone is either not patient or not kind and vice versa.
Everyone who is wise is not rich or not quiet and vice versa.
Paul is both brave and quiet.
Someone is both not strong and wise.
Someone is not rich or old.
Fred is both wise and quiet.
Someone is both not humble and not quiet.
Someone is both creative and old.
Alice is not humble or not old.
Someone is curious. | Fred is not patient. | entailment | ((?[X]:((humble(X)|~generous(X))))=>(?[X]:((rich(X)|~wise(X)))))&
((?[X]:((~creative(X)&~curious(X))))=>(brave(mary)))&
((?[X]:((brave(X)&wise(X))))<=>(?[X]:((~rich(X)<~>kind(X)))))&
(![X]:((~old(X)<~>~rich(X))<=>(~tall(X)|calm(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>(?[X]:((~kind(X)&kind(X)))))&
(![X]:((generous(X)&~old(X))<=>(quiet(X)&~tall(X))))&
(![X]:(funny(X)<=>(~curious(X)|~patient(X))))&
(![X]:(~wise(X)=>(wise(X)<~>~kind(X))))&
(![X]:(~quiet(X)=>(quiet(X)<~>~humble(X))))&
(![X]:((quiet(X)<~>~humble(X))=>~patient(X)))&
(![X]:((~calm(X)<~>~funny(X))<=>brave(X)))&
(((~brave(fred)&old(fred)))<=>(?[X]:(~brave(X))))&
(![X]:(~patient(X)<=>old(X)))&
(![X]:((~strong(X)&strong(X))=>~funny(X)))&
(((strong(alice)&~funny(alice)))<=>(?[X]:((~patient(X)<~>~kind(X)))))&
(![X]:(wise(X)<=>(~rich(X)|~quiet(X))))&
((brave(paul)&quiet(paul)))&
(?[X]:((~strong(X)&wise(X))))&
(?[X]:((~rich(X)|old(X))))&
((wise(fred)&quiet(fred)))&
(?[X]:((~humble(X)&~quiet(X))))&
(?[X]:((creative(X)&old(X))))&
((~humble(alice)|~old(alice)))&
(?[X]:(curious(X))) | ~patient(fred) | [
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7754365811643136588194688
% SZS output start Proof for 7754365811643136588194688
4. ! [X0] : ((~old(X0) <~> ~rich(X0)) <=> (calm(X0) | ~tall(X0))) [input p3]
5. ? [X0] : (~brave(X0) <~> ~kind(X0)) <=> ? [X0] : (kind(X0) & ~kind(X0)) [input p4]
7. ! [X0] : (funny(X0) <=> (~patient(X0) | ~curious(X0))) [input p6]
8. ! [X0] : (~wise(X0) => (wise(X0) <~> ~kind(X0))) [input p7]
9. ! [X0] : (~quiet(X0) => (quiet(X0) <~> ~humble(X0))) [input p8]
10. ! [X0] : ((quiet(X0) <~> ~humble(X0)) => ~patient(X0)) [input p9]
11. ! [X0] : ((~calm(X0) <~> ~funny(X0)) <=> brave(X0)) [input p10]
12. (old(fred) & ~brave(fred)) <=> ? [X0] : ~brave(X0) [input p11]
13. ! [X0] : (~patient(X0) <=> old(X0)) [input p12]
15. (~funny(alice) & strong(alice)) <=> ? [X0] : (~patient(X0) <~> ~kind(X0)) [input p14]
16. ! [X0] : (wise(X0) <=> (~quiet(X0) | ~rich(X0))) [input p15]
21. ? [X0] : (~quiet(X0) & ~humble(X0)) [input p20]
25. patient(fred) [input hypothesis]
28. ? [X0] : (~brave(X0) <~> ~kind(X0)) <=> ? [X1] : (kind(X1) & ~kind(X1)) [rectify 5]
32. ! [X0] : ((wise(X0) <~> ~kind(X0)) | wise(X0)) [ennf transformation 8]
33. ! [X0] : ((quiet(X0) <~> ~humble(X0)) | quiet(X0)) [ennf transformation 9]
34. ! [X0] : (~patient(X0) | (quiet(X0) <=> ~humble(X0))) [ennf transformation 10]
45. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~calm(X0) & tall(X0))) & ((calm(X0) | ~tall(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [nnf transformation 4]
46. ! [X0] : ((((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~calm(X0) & tall(X0))) & (calm(X0) | ~tall(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0))))) [flattening 45]
47. (? [X0] : ((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | ! [X1] : (~kind(X1) | kind(X1))) & (? [X1] : (kind(X1) & ~kind(X1)) | ! [X0] : ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) [nnf transformation 28]
48. (? [X0] : ((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) | ! [X1] : (~kind(X1) | kind(X1))) & (? [X2] : (kind(X2) & ~kind(X2)) | ! [X3] : ((~brave(X3) | kind(X3)) & (~kind(X3) | brave(X3)))) [rectify 47]
49. ? [X0] : ((kind(X0) | brave(X0)) & (~kind(X0) | ~brave(X0))) => ((kind(sK3) | brave(sK3)) & (~kind(sK3) | ~brave(sK3))) [choice axiom]
50. ? [X2] : (kind(X2) & ~kind(X2)) => (kind(sK4) & ~kind(sK4)) [choice axiom]
51. (((kind(sK3) | brave(sK3)) & (~kind(sK3) | ~brave(sK3))) | ! [X1] : (~kind(X1) | kind(X1))) & ((kind(sK4) & ~kind(sK4)) | ! [X3] : ((~brave(X3) | kind(X3)) & (~kind(X3) | brave(X3)))) [skolemisation 48,50,49]
54. ! [X0] : ((funny(X0) | (patient(X0) & curious(X0))) & ((~patient(X0) | ~curious(X0)) | ~funny(X0))) [nnf transformation 7]
55. ! [X0] : ((funny(X0) | (patient(X0) & curious(X0))) & (~patient(X0) | ~curious(X0) | ~funny(X0))) [flattening 54]
56. ! [X0] : (((kind(X0) | ~wise(X0)) & (~kind(X0) | wise(X0))) | wise(X0)) [nnf transformation 32]
57. ! [X0] : (((humble(X0) | ~quiet(X0)) & (~humble(X0) | quiet(X0))) | quiet(X0)) [nnf transformation 33]
58. ! [X0] : (~patient(X0) | ((quiet(X0) | humble(X0)) & (~humble(X0) | ~quiet(X0)))) [nnf transformation 34]
59. ! [X0] : ((((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | ~brave(X0)) & (brave(X0) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0))))) [nnf transformation 11]
60. ((old(fred) & ~brave(fred)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (~old(fred) | brave(fred))) [nnf transformation 12]
61. ((old(fred) & ~brave(fred)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | ~old(fred) | brave(fred)) [flattening 60]
62. ((old(fred) & ~brave(fred)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | ~old(fred) | brave(fred)) [rectify 61]
63. ? [X1] : ~brave(X1) => ~brave(sK5) [choice axiom]
64. ((old(fred) & ~brave(fred)) | ! [X0] : brave(X0)) & (~brave(sK5) | ~old(fred) | brave(fred)) [skolemisation 62,63]
65. ! [X0] : ((~patient(X0) | ~old(X0)) & (old(X0) | patient(X0))) [nnf transformation 13]
66. ((~funny(alice) & strong(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (? [X0] : ((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (funny(alice) | ~strong(alice))) [nnf transformation 15]
67. ((~funny(alice) & strong(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (? [X0] : ((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | funny(alice) | ~strong(alice)) [flattening 66]
68. ((~funny(alice) & strong(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (? [X1] : ((kind(X1) | patient(X1)) & (~kind(X1) | ~patient(X1))) | funny(alice) | ~strong(alice)) [rectify 67]
69. ? [X1] : ((kind(X1) | patient(X1)) & (~kind(X1) | ~patient(X1))) => ((kind(sK6) | patient(sK6)) & (~kind(sK6) | ~patient(sK6))) [choice axiom]
70. ((~funny(alice) & strong(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (((kind(sK6) | patient(sK6)) & (~kind(sK6) | ~patient(sK6))) | funny(alice) | ~strong(alice)) [skolemisation 68,69]
71. ! [X0] : ((wise(X0) | (quiet(X0) & rich(X0))) & ((~quiet(X0) | ~rich(X0)) | ~wise(X0))) [nnf transformation 16]
72. ! [X0] : ((wise(X0) | (quiet(X0) & rich(X0))) & (~quiet(X0) | ~rich(X0) | ~wise(X0))) [flattening 71]
77. ? [X0] : (~quiet(X0) & ~humble(X0)) => (~quiet(sK9) & ~humble(sK9)) [choice axiom]
78. ~quiet(sK9) & ~humble(sK9) [skolemisation 21,77]
96. ~calm(X0) | old(X0) | rich(X0) [cnf transformation 46]
98. ~kind(sK4) | ~brave(X3) | kind(X3) [cnf transformation 51]
100. kind(sK4) | ~brave(X3) | kind(X3) [cnf transformation 51]
109. patient(X0) | funny(X0) [cnf transformation 55]
110. ~kind(X0) | wise(X0) | wise(X0) [cnf transformation 56]
112. ~humble(X0) | quiet(X0) | quiet(X0) [cnf transformation 57]
115. ~patient(X0) | quiet(X0) | humble(X0) [cnf transformation 58]
119. ~brave(X0) | calm(X0) | funny(X0) [cnf transformation 59]
122. old(fred) | brave(X0) [cnf transformation 64]
124. ~patient(X0) | ~old(X0) [cnf transformation 65]
130. ~funny(alice) | ~kind(X0) | patient(X0) [cnf transformation 70]
132. ~quiet(X0) | ~rich(X0) | ~wise(X0) [cnf transformation 72]
143. ~quiet(sK9) [cnf transformation 78]
147. patient(fred) [cnf transformation 25]
148. ~humble(X0) | quiet(X0) [duplicate literal removal 112]
149. ~kind(X0) | wise(X0) [duplicate literal removal 110]
198. 12 <=> ! [X3] : (~brave(X3) | kind(X3)) [avatar definition]
199. ~brave(X3) | kind(X3) <- (12) [avatar component clause 198]
201. 13 <=> kind(sK4) [avatar definition]
204. 12 | 13 [avatar split clause 100,201,198]
209. 12 | ~13 [avatar split clause 98,201,198]
211. ~patient(X0) | quiet(X0) [subsumption resolution 115,148]
214. 15 <=> ! [X0] : brave(X0) [avatar definition]
215. brave(X0) <- (15) [avatar component clause 214]
217. 16 <=> old(fred) [avatar definition]
220. 15 | 16 [avatar split clause 122,217,214]
235. 20 <=> funny(alice) [avatar definition]
237. ~funny(alice) <- (~20) [avatar component clause 235]
240. 21 <=> ! [X0] : (~kind(X0) | patient(X0)) [avatar definition]
241. ~kind(X0) | patient(X0) <- (21) [avatar component clause 240]
242. 21 | ~20 [avatar split clause 130,235,240]
273. 28 <=> old(alice) [avatar definition]
274. old(alice) <- (28) [avatar component clause 273]
277. kind(X3) <- (12, 15) [subsumption resolution 199,215]
290. ~old(fred) [resolution 124,147]
292. ~old(X1) | funny(X1) [resolution 124,109]
299. funny(X1) | quiet(X1) [resolution 211,109]
308. patient(X0) <- (12, 15, 21) [resolution 241,277]
321. quiet(X2) <- (12, 15, 21) [resolution 308,211]
324. $false <- (12, 15, 21) [resolution 321,143]
325. ~12 | ~15 | ~21 [avatar contradiction clause 324]
326. ~16 [avatar split clause 290,217]
339. kind(X0) <- (12, 15) [resolution 199,215]
346. wise(X1) <- (12, 15) [resolution 339,149]
417. funny(X0) | calm(X0) <- (15) [resolution 119,215]
440. quiet(alice) <- (~20) [resolution 299,237]
455. ~rich(alice) | ~wise(alice) <- (~20) [resolution 440,132]
458. ~rich(alice) <- (12, 15, ~20) [subsumption resolution 455,346]
472. calm(alice) <- (15, ~20) [resolution 417,237]
478. old(alice) | rich(alice) <- (15, ~20) [resolution 472,96]
480. old(alice) <- (12, 15, ~20) [subsumption resolution 478,458]
481. 28 | ~12 | ~15 | 20 [avatar split clause 480,235,214,198,273]
482. funny(alice) <- (28) [resolution 274,292]
484. $false <- (~20, 28) [subsumption resolution 482,237]
485. 20 | ~28 [avatar contradiction clause 484]
486. $false [avatar sat refutation 204,209,220,242,325,326,481,485]
% SZS output end Proof for 7754365811643136588194688
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and creative is either not patient or not generous and vice versa.
If mary is either patient or kind then paul is both not wise and creative.
If john is kind then someone is not generous.
If susan is funny then someone is tall or not patient.
Everyone who is not generous is not kind.
If someone is not humble then paul is both not rich and quiet and vice versa.
If alice is both humble and funny then mary is generous or creative.
Everyone who is either generous or not generous is either creative or not rich.
If paul is both rich and generous then someone is either not humble or not tall and vice versa.
Everyone who is not kind is either not tall or not happy.
If lucy is either funny or not brave then susan is either wise or not curious and vice versa.
Everyone who is either wise or not wise is not strong or not tall.
Everyone who is tall is not humble and vice versa.
If lucy is not funny then someone is calm and vice versa.
If susan is either creative or calm then fred is both curious and not calm.
Everyone who is both wise and patient is both tall and rich and vice versa.
Lucy is both humble and not happy.
Paul is not wise or not brave.
Fred is curious or not funny.
Mary is either brave or not generous.
Someone is not patient.
Paul is old. | Mary is tall. | contradiction | (![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>~generous(X))))&
(((patient(mary)<~>kind(mary)))=>((~wise(paul)&creative(paul))))&
((kind(john))=>(?[X]:(~generous(X))))&
((funny(susan))=>(?[X]:((tall(X)|~patient(X)))))&
(![X]:(~generous(X)=>~kind(X)))&
((?[X]:(~humble(X)))<=>((~rich(paul)&quiet(paul))))&
(((humble(alice)&funny(alice)))=>((generous(mary)|creative(mary))))&
(![X]:((generous(X)<~>~generous(X))=>(creative(X)<~>~rich(X))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~tall(X)<~>~happy(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((wise(susan)<~>~curious(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)|~tall(X))))&
(![X]:(tall(X)<=>~humble(X)))&
((~funny(lucy))<=>(?[X]:(calm(X))))&
(((creative(susan)<~>calm(susan)))=>((curious(fred)&~calm(fred))))&
(![X]:((wise(X)&patient(X))<=>(tall(X)&rich(X))))&
((humble(lucy)&~happy(lucy)))&
((~wise(paul)|~brave(paul)))&
((curious(fred)|~funny(fred)))&
((brave(mary)<~>~generous(mary)))&
(?[X]:(~patient(X)))&
(old(paul)) | tall(mary) | [
"p5",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2060166959633461589622327
% SZS output start Proof for 2060166959633461589622327
6. ? [X0] : ~humble(X0) <=> (quiet(paul) & ~rich(paul)) [input p5]
9. (generous(paul) & rich(paul)) <=> ? [X0] : (~humble(X0) <~> ~tall(X0)) [input p8]
13. ! [X0] : (tall(X0) <=> ~humble(X0)) [input p12]
23. tall(mary) [input hypothesis]
42. (? [X0] : ~humble(X0) | (~quiet(paul) | rich(paul))) & ((quiet(paul) & ~rich(paul)) | ! [X0] : humble(X0)) [nnf transformation 6]
43. (? [X0] : ~humble(X0) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X0] : humble(X0)) [flattening 42]
44. (? [X0] : ~humble(X0) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X1] : humble(X1)) [rectify 43]
45. ? [X0] : ~humble(X0) => ~humble(sK2) [choice axiom]
46. (~humble(sK2) | ~quiet(paul) | rich(paul)) & ((quiet(paul) & ~rich(paul)) | ! [X1] : humble(X1)) [skolemisation 44,45]
48. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | (~generous(paul) | ~rich(paul))) [nnf transformation 9]
49. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | ~generous(paul) | ~rich(paul)) [flattening 48]
50. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) | ~generous(paul) | ~rich(paul)) [rectify 49]
51. ? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) => ((tall(sK3) | humble(sK3)) & (~tall(sK3) | ~humble(sK3))) [choice axiom]
52. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (((tall(sK3) | humble(sK3)) & (~tall(sK3) | ~humble(sK3))) | ~generous(paul) | ~rich(paul)) [skolemisation 50,51]
55. ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 13]
79. ~rich(paul) | humble(X1) [cnf transformation 46]
89. rich(paul) | ~tall(X0) | humble(X0) [cnf transformation 52]
103. ~humble(X0) | ~tall(X0) [cnf transformation 55]
104. humble(X0) | tall(X0) [cnf transformation 55]
122. tall(mary) [cnf transformation 23]
173. 10 <=> rich(paul) [avatar definition]
186. 13 <=> ! [X1] : humble(X1) [avatar definition]
187. humble(X1) <- (13) [avatar component clause 186]
189. 13 | ~10 [avatar split clause 79,173,186]
218. 20 <=> ! [X0] : (~tall(X0) | humble(X0)) [avatar definition]
219. ~tall(X0) | humble(X0) <- (20) [avatar component clause 218]
222. 20 | 10 [avatar split clause 89,173,218]
302. humble(X0) <- (20) [subsumption resolution 219,104]
303. 13 | ~20 [avatar split clause 302,218,186]
306. ~tall(X0) <- (13) [resolution 103,187]
312. $false <- (13) [resolution 306,122]
313. ~13 [avatar contradiction clause 312]
314. $false [avatar sat refutation 189,222,303,313]
% SZS output end Proof for 2060166959633461589622327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm and not old then someone is not old.
If paul is generous then someone is strong and vice versa.
Everyone who is happy is both not generous and kind.
Everyone who is not generous or brave is either not creative or not strong.
If someone is old then someone is not generous and vice versa.
Everyone who is not wise is either not generous or rich.
Everyone who is rich or humble is kind or old.
Everyone who is not funny is either funny or tall and vice versa.
If susan is wise then someone is not humble.
If someone is patient then alice is both humble and not funny and vice versa.
Everyone who is curious is either not happy or happy and vice versa.
If paul is not brave then lucy is both brave and not generous.
Everyone who is both not humble and patient is both funny and brave and vice versa.
Everyone who is both not happy and old is old or not funny and vice versa.
If fred is humble or creative then someone is either not patient or not calm and vice versa.
If someone is not brave then lucy is old.
Alice is rich or patient.
Alice is both not funny and generous.
Lucy is either patient or not tall.
Susan is old or not generous.
Someone is not strong or not calm.
Someone is old or not strong.
Lucy is generous or humble.
Someone is either kind or not humble. | Lucy is generous. | neutral | ((?[X]:((~calm(X)&~old(X))))=>(?[X]:(~old(X))))&
((generous(paul))<=>(?[X]:(strong(X))))&
(![X]:(happy(X)=>(~generous(X)&kind(X))))&
(![X]:((~generous(X)|brave(X))=>(~creative(X)<~>~strong(X))))&
((?[X]:(old(X)))<=>(?[X]:(~generous(X))))&
(![X]:(~wise(X)=>(~generous(X)<~>rich(X))))&
(![X]:((rich(X)|humble(X))=>(kind(X)|old(X))))&
(![X]:(~funny(X)<=>(funny(X)<~>tall(X))))&
((wise(susan))=>(?[X]:(~humble(X))))&
((?[X]:(patient(X)))<=>((humble(alice)&~funny(alice))))&
(![X]:(curious(X)<=>(~happy(X)<~>happy(X))))&
((~brave(paul))=>((brave(lucy)&~generous(lucy))))&
(![X]:((~humble(X)&patient(X))<=>(funny(X)&brave(X))))&
(![X]:((~happy(X)&old(X))<=>(old(X)|~funny(X))))&
(((humble(fred)|creative(fred)))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
((?[X]:(~brave(X)))=>(old(lucy)))&
((rich(alice)|patient(alice)))&
((~funny(alice)&generous(alice)))&
((patient(lucy)<~>~tall(lucy)))&
((old(susan)|~generous(susan)))&
(?[X]:((~strong(X)|~calm(X))))&
(?[X]:((old(X)|~strong(X))))&
((generous(lucy)|humble(lucy)))&
(?[X]:((kind(X)<~>~humble(X)))) | generous(lucy) | [] | null | 0 |
If mary is both rich and happy then someone is either not kind or not rich. If someone is not happy or not brave then susan is both calm and not rich. If someone is either not funny or funny then paul is either not calm or not tall and vice versa. If someone is both generous and not generous then someone is kind and vice versa. Everyone who is not funny is not calm or not generous and vice versa. If alice is both patient and not generous then someone is wise. If susan is tall then someone is not brave or not happy and vice versa. If someone is either not calm or not brave then someone is both generous and not curious. Everyone who is both rich and funny is not happy and vice versa. Everyone who is both kind and creative is quiet and vice versa. Everyone who is happy or old is both not funny and humble. If lucy is either not generous or generous then someone is not funny or generous and vice versa. Everyone who is tall or creative is either kind or not humble and vice versa. Everyone who is not quiet is either not strong or funny and vice versa. If someone is not brave or humble then someone is either not brave or not generous. Everyone who is not strong or wise is either old or not rich. Someone is both not strong and curious. Someone is not strong. Susan is either calm or kind. Someone is either patient or brave. | Susan is not patient. | neutral | (((rich(mary)&happy(mary)))=>(?[X]:((~kind(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|~brave(X))))=>((calm(susan)&~rich(susan))))&
((?[X]:((~funny(X)<~>funny(X))))<=>((~calm(paul)<~>~tall(paul))))&
((?[X]:((generous(X)&~generous(X))))<=>(?[X]:(kind(X))))&
(![X]:(~funny(X)<=>(~calm(X)|~generous(X))))&
(((patient(alice)&~generous(alice)))=>(?[X]:(wise(X))))&
((tall(susan))<=>(?[X]:((~brave(X)|~happy(X)))))&
((?[X]:((~calm(X)<~>~brave(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((rich(X)&funny(X))<=>~happy(X)))&
(![X]:((kind(X)&creative(X))<=>quiet(X)))&
(![X]:((happy(X)|old(X))=>(~funny(X)&humble(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((tall(X)|creative(X))<=>(kind(X)<~>~humble(X))))&
(![X]:(~quiet(X)<=>(~strong(X)<~>funny(X))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:((~strong(X)|wise(X))=>(old(X)<~>~rich(X))))&
(?[X]:((~strong(X)&curious(X))))&
(?[X]:(~strong(X)))&
((calm(susan)<~>kind(susan)))&
(?[X]:((patient(X)<~>brave(X)))) | ~patient(susan) | [] | null | 0 |
Everyone who is either funny or happy is not funny or humble and vice versa. If someone is both not curious and humble then someone is either not old or patient and vice versa. Everyone who is creative or patient is not kind. If someone is not funny then someone is either kind or strong. Everyone who is either kind or calm is patient or curious and vice versa. If someone is either calm or not humble then someone is either rich or not humble. If fred is not brave or generous then john is either not strong or not old and vice versa. If someone is wise or not curious then susan is quiet. Everyone who is not quiet or quiet is both quiet and not happy and vice versa. If someone is creative then someone is not tall and vice versa. If someone is not generous or not strong then someone is either not calm or calm. If john is tall or not quiet then someone is either creative or not happy and vice versa. Everyone who is both tall and generous is rich and vice versa. Everyone who is wise or not old is generous. Everyone who is either not tall or calm is both happy and not wise and vice versa. Everyone who is not kind or not patient is both generous and rich. Someone is funny or not generous. Alice is both not happy and not old. Paul is either not happy or not strong. Someone is not happy or not wise. Someone is generous or brave. Alice is both wise and rich. Someone is both not old and not wise. | John is patient. | contradiction | (![X]:((funny(X)<~>happy(X))<=>(~funny(X)|humble(X))))&
((?[X]:((~curious(X)&humble(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(![X]:((creative(X)|patient(X))=>~kind(X)))&
((?[X]:(~funny(X)))=>(?[X]:((kind(X)<~>strong(X)))))&
(![X]:((kind(X)<~>calm(X))<=>(patient(X)|curious(X))))&
((?[X]:((calm(X)<~>~humble(X))))=>(?[X]:((rich(X)<~>~humble(X)))))&
(((~brave(fred)|generous(fred)))<=>((~strong(john)<~>~old(john))))&
((?[X]:((wise(X)|~curious(X))))=>(quiet(susan)))&
(![X]:((~quiet(X)|quiet(X))<=>(quiet(X)&~happy(X))))&
((?[X]:(creative(X)))<=>(?[X]:(~tall(X))))&
((?[X]:((~generous(X)|~strong(X))))=>(?[X]:((~calm(X)<~>calm(X)))))&
(((tall(john)|~quiet(john)))<=>(?[X]:((creative(X)<~>~happy(X)))))&
(![X]:((tall(X)&generous(X))<=>rich(X)))&
(![X]:((wise(X)|~old(X))=>generous(X)))&
(![X]:((~tall(X)<~>calm(X))<=>(happy(X)&~wise(X))))&
(![X]:((~kind(X)|~patient(X))=>(generous(X)&rich(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~happy(alice)&~old(alice)))&
((~happy(paul)<~>~strong(paul)))&
(?[X]:((~happy(X)|~wise(X))))&
(?[X]:((generous(X)|brave(X))))&
((wise(alice)&rich(alice)))&
(?[X]:((~old(X)&~wise(X)))) | patient(john) | [
"p2",
"p4",
"p8",
"p9",
"p11",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 141384766539966629523914
% SZS output start Proof for 141384766539966629523914
3. ! [X0] : ((patient(X0) | creative(X0)) => ~kind(X0)) [input p2]
5. ! [X0] : ((kind(X0) <~> calm(X0)) <=> (curious(X0) | patient(X0))) [input p4]
9. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~happy(X0) & quiet(X0))) [input p8]
10. ? [X0] : creative(X0) <=> ? [X0] : ~tall(X0) [input p9]
12. (~quiet(john) | tall(john)) <=> ? [X0] : (creative(X0) <~> ~happy(X0)) [input p11]
13. ! [X0] : ((generous(X0) & tall(X0)) <=> rich(X0)) [input p12]
15. ! [X0] : ((~tall(X0) <~> calm(X0)) <=> (~wise(X0) & happy(X0))) [input p14]
16. ! [X0] : ((~patient(X0) | ~kind(X0)) => (rich(X0) & generous(X0))) [input p15]
24. patient(john) [input hypothesis]
28. ? [X0] : creative(X0) <=> ? [X1] : ~tall(X1) [rectify 10]
30. ! [X0] : (~kind(X0) | (~patient(X0) & ~creative(X0))) [ennf transformation 3]
36. ! [X0] : ((rich(X0) & generous(X0)) | (patient(X0) & kind(X0))) [ennf transformation 16]
48. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [nnf transformation 5]
49. ! [X0] : ((((~calm(X0) | ~kind(X0)) & (calm(X0) | kind(X0))) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | ((kind(X0) | ~calm(X0)) & (calm(X0) | ~kind(X0))))) [flattening 48]
56. ! [X0] : (((quiet(X0) | ~quiet(X0)) | (happy(X0) | ~quiet(X0))) & ((~happy(X0) & quiet(X0)) | (~quiet(X0) & quiet(X0)))) [nnf transformation 9]
57. ! [X0] : ((quiet(X0) | ~quiet(X0) | happy(X0) | ~quiet(X0)) & ((~happy(X0) & quiet(X0)) | (~quiet(X0) & quiet(X0)))) [flattening 56]
58. (? [X0] : creative(X0) | ! [X1] : tall(X1)) & (? [X1] : ~tall(X1) | ! [X0] : ~creative(X0)) [nnf transformation 28]
59. (? [X0] : creative(X0) | ! [X1] : tall(X1)) & (? [X2] : ~tall(X2) | ! [X3] : ~creative(X3)) [rectify 58]
60. ? [X0] : creative(X0) => creative(sK4) [choice axiom]
61. ? [X2] : ~tall(X2) => ~tall(sK5) [choice axiom]
62. (creative(sK4) | ! [X1] : tall(X1)) & (~tall(sK5) | ! [X3] : ~creative(X3)) [skolemisation 59,61,60]
67. ((~quiet(john) | tall(john)) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (quiet(john) & ~tall(john))) [nnf transformation 12]
68. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X0] : ((happy(X0) | ~creative(X0)) & (~happy(X0) | creative(X0))) | (quiet(john) & ~tall(john))) [flattening 67]
69. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) | (quiet(john) & ~tall(john))) [rectify 68]
70. ? [X1] : ((happy(X1) | ~creative(X1)) & (~happy(X1) | creative(X1))) => ((happy(sK7) | ~creative(sK7)) & (~happy(sK7) | creative(sK7))) [choice axiom]
71. (~quiet(john) | tall(john) | ! [X0] : ((creative(X0) | happy(X0)) & (~happy(X0) | ~creative(X0)))) & (((happy(sK7) | ~creative(sK7)) & (~happy(sK7) | creative(sK7))) | (quiet(john) & ~tall(john))) [skolemisation 69,70]
72. ! [X0] : (((generous(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | (~generous(X0) | ~tall(X0)))) [nnf transformation 13]
73. ! [X0] : (((generous(X0) & tall(X0)) | ~rich(X0)) & (rich(X0) | ~generous(X0) | ~tall(X0))) [flattening 72]
74. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [nnf transformation 15]
75. ! [X0] : ((((~calm(X0) | tall(X0)) & (calm(X0) | ~tall(X0))) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))))) [flattening 74]
97. ~kind(X0) | ~creative(X0) [cnf transformation 30]
98. ~kind(X0) | ~patient(X0) [cnf transformation 30]
103. calm(X0) | kind(X0) | ~patient(X0) [cnf transformation 49]
119. quiet(X0) | quiet(X0) [cnf transformation 57]
121. ~happy(X0) | quiet(X0) [cnf transformation 57]
122. ~quiet(X0) | ~happy(X0) [cnf transformation 57]
124. ~tall(sK5) | ~creative(X3) [cnf transformation 62]
135. ~quiet(john) | tall(john) | creative(X0) | happy(X0) [cnf transformation 71]
137. ~rich(X0) | tall(X0) [cnf transformation 73]
142. happy(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 75]
149. rich(X0) | kind(X0) [cnf transformation 36]
162. patient(john) [cnf transformation 24]
163. quiet(X0) [duplicate literal removal 119]
212. ~patient(X0) | calm(X0) [subsumption resolution 103,98]
266. ~happy(X0) [subsumption resolution 121,122]
276. 24 <=> ! [X3] : ~creative(X3) [avatar definition]
277. ~creative(X3) <- (24) [avatar component clause 276]
279. 25 <=> tall(sK5) [avatar definition]
281. ~tall(sK5) <- (~25) [avatar component clause 279]
282. 24 | ~25 [avatar split clause 124,279,276]
283. tall(john) | creative(X0) | happy(X0) [subsumption resolution 135,163]
284. tall(john) | creative(X0) [subsumption resolution 283,266]
286. 26 <=> ! [X0] : creative(X0) [avatar definition]
287. creative(X0) <- (26) [avatar component clause 286]
289. 27 <=> tall(john) [avatar definition]
291. tall(john) <- (27) [avatar component clause 289]
292. 26 | 27 [avatar split clause 284,289,286]
299. ~tall(X0) | ~calm(X0) [subsumption resolution 142,266]
337. tall(X1) | kind(X1) [resolution 149,137]
348. calm(john) [resolution 212,162]
350. ~calm(john) <- (27) [resolution 299,291]
352. $false <- (27) [subsumption resolution 350,348]
353. ~27 [avatar contradiction clause 352]
366. kind(sK5) <- (~25) [resolution 337,281]
374. ~creative(sK5) <- (~25) [resolution 366,97]
375. $false <- (~25, 26) [subsumption resolution 374,287]
376. 25 | ~26 [avatar contradiction clause 375]
377. $false <- (24, 26) [subsumption resolution 277,287]
378. ~24 | ~26 [avatar contradiction clause 377]
379. $false [avatar sat refutation 282,292,353,376,378]
% SZS output end Proof for 141384766539966629523914
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet then alice is not patient and vice versa. If john is either not old or brave then someone is not happy and vice versa. If someone is not funny then lucy is both rich and not creative. If lucy is not creative or rich then alice is not tall and vice versa. If someone is both not kind and wise then susan is either creative or not kind. Everyone who is both kind and funny is generous and vice versa. If someone is either not tall or not wise then someone is old and vice versa. Everyone who is either calm or funny is either not old or not strong. If john is both kind and not humble then susan is both not quiet and not calm and vice versa. Everyone who is either curious or patient is either curious or not calm and vice versa. Everyone who is both humble and strong is patient or kind and vice versa. If someone is either not kind or patient then fred is patient. If fred is old then fred is either not funny or rich. Everyone who is both not old and quiet is both patient and not humble and vice versa. If alice is not strong then paul is quiet or old. Everyone who is either wise or not kind is curious. Paul is strong. Someone is not generous. Someone is either not patient or generous. Lucy is either rich or strong. Lucy is rich or not old. Susan is not curious. Paul is either not quiet or not tall. | Lucy is not calm. | neutral | ((~quiet(john))<=>(~patient(alice)))&
(((~old(john)<~>brave(john)))<=>(?[X]:(~happy(X))))&
((?[X]:(~funny(X)))=>((rich(lucy)&~creative(lucy))))&
(((~creative(lucy)|rich(lucy)))<=>(~tall(alice)))&
((?[X]:((~kind(X)&wise(X))))=>((creative(susan)<~>~kind(susan))))&
(![X]:((kind(X)&funny(X))<=>generous(X)))&
((?[X]:((~tall(X)<~>~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>funny(X))=>(~old(X)<~>~strong(X))))&
(((kind(john)&~humble(john)))<=>((~quiet(susan)&~calm(susan))))&
(![X]:((curious(X)<~>patient(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((humble(X)&strong(X))<=>(patient(X)|kind(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(patient(fred)))&
((old(fred))=>((~funny(fred)<~>rich(fred))))&
(![X]:((~old(X)&quiet(X))<=>(patient(X)&~humble(X))))&
((~strong(alice))=>((quiet(paul)|old(paul))))&
(![X]:((wise(X)<~>~kind(X))=>curious(X)))&
(strong(paul))&
(?[X]:(~generous(X)))&
(?[X]:((~patient(X)<~>generous(X))))&
((rich(lucy)<~>strong(lucy)))&
((rich(lucy)|~old(lucy)))&
(~curious(susan))&
((~quiet(paul)<~>~tall(paul))) | ~calm(lucy) | [] | null | 0 |
Everyone who is not curious is generous or not patient.
Everyone who is not kind is both not curious and not generous.
If someone is either not kind or not tall then someone is either curious or not wise and vice versa.
Everyone who is funny or not wise is tall.
If someone is both old and creative then someone is not strong or not patient and vice versa.
If mary is tall or humble then someone is both strong and not curious and vice versa.
Everyone who is not kind is happy and vice versa.
If someone is both not rich and patient then susan is not old.
If fred is both not happy and tall then someone is either not rich or not brave.
Everyone who is either not brave or not wise is curious or calm.
Everyone who is both not funny and not happy is not curious and vice versa.
Everyone who is either funny or not humble is not tall.
If someone is not old or quiet then someone is not kind and vice versa.
Everyone who is calm or wise is either wise or not wise.
Everyone who is kind is strong and vice versa.
Everyone who is both happy and old is both not kind and strong.
Mary is not happy.
Someone is not generous.
Susan is not rich or old.
Alice is not kind or kind.
Someone is either tall or not creative.
Fred is either tall or brave.
Mary is generous. | Susan is not quiet. | entailment | (![X]:(~curious(X)=>(generous(X)|~patient(X))))&
(![X]:(~kind(X)=>(~curious(X)&~generous(X))))&
((?[X]:((~kind(X)<~>~tall(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
(![X]:((funny(X)|~wise(X))=>tall(X)))&
((?[X]:((old(X)&creative(X))))<=>(?[X]:((~strong(X)|~patient(X)))))&
(((tall(mary)|humble(mary)))<=>(?[X]:((strong(X)&~curious(X)))))&
(![X]:(~kind(X)<=>happy(X)))&
((?[X]:((~rich(X)&patient(X))))=>(~old(susan)))&
(((~happy(fred)&tall(fred)))=>(?[X]:((~rich(X)<~>~brave(X)))))&
(![X]:((~brave(X)<~>~wise(X))=>(curious(X)|calm(X))))&
(![X]:((~funny(X)&~happy(X))<=>~curious(X)))&
(![X]:((funny(X)<~>~humble(X))=>~tall(X)))&
((?[X]:((~old(X)|quiet(X))))<=>(?[X]:(~kind(X))))&
(![X]:((calm(X)|wise(X))=>(wise(X)<~>~wise(X))))&
(![X]:(kind(X)<=>strong(X)))&
(![X]:((happy(X)&old(X))=>(~kind(X)&strong(X))))&
(~happy(mary))&
(?[X]:(~generous(X)))&
((~rich(susan)|old(susan)))&
((~kind(alice)|kind(alice)))&
(?[X]:((tall(X)<~>~creative(X))))&
((tall(fred)<~>brave(fred)))&
(generous(mary)) | ~quiet(susan) | [
"p1",
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1736494294000221635746221
% SZS output start Proof for 1736494294000221635746221
2. ! [X0] : (~kind(X0) => (~generous(X0) & ~curious(X0))) [input p1]
7. ! [X0] : (~kind(X0) <=> happy(X0)) [input p6]
11. ! [X0] : ((~happy(X0) & ~funny(X0)) <=> ~curious(X0)) [input p10]
13. ? [X0] : (quiet(X0) | ~old(X0)) <=> ? [X0] : ~kind(X0) [input p12]
24. quiet(susan) [input hypothesis]
27. ? [X0] : (quiet(X0) | ~old(X0)) <=> ? [X1] : ~kind(X1) [rectify 13]
30. ! [X0] : ((~generous(X0) & ~curious(X0)) | kind(X0)) [ennf transformation 2]
56. ! [X0] : ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))) [nnf transformation 7]
61. ! [X0] : (((~happy(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | (happy(X0) | funny(X0)))) [nnf transformation 11]
62. ! [X0] : (((~happy(X0) & ~funny(X0)) | curious(X0)) & (~curious(X0) | happy(X0) | funny(X0))) [flattening 61]
64. (? [X0] : (quiet(X0) | ~old(X0)) | ! [X1] : kind(X1)) & (? [X1] : ~kind(X1) | ! [X0] : (~quiet(X0) & old(X0))) [nnf transformation 27]
65. (? [X0] : (quiet(X0) | ~old(X0)) | ! [X1] : kind(X1)) & (? [X2] : ~kind(X2) | ! [X3] : (~quiet(X3) & old(X3))) [rectify 64]
66. ? [X0] : (quiet(X0) | ~old(X0)) => (quiet(sK6) | ~old(sK6)) [choice axiom]
67. ? [X2] : ~kind(X2) => ~kind(sK7) [choice axiom]
68. ((quiet(sK6) | ~old(sK6)) | ! [X1] : kind(X1)) & (~kind(sK7) | ! [X3] : (~quiet(X3) & old(X3))) [skolemisation 65,67,66]
78. ~curious(X0) | kind(X0) [cnf transformation 30]
100. happy(X0) | kind(X0) [cnf transformation 56]
109. ~happy(X0) | curious(X0) [cnf transformation 62]
113. ~kind(sK7) | ~quiet(X3) [cnf transformation 68]
132. quiet(susan) [cnf transformation 24]
253. 27 <=> ! [X1] : kind(X1) [avatar definition]
254. kind(X1) <- (27) [avatar component clause 253]
265. 30 <=> ! [X3] : ~quiet(X3) [avatar definition]
266. ~quiet(X3) <- (30) [avatar component clause 265]
268. 31 <=> kind(sK7) [avatar definition]
270. ~kind(sK7) <- (~31) [avatar component clause 268]
271. 30 | ~31 [avatar split clause 113,268,265]
305. curious(X0) | kind(X0) [resolution 109,100]
306. kind(X0) [subsumption resolution 305,78]
307. 27 [avatar split clause 306,253]
308. $false <- (27, ~31) [resolution 254,270]
311. ~27 | 31 [avatar contradiction clause 308]
313. $false <- (30) [resolution 266,132]
314. ~30 [avatar contradiction clause 313]
315. $false [avatar sat refutation 271,307,311,314]
% SZS output end Proof for 1736494294000221635746221
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then john is either brave or not humble and vice versa.
Everyone who is old is not old.
If someone is not creative then mary is either calm or not kind.
Everyone who is patient or not happy is both happy and not brave.
Everyone who is happy is both not funny and not old.
If someone is both not tall and patient then someone is both not curious and not old.
Everyone who is both humble and not humble is either patient or not old and vice versa.
If alice is not calm or curious then john is kind or not brave.
If fred is tall or wise then someone is both funny and wise.
If someone is either wise or generous then someone is both not creative and not old and vice versa.
If someone is either not humble or patient then lucy is not tall and vice versa.
Everyone who is not generous is either kind or creative.
If fred is either kind or not tall then someone is both old and not funny and vice versa.
If someone is both happy and calm then someone is both brave and old.
If someone is not creative or not kind then alice is patient and vice versa.
Paul is either tall or not strong.
Susan is brave or not tall.
John is either curious or generous.
Mary is both rich and not strong.
John is strong or humble. | Alice is patient. | entailment | ((?[X]:(~brave(X)))<=>((brave(john)<~>~humble(john))))&
(![X]:(old(X)=>~old(X)))&
((?[X]:(~creative(X)))=>((calm(mary)<~>~kind(mary))))&
(![X]:((patient(X)|~happy(X))=>(happy(X)&~brave(X))))&
(![X]:(happy(X)=>(~funny(X)&~old(X))))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~curious(X)&~old(X)))))&
(![X]:((humble(X)&~humble(X))<=>(patient(X)<~>~old(X))))&
(((~calm(alice)|curious(alice)))=>((kind(john)|~brave(john))))&
(((tall(fred)|wise(fred)))=>(?[X]:((funny(X)&wise(X)))))&
((?[X]:((wise(X)<~>generous(X))))<=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(~tall(lucy)))&
(![X]:(~generous(X)=>(kind(X)<~>creative(X))))&
(((kind(fred)<~>~tall(fred)))<=>(?[X]:((old(X)&~funny(X)))))&
((?[X]:((happy(X)&calm(X))))=>(?[X]:((brave(X)&old(X)))))&
((?[X]:((~creative(X)|~kind(X))))<=>(patient(alice)))&
((tall(paul)<~>~strong(paul)))&
((brave(susan)|~tall(susan)))&
((curious(john)<~>generous(john)))&
((rich(mary)&~strong(mary)))&
((strong(john)|humble(john))) | patient(alice) | [
"p1",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 8871874184972055358752239
% SZS output start Proof for 8871874184972055358752239
2. ! [X0] : (old(X0) => ~old(X0)) [input p1]
7. ! [X0] : ((~humble(X0) & humble(X0)) <=> (patient(X0) <~> ~old(X0))) [input p6]
21. ~patient(alice) [input hypothesis]
26. ! [X0] : (~old(X0) | ~old(X0)) [ennf transformation 2]
44. ! [X0] : (((~humble(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | (humble(X0) | ~humble(X0)))) [nnf transformation 7]
45. ! [X0] : (((~humble(X0) & humble(X0)) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) & (((old(X0) | ~patient(X0)) & (~old(X0) | patient(X0))) | humble(X0) | ~humble(X0))) [flattening 44]
75. ~old(X0) | ~old(X0) [cnf transformation 26]
89. humble(X0) | patient(X0) | old(X0) [cnf transformation 45]
91. ~humble(X0) | patient(X0) | old(X0) [cnf transformation 45]
128. ~patient(alice) [cnf transformation 21]
130. ~old(X0) [duplicate literal removal 75]
172. ~humble(X0) | patient(X0) [subsumption resolution 91,130]
173. humble(X0) | patient(X0) [subsumption resolution 89,130]
174. patient(X0) [subsumption resolution 173,172]
300. $false [subsumption resolution 128,174]
% SZS output end Proof for 8871874184972055358752239
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or strong then someone is either not calm or not wise and vice versa. If paul is either creative or not generous then someone is not strong. If someone is happy or not wise then someone is not strong and vice versa. Everyone who is strong or 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. Someone is both old and tall. Someone is quiet. Someone is old or not funny. Someone is not happy. Someone is either not happy or not creative. Someone is creative. Someone is both curious and not calm. | Mary is wise. | neutral | ((?[X]:((happy(X)|strong(X))))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
(((creative(paul)<~>~generous(paul)))=>(?[X]:(~strong(X))))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:(~strong(X))))&
(![X]:((strong(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]:((old(X)&tall(X))))&
(?[X]:(quiet(X)))&
(?[X]:((old(X)|~funny(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(?[X]:(creative(X)))&
(?[X]:((curious(X)&~calm(X)))) | wise(mary) | [] | null | 0 |
If someone is not rich then someone is either not quiet or quiet. If susan is not kind or not funny then someone is not rich or creative and vice versa. Everyone who is not strong is both humble and calm. Everyone who is wise or humble is both quiet and not funny and vice versa. Everyone who is not generous is not old. If paul is creative then lucy is both rich and not wise and vice versa. Everyone who is either tall or wise is either not strong or not calm. Everyone who is strong or creative is both not curious and generous. If someone is both wise and kind then alice is both humble and tall and vice versa. If someone is either not wise or not happy then paul is not humble or kind and vice versa. If someone is not happy or not rich then someone is both patient and generous and vice versa. Everyone who is patient is rich or not wise and vice versa. If fred is both funny and not patient then lucy is tall and vice versa. Everyone who is strong or not humble is not quiet or not generous and vice versa. Everyone who is not tall is both happy and not wise. Someone is either not strong or not quiet. Fred is both not calm and brave. Someone is both rich and not tall. Someone is either not humble or not generous. Someone is both wise and rich. | Alice is not creative. | neutral | ((?[X]:(~rich(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(((~kind(susan)|~funny(susan)))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:(~strong(X)=>(humble(X)&calm(X))))&
(![X]:((wise(X)|humble(X))<=>(quiet(X)&~funny(X))))&
(![X]:(~generous(X)=>~old(X)))&
((creative(paul))<=>((rich(lucy)&~wise(lucy))))&
(![X]:((tall(X)<~>wise(X))=>(~strong(X)<~>~calm(X))))&
(![X]:((strong(X)|creative(X))=>(~curious(X)&generous(X))))&
((?[X]:((wise(X)&kind(X))))<=>((humble(alice)&tall(alice))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>((~humble(paul)|kind(paul))))&
((?[X]:((~happy(X)|~rich(X))))<=>(?[X]:((patient(X)&generous(X)))))&
(![X]:(patient(X)<=>(rich(X)|~wise(X))))&
(((funny(fred)&~patient(fred)))<=>(tall(lucy)))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(![X]:(~tall(X)=>(happy(X)&~wise(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~calm(fred)&brave(fred)))&
(?[X]:((rich(X)&~tall(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((wise(X)&rich(X)))) | ~creative(alice) | [] | null | 0 |
If alice is rich then john is both curious and quiet and vice versa.
Everyone who is tall is strong or not kind and vice versa.
If someone is both not brave and kind then fred is either not rich or happy and vice versa.
Everyone who is both not old and kind is both tall and quiet and vice versa.
If someone is not strong then paul is both not creative and not happy and vice versa.
Everyone who is both strong and not rich is either not funny or happy and vice versa.
If someone is patient then someone is either old or not curious and vice versa.
If someone is both not old and funny then john is not humble or creative.
If john is both not creative and not humble then someone is not brave and vice versa.
If someone is patient or tall then alice is patient and vice versa.
If fred is both not kind and not happy then someone is either not happy or strong and vice versa.
If mary is both not calm and not creative then someone is both kind and not old and vice versa.
If susan is both brave and not quiet then paul is both generous and tall.
Everyone who is happy or funny is not rich.
Everyone who is either not tall or tall is either humble or rich and vice versa.
If john is not tall or not wise then someone is both calm and not generous and vice versa.
Someone is both creative and tall.
Someone is either not funny or not curious.
John is not kind or kind.
Someone is not brave or not wise.
Someone is either not old or not wise.
Susan is not curious. | Susan is not funny. | entailment | ((rich(alice))<=>((curious(john)&quiet(john))))&
(![X]:(tall(X)<=>(strong(X)|~kind(X))))&
((?[X]:((~brave(X)&kind(X))))<=>((~rich(fred)<~>happy(fred))))&
(![X]:((~old(X)&kind(X))<=>(tall(X)&quiet(X))))&
((?[X]:(~strong(X)))<=>((~creative(paul)&~happy(paul))))&
(![X]:((strong(X)&~rich(X))<=>(~funny(X)<~>happy(X))))&
((?[X]:(patient(X)))<=>(?[X]:((old(X)<~>~curious(X)))))&
((?[X]:((~old(X)&funny(X))))=>((~humble(john)|creative(john))))&
(((~creative(john)&~humble(john)))<=>(?[X]:(~brave(X))))&
((?[X]:((patient(X)|tall(X))))<=>(patient(alice)))&
(((~kind(fred)&~happy(fred)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(((~calm(mary)&~creative(mary)))<=>(?[X]:((kind(X)&~old(X)))))&
(((brave(susan)&~quiet(susan)))=>((generous(paul)&tall(paul))))&
(![X]:((happy(X)|funny(X))=>~rich(X)))&
(![X]:((~tall(X)<~>tall(X))<=>(humble(X)<~>rich(X))))&
(((~tall(john)|~wise(john)))<=>(?[X]:((calm(X)&~generous(X)))))&
(?[X]:((creative(X)&tall(X))))&
(?[X]:((~funny(X)<~>~curious(X))))&
((~kind(john)|kind(john)))&
(?[X]:((~brave(X)|~wise(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(~curious(susan)) | ~funny(susan) | [
"p2",
"p5",
"p8",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6966885115881838036179192
% SZS output start Proof for 6966885115881838036179192
3. ? [X0] : (kind(X0) & ~brave(X0)) <=> (~rich(fred) <~> happy(fred)) [input p2]
6. ! [X0] : ((~rich(X0) & strong(X0)) <=> (~funny(X0) <~> happy(X0))) [input p5]
9. (~humble(john) & ~creative(john)) <=> ? [X0] : ~brave(X0) [input p8]
11. (~happy(fred) & ~kind(fred)) <=> ? [X0] : (~happy(X0) <~> strong(X0)) [input p10]
14. ! [X0] : ((funny(X0) | happy(X0)) => ~rich(X0)) [input p13]
15. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> (humble(X0) <~> rich(X0))) [input p14]
23. funny(susan) [input hypothesis]
29. ! [X0] : (~rich(X0) | (~funny(X0) & ~happy(X0))) [ennf transformation 14]
34. (? [X0] : (kind(X0) & ~brave(X0)) | ((~rich(fred) | ~happy(fred)) & (happy(fred) | rich(fred)))) & (((~happy(fred) | rich(fred)) & (happy(fred) | ~rich(fred))) | ! [X0] : (~kind(X0) | brave(X0))) [nnf transformation 3]
35. (? [X0] : (kind(X0) & ~brave(X0)) | ((~rich(fred) | ~happy(fred)) & (happy(fred) | rich(fred)))) & (((~happy(fred) | rich(fred)) & (happy(fred) | ~rich(fred))) | ! [X1] : (~kind(X1) | brave(X1))) [rectify 34]
36. ? [X0] : (kind(X0) & ~brave(X0)) => (kind(sK0) & ~brave(sK0)) [choice axiom]
37. ((kind(sK0) & ~brave(sK0)) | ((~rich(fred) | ~happy(fred)) & (happy(fred) | rich(fred)))) & (((~happy(fred) | rich(fred)) & (happy(fred) | ~rich(fred))) | ! [X1] : (~kind(X1) | brave(X1))) [skolemisation 35,36]
45. ! [X0] : (((~rich(X0) & strong(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | (rich(X0) | ~strong(X0)))) [nnf transformation 6]
46. ! [X0] : (((~rich(X0) & strong(X0)) | ((~funny(X0) | ~happy(X0)) & (happy(X0) | funny(X0)))) & (((~happy(X0) | funny(X0)) & (happy(X0) | ~funny(X0))) | rich(X0) | ~strong(X0))) [flattening 45]
52. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | (humble(john) | creative(john))) [nnf transformation 9]
53. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X0] : ~brave(X0) | humble(john) | creative(john)) [flattening 52]
54. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (? [X1] : ~brave(X1) | humble(john) | creative(john)) [rectify 53]
55. ? [X1] : ~brave(X1) => ~brave(sK4) [choice axiom]
56. ((~humble(john) & ~creative(john)) | ! [X0] : brave(X0)) & (~brave(sK4) | humble(john) | creative(john)) [skolemisation 54,55]
61. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | (happy(fred) | kind(fred))) [nnf transformation 11]
62. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (? [X0] : ((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | happy(fred) | kind(fred)) [flattening 61]
63. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (? [X1] : ((~strong(X1) | happy(X1)) & (strong(X1) | ~happy(X1))) | happy(fred) | kind(fred)) [rectify 62]
64. ? [X1] : ((~strong(X1) | happy(X1)) & (strong(X1) | ~happy(X1))) => ((~strong(sK6) | happy(sK6)) & (strong(sK6) | ~happy(sK6))) [choice axiom]
65. ((~happy(fred) & ~kind(fred)) | ! [X0] : ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (((~strong(sK6) | happy(sK6)) & (strong(sK6) | ~happy(sK6))) | happy(fred) | kind(fred)) [skolemisation 63,64]
71. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((humble(X0) | ~rich(X0)) & (rich(X0) | ~humble(X0)))) & (((~rich(X0) | ~humble(X0)) & (rich(X0) | humble(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 15]
95. ~brave(sK0) | happy(fred) | rich(fred) [cnf transformation 37]
106. ~funny(X0) | happy(X0) | rich(X0) | ~strong(X0) [cnf transformation 46]
109. ~funny(X0) | strong(X0) | ~happy(X0) [cnf transformation 46]
110. ~rich(X0) | happy(X0) | funny(X0) [cnf transformation 46]
119. ~humble(john) | brave(X0) [cnf transformation 56]
127. ~happy(fred) | strong(X0) | happy(X0) [cnf transformation 65]
128. ~happy(fred) | ~happy(X0) | ~strong(X0) [cnf transformation 65]
135. ~happy(X0) | ~rich(X0) [cnf transformation 29]
136. ~funny(X0) | ~rich(X0) [cnf transformation 29]
137. rich(X0) | humble(X0) | tall(X0) | tall(X0) [cnf transformation 71]
138. rich(X0) | humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 71]
159. funny(susan) [cnf transformation 23]
160. rich(X0) | humble(X0) | tall(X0) [duplicate literal removal 137]
161. ~tall(X0) | humble(X0) | rich(X0) [duplicate literal removal 138]
180. 4 <=> happy(fred) [avatar definition]
182. ~happy(fred) <- (~4) [avatar component clause 180]
184. 5 <=> rich(fred) [avatar definition]
185. rich(fred) <- (5) [avatar component clause 184]
194. 7 <=> brave(sK0) [avatar definition]
196. ~brave(sK0) <- (~7) [avatar component clause 194]
198. 5 | 4 | ~7 [avatar split clause 95,194,180,184]
253. 20 <=> humble(john) [avatar definition]
255. ~humble(john) <- (~20) [avatar component clause 253]
262. 22 <=> ! [X0] : brave(X0) [avatar definition]
263. brave(X0) <- (22) [avatar component clause 262]
264. 22 | ~20 [avatar split clause 119,253,262]
290. 28 <=> ! [X0] : (~happy(X0) | ~strong(X0)) [avatar definition]
291. ~happy(X0) | ~strong(X0) <- (28) [avatar component clause 290]
292. 28 | ~4 [avatar split clause 128,180,290]
294. 29 <=> ! [X0] : (strong(X0) | happy(X0)) [avatar definition]
295. happy(X0) | strong(X0) <- (29) [avatar component clause 294]
296. 29 | ~4 [avatar split clause 127,180,294]
355. humble(X0) | rich(X0) [subsumption resolution 160,161]
410. ~rich(susan) [resolution 136,159]
444. strong(susan) | ~happy(susan) [resolution 109,159]
449. 57 <=> happy(susan) [avatar definition]
450. happy(susan) <- (57) [avatar component clause 449]
453. 58 <=> strong(susan) [avatar definition]
455. strong(susan) <- (58) [avatar component clause 453]
456. ~57 | 58 [avatar split clause 444,453,449]
468. 61 <=> funny(john) [avatar definition]
470. funny(john) <- (61) [avatar component clause 468]
472. 62 <=> happy(john) [avatar definition]
474. happy(john) <- (62) [avatar component clause 472]
477. $false <- (~7, 22) [resolution 263,196]
482. 7 | ~22 [avatar contradiction clause 477]
483. rich(john) <- (~20) [resolution 255,355]
490. happy(john) | funny(john) <- (~20) [resolution 483,110]
515. ~rich(john) <- (61) [resolution 470,136]
521. $false <- (~20, 61) [subsumption resolution 515,483]
522. 20 | ~61 [avatar contradiction clause 521]
523. 61 | 62 | 20 [avatar split clause 490,253,472,468]
525. happy(susan) | rich(susan) | ~strong(susan) [resolution 106,159]
537. happy(fred) | funny(fred) <- (5) [resolution 185,110]
538. funny(fred) <- (~4, 5) [subsumption resolution 537,182]
547. ~rich(fred) <- (~4, 5) [resolution 538,136]
548. $false <- (~4, 5) [subsumption resolution 547,185]
549. 4 | ~5 [avatar contradiction clause 548]
565. rich(john) <- (~20) [resolution 255,355]
594. happy(susan) | ~strong(susan) [subsumption resolution 525,410]
595. happy(susan) <- (29) [subsumption resolution 594,295]
596. 57 | ~29 [avatar split clause 595,294,449]
601. ~strong(susan) <- (28, 57) [resolution 450,291]
604. $false <- (28, 57, 58) [subsumption resolution 601,455]
605. ~28 | ~57 | ~58 [avatar contradiction clause 604]
685. ~rich(john) <- (62) [resolution 474,135]
686. $false <- (~20, 62) [subsumption resolution 685,565]
687. 20 | ~62 [avatar contradiction clause 686]
688. $false [avatar sat refutation 198,264,292,296,456,482,522,523,549,596,605,687]
% SZS output end Proof for 6966885115881838036179192
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is either patient or generous then someone is either not strong or patient. If lucy is either not generous or creative then paul is not funny or brave. If fred is kind then fred is either not curious or creative. Everyone who is not old or kind is tall and vice versa. Everyone who is either not funny or not curious is not calm or not strong and vice versa. If someone is not rich then someone is strong or not old and vice versa. Everyone who is old or not humble is curious or not funny. If someone is both not wise and funny then someone is either strong or not generous and vice versa. Everyone who is either calm or brave is strong or funny. If someone is both generous and quiet then someone is not creative or not humble and vice versa. If someone is both not brave and humble then someone is calm and vice versa. If john is quiet then susan is not generous or not quiet and vice versa. Everyone who is either not strong or funny is both not calm and strong and vice versa. If someone is either not curious or not creative then lucy is either not patient or not old. If someone is not humble then someone is curious. Everyone who is not quiet or funny is not generous and vice versa. Someone is both not generous and quiet. Someone is either not quiet or not tall. Someone is not old or not kind. Alice is not brave. Someone is either not rich or old. Mary is either tall or not wise. | Paul is curious. | contradiction | (((patient(john)<~>generous(john)))=>(?[X]:((~strong(X)<~>patient(X)))))&
(((~generous(lucy)<~>creative(lucy)))=>((~funny(paul)|brave(paul))))&
((kind(fred))=>((~curious(fred)<~>creative(fred))))&
(![X]:((~old(X)|kind(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~curious(X))<=>(~calm(X)|~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)|~humble(X))=>(curious(X)|~funny(X))))&
((?[X]:((~wise(X)&funny(X))))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>brave(X))=>(strong(X)|funny(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:(calm(X))))&
((quiet(john))<=>((~generous(susan)|~quiet(susan))))&
(![X]:((~strong(X)<~>funny(X))<=>(~calm(X)&strong(X))))&
((?[X]:((~curious(X)<~>~creative(X))))=>((~patient(lucy)<~>~old(lucy))))&
((?[X]:(~humble(X)))=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)|funny(X))<=>~generous(X)))&
(?[X]:((~generous(X)&quiet(X))))&
(?[X]:((~quiet(X)<~>~tall(X))))&
(?[X]:((~old(X)|~kind(X))))&
(~brave(alice))&
(?[X]:((~rich(X)<~>old(X))))&
((tall(mary)<~>~wise(mary))) | curious(paul) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6142921518849840178292643
% SZS output start Proof for 6142921518849840178292643
5. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> (~strong(X0) | ~calm(X0))) [input p4]
13. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (strong(X0) & ~calm(X0))) [input p12]
23. curious(paul) [input hypothesis]
46. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 5]
47. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [flattening 46]
71. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 13]
72. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 71]
101. ~calm(X0) | ~strong(X0) | ~curious(X0) | funny(X0) [cnf transformation 47]
103. ~curious(X0) | ~funny(X0) | calm(X0) [cnf transformation 47]
104. ~curious(X0) | ~funny(X0) | strong(X0) [cnf transformation 47]
132. ~calm(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 72]
133. strong(X0) | funny(X0) | strong(X0) [cnf transformation 72]
135. funny(X0) | ~strong(X0) | ~strong(X0) | calm(X0) [cnf transformation 72]
155. curious(paul) [cnf transformation 23]
156. funny(X0) | strong(X0) [duplicate literal removal 133]
157. ~strong(X0) | funny(X0) | calm(X0) [duplicate literal removal 135]
187. 7 <=> funny(paul) [avatar definition]
188. funny(paul) <- (7) [avatar component clause 187]
189. ~funny(paul) <- (~7) [avatar component clause 187]
399. strong(paul) <- (~7) [resolution 156,189]
407. ~funny(paul) | calm(paul) [resolution 103,155]
409. ~funny(paul) | strong(paul) [resolution 104,155]
459. funny(paul) | calm(paul) <- (~7) [resolution 157,399]
461. calm(paul) <- (~7) [subsumption resolution 459,189]
504. ~strong(paul) | ~curious(paul) | funny(paul) <- (~7) [resolution 461,101]
506. ~curious(paul) | funny(paul) <- (~7) [subsumption resolution 504,399]
507. funny(paul) <- (~7) [subsumption resolution 506,155]
508. $false <- (~7) [subsumption resolution 507,189]
509. 7 [avatar contradiction clause 508]
510. strong(paul) [subsumption resolution 409,156]
512. 63 <=> calm(paul) [avatar definition]
514. calm(paul) <- (63) [avatar component clause 512]
515. 63 | ~7 [avatar split clause 407,187,512]
522. ~strong(paul) | ~funny(paul) <- (63) [resolution 514,132]
523. ~funny(paul) <- (63) [subsumption resolution 522,510]
524. $false <- (7, 63) [subsumption resolution 523,188]
525. ~7 | ~63 [avatar contradiction clause 524]
526. $false [avatar sat refutation 509,515,525]
% SZS output end Proof for 6142921518849840178292643
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and not creative is either creative or not wise and vice versa.
Everyone who is either not creative or kind is not calm.
Everyone who is generous or quiet is kind and vice versa.
If someone is wise or not wise then someone is not humble or not wise and vice versa.
If someone is not calm then someone is strong and vice versa.
Everyone who is both not quiet and brave is not tall.
Everyone who is both not humble and not creative is not funny and vice versa.
Everyone who is both not calm and humble is not patient or not happy and vice versa.
If someone is both not wise and kind then someone is both not rich and curious and vice versa.
Everyone who is either wise or calm is either not generous or happy and vice versa.
If susan is both not curious and not generous then fred is not creative.
Everyone who is both humble and calm is either kind or not quiet.
If fred is both calm and not humble then someone is wise or not generous and vice versa.
If alice is both not happy and not creative then lucy is curious or rich and vice versa.
Everyone who is tall or curious is not kind.
Everyone who is either quiet or not rich is not happy and vice versa.
Fred is not creative.
Paul is creative or not generous.
Alice is strong.
Someone is not strong.
Paul is patient or calm.
John is either not strong or not rich.
Paul is either humble or not rich. | Paul is not quiet. | contradiction | (![X]:((humble(X)&~creative(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((~creative(X)<~>kind(X))=>~calm(X)))&
(![X]:((generous(X)|quiet(X))<=>kind(X)))&
((?[X]:((wise(X)|~wise(X))))<=>(?[X]:((~humble(X)|~wise(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)&brave(X))=>~tall(X)))&
(![X]:((~humble(X)&~creative(X))<=>~funny(X)))&
(![X]:((~calm(X)&humble(X))<=>(~patient(X)|~happy(X))))&
((?[X]:((~wise(X)&kind(X))))<=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((wise(X)<~>calm(X))<=>(~generous(X)<~>happy(X))))&
(((~curious(susan)&~generous(susan)))=>(~creative(fred)))&
(![X]:((humble(X)&calm(X))=>(kind(X)<~>~quiet(X))))&
(((calm(fred)&~humble(fred)))<=>(?[X]:((wise(X)|~generous(X)))))&
(((~happy(alice)&~creative(alice)))<=>((curious(lucy)|rich(lucy))))&
(![X]:((tall(X)|curious(X))=>~kind(X)))&
(![X]:((quiet(X)<~>~rich(X))<=>~happy(X)))&
(~creative(fred))&
((creative(paul)|~generous(paul)))&
(strong(alice))&
(?[X]:(~strong(X)))&
((patient(paul)|calm(paul)))&
((~strong(john)<~>~rich(john)))&
((humble(paul)<~>~rich(paul))) | ~quiet(paul) | [
"p0",
"p1",
"p2",
"p7",
"p9",
"p11",
"p15",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6111140033086363289994384
% SZS output start Proof for 6111140033086363289994384
1. ! [X0] : ((~creative(X0) & humble(X0)) <=> (creative(X0) <~> ~wise(X0))) [input p0]
2. ! [X0] : ((~creative(X0) <~> kind(X0)) => ~calm(X0)) [input p1]
3. ! [X0] : ((quiet(X0) | generous(X0)) <=> kind(X0)) [input p2]
8. ! [X0] : ((humble(X0) & ~calm(X0)) <=> (~happy(X0) | ~patient(X0))) [input p7]
10. ! [X0] : ((wise(X0) <~> calm(X0)) <=> (~generous(X0) <~> happy(X0))) [input p9]
12. ! [X0] : ((calm(X0) & humble(X0)) => (kind(X0) <~> ~quiet(X0))) [input p11]
16. ! [X0] : ((quiet(X0) <~> ~rich(X0)) <=> ~happy(X0)) [input p15]
21. calm(paul) | patient(paul) [input p20]
23. humble(paul) <~> ~rich(paul) [input p22]
24. ~quiet(paul) [input hypothesis]
30. ! [X0] : (~calm(X0) | (~creative(X0) <=> kind(X0))) [ennf transformation 2]
33. ! [X0] : ((kind(X0) <~> ~quiet(X0)) | (~calm(X0) | ~humble(X0))) [ennf transformation 12]
34. ! [X0] : ((kind(X0) <~> ~quiet(X0)) | ~calm(X0) | ~humble(X0)) [flattening 33]
36. ! [X0] : (((~creative(X0) & humble(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | (creative(X0) | ~humble(X0)))) [nnf transformation 1]
37. ! [X0] : (((~creative(X0) & humble(X0)) | ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0)))) & (((wise(X0) | ~creative(X0)) & (~wise(X0) | creative(X0))) | creative(X0) | ~humble(X0))) [flattening 36]
38. ! [X0] : (~calm(X0) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0)))) [nnf transformation 30]
39. ! [X0] : (((quiet(X0) | generous(X0)) | ~kind(X0)) & (kind(X0) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | generous(X0) | ~kind(X0)) & (kind(X0) | (~quiet(X0) & ~generous(X0)))) [flattening 39]
51. ! [X0] : (((humble(X0) & ~calm(X0)) | (happy(X0) & patient(X0))) & ((~happy(X0) | ~patient(X0)) | (~humble(X0) | calm(X0)))) [nnf transformation 8]
52. ! [X0] : (((humble(X0) & ~calm(X0)) | (happy(X0) & patient(X0))) & (~happy(X0) | ~patient(X0) | ~humble(X0) | calm(X0))) [flattening 51]
58. ! [X0] : ((((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | ((~generous(X0) | ~happy(X0)) & (happy(X0) | generous(X0)))) & (((~happy(X0) | generous(X0)) & (happy(X0) | ~generous(X0))) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0))))) [nnf transformation 10]
59. ! [X0] : (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ~calm(X0) | ~humble(X0)) [nnf transformation 34]
67. ! [X0] : ((((rich(X0) | ~quiet(X0)) & (~rich(X0) | quiet(X0))) | happy(X0)) & (~happy(X0) | ((quiet(X0) | rich(X0)) & (~rich(X0) | ~quiet(X0))))) [nnf transformation 16]
71. (rich(paul) | ~humble(paul)) & (~rich(paul) | humble(paul)) [nnf transformation 23]
76. ~creative(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 37]
78. ~calm(X0) | kind(X0) | creative(X0) [cnf transformation 38]
80. ~generous(X0) | kind(X0) [cnf transformation 40]
89. ~happy(X0) | ~patient(X0) | ~humble(X0) | calm(X0) [cnf transformation 52]
90. ~calm(X0) | patient(X0) [cnf transformation 52]
91. ~calm(X0) | happy(X0) [cnf transformation 52]
93. happy(X0) | humble(X0) [cnf transformation 52]
101. ~happy(X0) | generous(X0) | wise(X0) | ~calm(X0) [cnf transformation 58]
102. calm(X0) | wise(X0) | happy(X0) | generous(X0) [cnf transformation 58]
108. ~calm(X0) | ~kind(X0) | quiet(X0) | ~humble(X0) [cnf transformation 59]
121. ~happy(X0) | quiet(X0) | rich(X0) [cnf transformation 67]
122. ~rich(X0) | quiet(X0) | happy(X0) [cnf transformation 67]
128. calm(paul) | patient(paul) [cnf transformation 21]
131. ~rich(paul) | humble(paul) [cnf transformation 71]
132. rich(paul) | ~humble(paul) [cnf transformation 71]
133. ~quiet(paul) [cnf transformation 24]
135. ~wise(X0) | ~creative(X0) [duplicate literal removal 76]
180. happy(X0) | wise(X0) | generous(X0) [subsumption resolution 102,91]
181. ~calm(X0) | wise(X0) | generous(X0) [subsumption resolution 101,180]
246. 24 <=> creative(paul) [avatar definition]
248. creative(paul) <- (24) [avatar component clause 246]
250. 25 <=> generous(paul) [avatar definition]
251. generous(paul) <- (25) [avatar component clause 250]
254. patient(paul) [subsumption resolution 128,90]
266. 28 <=> humble(paul) [avatar definition]
267. humble(paul) <- (28) [avatar component clause 266]
268. ~humble(paul) <- (~28) [avatar component clause 266]
270. 29 <=> rich(paul) [avatar definition]
271. ~rich(paul) <- (~29) [avatar component clause 270]
272. rich(paul) <- (29) [avatar component clause 270]
273. ~28 | 29 [avatar split clause 132,270,266]
274. 28 | ~29 [avatar split clause 131,270,266]
335. rich(X0) | quiet(X0) | humble(X0) [resolution 121,93]
347. 34 <=> calm(paul) [avatar definition]
348. calm(paul) <- (34) [avatar component clause 347]
351. 35 <=> wise(paul) [avatar definition]
352. wise(paul) <- (35) [avatar component clause 351]
403. ~creative(paul) <- (35) [resolution 352,135]
404. $false <- (24, 35) [subsumption resolution 403,248]
405. ~24 | ~35 [avatar contradiction clause 404]
434. quiet(paul) | humble(paul) <- (~29) [resolution 335,271]
447. humble(paul) <- (~29) [subsumption resolution 434,133]
448. $false <- (~28, ~29) [subsumption resolution 447,268]
449. 28 | 29 [avatar contradiction clause 448]
450. quiet(paul) | happy(paul) <- (29) [resolution 272,122]
452. happy(paul) <- (29) [subsumption resolution 450,133]
455. ~patient(paul) | ~humble(paul) | calm(paul) <- (29) [resolution 452,89]
457. ~humble(paul) | calm(paul) <- (29) [subsumption resolution 455,254]
458. calm(paul) <- (28, 29) [subsumption resolution 457,267]
461. 34 | ~28 | ~29 [avatar split clause 458,270,266,347]
462. ~kind(paul) | quiet(paul) | ~humble(paul) <- (34) [resolution 348,108]
463. wise(paul) | generous(paul) <- (34) [resolution 348,181]
465. kind(paul) | creative(paul) <- (34) [resolution 348,78]
468. ~kind(paul) | ~humble(paul) <- (34) [subsumption resolution 462,133]
469. ~kind(paul) <- (28, 34) [subsumption resolution 468,267]
473. creative(paul) <- (28, 34) [subsumption resolution 465,469]
474. 24 | ~28 | ~34 [avatar split clause 473,347,266,246]
482. 25 | 35 | ~34 [avatar split clause 463,347,351,250]
519. kind(paul) <- (25) [resolution 251,80]
520. $false <- (25, 28, 34) [subsumption resolution 519,469]
521. ~25 | ~28 | ~34 [avatar contradiction clause 520]
522. $false [avatar sat refutation 273,274,405,449,461,474,482,521]
% SZS output end Proof for 6111140033086363289994384
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or patient then alice is creative and vice versa.
Everyone who is rich is kind and vice versa.
If john is not patient or rich then paul is either not funny or not humble and vice versa.
Everyone who is both happy and not wise is not quiet or rich.
If someone is both curious and creative then someone is not humble or curious and vice versa.
Everyone who is both old and not wise is both not curious and not old.
If fred is either not quiet or not patient then someone is both not brave and creative and vice versa.
If paul is both not humble and not strong then susan is either happy or not rich and vice versa.
Everyone who is not humble is either wise or not kind and vice versa.
Everyone who is either not wise or happy is either not quiet or not humble.
Everyone who is not strong is not happy or not brave and vice versa.
Everyone who is tall is both humble and not funny.
If paul is either creative or old then someone is either not old or old.
If paul is not patient then someone is not quiet.
Everyone who is both not happy and not curious is either not happy or kind.
If alice is happy or not tall then mary is either not brave or quiet.
Paul is not quiet or tall.
Fred is either not wise or creative.
Paul is both humble and not brave.
John is both not tall and not old.
Someone is calm or not humble.
Someone is both not rich and brave.
Paul is kind or not happy. | Paul is patient. | neutral | ((?[X]:((curious(X)|patient(X))))<=>(creative(alice)))&
(![X]:(rich(X)<=>kind(X)))&
(((~patient(john)|rich(john)))<=>((~funny(paul)<~>~humble(paul))))&
(![X]:((happy(X)&~wise(X))=>(~quiet(X)|rich(X))))&
((?[X]:((curious(X)&creative(X))))<=>(?[X]:((~humble(X)|curious(X)))))&
(![X]:((old(X)&~wise(X))=>(~curious(X)&~old(X))))&
(((~quiet(fred)<~>~patient(fred)))<=>(?[X]:((~brave(X)&creative(X)))))&
(((~humble(paul)&~strong(paul)))<=>((happy(susan)<~>~rich(susan))))&
(![X]:(~humble(X)<=>(wise(X)<~>~kind(X))))&
(![X]:((~wise(X)<~>happy(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:(~strong(X)<=>(~happy(X)|~brave(X))))&
(![X]:(tall(X)=>(humble(X)&~funny(X))))&
(((creative(paul)<~>old(paul)))=>(?[X]:((~old(X)<~>old(X)))))&
((~patient(paul))=>(?[X]:(~quiet(X))))&
(![X]:((~happy(X)&~curious(X))=>(~happy(X)<~>kind(X))))&
(((happy(alice)|~tall(alice)))=>((~brave(mary)<~>quiet(mary))))&
((~quiet(paul)|tall(paul)))&
((~wise(fred)<~>creative(fred)))&
((humble(paul)&~brave(paul)))&
((~tall(john)&~old(john)))&
(?[X]:((calm(X)|~humble(X))))&
(?[X]:((~rich(X)&brave(X))))&
((kind(paul)|~happy(paul))) | patient(paul) | [] | null | 0 |
If someone is either funny or not calm then someone is both not rich and not funny. Everyone who is both kind and not patient is curious or not creative. Everyone who is tall is either tall or funny and vice versa. If someone is either not tall or not calm then john is not old or not generous. Everyone who is both creative and not generous is strong or kind. If fred is calm then alice is either not generous or wise. Everyone who is calm is both not old and quiet and vice versa. Everyone who is not kind or not curious is either not creative or not happy. If someone is both tall and not humble then someone is wise and vice versa. Everyone who is both not patient and not quiet is either not funny or not patient. If paul is not creative or generous then mary is both generous and patient. Everyone who is either quiet or patient is both happy and not old. Everyone who is either kind or old is either not old or funny and vice versa. Everyone who is either calm or not patient is not calm. Everyone who is not old is either funny or not wise and vice versa. Everyone who is either not calm or funny is not old and vice versa. Mary is kind. John is generous. Someone is not generous. Someone is either not funny or not curious. | Alice is happy. | entailment | ((?[X]:((funny(X)<~>~calm(X))))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((kind(X)&~patient(X))=>(curious(X)|~creative(X))))&
(![X]:(tall(X)<=>(tall(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>~calm(X))))=>((~old(john)|~generous(john))))&
(![X]:((creative(X)&~generous(X))=>(strong(X)|kind(X))))&
((calm(fred))=>((~generous(alice)<~>wise(alice))))&
(![X]:(calm(X)<=>(~old(X)&quiet(X))))&
(![X]:((~kind(X)|~curious(X))=>(~creative(X)<~>~happy(X))))&
((?[X]:((tall(X)&~humble(X))))<=>(?[X]:(wise(X))))&
(![X]:((~patient(X)&~quiet(X))=>(~funny(X)<~>~patient(X))))&
(((~creative(paul)|generous(paul)))=>((generous(mary)&patient(mary))))&
(![X]:((quiet(X)<~>patient(X))=>(happy(X)&~old(X))))&
(![X]:((kind(X)<~>old(X))<=>(~old(X)<~>funny(X))))&
(![X]:((calm(X)<~>~patient(X))=>~calm(X)))&
(![X]:(~old(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>funny(X))<=>~old(X)))&
(kind(mary))&
(generous(john))&
(?[X]:(~generous(X)))&
(?[X]:((~funny(X)<~>~curious(X)))) | happy(alice) | [
"p2",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 277728176426231475450868
% SZS output start Proof for 277728176426231475450868
3. ! [X0] : (tall(X0) <=> (tall(X0) <~> funny(X0))) [input p2]
7. ! [X0] : (calm(X0) <=> (quiet(X0) & ~old(X0))) [input p6]
10. ! [X0] : ((~quiet(X0) & ~patient(X0)) => (~funny(X0) <~> ~patient(X0))) [input p9]
12. ! [X0] : ((quiet(X0) <~> patient(X0)) => (~old(X0) & happy(X0))) [input p11]
16. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> ~old(X0)) [input p15]
21. ~happy(alice) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> ~patient(X0)) | (quiet(X0) | patient(X0))) [ennf transformation 10]
34. ! [X0] : ((~funny(X0) <~> ~patient(X0)) | quiet(X0) | patient(X0)) [flattening 33]
36. ! [X0] : ((~old(X0) & happy(X0)) | (quiet(X0) <=> patient(X0))) [ennf transformation 12]
42. ! [X0] : ((tall(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0)))) & (((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | ~tall(X0))) [nnf transformation 3]
45. ! [X0] : ((calm(X0) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 7]
46. ! [X0] : ((calm(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | ~calm(X0))) [flattening 45]
53. ! [X0] : (((patient(X0) | funny(X0)) & (~patient(X0) | ~funny(X0))) | quiet(X0) | patient(X0)) [nnf transformation 34]
54. ! [X0] : ((~old(X0) & happy(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) [nnf transformation 36]
58. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | old(X0)) & (~old(X0) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 16]
68. ~funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 42]
70. tall(X0) | tall(X0) | ~funny(X0) [cnf transformation 42]
75. ~old(X0) | ~calm(X0) [cnf transformation 46]
77. ~quiet(X0) | calm(X0) | old(X0) [cnf transformation 46]
86. patient(X0) | funny(X0) | quiet(X0) | patient(X0) [cnf transformation 53]
92. happy(X0) | quiet(X0) | ~patient(X0) [cnf transformation 54]
109. ~old(X0) | funny(X0) | calm(X0) [cnf transformation 58]
111. funny(X0) | ~calm(X0) | old(X0) [cnf transformation 58]
118. ~happy(alice) [cnf transformation 21]
124. patient(X0) | funny(X0) | quiet(X0) [duplicate literal removal 86]
125. ~funny(X0) | ~tall(X0) [duplicate literal removal 68]
126. ~funny(X0) | tall(X0) [duplicate literal removal 70]
139. ~funny(X0) [subsumption resolution 125,126]
191. quiet(X0) | patient(X0) [subsumption resolution 124,139]
214. happy(X0) | quiet(X0) [subsumption resolution 92,191]
221. ~calm(X0) | old(X0) [subsumption resolution 111,139]
222. ~calm(X0) [subsumption resolution 221,75]
223. ~old(X0) | calm(X0) [subsumption resolution 109,139]
224. ~old(X0) [subsumption resolution 223,222]
227. quiet(alice) [resolution 214,118]
236. calm(alice) | old(alice) [resolution 77,227]
239. old(alice) [subsumption resolution 236,222]
240. $false [subsumption resolution 239,224]
% SZS output end Proof for 277728176426231475450868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not creative is either creative or not wise and vice versa.
Everyone who is either not creative or kind is not calm.
Everyone who is generous or quiet is kind and vice versa.
If someone is wise or not wise then someone is not humble or not wise and vice versa.
If someone is not calm then someone is strong and vice versa.
Everyone who is both not quiet and brave is not tall.
Everyone who is both not humble and not creative is not funny and vice versa.
Everyone who is both not calm and humble is not patient or not happy and vice versa.
If someone is both not wise and kind then someone is both not rich and curious and vice versa.
Everyone who is either wise or calm is either not generous or happy and vice versa.
If susan is both not curious and not generous then fred is not creative.
Everyone who is both humble and calm is either kind or not quiet.
If fred is both calm and not humble then someone is wise or not generous and vice versa.
If alice is both not happy and not creative then lucy is curious or rich and vice versa.
Everyone who is tall or curious is not kind.
Everyone who is either quiet or not rich is not happy and vice versa.
Fred is not creative.
Paul is creative or not generous.
Alice is strong.
Someone is not strong.
Paul is patient or calm.
John is either not strong or not rich.
Paul is either humble or not rich. | John is not rich. | neutral | (![X]:((humble(X)&~creative(X))<=>(creative(X)<~>~wise(X))))&
(![X]:((~creative(X)<~>kind(X))=>~calm(X)))&
(![X]:((generous(X)|quiet(X))<=>kind(X)))&
((?[X]:((wise(X)|~wise(X))))<=>(?[X]:((~humble(X)|~wise(X)))))&
((?[X]:(~calm(X)))<=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)&brave(X))=>~tall(X)))&
(![X]:((~humble(X)&~creative(X))<=>~funny(X)))&
(![X]:((~calm(X)&humble(X))<=>(~patient(X)|~happy(X))))&
((?[X]:((~wise(X)&kind(X))))<=>(?[X]:((~rich(X)&curious(X)))))&
(![X]:((wise(X)<~>calm(X))<=>(~generous(X)<~>happy(X))))&
(((~curious(susan)&~generous(susan)))=>(~creative(fred)))&
(![X]:((humble(X)&calm(X))=>(kind(X)<~>~quiet(X))))&
(((calm(fred)&~humble(fred)))<=>(?[X]:((wise(X)|~generous(X)))))&
(((~happy(alice)&~creative(alice)))<=>((curious(lucy)|rich(lucy))))&
(![X]:((tall(X)|curious(X))=>~kind(X)))&
(![X]:((quiet(X)<~>~rich(X))<=>~happy(X)))&
(~creative(fred))&
((creative(paul)|~generous(paul)))&
(strong(alice))&
(?[X]:(~strong(X)))&
((patient(paul)|calm(paul)))&
((~strong(john)<~>~rich(john)))&
((humble(paul)<~>~rich(paul))) | ~rich(john) | [] | null | 0 |
If someone is both not old and not humble then someone is kind or creative.
Everyone who is both kind and not generous is either generous or not generous and vice versa.
Everyone who is wise is either not generous or old and vice versa.
Everyone who is brave or not curious is generous.
Everyone who is not patient or creative is either happy or wise.
Everyone who is curious is either not kind or not quiet and vice versa.
If someone is not quiet or not strong then someone is both not creative and strong.
Everyone who is either quiet or calm is patient or not creative and vice versa.
Everyone who is both generous and creative is strong or not humble.
Everyone who is not curious is either not old or funny.
If alice is funny then mary is both not brave and not creative and vice versa.
If someone is both funny and not happy then fred is not calm or old.
If someone is both rich and humble then someone is both wise and not brave and vice versa.
If someone is creative or not rich then john is funny and vice versa.
If someone is both calm and not creative then someone is creative or not kind.
Someone is brave or not creative.
Paul is either not generous or not curious.
Paul is both not happy and not calm.
Paul is not funny or curious.
Someone is both not strong and not old.
Fred is not rich.
Paul is either generous or rich. | Alice is creative. | neutral | ((?[X]:((~old(X)&~humble(X))))=>(?[X]:((kind(X)|creative(X)))))&
(![X]:((kind(X)&~generous(X))<=>(generous(X)<~>~generous(X))))&
(![X]:(wise(X)<=>(~generous(X)<~>old(X))))&
(![X]:((brave(X)|~curious(X))=>generous(X)))&
(![X]:((~patient(X)|creative(X))=>(happy(X)<~>wise(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>~quiet(X))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:((~creative(X)&strong(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(patient(X)|~creative(X))))&
(![X]:((generous(X)&creative(X))=>(strong(X)|~humble(X))))&
(![X]:(~curious(X)=>(~old(X)<~>funny(X))))&
((funny(alice))<=>((~brave(mary)&~creative(mary))))&
((?[X]:((funny(X)&~happy(X))))=>((~calm(fred)|old(fred))))&
((?[X]:((rich(X)&humble(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
((?[X]:((creative(X)|~rich(X))))<=>(funny(john)))&
((?[X]:((calm(X)&~creative(X))))=>(?[X]:((creative(X)|~kind(X)))))&
(?[X]:((brave(X)|~creative(X))))&
((~generous(paul)<~>~curious(paul)))&
((~happy(paul)&~calm(paul)))&
((~funny(paul)|curious(paul)))&
(?[X]:((~strong(X)&~old(X))))&
(~rich(fred))&
((generous(paul)<~>rich(paul))) | creative(alice) | [] | null | 0 |
Everyone who is either strong or quiet is not creative or not strong and vice versa.
If fred is quiet or patient then someone is not wise.
If someone is either calm or not rich then john is old or calm.
Everyone who is both old and brave is calm or not strong and vice versa.
If alice is kind or not rich then alice is both not curious and rich and vice versa.
Everyone who is either happy or old is not humble and vice versa.
Everyone who is not funny is either not calm or not brave.
Everyone who is not tall or happy is not calm or patient.
Everyone who is either not rich or creative is not generous.
Everyone who is both not brave and not creative is either calm or creative and vice versa.
Everyone who is both happy and not tall is both not funny and tall.
Everyone who is not rich is strong or wise and vice versa.
Everyone who is old is calm and vice versa.
Everyone who is either quiet or funny is both not strong and not kind.
Everyone who is both not calm and not strong is either kind or not creative and vice versa.
Mary is tall.
Fred is not wise or not tall.
Lucy is patient.
Alice is creative.
Someone is calm.
Someone is not calm or not creative.
Fred is not strong.
Alice is either not tall or curious. | Alice is not generous. | entailment | (![X]:((strong(X)<~>quiet(X))<=>(~creative(X)|~strong(X))))&
(((quiet(fred)|patient(fred)))=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~rich(X))))=>((old(john)|calm(john))))&
(![X]:((old(X)&brave(X))<=>(calm(X)|~strong(X))))&
(((kind(alice)|~rich(alice)))<=>((~curious(alice)&rich(alice))))&
(![X]:((happy(X)<~>old(X))<=>~humble(X)))&
(![X]:(~funny(X)=>(~calm(X)<~>~brave(X))))&
(![X]:((~tall(X)|happy(X))=>(~calm(X)|patient(X))))&
(![X]:((~rich(X)<~>creative(X))=>~generous(X)))&
(![X]:((~brave(X)&~creative(X))<=>(calm(X)<~>creative(X))))&
(![X]:((happy(X)&~tall(X))=>(~funny(X)&tall(X))))&
(![X]:(~rich(X)<=>(strong(X)|wise(X))))&
(![X]:(old(X)<=>calm(X)))&
(![X]:((quiet(X)<~>funny(X))=>(~strong(X)&~kind(X))))&
(![X]:((~calm(X)&~strong(X))<=>(kind(X)<~>~creative(X))))&
(tall(mary))&
((~wise(fred)|~tall(fred)))&
(patient(lucy))&
(creative(alice))&
(?[X]:(calm(X)))&
(?[X]:((~calm(X)|~creative(X))))&
(~strong(fred))&
((~tall(alice)<~>curious(alice))) | ~generous(alice) | [
"p4",
"p8",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4481197845338819010763091
% SZS output start Proof for 4481197845338819010763091
5. (~rich(alice) | kind(alice)) <=> (rich(alice) & ~curious(alice)) [input p4]
9. ! [X0] : ((~rich(X0) <~> creative(X0)) => ~generous(X0)) [input p8]
19. creative(alice) [input p18]
24. generous(alice) [input hypothesis]
33. ! [X0] : (~generous(X0) | (~rich(X0) <=> creative(X0))) [ennf transformation 9]
42. ((~rich(alice) | kind(alice)) | (~rich(alice) | curious(alice))) & ((rich(alice) & ~curious(alice)) | (rich(alice) & ~kind(alice))) [nnf transformation 5]
43. (~rich(alice) | kind(alice) | ~rich(alice) | curious(alice)) & ((rich(alice) & ~curious(alice)) | (rich(alice) & ~kind(alice))) [flattening 42]
45. ! [X0] : (~generous(X0) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [nnf transformation 33]
77. rich(alice) | rich(alice) [cnf transformation 43]
83. ~generous(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 45]
108. creative(alice) [cnf transformation 19]
114. generous(alice) [cnf transformation 24]
117. rich(alice) [duplicate literal removal 77]
161. 10 <=> rich(alice) [avatar definition]
162. rich(alice) <- (10) [avatar component clause 161]
165. 10 [avatar split clause 117,161]
250. ~rich(alice) | ~creative(alice) [resolution 83,114]
251. ~creative(alice) <- (10) [subsumption resolution 250,162]
252. $false <- (10) [subsumption resolution 251,108]
253. ~10 [avatar contradiction clause 252]
254. $false [avatar sat refutation 165,253]
% SZS output end Proof for 4481197845338819010763091
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not generous is not happy or not kind and vice versa.
If someone is either not calm or not generous then someone is rich or wise and vice versa.
Everyone who is either kind or humble is either not patient or not old and vice versa.
Everyone who is old is either humble or not generous.
Everyone who is either not calm or kind is not happy and vice versa.
If someone is both not brave and wise then alice is curious or generous and vice versa.
If someone is either not wise or humble then mary is both not patient and generous and vice versa.
Everyone who is happy is not wise and vice versa.
Everyone who is either not rich or not funny is generous or not patient.
Everyone who is old is both calm and generous.
Everyone who is creative is both not patient and not brave.
If someone is not curious or not wise then someone is either not quiet or patient and vice versa.
Everyone who is not quiet is either not brave or not funny.
If someone is both generous and not wise then susan is either not rich or not curious.
Everyone who is happy is either generous or not humble and vice versa.
If paul is funny then mary is humble or not kind and vice versa.
Paul is not quiet or not wise.
Someone is not tall.
Someone is brave or not curious.
Lucy is brave or patient.
Someone is both not tall and not calm.
Fred is either not tall or calm.
Someone is both quiet and strong. | Lucy is not old. | entailment | (![X]:((~strong(X)&~generous(X))<=>(~happy(X)|~kind(X))))&
((?[X]:((~calm(X)<~>~generous(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)<~>humble(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(old(X)=>(humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>kind(X))<=>~happy(X)))&
((?[X]:((~brave(X)&wise(X))))<=>((curious(alice)|generous(alice))))&
((?[X]:((~wise(X)<~>humble(X))))<=>((~patient(mary)&generous(mary))))&
(![X]:(happy(X)<=>~wise(X)))&
(![X]:((~rich(X)<~>~funny(X))=>(generous(X)|~patient(X))))&
(![X]:(old(X)=>(calm(X)&generous(X))))&
(![X]:(creative(X)=>(~patient(X)&~brave(X))))&
((?[X]:((~curious(X)|~wise(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:(~quiet(X)=>(~brave(X)<~>~funny(X))))&
((?[X]:((generous(X)&~wise(X))))=>((~rich(susan)<~>~curious(susan))))&
(![X]:(happy(X)<=>(generous(X)<~>~humble(X))))&
((funny(paul))<=>((humble(mary)|~kind(mary))))&
((~quiet(paul)|~wise(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((brave(X)|~curious(X))))&
((brave(lucy)|patient(lucy)))&
(?[X]:((~tall(X)&~calm(X))))&
((~tall(fred)<~>calm(fred)))&
(?[X]:((quiet(X)&strong(X)))) | ~old(lucy) | [
"p0",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6043770488796780788869580
% SZS output start Proof for 6043770488796780788869580
1. ! [X0] : ((~generous(X0) & ~strong(X0)) <=> (~kind(X0) | ~happy(X0))) [input p0]
5. ! [X0] : ((~calm(X0) <~> kind(X0)) <=> ~happy(X0)) [input p4]
10. ! [X0] : (old(X0) => (generous(X0) & calm(X0))) [input p9]
24. old(lucy) [input hypothesis]
31. ! [X0] : ((generous(X0) & calm(X0)) | ~old(X0)) [ennf transformation 10]
34. ! [X0] : (((~generous(X0) & ~strong(X0)) | (kind(X0) & happy(X0))) & ((~kind(X0) | ~happy(X0)) | (generous(X0) | strong(X0)))) [nnf transformation 1]
35. ! [X0] : (((~generous(X0) & ~strong(X0)) | (kind(X0) & happy(X0))) & (~kind(X0) | ~happy(X0) | generous(X0) | strong(X0))) [flattening 34]
43. ! [X0] : ((((~kind(X0) | calm(X0)) & (kind(X0) | ~calm(X0))) | happy(X0)) & (~happy(X0) | ((~calm(X0) | ~kind(X0)) & (kind(X0) | calm(X0))))) [nnf transformation 5]
78. ~generous(X0) | happy(X0) [cnf transformation 35]
79. ~generous(X0) | kind(X0) [cnf transformation 35]
97. ~calm(X0) | ~happy(X0) | ~kind(X0) [cnf transformation 43]
115. ~old(X0) | calm(X0) [cnf transformation 31]
116. ~old(X0) | generous(X0) [cnf transformation 31]
144. old(lucy) [cnf transformation 24]
342. calm(lucy) [resolution 115,144]
343. generous(lucy) [resolution 116,144]
349. kind(lucy) [resolution 343,79]
350. happy(lucy) [resolution 343,78]
388. ~happy(lucy) | ~kind(lucy) [resolution 97,342]
398. ~kind(lucy) [subsumption resolution 388,350]
399. $false [subsumption resolution 398,349]
% SZS output end Proof for 6043770488796780788869580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not kind then someone is either funny or not strong and vice versa.
Everyone who is either rich or not calm is old or not creative.
Everyone who is not humble is either not quiet or wise and vice versa.
If lucy is both generous and not patient then susan is both rich and not rich and vice versa.
If fred is humble or strong then john is quiet or strong.
If someone is either not rich or wise then someone is both quiet and not creative and vice versa.
Everyone who is not wise or kind is both quiet and humble and vice versa.
If john is humble then someone is both not wise and kind.
If alice is both generous and wise then someone is curious or rich.
If someone is kind or not funny then mary is either old or not curious and vice versa.
Everyone who is not tall is curious or tall.
Everyone who is not kind is not happy or creative and vice versa.
Everyone who is both kind and not happy is not old and vice versa.
Everyone who is not curious is both brave and not old.
If someone is curious then someone is both happy and creative and vice versa.
Everyone who is not funny or not strong is both not tall and creative and vice versa.
Someone is strong or funny.
Susan is either not brave or not wise.
Someone is not happy.
Someone is both calm and not strong.
Mary is not happy.
Someone is not quiet or not funny. | Alice is wise. | neutral | ((?[X]:(~kind(X)))<=>(?[X]:((funny(X)<~>~strong(X)))))&
(![X]:((rich(X)<~>~calm(X))=>(old(X)|~creative(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>wise(X))))&
(((generous(lucy)&~patient(lucy)))<=>((rich(susan)&~rich(susan))))&
(((humble(fred)|strong(fred)))=>((quiet(john)|strong(john))))&
((?[X]:((~rich(X)<~>wise(X))))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~wise(X)|kind(X))<=>(quiet(X)&humble(X))))&
((humble(john))=>(?[X]:((~wise(X)&kind(X)))))&
(((generous(alice)&wise(alice)))=>(?[X]:((curious(X)|rich(X)))))&
((?[X]:((kind(X)|~funny(X))))<=>((old(mary)<~>~curious(mary))))&
(![X]:(~tall(X)=>(curious(X)|tall(X))))&
(![X]:(~kind(X)<=>(~happy(X)|creative(X))))&
(![X]:((kind(X)&~happy(X))<=>~old(X)))&
(![X]:(~curious(X)=>(brave(X)&~old(X))))&
((?[X]:(curious(X)))<=>(?[X]:((happy(X)&creative(X)))))&
(![X]:((~funny(X)|~strong(X))<=>(~tall(X)&creative(X))))&
(?[X]:((strong(X)|funny(X))))&
((~brave(susan)<~>~wise(susan)))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)&~strong(X))))&
(~happy(mary))&
(?[X]:((~quiet(X)|~funny(X)))) | wise(alice) | [] | null | 0 |
Everyone who is not patient or not old is not wise or calm and vice versa.
If someone is not creative or not generous then susan is not tall.
Everyone who is either not strong or not quiet is both old and brave and vice versa.
Everyone who is not patient or wise is both not wise and not funny.
Everyone who is funny is both calm and funny and vice versa.
Everyone who is both not happy and not humble is not creative or calm and vice versa.
Everyone who is happy is generous or happy.
If lucy is not strong then paul is old or rich.
If someone is either not curious or not quiet then someone is either generous or not tall.
Everyone who is both not kind and not patient is not calm and vice versa.
If paul is either curious or not creative then someone is tall.
If someone is both not quiet and brave then someone is both calm and strong.
Everyone who is quiet or not quiet is not creative and vice versa.
If mary is either not creative or not curious then someone is not funny and vice versa.
If susan is patient or not brave then alice is both not humble and not tall.
Someone is both strong and tall.
Someone is funny or not humble.
Mary is either not strong or tall.
Susan is not brave.
Paul is creative or not patient.
Mary is either generous or not generous. | Mary is not happy. | entailment | (![X]:((~patient(X)|~old(X))<=>(~wise(X)|calm(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(~tall(susan)))&
(![X]:((~strong(X)<~>~quiet(X))<=>(old(X)&brave(X))))&
(![X]:((~patient(X)|wise(X))=>(~wise(X)&~funny(X))))&
(![X]:(funny(X)<=>(calm(X)&funny(X))))&
(![X]:((~happy(X)&~humble(X))<=>(~creative(X)|calm(X))))&
(![X]:(happy(X)=>(generous(X)|happy(X))))&
((~strong(lucy))=>((old(paul)|rich(paul))))&
((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((~kind(X)&~patient(X))<=>~calm(X)))&
(((curious(paul)<~>~creative(paul)))=>(?[X]:(tall(X))))&
((?[X]:((~quiet(X)&brave(X))))=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((quiet(X)|~quiet(X))<=>~creative(X)))&
(((~creative(mary)<~>~curious(mary)))<=>(?[X]:(~funny(X))))&
(((patient(susan)|~brave(susan)))=>((~humble(alice)&~tall(alice))))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:((funny(X)|~humble(X))))&
((~strong(mary)<~>tall(mary)))&
(~brave(susan))&
((creative(paul)|~patient(paul)))&
((generous(mary)<~>~generous(mary))) | ~happy(mary) | [
"p5",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3133771370416257456962792
% SZS output start Proof for 3133771370416257456962792
6. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> (calm(X0) | ~creative(X0))) [input p5]
13. ! [X0] : ((~quiet(X0) | quiet(X0)) <=> ~creative(X0)) [input p12]
22. happy(mary) [input hypothesis]
40. ! [X0] : (((~humble(X0) & ~happy(X0)) | (~calm(X0) & creative(X0))) & ((calm(X0) | ~creative(X0)) | (humble(X0) | happy(X0)))) [nnf transformation 6]
41. ! [X0] : (((~humble(X0) & ~happy(X0)) | (~calm(X0) & creative(X0))) & (calm(X0) | ~creative(X0) | humble(X0) | happy(X0))) [flattening 40]
54. ! [X0] : (((~quiet(X0) | quiet(X0)) | creative(X0)) & (~creative(X0) | (quiet(X0) & ~quiet(X0)))) [nnf transformation 13]
55. ! [X0] : ((~quiet(X0) | quiet(X0) | creative(X0)) & (~creative(X0) | (quiet(X0) & ~quiet(X0)))) [flattening 54]
86. ~happy(X0) | creative(X0) [cnf transformation 41]
102. ~creative(X0) | ~quiet(X0) [cnf transformation 55]
103. ~creative(X0) | quiet(X0) [cnf transformation 55]
122. happy(mary) [cnf transformation 22]
181. ~creative(X0) [subsumption resolution 102,103]
242. creative(mary) [resolution 86,122]
243. $false [subsumption resolution 242,181]
% SZS output end Proof for 3133771370416257456962792
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is either not calm or not old.
Everyone who is not strong is funny and vice versa.
Everyone who is both quiet and not generous is not wise or brave and vice versa.
Everyone who is kind is not quiet.
If someone is not brave then someone is not calm or tall.
If someone is not rich then someone is both brave and kind.
Everyone who is either not happy or not humble is both not creative and not humble and vice versa.
Everyone who is not strong or quiet is tall or not funny.
If someone is both not kind and old then someone is not patient and vice versa.
Everyone who is not patient is patient or not funny and vice versa.
Everyone who is not happy is either old or not wise.
If someone is not tall then someone is either curious or happy and vice versa.
Everyone who is not rich is curious or patient and vice versa.
Everyone who is not brave is not rich.
Someone is both wise and tall.
Someone is not happy.
Alice is both not old and tall.
John is happy. | Alice is not happy. | neutral | (![X]:(calm(X)=>(~calm(X)<~>~old(X))))&
(![X]:(~strong(X)<=>funny(X)))&
(![X]:((quiet(X)&~generous(X))<=>(~wise(X)|brave(X))))&
(![X]:(kind(X)=>~quiet(X)))&
((?[X]:(~brave(X)))=>(?[X]:((~calm(X)|tall(X)))))&
((?[X]:(~rich(X)))=>(?[X]:((brave(X)&kind(X)))))&
(![X]:((~happy(X)<~>~humble(X))<=>(~creative(X)&~humble(X))))&
(![X]:((~strong(X)|quiet(X))=>(tall(X)|~funny(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~patient(X)<=>(patient(X)|~funny(X))))&
(![X]:(~happy(X)=>(old(X)<~>~wise(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((curious(X)<~>happy(X)))))&
(![X]:(~rich(X)<=>(curious(X)|patient(X))))&
(![X]:(~brave(X)=>~rich(X)))&
(?[X]:((wise(X)&tall(X))))&
(?[X]:(~happy(X)))&
((~old(alice)&tall(alice)))&
(happy(john)) | ~happy(alice) | [] | null | 0 |
If someone is both not quiet and not calm then mary is either not humble or not happy.
Everyone who is either quiet or kind is wise or not generous.
Everyone who is not generous is humble or kind and vice versa.
If alice is both calm and rich then alice is both generous and kind.
If someone is both strong and patient then susan is curious and vice versa.
Everyone who is both not happy and curious is both generous and not rich and vice versa.
If fred is both calm and not rich then someone is old and vice versa.
Everyone who is not rich is not curious and vice versa.
Everyone who is not brave or creative is kind or calm and vice versa.
Everyone who is both rich and funny is not curious or wise.
Everyone who is not creative is calm or not calm and vice versa.
If someone is not funny or tall then someone is both strong and not humble and vice versa.
Everyone who is either rich or not calm is both not rich and calm and vice versa.
If susan is not curious then someone is both patient and generous and vice versa.
Everyone who is rich or wise is not brave and vice versa.
If john is both strong and not humble then someone is not brave and vice versa.
Alice is either not happy or not strong.
Lucy is patient or not quiet.
Susan is either not strong or wise.
Mary is not strong.
Alice is kind or happy.
Susan is both quiet and not generous. | Fred is not tall. | neutral | ((?[X]:((~quiet(X)&~calm(X))))=>((~humble(mary)<~>~happy(mary))))&
(![X]:((quiet(X)<~>kind(X))=>(wise(X)|~generous(X))))&
(![X]:(~generous(X)<=>(humble(X)|kind(X))))&
(((calm(alice)&rich(alice)))=>((generous(alice)&kind(alice))))&
((?[X]:((strong(X)&patient(X))))<=>(curious(susan)))&
(![X]:((~happy(X)&curious(X))<=>(generous(X)&~rich(X))))&
(((calm(fred)&~rich(fred)))<=>(?[X]:(old(X))))&
(![X]:(~rich(X)<=>~curious(X)))&
(![X]:((~brave(X)|creative(X))<=>(kind(X)|calm(X))))&
(![X]:((rich(X)&funny(X))=>(~curious(X)|wise(X))))&
(![X]:(~creative(X)<=>(calm(X)|~calm(X))))&
((?[X]:((~funny(X)|tall(X))))<=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:((rich(X)<~>~calm(X))<=>(~rich(X)&calm(X))))&
((~curious(susan))<=>(?[X]:((patient(X)&generous(X)))))&
(![X]:((rich(X)|wise(X))<=>~brave(X)))&
(((strong(john)&~humble(john)))<=>(?[X]:(~brave(X))))&
((~happy(alice)<~>~strong(alice)))&
((patient(lucy)|~quiet(lucy)))&
((~strong(susan)<~>wise(susan)))&
(~strong(mary))&
((kind(alice)|happy(alice)))&
((quiet(susan)&~generous(susan))) | ~tall(fred) | [] | null | 0 |
Everyone who is not kind or tall is both not wise and tall. Everyone who is strong or happy is tall. Everyone who is not creative or kind is either old or not curious and vice versa. Everyone who is either creative or not patient is not strong and vice versa. Everyone who is both creative and not rich is both creative and happy and vice versa. Everyone who is not rich or patient is curious. If alice is not strong then susan is both not happy and quiet and vice versa. If someone is both not creative and not generous then someone is creative. Everyone who is humble is both not wise and not tall. Everyone who is strong is not kind and vice versa. Everyone who is not strong or not happy is both rich and not curious. Everyone who is not kind or not patient is calm or wise and vice versa. Everyone who is brave or generous is tall or not tall and vice versa. If john is either not happy or kind then someone is not rich or not quiet and vice versa. If someone is both curious and not kind then john is not creative. Everyone who is rich is brave and vice versa. Alice is brave. Susan is either old or not brave. Someone is rich or funny. Someone is not creative or not calm. Mary is not generous. Susan is either not quiet or humble. Paul is wise or not old. | Susan is humble. | contradiction | (![X]:((~kind(X)|tall(X))=>(~wise(X)&tall(X))))&
(![X]:((strong(X)|happy(X))=>tall(X)))&
(![X]:((~creative(X)|kind(X))<=>(old(X)<~>~curious(X))))&
(![X]:((creative(X)<~>~patient(X))<=>~strong(X)))&
(![X]:((creative(X)&~rich(X))<=>(creative(X)&happy(X))))&
(![X]:((~rich(X)|patient(X))=>curious(X)))&
((~strong(alice))<=>((~happy(susan)&quiet(susan))))&
((?[X]:((~creative(X)&~generous(X))))=>(?[X]:(creative(X))))&
(![X]:(humble(X)=>(~wise(X)&~tall(X))))&
(![X]:(strong(X)<=>~kind(X)))&
(![X]:((~strong(X)|~happy(X))=>(rich(X)&~curious(X))))&
(![X]:((~kind(X)|~patient(X))<=>(calm(X)|wise(X))))&
(![X]:((brave(X)|generous(X))<=>(tall(X)|~tall(X))))&
(((~happy(john)<~>kind(john)))<=>(?[X]:((~rich(X)|~quiet(X)))))&
((?[X]:((curious(X)&~kind(X))))=>(~creative(john)))&
(![X]:(rich(X)<=>brave(X)))&
(brave(alice))&
((old(susan)<~>~brave(susan)))&
(?[X]:((rich(X)|funny(X))))&
(?[X]:((~creative(X)|~calm(X))))&
(~generous(mary))&
((~quiet(susan)<~>humble(susan)))&
((wise(paul)|~old(paul))) | humble(susan) | [
"p0",
"p1",
"p2",
"p8",
"p10",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5072900649347529043941319
% SZS output start Proof for 5072900649347529043941319
1. ! [X0] : ((tall(X0) | ~kind(X0)) => (tall(X0) & ~wise(X0))) [input p0]
2. ! [X0] : ((happy(X0) | strong(X0)) => tall(X0)) [input p1]
3. ! [X0] : ((kind(X0) | ~creative(X0)) <=> (old(X0) <~> ~curious(X0))) [input p2]
9. ! [X0] : (humble(X0) => (~tall(X0) & ~wise(X0))) [input p8]
11. ! [X0] : ((~happy(X0) | ~strong(X0)) => (~curious(X0) & rich(X0))) [input p10]
16. ! [X0] : (rich(X0) <=> brave(X0)) [input p15]
18. old(susan) <~> ~brave(susan) [input p17]
24. humble(susan) [input hypothesis]
27. ! [X0] : ((tall(X0) & ~wise(X0)) | (~tall(X0) & kind(X0))) [ennf transformation 1]
28. ! [X0] : (tall(X0) | (~happy(X0) & ~strong(X0))) [ennf transformation 2]
31. ! [X0] : ((~tall(X0) & ~wise(X0)) | ~humble(X0)) [ennf transformation 9]
32. ! [X0] : ((~curious(X0) & rich(X0)) | (happy(X0) & strong(X0))) [ennf transformation 11]
34. ! [X0] : (((kind(X0) | ~creative(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) & (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~kind(X0) & creative(X0)))) [nnf transformation 3]
35. ! [X0] : ((kind(X0) | ~creative(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0)))) & (((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~kind(X0) & creative(X0)))) [flattening 34]
53. ! [X0] : ((rich(X0) | ~brave(X0)) & (brave(X0) | ~rich(X0))) [nnf transformation 16]
54. (brave(susan) | ~old(susan)) & (~brave(susan) | old(susan)) [nnf transformation 18]
60. tall(X0) | kind(X0) [cnf transformation 27]
63. ~happy(X0) | tall(X0) [cnf transformation 28]
67. ~old(X0) | curious(X0) | ~kind(X0) [cnf transformation 35]
85. ~humble(X0) | ~tall(X0) [cnf transformation 31]
89. rich(X0) | happy(X0) [cnf transformation 32]
91. ~curious(X0) | happy(X0) [cnf transformation 32]
107. ~rich(X0) | brave(X0) [cnf transformation 53]
110. ~brave(susan) | old(susan) [cnf transformation 54]
117. humble(susan) [cnf transformation 24]
119. 1 <=> happy(susan) [avatar definition]
120. ~happy(susan) <- (~1) [avatar component clause 119]
121. happy(susan) <- (1) [avatar component clause 119]
181. 14 <=> old(susan) [avatar definition]
182. old(susan) <- (14) [avatar component clause 181]
185. 15 <=> brave(susan) [avatar definition]
186. ~brave(susan) <- (~15) [avatar component clause 185]
189. 14 | ~15 [avatar split clause 110,185,181]
200. 18 <=> humble(susan) [avatar definition]
201. humble(susan) <- (18) [avatar component clause 200]
214. 18 [avatar split clause 117,200]
216. ~tall(susan) <- (18) [resolution 85,201]
217. kind(susan) <- (18) [resolution 216,60]
221. brave(X0) | happy(X0) [resolution 107,89]
230. happy(susan) <- (~15) [resolution 221,186]
232. $false <- (~1, ~15) [subsumption resolution 230,120]
233. 1 | 15 [avatar contradiction clause 232]
242. 22 <=> curious(susan) [avatar definition]
244. curious(susan) <- (22) [avatar component clause 242]
246. tall(susan) <- (1) [resolution 121,63]
247. $false <- (1, 18) [subsumption resolution 246,216]
248. ~1 | ~18 [avatar contradiction clause 247]
252. curious(susan) | ~kind(susan) <- (14) [resolution 67,182]
253. curious(susan) <- (14, 18) [subsumption resolution 252,217]
254. 22 | ~14 | ~18 [avatar split clause 253,200,181,242]
257. happy(susan) <- (22) [resolution 244,91]
259. $false <- (~1, 22) [subsumption resolution 257,120]
260. 1 | ~22 [avatar contradiction clause 259]
261. $false [avatar sat refutation 189,214,233,248,254,260]
% SZS output end Proof for 5072900649347529043941319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not calm is not patient. Everyone who is humble or quiet is both tall and calm. Everyone who is both not old and happy is both funny and humble. If lucy is not strong or not curious then fred is either not wise or not generous. If susan is either generous or not tall then someone is not humble or rich. Everyone who is old is either not generous or funny and vice versa. If someone is rich or not calm then someone is both calm and not funny and vice versa. If someone is not strong then someone is both funny and not humble. Everyone who is both rich and wise is either generous or funny and vice versa. Everyone who is either not kind or old is humble and vice versa. Everyone who is either kind or tall is both not kind and not generous. If alice is not curious then fred is both not brave and not creative and vice versa. If john is either not happy or not strong then paul is not funny or not calm. If lucy is not quiet then lucy is funny or patient and vice versa. Everyone who is either strong or generous is not strong and vice versa. Everyone who is curious is not kind and vice versa. Fred is both curious and not calm. John is patient or not funny. John is not strong. Someone is funny or creative. Mary is either happy or quiet. Someone is not wise or not creative. | Lucy is not generous. | contradiction | (![X]:((~creative(X)|~calm(X))=>~patient(X)))&
(![X]:((humble(X)|quiet(X))=>(tall(X)&calm(X))))&
(![X]:((~old(X)&happy(X))=>(funny(X)&humble(X))))&
(((~strong(lucy)|~curious(lucy)))=>((~wise(fred)<~>~generous(fred))))&
(((generous(susan)<~>~tall(susan)))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:(old(X)<=>(~generous(X)<~>funny(X))))&
((?[X]:((rich(X)|~calm(X))))<=>(?[X]:((calm(X)&~funny(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((funny(X)&~humble(X)))))&
(![X]:((rich(X)&wise(X))<=>(generous(X)<~>funny(X))))&
(![X]:((~kind(X)<~>old(X))<=>humble(X)))&
(![X]:((kind(X)<~>tall(X))=>(~kind(X)&~generous(X))))&
((~curious(alice))<=>((~brave(fred)&~creative(fred))))&
(((~happy(john)<~>~strong(john)))=>((~funny(paul)|~calm(paul))))&
((~quiet(lucy))<=>((funny(lucy)|patient(lucy))))&
(![X]:((strong(X)<~>generous(X))<=>~strong(X)))&
(![X]:(curious(X)<=>~kind(X)))&
((curious(fred)&~calm(fred)))&
((patient(john)|~funny(john)))&
(~strong(john))&
(?[X]:((funny(X)|creative(X))))&
((happy(mary)<~>quiet(mary)))&
(?[X]:((~wise(X)|~creative(X)))) | ~generous(lucy) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3178888320699509312969120
% SZS output start Proof for 3178888320699509312969120
15. ! [X0] : ((strong(X0) <~> generous(X0)) <=> ~strong(X0)) [input p14]
23. ~generous(lucy) [input hypothesis]
58. ! [X0] : ((((~generous(X0) | ~strong(X0)) & (generous(X0) | strong(X0))) | strong(X0)) & (~strong(X0) | ((strong(X0) | ~generous(X0)) & (generous(X0) | ~strong(X0))))) [nnf transformation 15]
112. ~strong(X0) | generous(X0) | ~strong(X0) [cnf transformation 58]
114. generous(X0) | strong(X0) | strong(X0) [cnf transformation 58]
126. ~generous(lucy) [cnf transformation 23]
127. ~strong(X0) | generous(X0) [duplicate literal removal 112]
128. generous(X0) | strong(X0) [duplicate literal removal 114]
259. generous(X0) [subsumption resolution 127,128]
298. $false [subsumption resolution 126,259]
% SZS output end Proof for 3178888320699509312969120
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or curious is both quiet and not creative.
If fred is either not kind or not rich then alice is either not tall or patient.
Everyone who is both not tall and calm is brave or not rich and vice versa.
If paul is tall then alice is both curious and wise and vice versa.
Everyone who is tall or humble is kind or creative and vice versa.
Everyone who is old is either rich or funny and vice versa.
Everyone who is both not happy and brave is wise or not tall.
Everyone who is both not kind and not generous is both creative and not wise.
Everyone who is both generous and humble is both old and not brave.
Everyone who is either not curious or tall is not calm or calm.
Everyone who is funny is either calm or brave and vice versa.
If someone is both not quiet and tall then someone is calm.
Everyone who is curious or not funny is creative or not happy and vice versa.
If someone is either calm or not kind then alice is both not generous and old.
If someone is not calm or not old then someone is patient.
Someone is either not rich or creative.
Paul is not rich.
John is both not creative and not curious.
Paul is brave or not happy.
Lucy is both not quiet and not brave.
Someone is either not brave or not generous.
Fred is generous.
John is either not tall or generous. | Alice is not funny. | neutral | (![X]:((~happy(X)|curious(X))=>(quiet(X)&~creative(X))))&
(((~kind(fred)<~>~rich(fred)))=>((~tall(alice)<~>patient(alice))))&
(![X]:((~tall(X)&calm(X))<=>(brave(X)|~rich(X))))&
((tall(paul))<=>((curious(alice)&wise(alice))))&
(![X]:((tall(X)|humble(X))<=>(kind(X)|creative(X))))&
(![X]:(old(X)<=>(rich(X)<~>funny(X))))&
(![X]:((~happy(X)&brave(X))=>(wise(X)|~tall(X))))&
(![X]:((~kind(X)&~generous(X))=>(creative(X)&~wise(X))))&
(![X]:((generous(X)&humble(X))=>(old(X)&~brave(X))))&
(![X]:((~curious(X)<~>tall(X))=>(~calm(X)|calm(X))))&
(![X]:(funny(X)<=>(calm(X)<~>brave(X))))&
((?[X]:((~quiet(X)&tall(X))))=>(?[X]:(calm(X))))&
(![X]:((curious(X)|~funny(X))<=>(creative(X)|~happy(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((~generous(alice)&old(alice))))&
((?[X]:((~calm(X)|~old(X))))=>(?[X]:(patient(X))))&
(?[X]:((~rich(X)<~>creative(X))))&
(~rich(paul))&
((~creative(john)&~curious(john)))&
((brave(paul)|~happy(paul)))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(generous(fred))&
((~tall(john)<~>generous(john))) | ~funny(alice) | [] | null | 0 |
Everyone who is brave or not tall is either not quiet or wise and vice versa. If fred is both not creative and quiet then alice is both not calm and creative and vice versa. Everyone who is not quiet is not strong and vice versa. If someone is not creative then alice is either not strong or old. If someone is either calm or quiet then lucy is not generous. Everyone who is either rich or not brave is both humble and not creative. If fred is old or not humble then susan is either generous or curious. Everyone who is not creative or kind is not calm or not creative and vice versa. Everyone who is either brave or not happy is both not wise and not rich. If someone is not calm then lucy is either curious or not calm. Everyone who is rich or not strong is either not kind or kind and vice versa. If someone is either not strong or not wise then someone is either not wise or not tall. Everyone who is both not rich and not happy is either not brave or not funny and vice versa. If lucy is both not wise and wise then paul is either not generous or not funny and vice versa. If someone is not curious then someone is not brave or not patient and vice versa. If paul is tall or not kind then someone is old and vice versa. Someone is not rich or not creative. Someone is not funny or patient. Paul is strong. Alice is not old. Someone is both humble and quiet. Mary is either brave or strong. Mary is brave or not calm. Someone is creative or not kind. | Paul is rich. | entailment | (![X]:((brave(X)|~tall(X))<=>(~quiet(X)<~>wise(X))))&
(((~creative(fred)&quiet(fred)))<=>((~calm(alice)&creative(alice))))&
(![X]:(~quiet(X)<=>~strong(X)))&
((?[X]:(~creative(X)))=>((~strong(alice)<~>old(alice))))&
((?[X]:((calm(X)<~>quiet(X))))=>(~generous(lucy)))&
(![X]:((rich(X)<~>~brave(X))=>(humble(X)&~creative(X))))&
(((old(fred)|~humble(fred)))=>((generous(susan)<~>curious(susan))))&
(![X]:((~creative(X)|kind(X))<=>(~calm(X)|~creative(X))))&
(![X]:((brave(X)<~>~happy(X))=>(~wise(X)&~rich(X))))&
((?[X]:(~calm(X)))=>((curious(lucy)<~>~calm(lucy))))&
(![X]:((rich(X)|~strong(X))<=>(~kind(X)<~>kind(X))))&
((?[X]:((~strong(X)<~>~wise(X))))=>(?[X]:((~wise(X)<~>~tall(X)))))&
(![X]:((~rich(X)&~happy(X))<=>(~brave(X)<~>~funny(X))))&
(((~wise(lucy)&wise(lucy)))<=>((~generous(paul)<~>~funny(paul))))&
((?[X]:(~curious(X)))<=>(?[X]:((~brave(X)|~patient(X)))))&
(((tall(paul)|~kind(paul)))<=>(?[X]:(old(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((~funny(X)|patient(X))))&
(strong(paul))&
(~old(alice))&
(?[X]:((humble(X)&quiet(X))))&
((brave(mary)<~>strong(mary)))&
((brave(mary)|~calm(mary)))&
(?[X]:((creative(X)|~kind(X)))) | rich(paul) | [
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7176304782436501184302281
% SZS output start Proof for 7176304782436501184302281
11. ! [X0] : ((~strong(X0) | rich(X0)) <=> (~kind(X0) <~> kind(X0))) [input p10]
19. strong(paul) [input p18]
25. ~rich(paul) [input hypothesis]
51. ! [X0] : (((~strong(X0) | rich(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (strong(X0) & ~rich(X0)))) [nnf transformation 11]
52. ! [X0] : ((~strong(X0) | rich(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (strong(X0) & ~rich(X0)))) [flattening 51]
114. ~strong(X0) | rich(X0) | kind(X0) | kind(X0) [cnf transformation 52]
115. ~strong(X0) | rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 52]
140. strong(paul) [cnf transformation 19]
147. ~rich(paul) [cnf transformation 25]
148. ~strong(X0) | rich(X0) | kind(X0) [duplicate literal removal 114]
149. ~strong(X0) | rich(X0) | ~kind(X0) [duplicate literal removal 115]
222. ~strong(X0) | rich(X0) [subsumption resolution 148,149]
346. rich(paul) [resolution 222,140]
347. $false [subsumption resolution 346,147]
% SZS output end Proof for 7176304782436501184302281
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not tall is not curious and vice versa.
Everyone who is not humble is rich.
If lucy is either not tall or funny then mary is not rich or kind.
If someone is not kind then fred is both not funny and kind.
If mary is both not humble and not strong then paul is either curious or not wise and vice versa.
Everyone who is both wise and not humble is either not patient or not kind.
Everyone who is either rich or tall is both not brave and humble and vice versa.
If someone is either happy or wise then someone is not curious and vice versa.
Everyone who is happy is patient or calm and vice versa.
If lucy is calm then someone is not calm and vice versa.
If paul is both not creative and not strong then alice is not quiet and vice versa.
If susan is both kind and not funny then susan is creative.
If someone is not quiet then someone is not quiet or humble and vice versa.
If lucy is wise or old then susan is either not curious or not old.
If susan is generous then someone is rich.
Everyone who is either not happy or not creative is not calm and vice versa.
Someone is both rich and strong.
Lucy is not happy or quiet.
Lucy is both old and not strong.
Someone is either brave or not rich.
Lucy is kind.
Someone is either not calm or tall.
Someone is both not humble and calm. | Mary is rich. | neutral | (![X]:((rich(X)<~>~tall(X))<=>~curious(X)))&
(![X]:(~humble(X)=>rich(X)))&
(((~tall(lucy)<~>funny(lucy)))=>((~rich(mary)|kind(mary))))&
((?[X]:(~kind(X)))=>((~funny(fred)&kind(fred))))&
(((~humble(mary)&~strong(mary)))<=>((curious(paul)<~>~wise(paul))))&
(![X]:((wise(X)&~humble(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((rich(X)<~>tall(X))<=>(~brave(X)&humble(X))))&
((?[X]:((happy(X)<~>wise(X))))<=>(?[X]:(~curious(X))))&
(![X]:(happy(X)<=>(patient(X)|calm(X))))&
((calm(lucy))<=>(?[X]:(~calm(X))))&
(((~creative(paul)&~strong(paul)))<=>(~quiet(alice)))&
(((kind(susan)&~funny(susan)))=>(creative(susan)))&
((?[X]:(~quiet(X)))<=>(?[X]:((~quiet(X)|humble(X)))))&
(((wise(lucy)|old(lucy)))=>((~curious(susan)<~>~old(susan))))&
((generous(susan))=>(?[X]:(rich(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>~calm(X)))&
(?[X]:((rich(X)&strong(X))))&
((~happy(lucy)|quiet(lucy)))&
((old(lucy)&~strong(lucy)))&
(?[X]:((brave(X)<~>~rich(X))))&
(kind(lucy))&
(?[X]:((~calm(X)<~>tall(X))))&
(?[X]:((~humble(X)&calm(X)))) | rich(mary) | [] | null | 0 |
Everyone who is calm is tall and vice versa.
Everyone who is calm is generous.
Everyone who is wise is not curious and vice versa.
If someone is not happy or not tall then alice is not strong.
Everyone who is both funny and happy is both not curious and strong.
If susan is calm or not kind then someone is creative and vice versa.
If lucy is happy or strong then susan is generous or curious and vice versa.
Everyone who is both not creative and rich is quiet or humble.
Everyone who is both humble and creative is strong or brave.
Everyone who is not generous is not happy and vice versa.
If lucy is wise or not strong then someone is creative and vice versa.
If paul is both tall and humble then mary is curious.
If fred is either not quiet or not creative then susan is both generous and humble and vice versa.
If someone is generous or not old then someone is calm.
If alice is not quiet then paul is either calm or old and vice versa.
If fred is both not wise and strong then someone is not wise or rich and vice versa.
Someone is both curious and not quiet.
Mary is calm or not kind.
Susan is kind.
Paul is wise.
Mary is not wise.
Alice is brave or not quiet.
Mary is either not quiet or not wise. | Susan is not kind. | contradiction | (![X]:(calm(X)<=>tall(X)))&
(![X]:(calm(X)=>generous(X)))&
(![X]:(wise(X)<=>~curious(X)))&
((?[X]:((~happy(X)|~tall(X))))=>(~strong(alice)))&
(![X]:((funny(X)&happy(X))=>(~curious(X)&strong(X))))&
(((calm(susan)|~kind(susan)))<=>(?[X]:(creative(X))))&
(((happy(lucy)|strong(lucy)))<=>((generous(susan)|curious(susan))))&
(![X]:((~creative(X)&rich(X))=>(quiet(X)|humble(X))))&
(![X]:((humble(X)&creative(X))=>(strong(X)|brave(X))))&
(![X]:(~generous(X)<=>~happy(X)))&
(((wise(lucy)|~strong(lucy)))<=>(?[X]:(creative(X))))&
(((tall(paul)&humble(paul)))=>(curious(mary)))&
(((~quiet(fred)<~>~creative(fred)))<=>((generous(susan)&humble(susan))))&
((?[X]:((generous(X)|~old(X))))=>(?[X]:(calm(X))))&
((~quiet(alice))<=>((calm(paul)<~>old(paul))))&
(((~wise(fred)&strong(fred)))<=>(?[X]:((~wise(X)|rich(X)))))&
(?[X]:((curious(X)&~quiet(X))))&
((calm(mary)|~kind(mary)))&
(kind(susan))&
(wise(paul))&
(~wise(mary))&
((brave(alice)|~quiet(alice)))&
((~quiet(mary)<~>~wise(mary))) | ~kind(susan) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7949715704266631407482313
% SZS output start Proof for 7949715704266631407482313
19. kind(susan) [input p18]
24. ~kind(susan) [input hypothesis]
106. kind(susan) [cnf transformation 19]
111. ~kind(susan) [cnf transformation 24]
132. 6 <=> kind(susan) [avatar definition]
268. 6 [avatar split clause 106,132]
270. ~6 [avatar split clause 111,132]
271. $false [avatar sat refutation 268,270]
% SZS output end Proof for 7949715704266631407482313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not funny or not generous then paul is both not patient and not tall and vice versa.
If someone is calm then fred is funny.
Everyone who is either funny or not happy is funny or not old and vice versa.
Everyone who is either not creative or not wise is not patient.
If someone is both calm and not humble then someone is either quiet or creative and vice versa.
If someone is both not creative and not tall then someone is not patient or quiet and vice versa.
Everyone who is either not curious or quiet is either funny or happy and vice versa.
Everyone who is both humble and not old is both not curious and not kind and vice versa.
If someone is either quiet or curious then someone is both quiet and not quiet and vice versa.
If alice is either not quiet or old then someone is either not wise or not strong and vice versa.
If someone is both creative and strong then someone is not brave.
If fred is wise or not funny then someone is not old or rich and vice versa.
If someone is either kind or curious then john is wise or not creative.
Everyone who is not brave is both not patient and not calm.
If someone is either not humble or brave then someone is both not funny and generous and vice versa.
Everyone who is not kind is both not happy and calm and vice versa.
Lucy is patient.
Susan is humble or strong.
John is not creative.
Someone is not funny or not old.
Paul is old or funny. | Paul is happy. | entailment | ((?[X]:((~funny(X)<~>~generous(X))))<=>((~patient(paul)&~tall(paul))))&
((?[X]:(calm(X)))=>(funny(fred)))&
(![X]:((funny(X)<~>~happy(X))<=>(funny(X)|~old(X))))&
(![X]:((~creative(X)<~>~wise(X))=>~patient(X)))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
((?[X]:((~creative(X)&~tall(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~curious(X)<~>quiet(X))<=>(funny(X)<~>happy(X))))&
(![X]:((humble(X)&~old(X))<=>(~curious(X)&~kind(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(((~quiet(alice)<~>old(alice)))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((creative(X)&strong(X))))=>(?[X]:(~brave(X))))&
(((wise(fred)|~funny(fred)))<=>(?[X]:((~old(X)|rich(X)))))&
((?[X]:((kind(X)<~>curious(X))))=>((wise(john)|~creative(john))))&
(![X]:(~brave(X)=>(~patient(X)&~calm(X))))&
((?[X]:((~humble(X)<~>brave(X))))<=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:(~kind(X)<=>(~happy(X)&calm(X))))&
(patient(lucy))&
((humble(susan)|strong(susan)))&
(~creative(john))&
(?[X]:((~funny(X)|~old(X))))&
((old(paul)|funny(paul))) | happy(paul) | [
"p2",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6454320143325720890538667
% SZS output start Proof for 6454320143325720890538667
3. ! [X0] : ((funny(X0) <~> ~happy(X0)) <=> (~old(X0) | funny(X0))) [input p2]
21. funny(paul) | old(paul) [input p20]
22. ~happy(paul) [input hypothesis]
39. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (old(X0) & ~funny(X0))) & ((~old(X0) | funny(X0)) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [nnf transformation 3]
40. ! [X0] : ((((happy(X0) | ~funny(X0)) & (~happy(X0) | funny(X0))) | (old(X0) & ~funny(X0))) & (~old(X0) | funny(X0) | ((funny(X0) | happy(X0)) & (~happy(X0) | ~funny(X0))))) [flattening 39]
90. ~old(X0) | funny(X0) | funny(X0) | happy(X0) [cnf transformation 40]
93. happy(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 40]
156. funny(paul) | old(paul) [cnf transformation 21]
157. ~happy(paul) [cnf transformation 22]
158. ~old(X0) | funny(X0) | happy(X0) [duplicate literal removal 90]
159. ~funny(X0) | happy(X0) [duplicate literal removal 93]
196. ~old(X0) | happy(X0) [subsumption resolution 158,159]
400. 53 <=> old(paul) [avatar definition]
402. old(paul) <- (53) [avatar component clause 400]
404. 54 <=> funny(paul) [avatar definition]
406. funny(paul) <- (54) [avatar component clause 404]
407. 53 | 54 [avatar split clause 156,404,400]
409. happy(paul) <- (53) [resolution 196,402]
410. $false <- (53) [subsumption resolution 409,157]
411. ~53 [avatar contradiction clause 410]
412. happy(paul) <- (54) [resolution 406,159]
413. $false <- (54) [subsumption resolution 412,157]
414. ~54 [avatar contradiction clause 413]
415. $false [avatar sat refutation 407,411,414]
% SZS output end Proof for 6454320143325720890538667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is either tall or not calm then someone is either strong or not humble. If john is rich or patient then john is kind or happy and vice versa. If someone is not tall then susan is curious and vice versa. Everyone who is either not humble or not quiet is either not generous or funny and vice versa. If someone is both wise and quiet then someone is funny and vice versa. If alice is either not wise or rich then lucy is either quiet or not happy. If someone is either not generous or not strong then lucy is both not strong and not funny. If mary is both not happy and not curious then lucy is either rich or generous. Everyone who is strong is both not happy and generous. Everyone who is both not brave and not rich is either not patient or wise. If someone is either happy or not curious then fred is humble or not patient and vice versa. Everyone who is strong is either not patient or brave. If john is not creative then paul is both strong and creative and vice versa. If john is quiet or strong then alice is not old or not creative and vice versa. Everyone who is both kind and generous is either happy or not calm. Everyone who is tall is not strong. John is both not strong and curious. Susan is either not brave or generous. John is either brave or kind. Alice is either happy or not tall. Paul is both not rich and calm. Someone is both funny and not wise. John is quiet. | John is not curious. | contradiction | ((?[X]:((tall(X)<~>~calm(X))))=>(?[X]:((strong(X)<~>~humble(X)))))&
(((rich(john)|patient(john)))<=>((kind(john)|happy(john))))&
((?[X]:(~tall(X)))<=>(curious(susan)))&
(![X]:((~humble(X)<~>~quiet(X))<=>(~generous(X)<~>funny(X))))&
((?[X]:((wise(X)&quiet(X))))<=>(?[X]:(funny(X))))&
(((~wise(alice)<~>rich(alice)))=>((quiet(lucy)<~>~happy(lucy))))&
((?[X]:((~generous(X)<~>~strong(X))))=>((~strong(lucy)&~funny(lucy))))&
(((~happy(mary)&~curious(mary)))=>((rich(lucy)<~>generous(lucy))))&
(![X]:(strong(X)=>(~happy(X)&generous(X))))&
(![X]:((~brave(X)&~rich(X))=>(~patient(X)<~>wise(X))))&
((?[X]:((happy(X)<~>~curious(X))))<=>((humble(fred)|~patient(fred))))&
(![X]:(strong(X)=>(~patient(X)<~>brave(X))))&
((~creative(john))<=>((strong(paul)&creative(paul))))&
(((quiet(john)|strong(john)))<=>((~old(alice)|~creative(alice))))&
(![X]:((kind(X)&generous(X))=>(happy(X)<~>~calm(X))))&
(![X]:(tall(X)=>~strong(X)))&
((~strong(john)&curious(john)))&
((~brave(susan)<~>generous(susan)))&
((brave(john)<~>kind(john)))&
((happy(alice)<~>~tall(alice)))&
((~rich(paul)&calm(paul)))&
(?[X]:((funny(X)&~wise(X))))&
(quiet(john)) | ~curious(john) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 624537402471891194979457
% SZS output start Proof for 624537402471891194979457
17. curious(john) & ~strong(john) [input p16]
24. ~curious(john) [input hypothesis]
129. curious(john) [cnf transformation 17]
141. ~curious(john) [cnf transformation 24]
362. $false [subsumption resolution 141,129]
% SZS output end Proof for 624537402471891194979457
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and not humble is either funny or not humble.
If someone is both not happy and tall then someone is not humble.
Everyone who is both calm and not quiet is strong.
Everyone who is curious or funny is either not old or not patient and vice versa.
Everyone who is either tall or not kind is not generous and vice versa.
If someone is both quiet and not kind then alice is humble or old.
Everyone who is both not old and brave is not happy or not generous and vice versa.
If someone is not happy then someone is patient or not old.
Everyone who is brave is both generous and creative.
Everyone who is both brave and not humble is either not humble or kind and vice versa.
Everyone who is either not kind or not generous is either funny or creative.
If mary is generous then mary is quiet and vice versa.
Everyone who is humble is not rich or brave.
If someone is both not curious and rich then someone is either not rich or humble and vice versa.
If lucy is either not creative or old then alice is not strong or not funny.
If someone is not creative or old then john is either old or patient and vice versa.
Someone is creative.
Someone is not rich or not creative.
Someone is humble.
Fred is both not creative and not funny.
Someone is both strong and not patient.
Susan is strong.
Lucy is either tall or not patient.
Alice is wise. | Fred is not kind. | contradiction | (![X]:((~calm(X)&~humble(X))=>(funny(X)<~>~humble(X))))&
((?[X]:((~happy(X)&tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((calm(X)&~quiet(X))=>strong(X)))&
(![X]:((curious(X)|funny(X))<=>(~old(X)<~>~patient(X))))&
(![X]:((tall(X)<~>~kind(X))<=>~generous(X)))&
((?[X]:((quiet(X)&~kind(X))))=>((humble(alice)|old(alice))))&
(![X]:((~old(X)&brave(X))<=>(~happy(X)|~generous(X))))&
((?[X]:(~happy(X)))=>(?[X]:((patient(X)|~old(X)))))&
(![X]:(brave(X)=>(generous(X)&creative(X))))&
(![X]:((brave(X)&~humble(X))<=>(~humble(X)<~>kind(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(funny(X)<~>creative(X))))&
((generous(mary))<=>(quiet(mary)))&
(![X]:(humble(X)=>(~rich(X)|brave(X))))&
((?[X]:((~curious(X)&rich(X))))<=>(?[X]:((~rich(X)<~>humble(X)))))&
(((~creative(lucy)<~>old(lucy)))=>((~strong(alice)|~funny(alice))))&
((?[X]:((~creative(X)|old(X))))<=>((old(john)<~>patient(john))))&
(?[X]:(creative(X)))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:(humble(X)))&
((~creative(fred)&~funny(fred)))&
(?[X]:((strong(X)&~patient(X))))&
(strong(susan))&
((tall(lucy)<~>~patient(lucy)))&
(wise(alice)) | ~kind(fred) | [
"p6",
"p8",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 242543740524611776860132
% SZS output start Proof for 242543740524611776860132
7. ! [X0] : ((brave(X0) & ~old(X0)) <=> (~generous(X0) | ~happy(X0))) [input p6]
9. ! [X0] : (brave(X0) => (creative(X0) & generous(X0))) [input p8]
11. ! [X0] : ((~kind(X0) <~> ~generous(X0)) => (funny(X0) <~> creative(X0))) [input p10]
20. ~funny(fred) & ~creative(fred) [input p19]
25. ~kind(fred) [input hypothesis]
38. ! [X0] : ((creative(X0) & generous(X0)) | ~brave(X0)) [ennf transformation 9]
39. ! [X0] : ((funny(X0) <~> creative(X0)) | (~kind(X0) <=> ~generous(X0))) [ennf transformation 11]
51. ! [X0] : (((brave(X0) & ~old(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (~brave(X0) | old(X0)))) [nnf transformation 7]
52. ! [X0] : (((brave(X0) & ~old(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | ~brave(X0) | old(X0))) [flattening 51]
58. ! [X0] : (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | ((~kind(X0) | generous(X0)) & (~generous(X0) | kind(X0)))) [nnf transformation 39]
98. brave(X0) | generous(X0) [cnf transformation 52]
100. generous(X0) | ~brave(X0) [cnf transformation 38]
108. creative(X0) | funny(X0) | ~generous(X0) | kind(X0) [cnf transformation 58]
132. ~creative(fred) [cnf transformation 20]
133. ~funny(fred) [cnf transformation 20]
139. ~kind(fred) [cnf transformation 25]
175. generous(X0) [subsumption resolution 100,98]
178. creative(X0) | funny(X0) | kind(X0) [subsumption resolution 108,175]
327. funny(fred) | kind(fred) [resolution 178,132]
331. kind(fred) [subsumption resolution 327,133]
332. $false [subsumption resolution 331,139]
% SZS output end Proof for 242543740524611776860132
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or creative is not calm and vice versa. Everyone who is both patient and humble is creative and vice versa. If someone is not quiet then someone is either strong or not generous. Everyone who is quiet or not strong is both quiet and calm and vice versa. Everyone who is both not kind and happy is not creative and vice versa. Everyone who is both funny and not curious is wise and vice versa. Everyone who is not old is quiet. Everyone who is either not happy or not wise is not rich or old and vice versa. If fred is not brave then someone is not creative or not funny and vice versa. If fred is either not wise or old then someone is both not funny and not tall. Everyone who is old is not wise or not patient. If lucy is either not patient or not creative then someone is brave or wise and vice versa. Everyone who is not rich is not humble or strong and vice versa. If paul is not strong then mary is not funny or not happy. Everyone who is not creative or not curious is both not strong and not patient and vice versa. If paul is either not curious or humble then someone is generous. Lucy is either patient or not patient. Someone is either strong or not tall. Alice is tall. Alice is either not patient or not calm. Alice is creative. Lucy is happy or not kind. | Alice is strong. | entailment | (![X]:((~creative(X)|creative(X))<=>~calm(X)))&
(![X]:((patient(X)&humble(X))<=>creative(X)))&
((?[X]:(~quiet(X)))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((quiet(X)|~strong(X))<=>(quiet(X)&calm(X))))&
(![X]:((~kind(X)&happy(X))<=>~creative(X)))&
(![X]:((funny(X)&~curious(X))<=>wise(X)))&
(![X]:(~old(X)=>quiet(X)))&
(![X]:((~happy(X)<~>~wise(X))<=>(~rich(X)|old(X))))&
((~brave(fred))<=>(?[X]:((~creative(X)|~funny(X)))))&
(((~wise(fred)<~>old(fred)))=>(?[X]:((~funny(X)&~tall(X)))))&
(![X]:(old(X)=>(~wise(X)|~patient(X))))&
(((~patient(lucy)<~>~creative(lucy)))<=>(?[X]:((brave(X)|wise(X)))))&
(![X]:(~rich(X)<=>(~humble(X)|strong(X))))&
((~strong(paul))=>((~funny(mary)|~happy(mary))))&
(![X]:((~creative(X)|~curious(X))<=>(~strong(X)&~patient(X))))&
(((~curious(paul)<~>humble(paul)))=>(?[X]:(generous(X))))&
((patient(lucy)<~>~patient(lucy)))&
(?[X]:((strong(X)<~>~tall(X))))&
(tall(alice))&
((~patient(alice)<~>~calm(alice)))&
(creative(alice))&
((happy(lucy)|~kind(lucy))) | strong(alice) | [
"p0",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 848808047439714065142197
% SZS output start Proof for 848808047439714065142197
1. ! [X0] : ((creative(X0) | ~creative(X0)) <=> ~calm(X0)) [input p0]
4. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (calm(X0) & quiet(X0))) [input p3]
23. ~strong(alice) [input hypothesis]
33. ! [X0] : (((creative(X0) | ~creative(X0)) | calm(X0)) & (~calm(X0) | (~creative(X0) & creative(X0)))) [nnf transformation 1]
34. ! [X0] : ((creative(X0) | ~creative(X0) | calm(X0)) & (~calm(X0) | (~creative(X0) & creative(X0)))) [flattening 33]
41. ! [X0] : (((~strong(X0) | quiet(X0)) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | (strong(X0) & ~quiet(X0)))) [nnf transformation 4]
42. ! [X0] : ((~strong(X0) | quiet(X0) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | (strong(X0) & ~quiet(X0)))) [flattening 41]
72. ~calm(X0) | creative(X0) [cnf transformation 34]
73. ~calm(X0) | ~creative(X0) [cnf transformation 34]
83. calm(X0) | strong(X0) [cnf transformation 42]
132. ~strong(alice) [cnf transformation 23]
133. ~calm(X0) [subsumption resolution 72,73]
147. strong(X0) [subsumption resolution 83,133]
246. $false [subsumption resolution 132,147]
% SZS output end Proof for 848808047439714065142197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not strong and creative.
If lucy is both patient and not strong then someone is not old or strong.
Everyone who is either not creative or not wise is not patient.
If someone is either quiet or curious then someone is both not brave and curious.
If lucy is not tall or not generous then mary is funny and vice versa.
If mary is both tall and old then someone is both not wise and brave and vice versa.
Everyone who is both not quiet and old is either quiet or not happy and vice versa.
Everyone who is both not curious and not happy is either rich or strong and vice versa.
Everyone who is wise is both brave and happy and vice versa.
If paul is either strong or not curious then alice is both not tall and brave and vice versa.
Everyone who is both old and humble is either wise or patient.
Everyone who is not old is not creative or not brave and vice versa.
If susan is either tall or not curious then susan is both generous and kind.
Everyone who is old is not funny.
If mary is either happy or not curious then someone is both brave and not tall.
Everyone who is either humble or not strong is kind and vice versa.
Someone is both not funny and strong.
Mary is either not humble or not curious.
Someone is not tall or not quiet.
Someone is either not wise or not funny.
Paul is either humble or not strong.
Someone is not generous.
John is both creative and not curious.
Paul is both happy and not curious. | Paul is not quiet. | entailment | (![X]:(~creative(X)=>(~strong(X)&creative(X))))&
(((patient(lucy)&~strong(lucy)))=>(?[X]:((~old(X)|strong(X)))))&
(![X]:((~creative(X)<~>~wise(X))=>~patient(X)))&
((?[X]:((quiet(X)<~>curious(X))))=>(?[X]:((~brave(X)&curious(X)))))&
(((~tall(lucy)|~generous(lucy)))<=>(funny(mary)))&
(((tall(mary)&old(mary)))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((~quiet(X)&old(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((~curious(X)&~happy(X))<=>(rich(X)<~>strong(X))))&
(![X]:(wise(X)<=>(brave(X)&happy(X))))&
(((strong(paul)<~>~curious(paul)))<=>((~tall(alice)&brave(alice))))&
(![X]:((old(X)&humble(X))=>(wise(X)<~>patient(X))))&
(![X]:(~old(X)<=>(~creative(X)|~brave(X))))&
(((tall(susan)<~>~curious(susan)))=>((generous(susan)&kind(susan))))&
(![X]:(old(X)=>~funny(X)))&
(((happy(mary)<~>~curious(mary)))=>(?[X]:((brave(X)&~tall(X)))))&
(![X]:((humble(X)<~>~strong(X))<=>kind(X)))&
(?[X]:((~funny(X)&strong(X))))&
((~humble(mary)<~>~curious(mary)))&
(?[X]:((~tall(X)|~quiet(X))))&
(?[X]:((~wise(X)<~>~funny(X))))&
((humble(paul)<~>~strong(paul)))&
(?[X]:(~generous(X)))&
((creative(john)&~curious(john)))&
((happy(paul)&~curious(paul))) | ~quiet(paul) | [
"p6",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8778516750701472386547084
% SZS output start Proof for 8778516750701472386547084
7. ! [X0] : ((old(X0) & ~quiet(X0)) <=> (quiet(X0) <~> ~happy(X0))) [input p6]
24. ~curious(paul) & happy(paul) [input p23]
25. quiet(paul) [input hypothesis]
53. ! [X0] : (((old(X0) & ~quiet(X0)) | ((quiet(X0) | happy(X0)) & (~happy(X0) | ~quiet(X0)))) & (((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) | (~old(X0) | quiet(X0)))) [nnf transformation 7]
54. ! [X0] : (((old(X0) & ~quiet(X0)) | ((quiet(X0) | happy(X0)) & (~happy(X0) | ~quiet(X0)))) & (((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) | ~old(X0) | quiet(X0))) [flattening 53]
98. ~quiet(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 54]
145. happy(paul) [cnf transformation 24]
147. quiet(paul) [cnf transformation 25]
149. ~happy(X0) | ~quiet(X0) [duplicate literal removal 98]
326. ~quiet(paul) [resolution 149,145]
328. $false [subsumption resolution 326,147]
% SZS output end Proof for 8778516750701472386547084
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or brave is either brave or not funny and vice versa. If alice is brave or happy then someone is not generous and vice versa. If paul is either not patient or tall then susan is both not wise and brave and vice versa. If alice is either creative or not happy then lucy is creative or wise. If mary is both not happy and quiet then someone is not tall or curious. Everyone who is both patient and not brave is not funny or not strong and vice versa. If alice is either not kind or not rich then someone is both brave and not funny and vice versa. If someone is tall then someone is either old or not patient. If susan is calm or happy then lucy is calm. Everyone who is either not patient or not brave is curious or not wise. If john is either not funny or not wise then fred is both not brave and not generous and vice versa. If alice is both not rich and not tall then someone is rich and vice versa. If lucy is patient or not rich then fred is strong or kind. Everyone who is happy is curious and vice versa. Everyone who is not tall or creative is calm. Everyone who is not curious or not old is either not kind or not strong and vice versa. Susan is not strong. Someone is both brave and not tall. Someone is creative or not kind. Alice is both generous and tall. Lucy is either rich or not rich. Someone is both not funny and not brave. Mary is not humble. Someone is not calm or brave. | John is quiet. | neutral | (![X]:((humble(X)|brave(X))<=>(brave(X)<~>~funny(X))))&
(((brave(alice)|happy(alice)))<=>(?[X]:(~generous(X))))&
(((~patient(paul)<~>tall(paul)))<=>((~wise(susan)&brave(susan))))&
(((creative(alice)<~>~happy(alice)))=>((creative(lucy)|wise(lucy))))&
(((~happy(mary)&quiet(mary)))=>(?[X]:((~tall(X)|curious(X)))))&
(![X]:((patient(X)&~brave(X))<=>(~funny(X)|~strong(X))))&
(((~kind(alice)<~>~rich(alice)))<=>(?[X]:((brave(X)&~funny(X)))))&
((?[X]:(tall(X)))=>(?[X]:((old(X)<~>~patient(X)))))&
(((calm(susan)|happy(susan)))=>(calm(lucy)))&
(![X]:((~patient(X)<~>~brave(X))=>(curious(X)|~wise(X))))&
(((~funny(john)<~>~wise(john)))<=>((~brave(fred)&~generous(fred))))&
(((~rich(alice)&~tall(alice)))<=>(?[X]:(rich(X))))&
(((patient(lucy)|~rich(lucy)))=>((strong(fred)|kind(fred))))&
(![X]:(happy(X)<=>curious(X)))&
(![X]:((~tall(X)|creative(X))=>calm(X)))&
(![X]:((~curious(X)|~old(X))<=>(~kind(X)<~>~strong(X))))&
(~strong(susan))&
(?[X]:((brave(X)&~tall(X))))&
(?[X]:((creative(X)|~kind(X))))&
((generous(alice)&tall(alice)))&
((rich(lucy)<~>~rich(lucy)))&
(?[X]:((~funny(X)&~brave(X))))&
(~humble(mary))&
(?[X]:((~calm(X)|brave(X)))) | quiet(john) | [] | null | 0 |
Everyone who is generous is either happy or tall. Everyone who is brave or old is either not curious or creative and vice versa. Everyone who is not funny or not wise is both not rich and not wise and vice versa. If someone is either not rich or not old then mary is both funny and not creative and vice versa. If john is both not kind and wise then someone is either happy or not humble. Everyone who is not generous is both generous and patient and vice versa. If john is not calm or not funny then mary is patient and vice versa. If susan is both kind and not rich then someone is either wise or calm and vice versa. If someone is not humble then susan is not patient and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is not generous or wise is not wise or not patient and vice versa. If someone is not creative then someone is both quiet and patient. Everyone who is both happy and calm is either humble or calm. If someone is either not funny or quiet then someone is creative or not wise. Everyone who is creative is not tall or not rich. Someone is both not happy and not kind. Fred is either not creative or not strong. Alice is either creative or not kind. Fred is either strong or not old. | Fred is old. | contradiction | (![X]:(generous(X)=>(happy(X)<~>tall(X))))&
(![X]:((brave(X)|old(X))<=>(~curious(X)<~>creative(X))))&
(![X]:((~funny(X)|~wise(X))<=>(~rich(X)&~wise(X))))&
((?[X]:((~rich(X)<~>~old(X))))<=>((funny(mary)&~creative(mary))))&
(((~kind(john)&wise(john)))=>(?[X]:((happy(X)<~>~humble(X)))))&
(![X]:(~generous(X)<=>(generous(X)&patient(X))))&
(((~calm(john)|~funny(john)))<=>(patient(mary)))&
(((kind(susan)&~rich(susan)))<=>(?[X]:((wise(X)<~>calm(X)))))&
((?[X]:(~humble(X)))<=>(~patient(susan)))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((~generous(X)|wise(X))<=>(~wise(X)|~patient(X))))&
((?[X]:(~creative(X)))=>(?[X]:((quiet(X)&patient(X)))))&
(![X]:((happy(X)&calm(X))=>(humble(X)<~>calm(X))))&
((?[X]:((~funny(X)<~>quiet(X))))=>(?[X]:((creative(X)|~wise(X)))))&
(![X]:(creative(X)=>(~tall(X)|~rich(X))))&
(?[X]:((~happy(X)&~kind(X))))&
((~creative(fred)<~>~strong(fred)))&
((creative(alice)<~>~kind(alice)))&
((strong(fred)<~>~old(fred))) | old(fred) | [
"p5",
"p10",
"p11",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5315304548538488194761394
% SZS output start Proof for 5315304548538488194761394
6. ! [X0] : (~generous(X0) <=> (patient(X0) & generous(X0))) [input p5]
11. ! [X0] : ((wise(X0) | ~generous(X0)) <=> (~patient(X0) | ~wise(X0))) [input p10]
12. ? [X0] : ~creative(X0) => ? [X0] : (patient(X0) & quiet(X0)) [input p11]
17. ~creative(fred) <~> ~strong(fred) [input p16]
19. strong(fred) <~> ~old(fred) [input p18]
20. old(fred) [input hypothesis]
21. ? [X0] : ~creative(X0) => ? [X1] : (patient(X1) & quiet(X1)) [rectify 12]
26. ? [X1] : (patient(X1) & quiet(X1)) | ! [X0] : creative(X0) [ennf transformation 21]
45. ! [X0] : ((~generous(X0) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | generous(X0))) [nnf transformation 6]
46. ! [X0] : ((~generous(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | generous(X0))) [flattening 45]
59. ! [X0] : (((wise(X0) | ~generous(X0)) | (patient(X0) & wise(X0))) & ((~patient(X0) | ~wise(X0)) | (~wise(X0) & generous(X0)))) [nnf transformation 11]
60. ! [X0] : ((wise(X0) | ~generous(X0) | (patient(X0) & wise(X0))) & (~patient(X0) | ~wise(X0) | (~wise(X0) & generous(X0)))) [flattening 59]
61. ? [X0] : (patient(X0) & quiet(X0)) | ! [X1] : creative(X1) [rectify 26]
62. ? [X0] : (patient(X0) & quiet(X0)) => (patient(sK4) & quiet(sK4)) [choice axiom]
63. (patient(sK4) & quiet(sK4)) | ! [X1] : creative(X1) [skolemisation 61,62]
71. (strong(fred) | creative(fred)) & (~strong(fred) | ~creative(fred)) [nnf transformation 17]
73. (old(fred) | ~strong(fred)) & (~old(fred) | strong(fred)) [nnf transformation 19]
95. generous(X0) | generous(X0) [cnf transformation 46]
112. ~patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 60]
113. wise(X0) | ~generous(X0) | wise(X0) [cnf transformation 60]
116. patient(sK4) | creative(X1) [cnf transformation 63]
124. ~strong(fred) | ~creative(fred) [cnf transformation 71]
128. ~old(fred) | strong(fred) [cnf transformation 73]
130. old(fred) [cnf transformation 20]
132. ~patient(X0) | ~wise(X0) [duplicate literal removal 112]
133. wise(X0) | ~generous(X0) [duplicate literal removal 113]
134. generous(X0) [duplicate literal removal 95]
239. wise(X0) [subsumption resolution 133,134]
240. ~patient(X0) [subsumption resolution 132,239]
241. creative(X1) [subsumption resolution 116,240]
243. ~strong(fred) [subsumption resolution 124,241]
245. ~old(fred) [subsumption resolution 128,243]
246. $false [subsumption resolution 130,245]
% SZS output end Proof for 5315304548538488194761394
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or kind is both not quiet and tall.
If paul is not rich then mary is both brave and not curious and vice versa.
If someone is not funny then paul is kind or not tall and vice versa.
If fred is either not funny or patient then someone is both not creative and not kind.
If someone is either not humble or not generous then mary is brave.
Everyone who is both not patient and not wise is happy or not quiet and vice versa.
If someone is both not wise and brave then mary is both old and not patient.
Everyone who is either not creative or not strong is rich.
Everyone who is kind is both wise and not rich and vice versa.
Everyone who is either not tall or not strong is kind or not funny and vice versa.
If someone is both rich and not creative then paul is not patient or humble and vice versa.
If someone is both kind and quiet then someone is both happy and not funny and vice versa.
Everyone who is both curious and not strong is not calm and vice versa.
If john is either calm or wise then mary is humble.
Everyone who is tall is not strong or not kind and vice versa.
If mary is both not generous and not wise then someone is both not patient and tall and vice versa.
Mary is curious or not generous.
Fred is not quiet or not kind.
Fred is either not strong or tall.
Someone is kind or not wise.
Someone is either not happy or patient.
Susan is either not brave or not creative.
Someone is not kind or kind. | Mary is generous. | contradiction | (![X]:((quiet(X)|kind(X))=>(~quiet(X)&tall(X))))&
((~rich(paul))<=>((brave(mary)&~curious(mary))))&
((?[X]:(~funny(X)))<=>((kind(paul)|~tall(paul))))&
(((~funny(fred)<~>patient(fred)))=>(?[X]:((~creative(X)&~kind(X)))))&
((?[X]:((~humble(X)<~>~generous(X))))=>(brave(mary)))&
(![X]:((~patient(X)&~wise(X))<=>(happy(X)|~quiet(X))))&
((?[X]:((~wise(X)&brave(X))))=>((old(mary)&~patient(mary))))&
(![X]:((~creative(X)<~>~strong(X))=>rich(X)))&
(![X]:(kind(X)<=>(wise(X)&~rich(X))))&
(![X]:((~tall(X)<~>~strong(X))<=>(kind(X)|~funny(X))))&
((?[X]:((rich(X)&~creative(X))))<=>((~patient(paul)|humble(paul))))&
((?[X]:((kind(X)&quiet(X))))<=>(?[X]:((happy(X)&~funny(X)))))&
(![X]:((curious(X)&~strong(X))<=>~calm(X)))&
(((calm(john)<~>wise(john)))=>(humble(mary)))&
(![X]:(tall(X)<=>(~strong(X)|~kind(X))))&
(((~generous(mary)&~wise(mary)))<=>(?[X]:((~patient(X)&tall(X)))))&
((curious(mary)|~generous(mary)))&
((~quiet(fred)|~kind(fred)))&
((~strong(fred)<~>tall(fred)))&
(?[X]:((kind(X)|~wise(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
((~brave(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)|kind(X)))) | generous(mary) | [
"p0",
"p5",
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7791940915869478789374395
% SZS output start Proof for 7791940915869478789374395
1. ! [X0] : ((kind(X0) | quiet(X0)) => (tall(X0) & ~quiet(X0))) [input p0]
6. ! [X0] : ((~wise(X0) & ~patient(X0)) <=> (~quiet(X0) | happy(X0))) [input p5]
9. ! [X0] : (kind(X0) <=> (~rich(X0) & wise(X0))) [input p8]
15. ! [X0] : (tall(X0) <=> (~kind(X0) | ~strong(X0))) [input p14]
16. (~wise(mary) & ~generous(mary)) <=> ? [X0] : (tall(X0) & ~patient(X0)) [input p15]
24. generous(mary) [input hypothesis]
27. ! [X0] : ((tall(X0) & ~quiet(X0)) | (~kind(X0) & ~quiet(X0))) [ennf transformation 1]
44. ! [X0] : (((~wise(X0) & ~patient(X0)) | (quiet(X0) & ~happy(X0))) & ((~quiet(X0) | happy(X0)) | (wise(X0) | patient(X0)))) [nnf transformation 6]
45. ! [X0] : (((~wise(X0) & ~patient(X0)) | (quiet(X0) & ~happy(X0))) & (~quiet(X0) | happy(X0) | wise(X0) | patient(X0))) [flattening 44]
47. ! [X0] : ((kind(X0) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | ~kind(X0))) [nnf transformation 9]
48. ! [X0] : ((kind(X0) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | ~kind(X0))) [flattening 47]
64. ! [X0] : ((tall(X0) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | ~tall(X0))) [nnf transformation 15]
65. ! [X0] : ((tall(X0) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | ~tall(X0))) [flattening 64]
66. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & (? [X0] : (tall(X0) & ~patient(X0)) | (wise(mary) | generous(mary))) [nnf transformation 16]
67. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & (? [X0] : (tall(X0) & ~patient(X0)) | wise(mary) | generous(mary)) [flattening 66]
68. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & (? [X1] : (tall(X1) & ~patient(X1)) | wise(mary) | generous(mary)) [rectify 67]
69. ? [X1] : (tall(X1) & ~patient(X1)) => (tall(sK5) & ~patient(sK5)) [choice axiom]
70. ((~wise(mary) & ~generous(mary)) | ! [X0] : (~tall(X0) | patient(X0))) & ((tall(sK5) & ~patient(sK5)) | wise(mary) | generous(mary)) [skolemisation 68,69]
80. ~quiet(X0) | ~quiet(X0) [cnf transformation 27]
98. ~patient(X0) | quiet(X0) [cnf transformation 45]
100. ~wise(X0) | quiet(X0) [cnf transformation 45]
104. wise(X0) | ~kind(X0) [cnf transformation 48]
129. tall(X0) | kind(X0) [cnf transformation 65]
132. ~generous(mary) | ~tall(X0) | patient(X0) [cnf transformation 70]
144. generous(mary) [cnf transformation 24]
145. ~quiet(X0) [duplicate literal removal 80]
207. ~wise(X0) [subsumption resolution 100,145]
208. ~patient(X0) [subsumption resolution 98,145]
209. ~kind(X0) [subsumption resolution 104,207]
241. tall(X0) [subsumption resolution 129,209]
242. ~generous(mary) | patient(X0) [subsumption resolution 132,241]
243. ~generous(mary) [subsumption resolution 242,208]
256. $false [subsumption resolution 144,243]
% SZS output end Proof for 7791940915869478789374395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or tall is not calm and vice versa.
If john is old then mary is calm or brave.
If someone is brave or calm then someone is both not calm and not quiet.
Everyone who is generous is either not curious or not calm.
Everyone who is not old is creative.
Everyone who is both not curious and not calm is either not happy or brave and vice versa.
Everyone who is strong or tall is both humble and brave.
If lucy is either generous or not strong then someone is old or not calm and vice versa.
Everyone who is generous is rich or not happy and vice versa.
Everyone who is either not calm or curious is not quiet or humble.
Everyone who is not kind or funny is not brave.
Everyone who is either not creative or tall is either calm or not generous and vice versa.
Everyone who is not wise or not happy is either not generous or not wise and vice versa.
Everyone who is either not wise or quiet is either not generous or wise.
Everyone who is strong is tall or not wise and vice versa.
If paul is not creative or not curious then someone is not wise or not old and vice versa.
Lucy is either humble or old.
Someone is not curious or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous.
Fred is not generous or not patient.
Someone is not wise or not old. | Mary is calm. | entailment | (![X]:((~patient(X)|tall(X))<=>~calm(X)))&
((old(john))=>((calm(mary)|brave(mary))))&
((?[X]:((brave(X)|calm(X))))=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:(generous(X)=>(~curious(X)<~>~calm(X))))&
(![X]:(~old(X)=>creative(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
(![X]:(strong(X)<=>(tall(X)|~wise(X))))&
(((~creative(paul)|~curious(paul)))<=>(?[X]:((~wise(X)|~old(X)))))&
((humble(lucy)<~>old(lucy)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X))))&
((~generous(fred)|~patient(fred)))&
(?[X]:((~wise(X)|~old(X)))) | calm(mary) | [
"p0",
"p8",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5906952347316359722715264
% SZS output start Proof for 5906952347316359722715264
1. ! [X0] : ((tall(X0) | ~patient(X0)) <=> ~calm(X0)) [input p0]
9. ! [X0] : (generous(X0) <=> (~happy(X0) | rich(X0))) [input p8]
12. ! [X0] : ((~creative(X0) <~> tall(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p11]
13. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p12]
19. ~creative(mary) <~> tall(mary) [input p18]
24. ~calm(mary) [input hypothesis]
37. ! [X0] : (((tall(X0) | ~patient(X0)) | calm(X0)) & (~calm(X0) | (~tall(X0) & patient(X0)))) [nnf transformation 1]
38. ! [X0] : ((tall(X0) | ~patient(X0) | calm(X0)) & (~calm(X0) | (~tall(X0) & patient(X0)))) [flattening 37]
49. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | ~generous(X0))) [nnf transformation 9]
50. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ~generous(X0))) [flattening 49]
52. ! [X0] : ((((~tall(X0) | creative(X0)) & (tall(X0) | ~creative(X0))) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | ((~creative(X0) | ~tall(X0)) & (tall(X0) | creative(X0))))) [nnf transformation 12]
53. ! [X0] : (((~happy(X0) | ~wise(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [nnf transformation 13]
54. ! [X0] : ((~happy(X0) | ~wise(X0) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [flattening 53]
66. (~tall(mary) | creative(mary)) & (tall(mary) | ~creative(mary)) [nnf transformation 19]
72. ~calm(X0) | ~tall(X0) [cnf transformation 38]
100. happy(X0) | generous(X0) [cnf transformation 50]
104. ~generous(X0) | calm(X0) | tall(X0) | creative(X0) [cnf transformation 52]
105. ~generous(X0) | calm(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 52]
114. wise(X0) | generous(X0) | wise(X0) [cnf transformation 54]
116. ~happy(X0) | ~wise(X0) | ~wise(X0) | generous(X0) [cnf transformation 54]
132. tall(mary) | ~creative(mary) [cnf transformation 66]
133. ~tall(mary) | creative(mary) [cnf transformation 66]
138. ~calm(mary) [cnf transformation 24]
141. wise(X0) | generous(X0) [duplicate literal removal 114]
142. ~happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 116]
148. 2 <=> calm(mary) [avatar definition]
149. ~calm(mary) <- (~2) [avatar component clause 148]
205. ~creative(X0) | ~generous(X0) | ~tall(X0) [subsumption resolution 105,72]
206. ~wise(X0) | generous(X0) [subsumption resolution 142,100]
207. generous(X0) [subsumption resolution 141,206]
256. 24 <=> creative(mary) [avatar definition]
257. ~creative(mary) <- (~24) [avatar component clause 256]
258. creative(mary) <- (24) [avatar component clause 256]
260. 25 <=> tall(mary) [avatar definition]
261. tall(mary) <- (25) [avatar component clause 260]
262. ~tall(mary) <- (~25) [avatar component clause 260]
263. 24 | ~25 [avatar split clause 133,260,256]
264. ~24 | 25 [avatar split clause 132,260,256]
284. ~2 [avatar split clause 138,148]
352. creative(X0) | tall(X0) | calm(X0) [resolution 104,207]
393. tall(mary) | calm(mary) <- (~24) [resolution 352,257]
398. calm(mary) <- (~24, ~25) [subsumption resolution 393,262]
399. $false <- (~2, ~24, ~25) [subsumption resolution 398,149]
400. 2 | 24 | 25 [avatar contradiction clause 399]
402. ~generous(mary) | ~tall(mary) <- (24) [resolution 258,205]
404. ~tall(mary) <- (24) [subsumption resolution 402,207]
405. $false <- (24, 25) [subsumption resolution 404,261]
406. ~24 | ~25 [avatar contradiction clause 405]
407. $false [avatar sat refutation 263,264,284,400,406]
% SZS output end Proof for 5906952347316359722715264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not rich and funny is either old or patient and vice versa.
Everyone who is humble is both wise and kind and vice versa.
If fred is either not patient or not generous then someone is not happy or kind.
Everyone who is not quiet or funny is both strong and not funny and vice versa.
Everyone who is either not quiet or funny is both not wise and not curious.
If someone is not tall then alice is not tall and vice versa.
Everyone who is wise or creative is both not creative and not patient and vice versa.
If lucy is generous or creative then alice is either not calm or strong and vice versa.
Everyone who is not wise or patient is both funny and not funny and vice versa.
If someone is either strong or patient then someone is both not old and not strong.
If alice is both creative and generous then someone is either not patient or not kind and vice versa.
If someone is either not old or not calm then alice is both not tall and quiet.
Everyone who is wise or not quiet is not brave or wise and vice versa.
Everyone who is generous is both quiet and curious.
Everyone who is not funny or strong is both calm and not rich.
Someone is generous or calm.
Someone is either funny or not rich.
Someone is patient or not humble.
Fred is brave.
Someone is either creative or not rich. | Alice is not kind. | entailment | (![X]:((~rich(X)&funny(X))<=>(old(X)<~>patient(X))))&
(![X]:(humble(X)<=>(wise(X)&kind(X))))&
(((~patient(fred)<~>~generous(fred)))=>(?[X]:((~happy(X)|kind(X)))))&
(![X]:((~quiet(X)|funny(X))<=>(strong(X)&~funny(X))))&
(![X]:((~quiet(X)<~>funny(X))=>(~wise(X)&~curious(X))))&
((?[X]:(~tall(X)))<=>(~tall(alice)))&
(![X]:((wise(X)|creative(X))<=>(~creative(X)&~patient(X))))&
(((generous(lucy)|creative(lucy)))<=>((~calm(alice)<~>strong(alice))))&
(![X]:((~wise(X)|patient(X))<=>(funny(X)&~funny(X))))&
((?[X]:((strong(X)<~>patient(X))))=>(?[X]:((~old(X)&~strong(X)))))&
(((creative(alice)&generous(alice)))<=>(?[X]:((~patient(X)<~>~kind(X)))))&
((?[X]:((~old(X)<~>~calm(X))))=>((~tall(alice)&quiet(alice))))&
(![X]:((wise(X)|~quiet(X))<=>(~brave(X)|wise(X))))&
(![X]:(generous(X)=>(quiet(X)&curious(X))))&
(![X]:((~funny(X)|strong(X))=>(calm(X)&~rich(X))))&
(?[X]:((generous(X)|calm(X))))&
(?[X]:((funny(X)<~>~rich(X))))&
(?[X]:((patient(X)|~humble(X))))&
(brave(fred))&
(?[X]:((creative(X)<~>~rich(X)))) | ~kind(alice) | [
"p3",
"p6",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3702124920933437917444745
% SZS output start Proof for 3702124920933437917444745
4. ! [X0] : ((funny(X0) | ~quiet(X0)) <=> (~funny(X0) & strong(X0))) [input p3]
7. ! [X0] : ((creative(X0) | wise(X0)) <=> (~patient(X0) & ~creative(X0))) [input p6]
9. ! [X0] : ((patient(X0) | ~wise(X0)) <=> (~funny(X0) & funny(X0))) [input p8]
11. (generous(alice) & creative(alice)) <=> ? [X0] : (~patient(X0) <~> ~kind(X0)) [input p10]
21. kind(alice) [input hypothesis]
34. ! [X0] : (((funny(X0) | ~quiet(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (~funny(X0) & quiet(X0)))) [nnf transformation 4]
35. ! [X0] : ((funny(X0) | ~quiet(X0) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | (~funny(X0) & quiet(X0)))) [flattening 34]
41. ! [X0] : (((creative(X0) | wise(X0)) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 7]
42. ! [X0] : ((creative(X0) | wise(X0) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 41]
45. ! [X0] : (((patient(X0) | ~wise(X0)) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | (~patient(X0) & wise(X0)))) [nnf transformation 9]
46. ! [X0] : ((patient(X0) | ~wise(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | (~patient(X0) & wise(X0)))) [flattening 45]
51. ((generous(alice) & creative(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (? [X0] : ((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (~generous(alice) | ~creative(alice))) [nnf transformation 11]
52. ((generous(alice) & creative(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (? [X0] : ((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | ~generous(alice) | ~creative(alice)) [flattening 51]
53. ((generous(alice) & creative(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (? [X1] : ((kind(X1) | patient(X1)) & (~kind(X1) | ~patient(X1))) | ~generous(alice) | ~creative(alice)) [rectify 52]
54. ? [X1] : ((kind(X1) | patient(X1)) & (~kind(X1) | ~patient(X1))) => ((kind(sK2) | patient(sK2)) & (~kind(sK2) | ~patient(sK2))) [choice axiom]
55. ((generous(alice) & creative(alice)) | ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0)))) & (((kind(sK2) | patient(sK2)) & (~kind(sK2) | ~patient(sK2))) | ~generous(alice) | ~creative(alice)) [skolemisation 53,54]
79. ~funny(X0) | ~funny(X0) [cnf transformation 35]
88. ~creative(X0) | ~creative(X0) [cnf transformation 42]
99. funny(X0) | ~patient(X0) [cnf transformation 46]
109. creative(alice) | ~kind(X0) | patient(X0) [cnf transformation 55]
134. kind(alice) [cnf transformation 21]
135. ~creative(X0) [duplicate literal removal 88]
137. ~funny(X0) [duplicate literal removal 79]
172. ~patient(X0) [subsumption resolution 99,137]
191. 10 <=> ! [X0] : ~kind(X0) [avatar definition]
192. ~kind(X0) <- (10) [avatar component clause 191]
198. ~kind(X0) | patient(X0) [subsumption resolution 109,135]
199. ~kind(X0) [subsumption resolution 198,172]
200. 10 [avatar split clause 199,191]
220. $false <- (10) [resolution 192,134]
221. ~10 [avatar contradiction clause 220]
222. $false [avatar sat refutation 200,221]
% SZS output end Proof for 3702124920933437917444745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is patient.
Everyone who is curious is both not patient and patient and vice versa.
Everyone who is both not old and old is not tall or not calm.
Everyone who is both not brave and not generous is either kind or humble and vice versa.
Everyone who is not generous or funny is both kind and not humble and vice versa.
Everyone who is both old and generous is old.
If someone is both humble and funny then someone is not generous.
Everyone who is either quiet or creative is not rich or brave and vice versa.
Everyone who is not calm is tall.
If someone is kind then susan is either quiet or rich and vice versa.
Everyone who is not creative or generous is either not old or not patient and vice versa.
Everyone who is rich is not wise or not happy and vice versa.
If susan is kind or not happy then someone is calm or patient and vice versa.
If fred is either old or humble then someone is generous or strong and vice versa.
If susan is either old or quiet then someone is rich.
Everyone who is both not old and humble is calm and vice versa.
Susan is both calm and not strong.
Someone is either strong or not quiet.
Someone is either not rich or strong.
Fred is either creative or generous.
Someone is not quiet.
Paul is creative.
Someone is either strong or not humble. | Fred is not wise. | neutral | (![X]:(happy(X)=>patient(X)))&
(![X]:(curious(X)<=>(~patient(X)&patient(X))))&
(![X]:((~old(X)&old(X))=>(~tall(X)|~calm(X))))&
(![X]:((~brave(X)&~generous(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~generous(X)|funny(X))<=>(kind(X)&~humble(X))))&
(![X]:((old(X)&generous(X))=>old(X)))&
((?[X]:((humble(X)&funny(X))))=>(?[X]:(~generous(X))))&
(![X]:((quiet(X)<~>creative(X))<=>(~rich(X)|brave(X))))&
(![X]:(~calm(X)=>tall(X)))&
((?[X]:(kind(X)))<=>((quiet(susan)<~>rich(susan))))&
(![X]:((~creative(X)|generous(X))<=>(~old(X)<~>~patient(X))))&
(![X]:(rich(X)<=>(~wise(X)|~happy(X))))&
(((kind(susan)|~happy(susan)))<=>(?[X]:((calm(X)|patient(X)))))&
(((old(fred)<~>humble(fred)))<=>(?[X]:((generous(X)|strong(X)))))&
(((old(susan)<~>quiet(susan)))=>(?[X]:(rich(X))))&
(![X]:((~old(X)&humble(X))<=>calm(X)))&
((calm(susan)&~strong(susan)))&
(?[X]:((strong(X)<~>~quiet(X))))&
(?[X]:((~rich(X)<~>strong(X))))&
((creative(fred)<~>generous(fred)))&
(?[X]:(~quiet(X)))&
(creative(paul))&
(?[X]:((strong(X)<~>~humble(X)))) | ~wise(fred) | [] | null | 0 |
If lucy is either old or quiet then someone is not funny. Everyone who is both not rich and not tall is not strong or funny and vice versa. Everyone who is both humble and not kind is kind and vice versa. Everyone who is patient is creative or not generous. Everyone who is brave or old is either not brave or not rich and vice versa. Everyone who is not kind is both not funny and not old and vice versa. Everyone who is not quiet is not patient or not kind. Everyone who is both not calm and not brave is both wise and rich and vice versa. Everyone who is both wise and happy is not creative. Everyone who is either strong or not old is either brave or strong. Everyone who is tall is not creative or wise. Everyone who is not strong or calm is not strong. Everyone who is not happy or creative is not curious or wise. Everyone who is either not creative or calm is either patient or not generous and vice versa. If fred is not generous or creative then alice is old and vice versa. Everyone who is either generous or rich is rich or generous. Someone is either not patient or not kind. John is not calm or rich. Lucy is either rich or not curious. Fred is not curious or not creative. Someone is not funny or brave. Someone is either not quiet or not calm. Someone is quiet. | Alice is not brave. | contradiction | (((old(lucy)<~>quiet(lucy)))=>(?[X]:(~funny(X))))&
(![X]:((~rich(X)&~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~strong(X)|calm(X))=>~strong(X)))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
(![X]:((generous(X)<~>rich(X))=>(rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
((~calm(john)|rich(john)))&
((rich(lucy)<~>~curious(lucy)))&
((~curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:(quiet(X))) | ~brave(alice) | [
"p2",
"p4",
"p5",
"p7",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8926541698453024788609458
% SZS output start Proof for 8926541698453024788609458
3. ! [X0] : ((~kind(X0) & humble(X0)) <=> kind(X0)) [input p2]
5. ! [X0] : ((old(X0) | brave(X0)) <=> (~brave(X0) <~> ~rich(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> (~old(X0) & ~funny(X0))) [input p5]
8. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> (rich(X0) & wise(X0))) [input p7]
10. ! [X0] : ((strong(X0) <~> ~old(X0)) => (brave(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((calm(X0) | ~strong(X0)) => ~strong(X0)) [input p11]
24. ~brave(alice) [input hypothesis]
32. ! [X0] : ((brave(X0) <~> strong(X0)) | (strong(X0) <=> ~old(X0))) [ennf transformation 10]
35. ! [X0] : (~strong(X0) | (~calm(X0) & strong(X0))) [ennf transformation 12]
45. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 3]
46. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~humble(X0))) [flattening 45]
47. ! [X0] : (((old(X0) | brave(X0)) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0)))) & (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | (~old(X0) & ~brave(X0)))) [nnf transformation 5]
48. ! [X0] : ((old(X0) | brave(X0) | ((~brave(X0) | rich(X0)) & (~rich(X0) | brave(X0)))) & (((rich(X0) | brave(X0)) & (~rich(X0) | ~brave(X0))) | (~old(X0) & ~brave(X0)))) [flattening 47]
49. ! [X0] : ((~kind(X0) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 6]
50. ! [X0] : ((~kind(X0) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | kind(X0))) [flattening 49]
51. ! [X0] : (((~brave(X0) & ~calm(X0)) | (~rich(X0) | ~wise(X0))) & ((rich(X0) & wise(X0)) | (brave(X0) | calm(X0)))) [nnf transformation 8]
52. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~rich(X0) | ~wise(X0)) & ((rich(X0) & wise(X0)) | brave(X0) | calm(X0))) [flattening 51]
53. ! [X0] : (((~strong(X0) | ~brave(X0)) & (strong(X0) | brave(X0))) | ((strong(X0) | old(X0)) & (~old(X0) | ~strong(X0)))) [nnf transformation 32]
78. ~kind(X0) | ~kind(X0) [cnf transformation 46]
84. old(X0) | brave(X0) | ~rich(X0) | brave(X0) [cnf transformation 48]
87. ~old(X0) | kind(X0) [cnf transformation 50]
91. calm(X0) | brave(X0) | rich(X0) [cnf transformation 52]
96. strong(X0) | brave(X0) | strong(X0) | old(X0) [cnf transformation 53]
101. ~calm(X0) | ~strong(X0) [cnf transformation 35]
127. ~brave(alice) [cnf transformation 24]
130. strong(X0) | brave(X0) | old(X0) [duplicate literal removal 96]
133. ~rich(X0) | brave(X0) | old(X0) [duplicate literal removal 84]
135. ~kind(X0) [duplicate literal removal 78]
151. ~old(X0) [subsumption resolution 87,135]
153. brave(X0) | strong(X0) [subsumption resolution 130,151]
196. brave(X0) | rich(X0) | ~strong(X0) [resolution 91,101]
211. brave(X0) | rich(X0) [subsumption resolution 196,153]
216. rich(alice) [resolution 211,127]
222. brave(alice) | old(alice) [resolution 133,216]
225. old(alice) [subsumption resolution 222,127]
226. $false [subsumption resolution 225,151]
% SZS output end Proof for 8926541698453024788609458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then fred is either creative or generous. Everyone who is not kind or not old is wise and vice versa. Everyone who is kind is funny or not rich. If paul is not funny or calm then paul is not generous or humble and vice versa. Everyone who is both happy and not curious is not happy or curious. Everyone who is not curious is both not generous and not humble. If someone is either patient or funny then someone is either brave or wise and vice versa. Everyone who is not creative is not patient. If someone is not old then someone is both not brave and not tall. Everyone who is both calm and not old is either brave or not tall. Everyone who is both not generous and not rich is either not creative or rich and vice versa. Everyone who is both not quiet and kind is creative or not generous. If someone is old or not tall then alice is both patient and calm and vice versa. Everyone who is either tall or calm is not tall or not rich and vice versa. Everyone who is humble or not funny is either not tall or not kind and vice versa. If someone is both creative and generous then someone is either calm or rich and vice versa. Fred is either not wise or wise. Someone is both curious and rich. Someone is not funny. Paul is brave. Paul is either kind or not funny. Fred is either happy or creative. John is either funny or tall. Alice is funny. | Alice is curious. | entailment | ((?[X]:(quiet(X)))=>((creative(fred)<~>generous(fred))))&
(![X]:((~kind(X)|~old(X))<=>wise(X)))&
(![X]:(kind(X)=>(funny(X)|~rich(X))))&
(((~funny(paul)|calm(paul)))<=>((~generous(paul)|humble(paul))))&
(![X]:((happy(X)&~curious(X))=>(~happy(X)|curious(X))))&
(![X]:(~curious(X)=>(~generous(X)&~humble(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>(?[X]:((brave(X)<~>wise(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
((?[X]:(~old(X)))=>(?[X]:((~brave(X)&~tall(X)))))&
(![X]:((calm(X)&~old(X))=>(brave(X)<~>~tall(X))))&
(![X]:((~generous(X)&~rich(X))<=>(~creative(X)<~>rich(X))))&
(![X]:((~quiet(X)&kind(X))=>(creative(X)|~generous(X))))&
((?[X]:((old(X)|~tall(X))))<=>((patient(alice)&calm(alice))))&
(![X]:((tall(X)<~>calm(X))<=>(~tall(X)|~rich(X))))&
(![X]:((humble(X)|~funny(X))<=>(~tall(X)<~>~kind(X))))&
((?[X]:((creative(X)&generous(X))))<=>(?[X]:((calm(X)<~>rich(X)))))&
((~wise(fred)<~>wise(fred)))&
(?[X]:((curious(X)&rich(X))))&
(?[X]:(~funny(X)))&
(brave(paul))&
((kind(paul)<~>~funny(paul)))&
((happy(fred)<~>creative(fred)))&
((funny(john)<~>tall(john)))&
(funny(alice)) | curious(alice) | [
"p5",
"p7",
"p8",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2318174782612802907689590
% SZS output start Proof for 2318174782612802907689590
6. ! [X0] : (~curious(X0) => (~humble(X0) & ~generous(X0))) [input p5]
8. ! [X0] : (~creative(X0) => ~patient(X0)) [input p7]
9. ? [X0] : ~old(X0) => ? [X0] : (~tall(X0) & ~brave(X0)) [input p8]
11. ! [X0] : ((~rich(X0) & ~generous(X0)) <=> (~creative(X0) <~> rich(X0))) [input p10]
13. ? [X0] : (~tall(X0) | old(X0)) <=> (calm(alice) & patient(alice)) [input p12]
25. ~curious(alice) [input hypothesis]
27. ? [X0] : ~old(X0) => ? [X1] : (~tall(X1) & ~brave(X1)) [rectify 9]
34. ! [X0] : ((~humble(X0) & ~generous(X0)) | curious(X0)) [ennf transformation 6]
35. ! [X0] : (~patient(X0) | creative(X0)) [ennf transformation 8]
36. ? [X1] : (~tall(X1) & ~brave(X1)) | ! [X0] : old(X0) [ennf transformation 27]
51. ? [X0] : (~tall(X0) & ~brave(X0)) | ! [X1] : old(X1) [rectify 36]
52. ? [X0] : (~tall(X0) & ~brave(X0)) => (~tall(sK2) & ~brave(sK2)) [choice axiom]
53. (~tall(sK2) & ~brave(sK2)) | ! [X1] : old(X1) [skolemisation 51,52]
55. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | (rich(X0) | generous(X0)))) [nnf transformation 11]
56. ! [X0] : (((~rich(X0) & ~generous(X0)) | ((~creative(X0) | ~rich(X0)) & (rich(X0) | creative(X0)))) & (((~rich(X0) | creative(X0)) & (rich(X0) | ~creative(X0))) | rich(X0) | generous(X0))) [flattening 55]
57. (? [X0] : (~tall(X0) | old(X0)) | (~calm(alice) | ~patient(alice))) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [nnf transformation 13]
58. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X0] : (tall(X0) & ~old(X0))) [flattening 57]
59. (? [X0] : (~tall(X0) | old(X0)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [rectify 58]
60. ? [X0] : (~tall(X0) | old(X0)) => (~tall(sK3) | old(sK3)) [choice axiom]
61. ((~tall(sK3) | old(sK3)) | ~calm(alice) | ~patient(alice)) & ((calm(alice) & patient(alice)) | ! [X1] : (tall(X1) & ~old(X1))) [skolemisation 59,60]
90. ~generous(X0) | curious(X0) [cnf transformation 34]
100. ~patient(X0) | creative(X0) [cnf transformation 35]
102. ~tall(sK2) | old(X1) [cnf transformation 53]
105. rich(X0) | ~creative(X0) | rich(X0) | generous(X0) [cnf transformation 56]
110. ~rich(X0) | ~creative(X0) | ~rich(X0) [cnf transformation 56]
112. patient(alice) | ~old(X1) [cnf transformation 61]
113. patient(alice) | tall(X1) [cnf transformation 61]
148. ~curious(alice) [cnf transformation 25]
151. rich(X0) | ~creative(X0) | generous(X0) [duplicate literal removal 105]
152. ~rich(X0) | ~creative(X0) [duplicate literal removal 110]
224. 16 <=> ! [X1] : old(X1) [avatar definition]
225. old(X1) <- (16) [avatar component clause 224]
227. 17 <=> tall(sK2) [avatar definition]
229. ~tall(sK2) <- (~17) [avatar component clause 227]
230. 16 | ~17 [avatar split clause 102,227,224]
236. ~creative(X0) | generous(X0) [subsumption resolution 151,152]
238. 19 <=> patient(alice) [avatar definition]
239. patient(alice) <- (19) [avatar component clause 238]
255. 23 <=> ! [X1] : tall(X1) [avatar definition]
256. tall(X1) <- (23) [avatar component clause 255]
259. 24 <=> ! [X1] : ~old(X1) [avatar definition]
260. ~old(X1) <- (24) [avatar component clause 259]
262. 23 | 19 [avatar split clause 113,238,255]
263. 24 | 19 [avatar split clause 112,238,259]
322. creative(alice) <- (19) [resolution 100,239]
329. generous(alice) <- (19) [resolution 236,322]
386. curious(alice) <- (19) [resolution 329,90]
387. $false <- (19) [subsumption resolution 386,148]
388. ~19 [avatar contradiction clause 387]
393. $false <- (~17, 23) [resolution 256,229]
396. 17 | ~23 [avatar contradiction clause 393]
399. $false <- (16, 24) [subsumption resolution 225,260]
400. ~16 | ~24 [avatar contradiction clause 399]
401. $false [avatar sat refutation 230,262,263,388,396,400]
% SZS output end Proof for 2318174782612802907689590
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not happy and not rich then someone is tall or not funny. Everyone who is not old is not curious. If alice is either calm or quiet then susan is not funny or not strong. Everyone who is both not rich and quiet is both not funny and old and vice versa. Everyone who is quiet is either happy or not quiet and vice versa. If mary is not brave or not funny then lucy is either creative or wise. Everyone who is brave or not kind is either happy or not tall and vice versa. Everyone who is both not tall and not old is either not wise or not brave and vice versa. Everyone who is not wise is either brave or not tall. If someone is both brave and not funny then someone is not old or not funny. Everyone who is both wise and not rich is both not strong and not generous and vice versa. If someone is not happy or happy then alice is patient or rich and vice versa. Everyone who is rich is brave or not rich and vice versa. Everyone who is either not generous or wise is wise or not brave and vice versa. Everyone who is tall or not tall is either not funny or kind. Everyone who is old is either kind or not kind and vice versa. Someone is not humble or funny. Lucy is both not quiet and funny. Fred is old. Susan is wise or not old. Susan is not creative or not generous. | Susan is kind. | entailment | (((~happy(fred)&~rich(fred)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:(~old(X)=>~curious(X)))&
(((calm(alice)<~>quiet(alice)))=>((~funny(susan)|~strong(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(~funny(X)&old(X))))&
(![X]:(quiet(X)<=>(happy(X)<~>~quiet(X))))&
(((~brave(mary)|~funny(mary)))=>((creative(lucy)<~>wise(lucy))))&
(![X]:((brave(X)|~kind(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~tall(X)&~old(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(brave(X)<~>~tall(X))))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((wise(X)&~rich(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((~happy(X)|happy(X))))<=>((patient(alice)|rich(alice))))&
(![X]:(rich(X)<=>(brave(X)|~rich(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(wise(X)|~brave(X))))&
(![X]:((tall(X)|~tall(X))=>(~funny(X)<~>kind(X))))&
(![X]:(old(X)<=>(kind(X)<~>~kind(X))))&
(?[X]:((~humble(X)|funny(X))))&
((~quiet(lucy)&funny(lucy)))&
(old(fred))&
((wise(susan)|~old(susan)))&
((~creative(susan)|~generous(susan))) | kind(susan) | [
"p3",
"p4",
"p6",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8876737301175620293520020
% SZS output start Proof for 8876737301175620293520020
4. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> (old(X0) & ~funny(X0))) [input p3]
5. ! [X0] : (quiet(X0) <=> (happy(X0) <~> ~quiet(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | brave(X0)) <=> (happy(X0) <~> ~tall(X0))) [input p6]
13. ! [X0] : (rich(X0) <=> (~rich(X0) | brave(X0))) [input p12]
15. ! [X0] : ((~tall(X0) | tall(X0)) => (~funny(X0) <~> kind(X0))) [input p14]
16. ! [X0] : (old(X0) <=> (kind(X0) <~> ~kind(X0))) [input p15]
22. ~kind(susan) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> kind(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 15]
37. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (~quiet(X0) | rich(X0)))) [nnf transformation 4]
38. ! [X0] : (((quiet(X0) & ~rich(X0)) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | ~quiet(X0) | rich(X0))) [flattening 37]
39. ! [X0] : ((quiet(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) & (((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ~quiet(X0))) [nnf transformation 5]
41. ! [X0] : (((~kind(X0) | brave(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((~kind(X0) | brave(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [flattening 41]
56. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 13]
57. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | ~rich(X0))) [flattening 56]
60. ! [X0] : (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (tall(X0) & ~tall(X0))) [nnf transformation 33]
61. ! [X0] : ((old(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~old(X0))) [nnf transformation 16]
67. ~old(X0) | ~rich(X0) | funny(X0) [cnf transformation 38]
69. ~quiet(X0) | happy(X0) | ~quiet(X0) [cnf transformation 39]
72. quiet(X0) | happy(X0) | quiet(X0) [cnf transformation 39]
80. tall(X0) | ~happy(X0) | kind(X0) [cnf transformation 42]
102. rich(X0) | rich(X0) [cnf transformation 57]
109. kind(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 60]
115. old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 61]
116. old(X0) | kind(X0) | kind(X0) [cnf transformation 61]
122. ~kind(susan) [cnf transformation 22]
123. old(X0) | ~kind(X0) [duplicate literal removal 115]
124. kind(X0) | old(X0) [duplicate literal removal 116]
128. rich(X0) [duplicate literal removal 102]
129. ~quiet(X0) | happy(X0) [duplicate literal removal 69]
130. quiet(X0) | happy(X0) [duplicate literal removal 72]
166. happy(X0) [subsumption resolution 129,130]
188. kind(X0) | tall(X0) [subsumption resolution 80,166]
218. ~funny(X0) | kind(X0) [subsumption resolution 109,188]
219. old(X0) [subsumption resolution 123,124]
254. ~rich(X0) | funny(X0) [resolution 67,219]
255. funny(X0) [subsumption resolution 254,128]
256. kind(X0) [resolution 255,218]
265. $false [resolution 256,122]
% SZS output end Proof for 8876737301175620293520020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong or rich then someone is humble.
Everyone who is both funny and happy is both curious and not quiet.
Everyone who is both not happy and not tall is not patient or generous.
If lucy is not curious then someone is not funny or humble.
If lucy is not curious or creative then paul is either rich or not patient.
If john is either calm or tall then someone is either not curious or not funny and vice versa.
Everyone who is not quiet or not kind is curious or old and vice versa.
Everyone who is both creative and tall is either rich or calm.
Everyone who is not old is kind and vice versa.
Everyone who is either not quiet or not humble is brave or happy and vice versa.
Everyone who is kind is quiet and vice versa.
If someone is happy then someone is not funny or brave.
If someone is not old or generous then susan is not tall and vice versa.
If someone is either not calm or not humble then someone is either curious or happy and vice versa.
If john is either not calm or curious then fred is both not quiet and not creative and vice versa.
If paul is not brave then lucy is both curious and kind.
Someone is both curious and not humble.
Someone is calm.
Paul is old.
Someone is not brave or not patient.
Susan is tall or not rich.
Mary is not wise or not quiet.
Someone is creative or not strong.
Someone is both wise and patient. | Susan is rich. | neutral | (((~strong(john)|rich(john)))=>(?[X]:(humble(X))))&
(![X]:((funny(X)&happy(X))=>(curious(X)&~quiet(X))))&
(![X]:((~happy(X)&~tall(X))=>(~patient(X)|generous(X))))&
((~curious(lucy))=>(?[X]:((~funny(X)|humble(X)))))&
(((~curious(lucy)|creative(lucy)))=>((rich(paul)<~>~patient(paul))))&
(((calm(john)<~>tall(john)))<=>(?[X]:((~curious(X)<~>~funny(X)))))&
(![X]:((~quiet(X)|~kind(X))<=>(curious(X)|old(X))))&
(![X]:((creative(X)&tall(X))=>(rich(X)<~>calm(X))))&
(![X]:(~old(X)<=>kind(X)))&
(![X]:((~quiet(X)<~>~humble(X))<=>(brave(X)|happy(X))))&
(![X]:(kind(X)<=>quiet(X)))&
((?[X]:(happy(X)))=>(?[X]:((~funny(X)|brave(X)))))&
((?[X]:((~old(X)|generous(X))))<=>(~tall(susan)))&
((?[X]:((~calm(X)<~>~humble(X))))<=>(?[X]:((curious(X)<~>happy(X)))))&
(((~calm(john)<~>curious(john)))<=>((~quiet(fred)&~creative(fred))))&
((~brave(paul))=>((curious(lucy)&kind(lucy))))&
(?[X]:((curious(X)&~humble(X))))&
(?[X]:(calm(X)))&
(old(paul))&
(?[X]:((~brave(X)|~patient(X))))&
((tall(susan)|~rich(susan)))&
((~wise(mary)|~quiet(mary)))&
(?[X]:((creative(X)|~strong(X))))&
(?[X]:((wise(X)&patient(X)))) | rich(susan) | [] | null | 0 |
Everyone who is either not calm or patient is not calm or brave and vice versa. If someone is either not generous or not calm then someone is both curious and patient. If mary is both kind and wise then susan is not funny. If john is either wise or rich then john is both not wise and calm and vice versa. Everyone who is humble is either not curious or not quiet. If someone is both not kind and quiet then fred is either happy or calm. If someone is tall or quiet then paul is both not brave and not rich. Everyone who is not funny or not creative is either humble or wise. Everyone who is both not calm and brave is not happy or not curious and vice versa. Everyone who is not kind or rich is either patient or not quiet and vice versa. Everyone who is not patient or not brave is either not calm or not strong and vice versa. Everyone who is either not quiet or not kind is not generous. Everyone who is either strong or wise is either not funny or kind and vice versa. Everyone who is curious is not old and vice versa. Everyone who is not brave is not quiet or not calm and vice versa. If someone is happy or funny then fred is either not old or old. Mary is either not kind or rich. Mary is either not quiet or creative. Someone is not brave or not old. Someone is either not quiet or not humble. Someone is not calm. Paul is either not kind or curious. Someone is not generous or curious. | Paul is old. | contradiction | (![X]:((~calm(X)<~>patient(X))<=>(~calm(X)|brave(X))))&
((?[X]:((~generous(X)<~>~calm(X))))=>(?[X]:((curious(X)&patient(X)))))&
(((kind(mary)&wise(mary)))=>(~funny(susan)))&
(((wise(john)<~>rich(john)))<=>((~wise(john)&calm(john))))&
(![X]:(humble(X)=>(~curious(X)<~>~quiet(X))))&
((?[X]:((~kind(X)&quiet(X))))=>((happy(fred)<~>calm(fred))))&
((?[X]:((tall(X)|quiet(X))))=>((~brave(paul)&~rich(paul))))&
(![X]:((~funny(X)|~creative(X))=>(humble(X)<~>wise(X))))&
(![X]:((~calm(X)&brave(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~kind(X)|rich(X))<=>(patient(X)<~>~quiet(X))))&
(![X]:((~patient(X)|~brave(X))<=>(~calm(X)<~>~strong(X))))&
(![X]:((~quiet(X)<~>~kind(X))=>~generous(X)))&
(![X]:((strong(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:(curious(X)<=>~old(X)))&
(![X]:(~brave(X)<=>(~quiet(X)|~calm(X))))&
((?[X]:((happy(X)|funny(X))))=>((~old(fred)<~>old(fred))))&
((~kind(mary)<~>rich(mary)))&
((~quiet(mary)<~>creative(mary)))&
(?[X]:((~brave(X)|~old(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:(~calm(X)))&
((~kind(paul)<~>curious(paul)))&
(?[X]:((~generous(X)|curious(X)))) | old(paul) | [
"p6",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5352573668966871633829905
% SZS output start Proof for 5352573668966871633829905
7. ? [X0] : (quiet(X0) | tall(X0)) => (~rich(paul) & ~brave(paul)) [input p6]
9. ! [X0] : ((brave(X0) & ~calm(X0)) <=> (~curious(X0) | ~happy(X0))) [input p8]
14. ! [X0] : (curious(X0) <=> ~old(X0)) [input p13]
15. ! [X0] : (~brave(X0) <=> (~calm(X0) | ~quiet(X0))) [input p14]
24. old(paul) [input hypothesis]
26. ? [X0] : quiet(X0) => (~rich(paul) & ~brave(paul)) [pure predicate removal 7]
32. (~rich(paul) & ~brave(paul)) | ! [X0] : ~quiet(X0) [ennf transformation 26]
47. ! [X0] : (((brave(X0) & ~calm(X0)) | (curious(X0) & happy(X0))) & ((~curious(X0) | ~happy(X0)) | (~brave(X0) | calm(X0)))) [nnf transformation 9]
48. ! [X0] : (((brave(X0) & ~calm(X0)) | (curious(X0) & happy(X0))) & (~curious(X0) | ~happy(X0) | ~brave(X0) | calm(X0))) [flattening 47]
55. ! [X0] : ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0))) [nnf transformation 14]
56. ! [X0] : ((~brave(X0) | (calm(X0) & quiet(X0))) & ((~calm(X0) | ~quiet(X0)) | brave(X0))) [nnf transformation 15]
57. ! [X0] : ((~brave(X0) | (calm(X0) & quiet(X0))) & (~calm(X0) | ~quiet(X0) | brave(X0))) [flattening 56]
92. ~brave(paul) | ~quiet(X0) [cnf transformation 32]
102. curious(X0) | brave(X0) [cnf transformation 48]
125. ~old(X0) | ~curious(X0) [cnf transformation 55]
128. ~brave(X0) | quiet(X0) [cnf transformation 57]
145. old(paul) [cnf transformation 24]
212. 14 <=> ! [X0] : ~quiet(X0) [avatar definition]
213. ~quiet(X0) <- (14) [avatar component clause 212]
220. 16 <=> brave(paul) [avatar definition]
221. brave(paul) <- (16) [avatar component clause 220]
223. 14 | ~16 [avatar split clause 92,220,212]
267. 25 <=> curious(paul) [avatar definition]
269. ~curious(paul) <- (~25) [avatar component clause 267]
281. brave(paul) <- (~25) [resolution 102,269]
284. 16 | 25 [avatar split clause 281,267,220]
287. ~curious(paul) [resolution 125,145]
289. quiet(paul) <- (16) [resolution 128,221]
290. $false <- (14, 16) [subsumption resolution 289,213]
291. ~14 | ~16 [avatar contradiction clause 290]
292. ~25 [avatar split clause 287,267]
293. $false [avatar sat refutation 223,284,291,292]
% SZS output end Proof for 5352573668966871633829905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or kind is wise or not patient.
If susan is not strong then john is either humble or not patient and vice versa.
Everyone who is both not creative and calm is patient or curious and vice versa.
If alice is rich or not creative then someone is not patient and vice versa.
If someone is not patient or brave then john is both happy and not patient and vice versa.
If someone is both not calm and not creative then someone is both not calm and not generous and vice versa.
If someone is not strong or not kind then someone is both funny and not calm and vice versa.
Everyone who is both patient and not patient is quiet.
Everyone who is both not strong and patient is not curious or creative and vice versa.
Everyone who is strong or not old is curious or not funny.
Everyone who is both tall and quiet is calm or not tall and vice versa.
If lucy is both patient and not wise then mary is either patient or old and vice versa.
Everyone who is both funny and not rich is not old.
If someone is kind or humble then someone is either strong or funny.
If someone is both not curious and strong then someone is both not old and patient.
Susan is patient.
Someone is both old and strong.
Mary is not old.
Someone is either not happy or quiet.
Someone is either not tall or happy.
Susan is either brave or not generous. | John is humble. | entailment | (![X]:((~generous(X)|kind(X))=>(wise(X)|~patient(X))))&
((~strong(susan))<=>((humble(john)<~>~patient(john))))&
(![X]:((~creative(X)&calm(X))<=>(patient(X)|curious(X))))&
(((rich(alice)|~creative(alice)))<=>(?[X]:(~patient(X))))&
((?[X]:((~patient(X)|brave(X))))<=>((happy(john)&~patient(john))))&
((?[X]:((~calm(X)&~creative(X))))<=>(?[X]:((~calm(X)&~generous(X)))))&
((?[X]:((~strong(X)|~kind(X))))<=>(?[X]:((funny(X)&~calm(X)))))&
(![X]:((patient(X)&~patient(X))=>quiet(X)))&
(![X]:((~strong(X)&patient(X))<=>(~curious(X)|creative(X))))&
(![X]:((strong(X)|~old(X))=>(curious(X)|~funny(X))))&
(![X]:((tall(X)&quiet(X))<=>(calm(X)|~tall(X))))&
(((patient(lucy)&~wise(lucy)))<=>((patient(mary)<~>old(mary))))&
(![X]:((funny(X)&~rich(X))=>~old(X)))&
((?[X]:((kind(X)|humble(X))))=>(?[X]:((strong(X)<~>funny(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((~old(X)&patient(X)))))&
(patient(susan))&
(?[X]:((old(X)&strong(X))))&
(~old(mary))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((~tall(X)<~>happy(X))))&
((brave(susan)<~>~generous(susan))) | humble(john) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7734155020464509657375567
% SZS output start Proof for 7734155020464509657375567
2. ~strong(susan) <=> (humble(john) <~> ~patient(john)) [input p1]
3. ! [X0] : ((calm(X0) & ~creative(X0)) <=> (curious(X0) | patient(X0))) [input p2]
4. (~creative(alice) | rich(alice)) <=> ? [X0] : ~patient(X0) [input p3]
5. ? [X0] : (brave(X0) | ~patient(X0)) <=> (~patient(john) & happy(john)) [input p4]
7. ? [X0] : (~kind(X0) | ~strong(X0)) <=> ? [X0] : (~calm(X0) & funny(X0)) [input p6]
9. ! [X0] : ((patient(X0) & ~strong(X0)) <=> (creative(X0) | ~curious(X0))) [input p8]
22. ~humble(john) [input hypothesis]
24. ? [X0] : (~kind(X0) | ~strong(X0)) <=> ? [X1] : (~calm(X1) & funny(X1)) [rectify 7]
37. (~strong(susan) | ((humble(john) | patient(john)) & (~patient(john) | ~humble(john)))) & (((patient(john) | ~humble(john)) & (~patient(john) | humble(john))) | strong(susan)) [nnf transformation 2]
38. ! [X0] : (((calm(X0) & ~creative(X0)) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | (~calm(X0) | creative(X0)))) [nnf transformation 3]
39. ! [X0] : (((calm(X0) & ~creative(X0)) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | ~calm(X0) | creative(X0))) [flattening 38]
40. ((~creative(alice) | rich(alice)) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (creative(alice) & ~rich(alice))) [nnf transformation 4]
41. (~creative(alice) | rich(alice) | ! [X0] : patient(X0)) & (? [X0] : ~patient(X0) | (creative(alice) & ~rich(alice))) [flattening 40]
42. (~creative(alice) | rich(alice) | ! [X0] : patient(X0)) & (? [X1] : ~patient(X1) | (creative(alice) & ~rich(alice))) [rectify 41]
43. ? [X1] : ~patient(X1) => ~patient(sK0) [choice axiom]
44. (~creative(alice) | rich(alice) | ! [X0] : patient(X0)) & (~patient(sK0) | (creative(alice) & ~rich(alice))) [skolemisation 42,43]
45. (? [X0] : (brave(X0) | ~patient(X0)) | (patient(john) | ~happy(john))) & ((~patient(john) & happy(john)) | ! [X0] : (~brave(X0) & patient(X0))) [nnf transformation 5]
46. (? [X0] : (brave(X0) | ~patient(X0)) | patient(john) | ~happy(john)) & ((~patient(john) & happy(john)) | ! [X0] : (~brave(X0) & patient(X0))) [flattening 45]
47. (? [X0] : (brave(X0) | ~patient(X0)) | patient(john) | ~happy(john)) & ((~patient(john) & happy(john)) | ! [X1] : (~brave(X1) & patient(X1))) [rectify 46]
48. ? [X0] : (brave(X0) | ~patient(X0)) => (brave(sK1) | ~patient(sK1)) [choice axiom]
49. ((brave(sK1) | ~patient(sK1)) | patient(john) | ~happy(john)) & ((~patient(john) & happy(john)) | ! [X1] : (~brave(X1) & patient(X1))) [skolemisation 47,48]
55. (? [X0] : (~kind(X0) | ~strong(X0)) | ! [X1] : (calm(X1) | ~funny(X1))) & (? [X1] : (~calm(X1) & funny(X1)) | ! [X0] : (kind(X0) & strong(X0))) [nnf transformation 24]
56. (? [X0] : (~kind(X0) | ~strong(X0)) | ! [X1] : (calm(X1) | ~funny(X1))) & (? [X2] : (~calm(X2) & funny(X2)) | ! [X3] : (kind(X3) & strong(X3))) [rectify 55]
57. ? [X0] : (~kind(X0) | ~strong(X0)) => (~kind(sK4) | ~strong(sK4)) [choice axiom]
58. ? [X2] : (~calm(X2) & funny(X2)) => (~calm(sK5) & funny(sK5)) [choice axiom]
59. ((~kind(sK4) | ~strong(sK4)) | ! [X1] : (calm(X1) | ~funny(X1))) & ((~calm(sK5) & funny(sK5)) | ! [X3] : (kind(X3) & strong(X3))) [skolemisation 56,58,57]
60. ! [X0] : (((patient(X0) & ~strong(X0)) | (~creative(X0) & curious(X0))) & ((creative(X0) | ~curious(X0)) | (~patient(X0) | strong(X0)))) [nnf transformation 9]
61. ! [X0] : (((patient(X0) & ~strong(X0)) | (~creative(X0) & curious(X0))) & (creative(X0) | ~curious(X0) | ~patient(X0) | strong(X0))) [flattening 60]
87. ~strong(susan) | humble(john) | patient(john) [cnf transformation 37]
89. ~creative(X0) | ~patient(X0) [cnf transformation 39]
91. ~patient(X0) | calm(X0) [cnf transformation 39]
92. ~curious(X0) | calm(X0) [cnf transformation 39]
94. ~patient(sK0) | creative(alice) [cnf transformation 44]
98. ~patient(john) | patient(X1) [cnf transformation 49]
107. ~calm(sK5) | strong(X3) [cnf transformation 59]
114. curious(X0) | patient(X0) [cnf transformation 61]
115. patient(X0) | ~creative(X0) [cnf transformation 61]
146. ~humble(john) [cnf transformation 22]
150. 1 <=> patient(john) [avatar definition]
154. 2 <=> humble(john) [avatar definition]
158. 3 <=> strong(susan) [avatar definition]
160. ~strong(susan) <- (~3) [avatar component clause 158]
161. 1 | 2 | ~3 [avatar split clause 87,158,154,150]
166. 4 <=> ! [X0] : patient(X0) [avatar definition]
167. patient(X0) <- (4) [avatar component clause 166]
173. 6 <=> creative(alice) [avatar definition]
174. creative(alice) <- (6) [avatar component clause 173]
178. 7 <=> patient(sK0) [avatar definition]
180. ~patient(sK0) <- (~7) [avatar component clause 178]
181. 6 | ~7 [avatar split clause 94,178,173]
200. 4 | ~1 [avatar split clause 98,150,166]
245. 22 <=> calm(sK5) [avatar definition]
247. ~calm(sK5) <- (~22) [avatar component clause 245]
250. 23 <=> ! [X3] : strong(X3) [avatar definition]
251. strong(X3) <- (23) [avatar component clause 250]
252. 23 | ~22 [avatar split clause 107,245,250]
259. ~creative(X0) [subsumption resolution 115,89]
324. ~2 [avatar split clause 146,154]
327. $false <- (~3, 23) [subsumption resolution 160,251]
328. 3 | ~23 [avatar contradiction clause 327]
334. patient(X0) | calm(X0) [resolution 114,92]
336. calm(X0) [subsumption resolution 334,91]
343. $false <- (~22) [resolution 336,247]
344. 22 [avatar contradiction clause 343]
350. $false <- (4, ~7) [resolution 167,180]
353. ~4 | 7 [avatar contradiction clause 350]
356. $false <- (6) [subsumption resolution 174,259]
357. ~6 [avatar contradiction clause 356]
358. $false [avatar sat refutation 161,181,200,252,324,328,344,353,357]
% SZS output end Proof for 7734155020464509657375567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either tall or humble. Everyone who is either old or not rich is rich or strong. If someone is either rich or not quiet then someone is quiet or creative and vice versa. Everyone who is not rich is both tall and not quiet and vice versa. Everyone who is either not funny or not rich is both not generous and not quiet and vice versa. Everyone who is curious or patient is either tall or not tall and vice versa. Everyone who is not funny or not tall is either tall or brave. If paul is rich then paul is either not generous or patient. Everyone who is either happy or not creative is not happy and vice versa. If someone is either humble or strong then someone is tall or not creative. Everyone who is either not quiet or quiet is both quiet and not kind and vice versa. Everyone who is both creative and not kind is either not wise or calm and vice versa. Everyone who is tall is either not funny or not creative. If mary is quiet then fred is either rich or not curious and vice versa. If someone is both quiet and not strong then someone is not happy and vice versa. Everyone who is not creative or creative is either not kind or not generous. Someone is either not patient or strong. Someone is both old and rich. Susan is either not wise or old. Alice is both not creative and not wise. Susan is quiet or creative. Susan is not strong. Alice is strong or wise. | Fred is creative. | contradiction | (![X]:(~brave(X)=>(tall(X)<~>humble(X))))&
(![X]:((old(X)<~>~rich(X))=>(rich(X)|strong(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(~rich(X)<=>(tall(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>(~generous(X)&~quiet(X))))&
(![X]:((curious(X)|patient(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((~funny(X)|~tall(X))=>(tall(X)<~>brave(X))))&
((rich(paul))=>((~generous(paul)<~>patient(paul))))&
(![X]:((happy(X)<~>~creative(X))<=>~happy(X)))&
((?[X]:((humble(X)<~>strong(X))))=>(?[X]:((tall(X)|~creative(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(quiet(X)&~kind(X))))&
(![X]:((creative(X)&~kind(X))<=>(~wise(X)<~>calm(X))))&
(![X]:(tall(X)=>(~funny(X)<~>~creative(X))))&
((quiet(mary))<=>((rich(fred)<~>~curious(fred))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~creative(X)|creative(X))=>(~kind(X)<~>~generous(X))))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((old(X)&rich(X))))&
((~wise(susan)<~>old(susan)))&
((~creative(alice)&~wise(alice)))&
((quiet(susan)|creative(susan)))&
(~strong(susan))&
((strong(alice)|wise(alice))) | creative(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1871851733227924431273390
% SZS output start Proof for 1871851733227924431273390
9. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> ~happy(X0)) [input p8]
24. creative(fred) [input hypothesis]
51. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 9]
105. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 51]
107. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 51]
147. creative(fred) [cnf transformation 24]
154. ~happy(X0) | ~creative(X0) [duplicate literal removal 105]
155. ~creative(X0) | happy(X0) [duplicate literal removal 107]
161. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
162. ~creative(X1) <- (1) [avatar component clause 161]
211. ~creative(X0) [subsumption resolution 154,155]
212. 1 [avatar split clause 211,161]
289. $false <- (1) [resolution 162,147]
290. ~1 [avatar contradiction clause 289]
291. $false [avatar sat refutation 212,290]
% SZS output end Proof for 1871851733227924431273390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both creative and tall then alice is both funny and generous.
If fred is rich or not calm then mary is either kind or not kind and vice versa.
Everyone who is either not curious or not rich is either not wise or wise and vice versa.
If paul is either happy or not wise then someone is both happy and rich.
If someone is patient or old then mary is both not quiet and funny and vice versa.
If someone is either wise or not strong then mary is rich or old.
Everyone who is both not calm and quiet is not old or funny and vice versa.
Everyone who is not kind is both not tall and humble and vice versa.
Everyone who is kind is both funny and calm and vice versa.
Everyone who is not creative is both happy and brave and vice versa.
Everyone who is either patient or not generous is not strong and vice versa.
Everyone who is creative or wise is not old and vice versa.
Everyone who is curious or not funny is not creative.
Everyone who is either not creative or calm is kind and vice versa.
If someone is either not rich or not wise then fred is both patient and not tall.
If lucy is both strong and not rich then lucy is either curious or quiet.
Someone is quiet.
Fred is brave or not curious.
Someone is generous or not happy.
Susan is not wise or not happy.
Susan is not patient or not creative. | Paul is not wise. | contradiction | (((creative(lucy)&tall(lucy)))=>((funny(alice)&generous(alice))))&
(((rich(fred)|~calm(fred)))<=>((kind(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~wise(X)<~>wise(X))))&
(((happy(paul)<~>~wise(paul)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((patient(X)|old(X))))<=>((~quiet(mary)&funny(mary))))&
((?[X]:((wise(X)<~>~strong(X))))=>((rich(mary)|old(mary))))&
(![X]:((~calm(X)&quiet(X))<=>(~old(X)|funny(X))))&
(![X]:(~kind(X)<=>(~tall(X)&humble(X))))&
(![X]:(kind(X)<=>(funny(X)&calm(X))))&
(![X]:(~creative(X)<=>(happy(X)&brave(X))))&
(![X]:((patient(X)<~>~generous(X))<=>~strong(X)))&
(![X]:((creative(X)|wise(X))<=>~old(X)))&
(![X]:((curious(X)|~funny(X))=>~creative(X)))&
(![X]:((~creative(X)<~>calm(X))<=>kind(X)))&
((?[X]:((~rich(X)<~>~wise(X))))=>((patient(fred)&~tall(fred))))&
(((strong(lucy)&~rich(lucy)))=>((curious(lucy)<~>quiet(lucy))))&
(?[X]:(quiet(X)))&
((brave(fred)|~curious(fred)))&
(?[X]:((generous(X)|~happy(X))))&
((~wise(susan)|~happy(susan)))&
((~patient(susan)|~creative(susan))) | ~wise(paul) | [
"p2",
"p4",
"p6",
"p8",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3674048736632413098110795
% SZS output start Proof for 3674048736632413098110795
3. ! [X0] : ((~curious(X0) <~> ~rich(X0)) <=> (~wise(X0) <~> wise(X0))) [input p2]
5. ? [X0] : (old(X0) | patient(X0)) <=> (funny(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (funny(X0) | ~old(X0))) [input p6]
9. ! [X0] : (kind(X0) <=> (calm(X0) & funny(X0))) [input p8]
13. ! [X0] : ((~funny(X0) | curious(X0)) => ~creative(X0)) [input p12]
14. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> kind(X0)) [input p13]
15. ? [X0] : (~rich(X0) <~> ~wise(X0)) => (~tall(fred) & patient(fred)) [input p14]
22. ~wise(paul) [input hypothesis]
28. ! [X0] : (~creative(X0) | (funny(X0) & ~curious(X0))) [ennf transformation 13]
29. (~tall(fred) & patient(fred)) | ! [X0] : (~rich(X0) <=> ~wise(X0)) [ennf transformation 15]
34. ! [X0] : ((((rich(X0) | curious(X0)) & (~rich(X0) | ~curious(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ((~curious(X0) | rich(X0)) & (~rich(X0) | curious(X0))))) [nnf transformation 3]
38. (? [X0] : (old(X0) | patient(X0)) | (~funny(mary) | quiet(mary))) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 5]
39. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [flattening 38]
40. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [rectify 39]
41. ? [X0] : (old(X0) | patient(X0)) => (old(sK1) | patient(sK1)) [choice axiom]
42. ((old(sK1) | patient(sK1)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [skolemisation 40,41]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ~quiet(X0) | calm(X0))) [flattening 44]
48. ! [X0] : ((kind(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~kind(X0))) [nnf transformation 9]
49. ! [X0] : ((kind(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~kind(X0))) [flattening 48]
55. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 14]
56. (~tall(fred) & patient(fred)) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0))) [nnf transformation 29]
76. rich(X0) | curious(X0) | wise(X0) | wise(X0) [cnf transformation 34]
77. rich(X0) | curious(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 34]
82. ~quiet(mary) | ~patient(X1) [cnf transformation 42]
83. ~quiet(mary) | ~old(X1) [cnf transformation 42]
85. funny(mary) | ~old(X1) [cnf transformation 42]
90. ~calm(X0) | old(X0) [cnf transformation 45]
92. quiet(X0) | old(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 45]
98. ~kind(X0) | calm(X0) [cnf transformation 49]
110. ~curious(X0) | ~creative(X0) [cnf transformation 28]
112. kind(X0) | calm(X0) | creative(X0) [cnf transformation 55]
115. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 55]
117. patient(fred) | ~rich(X0) | wise(X0) [cnf transformation 56]
127. ~wise(paul) [cnf transformation 22]
130. rich(X0) | curious(X0) | wise(X0) [duplicate literal removal 76]
131. rich(X0) | curious(X0) | ~wise(X0) [duplicate literal removal 77]
166. curious(X0) | rich(X0) [subsumption resolution 130,131]
169. 8 <=> wise(paul) [avatar definition]
170. ~wise(paul) <- (~8) [avatar component clause 169]
189. 12 <=> quiet(mary) [avatar definition]
190. ~quiet(mary) <- (~12) [avatar component clause 189]
193. 13 <=> funny(mary) [avatar definition]
194. funny(mary) <- (13) [avatar component clause 193]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 13 [avatar split clause 85,193,206]
210. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
211. ~patient(X1) <- (17) [avatar component clause 210]
213. 16 | ~12 [avatar split clause 83,189,206]
214. 17 | ~12 [avatar split clause 82,189,210]
223. 20 <=> old(mary) [avatar definition]
225. old(mary) <- (20) [avatar component clause 223]
231. ~kind(X0) | creative(X0) [subsumption resolution 115,98]
232. calm(X0) | creative(X0) [subsumption resolution 112,231]
234. 22 <=> ! [X0] : (~rich(X0) | wise(X0)) [avatar definition]
235. ~rich(X0) | wise(X0) <- (22) [avatar component clause 234]
246. 25 <=> patient(fred) [avatar definition]
248. patient(fred) <- (25) [avatar component clause 246]
249. 22 | 25 [avatar split clause 117,246,234]
301. ~8 [avatar split clause 127,169]
302. old(mary) <- (~12) [resolution 92,190]
304. 20 | 12 [avatar split clause 302,189,223]
310. quiet(mary) <- (13) [resolution 93,194]
311. $false <- (~12, 13) [subsumption resolution 310,190]
312. 12 | ~13 [avatar contradiction clause 311]
313. $false <- (16, 20) [resolution 207,225]
316. ~16 | ~20 [avatar contradiction clause 313]
322. ~creative(X0) | rich(X0) [resolution 166,110]
328. creative(X1) | old(X1) [resolution 232,90]
329. creative(X1) <- (16) [subsumption resolution 328,207]
346. rich(X0) <- (16) [resolution 322,329]
351. wise(X0) <- (16, 22) [resolution 346,235]
357. $false <- (~8, 16, 22) [resolution 351,170]
362. 8 | ~16 | ~22 [avatar contradiction clause 357]
363. $false <- (17, 25) [subsumption resolution 248,211]
364. ~17 | ~25 [avatar contradiction clause 363]
365. $false [avatar sat refutation 208,213,214,249,301,304,312,316,362,364]
% SZS output end Proof for 3674048736632413098110795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both quiet and not humble then mary is both not humble and quiet.
Everyone who is creative is not brave and vice versa.
If someone is not brave then mary is both not old and happy.
If someone is not patient or not strong then someone is happy and vice versa.
Everyone who is either not old or not creative is either not funny or not happy and vice versa.
Everyone who is humble is both not strong and curious and vice versa.
Everyone who is not old or calm is not old and vice versa.
If fred is either not rich or old then someone is both not patient and funny and vice versa.
Everyone who is not kind is either not creative or not kind and vice versa.
Everyone who is both not generous and not patient is not humble or kind.
If lucy is humble or not calm then lucy is not strong or not creative.
If alice is both not old and not patient then fred is not funny and vice versa.
Everyone who is not rich or quiet is strong or not kind and vice versa.
Everyone who is both not calm and not creative is either not kind or strong.
If someone is not curious then someone is either generous or not quiet.
If john is either brave or quiet then susan is not happy and vice versa.
Someone is not calm.
Lucy is not happy or creative.
Someone is strong.
Someone is not patient or funny.
Fred is both generous and not brave.
Someone is both not brave and not funny.
Someone is both not old and kind.
Alice is either old or wise. | Lucy is calm. | neutral | ((?[X]:((quiet(X)&~humble(X))))=>((~humble(mary)&quiet(mary))))&
(![X]:(creative(X)<=>~brave(X)))&
((?[X]:(~brave(X)))=>((~old(mary)&happy(mary))))&
((?[X]:((~patient(X)|~strong(X))))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)<~>~creative(X))<=>(~funny(X)<~>~happy(X))))&
(![X]:(humble(X)<=>(~strong(X)&curious(X))))&
(![X]:((~old(X)|calm(X))<=>~old(X)))&
(((~rich(fred)<~>old(fred)))<=>(?[X]:((~patient(X)&funny(X)))))&
(![X]:(~kind(X)<=>(~creative(X)<~>~kind(X))))&
(![X]:((~generous(X)&~patient(X))=>(~humble(X)|kind(X))))&
(((humble(lucy)|~calm(lucy)))=>((~strong(lucy)|~creative(lucy))))&
(((~old(alice)&~patient(alice)))<=>(~funny(fred)))&
(![X]:((~rich(X)|quiet(X))<=>(strong(X)|~kind(X))))&
(![X]:((~calm(X)&~creative(X))=>(~kind(X)<~>strong(X))))&
((?[X]:(~curious(X)))=>(?[X]:((generous(X)<~>~quiet(X)))))&
(((brave(john)<~>quiet(john)))<=>(~happy(susan)))&
(?[X]:(~calm(X)))&
((~happy(lucy)|creative(lucy)))&
(?[X]:(strong(X)))&
(?[X]:((~patient(X)|funny(X))))&
((generous(fred)&~brave(fred)))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:((~old(X)&kind(X))))&
((old(alice)<~>wise(alice))) | calm(lucy) | [] | null | 0 |
If susan is either brave or old then someone is either not kind or calm.
Everyone who is either old or not wise is both not quiet and curious and vice versa.
If susan is either not tall or quiet then someone is both not kind and not quiet.
If mary is not patient then someone is either not generous or calm and vice versa.
Everyone who is not rich is curious or not humble and vice versa.
If someone is both not patient and not kind then someone is either not tall or not curious and vice versa.
If someone is both wise and calm then john is either not old or not calm and vice versa.
If paul is not funny then someone is either brave or strong.
Everyone who is generous is both not quiet and calm and vice versa.
If fred is either not happy or not quiet then mary is not patient and vice versa.
Everyone who is both tall and generous is quiet or rich.
Everyone who is both not generous and humble is patient.
Everyone who is either strong or funny is either not brave or creative and vice versa.
If someone is not strong then john is tall.
Everyone who is both strong and generous is both generous and not calm.
Everyone who is both not humble and not generous is either not curious or not strong and vice versa.
Someone is not wise or strong.
Susan is either not creative or happy.
Paul is generous.
Someone is both happy and not tall.
John is both not calm and not happy.
Someone is calm.
Someone is not tall.
Someone is not curious. | Paul is not curious. | entailment | (((brave(susan)<~>old(susan)))=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:((old(X)<~>~wise(X))<=>(~quiet(X)&curious(X))))&
(((~tall(susan)<~>quiet(susan)))=>(?[X]:((~kind(X)&~quiet(X)))))&
((~patient(mary))<=>(?[X]:((~generous(X)<~>calm(X)))))&
(![X]:(~rich(X)<=>(curious(X)|~humble(X))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:((~tall(X)<~>~curious(X)))))&
((?[X]:((wise(X)&calm(X))))<=>((~old(john)<~>~calm(john))))&
((~funny(paul))=>(?[X]:((brave(X)<~>strong(X)))))&
(![X]:(generous(X)<=>(~quiet(X)&calm(X))))&
(((~happy(fred)<~>~quiet(fred)))<=>(~patient(mary)))&
(![X]:((tall(X)&generous(X))=>(quiet(X)|rich(X))))&
(![X]:((~generous(X)&humble(X))=>patient(X)))&
(![X]:((strong(X)<~>funny(X))<=>(~brave(X)<~>creative(X))))&
((?[X]:(~strong(X)))=>(tall(john)))&
(![X]:((strong(X)&generous(X))=>(generous(X)&~calm(X))))&
(![X]:((~humble(X)&~generous(X))<=>(~curious(X)<~>~strong(X))))&
(?[X]:((~wise(X)|strong(X))))&
((~creative(susan)<~>happy(susan)))&
(generous(paul))&
(?[X]:((happy(X)&~tall(X))))&
((~calm(john)&~happy(john)))&
(?[X]:(calm(X)))&
(?[X]:(~tall(X)))&
(?[X]:(~curious(X))) | ~curious(paul) | [
"p8",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9071977408777298482140046
% SZS output start Proof for 9071977408777298482140046
9. ! [X0] : (generous(X0) <=> (calm(X0) & ~quiet(X0))) [input p8]
15. ! [X0] : ((generous(X0) & strong(X0)) => (~calm(X0) & generous(X0))) [input p14]
16. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (~curious(X0) <~> ~strong(X0))) [input p15]
19. generous(paul) [input p18]
25. curious(paul) [input hypothesis]
37. ! [X0] : ((~calm(X0) & generous(X0)) | (~generous(X0) | ~strong(X0))) [ennf transformation 15]
38. ! [X0] : ((~calm(X0) & generous(X0)) | ~generous(X0) | ~strong(X0)) [flattening 37]
63. ! [X0] : ((generous(X0) | (~calm(X0) | quiet(X0))) & ((calm(X0) & ~quiet(X0)) | ~generous(X0))) [nnf transformation 9]
64. ! [X0] : ((generous(X0) | ~calm(X0) | quiet(X0)) & ((calm(X0) & ~quiet(X0)) | ~generous(X0))) [flattening 63]
67. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0)))) & (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 16]
68. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~curious(X0) | strong(X0)) & (~strong(X0) | curious(X0)))) & (((strong(X0) | curious(X0)) & (~strong(X0) | ~curious(X0))) | generous(X0) | humble(X0))) [flattening 67]
115. ~generous(X0) | calm(X0) [cnf transformation 64]
133. ~calm(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 38]
139. ~generous(X0) | ~curious(X0) | strong(X0) [cnf transformation 68]
143. generous(paul) [cnf transformation 19]
151. curious(paul) [cnf transformation 25]
305. ~strong(X0) | ~generous(X0) [subsumption resolution 133,115]
306. ~generous(X0) | ~curious(X0) [subsumption resolution 139,305]
345. ~curious(paul) [resolution 306,143]
346. $false [subsumption resolution 345,151]
% SZS output end Proof for 9071977408777298482140046
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or curious then someone is curious or not funny and vice versa.
Everyone who is creative or brave is both not funny and not strong.
Everyone who is both patient and not brave is not happy and vice versa.
Everyone who is not quiet or not patient is not funny or not wise and vice versa.
If alice is calm or not rich then someone is either not strong or not patient.
Everyone who is both humble and rich is both not generous and quiet and vice versa.
Everyone who is either curious or strong is both funny and kind.
Everyone who is not happy is either not brave or not funny and vice versa.
Everyone who is rich is both creative and not strong and vice versa.
Everyone who is old is either funny or not brave and vice versa.
If john is either patient or strong then someone is either patient or not funny.
Everyone who is patient is both not tall and brave and vice versa.
Everyone who is both kind and brave is either rich or kind and vice versa.
Everyone who is quiet is either calm or wise and vice versa.
If susan is both not patient and old then someone is either not funny or tall.
Everyone who is not generous or not brave is either kind or strong.
Someone is either not happy or not quiet.
Lucy is either not rich or kind.
Someone is not kind or tall.
Paul is both tall and not patient.
Fred is both calm and generous.
Susan is tall.
Fred is either not wise or happy.
Lucy is both calm and curious. | Lucy is happy. | entailment | ((?[X]:((~strong(X)|curious(X))))<=>(?[X]:((curious(X)|~funny(X)))))&
(![X]:((creative(X)|brave(X))=>(~funny(X)&~strong(X))))&
(![X]:((patient(X)&~brave(X))<=>~happy(X)))&
(![X]:((~quiet(X)|~patient(X))<=>(~funny(X)|~wise(X))))&
(((calm(alice)|~rich(alice)))=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((humble(X)&rich(X))<=>(~generous(X)&quiet(X))))&
(![X]:((curious(X)<~>strong(X))=>(funny(X)&kind(X))))&
(![X]:(~happy(X)<=>(~brave(X)<~>~funny(X))))&
(![X]:(rich(X)<=>(creative(X)&~strong(X))))&
(![X]:(old(X)<=>(funny(X)<~>~brave(X))))&
(((patient(john)<~>strong(john)))=>(?[X]:((patient(X)<~>~funny(X)))))&
(![X]:(patient(X)<=>(~tall(X)&brave(X))))&
(![X]:((kind(X)&brave(X))<=>(rich(X)<~>kind(X))))&
(![X]:(quiet(X)<=>(calm(X)<~>wise(X))))&
(((~patient(susan)&old(susan)))=>(?[X]:((~funny(X)<~>tall(X)))))&
(![X]:((~generous(X)|~brave(X))=>(kind(X)<~>strong(X))))&
(?[X]:((~happy(X)<~>~quiet(X))))&
((~rich(lucy)<~>kind(lucy)))&
(?[X]:((~kind(X)|tall(X))))&
((tall(paul)&~patient(paul)))&
((calm(fred)&generous(fred)))&
(tall(susan))&
((~wise(fred)<~>happy(fred)))&
((calm(lucy)&curious(lucy))) | happy(lucy) | [
"p1",
"p2",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7025641528070068500592324
% SZS output start Proof for 7025641528070068500592324
2. ! [X0] : ((brave(X0) | creative(X0)) => (~strong(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((~brave(X0) & patient(X0)) <=> ~happy(X0)) [input p2]
8. ! [X0] : (~happy(X0) <=> (~brave(X0) <~> ~funny(X0))) [input p7]
12. ! [X0] : (patient(X0) <=> (brave(X0) & ~tall(X0))) [input p11]
25. ~happy(lucy) [input hypothesis]
28. ! [X0] : ((~strong(X0) & ~funny(X0)) | (~brave(X0) & ~creative(X0))) [ennf transformation 2]
41. ! [X0] : (((~brave(X0) & patient(X0)) | happy(X0)) & (~happy(X0) | (brave(X0) | ~patient(X0)))) [nnf transformation 3]
42. ! [X0] : (((~brave(X0) & patient(X0)) | happy(X0)) & (~happy(X0) | brave(X0) | ~patient(X0))) [flattening 41]
51. ! [X0] : ((~happy(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | happy(X0))) [nnf transformation 8]
58. ! [X0] : ((patient(X0) | (~brave(X0) | tall(X0))) & ((brave(X0) & ~tall(X0)) | ~patient(X0))) [nnf transformation 12]
59. ! [X0] : ((patient(X0) | ~brave(X0) | tall(X0)) & ((brave(X0) & ~tall(X0)) | ~patient(X0))) [flattening 58]
79. ~brave(X0) | ~funny(X0) [cnf transformation 28]
83. happy(X0) | patient(X0) [cnf transformation 42]
84. ~brave(X0) | happy(X0) [cnf transformation 42]
104. ~happy(X0) | ~brave(X0) | funny(X0) [cnf transformation 51]
115. brave(X0) | ~patient(X0) [cnf transformation 59]
147. ~happy(lucy) [cnf transformation 25]
199. ~happy(X0) | ~brave(X0) [subsumption resolution 104,79]
200. ~brave(X0) [subsumption resolution 199,84]
225. ~patient(X0) [subsumption resolution 115,200]
275. patient(lucy) [resolution 83,147]
277. $false [subsumption resolution 275,225]
% SZS output end Proof for 7025641528070068500592324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not humble or not calm and vice versa.
Everyone who is either not calm or not strong is not funny.
If fred is not brave or not curious then someone is both curious and not generous and vice versa.
Everyone who is both not happy and not curious is old or not wise.
Everyone who is curious or tall is not rich and vice versa.
If someone is quiet or not generous then fred is both not generous and strong.
Everyone who is either happy or not rich is not rich and vice versa.
If someone is creative then john is strong and vice versa.
If someone is creative then someone is curious.
Everyone who is not humble is both creative and rich and vice versa.
Everyone who is either not tall or tall is not strong.
Everyone who is funny is both happy and patient.
Everyone who is patient is tall or wise and vice versa.
If someone is both not humble and not calm then lucy is wise and vice versa.
If susan is both not brave and not creative then john is not creative.
Everyone who is quiet is not kind or creative.
Lucy is not creative.
Someone is either not tall or not patient.
Lucy is not quiet or patient.
Someone is either not funny or quiet.
Susan is not wise. | Susan is creative. | contradiction | (![X]:(~generous(X)<=>(~humble(X)|~calm(X))))&
(![X]:((~calm(X)<~>~strong(X))=>~funny(X)))&
(((~brave(fred)|~curious(fred)))<=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:((~happy(X)&~curious(X))=>(old(X)|~wise(X))))&
(![X]:((curious(X)|tall(X))<=>~rich(X)))&
((?[X]:((quiet(X)|~generous(X))))=>((~generous(fred)&strong(fred))))&
(![X]:((happy(X)<~>~rich(X))<=>~rich(X)))&
((?[X]:(creative(X)))<=>(strong(john)))&
((?[X]:(creative(X)))=>(?[X]:(curious(X))))&
(![X]:(~humble(X)<=>(creative(X)&rich(X))))&
(![X]:((~tall(X)<~>tall(X))=>~strong(X)))&
(![X]:(funny(X)=>(happy(X)&patient(X))))&
(![X]:(patient(X)<=>(tall(X)|wise(X))))&
((?[X]:((~humble(X)&~calm(X))))<=>(wise(lucy)))&
(((~brave(susan)&~creative(susan)))=>(~creative(john)))&
(![X]:(quiet(X)=>(~kind(X)|creative(X))))&
(~creative(lucy))&
(?[X]:((~tall(X)<~>~patient(X))))&
((~quiet(lucy)|patient(lucy)))&
(?[X]:((~funny(X)<~>quiet(X))))&
(~wise(susan)) | creative(susan) | [
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4692677040464559674683511
% SZS output start Proof for 4692677040464559674683511
8. ? [X0] : creative(X0) <=> strong(john) [input p7]
11. ! [X0] : ((~tall(X0) <~> tall(X0)) => ~strong(X0)) [input p10]
22. creative(susan) [input hypothesis]
29. ! [X0] : (~strong(X0) | (~tall(X0) <=> tall(X0))) [ennf transformation 11]
44. (? [X0] : creative(X0) | ~strong(john)) & (strong(john) | ! [X0] : ~creative(X0)) [nnf transformation 8]
45. (? [X0] : creative(X0) | ~strong(john)) & (strong(john) | ! [X1] : ~creative(X1)) [rectify 44]
46. ? [X0] : creative(X0) => creative(sK1) [choice axiom]
47. (creative(sK1) | ~strong(john)) & (strong(john) | ! [X1] : ~creative(X1)) [skolemisation 45,46]
53. ! [X0] : (~strong(X0) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 29]
87. strong(john) | ~creative(X1) [cnf transformation 47]
93. ~strong(X0) | tall(X0) | tall(X0) [cnf transformation 53]
94. ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 53]
111. creative(susan) [cnf transformation 22]
112. ~strong(X0) | tall(X0) [duplicate literal removal 93]
113. ~strong(X0) | ~tall(X0) [duplicate literal removal 94]
160. 10 <=> strong(john) [avatar definition]
161. strong(john) <- (10) [avatar component clause 160]
169. 12 <=> ! [X1] : ~creative(X1) [avatar definition]
170. ~creative(X1) <- (12) [avatar component clause 169]
171. 12 | 10 [avatar split clause 87,160,169]
177. ~strong(X0) [subsumption resolution 112,113]
202. 19 <=> creative(susan) [avatar definition]
204. creative(susan) <- (19) [avatar component clause 202]
222. 19 [avatar split clause 111,202]
229. $false <- (12, 19) [resolution 204,170]
230. ~12 | ~19 [avatar contradiction clause 229]
231. $false <- (10) [subsumption resolution 161,177]
232. ~10 [avatar contradiction clause 231]
233. $false [avatar sat refutation 171,222,230,232]
% SZS output end Proof for 4692677040464559674683511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not tall and not funny then paul is either not curious or happy and vice versa.
If mary is both creative and strong then mary is both not old and not calm.
If john is both not curious and strong then mary is either tall or rich and vice versa.
Everyone who is both kind and generous is either patient or not brave.
If lucy is not funny then paul is humble and vice versa.
Everyone who is both not funny and not wise is not kind and vice versa.
Everyone who is both calm and patient is both brave and quiet.
If someone is both not kind and strong then mary is not patient and vice versa.
If paul is not kind or generous then someone is not quiet or not humble and vice versa.
If john is not wise or not rich then lucy is not quiet and vice versa.
Everyone who is both happy and brave is both strong and quiet.
If someone is old then someone is both not funny and humble and vice versa.
Everyone who is either not tall or quiet is both not tall and not patient and vice versa.
Everyone who is both not tall and creative is funny or curious and vice versa.
Everyone who is strong is humble.
If someone is not old or not patient then paul is both creative and strong.
Mary is both not patient and brave.
Mary is old.
Someone is quiet or not wise.
Someone is generous or wise.
Someone is not rich or not generous.
Paul is rich.
Someone is both old and brave. | Lucy is calm. | neutral | (((~tall(mary)&~funny(mary)))<=>((~curious(paul)<~>happy(paul))))&
(((creative(mary)&strong(mary)))=>((~old(mary)&~calm(mary))))&
(((~curious(john)&strong(john)))<=>((tall(mary)<~>rich(mary))))&
(![X]:((kind(X)&generous(X))=>(patient(X)<~>~brave(X))))&
((~funny(lucy))<=>(humble(paul)))&
(![X]:((~funny(X)&~wise(X))<=>~kind(X)))&
(![X]:((calm(X)&patient(X))=>(brave(X)&quiet(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(~patient(mary)))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(((~wise(john)|~rich(john)))<=>(~quiet(lucy)))&
(![X]:((happy(X)&brave(X))=>(strong(X)&quiet(X))))&
((?[X]:(old(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&creative(X))<=>(funny(X)|curious(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~old(X)|~patient(X))))=>((creative(paul)&strong(paul))))&
((~patient(mary)&brave(mary)))&
(old(mary))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((generous(X)|wise(X))))&
(?[X]:((~rich(X)|~generous(X))))&
(rich(paul))&
(?[X]:((old(X)&brave(X)))) | calm(lucy) | [] | null | 0 |
If someone is both quiet and not humble then susan is strong and vice versa. If someone is tall then lucy is not brave and vice versa. Everyone who is either not wise or not brave is patient or curious and vice versa. Everyone who is not wise or not humble is not tall or kind and vice versa. Everyone who is not old or rich is patient. Everyone who is not curious is not quiet and vice versa. If someone is either not humble or happy then mary is happy and vice versa. Everyone who is either calm or not calm is creative and vice versa. Everyone who is quiet or not brave is rich and vice versa. Everyone who is both strong and curious is creative and vice versa. If alice is either curious or tall then paul is both brave and not curious. If john is either happy or rich then alice is both not funny and not generous. Everyone who is either tall or not old is either not strong or happy and vice versa. Everyone who is not creative or tall is either creative or wise and vice versa. If someone is quiet then someone is old or not curious. Someone is both not wise and quiet. Paul is both not brave and kind. Someone is humble. Susan is not old. John is either creative or generous. | Paul is tall. | contradiction | ((?[X]:((quiet(X)&~humble(X))))<=>(strong(susan)))&
((?[X]:(tall(X)))<=>(~brave(lucy)))&
(![X]:((~wise(X)<~>~brave(X))<=>(patient(X)|curious(X))))&
(![X]:((~wise(X)|~humble(X))<=>(~tall(X)|kind(X))))&
(![X]:((~old(X)|rich(X))=>patient(X)))&
(![X]:(~curious(X)<=>~quiet(X)))&
((?[X]:((~humble(X)<~>happy(X))))<=>(happy(mary)))&
(![X]:((calm(X)<~>~calm(X))<=>creative(X)))&
(![X]:((quiet(X)|~brave(X))<=>rich(X)))&
(![X]:((strong(X)&curious(X))<=>creative(X)))&
(((curious(alice)<~>tall(alice)))=>((brave(paul)&~curious(paul))))&
(((happy(john)<~>rich(john)))=>((~funny(alice)&~generous(alice))))&
(![X]:((tall(X)<~>~old(X))<=>(~strong(X)<~>happy(X))))&
(![X]:((~creative(X)|tall(X))<=>(creative(X)<~>wise(X))))&
((?[X]:(quiet(X)))=>(?[X]:((old(X)|~curious(X)))))&
(?[X]:((~wise(X)&quiet(X))))&
((~brave(paul)&kind(paul)))&
(?[X]:(humble(X)))&
(~old(susan))&
((creative(john)<~>generous(john))) | tall(paul) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p9",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7344795674739559208913293
% SZS output start Proof for 7344795674739559208913293
3. ! [X0] : ((~wise(X0) <~> ~brave(X0)) <=> (curious(X0) | patient(X0))) [input p2]
5. ! [X0] : ((rich(X0) | ~old(X0)) => patient(X0)) [input p4]
6. ! [X0] : (~curious(X0) <=> ~quiet(X0)) [input p5]
8. ! [X0] : ((calm(X0) <~> ~calm(X0)) <=> creative(X0)) [input p7]
9. ! [X0] : ((~brave(X0) | quiet(X0)) <=> rich(X0)) [input p8]
10. ! [X0] : ((curious(X0) & strong(X0)) <=> creative(X0)) [input p9]
14. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (creative(X0) <~> wise(X0))) [input p13]
17. kind(paul) & ~brave(paul) [input p16]
21. tall(paul) [input hypothesis]
24. ! [X0] : (patient(X0) | (~rich(X0) & old(X0))) [ennf transformation 5]
36. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~curious(X0) & ~patient(X0))) & ((curious(X0) | patient(X0)) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [nnf transformation 3]
37. ! [X0] : ((((brave(X0) | wise(X0)) & (~brave(X0) | ~wise(X0))) | (~curious(X0) & ~patient(X0))) & (curious(X0) | patient(X0) | ((~wise(X0) | brave(X0)) & (~brave(X0) | wise(X0))))) [flattening 36]
40. ! [X0] : ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0))) [nnf transformation 6]
45. ! [X0] : ((((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | ~creative(X0)) & (creative(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0))))) [nnf transformation 8]
46. ! [X0] : (((~brave(X0) | quiet(X0)) | ~rich(X0)) & (rich(X0) | (brave(X0) & ~quiet(X0)))) [nnf transformation 9]
47. ! [X0] : ((~brave(X0) | quiet(X0) | ~rich(X0)) & (rich(X0) | (brave(X0) & ~quiet(X0)))) [flattening 46]
48. ! [X0] : (((curious(X0) & strong(X0)) | ~creative(X0)) & (creative(X0) | (~curious(X0) | ~strong(X0)))) [nnf transformation 10]
49. ! [X0] : (((curious(X0) & strong(X0)) | ~creative(X0)) & (creative(X0) | ~curious(X0) | ~strong(X0))) [flattening 48]
53. ! [X0] : (((tall(X0) | ~creative(X0)) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & creative(X0)))) [nnf transformation 14]
54. ! [X0] : ((tall(X0) | ~creative(X0) | ((creative(X0) | ~wise(X0)) & (wise(X0) | ~creative(X0)))) & (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (~tall(X0) & creative(X0)))) [flattening 53]
72. ~patient(X0) | wise(X0) | brave(X0) [cnf transformation 37]
79. ~rich(X0) | patient(X0) [cnf transformation 24]
81. ~curious(X0) | quiet(X0) [cnf transformation 40]
86. creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
87. creative(X0) | calm(X0) | calm(X0) [cnf transformation 45]
90. ~quiet(X0) | rich(X0) [cnf transformation 47]
95. curious(X0) | ~creative(X0) [cnf transformation 49]
113. ~wise(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 54]
119. ~brave(paul) [cnf transformation 17]
125. tall(paul) [cnf transformation 21]
128. creative(X0) | ~calm(X0) [duplicate literal removal 86]
129. creative(X0) | calm(X0) [duplicate literal removal 87]
183. creative(X0) [subsumption resolution 128,129]
184. curious(X0) [subsumption resolution 95,183]
207. ~wise(X0) | ~tall(X0) [subsumption resolution 113,183]
225. quiet(X0) [resolution 81,184]
229. rich(X0) [resolution 90,225]
233. patient(X0) [resolution 229,79]
264. wise(X0) | brave(X0) [resolution 72,233]
555. ~tall(X3) | brave(X3) [resolution 264,207]
585. brave(paul) [resolution 555,125]
592. $false [subsumption resolution 585,119]
% SZS output end Proof for 7344795674739559208913293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is both tall and not generous.
If someone is either brave or not wise then someone is not creative or not brave.
If susan is either creative or rich then mary is both humble and not happy and vice versa.
Everyone who is either not happy or not creative is not brave or generous and vice versa.
Everyone who is either creative or tall is wise.
Everyone who is both humble and old is old or not wise.
Everyone who is not kind is not quiet or quiet.
Everyone who is rich is not funny.
If paul is either quiet or kind then someone is not tall.
Everyone who is strong or kind is not wise or not happy and vice versa.
Everyone who is both not old and not happy is humble and vice versa.
If someone is either not tall or rich then someone is curious.
Everyone who is strong is not patient and vice versa.
Everyone who is brave is either rich or old and vice versa.
If paul is either not rich or strong then susan is both not wise and kind and vice versa.
Everyone who is not rich or generous is both strong and not old and vice versa.
Fred is not strong.
Someone is either not generous or old.
Someone is not calm or quiet.
Someone is either not generous or not creative.
Someone is humble or not quiet.
Mary is not patient or not curious.
Paul is not funny or curious.
Someone is both tall and not rich. | Fred is not rich. | contradiction | (![X]:(~old(X)=>(tall(X)&~generous(X))))&
((?[X]:((brave(X)<~>~wise(X))))=>(?[X]:((~creative(X)|~brave(X)))))&
(((creative(susan)<~>rich(susan)))<=>((humble(mary)&~happy(mary))))&
(![X]:((~happy(X)<~>~creative(X))<=>(~brave(X)|generous(X))))&
(![X]:((creative(X)<~>tall(X))=>wise(X)))&
(![X]:((humble(X)&old(X))=>(old(X)|~wise(X))))&
(![X]:(~kind(X)=>(~quiet(X)|quiet(X))))&
(![X]:(rich(X)=>~funny(X)))&
(((quiet(paul)<~>kind(paul)))=>(?[X]:(~tall(X))))&
(![X]:((strong(X)|kind(X))<=>(~wise(X)|~happy(X))))&
(![X]:((~old(X)&~happy(X))<=>humble(X)))&
((?[X]:((~tall(X)<~>rich(X))))=>(?[X]:(curious(X))))&
(![X]:(strong(X)<=>~patient(X)))&
(![X]:(brave(X)<=>(rich(X)<~>old(X))))&
(((~rich(paul)<~>strong(paul)))<=>((~wise(susan)&kind(susan))))&
(![X]:((~rich(X)|generous(X))<=>(strong(X)&~old(X))))&
(~strong(fred))&
(?[X]:((~generous(X)<~>old(X))))&
(?[X]:((~calm(X)|quiet(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((humble(X)|~quiet(X))))&
((~patient(mary)|~curious(mary)))&
((~funny(paul)|curious(paul)))&
(?[X]:((tall(X)&~rich(X)))) | ~rich(fred) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5112658397784854618686261
% SZS output start Proof for 5112658397784854618686261
16. ! [X0] : ((generous(X0) | ~rich(X0)) <=> (~old(X0) & strong(X0))) [input p15]
17. ~strong(fred) [input p16]
25. ~rich(fred) [input hypothesis]
64. ! [X0] : (((generous(X0) | ~rich(X0)) | (old(X0) | ~strong(X0))) & ((~old(X0) & strong(X0)) | (~generous(X0) & rich(X0)))) [nnf transformation 16]
65. ! [X0] : ((generous(X0) | ~rich(X0) | old(X0) | ~strong(X0)) & ((~old(X0) & strong(X0)) | (~generous(X0) & rich(X0)))) [flattening 64]
119. strong(X0) | rich(X0) [cnf transformation 65]
124. ~strong(fred) [cnf transformation 17]
133. ~rich(fred) [cnf transformation 25]
244. rich(fred) [resolution 119,124]
246. $false [subsumption resolution 244,133]
% SZS output end Proof for 5112658397784854618686261
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and kind is calm and vice versa.
If fred is not tall then someone is either wise or not wise and vice versa.
If lucy is not tall or rich then paul is both not funny and not humble and vice versa.
Everyone who is both wise and not rich is not humble and vice versa.
If someone is brave then lucy is either humble or not funny and vice versa.
If someone is either calm or humble then alice is either not old or old and vice versa.
Everyone who is not happy or tall is either not strong or not old.
Everyone who is brave is rich.
If susan is not curious then susan is not humble or not calm.
Everyone who is either tall or not strong is funny or not creative and vice versa.
Everyone who is either not calm or creative is not rich and vice versa.
Everyone who is both not patient and not strong is not humble.
If alice is either not funny or generous then fred is either not wise or kind.
If someone is both not happy and not patient then fred is both not wise and not strong.
If paul is either not happy or happy then someone is either curious or wise.
Everyone who is not humble is not happy and vice versa.
Paul is not strong or not generous.
Lucy is strong or curious.
Paul is both not calm and not funny.
Mary is not strong.
Someone is strong or humble.
Lucy is not generous.
Someone is wise or not generous.
John is patient or funny. | Paul is not humble. | neutral | (![X]:((brave(X)&kind(X))<=>calm(X)))&
((~tall(fred))<=>(?[X]:((wise(X)<~>~wise(X)))))&
(((~tall(lucy)|rich(lucy)))<=>((~funny(paul)&~humble(paul))))&
(![X]:((wise(X)&~rich(X))<=>~humble(X)))&
((?[X]:(brave(X)))<=>((humble(lucy)<~>~funny(lucy))))&
((?[X]:((calm(X)<~>humble(X))))<=>((~old(alice)<~>old(alice))))&
(![X]:((~happy(X)|tall(X))=>(~strong(X)<~>~old(X))))&
(![X]:(brave(X)=>rich(X)))&
((~curious(susan))=>((~humble(susan)|~calm(susan))))&
(![X]:((tall(X)<~>~strong(X))<=>(funny(X)|~creative(X))))&
(![X]:((~calm(X)<~>creative(X))<=>~rich(X)))&
(![X]:((~patient(X)&~strong(X))=>~humble(X)))&
(((~funny(alice)<~>generous(alice)))=>((~wise(fred)<~>kind(fred))))&
((?[X]:((~happy(X)&~patient(X))))=>((~wise(fred)&~strong(fred))))&
(((~happy(paul)<~>happy(paul)))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:(~humble(X)<=>~happy(X)))&
((~strong(paul)|~generous(paul)))&
((strong(lucy)|curious(lucy)))&
((~calm(paul)&~funny(paul)))&
(~strong(mary))&
(?[X]:((strong(X)|humble(X))))&
(~generous(lucy))&
(?[X]:((wise(X)|~generous(X))))&
((patient(john)|funny(john))) | ~humble(paul) | [] | null | 0 |
Everyone who is not old is old.
Everyone who is both tall and not generous is both calm and not kind and vice versa.
If fred is both humble and brave then susan is both old and not strong.
If someone is either not calm or not creative then susan is wise.
If john is not old then someone is either not happy or not patient and vice versa.
Everyone who is patient or kind is both curious and strong.
Everyone who is funny is both not happy and patient and vice versa.
If someone is patient or not quiet then alice is both not generous and not funny and vice versa.
Everyone who is not creative is both not strong and generous.
If fred is not curious or humble then susan is strong.
If someone is not quiet then someone is not happy or not creative.
If someone is either happy or kind then susan is either not creative or not curious and vice versa.
Everyone who is both not creative and tall is both not brave and not calm and vice versa.
If paul is either wise or curious then john is both strong and old and vice versa.
If susan is not funny then someone is not kind or rich.
Everyone who is not tall or strong is either old or strong and vice versa.
Someone is humble or not humble.
Susan is old or not curious.
Fred is either not patient or happy.
Alice is either not humble or strong.
Someone is either not calm or humble.
Someone is not generous or not rich. | Paul is not brave. | contradiction | (![X]:(~old(X)=>old(X)))&
(![X]:((tall(X)&~generous(X))<=>(calm(X)&~kind(X))))&
(((humble(fred)&brave(fred)))=>((old(susan)&~strong(susan))))&
((?[X]:((~calm(X)<~>~creative(X))))=>(wise(susan)))&
((~old(john))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((patient(X)|kind(X))=>(curious(X)&strong(X))))&
(![X]:(funny(X)<=>(~happy(X)&patient(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>((~generous(alice)&~funny(alice))))&
(![X]:(~creative(X)=>(~strong(X)&generous(X))))&
(((~curious(fred)|humble(fred)))=>(strong(susan)))&
((?[X]:(~quiet(X)))=>(?[X]:((~happy(X)|~creative(X)))))&
((?[X]:((happy(X)<~>kind(X))))<=>((~creative(susan)<~>~curious(susan))))&
(![X]:((~creative(X)&tall(X))<=>(~brave(X)&~calm(X))))&
(((wise(paul)<~>curious(paul)))<=>((strong(john)&old(john))))&
((~funny(susan))=>(?[X]:((~kind(X)|rich(X)))))&
(![X]:((~tall(X)|strong(X))<=>(old(X)<~>strong(X))))&
(?[X]:((humble(X)|~humble(X))))&
((old(susan)|~curious(susan)))&
((~patient(fred)<~>happy(fred)))&
((~humble(alice)<~>strong(alice)))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:((~generous(X)|~rich(X)))) | ~brave(paul) | [
"p0",
"p1",
"p5",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4077707065508838843998206
% SZS output start Proof for 4077707065508838843998206
1. ! [X0] : (~old(X0) => old(X0)) [input p0]
2. ! [X0] : ((~generous(X0) & tall(X0)) <=> (~kind(X0) & calm(X0))) [input p1]
6. ! [X0] : ((kind(X0) | patient(X0)) => (strong(X0) & curious(X0))) [input p5]
13. ! [X0] : ((tall(X0) & ~creative(X0)) <=> (~calm(X0) & ~brave(X0))) [input p12]
16. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (old(X0) <~> strong(X0))) [input p15]
23. ~brave(paul) [input hypothesis]
25. ! [X0] : (old(X0) | old(X0)) [ennf transformation 1]
29. ! [X0] : ((strong(X0) & curious(X0)) | (~kind(X0) & ~patient(X0))) [ennf transformation 6]
34. ! [X0] : (((~generous(X0) & tall(X0)) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 2]
35. ! [X0] : (((~generous(X0) & tall(X0)) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | generous(X0) | ~tall(X0))) [flattening 34]
55. ! [X0] : (((tall(X0) & ~creative(X0)) | (calm(X0) | brave(X0))) & ((~calm(X0) & ~brave(X0)) | (~tall(X0) | creative(X0)))) [nnf transformation 13]
56. ! [X0] : (((tall(X0) & ~creative(X0)) | calm(X0) | brave(X0)) & ((~calm(X0) & ~brave(X0)) | ~tall(X0) | creative(X0))) [flattening 55]
61. ! [X0] : (((strong(X0) | ~tall(X0)) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~strong(X0) & tall(X0)))) [nnf transformation 16]
62. ! [X0] : ((strong(X0) | ~tall(X0) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) & (((~strong(X0) | ~old(X0)) & (strong(X0) | old(X0))) | (~strong(X0) & tall(X0)))) [flattening 61]
72. old(X0) | old(X0) [cnf transformation 25]
75. ~calm(X0) | kind(X0) | tall(X0) [cnf transformation 35]
88. ~kind(X0) | strong(X0) [cnf transformation 29]
113. brave(X0) | calm(X0) | tall(X0) [cnf transformation 56]
124. ~strong(X0) | ~old(X0) | ~strong(X0) [cnf transformation 62]
125. strong(X0) | ~tall(X0) | strong(X0) | ~old(X0) [cnf transformation 62]
136. ~brave(paul) [cnf transformation 23]
137. ~strong(X0) | ~old(X0) [duplicate literal removal 124]
138. strong(X0) | ~tall(X0) | ~old(X0) [duplicate literal removal 125]
139. old(X0) [duplicate literal removal 72]
270. ~tall(X0) | strong(X0) [subsumption resolution 138,139]
271. ~strong(X0) [subsumption resolution 137,139]
334. calm(paul) | tall(paul) [resolution 113,136]
337. 37 <=> tall(paul) [avatar definition]
339. tall(paul) <- (37) [avatar component clause 337]
341. 38 <=> calm(paul) [avatar definition]
343. calm(paul) <- (38) [avatar component clause 341]
344. 37 | 38 [avatar split clause 334,341,337]
347. kind(paul) | tall(paul) <- (38) [resolution 343,75]
358. 41 <=> kind(paul) [avatar definition]
360. kind(paul) <- (41) [avatar component clause 358]
362. 37 | 41 | ~38 [avatar split clause 347,341,358,337]
372. strong(paul) <- (41) [resolution 360,88]
374. $false <- (41) [subsumption resolution 372,271]
375. ~41 [avatar contradiction clause 374]
380. strong(paul) <- (37) [resolution 339,270]
381. $false <- (37) [subsumption resolution 380,271]
382. ~37 [avatar contradiction clause 381]
383. $false [avatar sat refutation 344,362,375,382]
% SZS output end Proof for 4077707065508838843998206
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not creative is both funny and not strong.
Everyone who is both not brave and funny is both strong and not kind.
Everyone who is not strong or not patient is both not creative and kind and vice versa.
If someone is not curious then someone is humble and vice versa.
If paul is either kind or rich then someone is brave and vice versa.
Everyone who is either generous or not creative is funny or calm and vice versa.
Everyone who is both not wise and humble is either curious or quiet.
Everyone who is either generous or rich is either not humble or not strong and vice versa.
If alice is rich or funny then alice is both brave and not creative and vice versa.
If someone is not calm or not rich then paul is patient or calm and vice versa.
Everyone who is calm is not kind or patient and vice versa.
If someone is not creative then lucy is generous and vice versa.
If fred is either strong or old then someone is either kind or humble.
If lucy is strong or generous then someone is not generous.
If mary is both not happy and humble then alice is not patient or not brave and vice versa.
If mary is happy or not tall then someone is not old.
Alice is both quiet and not patient.
Someone is not calm.
Susan is not quiet.
John is both not rich and calm.
Lucy is either not tall or happy.
Fred is not calm.
Susan is either not curious or not calm.
Alice is not calm. | John is patient. | entailment | (![X]:((~generous(X)|~creative(X))=>(funny(X)&~strong(X))))&
(![X]:((~brave(X)&funny(X))=>(strong(X)&~kind(X))))&
(![X]:((~strong(X)|~patient(X))<=>(~creative(X)&kind(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(humble(X))))&
(((kind(paul)<~>rich(paul)))<=>(?[X]:(brave(X))))&
(![X]:((generous(X)<~>~creative(X))<=>(funny(X)|calm(X))))&
(![X]:((~wise(X)&humble(X))=>(curious(X)<~>quiet(X))))&
(![X]:((generous(X)<~>rich(X))<=>(~humble(X)<~>~strong(X))))&
(((rich(alice)|funny(alice)))<=>((brave(alice)&~creative(alice))))&
((?[X]:((~calm(X)|~rich(X))))<=>((patient(paul)|calm(paul))))&
(![X]:(calm(X)<=>(~kind(X)|patient(X))))&
((?[X]:(~creative(X)))<=>(generous(lucy)))&
(((strong(fred)<~>old(fred)))=>(?[X]:((kind(X)<~>humble(X)))))&
(((strong(lucy)|generous(lucy)))=>(?[X]:(~generous(X))))&
(((~happy(mary)&humble(mary)))<=>((~patient(alice)|~brave(alice))))&
(((happy(mary)|~tall(mary)))=>(?[X]:(~old(X))))&
((quiet(alice)&~patient(alice)))&
(?[X]:(~calm(X)))&
(~quiet(susan))&
((~rich(john)&calm(john)))&
((~tall(lucy)<~>happy(lucy)))&
(~calm(fred))&
((~curious(susan)<~>~calm(susan)))&
(~calm(alice)) | patient(john) | [
"p2",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5368026731302559805120871
% SZS output start Proof for 5368026731302559805120871
3. ! [X0] : ((~patient(X0) | ~strong(X0)) <=> (kind(X0) & ~creative(X0))) [input p2]
11. ! [X0] : (calm(X0) <=> (patient(X0) | ~kind(X0))) [input p10]
20. calm(john) & ~rich(john) [input p19]
25. ~patient(john) [input hypothesis]
34. ! [X0] : (((~patient(X0) | ~strong(X0)) | (~kind(X0) | creative(X0))) & ((kind(X0) & ~creative(X0)) | (patient(X0) & strong(X0)))) [nnf transformation 3]
35. ! [X0] : ((~patient(X0) | ~strong(X0) | ~kind(X0) | creative(X0)) & ((kind(X0) & ~creative(X0)) | (patient(X0) & strong(X0)))) [flattening 34]
55. ! [X0] : ((calm(X0) | (~patient(X0) & kind(X0))) & ((patient(X0) | ~kind(X0)) | ~calm(X0))) [nnf transformation 11]
56. ! [X0] : ((calm(X0) | (~patient(X0) & kind(X0))) & (patient(X0) | ~kind(X0) | ~calm(X0))) [flattening 55]
83. patient(X0) | kind(X0) [cnf transformation 35]
114. patient(X0) | ~kind(X0) | ~calm(X0) [cnf transformation 56]
137. calm(john) [cnf transformation 20]
144. ~patient(john) [cnf transformation 25]
234. ~calm(X0) | patient(X0) [subsumption resolution 114,83]
356. patient(john) [resolution 234,137]
360. $false [subsumption resolution 356,144]
% SZS output end Proof for 5368026731302559805120871
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then someone is kind or not brave.
Everyone who is either not rich or not wise is either happy or not happy and vice versa.
If paul is both not old and not generous then paul is patient or not curious.
If john is both not kind and curious then someone is generous or not quiet and vice versa.
Everyone who is humble is either kind or funny and vice versa.
Everyone who is not quiet or rich is not strong or quiet.
Everyone who is not funny is not strong.
Everyone who is kind is either not generous or funny and vice versa.
Everyone who is both patient and not old is both curious and happy.
Everyone who is curious is both kind and strong.
If someone is either not quiet or curious then lucy is either not rich or quiet.
If alice is either generous or not curious then someone is both wise and not strong.
Everyone who is kind or not kind is both not happy and not strong.
If someone is either not patient or not calm then lucy is both curious and happy and vice versa.
If someone is not calm then susan is wise.
Everyone who is not tall is both quiet and wise.
Alice is not rich or not curious.
Someone is not brave.
Fred is not rich.
Someone is either generous or not patient.
Susan is both not creative and not old.
John is both not creative and funny. | Susan is wise. | entailment | ((?[X]:(curious(X)))=>(?[X]:((kind(X)|~brave(X)))))&
(![X]:((~rich(X)<~>~wise(X))<=>(happy(X)<~>~happy(X))))&
(((~old(paul)&~generous(paul)))=>((patient(paul)|~curious(paul))))&
(((~kind(john)&curious(john)))<=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:(humble(X)<=>(kind(X)<~>funny(X))))&
(![X]:((~quiet(X)|rich(X))=>(~strong(X)|quiet(X))))&
(![X]:(~funny(X)=>~strong(X)))&
(![X]:(kind(X)<=>(~generous(X)<~>funny(X))))&
(![X]:((patient(X)&~old(X))=>(curious(X)&happy(X))))&
(![X]:(curious(X)=>(kind(X)&strong(X))))&
((?[X]:((~quiet(X)<~>curious(X))))=>((~rich(lucy)<~>quiet(lucy))))&
(((generous(alice)<~>~curious(alice)))=>(?[X]:((wise(X)&~strong(X)))))&
(![X]:((kind(X)|~kind(X))=>(~happy(X)&~strong(X))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>((curious(lucy)&happy(lucy))))&
((?[X]:(~calm(X)))=>(wise(susan)))&
(![X]:(~tall(X)=>(quiet(X)&wise(X))))&
((~rich(alice)|~curious(alice)))&
(?[X]:(~brave(X)))&
(~rich(fred))&
(?[X]:((generous(X)<~>~patient(X))))&
((~creative(susan)&~old(susan)))&
((~creative(john)&funny(john))) | wise(susan) | [
"p3",
"p9",
"p12",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4592271388784561102489835
% SZS output start Proof for 4592271388784561102489835
4. (curious(john) & ~kind(john)) <=> ? [X0] : (~quiet(X0) | generous(X0)) [input p3]
10. ! [X0] : (curious(X0) => (strong(X0) & kind(X0))) [input p9]
13. ! [X0] : ((~kind(X0) | kind(X0)) => (~strong(X0) & ~happy(X0))) [input p12]
14. ? [X0] : (~patient(X0) <~> ~calm(X0)) <=> (happy(lucy) & curious(lucy)) [input p13]
15. ? [X0] : ~calm(X0) => wise(susan) [input p14]
20. ? [X0] : (generous(X0) <~> ~patient(X0)) [input p19]
23. ~wise(susan) [input hypothesis]
37. ! [X0] : ((strong(X0) & kind(X0)) | ~curious(X0)) [ennf transformation 10]
40. ! [X0] : ((~strong(X0) & ~happy(X0)) | (kind(X0) & ~kind(X0))) [ennf transformation 13]
41. wise(susan) | ! [X0] : calm(X0) [ennf transformation 15]
43. ((curious(john) & ~kind(john)) | ! [X0] : (quiet(X0) & ~generous(X0))) & (? [X0] : (~quiet(X0) | generous(X0)) | (~curious(john) | kind(john))) [nnf transformation 4]
44. ((curious(john) & ~kind(john)) | ! [X0] : (quiet(X0) & ~generous(X0))) & (? [X0] : (~quiet(X0) | generous(X0)) | ~curious(john) | kind(john)) [flattening 43]
45. ((curious(john) & ~kind(john)) | ! [X0] : (quiet(X0) & ~generous(X0))) & (? [X1] : (~quiet(X1) | generous(X1)) | ~curious(john) | kind(john)) [rectify 44]
46. ? [X1] : (~quiet(X1) | generous(X1)) => (~quiet(sK0) | generous(sK0)) [choice axiom]
47. ((curious(john) & ~kind(john)) | ! [X0] : (quiet(X0) & ~generous(X0))) & ((~quiet(sK0) | generous(sK0)) | ~curious(john) | kind(john)) [skolemisation 45,46]
53. (? [X0] : ((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~happy(lucy) | ~curious(lucy))) & ((happy(lucy) & curious(lucy)) | ! [X0] : ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) [nnf transformation 14]
54. (? [X0] : ((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~happy(lucy) | ~curious(lucy)) & ((happy(lucy) & curious(lucy)) | ! [X0] : ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) [flattening 53]
55. (? [X0] : ((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~happy(lucy) | ~curious(lucy)) & ((happy(lucy) & curious(lucy)) | ! [X1] : ((~patient(X1) | calm(X1)) & (~calm(X1) | patient(X1)))) [rectify 54]
56. ? [X0] : ((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) => ((calm(sK2) | patient(sK2)) & (~calm(sK2) | ~patient(sK2))) [choice axiom]
57. (((calm(sK2) | patient(sK2)) & (~calm(sK2) | ~patient(sK2))) | ~happy(lucy) | ~curious(lucy)) & ((happy(lucy) & curious(lucy)) | ! [X1] : ((~patient(X1) | calm(X1)) & (~calm(X1) | patient(X1)))) [skolemisation 55,56]
58. ? [X0] : ((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) [nnf transformation 20]
59. ? [X0] : ((patient(X0) | ~generous(X0)) & (~patient(X0) | generous(X0))) => ((patient(sK3) | ~generous(sK3)) & (~patient(sK3) | generous(sK3))) [choice axiom]
60. (patient(sK3) | ~generous(sK3)) & (~patient(sK3) | generous(sK3)) [skolemisation 58,59]
71. ~kind(john) | ~generous(X0) [cnf transformation 47]
73. curious(john) | ~generous(X0) [cnf transformation 47]
84. ~curious(X0) | kind(X0) [cnf transformation 37]
94. ~happy(X0) | ~kind(X0) [cnf transformation 40]
95. ~happy(X0) | kind(X0) [cnf transformation 40]
100. happy(lucy) | ~calm(X1) | patient(X1) [cnf transformation 57]
104. wise(susan) | calm(X0) [cnf transformation 41]
107. ~patient(sK3) | generous(sK3) [cnf transformation 60]
111. ~wise(susan) [cnf transformation 23]
140. 6 <=> curious(john) [avatar definition]
142. curious(john) <- (6) [avatar component clause 140]
145. 7 <=> ! [X0] : ~generous(X0) [avatar definition]
146. ~generous(X0) <- (7) [avatar component clause 145]
147. 7 | 6 [avatar split clause 73,140,145]
149. 8 <=> kind(john) [avatar definition]
151. ~kind(john) <- (~8) [avatar component clause 149]
153. 7 | ~8 [avatar split clause 71,149,145]
202. ~happy(X0) [subsumption resolution 94,95]
204. ~calm(X1) | patient(X1) [subsumption resolution 100,202]
206. 19 <=> ! [X0] : calm(X0) [avatar definition]
207. calm(X0) <- (19) [avatar component clause 206]
209. 20 <=> wise(susan) [avatar definition]
212. 19 | 20 [avatar split clause 104,209,206]
219. 22 <=> generous(sK3) [avatar definition]
220. generous(sK3) <- (22) [avatar component clause 219]
223. 23 <=> patient(sK3) [avatar definition]
224. ~patient(sK3) <- (~23) [avatar component clause 223]
227. 22 | ~23 [avatar split clause 107,223,219]
228. ~20 [avatar split clause 111,209]
229. kind(john) <- (6) [resolution 84,142]
231. $false <- (6, ~8) [subsumption resolution 229,151]
232. ~6 | 8 [avatar contradiction clause 231]
245. patient(X0) <- (19) [resolution 204,207]
246. $false <- (19, ~23) [resolution 245,224]
248. ~19 | 23 [avatar contradiction clause 246]
249. $false <- (7, 22) [subsumption resolution 220,146]
250. ~7 | ~22 [avatar contradiction clause 249]
251. $false [avatar sat refutation 147,153,212,227,228,232,248,250]
% SZS output end Proof for 4592271388784561102489835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or kind is not brave or brave and vice versa.
Everyone who is funny or not kind is either not strong or curious.
If someone is not rich then lucy is quiet and vice versa.
Everyone who is not happy is both strong and tall.
If mary is both not happy and not kind then fred is both not brave and calm.
Everyone who is both not curious and not tall is tall and vice versa.
Everyone who is not strong is happy.
Everyone who is both not kind and not happy is both not tall and not old and vice versa.
If someone is not kind then lucy is both old and not rich and vice versa.
If someone is not wise or rich then fred is not humble and vice versa.
If someone is either not brave or not funny then fred is both happy and not humble and vice versa.
Everyone who is not rich is rich or not brave and vice versa.
Everyone who is both old and not happy is brave.
Everyone who is wise is either not quiet or not brave and vice versa.
If someone is either old or not creative then lucy is not strong or quiet.
Everyone who is either not generous or brave is both not strong and funny.
Someone is generous.
Someone is strong.
Alice is both not quiet and humble.
Fred is either not brave or not strong.
Someone is not calm or strong.
Someone is either not brave or not humble.
Someone is both creative and not wise.
Paul is tall or happy. | Lucy is rich. | contradiction | (![X]:((~brave(X)|kind(X))<=>(~brave(X)|brave(X))))&
(![X]:((funny(X)|~kind(X))=>(~strong(X)<~>curious(X))))&
((?[X]:(~rich(X)))<=>(quiet(lucy)))&
(![X]:(~happy(X)=>(strong(X)&tall(X))))&
(((~happy(mary)&~kind(mary)))=>((~brave(fred)&calm(fred))))&
(![X]:((~curious(X)&~tall(X))<=>tall(X)))&
(![X]:(~strong(X)=>happy(X)))&
(![X]:((~kind(X)&~happy(X))<=>(~tall(X)&~old(X))))&
((?[X]:(~kind(X)))<=>((old(lucy)&~rich(lucy))))&
((?[X]:((~wise(X)|rich(X))))<=>(~humble(fred)))&
((?[X]:((~brave(X)<~>~funny(X))))<=>((happy(fred)&~humble(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~brave(X))))&
(![X]:((old(X)&~happy(X))=>brave(X)))&
(![X]:(wise(X)<=>(~quiet(X)<~>~brave(X))))&
((?[X]:((old(X)<~>~creative(X))))=>((~strong(lucy)|quiet(lucy))))&
(![X]:((~generous(X)<~>brave(X))=>(~strong(X)&funny(X))))&
(?[X]:(generous(X)))&
(?[X]:(strong(X)))&
((~quiet(alice)&humble(alice)))&
((~brave(fred)<~>~strong(fred)))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((creative(X)&~wise(X))))&
((tall(paul)|happy(paul))) | rich(lucy) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6904008008930178470518657
% SZS output start Proof for 6904008008930178470518657
12. ! [X0] : (~rich(X0) <=> (~brave(X0) | rich(X0))) [input p11]
25. rich(lucy) [input hypothesis]
61. ! [X0] : ((~rich(X0) | (brave(X0) & ~rich(X0))) & ((~brave(X0) | rich(X0)) | rich(X0))) [nnf transformation 12]
62. ! [X0] : ((~rich(X0) | (brave(X0) & ~rich(X0))) & (~brave(X0) | rich(X0) | rich(X0))) [flattening 61]
113. ~rich(X0) | ~rich(X0) [cnf transformation 62]
138. rich(lucy) [cnf transformation 25]
140. ~rich(X0) [duplicate literal removal 113]
184. 9 <=> rich(lucy) [avatar definition]
186. rich(lucy) <- (9) [avatar component clause 184]
211. 15 <=> ! [X1] : ~rich(X1) [avatar definition]
212. ~rich(X1) <- (15) [avatar component clause 211]
242. 15 [avatar split clause 140,211]
280. 9 [avatar split clause 138,184]
281. $false <- (9, 15) [subsumption resolution 186,212]
282. ~9 | ~15 [avatar contradiction clause 281]
285. $false [avatar sat refutation 242,280,282]
% SZS output end Proof for 6904008008930178470518657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not kind then someone is both not humble and quiet and vice versa.
Everyone who is not rich or patient is both not generous and not happy.
If someone is either not patient or not happy then paul is either old or not generous.
Everyone who is both not wise and strong is rich or curious and vice versa.
Everyone who is not funny is not kind and vice versa.
If john is either not patient or not curious then someone is brave and vice versa.
If someone is not patient then someone is either humble or not brave and vice versa.
If someone is both funny and rich then someone is not creative and vice versa.
Everyone who is either curious or rich is both strong and wise.
Everyone who is both happy and not curious is funny and vice versa.
If alice is not humble or old then fred is either funny or not old and vice versa.
Everyone who is both not creative and happy is generous and vice versa.
Everyone who is rich or brave is not patient.
If alice is not humble then someone is either not kind or not happy and vice versa.
If paul is both brave and wise then fred is not tall or curious and vice versa.
If someone is brave or creative then paul is either kind or brave.
Alice is both old and not brave.
Someone is both strong and quiet.
Someone is quiet.
Alice is either not rich or quiet.
Someone is both wise and quiet.
Someone is either rich or kind.
Mary is curious or not rich. | Mary is creative. | entailment | ((~kind(alice))<=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:((~rich(X)|patient(X))=>(~generous(X)&~happy(X))))&
((?[X]:((~patient(X)<~>~happy(X))))=>((old(paul)<~>~generous(paul))))&
(![X]:((~wise(X)&strong(X))<=>(rich(X)|curious(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(((~patient(john)<~>~curious(john)))<=>(?[X]:(brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((humble(X)<~>~brave(X)))))&
((?[X]:((funny(X)&rich(X))))<=>(?[X]:(~creative(X))))&
(![X]:((curious(X)<~>rich(X))=>(strong(X)&wise(X))))&
(![X]:((happy(X)&~curious(X))<=>funny(X)))&
(((~humble(alice)|old(alice)))<=>((funny(fred)<~>~old(fred))))&
(![X]:((~creative(X)&happy(X))<=>generous(X)))&
(![X]:((rich(X)|brave(X))=>~patient(X)))&
((~humble(alice))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
(((brave(paul)&wise(paul)))<=>((~tall(fred)|curious(fred))))&
((?[X]:((brave(X)|creative(X))))=>((kind(paul)<~>brave(paul))))&
((old(alice)&~brave(alice)))&
(?[X]:((strong(X)&quiet(X))))&
(?[X]:(quiet(X)))&
((~rich(alice)<~>quiet(alice)))&
(?[X]:((wise(X)&quiet(X))))&
(?[X]:((rich(X)<~>kind(X))))&
((curious(mary)|~rich(mary))) | creative(mary) | [
"p3",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 742463553350326675088203
% SZS output start Proof for 742463553350326675088203
4. ! [X0] : ((strong(X0) & ~wise(X0)) <=> (curious(X0) | rich(X0))) [input p3]
8. ? [X0] : (rich(X0) & funny(X0)) <=> ? [X0] : ~creative(X0) [input p7]
9. ! [X0] : ((curious(X0) <~> rich(X0)) => (wise(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~curious(X0) & happy(X0)) <=> funny(X0)) [input p9]
24. ~creative(mary) [input hypothesis]
26. ? [X0] : (rich(X0) & funny(X0)) <=> ? [X1] : ~creative(X1) [rectify 8]
29. ! [X0] : ((wise(X0) & strong(X0)) | (curious(X0) <=> rich(X0))) [ennf transformation 9]
37. ! [X0] : (((strong(X0) & ~wise(X0)) | (~curious(X0) & ~rich(X0))) & ((curious(X0) | rich(X0)) | (~strong(X0) | wise(X0)))) [nnf transformation 4]
38. ! [X0] : (((strong(X0) & ~wise(X0)) | (~curious(X0) & ~rich(X0))) & (curious(X0) | rich(X0) | ~strong(X0) | wise(X0))) [flattening 37]
49. (? [X0] : (rich(X0) & funny(X0)) | ! [X1] : creative(X1)) & (? [X1] : ~creative(X1) | ! [X0] : (~rich(X0) | ~funny(X0))) [nnf transformation 26]
50. (? [X0] : (rich(X0) & funny(X0)) | ! [X1] : creative(X1)) & (? [X2] : ~creative(X2) | ! [X3] : (~rich(X3) | ~funny(X3))) [rectify 49]
51. ? [X0] : (rich(X0) & funny(X0)) => (rich(sK4) & funny(sK4)) [choice axiom]
52. ? [X2] : ~creative(X2) => ~creative(sK5) [choice axiom]
53. ((rich(sK4) & funny(sK4)) | ! [X1] : creative(X1)) & (~creative(sK5) | ! [X3] : (~rich(X3) | ~funny(X3))) [skolemisation 50,52,51]
54. ! [X0] : ((wise(X0) & strong(X0)) | ((curious(X0) | ~rich(X0)) & (rich(X0) | ~curious(X0)))) [nnf transformation 29]
55. ! [X0] : (((~curious(X0) & happy(X0)) | ~funny(X0)) & (funny(X0) | (curious(X0) | ~happy(X0)))) [nnf transformation 10]
56. ! [X0] : (((~curious(X0) & happy(X0)) | ~funny(X0)) & (funny(X0) | curious(X0) | ~happy(X0))) [flattening 55]
90. ~wise(X0) | ~rich(X0) [cnf transformation 38]
105. funny(sK4) | creative(X1) [cnf transformation 53]
106. rich(sK4) | creative(X1) [cnf transformation 53]
110. wise(X0) | curious(X0) | ~rich(X0) [cnf transformation 54]
113. ~funny(X0) | ~curious(X0) [cnf transformation 56]
150. ~creative(mary) [cnf transformation 24]
236. 19 <=> ! [X1] : creative(X1) [avatar definition]
237. creative(X1) <- (19) [avatar component clause 236]
239. 20 <=> rich(sK4) [avatar definition]
241. rich(sK4) <- (20) [avatar component clause 239]
242. 19 | 20 [avatar split clause 106,239,236]
244. 21 <=> funny(sK4) [avatar definition]
246. funny(sK4) <- (21) [avatar component clause 244]
247. 19 | 21 [avatar split clause 105,244,236]
256. ~rich(X0) | curious(X0) [subsumption resolution 110,90]
351. $false <- (19) [resolution 237,150]
352. ~19 [avatar contradiction clause 351]
364. ~curious(sK4) <- (21) [resolution 113,246]
368. curious(sK4) <- (20) [resolution 256,241]
370. $false <- (20, 21) [subsumption resolution 368,364]
371. ~20 | ~21 [avatar contradiction clause 370]
372. $false [avatar sat refutation 242,247,352,371]
% SZS output end Proof for 742463553350326675088203
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either generous or not rich is both quiet and not tall. If someone is humble or not funny then alice is not humble or patient and vice versa. Everyone who is both not funny and not curious is not tall and vice versa. Everyone who is not curious is both generous and not kind and vice versa. Everyone who is not brave is both quiet and humble. Everyone who is both not quiet and quiet is not humble or kind and vice versa. If someone is not quiet or funny then someone is not creative or old and vice versa. If susan is both humble and calm then someone is not curious or not strong. Everyone who is either creative or quiet is both not patient and not generous. Everyone who is either rich or not humble is old and vice versa. Everyone who is either not happy or patient is both funny and not creative and vice versa. Everyone who is either old or creative is either not calm or not tall. Everyone who is rich is tall or old and vice versa. If someone is tall or not rich then someone is either quiet or creative and vice versa. Everyone who is kind or not generous is either strong or not quiet and vice versa. If someone is either calm or not wise then someone is not tall. Susan is tall or not strong. Lucy is not calm or not humble. Someone is generous or patient. Alice is both generous and not rich. Susan is not curious. Lucy is humble or quiet. Mary is either quiet or not creative. Someone is not patient. | Mary is not quiet. | neutral | (![X]:((generous(X)<~>~rich(X))=>(quiet(X)&~tall(X))))&
((?[X]:((humble(X)|~funny(X))))<=>((~humble(alice)|patient(alice))))&
(![X]:((~funny(X)&~curious(X))<=>~tall(X)))&
(![X]:(~curious(X)<=>(generous(X)&~kind(X))))&
(![X]:(~brave(X)=>(quiet(X)&humble(X))))&
(![X]:((~quiet(X)&quiet(X))<=>(~humble(X)|kind(X))))&
((?[X]:((~quiet(X)|funny(X))))<=>(?[X]:((~creative(X)|old(X)))))&
(((humble(susan)&calm(susan)))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((creative(X)<~>quiet(X))=>(~patient(X)&~generous(X))))&
(![X]:((rich(X)<~>~humble(X))<=>old(X)))&
(![X]:((~happy(X)<~>patient(X))<=>(funny(X)&~creative(X))))&
(![X]:((old(X)<~>creative(X))=>(~calm(X)<~>~tall(X))))&
(![X]:(rich(X)<=>(tall(X)|old(X))))&
((?[X]:((tall(X)|~rich(X))))<=>(?[X]:((quiet(X)<~>creative(X)))))&
(![X]:((kind(X)|~generous(X))<=>(strong(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>(?[X]:(~tall(X))))&
((tall(susan)|~strong(susan)))&
((~calm(lucy)|~humble(lucy)))&
(?[X]:((generous(X)|patient(X))))&
((generous(alice)&~rich(alice)))&
(~curious(susan))&
((humble(lucy)|quiet(lucy)))&
((quiet(mary)<~>~creative(mary)))&
(?[X]:(~patient(X))) | ~quiet(mary) | [] | null | 0 |
If someone is both not happy and patient then someone is both wise and not brave and vice versa. Everyone who is either not funny or not strong is either strong or humble. Everyone who is either old or humble is brave and vice versa. Everyone who is not kind or tall is both funny and rich and vice versa. Everyone who is old or patient is happy. Everyone who is strong or funny is either not kind or not curious. If john is both not wise and generous then john is both wise and not curious. Everyone who is funny is not quiet or creative and vice versa. Everyone who is either funny or not creative is generous or kind. Everyone who is either not strong or not old is calm. Everyone who is rich or not calm is not patient. If mary is strong or generous then paul is either rich or not kind. Everyone who is not patient or not rich is both not wise and not quiet. Everyone who is not tall or calm is either not creative or not wise and vice versa. If someone is patient or not funny then someone is not patient. Everyone who is strong is humble. Someone is either not strong or not generous. John is both funny and humble. Someone is both generous and tall. Alice is brave. Someone is either not curious or not tall. John is not tall. Someone is both not happy and rich. | John is curious. | contradiction | ((?[X]:((~happy(X)&patient(X))))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:((~funny(X)<~>~strong(X))=>(strong(X)<~>humble(X))))&
(![X]:((old(X)<~>humble(X))<=>brave(X)))&
(![X]:((~kind(X)|tall(X))<=>(funny(X)&rich(X))))&
(![X]:((old(X)|patient(X))=>happy(X)))&
(![X]:((strong(X)|funny(X))=>(~kind(X)<~>~curious(X))))&
(((~wise(john)&generous(john)))=>((wise(john)&~curious(john))))&
(![X]:(funny(X)<=>(~quiet(X)|creative(X))))&
(![X]:((funny(X)<~>~creative(X))=>(generous(X)|kind(X))))&
(![X]:((~strong(X)<~>~old(X))=>calm(X)))&
(![X]:((rich(X)|~calm(X))=>~patient(X)))&
(((strong(mary)|generous(mary)))=>((rich(paul)<~>~kind(paul))))&
(![X]:((~patient(X)|~rich(X))=>(~wise(X)&~quiet(X))))&
(![X]:((~tall(X)|calm(X))<=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:(~patient(X))))&
(![X]:(strong(X)=>humble(X)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((funny(john)&humble(john)))&
(?[X]:((generous(X)&tall(X))))&
(brave(alice))&
(?[X]:((~curious(X)<~>~tall(X))))&
(~tall(john))&
(?[X]:((~happy(X)&rich(X)))) | curious(john) | [
"p5",
"p6",
"p7",
"p8",
"p10",
"p12",
"p13",
"p17",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2435526084798218060671238
% SZS output start Proof for 2435526084798218060671238
6. ! [X0] : ((funny(X0) | strong(X0)) => (~kind(X0) <~> ~curious(X0))) [input p5]
7. (generous(john) & ~wise(john)) => (~curious(john) & wise(john)) [input p6]
8. ! [X0] : (funny(X0) <=> (creative(X0) | ~quiet(X0))) [input p7]
9. ! [X0] : ((funny(X0) <~> ~creative(X0)) => (kind(X0) | generous(X0))) [input p8]
11. ! [X0] : ((~calm(X0) | rich(X0)) => ~patient(X0)) [input p10]
13. ! [X0] : ((~rich(X0) | ~patient(X0)) => (~quiet(X0) & ~wise(X0))) [input p12]
14. ! [X0] : ((calm(X0) | ~tall(X0)) <=> (~creative(X0) <~> ~wise(X0))) [input p13]
18. humble(john) & funny(john) [input p17]
22. ~tall(john) [input p21]
24. curious(john) [input hypothesis]
29. ! [X0] : ((~kind(X0) <~> ~curious(X0)) | (~funny(X0) & ~strong(X0))) [ennf transformation 6]
30. (~curious(john) & wise(john)) | (~generous(john) | wise(john)) [ennf transformation 7]
31. (~curious(john) & wise(john)) | ~generous(john) | wise(john) [flattening 30]
32. ! [X0] : ((kind(X0) | generous(X0)) | (funny(X0) <=> ~creative(X0))) [ennf transformation 9]
33. ! [X0] : (kind(X0) | generous(X0) | (funny(X0) <=> ~creative(X0))) [flattening 32]
35. ! [X0] : (~patient(X0) | (calm(X0) & ~rich(X0))) [ennf transformation 11]
37. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (rich(X0) & patient(X0))) [ennf transformation 13]
49. ! [X0] : (((curious(X0) | kind(X0)) & (~curious(X0) | ~kind(X0))) | (~funny(X0) & ~strong(X0))) [nnf transformation 29]
50. ! [X0] : ((funny(X0) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ~funny(X0))) [nnf transformation 8]
51. ! [X0] : ((funny(X0) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ~funny(X0))) [flattening 50]
52. ! [X0] : (kind(X0) | generous(X0) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0)))) [nnf transformation 33]
55. ! [X0] : (((calm(X0) | ~tall(X0)) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | (~calm(X0) & tall(X0)))) [nnf transformation 14]
56. ! [X0] : ((calm(X0) | ~tall(X0) | ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0)))) & (((wise(X0) | creative(X0)) & (~wise(X0) | ~creative(X0))) | (~calm(X0) & tall(X0)))) [flattening 55]
90. ~curious(X0) | ~kind(X0) | ~funny(X0) [cnf transformation 49]
93. wise(john) | ~generous(john) | wise(john) [cnf transformation 31]
97. ~creative(X0) | funny(X0) [cnf transformation 51]
98. kind(X0) | generous(X0) | ~creative(X0) | ~funny(X0) [cnf transformation 52]
102. ~rich(X0) | ~patient(X0) [cnf transformation 35]
108. ~wise(X0) | patient(X0) [cnf transformation 37]
109. ~wise(X0) | rich(X0) [cnf transformation 37]
114. creative(X0) | wise(X0) | tall(X0) [cnf transformation 56]
123. funny(john) [cnf transformation 18]
130. ~tall(john) [cnf transformation 22]
133. curious(john) [cnf transformation 24]
134. wise(john) | ~generous(john) [duplicate literal removal 93]
166. 7 <=> wise(john) [avatar definition]
168. wise(john) <- (7) [avatar component clause 166]
170. 8 <=> generous(john) [avatar definition]
172. ~generous(john) <- (~8) [avatar component clause 170]
174. 9 <=> curious(john) [avatar definition]
175. curious(john) <- (9) [avatar component clause 174]
178. ~8 | 7 [avatar split clause 134,166,170]
179. ~creative(X0) | generous(X0) | kind(X0) [subsumption resolution 98,97]
236. 9 [avatar split clause 133,174]
293. 28 <=> kind(john) [avatar definition]
295. ~kind(john) <- (~28) [avatar component clause 293]
306. ~kind(john) | ~funny(john) <- (9) [resolution 90,175]
309. ~kind(john) <- (9) [subsumption resolution 306,123]
310. ~28 | ~9 [avatar split clause 309,174,293]
368. generous(X0) | kind(X0) | wise(X0) | tall(X0) [resolution 179,114]
446. kind(john) | wise(john) | tall(john) <- (~8) [resolution 368,172]
449. wise(john) | tall(john) <- (~8, ~28) [subsumption resolution 446,295]
450. wise(john) <- (~8, ~28) [subsumption resolution 449,130]
451. 7 | 8 | 28 [avatar split clause 450,293,170,166]
479. rich(john) <- (7) [resolution 168,109]
480. patient(john) <- (7) [resolution 168,108]
486. ~patient(john) <- (7) [resolution 479,102]
487. $false <- (7) [subsumption resolution 486,480]
488. ~7 [avatar contradiction clause 487]
489. $false [avatar sat refutation 178,236,310,451,488]
% SZS output end Proof for 2435526084798218060671238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or not wise then someone is either not rich or not old. If someone is not rich or funny then mary is not brave or old. If someone is either not quiet or not old then someone is not kind. If someone is not creative then paul is either calm or not funny. Everyone who is not generous or rich is both happy and generous and vice versa. If mary is either brave or calm then someone is not quiet or patient and vice versa. Everyone who is curious is either not brave or generous. Everyone who is both not old and not creative is not patient or not humble. Everyone who is both not strong and rich is both tall and not rich. If john is not quiet then someone is both not quiet and not curious. If someone is either not rich or not generous then mary is either not patient or patient and vice versa. If someone is not curious then someone is both not strong and not generous. Everyone who is not curious or not humble is not kind and vice versa. Everyone who is both not curious and generous is either not humble or not kind and vice versa. Everyone who is either not calm or curious is funny. Everyone who is not brave is both not funny and not curious and vice versa. Paul is kind or generous. Someone is generous or not calm. Mary is patient. Someone is either tall or calm. John is either funny or quiet. Lucy is not strong. Alice is not kind. Someone is strong. | Mary is calm. | contradiction | ((?[X]:((~creative(X)|~wise(X))))=>(?[X]:((~rich(X)<~>~old(X)))))&
((?[X]:((~rich(X)|funny(X))))=>((~brave(mary)|old(mary))))&
((?[X]:((~quiet(X)<~>~old(X))))=>(?[X]:(~kind(X))))&
((?[X]:(~creative(X)))=>((calm(paul)<~>~funny(paul))))&
(![X]:((~generous(X)|rich(X))<=>(happy(X)&generous(X))))&
(((brave(mary)<~>calm(mary)))<=>(?[X]:((~quiet(X)|patient(X)))))&
(![X]:(curious(X)=>(~brave(X)<~>generous(X))))&
(![X]:((~old(X)&~creative(X))=>(~patient(X)|~humble(X))))&
(![X]:((~strong(X)&rich(X))=>(tall(X)&~rich(X))))&
((~quiet(john))=>(?[X]:((~quiet(X)&~curious(X)))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>((~patient(mary)<~>patient(mary))))&
((?[X]:(~curious(X)))=>(?[X]:((~strong(X)&~generous(X)))))&
(![X]:((~curious(X)|~humble(X))<=>~kind(X)))&
(![X]:((~curious(X)&generous(X))<=>(~humble(X)<~>~kind(X))))&
(![X]:((~calm(X)<~>curious(X))=>funny(X)))&
(![X]:(~brave(X)<=>(~funny(X)&~curious(X))))&
((kind(paul)|generous(paul)))&
(?[X]:((generous(X)|~calm(X))))&
(patient(mary))&
(?[X]:((tall(X)<~>calm(X))))&
((funny(john)<~>quiet(john)))&
(~strong(lucy))&
(~kind(alice))&
(?[X]:(strong(X))) | calm(mary) | [
"p4",
"p5",
"p6",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 742596628784770622759849
% SZS output start Proof for 742596628784770622759849
5. ! [X0] : ((rich(X0) | ~generous(X0)) <=> (generous(X0) & happy(X0))) [input p4]
6. (brave(mary) <~> calm(mary)) <=> ? [X0] : (patient(X0) | ~quiet(X0)) [input p5]
7. ! [X0] : (curious(X0) => (~brave(X0) <~> generous(X0))) [input p6]
12. ? [X0] : ~curious(X0) => ? [X0] : (~generous(X0) & ~strong(X0)) [input p11]
19. patient(mary) [input p18]
25. calm(mary) [input hypothesis]
28. ? [X0] : ~curious(X0) => ? [X1] : (~generous(X1) & ~strong(X1)) [rectify 12]
36. ! [X0] : ((~brave(X0) <~> generous(X0)) | ~curious(X0)) [ennf transformation 7]
40. ? [X1] : (~generous(X1) & ~strong(X1)) | ! [X0] : curious(X0) [ennf transformation 28]
46. ! [X0] : (((rich(X0) | ~generous(X0)) | (~generous(X0) | ~happy(X0))) & ((generous(X0) & happy(X0)) | (~rich(X0) & generous(X0)))) [nnf transformation 5]
47. ! [X0] : ((rich(X0) | ~generous(X0) | ~generous(X0) | ~happy(X0)) & ((generous(X0) & happy(X0)) | (~rich(X0) & generous(X0)))) [flattening 46]
48. (((~calm(mary) | ~brave(mary)) & (calm(mary) | brave(mary))) | ! [X0] : (~patient(X0) & quiet(X0))) & (? [X0] : (patient(X0) | ~quiet(X0)) | ((brave(mary) | ~calm(mary)) & (calm(mary) | ~brave(mary)))) [nnf transformation 6]
49. (((~calm(mary) | ~brave(mary)) & (calm(mary) | brave(mary))) | ! [X0] : (~patient(X0) & quiet(X0))) & (? [X1] : (patient(X1) | ~quiet(X1)) | ((brave(mary) | ~calm(mary)) & (calm(mary) | ~brave(mary)))) [rectify 48]
50. ? [X1] : (patient(X1) | ~quiet(X1)) => (patient(sK1) | ~quiet(sK1)) [choice axiom]
51. (((~calm(mary) | ~brave(mary)) & (calm(mary) | brave(mary))) | ! [X0] : (~patient(X0) & quiet(X0))) & ((patient(sK1) | ~quiet(sK1)) | ((brave(mary) | ~calm(mary)) & (calm(mary) | ~brave(mary)))) [skolemisation 49,50]
52. ! [X0] : (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | ~curious(X0)) [nnf transformation 36]
59. ? [X0] : (~generous(X0) & ~strong(X0)) | ! [X1] : curious(X1) [rectify 40]
60. ? [X0] : (~generous(X0) & ~strong(X0)) => (~generous(sK4) & ~strong(sK4)) [choice axiom]
61. (~generous(sK4) & ~strong(sK4)) | ! [X1] : curious(X1) [skolemisation 59,60]
83. generous(X0) | generous(X0) [cnf transformation 47]
91. ~calm(mary) | ~brave(mary) | ~patient(X0) [cnf transformation 51]
93. ~generous(X0) | brave(X0) | ~curious(X0) [cnf transformation 52]
107. ~generous(sK4) | curious(X1) [cnf transformation 61]
124. patient(mary) [cnf transformation 19]
132. calm(mary) [cnf transformation 25]
138. generous(X0) [duplicate literal removal 83]
144. 2 <=> brave(mary) [avatar definition]
146. ~brave(mary) <- (~2) [avatar component clause 144]
169. 8 <=> ! [X0] : ~patient(X0) [avatar definition]
170. ~patient(X0) <- (8) [avatar component clause 169]
172. 9 <=> calm(mary) [avatar definition]
175. 8 | ~2 | ~9 [avatar split clause 91,172,144,169]
192. ~curious(X0) | brave(X0) [subsumption resolution 93,138]
209. 16 <=> patient(mary) [avatar definition]
210. patient(mary) <- (16) [avatar component clause 209]
219. curious(X1) [subsumption resolution 107,138]
222. 16 [avatar split clause 124,209]
239. 9 [avatar split clause 132,172]
240. brave(X0) [resolution 192,219]
241. $false <- (~2) [resolution 240,146]
242. 2 [avatar contradiction clause 241]
248. $false <- (8, 16) [resolution 170,210]
249. ~8 | ~16 [avatar contradiction clause 248]
250. $false [avatar sat refutation 175,222,239,242,249]
% SZS output end Proof for 742596628784770622759849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or kind is either not humble or not quiet and vice versa. Everyone who is rich or strong is calm or not brave and vice versa. If alice is either not tall or generous then paul is both not strong and funny. Everyone who is either brave or not brave is both not strong and generous. Everyone who is both not old and not curious is not happy or curious and vice versa. Everyone who is either happy or generous is either funny or not patient. If someone is either not kind or brave then susan is either humble or creative. Everyone who is both funny and not creative is either rich or not patient and vice versa. Everyone who is both generous and not patient is both not kind and humble. If someone is either strong or tall then alice is humble. Everyone who is both not calm and not curious is old or rich and vice versa. If someone is funny or not brave then someone is not curious or not kind and vice versa. If someone is not wise or not old then lucy is curious or not calm and vice versa. Everyone who is not calm is old. If alice is both not humble and funny then someone is not curious and vice versa. Mary is happy or not calm. Lucy is not strong. Someone is either calm or brave. Someone is either happy or funny. Someone is not quiet or strong. Lucy is not calm or brave. Mary is old. Lucy is either not rich or quiet. | Paul is curious. | contradiction | (![X]:((~calm(X)<~>kind(X))<=>(~humble(X)<~>~quiet(X))))&
(![X]:((rich(X)|strong(X))<=>(calm(X)|~brave(X))))&
(((~tall(alice)<~>generous(alice)))=>((~strong(paul)&funny(paul))))&
(![X]:((brave(X)<~>~brave(X))=>(~strong(X)&generous(X))))&
(![X]:((~old(X)&~curious(X))<=>(~happy(X)|curious(X))))&
(![X]:((happy(X)<~>generous(X))=>(funny(X)<~>~patient(X))))&
((?[X]:((~kind(X)<~>brave(X))))=>((humble(susan)<~>creative(susan))))&
(![X]:((funny(X)&~creative(X))<=>(rich(X)<~>~patient(X))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((happy(mary)|~calm(mary)))&
(~strong(lucy))&
(?[X]:((calm(X)<~>brave(X))))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy))) | curious(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 5796995689704985728669346
% SZS output start Proof for 5796995689704985728669346
5. ! [X0] : ((~curious(X0) & ~old(X0)) <=> (curious(X0) | ~happy(X0))) [input p4]
24. curious(paul) [input hypothesis]
39. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & ((curious(X0) | ~happy(X0)) | (curious(X0) | old(X0)))) [nnf transformation 5]
40. ! [X0] : (((~curious(X0) & ~old(X0)) | (~curious(X0) & happy(X0))) & (curious(X0) | ~happy(X0) | curious(X0) | old(X0))) [flattening 39]
96. ~curious(X0) | ~curious(X0) [cnf transformation 40]
143. curious(paul) [cnf transformation 24]
145. ~curious(X0) [duplicate literal removal 96]
290. $false [subsumption resolution 143,145]
% SZS output end Proof for 5796995689704985728669346
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and calm then fred is both brave and not rich.
Everyone who is either kind or not creative is tall or funny and vice versa.
If paul is both not wise and old then susan is both strong and not funny and vice versa.
Everyone who is old is generous or patient.
If someone is not humble or not patient then susan is not creative.
If susan is either not funny or not calm then fred is both tall and generous and vice versa.
Everyone who is kind or not wise is not humble or old.
Everyone who is either not rich or happy is both not funny and not creative.
Everyone who is quiet is not curious.
If fred is both wise and not quiet then fred is both not old and not creative.
Everyone who is both not calm and not kind is either not patient or brave and vice versa.
Everyone who is patient or not quiet is tall and vice versa.
If someone is either not generous or strong then alice is not old and vice versa.
If someone is tall then lucy is not calm or not creative.
If john is not curious then susan is both not generous and curious and vice versa.
Everyone who is not curious is funny or not kind and vice versa.
Susan is either rich or creative.
Fred is either curious or quiet.
Someone is curious or not rich.
Someone is both not generous and not tall.
Paul is calm.
Someone is kind.
Someone is old.
Someone is both generous and not funny. | John is funny. | contradiction | ((?[X]:((~brave(X)&calm(X))))=>((brave(fred)&~rich(fred))))&
(![X]:((kind(X)<~>~creative(X))<=>(tall(X)|funny(X))))&
(((~wise(paul)&old(paul)))<=>((strong(susan)&~funny(susan))))&
(![X]:(old(X)=>(generous(X)|patient(X))))&
((?[X]:((~humble(X)|~patient(X))))=>(~creative(susan)))&
(((~funny(susan)<~>~calm(susan)))<=>((tall(fred)&generous(fred))))&
(![X]:((kind(X)|~wise(X))=>(~humble(X)|old(X))))&
(![X]:((~rich(X)<~>happy(X))=>(~funny(X)&~creative(X))))&
(![X]:(quiet(X)=>~curious(X)))&
(((wise(fred)&~quiet(fred)))=>((~old(fred)&~creative(fred))))&
(![X]:((~calm(X)&~kind(X))<=>(~patient(X)<~>brave(X))))&
(![X]:((patient(X)|~quiet(X))<=>tall(X)))&
((?[X]:((~generous(X)<~>strong(X))))<=>(~old(alice)))&
((?[X]:(tall(X)))=>((~calm(lucy)|~creative(lucy))))&
((~curious(john))<=>((~generous(susan)&curious(susan))))&
(![X]:(~curious(X)<=>(funny(X)|~kind(X))))&
((rich(susan)<~>creative(susan)))&
((curious(fred)<~>quiet(fred)))&
(?[X]:((curious(X)|~rich(X))))&
(?[X]:((~generous(X)&~tall(X))))&
(calm(paul))&
(?[X]:(kind(X)))&
(?[X]:(old(X)))&
(?[X]:((generous(X)&~funny(X)))) | funny(john) | [
"p1",
"p4",
"p8",
"p11",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6689423717750477381615910
% SZS output start Proof for 6689423717750477381615910
2. ! [X0] : ((kind(X0) <~> ~creative(X0)) <=> (funny(X0) | tall(X0))) [input p1]
5. ? [X0] : (~patient(X0) | ~humble(X0)) => ~creative(susan) [input p4]
9. ! [X0] : (quiet(X0) => ~curious(X0)) [input p8]
12. ! [X0] : ((~quiet(X0) | patient(X0)) <=> tall(X0)) [input p11]
15. ~curious(john) <=> (curious(susan) & ~generous(susan)) [input p14]
16. ! [X0] : (~curious(X0) <=> (~kind(X0) | funny(X0))) [input p15]
20. ? [X0] : (~tall(X0) & ~generous(X0)) [input p19]
25. funny(john) [input hypothesis]
29. ~creative(susan) | ! [X0] : (patient(X0) & humble(X0)) [ennf transformation 5]
33. ! [X0] : (~curious(X0) | ~quiet(X0)) [ennf transformation 9]
38. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | (~funny(X0) & ~tall(X0))) & ((funny(X0) | tall(X0)) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [nnf transformation 2]
39. ! [X0] : ((((creative(X0) | ~kind(X0)) & (~creative(X0) | kind(X0))) | (~funny(X0) & ~tall(X0))) & (funny(X0) | tall(X0) | ((kind(X0) | creative(X0)) & (~creative(X0) | ~kind(X0))))) [flattening 38]
47. ! [X0] : (((~quiet(X0) | patient(X0)) | ~tall(X0)) & (tall(X0) | (quiet(X0) & ~patient(X0)))) [nnf transformation 12]
48. ! [X0] : ((~quiet(X0) | patient(X0) | ~tall(X0)) & (tall(X0) | (quiet(X0) & ~patient(X0)))) [flattening 47]
53. (~curious(john) | (~curious(susan) | generous(susan))) & ((curious(susan) & ~generous(susan)) | curious(john)) [nnf transformation 15]
54. (~curious(john) | ~curious(susan) | generous(susan)) & ((curious(susan) & ~generous(susan)) | curious(john)) [flattening 53]
55. ! [X0] : ((~curious(X0) | (kind(X0) & ~funny(X0))) & ((~kind(X0) | funny(X0)) | curious(X0))) [nnf transformation 16]
56. ! [X0] : ((~curious(X0) | (kind(X0) & ~funny(X0))) & (~kind(X0) | funny(X0) | curious(X0))) [flattening 55]
61. ? [X0] : (~tall(X0) & ~generous(X0)) => (~tall(sK2) & ~generous(sK2)) [choice axiom]
62. ~tall(sK2) & ~generous(sK2) [skolemisation 20,61]
75. ~tall(X0) | ~kind(X0) | creative(X0) [cnf transformation 39]
83. ~creative(susan) | patient(X0) [cnf transformation 29]
96. ~curious(X0) | ~quiet(X0) [cnf transformation 33]
105. ~patient(X0) | tall(X0) [cnf transformation 48]
106. quiet(X0) | tall(X0) [cnf transformation 48]
114. curious(susan) | curious(john) [cnf transformation 54]
117. ~curious(X0) | ~funny(X0) [cnf transformation 56]
118. ~curious(X0) | kind(X0) [cnf transformation 56]
125. ~tall(sK2) [cnf transformation 62]
131. funny(john) [cnf transformation 25]
166. 8 <=> ! [X0] : patient(X0) [avatar definition]
167. patient(X0) <- (8) [avatar component clause 166]
169. 9 <=> creative(susan) [avatar definition]
171. ~creative(susan) <- (~9) [avatar component clause 169]
172. 8 | ~9 [avatar split clause 83,169,166]
252. 27 <=> curious(susan) [avatar definition]
253. curious(susan) <- (27) [avatar component clause 252]
256. 28 <=> curious(john) [avatar definition]
257. curious(john) <- (28) [avatar component clause 256]
260. 28 | 27 [avatar split clause 114,252,256]
282. ~quiet(susan) <- (27) [resolution 96,253]
283. tall(X0) <- (8) [resolution 105,167]
284. tall(susan) <- (27) [resolution 106,282]
285. $false <- (8) [resolution 283,125]
288. ~8 [avatar contradiction clause 285]
290. kind(susan) <- (27) [resolution 118,253]
302. ~kind(susan) | creative(susan) <- (27) [resolution 75,284]
303. creative(susan) <- (27) [subsumption resolution 302,290]
304. $false <- (~9, 27) [subsumption resolution 303,171]
305. 9 | ~27 [avatar contradiction clause 304]
307. ~funny(john) <- (28) [resolution 257,117]
310. $false <- (28) [subsumption resolution 307,131]
311. ~28 [avatar contradiction clause 310]
312. $false [avatar sat refutation 172,260,288,305,311]
% SZS output end Proof for 6689423717750477381615910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not funny is either not creative or not brave. If someone is generous then someone is both calm and not kind. If john is not old then lucy is not creative or creative and vice versa. Everyone who is funny is both not humble and not generous. Everyone who is either tall or not generous is not kind or creative. If john is both not kind and tall then john is not humble or curious and vice versa. Everyone who is both old and patient is quiet and vice versa. Everyone who is tall is creative and vice versa. If paul is either patient or kind then someone is both not rich and not brave. If fred is either humble or not tall then someone is either not generous or happy. If lucy is not strong or strong then lucy is not rich or creative and vice versa. Everyone who is either not creative or not generous is both not humble and not calm. Everyone who is generous is not rich and vice versa. Everyone who is either not humble or generous is kind or humble. If john is not patient or not curious then someone is both not quiet and not patient and vice versa. Everyone who is either humble or not humble is either tall or rich and vice versa. Someone is either not calm or not curious. Fred is either humble or generous. Mary is both not brave and creative. Someone is generous. Someone is wise or not rich. Paul is both not generous and strong. Someone is calm. Someone is either not funny or generous. | Lucy is strong. | neutral | (![X]:((rich(X)<~>~funny(X))=>(~creative(X)<~>~brave(X))))&
((?[X]:(generous(X)))=>(?[X]:((calm(X)&~kind(X)))))&
((~old(john))<=>((~creative(lucy)|creative(lucy))))&
(![X]:(funny(X)=>(~humble(X)&~generous(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~kind(X)|creative(X))))&
(((~kind(john)&tall(john)))<=>((~humble(john)|curious(john))))&
(![X]:((old(X)&patient(X))<=>quiet(X)))&
(![X]:(tall(X)<=>creative(X)))&
(((patient(paul)<~>kind(paul)))=>(?[X]:((~rich(X)&~brave(X)))))&
(((humble(fred)<~>~tall(fred)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(((~strong(lucy)|strong(lucy)))<=>((~rich(lucy)|creative(lucy))))&
(![X]:((~creative(X)<~>~generous(X))=>(~humble(X)&~calm(X))))&
(![X]:(generous(X)<=>~rich(X)))&
(![X]:((~humble(X)<~>generous(X))=>(kind(X)|humble(X))))&
(((~patient(john)|~curious(john)))<=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((humble(X)<~>~humble(X))<=>(tall(X)<~>rich(X))))&
(?[X]:((~calm(X)<~>~curious(X))))&
((humble(fred)<~>generous(fred)))&
((~brave(mary)&creative(mary)))&
(?[X]:(generous(X)))&
(?[X]:((wise(X)|~rich(X))))&
((~generous(paul)&strong(paul)))&
(?[X]:(calm(X)))&
(?[X]:((~funny(X)<~>generous(X)))) | strong(lucy) | [] | null | 0 |
Everyone who is both old and wise is both patient and kind. Everyone who is both not wise and not happy is wise and vice versa. Everyone who is old or not tall is either quiet or patient. Everyone who is not rich or not happy is curious and vice versa. Everyone who is not strong is not tall or strong. Everyone who is not curious or happy is not humble or old. Everyone who is not tall is both not rich and kind and vice versa. Everyone who is not strong is either wise or strong. If someone is either quiet or old then someone is not kind or not curious. If mary is either wise or not kind then someone is tall and vice versa. If paul is not humble then lucy is not wise. Everyone who is rich or not tall is both not strong and not rich and vice versa. Everyone who is either not happy or wise is not curious or not patient and vice versa. Everyone who is not calm is not quiet or generous. Everyone who is either generous or not quiet is either not old or patient and vice versa. If someone is either humble or not creative then someone is either kind or rich and vice versa. Someone is not humble or not old. Someone is not quiet. Mary is tall or not humble. Someone is quiet. Someone is not creative or not rich. | Lucy is happy. | entailment | (![X]:((old(X)&wise(X))=>(patient(X)&kind(X))))&
(![X]:((~wise(X)&~happy(X))<=>wise(X)))&
(![X]:((old(X)|~tall(X))=>(quiet(X)<~>patient(X))))&
(![X]:((~rich(X)|~happy(X))<=>curious(X)))&
(![X]:(~strong(X)=>(~tall(X)|strong(X))))&
(![X]:((~curious(X)|happy(X))=>(~humble(X)|old(X))))&
(![X]:(~tall(X)<=>(~rich(X)&kind(X))))&
(![X]:(~strong(X)=>(wise(X)<~>strong(X))))&
((?[X]:((quiet(X)<~>old(X))))=>(?[X]:((~kind(X)|~curious(X)))))&
(((wise(mary)<~>~kind(mary)))<=>(?[X]:(tall(X))))&
((~humble(paul))=>(~wise(lucy)))&
(![X]:((rich(X)|~tall(X))<=>(~strong(X)&~rich(X))))&
(![X]:((~happy(X)<~>wise(X))<=>(~curious(X)|~patient(X))))&
(![X]:(~calm(X)=>(~quiet(X)|generous(X))))&
(![X]:((generous(X)<~>~quiet(X))<=>(~old(X)<~>patient(X))))&
((?[X]:((humble(X)<~>~creative(X))))<=>(?[X]:((kind(X)<~>rich(X)))))&
(?[X]:((~humble(X)|~old(X))))&
(?[X]:(~quiet(X)))&
((tall(mary)|~humble(mary)))&
(?[X]:(quiet(X)))&
(?[X]:((~creative(X)|~rich(X)))) | happy(lucy) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 6395190714908321376932096
% SZS output start Proof for 6395190714908321376932096
2. ! [X0] : ((~happy(X0) & ~wise(X0)) <=> wise(X0)) [input p1]
22. ~happy(lucy) [input hypothesis]
36. ! [X0] : (((~happy(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | (happy(X0) | wise(X0)))) [nnf transformation 2]
37. ! [X0] : (((~happy(X0) & ~wise(X0)) | ~wise(X0)) & (wise(X0) | happy(X0) | wise(X0))) [flattening 36]
72. wise(X0) | happy(X0) | wise(X0) [cnf transformation 37]
73. ~wise(X0) | ~wise(X0) [cnf transformation 37]
129. ~happy(lucy) [cnf transformation 22]
134. wise(X0) | happy(X0) [duplicate literal removal 72]
135. ~wise(X0) [duplicate literal removal 73]
136. happy(X0) [subsumption resolution 134,135]
209. $false [subsumption resolution 129,136]
% SZS output end Proof for 6395190714908321376932096
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If john is both brave and creative then someone is both calm and strong and vice versa.
Everyone who is either calm or not tall is not rich.
Everyone who is both quiet and not happy is either not wise or not calm.
Everyone who is wise is either happy or wise and vice versa.
If susan is not creative or quiet then alice is both not quiet and generous and vice versa.
If someone is both humble and not funny then fred is both not creative and not wise.
If someone is both wise and generous then fred is strong.
If someone is both strong and not happy then fred is either tall or old.
If someone is quiet or calm then someone is not happy and vice versa.
Everyone who is either not kind or not generous is not wise or kind.
If someone is either not tall or quiet then someone is both creative and tall and vice versa.
Everyone who is both not calm and not kind is happy or curious and vice versa.
If alice is either curious or generous then someone is both not curious and generous and vice versa.
Everyone who is not brave or rich is either humble or not funny.
If someone is either brave or not humble then someone is either brave or not calm and vice versa.
If someone is not happy or creative then someone is both strong and funny.
Someone is not brave or creative.
Someone is either old or not tall.
Someone is either not curious or wise.
Mary is not creative.
Someone is not funny or not rich.
Paul is not funny.
Someone is both not tall and curious.
Someone is both generous and not tall. | Fred is not happy. | entailment | (((brave(john)&creative(john)))<=>(?[X]:((calm(X)&strong(X)))))&
(![X]:((calm(X)<~>~tall(X))=>~rich(X)))&
(![X]:((quiet(X)&~happy(X))=>(~wise(X)<~>~calm(X))))&
(![X]:(wise(X)<=>(happy(X)<~>wise(X))))&
(((~creative(susan)|quiet(susan)))<=>((~quiet(alice)&generous(alice))))&
((?[X]:((humble(X)&~funny(X))))=>((~creative(fred)&~wise(fred))))&
((?[X]:((wise(X)&generous(X))))=>(strong(fred)))&
((?[X]:((strong(X)&~happy(X))))=>((tall(fred)<~>old(fred))))&
((?[X]:((quiet(X)|calm(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(~wise(X)|kind(X))))&
((?[X]:((~tall(X)<~>quiet(X))))<=>(?[X]:((creative(X)&tall(X)))))&
(![X]:((~calm(X)&~kind(X))<=>(happy(X)|curious(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:((~curious(X)&generous(X)))))&
(![X]:((~brave(X)|rich(X))=>(humble(X)<~>~funny(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
((?[X]:((~happy(X)|creative(X))))=>(?[X]:((strong(X)&funny(X)))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((old(X)<~>~tall(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
(~creative(mary))&
(?[X]:((~funny(X)|~rich(X))))&
(~funny(paul))&
(?[X]:((~tall(X)&curious(X))))&
(?[X]:((generous(X)&~tall(X)))) | ~happy(fred) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 9193181228799811624780900
% SZS output start Proof for 9193181228799811624780900
4. ! [X0] : (wise(X0) <=> (happy(X0) <~> wise(X0))) [input p3]
25. happy(fred) [input hypothesis]
48. ! [X0] : ((wise(X0) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0)))) & (((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | ~wise(X0))) [nnf transformation 4]
97. ~wise(X0) | ~happy(X0) | ~wise(X0) [cnf transformation 48]
98. wise(X0) | wise(X0) | ~happy(X0) [cnf transformation 48]
157. happy(fred) [cnf transformation 25]
159. ~wise(X0) | ~happy(X0) [duplicate literal removal 97]
160. wise(X0) | ~happy(X0) [duplicate literal removal 98]
184. ~happy(X0) [subsumption resolution 159,160]
387. $false [subsumption resolution 157,184]
% SZS output end Proof for 9193181228799811624780900
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not curious is not old or calm and vice versa.
Everyone who is either not humble or brave is not curious and vice versa.
If mary is either rich or not brave then someone is either quiet or not rich and vice versa.
Everyone who is either curious or funny is calm.
If someone is either curious or not funny then john is calm.
If alice is not strong then alice is not creative or creative and vice versa.
Everyone who is both not tall and rich is either not happy or brave and vice versa.
If john is not funny then fred is either not humble or wise and vice versa.
If john is either not calm or not wise then lucy is calm and vice versa.
Everyone who is both humble and not creative is curious or happy.
Everyone who is funny or not humble is either not generous or not rich and vice versa.
Everyone who is not calm or old is not wise or patient.
Everyone who is not funny is either not patient or not quiet and vice versa.
If alice is curious then mary is strong and vice versa.
If someone is both not happy and not humble then someone is not creative or kind.
Everyone who is either humble or happy is kind and vice versa.
Someone is curious or not happy.
Mary is both brave and not wise.
Susan is happy.
Someone is not creative or not happy.
Alice is not patient.
Paul is either not funny or not patient.
Someone is not old. | Lucy is wise. | neutral | (![X]:((old(X)<~>~curious(X))<=>(~old(X)|calm(X))))&
(![X]:((~humble(X)<~>brave(X))<=>~curious(X)))&
(((rich(mary)<~>~brave(mary)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((curious(X)<~>funny(X))=>calm(X)))&
((?[X]:((curious(X)<~>~funny(X))))=>(calm(john)))&
((~strong(alice))<=>((~creative(alice)|creative(alice))))&
(![X]:((~tall(X)&rich(X))<=>(~happy(X)<~>brave(X))))&
((~funny(john))<=>((~humble(fred)<~>wise(fred))))&
(((~calm(john)<~>~wise(john)))<=>(calm(lucy)))&
(![X]:((humble(X)&~creative(X))=>(curious(X)|happy(X))))&
(![X]:((funny(X)|~humble(X))<=>(~generous(X)<~>~rich(X))))&
(![X]:((~calm(X)|old(X))=>(~wise(X)|patient(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~quiet(X))))&
((curious(alice))<=>(strong(mary)))&
((?[X]:((~happy(X)&~humble(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((humble(X)<~>happy(X))<=>kind(X)))&
(?[X]:((curious(X)|~happy(X))))&
((brave(mary)&~wise(mary)))&
(happy(susan))&
(?[X]:((~creative(X)|~happy(X))))&
(~patient(alice))&
((~funny(paul)<~>~patient(paul)))&
(?[X]:(~old(X))) | wise(lucy) | [] | null | 0 |
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