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 both old and not curious is both wise and quiet and vice versa. Everyone who is either calm or creative is both quiet and curious and vice versa. If john is either not wise or not old then someone is not kind or not patient and vice versa. Everyone who is either calm or strong is calm. If someone is both not strong and generous then susan is not patient or not strong and vice versa. Everyone who is both not curious and not kind is both rich and tall and vice versa. Everyone who is both not patient and not rich is creative. If someone is not calm then someone is quiet or brave. Everyone who is both not patient and wise is either creative or not curious and vice versa. If paul is not brave or not strong then someone is not patient and vice versa. Everyone who is both not funny and humble is both not strong and not curious and vice versa. Everyone who is both not happy and not creative is both not tall and not quiet. If paul is both creative and generous then fred is generous or not creative. If lucy is either not calm or not wise then someone is both not old and strong. If mary is either brave or not strong then someone is tall or not strong. Everyone who is either rich or strong is either humble or not happy and vice versa. Someone is not rich. Someone is either tall or happy. Lucy is funny. Lucy is rich. Someone is not brave. Someone is humble or not tall. Someone is both not strong and not rich. Paul is brave or not old. | Paul is generous. | neutral | (![X]:((old(X)&~curious(X))<=>(wise(X)&quiet(X))))&
(![X]:((calm(X)<~>creative(X))<=>(quiet(X)&curious(X))))&
(((~wise(john)<~>~old(john)))<=>(?[X]:((~kind(X)|~patient(X)))))&
(![X]:((calm(X)<~>strong(X))=>calm(X)))&
((?[X]:((~strong(X)&generous(X))))<=>((~patient(susan)|~strong(susan))))&
(![X]:((~curious(X)&~kind(X))<=>(rich(X)&tall(X))))&
(![X]:((~patient(X)&~rich(X))=>creative(X)))&
((?[X]:(~calm(X)))=>(?[X]:((quiet(X)|brave(X)))))&
(![X]:((~patient(X)&wise(X))<=>(creative(X)<~>~curious(X))))&
(((~brave(paul)|~strong(paul)))<=>(?[X]:(~patient(X))))&
(![X]:((~funny(X)&humble(X))<=>(~strong(X)&~curious(X))))&
(![X]:((~happy(X)&~creative(X))=>(~tall(X)&~quiet(X))))&
(((creative(paul)&generous(paul)))=>((generous(fred)|~creative(fred))))&
(((~calm(lucy)<~>~wise(lucy)))=>(?[X]:((~old(X)&strong(X)))))&
(((brave(mary)<~>~strong(mary)))=>(?[X]:((tall(X)|~strong(X)))))&
(![X]:((rich(X)<~>strong(X))<=>(humble(X)<~>~happy(X))))&
(?[X]:(~rich(X)))&
(?[X]:((tall(X)<~>happy(X))))&
(funny(lucy))&
(rich(lucy))&
(?[X]:(~brave(X)))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:((~strong(X)&~rich(X))))&
((brave(paul)|~old(paul))) | generous(paul) | [] | null | 0 |
Everyone who is generous is both not rich and not quiet and vice versa. If fred is calm then paul is either tall or not calm. Everyone who is both not generous and not rich is either tall or not generous and vice versa. If lucy is patient then paul is not funny and vice versa. Everyone who is rich is not humble. If fred is not old then john is both not old and not humble. If john is either happy or wise then alice is funny or not kind and vice versa. Everyone who is either not rich or old is both humble and not kind. Everyone who is both kind and generous is either not creative or not curious. Everyone who is both not kind and generous is either not humble or not patient and vice versa. If paul is not rich then susan is either happy or kind. If someone is either not old or not kind then someone is patient and vice versa. If lucy is either tall or not humble then fred is either not brave or not creative. If someone is funny then someone is both not old and creative. If someone is both creative and calm then someone is both rich and wise. If paul is not funny then susan is not creative or not kind and vice versa. Someone is both not quiet and creative. Mary is both not patient and curious. Someone is both not curious and not wise. Alice is either not generous or generous. Someone is not generous. Lucy is both not rich and not humble. Someone is either not rich or not calm. Someone is rich. | Lucy is not quiet. | neutral | (![X]:(generous(X)<=>(~rich(X)&~quiet(X))))&
((calm(fred))=>((tall(paul)<~>~calm(paul))))&
(![X]:((~generous(X)&~rich(X))<=>(tall(X)<~>~generous(X))))&
((patient(lucy))<=>(~funny(paul)))&
(![X]:(rich(X)=>~humble(X)))&
((~old(fred))=>((~old(john)&~humble(john))))&
(((happy(john)<~>wise(john)))<=>((funny(alice)|~kind(alice))))&
(![X]:((~rich(X)<~>old(X))=>(humble(X)&~kind(X))))&
(![X]:((kind(X)&generous(X))=>(~creative(X)<~>~curious(X))))&
(![X]:((~kind(X)&generous(X))<=>(~humble(X)<~>~patient(X))))&
((~rich(paul))=>((happy(susan)<~>kind(susan))))&
((?[X]:((~old(X)<~>~kind(X))))<=>(?[X]:(patient(X))))&
(((tall(lucy)<~>~humble(lucy)))=>((~brave(fred)<~>~creative(fred))))&
((?[X]:(funny(X)))=>(?[X]:((~old(X)&creative(X)))))&
((?[X]:((creative(X)&calm(X))))=>(?[X]:((rich(X)&wise(X)))))&
((~funny(paul))<=>((~creative(susan)|~kind(susan))))&
(?[X]:((~quiet(X)&creative(X))))&
((~patient(mary)&curious(mary)))&
(?[X]:((~curious(X)&~wise(X))))&
((~generous(alice)<~>generous(alice)))&
(?[X]:(~generous(X)))&
((~rich(lucy)&~humble(lucy)))&
(?[X]:((~rich(X)<~>~calm(X))))&
(?[X]:(rich(X))) | ~quiet(lucy) | [] | null | 0 |
If someone is wise or not quiet then someone is tall and vice versa.
Everyone who is both curious and not calm is both not creative and not rich and vice versa.
Everyone who is not tall is either generous or brave.
If susan is either not rich or rich then john is not kind and vice versa.
If someone is either not curious or rich then someone is kind and vice versa.
Everyone who is either tall or humble is not rich and vice versa.
Everyone who is both kind and curious is either generous or not strong and vice versa.
If mary is not happy then someone is both rich and not patient.
If fred is curious or not brave then john is both old and not patient.
If someone is both not tall and not calm then someone is not strong and vice versa.
Everyone who is both tall and curious is quiet and vice versa.
Everyone who is both not wise and quiet is generous or creative.
Everyone who is either not brave or generous is not quiet and vice versa.
If someone is both not rich and not patient then someone is not quiet.
If paul is rich or quiet then someone is generous or quiet and vice versa.
If someone is either wise or not wise then alice is not generous.
Susan is both rich and calm.
Mary is humble.
Mary is either not old or strong.
Fred is not wise or happy.
Someone is either wise or not brave.
Someone is either not strong or old.
Someone is either generous or kind. | Mary is old. | entailment | ((?[X]:((wise(X)|~quiet(X))))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)&~calm(X))<=>(~creative(X)&~rich(X))))&
(![X]:(~tall(X)=>(generous(X)<~>brave(X))))&
(((~rich(susan)<~>rich(susan)))<=>(~kind(john)))&
((?[X]:((~curious(X)<~>rich(X))))<=>(?[X]:(kind(X))))&
(![X]:((tall(X)<~>humble(X))<=>~rich(X)))&
(![X]:((kind(X)&curious(X))<=>(generous(X)<~>~strong(X))))&
((~happy(mary))=>(?[X]:((rich(X)&~patient(X)))))&
(((curious(fred)|~brave(fred)))=>((old(john)&~patient(john))))&
((?[X]:((~tall(X)&~calm(X))))<=>(?[X]:(~strong(X))))&
(![X]:((tall(X)&curious(X))<=>quiet(X)))&
(![X]:((~wise(X)&quiet(X))=>(generous(X)|creative(X))))&
(![X]:((~brave(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:((~rich(X)&~patient(X))))=>(?[X]:(~quiet(X))))&
(((rich(paul)|quiet(paul)))<=>(?[X]:((generous(X)|quiet(X)))))&
((?[X]:((wise(X)<~>~wise(X))))=>(~generous(alice)))&
((rich(susan)&calm(susan)))&
(humble(mary))&
((~old(mary)<~>strong(mary)))&
((~wise(fred)|happy(fred)))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((generous(X)<~>kind(X)))) | old(mary) | [
"p2",
"p9",
"p10",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7404065958906386314694481
% SZS output start Proof for 7404065958906386314694481
3. ! [X0] : (~tall(X0) => (generous(X0) <~> brave(X0))) [input p2]
10. ? [X0] : (~calm(X0) & ~tall(X0)) <=> ? [X0] : ~strong(X0) [input p9]
11. ! [X0] : ((curious(X0) & tall(X0)) <=> quiet(X0)) [input p10]
13. ! [X0] : ((~brave(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p12]
19. ~old(mary) <~> strong(mary) [input p18]
24. ~old(mary) [input hypothesis]
27. ? [X0] : (~calm(X0) & ~tall(X0)) <=> ? [X1] : ~strong(X1) [rectify 10]
31. ! [X0] : ((generous(X0) <~> brave(X0)) | tall(X0)) [ennf transformation 3]
44. ! [X0] : (((~brave(X0) | ~generous(X0)) & (brave(X0) | generous(X0))) | tall(X0)) [nnf transformation 31]
54. (? [X0] : (~calm(X0) & ~tall(X0)) | ! [X1] : strong(X1)) & (? [X1] : ~strong(X1) | ! [X0] : (calm(X0) | tall(X0))) [nnf transformation 27]
55. (? [X0] : (~calm(X0) & ~tall(X0)) | ! [X1] : strong(X1)) & (? [X2] : ~strong(X2) | ! [X3] : (calm(X3) | tall(X3))) [rectify 54]
56. ? [X0] : (~calm(X0) & ~tall(X0)) => (~calm(sK4) & ~tall(sK4)) [choice axiom]
57. ? [X2] : ~strong(X2) => ~strong(sK5) [choice axiom]
58. ((~calm(sK4) & ~tall(sK4)) | ! [X1] : strong(X1)) & (~strong(sK5) | ! [X3] : (calm(X3) | tall(X3))) [skolemisation 55,57,56]
59. ! [X0] : (((curious(X0) & tall(X0)) | ~quiet(X0)) & (quiet(X0) | (~curious(X0) | ~tall(X0)))) [nnf transformation 11]
60. ! [X0] : (((curious(X0) & tall(X0)) | ~quiet(X0)) & (quiet(X0) | ~curious(X0) | ~tall(X0))) [flattening 59]
61. ! [X0] : ((((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | quiet(X0)) & (~quiet(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0))))) [nnf transformation 13]
71. (~strong(mary) | old(mary)) & (strong(mary) | ~old(mary)) [nnf transformation 19]
88. brave(X0) | generous(X0) | tall(X0) [cnf transformation 44]
89. ~brave(X0) | ~generous(X0) | tall(X0) [cnf transformation 44]
113. ~tall(sK4) | strong(X1) [cnf transformation 58]
116. ~quiet(X0) | tall(X0) [cnf transformation 60]
121. ~brave(X0) | generous(X0) | quiet(X0) [cnf transformation 61]
122. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 61]
134. ~strong(mary) | old(mary) [cnf transformation 71]
141. ~old(mary) [cnf transformation 24]
226. 19 <=> ! [X1] : strong(X1) [avatar definition]
227. strong(X1) <- (19) [avatar component clause 226]
234. 21 <=> tall(sK4) [avatar definition]
236. ~tall(sK4) <- (~21) [avatar component clause 234]
237. 19 | ~21 [avatar split clause 113,234,226]
291. 34 <=> old(mary) [avatar definition]
295. 35 <=> strong(mary) [avatar definition]
297. ~strong(mary) <- (~35) [avatar component clause 295]
298. 34 | ~35 [avatar split clause 134,295,291]
330. ~34 [avatar split clause 141,291]
468. generous(X0) | quiet(X0) | generous(X0) | tall(X0) [resolution 121,88]
469. generous(X0) | quiet(X0) | tall(X0) [duplicate literal removal 468]
471. generous(X0) | tall(X0) [subsumption resolution 469,116]
523. $false <- (19, ~35) [resolution 227,297]
526. ~19 | 35 [avatar contradiction clause 523]
624. tall(X0) | brave(X0) | quiet(X0) [resolution 471,122]
631. brave(X0) | tall(X0) [subsumption resolution 624,116]
799. tall(X2) | ~generous(X2) | tall(X2) [resolution 631,89]
800. tall(X2) | ~generous(X2) [duplicate literal removal 799]
801. tall(X2) [subsumption resolution 800,471]
849. $false <- (~21) [resolution 801,236]
853. 21 [avatar contradiction clause 849]
854. $false [avatar sat refutation 237,298,330,526,853]
% SZS output end Proof for 7404065958906386314694481
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not wise and not rich then susan is both patient and not kind.
If alice is either not kind or funny then someone is either not kind or funny.
If fred is not curious then john is not funny and vice versa.
Everyone who is both creative and funny is either not tall or funny and vice versa.
If someone is rich then paul is tall.
Everyone who is not creative is either not old or not humble and vice versa.
Everyone who is both not brave and not wise is either not generous or not happy.
If fred is quiet then john is either funny or not rich.
If someone is either not tall or kind then someone is both not funny and not wise.
If mary is either not old or not funny then mary is both creative and calm and vice versa.
Everyone who is not strong is not kind.
Everyone who is either not funny or creative is either wise or creative and vice versa.
If someone is either funny or old then john is both not happy and rich and vice versa.
Everyone who is either tall or not kind is both quiet and not happy and vice versa.
Everyone who is both not generous and funny is either old or not quiet.
Everyone who is either not calm or not strong is both not calm and not wise and vice versa.
John is both not happy and not wise.
Paul is both not strong and not patient.
John is not generous.
Someone is not old or old.
Susan is generous.
Lucy is either funny or not funny.
Paul is both not brave and tall. | John is creative. | neutral | ((?[X]:((~wise(X)&~rich(X))))=>((patient(susan)&~kind(susan))))&
(((~kind(alice)<~>funny(alice)))=>(?[X]:((~kind(X)<~>funny(X)))))&
((~curious(fred))<=>(~funny(john)))&
(![X]:((creative(X)&funny(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(rich(X)))=>(tall(paul)))&
(![X]:(~creative(X)<=>(~old(X)<~>~humble(X))))&
(![X]:((~brave(X)&~wise(X))=>(~generous(X)<~>~happy(X))))&
((quiet(fred))=>((funny(john)<~>~rich(john))))&
((?[X]:((~tall(X)<~>kind(X))))=>(?[X]:((~funny(X)&~wise(X)))))&
(((~old(mary)<~>~funny(mary)))<=>((creative(mary)&calm(mary))))&
(![X]:(~strong(X)=>~kind(X)))&
(![X]:((~funny(X)<~>creative(X))<=>(wise(X)<~>creative(X))))&
((?[X]:((funny(X)<~>old(X))))<=>((~happy(john)&rich(john))))&
(![X]:((tall(X)<~>~kind(X))<=>(quiet(X)&~happy(X))))&
(![X]:((~generous(X)&funny(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~calm(X)<~>~strong(X))<=>(~calm(X)&~wise(X))))&
((~happy(john)&~wise(john)))&
((~strong(paul)&~patient(paul)))&
(~generous(john))&
(?[X]:((~old(X)|old(X))))&
(generous(susan))&
((funny(lucy)<~>~funny(lucy)))&
((~brave(paul)&tall(paul))) | creative(john) | [] | null | 0 |
Everyone who is both brave and wise is either not generous or not happy. If alice is happy then fred is either brave or not calm. If alice is either not brave or patient then lucy is tall. If john is creative or calm then someone is not quiet or not patient. If someone is not generous then paul is not quiet. If alice is old or patient then paul is both not old and not brave and vice versa. Everyone who is either tall or not calm is both not creative and not brave and vice versa. Everyone who is rich or not wise is either tall or not calm. Everyone who is both funny and creative is not brave or not generous and vice versa. If someone is not curious or not funny then john is not quiet or not kind. If someone is both not kind and not calm then lucy is both not humble and not kind and vice versa. If someone is rich or calm then someone is either generous or patient. Everyone who is both not generous and patient is either kind or not calm and vice versa. Everyone who is either not old or not rich is not humble and vice versa. Everyone who is calm is rich. If someone is wise or not happy then someone is not curious or curious and vice versa. Fred is both not rich and not brave. Fred is both not patient and happy. Someone is either strong or not humble. Mary is either not tall or funny. Lucy is either funny or humble. Lucy is both not quiet and wise. Someone is either humble or calm. Mary is not patient. | Paul is not tall. | contradiction | (![X]:((brave(X)&wise(X))=>(~generous(X)<~>~happy(X))))&
((happy(alice))=>((brave(fred)<~>~calm(fred))))&
(((~brave(alice)<~>patient(alice)))=>(tall(lucy)))&
(((creative(john)|calm(john)))=>(?[X]:((~quiet(X)|~patient(X)))))&
((?[X]:(~generous(X)))=>(~quiet(paul)))&
(((old(alice)|patient(alice)))<=>((~old(paul)&~brave(paul))))&
(![X]:((tall(X)<~>~calm(X))<=>(~creative(X)&~brave(X))))&
(![X]:((rich(X)|~wise(X))=>(tall(X)<~>~calm(X))))&
(![X]:((funny(X)&creative(X))<=>(~brave(X)|~generous(X))))&
((?[X]:((~curious(X)|~funny(X))))=>((~quiet(john)|~kind(john))))&
((?[X]:((~kind(X)&~calm(X))))<=>((~humble(lucy)&~kind(lucy))))&
((?[X]:((rich(X)|calm(X))))=>(?[X]:((generous(X)<~>patient(X)))))&
(![X]:((~generous(X)&patient(X))<=>(kind(X)<~>~calm(X))))&
(![X]:((~old(X)<~>~rich(X))<=>~humble(X)))&
(![X]:(calm(X)=>rich(X)))&
((?[X]:((wise(X)|~happy(X))))<=>(?[X]:((~curious(X)|curious(X)))))&
((~rich(fred)&~brave(fred)))&
((~patient(fred)&happy(fred)))&
(?[X]:((strong(X)<~>~humble(X))))&
((~tall(mary)<~>funny(mary)))&
((funny(lucy)<~>humble(lucy)))&
((~quiet(lucy)&wise(lucy)))&
(?[X]:((humble(X)<~>calm(X))))&
(~patient(mary)) | ~tall(paul) | [
"p6",
"p7",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8788034370702728452638452
% SZS output start Proof for 8788034370702728452638452
7. ! [X0] : ((tall(X0) <~> ~calm(X0)) <=> (~brave(X0) & ~creative(X0))) [input p6]
8. ! [X0] : ((~wise(X0) | rich(X0)) => (tall(X0) <~> ~calm(X0))) [input p7]
9. ! [X0] : ((creative(X0) & funny(X0)) <=> (~generous(X0) | ~brave(X0))) [input p8]
15. ! [X0] : (calm(X0) => rich(X0)) [input p14]
25. ~tall(paul) [input hypothesis]
36. ! [X0] : ((tall(X0) <~> ~calm(X0)) | (wise(X0) & ~rich(X0))) [ennf transformation 8]
38. ! [X0] : (rich(X0) | ~calm(X0)) [ennf transformation 15]
44. ! [X0] : ((((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0))))) [nnf transformation 7]
45. ! [X0] : ((((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0))))) [flattening 44]
46. ! [X0] : (((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | (wise(X0) & ~rich(X0))) [nnf transformation 36]
47. ! [X0] : (((creative(X0) & funny(X0)) | (generous(X0) & brave(X0))) & ((~generous(X0) | ~brave(X0)) | (~creative(X0) | ~funny(X0)))) [nnf transformation 9]
48. ! [X0] : (((creative(X0) & funny(X0)) | (generous(X0) & brave(X0))) & (~generous(X0) | ~brave(X0) | ~creative(X0) | ~funny(X0))) [flattening 47]
86. ~creative(X0) | tall(X0) | calm(X0) [cnf transformation 45]
88. ~brave(X0) | tall(X0) | calm(X0) [cnf transformation 45]
91. ~rich(X0) | tall(X0) | ~calm(X0) [cnf transformation 46]
98. creative(X0) | brave(X0) [cnf transformation 48]
118. ~calm(X0) | rich(X0) [cnf transformation 38]
137. ~tall(paul) [cnf transformation 25]
285. tall(X1) | calm(X1) | brave(X1) [resolution 86,98]
286. tall(X1) | calm(X1) [subsumption resolution 285,88]
287. calm(paul) [resolution 286,137]
291. rich(paul) [resolution 287,118]
295. tall(paul) | ~calm(paul) [resolution 291,91]
296. ~calm(paul) [subsumption resolution 295,137]
297. $false [subsumption resolution 296,287]
% SZS output end Proof for 8788034370702728452638452
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either funny or brave then lucy is both not strong and strong. Everyone who is both creative and rich is either quiet or calm and vice versa. Everyone who is either brave or not humble is not rich. Everyone who is both not rich and happy is either old or not quiet and vice versa. Everyone who is either not generous or not calm is not quiet and vice versa. Everyone who is either not old or wise is both humble and tall. Everyone who is not brave or brave is both old and wise. Everyone who is either not old or not funny is curious and vice versa. If someone is both not old and not strong then someone is both funny and kind and vice versa. Everyone who is not rich is not creative or patient and vice versa. If alice is not generous or not humble then someone is not brave. Everyone who is brave or not quiet is both generous and curious and vice versa. If someone is not wise or not happy then someone is not creative and vice versa. Everyone who is not happy or old is either curious or not kind and vice versa. If someone is either not wise or calm then someone is curious or calm. Mary is either tall or strong. Someone is patient. Someone is both wise and not kind. Someone is either calm or not wise. Someone is not strong or not generous. Someone is curious. | Mary is generous. | entailment | (((funny(fred)<~>brave(fred)))=>((~strong(lucy)&strong(lucy))))&
(![X]:((creative(X)&rich(X))<=>(quiet(X)<~>calm(X))))&
(![X]:((brave(X)<~>~humble(X))=>~rich(X)))&
(![X]:((~rich(X)&happy(X))<=>(old(X)<~>~quiet(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>~quiet(X)))&
(![X]:((~old(X)<~>wise(X))=>(humble(X)&tall(X))))&
(![X]:((~brave(X)|brave(X))=>(old(X)&wise(X))))&
(![X]:((~old(X)<~>~funny(X))<=>curious(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:(~rich(X)<=>(~creative(X)|patient(X))))&
(((~generous(alice)|~humble(alice)))=>(?[X]:(~brave(X))))&
(![X]:((brave(X)|~quiet(X))<=>(generous(X)&curious(X))))&
((?[X]:((~wise(X)|~happy(X))))<=>(?[X]:(~creative(X))))&
(![X]:((~happy(X)|old(X))<=>(curious(X)<~>~kind(X))))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((curious(X)|calm(X)))))&
((tall(mary)<~>strong(mary)))&
(?[X]:(patient(X)))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
(?[X]:((~strong(X)|~generous(X))))&
(?[X]:(curious(X))) | generous(mary) | [
"p1",
"p3",
"p4",
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6758988993805323329541532
% SZS output start Proof for 6758988993805323329541532
2. ! [X0] : ((rich(X0) & creative(X0)) <=> (quiet(X0) <~> calm(X0))) [input p1]
4. ! [X0] : ((happy(X0) & ~rich(X0)) <=> (old(X0) <~> ~quiet(X0))) [input p3]
5. ! [X0] : ((~generous(X0) <~> ~calm(X0)) <=> ~quiet(X0)) [input p4]
7. ! [X0] : ((brave(X0) | ~brave(X0)) => (wise(X0) & old(X0))) [input p6]
12. ! [X0] : ((~quiet(X0) | brave(X0)) <=> (curious(X0) & generous(X0))) [input p11]
22. ~generous(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 7]
33. ! [X0] : (((rich(X0) & creative(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~rich(X0) | ~creative(X0)))) [nnf transformation 2]
34. ! [X0] : (((rich(X0) & creative(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~rich(X0) | ~creative(X0))) [flattening 33]
36. ! [X0] : (((happy(X0) & ~rich(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (~happy(X0) | rich(X0)))) [nnf transformation 4]
37. ! [X0] : (((happy(X0) & ~rich(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | ~happy(X0) | rich(X0))) [flattening 36]
38. ! [X0] : ((((calm(X0) | generous(X0)) & (~calm(X0) | ~generous(X0))) | quiet(X0)) & (~quiet(X0) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0))))) [nnf transformation 5]
50. ! [X0] : (((~quiet(X0) | brave(X0)) | (~curious(X0) | ~generous(X0))) & ((curious(X0) & generous(X0)) | (quiet(X0) & ~brave(X0)))) [nnf transformation 12]
51. ! [X0] : ((~quiet(X0) | brave(X0) | ~curious(X0) | ~generous(X0)) & ((curious(X0) & generous(X0)) | (quiet(X0) & ~brave(X0)))) [flattening 50]
83. ~quiet(X0) | calm(X0) | rich(X0) [cnf transformation 34]
89. ~old(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 37]
93. ~calm(X0) | ~quiet(X0) | generous(X0) [cnf transformation 38]
101. old(X0) | brave(X0) [cnf transformation 29]
102. ~brave(X0) | old(X0) [cnf transformation 29]
119. generous(X0) | quiet(X0) [cnf transformation 51]
143. ~generous(mary) [cnf transformation 22]
161. old(X0) [subsumption resolution 101,102]
243. quiet(mary) [resolution 119,143]
260. 21 <=> calm(mary) [avatar definition]
262. calm(mary) <- (21) [avatar component clause 260]
276. calm(mary) | rich(mary) [resolution 83,243]
278. 24 <=> rich(mary) [avatar definition]
280. rich(mary) <- (24) [avatar component clause 278]
281. 24 | 21 [avatar split clause 276,260,278]
292. ~quiet(X0) | ~rich(X0) [resolution 89,161]
320. ~quiet(mary) | generous(mary) <- (21) [resolution 93,262]
323. generous(mary) <- (21) [subsumption resolution 320,243]
324. $false <- (21) [subsumption resolution 323,143]
325. ~21 [avatar contradiction clause 324]
375. ~rich(mary) [resolution 292,243]
378. $false <- (24) [subsumption resolution 375,280]
379. ~24 [avatar contradiction clause 378]
382. $false [avatar sat refutation 281,325,379]
% SZS output end Proof for 6758988993805323329541532
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or patient is either happy or kind.
If paul is both not kind and not strong then someone is generous or strong and vice versa.
Everyone who is rich or funny is either kind or not strong and vice versa.
If alice is either quiet or not brave then someone is both not wise and not patient and vice versa.
If paul is quiet or patient then someone is brave or not old and vice versa.
Everyone who is not creative is not happy.
Everyone who is not generous or not rich is either humble or happy.
If mary is not rich or not brave then fred is both not patient and curious and vice versa.
If someone is generous or tall then john is not old and vice versa.
Everyone who is both not rich and happy is either not rich or not wise.
Everyone who is not generous or calm is either not brave or brave and vice versa.
Everyone who is not old or not creative is both not quiet and not humble.
Everyone who is either not humble or calm is rich or generous and vice versa.
Everyone who is both quiet and not generous is not kind and vice versa.
If paul is both brave and not kind then lucy is either not calm or brave and vice versa.
If someone is not rich or not funny then mary is both curious and humble.
Someone is either funny or not tall.
Someone is both rich and brave.
Mary is both not patient and curious.
Someone is both brave and not kind.
Lucy is either not curious or brave.
Susan is either not brave or not creative.
Someone is not brave. | Mary is curious. | entailment | (![X]:((~funny(X)|patient(X))=>(happy(X)<~>kind(X))))&
(((~kind(paul)&~strong(paul)))<=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((rich(X)|funny(X))<=>(kind(X)<~>~strong(X))))&
(((quiet(alice)<~>~brave(alice)))<=>(?[X]:((~wise(X)&~patient(X)))))&
(((quiet(paul)|patient(paul)))<=>(?[X]:((brave(X)|~old(X)))))&
(![X]:(~creative(X)=>~happy(X)))&
(![X]:((~generous(X)|~rich(X))=>(humble(X)<~>happy(X))))&
(((~rich(mary)|~brave(mary)))<=>((~patient(fred)&curious(fred))))&
((?[X]:((generous(X)|tall(X))))<=>(~old(john)))&
(![X]:((~rich(X)&happy(X))=>(~rich(X)<~>~wise(X))))&
(![X]:((~generous(X)|calm(X))<=>(~brave(X)<~>brave(X))))&
(![X]:((~old(X)|~creative(X))=>(~quiet(X)&~humble(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(rich(X)|generous(X))))&
(![X]:((quiet(X)&~generous(X))<=>~kind(X)))&
(((brave(paul)&~kind(paul)))<=>((~calm(lucy)<~>brave(lucy))))&
((?[X]:((~rich(X)|~funny(X))))=>((curious(mary)&humble(mary))))&
(?[X]:((funny(X)<~>~tall(X))))&
(?[X]:((rich(X)&brave(X))))&
((~patient(mary)&curious(mary)))&
(?[X]:((brave(X)&~kind(X))))&
((~curious(lucy)<~>brave(lucy)))&
((~brave(susan)<~>~creative(susan)))&
(?[X]:(~brave(X))) | curious(mary) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7549549493853737638177388
% SZS output start Proof for 7549549493853737638177388
19. curious(mary) & ~patient(mary) [input p18]
24. ~curious(mary) [input hypothesis]
150. curious(mary) [cnf transformation 19]
158. ~curious(mary) [cnf transformation 24]
313. 32 <=> curious(mary) [avatar definition]
328. 32 [avatar split clause 150,313]
345. ~32 [avatar split clause 158,313]
346. $false [avatar sat refutation 328,345]
% SZS output end Proof for 7549549493853737638177388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is patient or not generous and vice versa.
Everyone who is not humble is either rich or not rich and vice versa.
Everyone who is humble is both humble and not curious and vice versa.
If someone is not tall then paul is tall or not generous and vice versa.
Everyone who is both not calm and funny is not old or rich and vice versa.
Everyone who is not old is either kind or rich and vice versa.
If someone is not humble or not kind then someone is brave and vice versa.
Everyone who is not old is not tall or not wise.
If someone is both not tall and not funny then lucy is both not rich and brave and vice versa.
If lucy is either not brave or patient then paul is either not rich or creative.
If alice is both not humble and not curious then someone is happy or curious.
Everyone who is not old is tall.
Everyone who is either funny or not rich is both kind and not brave.
If someone is old or happy then someone is not curious or not kind and vice versa.
Everyone who is either generous or happy is not old or wise and vice versa.
Everyone who is either not funny or kind is not funny or brave.
Someone is either not strong or happy.
Someone is either curious or not quiet.
Paul is not funny or not calm.
Paul is humble or quiet.
Mary is both not calm and not curious.
Someone is brave or generous. | Mary is generous. | neutral | (![X]:(patient(X)<=>(patient(X)|~generous(X))))&
(![X]:(~humble(X)<=>(rich(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(humble(X)&~curious(X))))&
((?[X]:(~tall(X)))<=>((tall(paul)|~generous(paul))))&
(![X]:((~calm(X)&funny(X))<=>(~old(X)|rich(X))))&
(![X]:(~old(X)<=>(kind(X)<~>rich(X))))&
((?[X]:((~humble(X)|~kind(X))))<=>(?[X]:(brave(X))))&
(![X]:(~old(X)=>(~tall(X)|~wise(X))))&
((?[X]:((~tall(X)&~funny(X))))<=>((~rich(lucy)&brave(lucy))))&
(((~brave(lucy)<~>patient(lucy)))=>((~rich(paul)<~>creative(paul))))&
(((~humble(alice)&~curious(alice)))=>(?[X]:((happy(X)|curious(X)))))&
(![X]:(~old(X)=>tall(X)))&
(![X]:((funny(X)<~>~rich(X))=>(kind(X)&~brave(X))))&
((?[X]:((old(X)|happy(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
(![X]:((generous(X)<~>happy(X))<=>(~old(X)|wise(X))))&
(![X]:((~funny(X)<~>kind(X))=>(~funny(X)|brave(X))))&
(?[X]:((~strong(X)<~>happy(X))))&
(?[X]:((curious(X)<~>~quiet(X))))&
((~funny(paul)|~calm(paul)))&
((humble(paul)|quiet(paul)))&
((~calm(mary)&~curious(mary)))&
(?[X]:((brave(X)|generous(X)))) | generous(mary) | [] | null | 0 |
If susan is either not humble or not generous then fred is creative or not creative.
If someone is either creative or not happy then fred is either not creative or not tall and vice versa.
Everyone who is either not calm or strong is tall and vice versa.
If someone is brave or happy then susan is both quiet and not rich.
Everyone who is creative or not calm is not tall or old.
Everyone who is not calm or not rich is both generous and not humble and vice versa.
If fred is either strong or not quiet then paul is either humble or not humble.
If someone is quiet or not generous then someone is not creative.
Everyone who is quiet is either quiet or not kind.
Everyone who is kind or not kind is both calm and not patient and vice versa.
If john is both not patient and not creative then fred is wise.
Everyone who is not humble is not creative or curious.
If john is not happy then someone is either not wise or not old and vice versa.
Everyone who is either rich or happy is both happy and funny.
Everyone who is creative or happy is either not brave or not creative.
Everyone who is both curious and not wise is either not wise or not brave and vice versa.
Fred is quiet or not rich.
John is either patient or not wise.
Someone is not patient or funny.
Fred is either wise or not happy.
Alice is not rich.
Lucy is either not calm or wise.
Someone is brave or calm. | Susan is not calm. | contradiction | (((~humble(susan)<~>~generous(susan)))=>((creative(fred)|~creative(fred))))&
((?[X]:((creative(X)<~>~happy(X))))<=>((~creative(fred)<~>~tall(fred))))&
(![X]:((~calm(X)<~>strong(X))<=>tall(X)))&
((?[X]:((brave(X)|happy(X))))=>((quiet(susan)&~rich(susan))))&
(![X]:((creative(X)|~calm(X))=>(~tall(X)|old(X))))&
(![X]:((~calm(X)|~rich(X))<=>(generous(X)&~humble(X))))&
(((strong(fred)<~>~quiet(fred)))=>((humble(paul)<~>~humble(paul))))&
((?[X]:((quiet(X)|~generous(X))))=>(?[X]:(~creative(X))))&
(![X]:(quiet(X)=>(quiet(X)<~>~kind(X))))&
(![X]:((kind(X)|~kind(X))<=>(calm(X)&~patient(X))))&
(((~patient(john)&~creative(john)))=>(wise(fred)))&
(![X]:(~humble(X)=>(~creative(X)|curious(X))))&
((~happy(john))<=>(?[X]:((~wise(X)<~>~old(X)))))&
(![X]:((rich(X)<~>happy(X))=>(happy(X)&funny(X))))&
(![X]:((creative(X)|happy(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((curious(X)&~wise(X))<=>(~wise(X)<~>~brave(X))))&
((quiet(fred)|~rich(fred)))&
((patient(john)<~>~wise(john)))&
(?[X]:((~patient(X)|funny(X))))&
((wise(fred)<~>~happy(fred)))&
(~rich(alice))&
((~calm(lucy)<~>wise(lucy)))&
(?[X]:((brave(X)|calm(X)))) | ~calm(susan) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5207705191974828011671638
% SZS output start Proof for 5207705191974828011671638
10. ! [X0] : ((~kind(X0) | kind(X0)) <=> (~patient(X0) & calm(X0))) [input p9]
24. ~calm(susan) [input hypothesis]
55. ! [X0] : (((~kind(X0) | kind(X0)) | (patient(X0) | ~calm(X0))) & ((~patient(X0) & calm(X0)) | (kind(X0) & ~kind(X0)))) [nnf transformation 10]
56. ! [X0] : ((~kind(X0) | kind(X0) | patient(X0) | ~calm(X0)) & ((~patient(X0) & calm(X0)) | (kind(X0) & ~kind(X0)))) [flattening 55]
103. calm(X0) | ~kind(X0) [cnf transformation 56]
104. calm(X0) | kind(X0) [cnf transformation 56]
135. ~calm(susan) [cnf transformation 24]
202. calm(X0) [subsumption resolution 103,104]
253. $false [subsumption resolution 135,202]
% SZS output end Proof for 5207705191974828011671638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy or not creative is both kind and not patient. If paul is either happy or brave then someone is strong or not creative and vice versa. If mary is either kind or not tall then john is both not tall and not humble. If someone is both rich and old then someone is not quiet or not wise and vice versa. If alice is creative or calm then someone is both not calm and tall and vice versa. Everyone who is rich or not generous is rich. If mary is either not patient or funny then someone is both not happy and strong. Everyone who is either humble or not old is not curious. If john is both not humble and quiet then mary is brave and vice versa. If someone is not funny or not happy then alice is either strong or not funny. Everyone who is both kind and old is both rich and brave and vice versa. If fred is not old or not funny then fred is not wise or patient. Everyone who is both not rich and brave is curious or not quiet. Everyone who is old is either wise or not kind. If lucy is either not tall or quiet then someone is funny. If someone is kind then susan is old and vice versa. Paul is brave. Someone is not happy or old. Paul is patient. Alice is both not generous and not patient. Someone is either creative or not tall. Someone is both not patient and kind. Someone is either not rich or not creative. Susan is old or not curious. | Paul is not happy. | contradiction | (![X]:((~happy(X)|~creative(X))=>(kind(X)&~patient(X))))&
(((happy(paul)<~>brave(paul)))<=>(?[X]:((strong(X)|~creative(X)))))&
(((kind(mary)<~>~tall(mary)))=>((~tall(john)&~humble(john))))&
((?[X]:((rich(X)&old(X))))<=>(?[X]:((~quiet(X)|~wise(X)))))&
(((creative(alice)|calm(alice)))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((rich(X)|~generous(X))=>rich(X)))&
(((~patient(mary)<~>funny(mary)))=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:((humble(X)<~>~old(X))=>~curious(X)))&
(((~humble(john)&quiet(john)))<=>(brave(mary)))&
((?[X]:((~funny(X)|~happy(X))))=>((strong(alice)<~>~funny(alice))))&
(![X]:((kind(X)&old(X))<=>(rich(X)&brave(X))))&
(((~old(fred)|~funny(fred)))=>((~wise(fred)|patient(fred))))&
(![X]:((~rich(X)&brave(X))=>(curious(X)|~quiet(X))))&
(![X]:(old(X)=>(wise(X)<~>~kind(X))))&
(((~tall(lucy)<~>quiet(lucy)))=>(?[X]:(funny(X))))&
((?[X]:(kind(X)))<=>(old(susan)))&
(brave(paul))&
(?[X]:((~happy(X)|old(X))))&
(patient(paul))&
((~generous(alice)&~patient(alice)))&
(?[X]:((creative(X)<~>~tall(X))))&
(?[X]:((~patient(X)&kind(X))))&
(?[X]:((~rich(X)<~>~creative(X))))&
((old(susan)|~curious(susan))) | ~happy(paul) | [
"p0",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6502414244131385491603950
% SZS output start Proof for 6502414244131385491603950
1. ! [X0] : ((~creative(X0) | ~happy(X0)) => (~patient(X0) & kind(X0))) [input p0]
19. patient(paul) [input p18]
25. ~happy(paul) [input hypothesis]
27. ! [X0] : ((~patient(X0) & kind(X0)) | (creative(X0) & happy(X0))) [ennf transformation 1]
83. ~patient(X0) | happy(X0) [cnf transformation 27]
135. patient(paul) [cnf transformation 19]
145. ~happy(paul) [cnf transformation 25]
150. 2 <=> happy(paul) [avatar definition]
152. ~happy(paul) <- (~2) [avatar component clause 150]
377. ~2 [avatar split clause 145,150]
382. happy(paul) [resolution 83,135]
383. $false <- (~2) [subsumption resolution 382,152]
384. 2 [avatar contradiction clause 383]
385. $false [avatar sat refutation 377,384]
% SZS output end Proof for 6502414244131385491603950
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and strong is either humble or funny.
If lucy is humble or not generous then mary is humble.
Everyone who is not kind is both curious and old.
If mary is quiet or not generous then mary is either humble or not humble and vice versa.
If lucy is brave or not patient then susan is brave or calm and vice versa.
If alice is either creative or not calm then someone is either not generous or brave and vice versa.
Everyone who is creative is both not strong and rich and vice versa.
If someone is not patient or not curious then someone is both not funny and brave and vice versa.
Everyone who is not wise or not kind is not brave.
If mary is happy then someone is calm or not curious.
If john is not old then someone is either not generous or not happy and vice versa.
Everyone who is both humble and not funny is rich or funny.
Everyone who is strong or not funny is both funny and not calm.
Everyone who is both not humble and old is both not creative and patient.
Everyone who is not rich or generous is both not old and not patient.
Everyone who is both not creative and old is both wise and not calm.
Someone is either not old or not funny.
Lucy is not old or wise.
Paul is old.
Lucy is either not rich or humble.
Susan is strong or quiet.
Someone is both calm and brave. | Mary is not creative. | contradiction | (![X]:((~generous(X)&strong(X))=>(humble(X)<~>funny(X))))&
(((humble(lucy)|~generous(lucy)))=>(humble(mary)))&
(![X]:(~kind(X)=>(curious(X)&old(X))))&
(((quiet(mary)|~generous(mary)))<=>((humble(mary)<~>~humble(mary))))&
(((brave(lucy)|~patient(lucy)))<=>((brave(susan)|calm(susan))))&
(((creative(alice)<~>~calm(alice)))<=>(?[X]:((~generous(X)<~>brave(X)))))&
(![X]:(creative(X)<=>(~strong(X)&rich(X))))&
((?[X]:((~patient(X)|~curious(X))))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:((~wise(X)|~kind(X))=>~brave(X)))&
((happy(mary))=>(?[X]:((calm(X)|~curious(X)))))&
((~old(john))<=>(?[X]:((~generous(X)<~>~happy(X)))))&
(![X]:((humble(X)&~funny(X))=>(rich(X)|funny(X))))&
(![X]:((strong(X)|~funny(X))=>(funny(X)&~calm(X))))&
(![X]:((~humble(X)&old(X))=>(~creative(X)&patient(X))))&
(![X]:((~rich(X)|generous(X))=>(~old(X)&~patient(X))))&
(![X]:((~creative(X)&old(X))=>(wise(X)&~calm(X))))&
(?[X]:((~old(X)<~>~funny(X))))&
((~old(lucy)|wise(lucy)))&
(old(paul))&
((~rich(lucy)<~>humble(lucy)))&
((strong(susan)|quiet(susan)))&
(?[X]:((calm(X)&brave(X)))) | ~creative(mary) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3254449335374243220421184
% SZS output start Proof for 3254449335374243220421184
1. ! [X0] : ((strong(X0) & ~generous(X0)) => (humble(X0) <~> funny(X0))) [input p0]
2. (~generous(lucy) | humble(lucy)) => humble(mary) [input p1]
7. ! [X0] : (creative(X0) <=> (rich(X0) & ~strong(X0))) [input p6]
8. ? [X0] : (~curious(X0) | ~patient(X0)) <=> ? [X0] : (brave(X0) & ~funny(X0)) [input p7]
13. ! [X0] : ((~funny(X0) | strong(X0)) => (~calm(X0) & funny(X0))) [input p12]
15. ! [X0] : ((generous(X0) | ~rich(X0)) => (~patient(X0) & ~old(X0))) [input p14]
20. ~rich(lucy) <~> humble(lucy) [input p19]
23. ~creative(mary) [input hypothesis]
24. ? [X0] : (~curious(X0) | ~patient(X0)) <=> ? [X1] : (brave(X1) & ~funny(X1)) [rectify 8]
30. ! [X0] : ((humble(X0) <~> funny(X0)) | (~strong(X0) | generous(X0))) [ennf transformation 1]
31. ! [X0] : ((humble(X0) <~> funny(X0)) | ~strong(X0) | generous(X0)) [flattening 30]
32. humble(mary) | (generous(lucy) & ~humble(lucy)) [ennf transformation 2]
36. ! [X0] : ((~calm(X0) & funny(X0)) | (funny(X0) & ~strong(X0))) [ennf transformation 13]
39. ! [X0] : ((~patient(X0) & ~old(X0)) | (~generous(X0) & rich(X0))) [ennf transformation 15]
42. ! [X0] : (((~funny(X0) | ~humble(X0)) & (funny(X0) | humble(X0))) | ~strong(X0) | generous(X0)) [nnf transformation 31]
51. ! [X0] : ((creative(X0) | (~rich(X0) | strong(X0))) & ((rich(X0) & ~strong(X0)) | ~creative(X0))) [nnf transformation 7]
52. ! [X0] : ((creative(X0) | ~rich(X0) | strong(X0)) & ((rich(X0) & ~strong(X0)) | ~creative(X0))) [flattening 51]
53. (? [X0] : (~curious(X0) | ~patient(X0)) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X1] : (brave(X1) & ~funny(X1)) | ! [X0] : (curious(X0) & patient(X0))) [nnf transformation 24]
54. (? [X0] : (~curious(X0) | ~patient(X0)) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X2] : (brave(X2) & ~funny(X2)) | ! [X3] : (curious(X3) & patient(X3))) [rectify 53]
55. ? [X0] : (~curious(X0) | ~patient(X0)) => (~curious(sK1) | ~patient(sK1)) [choice axiom]
56. ? [X2] : (brave(X2) & ~funny(X2)) => (brave(sK2) & ~funny(sK2)) [choice axiom]
57. ((~curious(sK1) | ~patient(sK1)) | ! [X1] : (~brave(X1) | funny(X1))) & ((brave(sK2) & ~funny(sK2)) | ! [X3] : (curious(X3) & patient(X3))) [skolemisation 54,56,55]
67. (~humble(lucy) | rich(lucy)) & (humble(lucy) | ~rich(lucy)) [nnf transformation 20]
71. ~funny(X0) | ~humble(X0) | ~strong(X0) | generous(X0) [cnf transformation 42]
72. humble(mary) | ~humble(lucy) [cnf transformation 32]
94. ~rich(X0) | creative(X0) | strong(X0) [cnf transformation 52]
95. ~funny(sK2) | patient(X3) [cnf transformation 57]
107. funny(X0) | funny(X0) [cnf transformation 36]
114. ~patient(X0) | rich(X0) [cnf transformation 39]
115. ~patient(X0) | ~generous(X0) [cnf transformation 39]
120. humble(lucy) | ~rich(lucy) [cnf transformation 67]
125. ~creative(mary) [cnf transformation 23]
126. funny(X0) [duplicate literal removal 107]
135. 2 <=> humble(mary) [avatar definition]
137. humble(mary) <- (2) [avatar component clause 135]
140. 3 <=> humble(lucy) [avatar definition]
143. ~3 | 2 [avatar split clause 72,135,140]
225. 21 <=> ! [X3] : patient(X3) [avatar definition]
226. patient(X3) <- (21) [avatar component clause 225]
229. 22 <=> funny(sK2) [avatar definition]
231. ~funny(sK2) <- (~22) [avatar component clause 229]
233. 21 | ~22 [avatar split clause 95,229,225]
271. 31 <=> rich(lucy) [avatar definition]
272. ~rich(lucy) <- (~31) [avatar component clause 271]
275. ~31 | 3 [avatar split clause 120,140,271]
285. $false <- (~22) [subsumption resolution 231,126]
286. 22 [avatar contradiction clause 285]
302. rich(X0) <- (21) [resolution 114,226]
303. ~generous(X0) <- (21) [resolution 115,226]
304. $false <- (21, ~31) [resolution 302,272]
305. ~21 | 31 [avatar contradiction clause 304]
308. creative(X0) | strong(X0) <- (21) [resolution 94,302]
333. strong(mary) <- (21) [resolution 308,125]
354. ~humble(X0) | ~strong(X0) | generous(X0) [resolution 71,126]
355. ~humble(X0) | ~strong(X0) <- (21) [subsumption resolution 354,303]
356. ~strong(mary) <- (2, 21) [resolution 355,137]
358. $false <- (2, 21) [subsumption resolution 356,333]
359. ~2 | ~21 [avatar contradiction clause 358]
360. $false [avatar sat refutation 143,233,275,286,305,359]
% SZS output end Proof for 3254449335374243220421184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either curious or kind and vice versa.
Everyone who is both not funny and rich is both not calm and humble.
Everyone who is rich is funny or not curious.
If someone is both brave and patient then susan is happy and vice versa.
Everyone who is both quiet and not humble is brave or curious.
Everyone who is both not curious and not tall is either not tall or not happy and vice versa.
If someone is patient or kind then fred is either not quiet or not kind and vice versa.
Everyone who is not generous or not wise is humble or brave.
If paul is brave or wise then paul is not generous or not curious and vice versa.
If someone is creative then susan is tall.
Everyone who is both not strong and funny is either not humble or not calm and vice versa.
Everyone who is not rich or not happy is not old.
Everyone who is both not strong and not humble is not generous and vice versa.
Everyone who is not strong or patient is kind or not quiet.
If john is funny or not tall then someone is either brave or not wise and vice versa.
Everyone who is either not humble or rich is both not kind and not wise and vice versa.
Susan is both not strong and kind.
Susan is rich.
Someone is either rich or not strong.
Someone is both quiet and not kind.
John is humble or not tall.
Paul is both not rich and humble.
Someone is either rich or not curious. | Fred is tall. | neutral | (![X]:(~creative(X)<=>(curious(X)<~>kind(X))))&
(![X]:((~funny(X)&rich(X))=>(~calm(X)&humble(X))))&
(![X]:(rich(X)=>(funny(X)|~curious(X))))&
((?[X]:((brave(X)&patient(X))))<=>(happy(susan)))&
(![X]:((quiet(X)&~humble(X))=>(brave(X)|curious(X))))&
(![X]:((~curious(X)&~tall(X))<=>(~tall(X)<~>~happy(X))))&
((?[X]:((patient(X)|kind(X))))<=>((~quiet(fred)<~>~kind(fred))))&
(![X]:((~generous(X)|~wise(X))=>(humble(X)|brave(X))))&
(((brave(paul)|wise(paul)))<=>((~generous(paul)|~curious(paul))))&
((?[X]:(creative(X)))=>(tall(susan)))&
(![X]:((~strong(X)&funny(X))<=>(~humble(X)<~>~calm(X))))&
(![X]:((~rich(X)|~happy(X))=>~old(X)))&
(![X]:((~strong(X)&~humble(X))<=>~generous(X)))&
(![X]:((~strong(X)|patient(X))=>(kind(X)|~quiet(X))))&
(((funny(john)|~tall(john)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(![X]:((~humble(X)<~>rich(X))<=>(~kind(X)&~wise(X))))&
((~strong(susan)&kind(susan)))&
(rich(susan))&
(?[X]:((rich(X)<~>~strong(X))))&
(?[X]:((quiet(X)&~kind(X))))&
((humble(john)|~tall(john)))&
((~rich(paul)&humble(paul)))&
(?[X]:((rich(X)<~>~curious(X)))) | tall(fred) | [] | null | 0 |
If someone is not happy then someone is tall. Everyone who is both kind and not generous is either not brave or not generous and vice versa. Everyone who is generous is not brave and vice versa. If lucy is generous then john is creative. If fred is generous then someone is both creative and not strong. Everyone who is both not happy and tall is both brave and strong. If someone is not humble or not old then john is either not quiet or not old and vice versa. Everyone who is not kind is not strong or patient and vice versa. If paul is kind or not curious then someone is either curious or not rich. Everyone who is both calm and not funny is either creative or not wise. If someone is either not brave or not patient then someone is calm or happy. Everyone who is either not wise or not patient is humble or patient. Everyone who is patient or not strong is not curious and vice versa. If someone is either calm or not happy then someone is not tall. If someone is either calm or kind then lucy is both humble and not rich. John is happy or kind. Someone is not calm. Alice is strong or tall. Alice is old or not old. Paul is creative or not humble. Susan is not generous or curious. | John is not strong. | contradiction | ((?[X]:(~happy(X)))=>(?[X]:(tall(X))))&
(![X]:((kind(X)&~generous(X))<=>(~brave(X)<~>~generous(X))))&
(![X]:(generous(X)<=>~brave(X)))&
((generous(lucy))=>(creative(john)))&
((generous(fred))=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((~happy(X)&tall(X))=>(brave(X)&strong(X))))&
((?[X]:((~humble(X)|~old(X))))<=>((~quiet(john)<~>~old(john))))&
(![X]:(~kind(X)<=>(~strong(X)|patient(X))))&
(((kind(paul)|~curious(paul)))=>(?[X]:((curious(X)<~>~rich(X)))))&
(![X]:((calm(X)&~funny(X))=>(creative(X)<~>~wise(X))))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((calm(X)|happy(X)))))&
(![X]:((~wise(X)<~>~patient(X))=>(humble(X)|patient(X))))&
(![X]:((patient(X)|~strong(X))<=>~curious(X)))&
((?[X]:((calm(X)<~>~happy(X))))=>(?[X]:(~tall(X))))&
((?[X]:((calm(X)<~>kind(X))))=>((humble(lucy)&~rich(lucy))))&
((happy(john)|kind(john)))&
(?[X]:(~calm(X)))&
((strong(alice)|tall(alice)))&
((old(alice)|~old(alice)))&
((creative(paul)|~humble(paul)))&
((~generous(susan)|curious(susan))) | ~strong(john) | [
"p1",
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2117546397980434225611946
% SZS output start Proof for 2117546397980434225611946
2. ! [X0] : ((~generous(X0) & kind(X0)) <=> (~brave(X0) <~> ~generous(X0))) [input p1]
3. ! [X0] : (generous(X0) <=> ~brave(X0)) [input p2]
8. ! [X0] : (~kind(X0) <=> (patient(X0) | ~strong(X0))) [input p7]
22. ~strong(john) [input hypothesis]
43. ! [X0] : (((~generous(X0) & kind(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (generous(X0) | ~kind(X0)))) [nnf transformation 2]
44. ! [X0] : (((~generous(X0) & kind(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0)))) & (((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | generous(X0) | ~kind(X0))) [flattening 43]
45. ! [X0] : ((generous(X0) | brave(X0)) & (~brave(X0) | ~generous(X0))) [nnf transformation 3]
52. ! [X0] : ((~kind(X0) | (~patient(X0) & strong(X0))) & ((patient(X0) | ~strong(X0)) | kind(X0))) [nnf transformation 8]
53. ! [X0] : ((~kind(X0) | (~patient(X0) & strong(X0))) & (patient(X0) | ~strong(X0) | kind(X0))) [flattening 52]
75. ~brave(X0) | kind(X0) | generous(X0) [cnf transformation 44]
76. ~generous(X0) | ~generous(X0) | brave(X0) [cnf transformation 44]
78. ~brave(X0) | ~generous(X0) [cnf transformation 45]
79. generous(X0) | brave(X0) [cnf transformation 45]
90. ~kind(X0) | strong(X0) [cnf transformation 53]
114. ~strong(john) [cnf transformation 22]
117. ~generous(X0) | brave(X0) [duplicate literal removal 76]
127. brave(X0) [subsumption resolution 79,117]
128. ~generous(X0) [subsumption resolution 78,127]
239. kind(X0) | generous(X0) [resolution 75,127]
243. kind(X0) [subsumption resolution 239,128]
248. strong(X2) [resolution 243,90]
255. $false [resolution 248,114]
% SZS output end Proof for 2117546397980434225611946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not patient or wise then someone is either curious or not kind. If someone is both creative and not funny then mary is not old and vice versa. Everyone who is not old is kind. Everyone who is not quiet is both wise and not happy and vice versa. Everyone who is not calm or not old is both quiet and not curious and vice versa. If someone is both humble and calm then mary is kind or not patient and vice versa. Everyone who is wise or strong is both not strong and humble. Everyone who is both not humble and not calm is patient or rich and vice versa. Everyone who is both not humble and generous is not patient and vice versa. If someone is not creative then susan is both not brave and happy and vice versa. Everyone who is both creative and not quiet is either not old or not tall and vice versa. Everyone who is either not creative or not wise is either patient or tall and vice versa. If alice is both funny and not kind then alice is not quiet or not strong and vice versa. If someone is both not tall and tall then someone is calm. Everyone who is not brave is both creative and not tall and vice versa. John is not humble. John is not kind or not tall. Someone is either funny or not patient. Someone is strong or not rich. Someone is curious or not funny. Someone is not creative or not humble. Mary is either not wise or not funny. | Susan is not humble. | entailment | (((~patient(john)<~>wise(john)))=>(?[X]:((curious(X)<~>~kind(X)))))&
((?[X]:((creative(X)&~funny(X))))<=>(~old(mary)))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~quiet(X)<=>(wise(X)&~happy(X))))&
(![X]:((~calm(X)|~old(X))<=>(quiet(X)&~curious(X))))&
((?[X]:((humble(X)&calm(X))))<=>((kind(mary)|~patient(mary))))&
(![X]:((wise(X)|strong(X))=>(~strong(X)&humble(X))))&
(![X]:((~humble(X)&~calm(X))<=>(patient(X)|rich(X))))&
(![X]:((~humble(X)&generous(X))<=>~patient(X)))&
((?[X]:(~creative(X)))<=>((~brave(susan)&happy(susan))))&
(![X]:((creative(X)&~quiet(X))<=>(~old(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(((funny(alice)&~kind(alice)))<=>((~quiet(alice)|~strong(alice))))&
((?[X]:((~tall(X)&tall(X))))=>(?[X]:(calm(X))))&
(![X]:(~brave(X)<=>(creative(X)&~tall(X))))&
(~humble(john))&
((~kind(john)|~tall(john)))&
(?[X]:((funny(X)<~>~patient(X))))&
(?[X]:((strong(X)|~rich(X))))&
(?[X]:((curious(X)|~funny(X))))&
(?[X]:((~creative(X)|~humble(X))))&
((~wise(mary)<~>~funny(mary))) | ~humble(susan) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1350384883255138816780377
% SZS output start Proof for 1350384883255138816780377
8. ! [X0] : ((~calm(X0) & ~humble(X0)) <=> (rich(X0) | patient(X0))) [input p7]
9. ! [X0] : ((generous(X0) & ~humble(X0)) <=> ~patient(X0)) [input p8]
23. humble(susan) [input hypothesis]
45. ! [X0] : (((~calm(X0) & ~humble(X0)) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | (calm(X0) | humble(X0)))) [nnf transformation 8]
46. ! [X0] : (((~calm(X0) & ~humble(X0)) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | calm(X0) | humble(X0))) [flattening 45]
47. ! [X0] : (((generous(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | (~generous(X0) | humble(X0)))) [nnf transformation 9]
48. ! [X0] : (((generous(X0) & ~humble(X0)) | patient(X0)) & (~patient(X0) | ~generous(X0) | humble(X0))) [flattening 47]
100. ~humble(X0) | ~patient(X0) [cnf transformation 46]
105. ~humble(X0) | patient(X0) [cnf transformation 48]
142. humble(susan) [cnf transformation 23]
206. ~humble(X0) [subsumption resolution 105,100]
269. $false [subsumption resolution 142,206]
% SZS output end Proof for 1350384883255138816780377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not curious or not tall then john is both not tall and curious and vice versa. Everyone who is curious or not creative is either not brave or humble and vice versa. Everyone who is patient is both tall and not quiet. Everyone who is both creative and not tall is either not quiet or brave. If paul is wise then someone is not calm and vice versa. Everyone who is both patient and humble is either not generous or curious and vice versa. Everyone who is generous is tall. If john is both not curious and not rich then someone is not generous or kind and vice versa. Everyone who is both calm and not strong is not quiet. If fred is not generous then someone is both not rich and strong. If fred is both not rich and not strong then someone is either kind or rich and vice versa. Everyone who is both not humble and curious is not old or not funny. Everyone who is not quiet is either funny or kind and vice versa. Everyone who is both not humble and curious is either kind or not funny. Everyone who is old or not brave is either generous or not tall. Mary is not humble. Paul is either not quiet or curious. Someone is funny or not generous. Someone is both not humble and generous. Susan is not old. Someone is both happy and generous. Someone is either calm or happy. Someone is creative or old. | Paul is kind. | contradiction | (((~curious(john)<~>~tall(john)))<=>((~tall(john)&curious(john))))&
(![X]:((curious(X)|~creative(X))<=>(~brave(X)<~>humble(X))))&
(![X]:(patient(X)=>(tall(X)&~quiet(X))))&
(![X]:((creative(X)&~tall(X))=>(~quiet(X)<~>brave(X))))&
((wise(paul))<=>(?[X]:(~calm(X))))&
(![X]:((patient(X)&humble(X))<=>(~generous(X)<~>curious(X))))&
(![X]:(generous(X)=>tall(X)))&
(((~curious(john)&~rich(john)))<=>(?[X]:((~generous(X)|kind(X)))))&
(![X]:((calm(X)&~strong(X))=>~quiet(X)))&
((~generous(fred))=>(?[X]:((~rich(X)&strong(X)))))&
(((~rich(fred)&~strong(fred)))<=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:((~humble(X)&curious(X))=>(~old(X)|~funny(X))))&
(![X]:(~quiet(X)<=>(funny(X)<~>kind(X))))&
(![X]:((~humble(X)&curious(X))=>(kind(X)<~>~funny(X))))&
(![X]:((old(X)|~brave(X))=>(generous(X)<~>~tall(X))))&
(~humble(mary))&
((~quiet(paul)<~>curious(paul)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:((~humble(X)&generous(X))))&
(~old(susan))&
(?[X]:((happy(X)&generous(X))))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:((creative(X)|old(X)))) | kind(paul) | [
"p0",
"p2",
"p5",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 2579059034060531263740814
% SZS output start Proof for 2579059034060531263740814
1. (~curious(john) <~> ~tall(john)) <=> (curious(john) & ~tall(john)) [input p0]
3. ! [X0] : (patient(X0) => (~quiet(X0) & tall(X0))) [input p2]
6. ! [X0] : ((humble(X0) & patient(X0)) <=> (~generous(X0) <~> curious(X0))) [input p5]
7. ! [X0] : (generous(X0) => tall(X0)) [input p6]
8. (~rich(john) & ~curious(john)) <=> ? [X0] : (kind(X0) | ~generous(X0)) [input p7]
24. kind(paul) [input hypothesis]
25. ! [X0] : ((~quiet(X0) & tall(X0)) | ~patient(X0)) [ennf transformation 3]
28. ! [X0] : (tall(X0) | ~generous(X0)) [ennf transformation 7]
37. (((tall(john) | curious(john)) & (~tall(john) | ~curious(john))) | (~curious(john) | tall(john))) & ((curious(john) & ~tall(john)) | ((~curious(john) | tall(john)) & (~tall(john) | curious(john)))) [nnf transformation 1]
38. (((tall(john) | curious(john)) & (~tall(john) | ~curious(john))) | ~curious(john) | tall(john)) & ((curious(john) & ~tall(john)) | ((~curious(john) | tall(john)) & (~tall(john) | curious(john)))) [flattening 37]
46. ! [X0] : (((humble(X0) & patient(X0)) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | (~humble(X0) | ~patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((humble(X0) & patient(X0)) | ((~generous(X0) | ~curious(X0)) & (curious(X0) | generous(X0)))) & (((~curious(X0) | generous(X0)) & (curious(X0) | ~generous(X0))) | ~humble(X0) | ~patient(X0))) [flattening 46]
48. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & (? [X0] : (kind(X0) | ~generous(X0)) | (rich(john) | curious(john))) [nnf transformation 8]
49. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & (? [X0] : (kind(X0) | ~generous(X0)) | rich(john) | curious(john)) [flattening 48]
50. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & (? [X1] : (kind(X1) | ~generous(X1)) | rich(john) | curious(john)) [rectify 49]
51. ? [X1] : (kind(X1) | ~generous(X1)) => (kind(sK1) | ~generous(sK1)) [choice axiom]
52. ((~rich(john) & ~curious(john)) | ! [X0] : (~kind(X0) & generous(X0))) & ((kind(sK1) | ~generous(sK1)) | rich(john) | curious(john)) [skolemisation 50,51]
75. ~tall(john) | ~tall(john) | curious(john) [cnf transformation 38]
87. ~patient(X0) | tall(X0) [cnf transformation 25]
95. generous(X0) | curious(X0) | patient(X0) [cnf transformation 47]
99. ~generous(X0) | tall(X0) [cnf transformation 28]
102. ~curious(john) | ~kind(X0) [cnf transformation 52]
137. kind(paul) [cnf transformation 24]
138. ~tall(john) | curious(john) [duplicate literal removal 75]
143. 1 <=> tall(john) [avatar definition]
145. ~tall(john) <- (~1) [avatar component clause 143]
147. 2 <=> curious(john) [avatar definition]
148. ~curious(john) <- (~2) [avatar component clause 147]
151. 2 | ~1 [avatar split clause 138,143,147]
166. 6 <=> ! [X0] : ~kind(X0) [avatar definition]
167. ~kind(X0) <- (6) [avatar component clause 166]
177. 6 | ~2 [avatar split clause 102,147,166]
275. curious(X0) | patient(X0) | tall(X0) [resolution 95,99]
294. tall(X0) | curious(X0) [subsumption resolution 275,87]
295. $false <- (6) [resolution 167,137]
296. ~6 [avatar contradiction clause 295]
399. curious(john) <- (~1) [resolution 294,145]
401. $false <- (~1, ~2) [subsumption resolution 399,148]
402. 1 | 2 [avatar contradiction clause 401]
403. $false [avatar sat refutation 151,177,296,402]
% SZS output end Proof for 2579059034060531263740814
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not rich is not creative or not tall.
Everyone who is not humble or not wise is old.
If alice is both funny and not curious then fred is both quiet and wise and vice versa.
Everyone who is not generous is both creative and not humble.
Everyone who is both generous and not old is both calm and kind.
Everyone who is not quiet or not generous is either happy or generous.
If susan is both kind and creative then fred is both happy and not curious and vice versa.
If someone is happy then someone is either happy or not curious.
If lucy is funny or patient then susan is not tall.
If mary is curious then mary is both generous and patient and vice versa.
Everyone who is both kind and happy is either strong or quiet and vice versa.
Everyone who is both curious and not calm is both wise and not kind and vice versa.
If mary is calm or not happy then lucy is either not funny or happy.
If fred is both humble and not kind then someone is not quiet.
Everyone who is not rich is not patient or generous and vice versa.
Everyone who is either calm or not happy is not creative or rich.
Lucy is not rich or not wise.
John is either tall or calm.
Someone is either not quiet or tall.
Someone is not patient.
Mary is both not humble and old.
Lucy is either not kind or strong.
Susan is not strong or not tall.
Lucy is both quiet and not old. | Susan is calm. | neutral | (![X]:((curious(X)&~rich(X))=>(~creative(X)|~tall(X))))&
(![X]:((~humble(X)|~wise(X))=>old(X)))&
(((funny(alice)&~curious(alice)))<=>((quiet(fred)&wise(fred))))&
(![X]:(~generous(X)=>(creative(X)&~humble(X))))&
(![X]:((generous(X)&~old(X))=>(calm(X)&kind(X))))&
(![X]:((~quiet(X)|~generous(X))=>(happy(X)<~>generous(X))))&
(((kind(susan)&creative(susan)))<=>((happy(fred)&~curious(fred))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((funny(lucy)|patient(lucy)))=>(~tall(susan)))&
((curious(mary))<=>((generous(mary)&patient(mary))))&
(![X]:((kind(X)&happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((curious(X)&~calm(X))<=>(wise(X)&~kind(X))))&
(((calm(mary)|~happy(mary)))=>((~funny(lucy)<~>happy(lucy))))&
(((humble(fred)&~kind(fred)))=>(?[X]:(~quiet(X))))&
(![X]:(~rich(X)<=>(~patient(X)|generous(X))))&
(![X]:((calm(X)<~>~happy(X))=>(~creative(X)|rich(X))))&
((~rich(lucy)|~wise(lucy)))&
((tall(john)<~>calm(john)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~patient(X)))&
((~humble(mary)&old(mary)))&
((~kind(lucy)<~>strong(lucy)))&
((~strong(susan)|~tall(susan)))&
((quiet(lucy)&~old(lucy))) | calm(susan) | [] | null | 0 |
If someone is not kind then someone is both generous and not creative.
Everyone who is either not rich or not generous is either brave or old and vice versa.
Everyone who is either not kind or curious is either not funny or creative.
If fred is creative or not generous then someone is patient or not quiet and vice versa.
Everyone who is either creative or strong is either not humble or brave.
Everyone who is not strong is not old and vice versa.
Everyone who is both kind and quiet is curious and vice versa.
Everyone who is funny is either not generous or tall.
If someone is tall then someone is both not rich and not wise and vice versa.
Everyone who is not old is both strong and not happy and vice versa.
Everyone who is calm is not creative or old.
If susan is generous then fred is not strong and vice versa.
If someone is both happy and wise then someone is both calm and tall.
Everyone who is brave is either creative or curious and vice versa.
If someone is not brave then someone is either generous or not curious and vice versa.
Everyone who is not creative or tall is either calm or not happy.
Someone is either tall or funny.
Someone is not patient or not generous.
Someone is not patient.
Someone is strong or calm.
Someone is either kind or creative.
Someone is rich. | Susan is strong. | entailment | ((?[X]:(~kind(X)))=>(?[X]:((generous(X)&~creative(X)))))&
(![X]:((~rich(X)<~>~generous(X))<=>(brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>curious(X))=>(~funny(X)<~>creative(X))))&
(((creative(fred)|~generous(fred)))<=>(?[X]:((patient(X)|~quiet(X)))))&
(![X]:((creative(X)<~>strong(X))=>(~humble(X)<~>brave(X))))&
(![X]:(~strong(X)<=>~old(X)))&
(![X]:((kind(X)&quiet(X))<=>curious(X)))&
(![X]:(funny(X)=>(~generous(X)<~>tall(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:(~old(X)<=>(strong(X)&~happy(X))))&
(![X]:(calm(X)=>(~creative(X)|old(X))))&
((generous(susan))<=>(~strong(fred)))&
((?[X]:((happy(X)&wise(X))))=>(?[X]:((calm(X)&tall(X)))))&
(![X]:(brave(X)<=>(creative(X)<~>curious(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((generous(X)<~>~curious(X)))))&
(![X]:((~creative(X)|tall(X))=>(calm(X)<~>~happy(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~patient(X)|~generous(X))))&
(?[X]:(~patient(X)))&
(?[X]:((strong(X)|calm(X))))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:(rich(X))) | strong(susan) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8929131699168945334516992
% SZS output start Proof for 8929131699168945334516992
6. ! [X0] : (~strong(X0) <=> ~old(X0)) [input p5]
10. ! [X0] : (~old(X0) <=> (~happy(X0) & strong(X0))) [input p9]
23. ~strong(susan) [input hypothesis]
47. ! [X0] : ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0))) [nnf transformation 6]
56. ! [X0] : ((~old(X0) | (happy(X0) | ~strong(X0))) & ((~happy(X0) & strong(X0)) | old(X0))) [nnf transformation 10]
57. ! [X0] : ((~old(X0) | happy(X0) | ~strong(X0)) & ((~happy(X0) & strong(X0)) | old(X0))) [flattening 56]
105. ~old(X0) | strong(X0) [cnf transformation 47]
106. ~strong(X0) | old(X0) [cnf transformation 47]
115. strong(X0) | old(X0) [cnf transformation 57]
143. ~strong(susan) [cnf transformation 23]
205. old(X0) [subsumption resolution 115,106]
292. strong(X0) [resolution 105,205]
293. $false [resolution 292,143]
% SZS output end Proof for 8929131699168945334516992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Mary is wise. | 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))) | wise(mary) | [] | null | 0 |
If someone is either not strong or not old then fred is generous.
Everyone who is not generous or not old is creative or not rich and vice versa.
Everyone who is both kind and funny is both humble and not curious and vice versa.
Everyone who is either not wise or generous is not quiet or not rich.
If susan is both creative and quiet then susan is quiet or not happy.
If paul is either not creative or not old then john is both wise and not creative.
Everyone who is either not strong or funny is patient.
If someone is not creative then susan is either not generous or not tall.
Everyone who is both creative and generous is quiet.
Everyone who is not quiet is rich or not happy.
If someone is both not strong and calm then mary is either quiet or tall and vice versa.
Everyone who is not tall is both not tall and not generous.
Everyone who is both creative and not patient is old and vice versa.
Everyone who is humble or happy is not tall or curious and vice versa.
If alice is not patient then someone is both not old and not patient.
Everyone who is not old or not tall is either not funny or not creative and vice versa.
Paul is both not kind and calm.
John is curious.
Someone is not quiet.
Someone is either not creative or brave.
Someone is either wise or not kind.
John is not calm.
Someone is not strong. | Susan is creative. | neutral | ((?[X]:((~strong(X)<~>~old(X))))=>(generous(fred)))&
(![X]:((~generous(X)|~old(X))<=>(creative(X)|~rich(X))))&
(![X]:((kind(X)&funny(X))<=>(humble(X)&~curious(X))))&
(![X]:((~wise(X)<~>generous(X))=>(~quiet(X)|~rich(X))))&
(((creative(susan)&quiet(susan)))=>((quiet(susan)|~happy(susan))))&
(((~creative(paul)<~>~old(paul)))=>((wise(john)&~creative(john))))&
(![X]:((~strong(X)<~>funny(X))=>patient(X)))&
((?[X]:(~creative(X)))=>((~generous(susan)<~>~tall(susan))))&
(![X]:((creative(X)&generous(X))=>quiet(X)))&
(![X]:(~quiet(X)=>(rich(X)|~happy(X))))&
((?[X]:((~strong(X)&calm(X))))<=>((quiet(mary)<~>tall(mary))))&
(![X]:(~tall(X)=>(~tall(X)&~generous(X))))&
(![X]:((creative(X)&~patient(X))<=>old(X)))&
(![X]:((humble(X)|happy(X))<=>(~tall(X)|curious(X))))&
((~patient(alice))=>(?[X]:((~old(X)&~patient(X)))))&
(![X]:((~old(X)|~tall(X))<=>(~funny(X)<~>~creative(X))))&
((~kind(paul)&calm(paul)))&
(curious(john))&
(?[X]:(~quiet(X)))&
(?[X]:((~creative(X)<~>brave(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(~calm(john))&
(?[X]:(~strong(X))) | creative(susan) | [] | null | 0 |
Everyone who is calm or generous is both not rich and brave and vice versa.
Everyone who is not strong is either not humble or happy.
Everyone who is brave is not rich.
If mary is both not brave and kind then mary is not funny and vice versa.
Everyone who is either not kind or old is either happy or humble and vice versa.
Everyone who is not generous or curious is both creative and calm.
If lucy is either not funny or not generous then john is either wise or old and vice versa.
Everyone who is either creative or funny is both not creative and funny and vice versa.
Everyone who is strong or brave is not brave or quiet.
Everyone who is not tall or funny is either creative or happy.
Everyone who is both creative and happy is calm or not creative.
If someone is both not quiet and not creative then john is both not kind and calm.
If someone is not funny then susan is both not curious and not creative.
If someone is either not curious or generous then someone is not calm or humble.
Everyone who is both not creative and not wise is either old or humble.
Everyone who is brave or not creative is rich or humble.
Someone is not curious or not tall.
Someone is either rich or not calm.
Someone is not rich.
Alice is both not creative and not rich.
Someone is both old and creative.
Susan is either creative or not kind.
Fred is either not generous or not old.
Someone is both not wise and not calm. | Fred is not quiet. | contradiction | (![X]:((calm(X)|generous(X))<=>(~rich(X)&brave(X))))&
(![X]:(~strong(X)=>(~humble(X)<~>happy(X))))&
(![X]:(brave(X)=>~rich(X)))&
(((~brave(mary)&kind(mary)))<=>(~funny(mary)))&
(![X]:((~kind(X)<~>old(X))<=>(happy(X)<~>humble(X))))&
(![X]:((~generous(X)|curious(X))=>(creative(X)&calm(X))))&
(((~funny(lucy)<~>~generous(lucy)))<=>((wise(john)<~>old(john))))&
(![X]:((creative(X)<~>funny(X))<=>(~creative(X)&funny(X))))&
(![X]:((strong(X)|brave(X))=>(~brave(X)|quiet(X))))&
(![X]:((~tall(X)|funny(X))=>(creative(X)<~>happy(X))))&
(![X]:((creative(X)&happy(X))=>(calm(X)|~creative(X))))&
((?[X]:((~quiet(X)&~creative(X))))=>((~kind(john)&calm(john))))&
((?[X]:(~funny(X)))=>((~curious(susan)&~creative(susan))))&
((?[X]:((~curious(X)<~>generous(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~creative(X)&~wise(X))=>(old(X)<~>humble(X))))&
(![X]:((brave(X)|~creative(X))=>(rich(X)|humble(X))))&
(?[X]:((~curious(X)|~tall(X))))&
(?[X]:((rich(X)<~>~calm(X))))&
(?[X]:(~rich(X)))&
((~creative(alice)&~rich(alice)))&
(?[X]:((old(X)&creative(X))))&
((creative(susan)<~>~kind(susan)))&
((~generous(fred)<~>~old(fred)))&
(?[X]:((~wise(X)&~calm(X)))) | ~quiet(fred) | [
"p0",
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 613308875869804887061705
% SZS output start Proof for 613308875869804887061705
1. ! [X0] : ((generous(X0) | calm(X0)) <=> (brave(X0) & ~rich(X0))) [input p0]
6. ! [X0] : ((curious(X0) | ~generous(X0)) => (calm(X0) & creative(X0))) [input p5]
9. ! [X0] : ((brave(X0) | strong(X0)) => (quiet(X0) | ~brave(X0))) [input p8]
25. ~quiet(fred) [input hypothesis]
29. ! [X0] : ((calm(X0) & creative(X0)) | (~curious(X0) & generous(X0))) [ennf transformation 6]
30. ! [X0] : ((quiet(X0) | ~brave(X0)) | (~brave(X0) & ~strong(X0))) [ennf transformation 9]
31. ! [X0] : (quiet(X0) | ~brave(X0) | (~brave(X0) & ~strong(X0))) [flattening 30]
42. ! [X0] : (((generous(X0) | calm(X0)) | (~brave(X0) | rich(X0))) & ((brave(X0) & ~rich(X0)) | (~generous(X0) & ~calm(X0)))) [nnf transformation 1]
43. ! [X0] : ((generous(X0) | calm(X0) | ~brave(X0) | rich(X0)) & ((brave(X0) & ~rich(X0)) | (~generous(X0) & ~calm(X0)))) [flattening 42]
72. ~calm(X0) | brave(X0) [cnf transformation 43]
73. ~generous(X0) | brave(X0) [cnf transformation 43]
91. generous(X0) | calm(X0) [cnf transformation 29]
108. quiet(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 31]
138. ~quiet(fred) [cnf transformation 25]
140. ~brave(X0) | quiet(X0) [duplicate literal removal 108]
262. calm(X0) | brave(X0) [resolution 91,73]
263. brave(X0) [subsumption resolution 262,72]
270. quiet(X0) [resolution 140,263]
288. $false [resolution 270,138]
% SZS output end Proof for 613308875869804887061705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and happy is either generous or quiet and vice versa. Everyone who is both funny and not generous is both tall and humble and vice versa. If paul is not humble or wise then alice is not patient and vice versa. If mary is either humble or patient then someone is either creative or generous and vice versa. Everyone who is either not tall or tall is both humble and creative. Everyone who is not kind is either brave or not humble. Everyone who is happy or creative is humble. If fred is kind then someone is humble or curious. Everyone who is not rich is not funny or funny. If john is both not quiet and calm then someone is both not patient and calm. Everyone who is either not patient or not kind is not tall or not kind and vice versa. If paul is creative or not old then mary is either not rich or humble. Everyone who is not patient is calm or not old and vice versa. If someone is not humble or not funny then susan is not old and vice versa. Everyone who is either happy or wise is both generous and calm and vice versa. Everyone who is both not rich and strong is either calm or strong and vice versa. Someone is not happy or brave. John is not curious. Someone is happy or not wise. Paul is both not calm and happy. Someone is both not calm and happy. Fred is not rich. Susan is not tall or humble. | Mary is not tall. | entailment | (![X]:((rich(X)&happy(X))<=>(generous(X)<~>quiet(X))))&
(![X]:((funny(X)&~generous(X))<=>(tall(X)&humble(X))))&
(((~humble(paul)|wise(paul)))<=>(~patient(alice)))&
(((humble(mary)<~>patient(mary)))<=>(?[X]:((creative(X)<~>generous(X)))))&
(![X]:((~tall(X)<~>tall(X))=>(humble(X)&creative(X))))&
(![X]:(~kind(X)=>(brave(X)<~>~humble(X))))&
(![X]:((happy(X)|creative(X))=>humble(X)))&
((kind(fred))=>(?[X]:((humble(X)|curious(X)))))&
(![X]:(~rich(X)=>(~funny(X)|funny(X))))&
(((~quiet(john)&calm(john)))=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((~patient(X)<~>~kind(X))<=>(~tall(X)|~kind(X))))&
(((creative(paul)|~old(paul)))=>((~rich(mary)<~>humble(mary))))&
(![X]:(~patient(X)<=>(calm(X)|~old(X))))&
((?[X]:((~humble(X)|~funny(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>wise(X))<=>(generous(X)&calm(X))))&
(![X]:((~rich(X)&strong(X))<=>(calm(X)<~>strong(X))))&
(?[X]:((~happy(X)|brave(X))))&
(~curious(john))&
(?[X]:((happy(X)|~wise(X))))&
((~calm(paul)&happy(paul)))&
(?[X]:((~calm(X)&happy(X))))&
(~rich(fred))&
((~tall(susan)|humble(susan))) | ~tall(mary) | [
"p1",
"p3",
"p4",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4171891388426690921707729
% SZS output start Proof for 4171891388426690921707729
2. ! [X0] : ((~generous(X0) & funny(X0)) <=> (humble(X0) & tall(X0))) [input p1]
4. (humble(mary) <~> patient(mary)) <=> ? [X0] : (creative(X0) <~> generous(X0)) [input p3]
5. ! [X0] : ((~tall(X0) <~> tall(X0)) => (creative(X0) & humble(X0))) [input p4]
11. ! [X0] : ((~patient(X0) <~> ~kind(X0)) <=> (~kind(X0) | ~tall(X0))) [input p10]
24. tall(mary) [input hypothesis]
25. ! [X0] : ((creative(X0) & humble(X0)) | (~tall(X0) <=> tall(X0))) [ennf transformation 5]
36. ! [X0] : (((~generous(X0) & funny(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (generous(X0) | ~funny(X0)))) [nnf transformation 2]
37. ! [X0] : (((~generous(X0) & funny(X0)) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | generous(X0) | ~funny(X0))) [flattening 36]
40. (((~patient(mary) | ~humble(mary)) & (patient(mary) | humble(mary))) | ! [X0] : ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (? [X0] : ((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | ((humble(mary) | ~patient(mary)) & (patient(mary) | ~humble(mary)))) [nnf transformation 4]
41. (((~patient(mary) | ~humble(mary)) & (patient(mary) | humble(mary))) | ! [X0] : ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (? [X1] : ((~generous(X1) | ~creative(X1)) & (generous(X1) | creative(X1))) | ((humble(mary) | ~patient(mary)) & (patient(mary) | ~humble(mary)))) [rectify 40]
42. ? [X1] : ((~generous(X1) | ~creative(X1)) & (generous(X1) | creative(X1))) => ((~generous(sK0) | ~creative(sK0)) & (generous(sK0) | creative(sK0))) [choice axiom]
43. (((~patient(mary) | ~humble(mary)) & (patient(mary) | humble(mary))) | ! [X0] : ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(sK0) | ~creative(sK0)) & (generous(sK0) | creative(sK0))) | ((humble(mary) | ~patient(mary)) & (patient(mary) | ~humble(mary)))) [skolemisation 41,42]
44. ! [X0] : ((creative(X0) & humble(X0)) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0)))) [nnf transformation 25]
50. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [nnf transformation 11]
51. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [flattening 50]
78. ~humble(X0) | ~generous(X0) | ~tall(X0) [cnf transformation 37]
88. ~patient(mary) | ~humble(mary) | generous(X0) | ~creative(X0) [cnf transformation 43]
90. humble(X0) | tall(X0) | tall(X0) [cnf transformation 44]
91. humble(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 44]
92. creative(X0) | tall(X0) | tall(X0) [cnf transformation 44]
93. creative(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 44]
102. ~kind(X0) | ~tall(X0) | ~kind(X0) | patient(X0) [cnf transformation 51]
107. kind(X0) | patient(X0) | kind(X0) [cnf transformation 51]
139. tall(mary) [cnf transformation 24]
142. ~kind(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 102]
143. kind(X0) | patient(X0) [duplicate literal removal 107]
144. humble(X0) | tall(X0) [duplicate literal removal 90]
145. ~tall(X0) | humble(X0) [duplicate literal removal 91]
146. creative(X0) | tall(X0) [duplicate literal removal 92]
147. ~tall(X0) | creative(X0) [duplicate literal removal 93]
167. 5 <=> humble(mary) [avatar definition]
169. ~humble(mary) <- (~5) [avatar component clause 167]
171. 6 <=> patient(mary) [avatar definition]
176. 7 <=> ! [X0] : (generous(X0) | ~creative(X0)) [avatar definition]
177. generous(X0) | ~creative(X0) <- (7) [avatar component clause 176]
178. 7 | ~5 | ~6 [avatar split clause 88,171,167,176]
193. creative(X0) [subsumption resolution 146,147]
194. humble(X0) [subsumption resolution 144,145]
214. ~tall(X0) | patient(X0) [subsumption resolution 142,143]
261. generous(X0) <- (7) [subsumption resolution 177,193]
262. $false <- (~5) [subsumption resolution 169,194]
263. 5 [avatar contradiction clause 262]
272. patient(mary) [resolution 214,139]
282. ~generous(X0) | ~tall(X0) [resolution 78,194]
283. ~tall(X0) <- (7) [subsumption resolution 282,261]
284. $false <- (7) [resolution 283,139]
285. ~7 [avatar contradiction clause 284]
286. 6 [avatar split clause 272,171]
287. $false [avatar sat refutation 178,263,285,286]
% SZS output end Proof for 4171891388426690921707729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and calm is both not kind and not tall.
If someone is either not brave or humble then john is both not tall and patient.
If mary is not wise or quiet then someone is not wise and vice versa.
Everyone who is not happy is both not quiet and old.
Everyone who is both curious and strong is either patient or quiet and vice versa.
Everyone who is wise is both wise and not calm and vice versa.
Everyone who is either happy or humble is either brave or generous and vice versa.
Everyone who is not humble is either not happy or creative.
If someone is old then someone is both not calm and tall.
Everyone who is either strong or funny is either not curious or happy.
Everyone who is not calm is both funny and not funny and vice versa.
Everyone who is both not creative and not strong is both not generous and curious.
If susan is generous then someone is happy or not quiet.
Everyone who is not calm is strong or patient and vice versa.
If someone is either humble or not strong then someone is both strong and happy.
Everyone who is both not strong and not generous is either not generous or strong and vice versa.
Someone is funny or not strong.
Someone is either wise or not funny.
Susan is rich or not brave.
John is not happy or not generous. | Susan is not curious. | neutral | (![X]:((generous(X)&calm(X))=>(~kind(X)&~tall(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>((~tall(john)&patient(john))))&
(((~wise(mary)|quiet(mary)))<=>(?[X]:(~wise(X))))&
(![X]:(~happy(X)=>(~quiet(X)&old(X))))&
(![X]:((curious(X)&strong(X))<=>(patient(X)<~>quiet(X))))&
(![X]:(wise(X)<=>(wise(X)&~calm(X))))&
(![X]:((happy(X)<~>humble(X))<=>(brave(X)<~>generous(X))))&
(![X]:(~humble(X)=>(~happy(X)<~>creative(X))))&
((?[X]:(old(X)))=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((strong(X)<~>funny(X))=>(~curious(X)<~>happy(X))))&
(![X]:(~calm(X)<=>(funny(X)&~funny(X))))&
(![X]:((~creative(X)&~strong(X))=>(~generous(X)&curious(X))))&
((generous(susan))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:(~calm(X)<=>(strong(X)|patient(X))))&
((?[X]:((humble(X)<~>~strong(X))))=>(?[X]:((strong(X)&happy(X)))))&
(![X]:((~strong(X)&~generous(X))<=>(~generous(X)<~>strong(X))))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((wise(X)<~>~funny(X))))&
((rich(susan)|~brave(susan)))&
((~happy(john)|~generous(john))) | ~curious(susan) | [] | null | 0 |
If paul is not generous then lucy is not happy or rich.
Everyone who is not quiet or rich is patient.
Everyone who is both not old and happy is both not wise and patient and vice versa.
If john is either not happy or creative then someone is not brave or not tall.
Everyone who is either not funny or not creative is either not brave or wise and vice versa.
If someone is rich or wise then someone is either not brave or not wise and vice versa.
If john is not curious then someone is wise.
If mary is both humble and kind then someone is quiet and vice versa.
Everyone who is both not quiet and not old is either old or not wise and vice versa.
Everyone who is strong or rich is kind.
Everyone who is rich or not curious is both not wise and calm.
Everyone who is both curious and kind is either not rich or brave and vice versa.
Everyone who is patient is not brave and vice versa.
If mary is kind or humble then someone is either happy or wise.
If lucy is not generous or strong then someone is both creative and curious.
If alice is both not funny and not curious then susan is generous or not quiet.
Someone is not rich.
Someone is strong.
Mary is not humble.
John is either not happy or calm.
Someone is funny.
Lucy is brave or tall.
Paul is either humble or not strong. | Susan is kind. | entailment | ((~generous(paul))=>((~happy(lucy)|rich(lucy))))&
(![X]:((~quiet(X)|rich(X))=>patient(X)))&
(![X]:((~old(X)&happy(X))<=>(~wise(X)&patient(X))))&
(((~happy(john)<~>creative(john)))=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:((~funny(X)<~>~creative(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:((~brave(X)<~>~wise(X)))))&
((~curious(john))=>(?[X]:(wise(X))))&
(((humble(mary)&kind(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((~quiet(X)&~old(X))<=>(old(X)<~>~wise(X))))&
(![X]:((strong(X)|rich(X))=>kind(X)))&
(![X]:((rich(X)|~curious(X))=>(~wise(X)&calm(X))))&
(![X]:((curious(X)&kind(X))<=>(~rich(X)<~>brave(X))))&
(![X]:(patient(X)<=>~brave(X)))&
(((kind(mary)|humble(mary)))=>(?[X]:((happy(X)<~>wise(X)))))&
(((~generous(lucy)|strong(lucy)))=>(?[X]:((creative(X)&curious(X)))))&
(((~funny(alice)&~curious(alice)))=>((generous(susan)|~quiet(susan))))&
(?[X]:(~rich(X)))&
(?[X]:(strong(X)))&
(~humble(mary))&
((~happy(john)<~>calm(john)))&
(?[X]:(funny(X)))&
((brave(lucy)|tall(lucy)))&
((humble(paul)<~>~strong(paul))) | kind(susan) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3875853129939890482718490
% SZS output start Proof for 3875853129939890482718490
2. ! [X0] : ((rich(X0) | ~quiet(X0)) => patient(X0)) [input p1]
6. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X0] : (~brave(X0) <~> ~wise(X0)) [input p5]
8. (kind(mary) & humble(mary)) <=> ? [X0] : quiet(X0) [input p7]
9. ! [X0] : ((~old(X0) & ~quiet(X0)) <=> (old(X0) <~> ~wise(X0))) [input p8]
10. ! [X0] : ((rich(X0) | strong(X0)) => kind(X0)) [input p9]
12. ! [X0] : ((kind(X0) & curious(X0)) <=> (~rich(X0) <~> brave(X0))) [input p11]
13. ! [X0] : (patient(X0) <=> ~brave(X0)) [input p12]
19. ~humble(mary) [input p18]
24. ~kind(susan) [input hypothesis]
25. ? [X0] : (wise(X0) | rich(X0)) <=> ? [X1] : (~brave(X1) <~> ~wise(X1)) [rectify 6]
29. ! [X0] : (patient(X0) | (~rich(X0) & quiet(X0))) [ennf transformation 2]
32. ! [X0] : (kind(X0) | (~rich(X0) & ~strong(X0))) [ennf transformation 10]
42. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X1] : ((wise(X1) | brave(X1)) & (~wise(X1) | ~brave(X1))) | ! [X0] : (~wise(X0) & ~rich(X0))) [nnf transformation 25]
43. (? [X0] : (wise(X0) | rich(X0)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [rectify 42]
44. ? [X0] : (wise(X0) | rich(X0)) => (wise(sK1) | rich(sK1)) [choice axiom]
45. ? [X2] : ((wise(X2) | brave(X2)) & (~wise(X2) | ~brave(X2))) => ((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) [choice axiom]
46. ((wise(sK1) | rich(sK1)) | ! [X1] : ((~brave(X1) | wise(X1)) & (~wise(X1) | brave(X1)))) & (((wise(sK2) | brave(sK2)) & (~wise(sK2) | ~brave(sK2))) | ! [X3] : (~wise(X3) & ~rich(X3))) [skolemisation 43,45,44]
49. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | (~kind(mary) | ~humble(mary))) [nnf transformation 8]
50. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X0] : quiet(X0) | ~kind(mary) | ~humble(mary)) [flattening 49]
51. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (? [X1] : quiet(X1) | ~kind(mary) | ~humble(mary)) [rectify 50]
52. ? [X1] : quiet(X1) => quiet(sK4) [choice axiom]
53. ((kind(mary) & humble(mary)) | ! [X0] : ~quiet(X0)) & (quiet(sK4) | ~kind(mary) | ~humble(mary)) [skolemisation 51,52]
54. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | (old(X0) | quiet(X0)))) [nnf transformation 9]
55. ! [X0] : (((~old(X0) & ~quiet(X0)) | ((old(X0) | wise(X0)) & (~wise(X0) | ~old(X0)))) & (((wise(X0) | ~old(X0)) & (~wise(X0) | old(X0))) | old(X0) | quiet(X0))) [flattening 54]
56. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~kind(X0) | ~curious(X0)))) [nnf transformation 12]
57. ! [X0] : (((kind(X0) & curious(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~kind(X0) | ~curious(X0))) [flattening 56]
58. ! [X0] : ((patient(X0) | brave(X0)) & (~brave(X0) | ~patient(X0))) [nnf transformation 13]
72. patient(X0) | quiet(X0) [cnf transformation 29]
90. wise(sK2) | brave(sK2) | ~rich(X3) [cnf transformation 46]
91. wise(sK2) | brave(sK2) | ~wise(X3) [cnf transformation 46]
93. wise(sK1) | rich(sK1) | ~brave(X1) | wise(X1) [cnf transformation 46]
96. humble(mary) | ~quiet(X0) [cnf transformation 53]
98. ~wise(X0) | old(X0) | old(X0) | quiet(X0) [cnf transformation 55]
102. ~old(X0) | ~wise(X0) | ~old(X0) [cnf transformation 55]
105. ~rich(X0) | kind(X0) [cnf transformation 32]
114. kind(X0) | brave(X0) | rich(X0) [cnf transformation 57]
116. ~brave(X0) | ~patient(X0) [cnf transformation 58]
126. ~humble(mary) [cnf transformation 19]
133. ~kind(susan) [cnf transformation 24]
134. ~wise(X0) | old(X0) | quiet(X0) [duplicate literal removal 98]
135. ~wise(X0) | ~old(X0) [duplicate literal removal 102]
155. 5 <=> ! [X1] : (~brave(X1) | wise(X1)) [avatar definition]
156. ~brave(X1) | wise(X1) <- (5) [avatar component clause 155]
158. 6 <=> rich(sK1) [avatar definition]
160. rich(sK1) <- (6) [avatar component clause 158]
162. 7 <=> wise(sK1) [avatar definition]
164. wise(sK1) <- (7) [avatar component clause 162]
165. 5 | 6 | 7 [avatar split clause 93,162,158,155]
171. 9 <=> ! [X3] : ~wise(X3) [avatar definition]
172. ~wise(X3) <- (9) [avatar component clause 171]
174. 10 <=> brave(sK2) [avatar definition]
176. brave(sK2) <- (10) [avatar component clause 174]
178. 11 <=> wise(sK2) [avatar definition]
180. wise(sK2) <- (11) [avatar component clause 178]
181. 9 | 10 | 11 [avatar split clause 91,178,174,171]
183. 12 <=> ! [X3] : ~rich(X3) [avatar definition]
184. ~rich(X3) <- (12) [avatar component clause 183]
185. 12 | 10 | 11 [avatar split clause 90,178,174,183]
198. 15 <=> ! [X0] : ~quiet(X0) [avatar definition]
199. ~quiet(X0) <- (15) [avatar component clause 198]
206. 17 <=> humble(mary) [avatar definition]
209. 15 | 17 [avatar split clause 96,206,198]
215. ~wise(X0) | quiet(X0) [subsumption resolution 134,135]
216. kind(X0) | brave(X0) [subsumption resolution 114,105]
244. ~17 [avatar split clause 126,206]
275. ~patient(sK2) <- (10) [resolution 116,176]
278. quiet(sK2) <- (10) [resolution 275,72]
279. $false <- (10, 15) [subsumption resolution 278,199]
280. ~10 | ~15 [avatar contradiction clause 279]
289. quiet(sK2) <- (11) [resolution 215,180]
290. $false <- (11, 15) [subsumption resolution 289,199]
291. ~11 | ~15 [avatar contradiction clause 290]
292. $false <- (6, 12) [resolution 184,160]
293. ~6 | ~12 [avatar contradiction clause 292]
294. $false <- (7, 9) [subsumption resolution 164,172]
295. ~7 | ~9 [avatar contradiction clause 294]
296. ~brave(X1) <- (5, 9) [subsumption resolution 156,172]
298. brave(susan) [resolution 216,133]
300. $false <- (5, 9) [subsumption resolution 298,296]
301. ~5 | ~9 [avatar contradiction clause 300]
304. $false [avatar sat refutation 165,181,185,209,244,280,291,293,295,301]
% SZS output end Proof for 3875853129939890482718490
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both brave and happy then susan is kind or not humble. Everyone who is both creative and not generous is generous. Everyone who is both tall and wise is both not creative and generous. Everyone who is funny or not generous is both calm and creative. If someone is generous then lucy is either patient or creative. Everyone who is humble is both brave and not curious. Everyone who is either not creative or quiet is tall and vice versa. Everyone who is not strong or not tall is brave or not tall. If lucy is not tall or brave then fred is either wise or generous and vice versa. If paul is both not creative and creative then someone is not strong or not patient and vice versa. If someone is both not tall and generous then fred is both not happy and old and vice versa. If someone is not kind then someone is creative or happy and vice versa. If paul is either not rich or not tall then someone is both not wise and tall. If someone is both not old and old then someone is brave and vice versa. Everyone who is patient or tall is both tall and strong and vice versa. If someone is both funny and calm then someone is not strong or quiet. Someone is old. Fred is either patient or not rich. Someone is not quiet or funny. Someone is curious or not calm. Susan is either humble or creative. John is not humble or humble. Fred is either not curious or not creative. Paul is not calm or not patient. | Paul is not funny. | entailment | ((?[X]:((brave(X)&happy(X))))=>((kind(susan)|~humble(susan))))&
(![X]:((creative(X)&~generous(X))=>generous(X)))&
(![X]:((tall(X)&wise(X))=>(~creative(X)&generous(X))))&
(![X]:((funny(X)|~generous(X))=>(calm(X)&creative(X))))&
((?[X]:(generous(X)))=>((patient(lucy)<~>creative(lucy))))&
(![X]:(humble(X)=>(brave(X)&~curious(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>tall(X)))&
(![X]:((~strong(X)|~tall(X))=>(brave(X)|~tall(X))))&
(((~tall(lucy)|brave(lucy)))<=>((wise(fred)<~>generous(fred))))&
(((~creative(paul)&creative(paul)))<=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~tall(X)&generous(X))))<=>((~happy(fred)&old(fred))))&
((?[X]:(~kind(X)))<=>(?[X]:((creative(X)|happy(X)))))&
(((~rich(paul)<~>~tall(paul)))=>(?[X]:((~wise(X)&tall(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(brave(X))))&
(![X]:((patient(X)|tall(X))<=>(tall(X)&strong(X))))&
((?[X]:((funny(X)&calm(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(?[X]:(old(X)))&
((patient(fred)<~>~rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((curious(X)|~calm(X))))&
((humble(susan)<~>creative(susan)))&
((~humble(john)|humble(john)))&
((~curious(fred)<~>~creative(fred)))&
((~calm(paul)|~patient(paul))) | ~funny(paul) | [
"p3",
"p9",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7982010980713694436305850
% SZS output start Proof for 7982010980713694436305850
4. ! [X0] : ((~generous(X0) | funny(X0)) => (creative(X0) & calm(X0))) [input p3]
10. (creative(paul) & ~creative(paul)) <=> ? [X0] : (~patient(X0) | ~strong(X0)) [input p9]
24. ~patient(paul) | ~calm(paul) [input p23]
25. funny(paul) [input hypothesis]
35. ! [X0] : ((creative(X0) & calm(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 4]
46. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & (? [X0] : (~patient(X0) | ~strong(X0)) | (~creative(paul) | creative(paul))) [nnf transformation 10]
47. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & (? [X0] : (~patient(X0) | ~strong(X0)) | ~creative(paul) | creative(paul)) [flattening 46]
48. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & (? [X1] : (~patient(X1) | ~strong(X1)) | ~creative(paul) | creative(paul)) [rectify 47]
49. ? [X1] : (~patient(X1) | ~strong(X1)) => (~patient(sK0) | ~strong(sK0)) [choice axiom]
50. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & ((~patient(sK0) | ~strong(sK0)) | ~creative(paul) | creative(paul)) [skolemisation 48,49]
87. ~funny(X0) | calm(X0) [cnf transformation 35]
109. ~creative(paul) | patient(X0) [cnf transformation 50]
111. creative(paul) | patient(X0) [cnf transformation 50]
142. ~patient(paul) | ~calm(paul) [cnf transformation 24]
143. funny(paul) [cnf transformation 25]
189. 9 <=> ! [X0] : patient(X0) [avatar definition]
190. patient(X0) <- (9) [avatar component clause 189]
192. 10 <=> creative(paul) [avatar definition]
195. 9 | 10 [avatar split clause 111,192,189]
200. 9 | ~10 [avatar split clause 109,192,189]
333. 40 <=> calm(paul) [avatar definition]
337. 41 <=> patient(paul) [avatar definition]
339. ~patient(paul) <- (~41) [avatar component clause 337]
340. ~40 | ~41 [avatar split clause 142,337,333]
349. calm(paul) [resolution 87,143]
352. 40 [avatar split clause 349,333]
353. $false <- (9, ~41) [subsumption resolution 339,190]
354. ~9 | 41 [avatar contradiction clause 353]
355. $false [avatar sat refutation 195,200,340,352,354]
% SZS output end Proof for 7982010980713694436305850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is creative or old and vice versa.
If someone is rich or not tall then john is both not curious and kind.
Everyone who is both not rich and patient is not calm and vice versa.
Everyone who is either tall or not kind is both not creative and not happy and vice versa.
Everyone who is either not happy or not wise is either rich or brave.
Everyone who is both not quiet and not rich is both strong and not strong and vice versa.
Everyone who is not old is either brave or curious.
If lucy is quiet then mary is either not curious or happy and vice versa.
Everyone who is both humble and generous is both not humble and not curious and vice versa.
If lucy is either brave or creative then fred is not happy or not strong and vice versa.
Everyone who is not tall or not rich is creative and vice versa.
If someone is funny then someone is both not patient and not wise and vice versa.
Everyone who is both strong and happy is not wise or not rich and vice versa.
If john is either creative or not curious then someone is both not happy and not rich and vice versa.
Everyone who is either creative or not quiet is not patient or curious.
Everyone who is either kind or not wise is not calm or patient and vice versa.
Susan is quiet or strong.
Fred is brave or generous.
Someone is not wise.
Susan is kind or quiet.
Someone is both generous and not quiet.
John is not happy or quiet.
John is both happy and brave.
John is not patient or not creative. | Lucy is not calm. | contradiction | (![X]:(~curious(X)<=>(creative(X)|old(X))))&
((?[X]:((rich(X)|~tall(X))))=>((~curious(john)&kind(john))))&
(![X]:((~rich(X)&patient(X))<=>~calm(X)))&
(![X]:((tall(X)<~>~kind(X))<=>(~creative(X)&~happy(X))))&
(![X]:((~happy(X)<~>~wise(X))=>(rich(X)<~>brave(X))))&
(![X]:((~quiet(X)&~rich(X))<=>(strong(X)&~strong(X))))&
(![X]:(~old(X)=>(brave(X)<~>curious(X))))&
((quiet(lucy))<=>((~curious(mary)<~>happy(mary))))&
(![X]:((humble(X)&generous(X))<=>(~humble(X)&~curious(X))))&
(((brave(lucy)<~>creative(lucy)))<=>((~happy(fred)|~strong(fred))))&
(![X]:((~tall(X)|~rich(X))<=>creative(X)))&
((?[X]:(funny(X)))<=>(?[X]:((~patient(X)&~wise(X)))))&
(![X]:((strong(X)&happy(X))<=>(~wise(X)|~rich(X))))&
(((creative(john)<~>~curious(john)))<=>(?[X]:((~happy(X)&~rich(X)))))&
(![X]:((creative(X)<~>~quiet(X))=>(~patient(X)|curious(X))))&
(![X]:((kind(X)<~>~wise(X))<=>(~calm(X)|patient(X))))&
((quiet(susan)|strong(susan)))&
((brave(fred)|generous(fred)))&
(?[X]:(~wise(X)))&
((kind(susan)|quiet(susan)))&
(?[X]:((generous(X)&~quiet(X))))&
((~happy(john)|quiet(john)))&
((happy(john)&brave(john)))&
((~patient(john)|~creative(john))) | ~calm(lucy) | [
"p0",
"p2",
"p5",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1425292360478232843256757
% SZS output start Proof for 1425292360478232843256757
1. ! [X0] : (~curious(X0) <=> (old(X0) | creative(X0))) [input p0]
3. ! [X0] : ((patient(X0) & ~rich(X0)) <=> ~calm(X0)) [input p2]
6. ! [X0] : ((~rich(X0) & ~quiet(X0)) <=> (~strong(X0) & strong(X0))) [input p5]
11. ! [X0] : ((~rich(X0) | ~tall(X0)) <=> creative(X0)) [input p10]
15. ! [X0] : ((creative(X0) <~> ~quiet(X0)) => (curious(X0) | ~patient(X0))) [input p14]
25. ~calm(lucy) [input hypothesis]
30. ! [X0] : ((curious(X0) | ~patient(X0)) | (creative(X0) <=> ~quiet(X0))) [ennf transformation 15]
31. ! [X0] : (curious(X0) | ~patient(X0) | (creative(X0) <=> ~quiet(X0))) [flattening 30]
32. ! [X0] : ((~curious(X0) | (~old(X0) & ~creative(X0))) & ((old(X0) | creative(X0)) | curious(X0))) [nnf transformation 1]
33. ! [X0] : ((~curious(X0) | (~old(X0) & ~creative(X0))) & (old(X0) | creative(X0) | curious(X0))) [flattening 32]
34. ! [X0] : (((patient(X0) & ~rich(X0)) | calm(X0)) & (~calm(X0) | (~patient(X0) | rich(X0)))) [nnf transformation 3]
35. ! [X0] : (((patient(X0) & ~rich(X0)) | calm(X0)) & (~calm(X0) | ~patient(X0) | rich(X0))) [flattening 34]
39. ! [X0] : (((~rich(X0) & ~quiet(X0)) | (strong(X0) | ~strong(X0))) & ((~strong(X0) & strong(X0)) | (rich(X0) | quiet(X0)))) [nnf transformation 6]
40. ! [X0] : (((~rich(X0) & ~quiet(X0)) | strong(X0) | ~strong(X0)) & ((~strong(X0) & strong(X0)) | rich(X0) | quiet(X0))) [flattening 39]
47. ! [X0] : (((~rich(X0) | ~tall(X0)) | ~creative(X0)) & (creative(X0) | (rich(X0) & tall(X0)))) [nnf transformation 11]
48. ! [X0] : ((~rich(X0) | ~tall(X0) | ~creative(X0)) & (creative(X0) | (rich(X0) & tall(X0)))) [flattening 47]
60. ! [X0] : (curious(X0) | ~patient(X0) | ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0)))) [nnf transformation 31]
68. ~creative(X0) | ~curious(X0) [cnf transformation 33]
75. ~rich(X0) | calm(X0) [cnf transformation 35]
76. calm(X0) | patient(X0) [cnf transformation 35]
87. strong(X0) | rich(X0) | quiet(X0) [cnf transformation 40]
88. ~strong(X0) | rich(X0) | quiet(X0) [cnf transformation 40]
108. rich(X0) | creative(X0) [cnf transformation 48]
124. curious(X0) | ~patient(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 60]
142. ~calm(lucy) [cnf transformation 25]
163. quiet(X0) | rich(X0) [subsumption resolution 87,88]
174. 7 <=> quiet(lucy) [avatar definition]
175. ~quiet(lucy) <- (~7) [avatar component clause 174]
176. quiet(lucy) <- (7) [avatar component clause 174]
190. 10 <=> creative(lucy) [avatar definition]
238. ~quiet(X0) | ~patient(X0) | ~creative(X0) [subsumption resolution 124,68]
279. patient(lucy) [resolution 76,142]
295. rich(lucy) <- (~7) [resolution 163,175]
308. calm(lucy) <- (~7) [resolution 295,75]
309. $false <- (~7) [subsumption resolution 308,142]
310. 7 [avatar contradiction clause 309]
441. ~patient(lucy) | ~creative(lucy) <- (7) [resolution 238,176]
506. 45 <=> rich(lucy) [avatar definition]
507. rich(lucy) <- (45) [avatar component clause 506]
508. ~rich(lucy) <- (~45) [avatar component clause 506]
582. creative(lucy) <- (~45) [resolution 508,108]
585. 10 | 45 [avatar split clause 582,506,190]
586. ~creative(lucy) <- (7) [subsumption resolution 441,279]
587. ~10 | ~7 [avatar split clause 586,174,190]
593. calm(lucy) <- (45) [resolution 507,75]
594. $false <- (45) [subsumption resolution 593,142]
595. ~45 [avatar contradiction clause 594]
596. $false [avatar sat refutation 310,585,587,595]
% SZS output end Proof for 1425292360478232843256757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not quiet is both funny and not funny. If fred is either not creative or not calm then fred is either patient or happy and vice versa. Everyone who is not rich or happy is both funny and not kind. Everyone who is both calm and kind is both kind and not happy and vice versa. Everyone who is both not old and not creative is not patient or not strong and vice versa. Everyone who is either not generous or kind is both creative and not generous and vice versa. Everyone who is not calm or wise is calm and vice versa. Everyone who is patient is rich and vice versa. Everyone who is happy or not happy is funny or quiet. If someone is either strong or not calm then alice is either not kind or rich. If mary is either not patient or wise then someone is either not wise or humble. Everyone who is brave or not wise is both brave and creative. Everyone who is not humble or kind is not old and vice versa. If someone is both humble and not old then mary is humble or curious and vice versa. Everyone who is not calm or brave is not strong or brave and vice versa. If someone is both not brave and quiet then lucy is not kind. Someone is not creative or humble. Lucy is either quiet or tall. Someone is both generous and not old. Someone is both not rich and not kind. Someone is quiet. Someone is either not happy or strong. Someone is rich. | Fred is not funny. | contradiction | (![X]:((humble(X)|~quiet(X))=>(funny(X)&~funny(X))))&
(((~creative(fred)<~>~calm(fred)))<=>((patient(fred)<~>happy(fred))))&
(![X]:((~rich(X)|happy(X))=>(funny(X)&~kind(X))))&
(![X]:((calm(X)&kind(X))<=>(kind(X)&~happy(X))))&
(![X]:((~old(X)&~creative(X))<=>(~patient(X)|~strong(X))))&
(![X]:((~generous(X)<~>kind(X))<=>(creative(X)&~generous(X))))&
(![X]:((~calm(X)|wise(X))<=>calm(X)))&
(![X]:(patient(X)<=>rich(X)))&
(![X]:((happy(X)|~happy(X))=>(funny(X)|quiet(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~kind(alice)<~>rich(alice))))&
(((~patient(mary)<~>wise(mary)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((brave(X)|~wise(X))=>(brave(X)&creative(X))))&
(![X]:((~humble(X)|kind(X))<=>~old(X)))&
((?[X]:((humble(X)&~old(X))))<=>((humble(mary)|curious(mary))))&
(![X]:((~calm(X)|brave(X))<=>(~strong(X)|brave(X))))&
((?[X]:((~brave(X)&quiet(X))))=>(~kind(lucy)))&
(?[X]:((~creative(X)|humble(X))))&
((quiet(lucy)<~>tall(lucy)))&
(?[X]:((generous(X)&~old(X))))&
(?[X]:((~rich(X)&~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~happy(X)<~>strong(X))))&
(?[X]:(rich(X))) | ~funny(fred) | [
"p0",
"p1",
"p2",
"p4",
"p6",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5947735874430856907296556
% SZS output start Proof for 5947735874430856907296556
1. ! [X0] : ((~quiet(X0) | humble(X0)) => (~funny(X0) & funny(X0))) [input p0]
2. (~creative(fred) <~> ~calm(fred)) <=> (patient(fred) <~> happy(fred)) [input p1]
3. ! [X0] : ((happy(X0) | ~rich(X0)) => (~kind(X0) & funny(X0))) [input p2]
5. ! [X0] : ((~creative(X0) & ~old(X0)) <=> (~strong(X0) | ~patient(X0))) [input p4]
7. ! [X0] : ((wise(X0) | ~calm(X0)) <=> calm(X0)) [input p6]
12. ! [X0] : ((~wise(X0) | brave(X0)) => (creative(X0) & brave(X0))) [input p11]
13. ! [X0] : ((kind(X0) | ~humble(X0)) <=> ~old(X0)) [input p12]
15. ! [X0] : ((brave(X0) | ~calm(X0)) <=> (brave(X0) | ~strong(X0))) [input p14]
24. ~funny(fred) [input hypothesis]
25. ! [X0] : ((~funny(X0) & funny(X0)) | (quiet(X0) & ~humble(X0))) [ennf transformation 1]
26. ! [X0] : ((~kind(X0) & funny(X0)) | (~happy(X0) & rich(X0))) [ennf transformation 3]
31. ! [X0] : ((creative(X0) & brave(X0)) | (wise(X0) & ~brave(X0))) [ennf transformation 12]
33. (((calm(fred) | creative(fred)) & (~calm(fred) | ~creative(fred))) | ((patient(fred) | ~happy(fred)) & (happy(fred) | ~patient(fred)))) & (((~happy(fred) | ~patient(fred)) & (happy(fred) | patient(fred))) | ((~creative(fred) | calm(fred)) & (~calm(fred) | creative(fred)))) [nnf transformation 2]
36. ! [X0] : (((~creative(X0) & ~old(X0)) | (strong(X0) & patient(X0))) & ((~strong(X0) | ~patient(X0)) | (creative(X0) | old(X0)))) [nnf transformation 5]
37. ! [X0] : (((~creative(X0) & ~old(X0)) | (strong(X0) & patient(X0))) & (~strong(X0) | ~patient(X0) | creative(X0) | old(X0))) [flattening 36]
40. ! [X0] : (((wise(X0) | ~calm(X0)) | ~calm(X0)) & (calm(X0) | (~wise(X0) & calm(X0)))) [nnf transformation 7]
41. ! [X0] : ((wise(X0) | ~calm(X0) | ~calm(X0)) & (calm(X0) | (~wise(X0) & calm(X0)))) [flattening 40]
47. ! [X0] : (((kind(X0) | ~humble(X0)) | old(X0)) & (~old(X0) | (~kind(X0) & humble(X0)))) [nnf transformation 13]
48. ! [X0] : ((kind(X0) | ~humble(X0) | old(X0)) & (~old(X0) | (~kind(X0) & humble(X0)))) [flattening 47]
54. ! [X0] : (((brave(X0) | ~calm(X0)) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | (~brave(X0) & calm(X0)))) [nnf transformation 15]
55. ! [X0] : ((brave(X0) | ~calm(X0) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | (~brave(X0) & calm(X0)))) [flattening 54]
70. funny(X0) | ~humble(X0) [cnf transformation 25]
72. ~funny(X0) | ~humble(X0) [cnf transformation 25]
74. happy(fred) | patient(fred) | ~calm(fred) | creative(fred) [cnf transformation 33]
78. ~calm(fred) | ~creative(fred) | happy(fred) | ~patient(fred) [cnf transformation 33]
83. ~happy(X0) | funny(X0) [cnf transformation 26]
90. ~strong(X0) | ~patient(X0) | creative(X0) | old(X0) [cnf transformation 37]
93. ~creative(X0) | patient(X0) [cnf transformation 37]
94. ~creative(X0) | strong(X0) [cnf transformation 37]
101. calm(X0) | calm(X0) [cnf transformation 41]
118. ~brave(X0) | creative(X0) [cnf transformation 31]
120. ~old(X0) | humble(X0) [cnf transformation 48]
130. brave(X0) | ~calm(X0) | strong(X0) [cnf transformation 55]
144. ~funny(fred) [cnf transformation 24]
145. calm(X0) [duplicate literal removal 101]
150. ~humble(X0) [subsumption resolution 70,72]
152. 1 <=> happy(fred) [avatar definition]
153. happy(fred) <- (1) [avatar component clause 152]
156. 2 <=> patient(fred) [avatar definition]
157. ~patient(fred) <- (~2) [avatar component clause 156]
158. patient(fred) <- (2) [avatar component clause 156]
160. 3 <=> creative(fred) [avatar definition]
161. ~creative(fred) <- (~3) [avatar component clause 160]
162. creative(fred) <- (3) [avatar component clause 160]
164. 4 <=> calm(fred) [avatar definition]
165. ~calm(fred) <- (~4) [avatar component clause 164]
170. ~2 | 1 | ~3 | ~4 [avatar split clause 78,164,160,152,156]
174. 3 | ~4 | 2 | 1 [avatar split clause 74,152,156,164,160]
205. ~old(X0) [subsumption resolution 120,150]
207. brave(X0) | strong(X0) [subsumption resolution 130,145]
229. $false <- (~4) [subsumption resolution 165,145]
230. 4 [avatar contradiction clause 229]
237. patient(fred) <- (3) [resolution 93,162]
238. $false <- (~2, 3) [subsumption resolution 237,157]
239. 2 | ~3 [avatar contradiction clause 238]
240. funny(fred) <- (1) [resolution 153,83]
241. $false <- (1) [subsumption resolution 240,144]
242. ~1 [avatar contradiction clause 241]
258. strong(X0) | creative(X0) [resolution 207,118]
259. strong(X0) [subsumption resolution 258,94]
270. ~patient(X0) | creative(X0) | old(X0) [resolution 90,259]
271. ~patient(X0) | creative(X0) [subsumption resolution 270,205]
272. creative(fred) <- (2) [resolution 271,158]
275. $false <- (2, ~3) [subsumption resolution 272,161]
276. ~2 | 3 [avatar contradiction clause 275]
277. $false [avatar sat refutation 170,174,230,239,242,276]
% SZS output end Proof for 5947735874430856907296556
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not quiet or brave then paul is patient or old and vice versa.
Everyone who is either not rich or not humble is not tall and vice versa.
If someone is curious or rich then someone is both not tall and happy.
If alice is old or not rich then fred is both not humble and kind and vice versa.
If someone is not rich then lucy is either calm or not tall and vice versa.
Everyone who is not funny is not humble or not quiet and vice versa.
If someone is not patient then paul is both not brave and old and vice versa.
If someone is either creative or not rich then someone is not tall or not funny.
Everyone who is not patient or curious is either old or not calm and vice versa.
Everyone who is brave or not curious is both not quiet and not rich and vice versa.
Everyone who is both not tall and not quiet is happy and vice versa.
If someone is not rich or curious then someone is not humble and vice versa.
Everyone who is not old or curious is both kind and generous.
If someone is both not humble and funny then someone is both not brave and not patient and vice versa.
If alice is calm then someone is not patient.
Everyone who is happy is patient and vice versa.
Fred is funny or generous.
John is not wise or not brave.
Someone is either not kind or not tall.
Someone is both not strong and not calm.
Paul is either not creative or tall.
Mary is both not generous and not quiet.
John is humble or creative.
Someone is either not old or generous. | Susan is tall. | contradiction | (((~quiet(susan)<~>brave(susan)))<=>((patient(paul)|old(paul))))&
(![X]:((~rich(X)<~>~humble(X))<=>~tall(X)))&
((?[X]:((curious(X)|rich(X))))=>(?[X]:((~tall(X)&happy(X)))))&
(((old(alice)|~rich(alice)))<=>((~humble(fred)&kind(fred))))&
((?[X]:(~rich(X)))<=>((calm(lucy)<~>~tall(lucy))))&
(![X]:(~funny(X)<=>(~humble(X)|~quiet(X))))&
((?[X]:(~patient(X)))<=>((~brave(paul)&old(paul))))&
((?[X]:((creative(X)<~>~rich(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((~patient(X)|curious(X))<=>(old(X)<~>~calm(X))))&
(![X]:((brave(X)|~curious(X))<=>(~quiet(X)&~rich(X))))&
(![X]:((~tall(X)&~quiet(X))<=>happy(X)))&
((?[X]:((~rich(X)|curious(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~old(X)|curious(X))=>(kind(X)&generous(X))))&
((?[X]:((~humble(X)&funny(X))))<=>(?[X]:((~brave(X)&~patient(X)))))&
((calm(alice))=>(?[X]:(~patient(X))))&
(![X]:(happy(X)<=>patient(X)))&
((funny(fred)|generous(fred)))&
((~wise(john)|~brave(john)))&
(?[X]:((~kind(X)<~>~tall(X))))&
(?[X]:((~strong(X)&~calm(X))))&
((~creative(paul)<~>tall(paul)))&
((~generous(mary)&~quiet(mary)))&
((humble(john)|creative(john)))&
(?[X]:((~old(X)<~>generous(X)))) | tall(susan) | [
"p0",
"p5",
"p6",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 65888162983622519755690
% SZS output start Proof for 65888162983622519755690
1. (~quiet(susan) <~> brave(susan)) <=> (old(paul) | patient(paul)) [input p0]
6. ! [X0] : (~funny(X0) <=> (~quiet(X0) | ~humble(X0))) [input p5]
7. ? [X0] : ~patient(X0) <=> (old(paul) & ~brave(paul)) [input p6]
10. ! [X0] : ((~curious(X0) | brave(X0)) <=> (~rich(X0) & ~quiet(X0))) [input p9]
11. ! [X0] : ((~quiet(X0) & ~tall(X0)) <=> happy(X0)) [input p10]
14. ? [X0] : (funny(X0) & ~humble(X0)) <=> ? [X0] : (~patient(X0) & ~brave(X0)) [input p13]
16. ! [X0] : (happy(X0) <=> patient(X0)) [input p15]
25. tall(susan) [input hypothesis]
29. ? [X0] : (funny(X0) & ~humble(X0)) <=> ? [X1] : (~patient(X1) & ~brave(X1)) [rectify 14]
36. (((~brave(susan) | quiet(susan)) & (brave(susan) | ~quiet(susan))) | (~old(paul) & ~patient(paul))) & ((old(paul) | patient(paul)) | ((~quiet(susan) | ~brave(susan)) & (brave(susan) | quiet(susan)))) [nnf transformation 1]
37. (((~brave(susan) | quiet(susan)) & (brave(susan) | ~quiet(susan))) | (~old(paul) & ~patient(paul))) & (old(paul) | patient(paul) | ((~quiet(susan) | ~brave(susan)) & (brave(susan) | quiet(susan)))) [flattening 36]
48. ! [X0] : ((~funny(X0) | (quiet(X0) & humble(X0))) & ((~quiet(X0) | ~humble(X0)) | funny(X0))) [nnf transformation 6]
49. ! [X0] : ((~funny(X0) | (quiet(X0) & humble(X0))) & (~quiet(X0) | ~humble(X0) | funny(X0))) [flattening 48]
50. (? [X0] : ~patient(X0) | (~old(paul) | brave(paul))) & ((old(paul) & ~brave(paul)) | ! [X0] : patient(X0)) [nnf transformation 7]
51. (? [X0] : ~patient(X0) | ~old(paul) | brave(paul)) & ((old(paul) & ~brave(paul)) | ! [X0] : patient(X0)) [flattening 50]
52. (? [X0] : ~patient(X0) | ~old(paul) | brave(paul)) & ((old(paul) & ~brave(paul)) | ! [X1] : patient(X1)) [rectify 51]
53. ? [X0] : ~patient(X0) => ~patient(sK2) [choice axiom]
54. (~patient(sK2) | ~old(paul) | brave(paul)) & ((old(paul) & ~brave(paul)) | ! [X1] : patient(X1)) [skolemisation 52,53]
61. ! [X0] : (((~curious(X0) | brave(X0)) | (rich(X0) | quiet(X0))) & ((~rich(X0) & ~quiet(X0)) | (curious(X0) & ~brave(X0)))) [nnf transformation 10]
62. ! [X0] : ((~curious(X0) | brave(X0) | rich(X0) | quiet(X0)) & ((~rich(X0) & ~quiet(X0)) | (curious(X0) & ~brave(X0)))) [flattening 61]
63. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ~happy(X0)) & (happy(X0) | (quiet(X0) | tall(X0)))) [nnf transformation 11]
64. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ~happy(X0)) & (happy(X0) | quiet(X0) | tall(X0))) [flattening 63]
70. (? [X0] : (funny(X0) & ~humble(X0)) | ! [X1] : (patient(X1) | brave(X1))) & (? [X1] : (~patient(X1) & ~brave(X1)) | ! [X0] : (~funny(X0) | humble(X0))) [nnf transformation 29]
71. (? [X0] : (funny(X0) & ~humble(X0)) | ! [X1] : (patient(X1) | brave(X1))) & (? [X2] : (~patient(X2) & ~brave(X2)) | ! [X3] : (~funny(X3) | humble(X3))) [rectify 70]
72. ? [X0] : (funny(X0) & ~humble(X0)) => (funny(sK6) & ~humble(sK6)) [choice axiom]
73. ? [X2] : (~patient(X2) & ~brave(X2)) => (~patient(sK7) & ~brave(sK7)) [choice axiom]
74. ((funny(sK6) & ~humble(sK6)) | ! [X1] : (patient(X1) | brave(X1))) & ((~patient(sK7) & ~brave(sK7)) | ! [X3] : (~funny(X3) | humble(X3))) [skolemisation 71,73,72]
77. ! [X0] : ((happy(X0) | ~patient(X0)) & (patient(X0) | ~happy(X0))) [nnf transformation 16]
91. ~brave(susan) | quiet(susan) | ~patient(paul) [cnf transformation 37]
92. ~brave(susan) | quiet(susan) | ~old(paul) [cnf transformation 37]
111. ~funny(X0) | humble(X0) [cnf transformation 49]
114. old(paul) | patient(X1) [cnf transformation 54]
124. ~brave(X0) | ~quiet(X0) [cnf transformation 62]
130. ~happy(X0) | ~tall(X0) [cnf transformation 64]
141. ~humble(sK6) | patient(X1) | brave(X1) [cnf transformation 74]
142. funny(sK6) | patient(X1) | brave(X1) [cnf transformation 74]
145. ~patient(X0) | happy(X0) [cnf transformation 77]
157. tall(susan) [cnf transformation 25]
159. 1 <=> old(paul) [avatar definition]
163. 2 <=> quiet(susan) [avatar definition]
165. quiet(susan) <- (2) [avatar component clause 163]
167. 3 <=> brave(susan) [avatar definition]
168. brave(susan) <- (3) [avatar component clause 167]
169. ~brave(susan) <- (~3) [avatar component clause 167]
170. ~1 | 2 | ~3 [avatar split clause 92,167,163,159]
172. 4 <=> patient(paul) [avatar definition]
174. ~patient(paul) <- (~4) [avatar component clause 172]
175. ~4 | 2 | ~3 [avatar split clause 91,167,163,172]
248. 19 <=> ! [X1] : patient(X1) [avatar definition]
249. patient(X1) <- (19) [avatar component clause 248]
250. 19 | 1 [avatar split clause 114,159,248]
275. 25 <=> ! [X1] : (patient(X1) | brave(X1)) [avatar definition]
276. patient(X1) | brave(X1) <- (25) [avatar component clause 275]
278. 26 <=> funny(sK6) [avatar definition]
280. funny(sK6) <- (26) [avatar component clause 278]
281. 25 | 26 [avatar split clause 142,278,275]
283. 27 <=> humble(sK6) [avatar definition]
286. 25 | ~27 [avatar split clause 141,283,275]
336. $false <- (~4, 19) [subsumption resolution 174,249]
337. 4 | ~19 [avatar contradiction clause 336]
343. ~quiet(susan) <- (3) [resolution 124,168]
344. $false <- (2, 3) [subsumption resolution 343,165]
345. ~2 | ~3 [avatar contradiction clause 344]
678. humble(sK6) <- (26) [resolution 280,111]
681. 27 | ~26 [avatar split clause 678,278,283]
700. happy(X1) | brave(X1) <- (25) [resolution 276,145]
705. ~tall(X2) | brave(X2) <- (25) [resolution 700,130]
763. brave(susan) <- (25) [resolution 705,157]
766. $false <- (~3, 25) [subsumption resolution 763,169]
767. 3 | ~25 [avatar contradiction clause 766]
768. $false [avatar sat refutation 170,175,250,281,286,337,345,681,767]
% SZS output end Proof for 65888162983622519755690
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and not strong is not wise and vice versa. Everyone who is either not rich or not quiet is both brave and curious. Everyone who is creative or patient is either not quiet or not brave and vice versa. Everyone who is not generous is not kind or not creative and vice versa. Everyone who is either not patient or not creative is creative and vice versa. Everyone who is both curious and not quiet is wise and vice versa. Everyone who is not rich or creative is both old and rich and vice versa. Everyone who is either patient or strong is not humble and vice versa. Everyone who is not calm is either not kind or not rich and vice versa. If someone is not tall then susan is old or not happy. Everyone who is rich is old. Everyone who is both not brave and patient is not quiet or not patient. Everyone who is either not strong or rich is brave or calm. Everyone who is calm or not brave is not brave or funny and vice versa. If someone is both not tall and not creative then someone is either wise or funny and vice versa. If someone is both creative and not generous then john is both not creative and not tall and vice versa. Someone is either not creative or generous. Someone is both not patient and happy. Lucy is not patient. Someone is both rich and happy. John is not quiet or not brave. Someone is strong. | Susan is creative. | entailment | (![X]:((~quiet(X)&~strong(X))<=>~wise(X)))&
(![X]:((~rich(X)<~>~quiet(X))=>(brave(X)&curious(X))))&
(![X]:((creative(X)|patient(X))<=>(~quiet(X)<~>~brave(X))))&
(![X]:(~generous(X)<=>(~kind(X)|~creative(X))))&
(![X]:((~patient(X)<~>~creative(X))<=>creative(X)))&
(![X]:((curious(X)&~quiet(X))<=>wise(X)))&
(![X]:((~rich(X)|creative(X))<=>(old(X)&rich(X))))&
(![X]:((patient(X)<~>strong(X))<=>~humble(X)))&
(![X]:(~calm(X)<=>(~kind(X)<~>~rich(X))))&
((?[X]:(~tall(X)))=>((old(susan)|~happy(susan))))&
(![X]:(rich(X)=>old(X)))&
(![X]:((~brave(X)&patient(X))=>(~quiet(X)|~patient(X))))&
(![X]:((~strong(X)<~>rich(X))=>(brave(X)|calm(X))))&
(![X]:((calm(X)|~brave(X))<=>(~brave(X)|funny(X))))&
((?[X]:((~tall(X)&~creative(X))))<=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((creative(X)&~generous(X))))<=>((~creative(john)&~tall(john))))&
(?[X]:((~creative(X)<~>generous(X))))&
(?[X]:((~patient(X)&happy(X))))&
(~patient(lucy))&
(?[X]:((rich(X)&happy(X))))&
((~quiet(john)|~brave(john)))&
(?[X]:(strong(X))) | creative(susan) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2394046399989577161347028
% SZS output start Proof for 2394046399989577161347028
7. ! [X0] : ((creative(X0) | ~rich(X0)) <=> (rich(X0) & old(X0))) [input p6]
11. ! [X0] : (rich(X0) => old(X0)) [input p10]
23. ~creative(susan) [input hypothesis]
28. ! [X0] : (old(X0) | ~rich(X0)) [ennf transformation 11]
43. ! [X0] : (((creative(X0) | ~rich(X0)) | (~rich(X0) | ~old(X0))) & ((rich(X0) & old(X0)) | (~creative(X0) & rich(X0)))) [nnf transformation 7]
44. ! [X0] : ((creative(X0) | ~rich(X0) | ~rich(X0) | ~old(X0)) & ((rich(X0) & old(X0)) | (~creative(X0) & rich(X0)))) [flattening 43]
93. rich(X0) | rich(X0) [cnf transformation 44]
95. creative(X0) | ~rich(X0) | ~rich(X0) | ~old(X0) [cnf transformation 44]
101. old(X0) | ~rich(X0) [cnf transformation 28]
128. ~creative(susan) [cnf transformation 23]
130. rich(X0) [duplicate literal removal 93]
131. ~old(X0) | ~rich(X0) | creative(X0) [duplicate literal removal 95]
151. old(X0) [subsumption resolution 101,130]
244. ~rich(X0) | creative(X0) [resolution 131,151]
245. creative(X0) [subsumption resolution 244,130]
253. $false [resolution 245,128]
% SZS output end Proof for 2394046399989577161347028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then mary is not patient.
If susan is not generous or not funny then paul is not brave or not patient.
Everyone who is both not curious and humble is either humble or creative.
If someone is humble or tall then someone is both wise and not kind.
Everyone who is either not quiet or tall is tall or curious.
If someone is creative or quiet then fred is both tall and not rich.
If someone is not patient or not generous then someone is both not kind and calm and vice versa.
Everyone who is either not rich or calm is not quiet or not old and vice versa.
Everyone who is creative or rich is not rich.
Everyone who is either wise or not old is both not old and generous.
Everyone who is either strong or humble is either not humble or strong.
Everyone who is either not quiet or humble is either not tall or not rich.
If susan is both not funny and calm then someone is generous or brave and vice versa.
If someone is either not kind or not creative then fred is brave and vice versa.
Everyone who is not curious or not happy is both not generous and funny and vice versa.
If someone is either quiet or rich then someone is funny.
Paul is tall or patient.
Someone is not humble or not quiet.
Mary is not brave.
Someone is either calm or happy.
Someone is curious.
Someone is kind or rich.
Susan is both funny and not strong.
Lucy is either happy or old. | Susan is funny. | entailment | ((?[X]:(~old(X)))=>(~patient(mary)))&
(((~generous(susan)|~funny(susan)))=>((~brave(paul)|~patient(paul))))&
(![X]:((~curious(X)&humble(X))=>(humble(X)<~>creative(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~quiet(X)<~>tall(X))=>(tall(X)|curious(X))))&
((?[X]:((creative(X)|quiet(X))))=>((tall(fred)&~rich(fred))))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((~kind(X)&calm(X)))))&
(![X]:((~rich(X)<~>calm(X))<=>(~quiet(X)|~old(X))))&
(![X]:((creative(X)|rich(X))=>~rich(X)))&
(![X]:((wise(X)<~>~old(X))=>(~old(X)&generous(X))))&
(![X]:((strong(X)<~>humble(X))=>(~humble(X)<~>strong(X))))&
(![X]:((~quiet(X)<~>humble(X))=>(~tall(X)<~>~rich(X))))&
(((~funny(susan)&calm(susan)))<=>(?[X]:((generous(X)|brave(X)))))&
((?[X]:((~kind(X)<~>~creative(X))))<=>(brave(fred)))&
(![X]:((~curious(X)|~happy(X))<=>(~generous(X)&funny(X))))&
((?[X]:((quiet(X)<~>rich(X))))=>(?[X]:(funny(X))))&
((tall(paul)|patient(paul)))&
(?[X]:((~humble(X)|~quiet(X))))&
(~brave(mary))&
(?[X]:((calm(X)<~>happy(X))))&
(?[X]:(curious(X)))&
(?[X]:((kind(X)|rich(X))))&
((funny(susan)&~strong(susan)))&
((happy(lucy)<~>old(lucy))) | funny(susan) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 2298558065954810613525353
% SZS output start Proof for 2298558065954810613525353
23. ~strong(susan) & funny(susan) [input p22]
25. ~funny(susan) [input hypothesis]
146. funny(susan) [cnf transformation 23]
150. ~funny(susan) [cnf transformation 25]
166. 3 <=> funny(susan) [avatar definition]
327. 3 [avatar split clause 146,166]
338. ~3 [avatar split clause 150,166]
339. $false [avatar sat refutation 327,338]
% SZS output end Proof for 2298558065954810613525353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or not funny is kind. Everyone who is both not happy and quiet is not happy or humble and vice versa. If someone is either humble or not brave then paul is either not happy or funny and vice versa. Everyone who is either not patient or kind is rich. If someone is not calm then fred is both not funny and not curious and vice versa. If someone is strong then someone is patient or not happy and vice versa. If someone is both kind and not humble then alice is both not generous and kind and vice versa. Everyone who is not funny or not wise is either patient or funny and vice versa. If someone is calm then fred is not old or not quiet and vice versa. If john is either patient or not patient then someone is not tall or happy. If someone is either strong or not rich then john is both not wise and curious and vice versa. If someone is funny then paul is both kind and not happy and vice versa. Everyone who is either quiet or rich is either not wise or not quiet and vice versa. Everyone who is rich is not tall. Everyone who is calm is both humble and not patient and vice versa. If someone is calm then someone is funny. Someone is either brave or not humble. Someone is not calm or not patient. Someone is wise or not curious. Someone is both not rich and tall. Someone is either wise or not kind. Someone is both not humble and not strong. Alice is either not generous or generous. Someone is creative or wise. | Paul is tall. | contradiction | (![X]:((~strong(X)|~funny(X))=>kind(X)))&
(![X]:((~happy(X)&quiet(X))<=>(~happy(X)|humble(X))))&
((?[X]:((humble(X)<~>~brave(X))))<=>((~happy(paul)<~>funny(paul))))&
(![X]:((~patient(X)<~>kind(X))=>rich(X)))&
((?[X]:(~calm(X)))<=>((~funny(fred)&~curious(fred))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)|~happy(X)))))&
((?[X]:((kind(X)&~humble(X))))<=>((~generous(alice)&kind(alice))))&
(![X]:((~funny(X)|~wise(X))<=>(patient(X)<~>funny(X))))&
((?[X]:(calm(X)))<=>((~old(fred)|~quiet(fred))))&
(((patient(john)<~>~patient(john)))=>(?[X]:((~tall(X)|happy(X)))))&
((?[X]:((strong(X)<~>~rich(X))))<=>((~wise(john)&curious(john))))&
((?[X]:(funny(X)))<=>((kind(paul)&~happy(paul))))&
(![X]:((quiet(X)<~>rich(X))<=>(~wise(X)<~>~quiet(X))))&
(![X]:(rich(X)=>~tall(X)))&
(![X]:(calm(X)<=>(humble(X)&~patient(X))))&
((?[X]:(calm(X)))=>(?[X]:(funny(X))))&
(?[X]:((brave(X)<~>~humble(X))))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((wise(X)<~>~kind(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~generous(alice)<~>generous(alice)))&
(?[X]:((creative(X)|wise(X)))) | tall(paul) | [
"p0",
"p2",
"p3",
"p7",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4056554079344761592324275
% SZS output start Proof for 4056554079344761592324275
1. ! [X0] : ((~funny(X0) | ~strong(X0)) => kind(X0)) [input p0]
3. ? [X0] : (humble(X0) <~> ~brave(X0)) <=> (~happy(paul) <~> funny(paul)) [input p2]
4. ! [X0] : ((~patient(X0) <~> kind(X0)) => rich(X0)) [input p3]
8. ! [X0] : ((~wise(X0) | ~funny(X0)) <=> (patient(X0) <~> funny(X0))) [input p7]
12. ? [X0] : funny(X0) <=> (~happy(paul) & kind(paul)) [input p11]
14. ! [X0] : (rich(X0) => ~tall(X0)) [input p13]
17. ? [X0] : (brave(X0) <~> ~humble(X0)) [input p16]
25. tall(paul) [input hypothesis]
29. ! [X0] : (kind(X0) | (funny(X0) & strong(X0))) [ennf transformation 1]
30. ! [X0] : (rich(X0) | (~patient(X0) <=> kind(X0))) [ennf transformation 4]
32. ! [X0] : (~tall(X0) | ~rich(X0)) [ennf transformation 14]
36. (? [X0] : ((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ((~happy(paul) | ~funny(paul)) & (funny(paul) | happy(paul)))) & (((~funny(paul) | happy(paul)) & (funny(paul) | ~happy(paul))) | ! [X0] : ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0)))) [nnf transformation 3]
37. (? [X0] : ((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ((~happy(paul) | ~funny(paul)) & (funny(paul) | happy(paul)))) & (((~funny(paul) | happy(paul)) & (funny(paul) | ~happy(paul))) | ! [X1] : ((humble(X1) | brave(X1)) & (~brave(X1) | ~humble(X1)))) [rectify 36]
38. ? [X0] : ((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) => ((brave(sK0) | ~humble(sK0)) & (~brave(sK0) | humble(sK0))) [choice axiom]
39. (((brave(sK0) | ~humble(sK0)) & (~brave(sK0) | humble(sK0))) | ((~happy(paul) | ~funny(paul)) & (funny(paul) | happy(paul)))) & (((~funny(paul) | happy(paul)) & (funny(paul) | ~happy(paul))) | ! [X1] : ((humble(X1) | brave(X1)) & (~brave(X1) | ~humble(X1)))) [skolemisation 37,38]
40. ! [X0] : (rich(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0)))) [nnf transformation 30]
56. ! [X0] : (((~wise(X0) | ~funny(X0)) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) & (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (wise(X0) & funny(X0)))) [nnf transformation 8]
57. ! [X0] : ((~wise(X0) | ~funny(X0) | ((patient(X0) | ~funny(X0)) & (funny(X0) | ~patient(X0)))) & (((~funny(X0) | ~patient(X0)) & (funny(X0) | patient(X0))) | (wise(X0) & funny(X0)))) [flattening 56]
71. (? [X0] : funny(X0) | (happy(paul) | ~kind(paul))) & ((~happy(paul) & kind(paul)) | ! [X0] : ~funny(X0)) [nnf transformation 12]
72. (? [X0] : funny(X0) | happy(paul) | ~kind(paul)) & ((~happy(paul) & kind(paul)) | ! [X0] : ~funny(X0)) [flattening 71]
73. (? [X0] : funny(X0) | happy(paul) | ~kind(paul)) & ((~happy(paul) & kind(paul)) | ! [X1] : ~funny(X1)) [rectify 72]
74. ? [X0] : funny(X0) => funny(sK8) [choice axiom]
75. (funny(sK8) | happy(paul) | ~kind(paul)) & ((~happy(paul) & kind(paul)) | ! [X1] : ~funny(X1)) [skolemisation 73,74]
82. ? [X0] : ((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 17]
83. ? [X0] : ((humble(X0) | ~brave(X0)) & (~humble(X0) | brave(X0))) => ((humble(sK10) | ~brave(sK10)) & (~humble(sK10) | brave(sK10))) [choice axiom]
84. (humble(sK10) | ~brave(sK10)) & (~humble(sK10) | brave(sK10)) [skolemisation 82,83]
98. kind(X0) | funny(X0) [cnf transformation 29]
106. ~funny(paul) | happy(paul) | ~brave(X1) | ~humble(X1) [cnf transformation 39]
107. ~funny(paul) | happy(paul) | humble(X1) | brave(X1) [cnf transformation 39]
113. ~patient(X0) | rich(X0) | ~kind(X0) [cnf transformation 40]
124. funny(X0) | patient(X0) | funny(X0) [cnf transformation 57]
142. ~happy(paul) | ~funny(X1) [cnf transformation 75]
152. ~tall(X0) | ~rich(X0) [cnf transformation 32]
157. ~humble(sK10) | brave(sK10) [cnf transformation 84]
158. humble(sK10) | ~brave(sK10) [cnf transformation 84]
169. tall(paul) [cnf transformation 25]
176. patient(X0) | funny(X0) [duplicate literal removal 124]
179. 1 <=> funny(paul) [avatar definition]
180. funny(paul) <- (1) [avatar component clause 179]
183. 2 <=> happy(paul) [avatar definition]
199. 5 <=> ! [X1] : (humble(X1) | brave(X1)) [avatar definition]
200. brave(X1) | humble(X1) <- (5) [avatar component clause 199]
201. 5 | 2 | ~1 [avatar split clause 107,179,183,199]
203. 6 <=> ! [X1] : (~brave(X1) | ~humble(X1)) [avatar definition]
204. ~brave(X1) | ~humble(X1) <- (6) [avatar component clause 203]
205. 6 | 2 | ~1 [avatar split clause 106,179,183,203]
343. 37 <=> ! [X1] : ~funny(X1) [avatar definition]
344. ~funny(X1) <- (37) [avatar component clause 343]
345. 37 | ~2 [avatar split clause 142,183,343]
355. 39 <=> brave(sK10) [avatar definition]
356. brave(sK10) <- (39) [avatar component clause 355]
357. ~brave(sK10) <- (~39) [avatar component clause 355]
359. 40 <=> humble(sK10) [avatar definition]
360. ~humble(sK10) <- (~40) [avatar component clause 359]
361. humble(sK10) <- (40) [avatar component clause 359]
362. ~39 | 40 [avatar split clause 158,359,355]
363. 39 | ~40 [avatar split clause 157,359,355]
388. ~rich(paul) [resolution 152,169]
412. rich(X0) | ~kind(X0) | funny(X0) [resolution 113,176]
413. rich(X0) | funny(X0) [subsumption resolution 412,98]
445. funny(paul) [resolution 413,388]
449. 1 [avatar split clause 445,179]
451. humble(sK10) <- (5, ~39) [resolution 200,357]
454. $false <- (5, ~39, ~40) [subsumption resolution 451,360]
455. ~5 | 39 | 40 [avatar contradiction clause 454]
458. $false <- (1, 37) [resolution 344,180]
459. ~1 | ~37 [avatar contradiction clause 458]
471. ~humble(sK10) <- (6, 39) [resolution 204,356]
473. $false <- (6, 39, 40) [subsumption resolution 471,361]
474. ~6 | ~39 | ~40 [avatar contradiction clause 473]
475. $false [avatar sat refutation 201,205,345,362,363,449,455,459,474]
% SZS output end Proof for 4056554079344761592324275
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not tall is both patient and humble.
Everyone who is both not rich and not funny is both not generous and happy and vice versa.
Everyone who is both not kind and happy is either tall or not wise.
Everyone who is kind or not brave is both not curious and not quiet and vice versa.
Everyone who is not kind is not old or kind.
If fred is both quiet and not generous then someone is not wise and vice versa.
If someone is either calm or not calm then someone is either not creative or tall.
If alice is both old and generous then fred is rich or wise and vice versa.
Everyone who is both tall and not patient is not quiet.
If mary is both not creative and not strong then someone is creative or not happy.
Everyone who is both not rich and not brave is generous and vice versa.
Everyone who is either quiet or not creative is brave or not patient and vice versa.
Everyone who is humble is calm or not old and vice versa.
Everyone who is both quiet and not old is both humble and not rich.
Everyone who is either funny or not strong is humble or not calm and vice versa.
Everyone who is not old or not funny is not curious and vice versa.
Mary is not patient or not wise.
Susan is both kind and not happy.
Paul is old or not happy.
Someone is both not funny and rich.
Someone is both not creative and not kind.
Someone is either not strong or kind.
Someone is either not creative or not curious. | Alice is not wise. | neutral | (![X]:((patient(X)<~>~tall(X))=>(patient(X)&humble(X))))&
(![X]:((~rich(X)&~funny(X))<=>(~generous(X)&happy(X))))&
(![X]:((~kind(X)&happy(X))=>(tall(X)<~>~wise(X))))&
(![X]:((kind(X)|~brave(X))<=>(~curious(X)&~quiet(X))))&
(![X]:(~kind(X)=>(~old(X)|kind(X))))&
(((quiet(fred)&~generous(fred)))<=>(?[X]:(~wise(X))))&
((?[X]:((calm(X)<~>~calm(X))))=>(?[X]:((~creative(X)<~>tall(X)))))&
(((old(alice)&generous(alice)))<=>((rich(fred)|wise(fred))))&
(![X]:((tall(X)&~patient(X))=>~quiet(X)))&
(((~creative(mary)&~strong(mary)))=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:((~rich(X)&~brave(X))<=>generous(X)))&
(![X]:((quiet(X)<~>~creative(X))<=>(brave(X)|~patient(X))))&
(![X]:(humble(X)<=>(calm(X)|~old(X))))&
(![X]:((quiet(X)&~old(X))=>(humble(X)&~rich(X))))&
(![X]:((funny(X)<~>~strong(X))<=>(humble(X)|~calm(X))))&
(![X]:((~old(X)|~funny(X))<=>~curious(X)))&
((~patient(mary)|~wise(mary)))&
((kind(susan)&~happy(susan)))&
((old(paul)|~happy(paul)))&
(?[X]:((~funny(X)&rich(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(?[X]:((~strong(X)<~>kind(X))))&
(?[X]:((~creative(X)<~>~curious(X)))) | ~wise(alice) | [] | null | 0 |
If someone is both not creative and not strong then lucy is calm or creative.
Everyone who is patient or not strong is generous or curious.
Everyone who is not humble or curious is rich and vice versa.
Everyone who is both rich and not tall is both happy and kind and vice versa.
Everyone who is both curious and patient is both not rich and not tall and vice versa.
Everyone who is either curious or not tall is both humble and not happy.
Everyone who is not generous is both generous and curious.
Everyone who is both generous and not funny is either rich or not brave.
Everyone who is both not generous and tall is not happy or old and vice versa.
Everyone who is either curious or humble is both not calm and not funny and vice versa.
Everyone who is either not kind or not humble is not happy or not patient.
Everyone who is both calm and not calm is creative or not happy and vice versa.
Everyone who is both not creative and brave is both not strong and not quiet.
Everyone who is either not quiet or generous is old.
If someone is either old or generous then someone is either not calm or wise.
Everyone who is both not patient and strong is not humble or curious and vice versa.
Lucy is both not patient and happy.
Someone is either not funny or not old.
Paul is calm or not happy.
Mary is either happy or creative.
Someone is kind.
Someone is either strong or not calm.
Lucy is either not creative or creative.
Susan is funny. | Lucy is funny. | entailment | ((?[X]:((~creative(X)&~strong(X))))=>((calm(lucy)|creative(lucy))))&
(![X]:((patient(X)|~strong(X))=>(generous(X)|curious(X))))&
(![X]:((~humble(X)|curious(X))<=>rich(X)))&
(![X]:((rich(X)&~tall(X))<=>(happy(X)&kind(X))))&
(![X]:((curious(X)&patient(X))<=>(~rich(X)&~tall(X))))&
(![X]:((curious(X)<~>~tall(X))=>(humble(X)&~happy(X))))&
(![X]:(~generous(X)=>(generous(X)&curious(X))))&
(![X]:((generous(X)&~funny(X))=>(rich(X)<~>~brave(X))))&
(![X]:((~generous(X)&tall(X))<=>(~happy(X)|old(X))))&
(![X]:((curious(X)<~>humble(X))<=>(~calm(X)&~funny(X))))&
(![X]:((~kind(X)<~>~humble(X))=>(~happy(X)|~patient(X))))&
(![X]:((calm(X)&~calm(X))<=>(creative(X)|~happy(X))))&
(![X]:((~creative(X)&brave(X))=>(~strong(X)&~quiet(X))))&
(![X]:((~quiet(X)<~>generous(X))=>old(X)))&
((?[X]:((old(X)<~>generous(X))))=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((~patient(X)&strong(X))<=>(~humble(X)|curious(X))))&
((~patient(lucy)&happy(lucy)))&
(?[X]:((~funny(X)<~>~old(X))))&
((calm(paul)|~happy(paul)))&
((happy(mary)<~>creative(mary)))&
(?[X]:(kind(X)))&
(?[X]:((strong(X)<~>~calm(X))))&
((~creative(lucy)<~>creative(lucy)))&
(funny(susan)) | funny(lucy) | [
"p0",
"p2",
"p6",
"p7",
"p9",
"p11",
"p12",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2217517944544367660942774
% SZS output start Proof for 2217517944544367660942774
1. ? [X0] : (~strong(X0) & ~creative(X0)) => (creative(lucy) | calm(lucy)) [input p0]
3. ! [X0] : ((curious(X0) | ~humble(X0)) <=> rich(X0)) [input p2]
7. ! [X0] : (~generous(X0) => (curious(X0) & generous(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & generous(X0)) => (rich(X0) <~> ~brave(X0))) [input p7]
10. ! [X0] : ((curious(X0) <~> humble(X0)) <=> (~funny(X0) & ~calm(X0))) [input p9]
12. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~happy(X0) | creative(X0))) [input p11]
13. ! [X0] : ((brave(X0) & ~creative(X0)) => (~quiet(X0) & ~strong(X0))) [input p12]
16. ! [X0] : ((strong(X0) & ~patient(X0)) <=> (curious(X0) | ~humble(X0))) [input p15]
17. happy(lucy) & ~patient(lucy) [input p16]
25. ~funny(lucy) [input hypothesis]
27. (creative(lucy) | calm(lucy)) | ! [X0] : (strong(X0) | creative(X0)) [ennf transformation 1]
28. creative(lucy) | calm(lucy) | ! [X0] : (strong(X0) | creative(X0)) [flattening 27]
32. ! [X0] : ((curious(X0) & generous(X0)) | generous(X0)) [ennf transformation 7]
33. ! [X0] : ((rich(X0) <~> ~brave(X0)) | (funny(X0) | ~generous(X0))) [ennf transformation 8]
34. ! [X0] : ((rich(X0) <~> ~brave(X0)) | funny(X0) | ~generous(X0)) [flattening 33]
37. ! [X0] : ((~quiet(X0) & ~strong(X0)) | (~brave(X0) | creative(X0))) [ennf transformation 13]
38. ! [X0] : ((~quiet(X0) & ~strong(X0)) | ~brave(X0) | creative(X0)) [flattening 37]
41. ! [X0] : (((curious(X0) | ~humble(X0)) | ~rich(X0)) & (rich(X0) | (~curious(X0) & humble(X0)))) [nnf transformation 3]
42. ! [X0] : ((curious(X0) | ~humble(X0) | ~rich(X0)) & (rich(X0) | (~curious(X0) & humble(X0)))) [flattening 41]
48. ! [X0] : (((brave(X0) | ~rich(X0)) & (~brave(X0) | rich(X0))) | funny(X0) | ~generous(X0)) [nnf transformation 34]
51. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | (funny(X0) | calm(X0))) & ((~funny(X0) & ~calm(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [nnf transformation 10]
52. ! [X0] : ((((~humble(X0) | ~curious(X0)) & (humble(X0) | curious(X0))) | funny(X0) | calm(X0)) & ((~funny(X0) & ~calm(X0)) | ((curious(X0) | ~humble(X0)) & (humble(X0) | ~curious(X0))))) [flattening 51]
54. ! [X0] : (((~calm(X0) & calm(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 12]
55. ! [X0] : (((~calm(X0) & calm(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | calm(X0) | ~calm(X0))) [flattening 54]
61. ! [X0] : (((strong(X0) & ~patient(X0)) | (~curious(X0) & humble(X0))) & ((curious(X0) | ~humble(X0)) | (~strong(X0) | patient(X0)))) [nnf transformation 16]
62. ! [X0] : (((strong(X0) & ~patient(X0)) | (~curious(X0) & humble(X0))) & (curious(X0) | ~humble(X0) | ~strong(X0) | patient(X0))) [flattening 61]
73. creative(lucy) | calm(lucy) | strong(X0) | creative(X0) [cnf transformation 28]
76. rich(X0) | humble(X0) [cnf transformation 42]
77. ~curious(X0) | rich(X0) [cnf transformation 42]
91. generous(X0) | generous(X0) [cnf transformation 32]
94. brave(X0) | ~rich(X0) | funny(X0) | ~generous(X0) [cnf transformation 48]
101. ~humble(X0) | curious(X0) | ~calm(X0) [cnf transformation 52]
109. calm(X0) | ~creative(X0) [cnf transformation 55]
111. ~calm(X0) | ~creative(X0) [cnf transformation 55]
113. ~strong(X0) | ~brave(X0) | creative(X0) [cnf transformation 38]
121. ~humble(X0) | curious(X0) | ~strong(X0) | patient(X0) [cnf transformation 62]
124. humble(X0) | strong(X0) [cnf transformation 62]
125. ~curious(X0) | strong(X0) [cnf transformation 62]
126. ~patient(lucy) [cnf transformation 17]
139. ~funny(lucy) [cnf transformation 25]
140. generous(X0) [duplicate literal removal 91]
142. 1 <=> ! [X0] : (strong(X0) | creative(X0)) [avatar definition]
143. strong(X0) | creative(X0) <- (1) [avatar component clause 142]
145. 2 <=> calm(lucy) [avatar definition]
147. calm(lucy) <- (2) [avatar component clause 145]
149. 3 <=> creative(lucy) [avatar definition]
151. creative(lucy) <- (3) [avatar component clause 149]
152. 1 | 2 | 3 [avatar split clause 73,149,145,142]
155. ~rich(X0) | brave(X0) | funny(X0) [subsumption resolution 94,140]
161. ~creative(X0) [subsumption resolution 109,111]
163. ~brave(X0) | ~strong(X0) [subsumption resolution 113,161]
248. curious(X0) | ~calm(X0) | strong(X0) [resolution 101,124]
249. ~calm(X0) | strong(X0) [subsumption resolution 248,125]
283. brave(X0) | funny(X0) | humble(X0) [resolution 155,76]
329. funny(X1) | humble(X1) | ~strong(X1) [resolution 283,163]
331. funny(X1) | humble(X1) [subsumption resolution 329,124]
332. humble(lucy) [resolution 331,139]
336. curious(lucy) | ~strong(lucy) | patient(lucy) [resolution 332,121]
365. 19 <=> curious(lucy) [avatar definition]
367. curious(lucy) <- (19) [avatar component clause 365]
371. curious(lucy) | ~strong(lucy) [subsumption resolution 336,126]
373. 20 <=> strong(lucy) [avatar definition]
374. strong(lucy) <- (20) [avatar component clause 373]
375. ~strong(lucy) <- (~20) [avatar component clause 373]
376. ~20 | 19 [avatar split clause 371,365,373]
377. strong(X0) <- (1) [subsumption resolution 143,161]
378. $false <- (1, ~20) [subsumption resolution 375,377]
379. ~1 | 20 [avatar contradiction clause 378]
380. $false <- (3) [subsumption resolution 151,161]
381. ~3 [avatar contradiction clause 380]
382. strong(lucy) <- (2) [resolution 147,249]
386. 20 | ~2 [avatar split clause 382,145,373]
391. rich(lucy) <- (19) [resolution 367,77]
392. brave(lucy) | funny(lucy) <- (19) [resolution 391,155]
396. brave(lucy) <- (19) [subsumption resolution 392,139]
407. ~strong(lucy) <- (19) [resolution 396,163]
408. $false <- (19, 20) [subsumption resolution 407,374]
409. ~19 | ~20 [avatar contradiction clause 408]
410. $false [avatar sat refutation 152,376,379,381,386,409]
% SZS output end Proof for 2217517944544367660942774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is both not strong and not wise and vice versa.
Everyone who is both strong and not creative is both not brave and not rich and vice versa.
If someone is both not wise and not kind then mary is not quiet or not wise and vice versa.
Everyone who is not tall is funny and vice versa.
Everyone who is curious or not kind is both tall and not brave.
If lucy is not brave or funny then paul is either not strong or brave.
Everyone who is either wise or not happy is both brave and not funny.
Everyone who is tall is both not tall and old and vice versa.
Everyone who is wise is not calm and vice versa.
Everyone who is not kind is not funny.
Everyone who is calm is not funny.
Everyone who is either brave or patient is not old or patient and vice versa.
If mary is not wise then lucy is both rich and calm.
Everyone who is both not wise and curious is both rich and not kind and vice versa.
Someone is both brave and rich.
Susan is either not rich or humble.
Susan is either old or kind.
Someone is either patient or calm.
Susan is either brave or happy.
Alice is either not tall or strong.
Someone is both not brave and strong.
Someone is patient or not rich. | Mary is happy. | contradiction | ((?[X]:(~creative(X)))<=>(?[X]:((~strong(X)&~wise(X)))))&
(![X]:((strong(X)&~creative(X))<=>(~brave(X)&~rich(X))))&
((?[X]:((~wise(X)&~kind(X))))<=>((~quiet(mary)|~wise(mary))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((curious(X)|~kind(X))=>(tall(X)&~brave(X))))&
(((~brave(lucy)|funny(lucy)))=>((~strong(paul)<~>brave(paul))))&
(![X]:((wise(X)<~>~happy(X))=>(brave(X)&~funny(X))))&
(![X]:(tall(X)<=>(~tall(X)&old(X))))&
(![X]:(wise(X)<=>~calm(X)))&
(![X]:(~kind(X)=>~funny(X)))&
(![X]:(calm(X)=>~funny(X)))&
(![X]:((brave(X)<~>patient(X))<=>(~old(X)|patient(X))))&
((~wise(mary))=>((rich(lucy)&calm(lucy))))&
(![X]:((~wise(X)&curious(X))<=>(rich(X)&~kind(X))))&
(?[X]:((brave(X)&rich(X))))&
((~rich(susan)<~>humble(susan)))&
((old(susan)<~>kind(susan)))&
(?[X]:((patient(X)<~>calm(X))))&
((brave(susan)<~>happy(susan)))&
((~tall(alice)<~>strong(alice)))&
(?[X]:((~brave(X)&strong(X))))&
(?[X]:((patient(X)|~rich(X)))) | happy(mary) | [
"p2",
"p3",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 106584143773818858640236
% SZS output start Proof for 106584143773818858640236
3. ? [X0] : (~kind(X0) & ~wise(X0)) <=> (~wise(mary) | ~quiet(mary)) [input p2]
4. ! [X0] : (~tall(X0) <=> funny(X0)) [input p3]
7. ! [X0] : ((wise(X0) <~> ~happy(X0)) => (~funny(X0) & brave(X0))) [input p6]
8. ! [X0] : (tall(X0) <=> (old(X0) & ~tall(X0))) [input p7]
9. ! [X0] : (wise(X0) <=> ~calm(X0)) [input p8]
11. ! [X0] : (calm(X0) => ~funny(X0)) [input p10]
23. happy(mary) [input hypothesis]
27. ! [X0] : ((~funny(X0) & brave(X0)) | (wise(X0) <=> ~happy(X0))) [ennf transformation 7]
29. ! [X0] : (~funny(X0) | ~calm(X0)) [ennf transformation 11]
38. (? [X0] : (~kind(X0) & ~wise(X0)) | (wise(mary) & quiet(mary))) & ((~wise(mary) | ~quiet(mary)) | ! [X0] : (kind(X0) | wise(X0))) [nnf transformation 3]
39. (? [X0] : (~kind(X0) & ~wise(X0)) | (wise(mary) & quiet(mary))) & (~wise(mary) | ~quiet(mary) | ! [X0] : (kind(X0) | wise(X0))) [flattening 38]
40. (? [X0] : (~kind(X0) & ~wise(X0)) | (wise(mary) & quiet(mary))) & (~wise(mary) | ~quiet(mary) | ! [X1] : (kind(X1) | wise(X1))) [rectify 39]
41. ? [X0] : (~kind(X0) & ~wise(X0)) => (~kind(sK2) & ~wise(sK2)) [choice axiom]
42. ((~kind(sK2) & ~wise(sK2)) | (wise(mary) & quiet(mary))) & (~wise(mary) | ~quiet(mary) | ! [X1] : (kind(X1) | wise(X1))) [skolemisation 40,41]
43. ! [X0] : ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))) [nnf transformation 4]
45. ! [X0] : ((~funny(X0) & brave(X0)) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0)))) [nnf transformation 27]
46. ! [X0] : ((tall(X0) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | ~tall(X0))) [nnf transformation 8]
47. ! [X0] : ((tall(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | ~tall(X0))) [flattening 46]
48. ! [X0] : ((wise(X0) | calm(X0)) & (~calm(X0) | ~wise(X0))) [nnf transformation 9]
75. ~wise(sK2) | wise(mary) [cnf transformation 42]
78. funny(X0) | tall(X0) [cnf transformation 43]
90. ~happy(X0) | ~funny(X0) | ~wise(X0) [cnf transformation 45]
92. ~tall(X0) | ~tall(X0) [cnf transformation 47]
96. calm(X0) | wise(X0) [cnf transformation 48]
98. ~calm(X0) | ~funny(X0) [cnf transformation 29]
126. happy(mary) [cnf transformation 23]
129. ~tall(X0) [duplicate literal removal 92]
153. 6 <=> wise(mary) [avatar definition]
155. wise(mary) <- (6) [avatar component clause 153]
167. 9 <=> wise(sK2) [avatar definition]
169. ~wise(sK2) <- (~9) [avatar component clause 167]
170. 6 | ~9 [avatar split clause 75,167,153]
274. ~funny(X0) | wise(X0) [resolution 98,96]
276. wise(X0) | tall(X0) [resolution 274,78]
278. wise(X0) [subsumption resolution 276,129]
337. $false <- (~9) [resolution 278,169]
338. 9 [avatar contradiction clause 337]
343. ~funny(mary) | ~wise(mary) [resolution 90,126]
345. ~funny(mary) <- (6) [subsumption resolution 343,155]
346. tall(mary) <- (6) [resolution 345,78]
347. $false <- (6) [subsumption resolution 346,129]
348. ~6 [avatar contradiction clause 347]
349. $false [avatar sat refutation 170,338,348]
% SZS output end Proof for 106584143773818858640236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or strong then someone is humble.
Everyone who is funny or not calm is both old and patient and vice versa.
Everyone who is kind is both strong and patient and vice versa.
Everyone who is either strong or not rich is not old and vice versa.
If someone is kind then someone is both not happy and tall.
If someone is not strong or not rich then someone is either not kind or not funny and vice versa.
If someone is not brave then mary is rich and vice versa.
Everyone who is both not wise and not strong is not brave or curious.
If susan is not old then alice is not strong and vice versa.
If mary is happy then someone is both creative and not wise.
Everyone who is both not wise and not funny is either not creative or not rich.
Everyone who is either not humble or not happy is both not tall and happy and vice versa.
If someone is both not patient and not creative then susan is humble or generous and vice versa.
Everyone who is not rich or wise is both not calm and not rich.
Everyone who is either not tall or happy is happy and vice versa.
If susan is either not curious or not rich then paul is both not quiet and humble and vice versa.
Alice is both not generous and not humble.
Susan is not strong.
Someone is humble.
Paul is tall or quiet.
Mary is both not brave and creative.
Paul is both patient and tall.
Alice is both not curious and not kind. | Susan is tall. | entailment | ((?[X]:((~old(X)<~>strong(X))))=>(?[X]:(humble(X))))&
(![X]:((funny(X)|~calm(X))<=>(old(X)&patient(X))))&
(![X]:(kind(X)<=>(strong(X)&patient(X))))&
(![X]:((strong(X)<~>~rich(X))<=>~old(X)))&
((?[X]:(kind(X)))=>(?[X]:((~happy(X)&tall(X)))))&
((?[X]:((~strong(X)|~rich(X))))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:(~brave(X)))<=>(rich(mary)))&
(![X]:((~wise(X)&~strong(X))=>(~brave(X)|curious(X))))&
((~old(susan))<=>(~strong(alice)))&
((happy(mary))=>(?[X]:((creative(X)&~wise(X)))))&
(![X]:((~wise(X)&~funny(X))=>(~creative(X)<~>~rich(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~tall(X)&happy(X))))&
((?[X]:((~patient(X)&~creative(X))))<=>((humble(susan)|generous(susan))))&
(![X]:((~rich(X)|wise(X))=>(~calm(X)&~rich(X))))&
(![X]:((~tall(X)<~>happy(X))<=>happy(X)))&
(((~curious(susan)<~>~rich(susan)))<=>((~quiet(paul)&humble(paul))))&
((~generous(alice)&~humble(alice)))&
(~strong(susan))&
(?[X]:(humble(X)))&
((tall(paul)|quiet(paul)))&
((~brave(mary)&creative(mary)))&
((patient(paul)&tall(paul)))&
((~curious(alice)&~kind(alice))) | tall(susan) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 119647177124299793984751
% SZS output start Proof for 119647177124299793984751
15. ! [X0] : ((~tall(X0) <~> happy(X0)) <=> happy(X0)) [input p14]
24. ~tall(susan) [input hypothesis]
68. ! [X0] : ((((~happy(X0) | tall(X0)) & (happy(X0) | ~tall(X0))) | ~happy(X0)) & (happy(X0) | ((~tall(X0) | ~happy(X0)) & (happy(X0) | tall(X0))))) [nnf transformation 15]
119. happy(X0) | happy(X0) | tall(X0) [cnf transformation 68]
122. ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 68]
140. ~tall(susan) [cnf transformation 24]
141. happy(X0) | tall(X0) [duplicate literal removal 119]
142. ~happy(X0) | tall(X0) [duplicate literal removal 122]
265. tall(X0) [subsumption resolution 141,142]
288. $false [subsumption resolution 140,265]
% SZS output end Proof for 119647177124299793984751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not wise or not strong then someone is both not patient and rich and vice versa. If someone is curious then susan is not brave or rich and vice versa. If alice is kind then someone is not strong or not curious and vice versa. Everyone who is both brave and not strong is patient or not quiet and vice versa. If mary is both funny and not tall then mary is patient and vice versa. If paul is both not quiet and not rich then someone is rich or not funny and vice versa. Everyone who is generous is either not kind or not humble. Everyone who is rich or not rich is not kind. If susan is either not creative or old then someone is generous or calm and vice versa. Everyone who is both not funny and not happy is curious or kind. Everyone who is not generous is not quiet or old and vice versa. If someone is not old then paul is not curious or old and vice versa. Everyone who is either wise or not tall is both not wise and not happy and vice versa. Everyone who is rich or wise is creative and vice versa. Someone is not funny or not patient. John is both not happy and old. Mary is not humble. Someone is tall or not patient. Someone is either not quiet or calm. Alice is strong or not patient. Someone is both strong and calm. John is not humble. | Alice is not kind. | entailment | (((~wise(susan)<~>~strong(susan)))<=>(?[X]:((~patient(X)&rich(X)))))&
((?[X]:(curious(X)))<=>((~brave(susan)|rich(susan))))&
((kind(alice))<=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:((brave(X)&~strong(X))<=>(patient(X)|~quiet(X))))&
(((funny(mary)&~tall(mary)))<=>(patient(mary)))&
(((~quiet(paul)&~rich(paul)))<=>(?[X]:((rich(X)|~funny(X)))))&
(![X]:(generous(X)=>(~kind(X)<~>~humble(X))))&
(![X]:((rich(X)|~rich(X))=>~kind(X)))&
(((~creative(susan)<~>old(susan)))<=>(?[X]:((generous(X)|calm(X)))))&
(![X]:((~funny(X)&~happy(X))=>(curious(X)|kind(X))))&
(![X]:(~generous(X)<=>(~quiet(X)|old(X))))&
((?[X]:(~old(X)))<=>((~curious(paul)|old(paul))))&
(![X]:((wise(X)<~>~tall(X))<=>(~wise(X)&~happy(X))))&
(![X]:((rich(X)|wise(X))<=>creative(X)))&
(?[X]:((~funny(X)|~patient(X))))&
((~happy(john)&old(john)))&
(~humble(mary))&
(?[X]:((tall(X)|~patient(X))))&
(?[X]:((~quiet(X)<~>calm(X))))&
((strong(alice)|~patient(alice)))&
(?[X]:((strong(X)&calm(X))))&
(~humble(john)) | ~kind(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3509922811014791744459555
% SZS output start Proof for 3509922811014791744459555
8. ! [X0] : ((~rich(X0) | rich(X0)) => ~kind(X0)) [input p7]
23. kind(alice) [input hypothesis]
25. ! [X0] : (~kind(X0) | (rich(X0) & ~rich(X0))) [ennf transformation 8]
102. ~kind(X0) | ~rich(X0) [cnf transformation 25]
103. ~kind(X0) | rich(X0) [cnf transformation 25]
137. kind(alice) [cnf transformation 23]
246. ~kind(X0) [subsumption resolution 102,103]
323. $false [subsumption resolution 137,246]
% SZS output end Proof for 3509922811014791744459555
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or not funny then someone is both not curious and not rich and vice versa.
If someone is either not curious or not old then fred is tall.
Everyone who is either not patient or strong is not funny or not humble and vice versa.
If someone is not happy then someone is calm or rich.
If paul is both tall and not wise then someone is either not kind or not quiet.
If susan is curious then someone is wise.
If lucy is both not old and not calm then fred is both wise and curious.
If lucy is not calm then lucy is strong.
If someone is both wise and rich then fred is not creative or not quiet.
Everyone who is both creative and funny is both strong and not curious.
Everyone who is either not brave or not calm is not quiet or creative.
Everyone who is either not old or kind is strong or not brave.
If someone is both not patient and tall then fred is either brave or not curious.
Everyone who is not funny or old is either old or not creative and vice versa.
Everyone who is both not funny and not rich is not humble.
Everyone who is either not old or happy is either not quiet or not kind and vice versa.
Susan is both happy and not kind.
Someone is not creative or old.
Someone is either not rich or not happy.
Someone is both not old and strong.
Fred is not calm or happy.
Paul is not tall or not strong.
Susan is either not quiet or not happy. | Paul is not wise. | neutral | (((~rich(lucy)|~funny(lucy)))<=>(?[X]:((~curious(X)&~rich(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>(tall(fred)))&
(![X]:((~patient(X)<~>strong(X))<=>(~funny(X)|~humble(X))))&
((?[X]:(~happy(X)))=>(?[X]:((calm(X)|rich(X)))))&
(((tall(paul)&~wise(paul)))=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((curious(susan))=>(?[X]:(wise(X))))&
(((~old(lucy)&~calm(lucy)))=>((wise(fred)&curious(fred))))&
((~calm(lucy))=>(strong(lucy)))&
((?[X]:((wise(X)&rich(X))))=>((~creative(fred)|~quiet(fred))))&
(![X]:((creative(X)&funny(X))=>(strong(X)&~curious(X))))&
(![X]:((~brave(X)<~>~calm(X))=>(~quiet(X)|creative(X))))&
(![X]:((~old(X)<~>kind(X))=>(strong(X)|~brave(X))))&
((?[X]:((~patient(X)&tall(X))))=>((brave(fred)<~>~curious(fred))))&
(![X]:((~funny(X)|old(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~funny(X)&~rich(X))=>~humble(X)))&
(![X]:((~old(X)<~>happy(X))<=>(~quiet(X)<~>~kind(X))))&
((happy(susan)&~kind(susan)))&
(?[X]:((~creative(X)|old(X))))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((~old(X)&strong(X))))&
((~calm(fred)|happy(fred)))&
((~tall(paul)|~strong(paul)))&
((~quiet(susan)<~>~happy(susan))) | ~wise(paul) | [] | null | 0 |
If susan is funny or generous then someone is strong or not quiet and vice versa.
If someone is either not funny or not old then someone is funny or not generous and vice versa.
Everyone who is either calm or quiet is either not generous or happy and vice versa.
If someone is wise then someone is not tall or creative and vice versa.
Everyone who is not creative or not generous is not strong or kind and vice versa.
Everyone who is not brave or not strong is both brave and generous and vice versa.
Everyone who is either brave or not calm is both not funny and kind and vice versa.
If john is either rich or curious then someone is not humble and vice versa.
If someone is funny then susan is old or not humble and vice versa.
If lucy is either not quiet or happy then paul is not creative.
If alice is either humble or not quiet then someone is both kind and not creative and vice versa.
If john is both tall and not happy then someone is both happy and creative.
If someone is both funny and not tall then someone is not brave.
Everyone who is either strong or not brave is either generous or not rich and vice versa.
If fred is either funny or not rich then someone is curious or not kind and vice versa.
Everyone who is both brave and not old is both rich and not funny.
Someone is brave.
Someone is both brave and not happy.
Someone is not calm.
Paul is not happy.
Someone is either not humble or kind.
Fred is both not creative and patient. | Susan is patient. | neutral | (((funny(susan)|generous(susan)))<=>(?[X]:((strong(X)|~quiet(X)))))&
((?[X]:((~funny(X)<~>~old(X))))<=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((calm(X)<~>quiet(X))<=>(~generous(X)<~>happy(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~tall(X)|creative(X)))))&
(![X]:((~creative(X)|~generous(X))<=>(~strong(X)|kind(X))))&
(![X]:((~brave(X)|~strong(X))<=>(brave(X)&generous(X))))&
(![X]:((brave(X)<~>~calm(X))<=>(~funny(X)&kind(X))))&
(((rich(john)<~>curious(john)))<=>(?[X]:(~humble(X))))&
((?[X]:(funny(X)))<=>((old(susan)|~humble(susan))))&
(((~quiet(lucy)<~>happy(lucy)))=>(~creative(paul)))&
(((humble(alice)<~>~quiet(alice)))<=>(?[X]:((kind(X)&~creative(X)))))&
(((tall(john)&~happy(john)))=>(?[X]:((happy(X)&creative(X)))))&
((?[X]:((funny(X)&~tall(X))))=>(?[X]:(~brave(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(generous(X)<~>~rich(X))))&
(((funny(fred)<~>~rich(fred)))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((brave(X)&~old(X))=>(rich(X)&~funny(X))))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~happy(X))))&
(?[X]:(~calm(X)))&
(~happy(paul))&
(?[X]:((~humble(X)<~>kind(X))))&
((~creative(fred)&patient(fred))) | patient(susan) | [] | null | 0 |
Everyone who is wise or not tall is both humble and not generous and vice versa.
If mary is not generous then susan is humble or not tall.
If someone is either rich or not creative then susan is both not creative and calm.
If someone is kind or not generous then someone is not funny or not creative.
Everyone who is both not quiet and not brave is either rich or quiet.
If john is both calm and tall then someone is not kind.
If fred is both not generous and humble then someone is calm or not kind and vice versa.
If mary is both not wise and not quiet then susan is not brave or funny and vice versa.
Everyone who is either not happy or not curious is curious or not strong.
Everyone who is happy is both happy and tall and vice versa.
Everyone who is either old or calm is both not wise and not calm.
Everyone who is either curious or patient is not strong or quiet and vice versa.
Everyone who is funny or not wise is not creative.
Everyone who is both not calm and tall is either brave or not wise.
Everyone who is not creative is either funny or not creative and vice versa.
Everyone who is both strong and not strong is generous or not curious and vice versa.
Fred is calm.
Paul is not brave.
Someone is both old and calm.
Someone is either not generous or not curious.
Someone is not calm. | Susan is happy. | neutral | (![X]:((wise(X)|~tall(X))<=>(humble(X)&~generous(X))))&
((~generous(mary))=>((humble(susan)|~tall(susan))))&
((?[X]:((rich(X)<~>~creative(X))))=>((~creative(susan)&calm(susan))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:((~funny(X)|~creative(X)))))&
(![X]:((~quiet(X)&~brave(X))=>(rich(X)<~>quiet(X))))&
(((calm(john)&tall(john)))=>(?[X]:(~kind(X))))&
(((~generous(fred)&humble(fred)))<=>(?[X]:((calm(X)|~kind(X)))))&
(((~wise(mary)&~quiet(mary)))<=>((~brave(susan)|funny(susan))))&
(![X]:((~happy(X)<~>~curious(X))=>(curious(X)|~strong(X))))&
(![X]:(happy(X)<=>(happy(X)&tall(X))))&
(![X]:((old(X)<~>calm(X))=>(~wise(X)&~calm(X))))&
(![X]:((curious(X)<~>patient(X))<=>(~strong(X)|quiet(X))))&
(![X]:((funny(X)|~wise(X))=>~creative(X)))&
(![X]:((~calm(X)&tall(X))=>(brave(X)<~>~wise(X))))&
(![X]:(~creative(X)<=>(funny(X)<~>~creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(generous(X)|~curious(X))))&
(calm(fred))&
(~brave(paul))&
(?[X]:((old(X)&calm(X))))&
(?[X]:((~generous(X)<~>~curious(X))))&
(?[X]:(~calm(X))) | happy(susan) | [] | null | 0 |
Everyone who is either patient or not strong is both not calm and not patient.
If someone is curious then someone is not rich.
Everyone who is not old or not brave is both not calm and not happy.
If mary is curious or not calm then fred is either wise or brave and vice versa.
Everyone who is not tall or not old is not tall or patient and vice versa.
Everyone who is calm is quiet or not wise and vice versa.
Everyone who is generous or not wise is either creative or rich and vice versa.
If someone is generous then john is both kind and not rich and vice versa.
If fred is both not wise and calm then alice is both not strong and quiet and vice versa.
Everyone who is both strong and not patient is quiet and vice versa.
If someone is creative then someone is both not patient and old and vice versa.
Everyone who is not old is not generous.
If susan is either generous or not patient then susan is not creative and vice versa.
Everyone who is old or not curious is both not rich and strong and vice versa.
If someone is happy or not rich then john is either creative or brave.
Everyone who is not curious or rich is both not curious and not calm and vice versa.
Alice is not old.
Someone is either not brave or strong.
Mary is generous or old.
Someone is both not rich and humble.
Lucy is kind or not happy.
Mary is not patient.
Someone is kind or not brave.
Someone is not happy. | Alice is strong. | contradiction | (![X]:((patient(X)<~>~strong(X))=>(~calm(X)&~patient(X))))&
((?[X]:(curious(X)))=>(?[X]:(~rich(X))))&
(![X]:((~old(X)|~brave(X))=>(~calm(X)&~happy(X))))&
(((curious(mary)|~calm(mary)))<=>((wise(fred)<~>brave(fred))))&
(![X]:((~tall(X)|~old(X))<=>(~tall(X)|patient(X))))&
(![X]:(calm(X)<=>(quiet(X)|~wise(X))))&
(![X]:((generous(X)|~wise(X))<=>(creative(X)<~>rich(X))))&
((?[X]:(generous(X)))<=>((kind(john)&~rich(john))))&
(((~wise(fred)&calm(fred)))<=>((~strong(alice)&quiet(alice))))&
(![X]:((strong(X)&~patient(X))<=>quiet(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:(~old(X)=>~generous(X)))&
(((generous(susan)<~>~patient(susan)))<=>(~creative(susan)))&
(![X]:((old(X)|~curious(X))<=>(~rich(X)&strong(X))))&
((?[X]:((happy(X)|~rich(X))))=>((creative(john)<~>brave(john))))&
(![X]:((~curious(X)|rich(X))<=>(~curious(X)&~calm(X))))&
(~old(alice))&
(?[X]:((~brave(X)<~>strong(X))))&
((generous(mary)|old(mary)))&
(?[X]:((~rich(X)&humble(X))))&
((kind(lucy)|~happy(lucy)))&
(~patient(mary))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:(~happy(X))) | strong(alice) | [
"p0",
"p2",
"p5",
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 641937276985492633334543
% SZS output start Proof for 641937276985492633334543
1. ! [X0] : ((patient(X0) <~> ~strong(X0)) => (~patient(X0) & ~calm(X0))) [input p0]
3. ! [X0] : ((~brave(X0) | ~old(X0)) => (~happy(X0) & ~calm(X0))) [input p2]
6. ! [X0] : (calm(X0) <=> (~wise(X0) | quiet(X0))) [input p5]
10. ! [X0] : ((~patient(X0) & strong(X0)) <=> quiet(X0)) [input p9]
17. ~old(alice) [input p16]
25. strong(alice) [input hypothesis]
30. ! [X0] : ((~brave(X0) | ~old(X0)) => ~calm(X0)) [pure predicate removal 3]
33. ! [X0] : ((~patient(X0) & ~calm(X0)) | (patient(X0) <=> ~strong(X0))) [ennf transformation 1]
35. ! [X0] : (~calm(X0) | (brave(X0) & old(X0))) [ennf transformation 30]
38. ! [X0] : ((~patient(X0) & ~calm(X0)) | ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0)))) [nnf transformation 33]
46. ! [X0] : ((calm(X0) | (wise(X0) & ~quiet(X0))) & ((~wise(X0) | quiet(X0)) | ~calm(X0))) [nnf transformation 6]
47. ! [X0] : ((calm(X0) | (wise(X0) & ~quiet(X0))) & (~wise(X0) | quiet(X0) | ~calm(X0))) [flattening 46]
57. ! [X0] : (((~patient(X0) & strong(X0)) | ~quiet(X0)) & (quiet(X0) | (patient(X0) | ~strong(X0)))) [nnf transformation 10]
58. ! [X0] : (((~patient(X0) & strong(X0)) | ~quiet(X0)) & (quiet(X0) | patient(X0) | ~strong(X0))) [flattening 57]
79. ~patient(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 38]
82. ~calm(X0) | old(X0) [cnf transformation 35]
95. ~quiet(X0) | calm(X0) [cnf transformation 47]
110. quiet(X0) | patient(X0) | ~strong(X0) [cnf transformation 58]
133. ~old(alice) [cnf transformation 17]
140. strong(alice) [cnf transformation 25]
141. ~strong(X0) | ~patient(X0) [duplicate literal removal 79]
191. 11 <=> strong(alice) [avatar definition]
193. strong(alice) <- (11) [avatar component clause 191]
195. 12 <=> quiet(alice) [avatar definition]
196. quiet(alice) <- (12) [avatar component clause 195]
208. ~strong(X0) | quiet(X0) [subsumption resolution 110,141]
280. 11 [avatar split clause 140,191]
297. quiet(alice) <- (11) [resolution 208,193]
300. 12 | ~11 [avatar split clause 297,191,195]
303. calm(alice) <- (12) [resolution 196,95]
316. old(alice) <- (12) [resolution 303,82]
317. $false <- (12) [subsumption resolution 316,133]
318. ~12 [avatar contradiction clause 317]
319. $false [avatar sat refutation 280,300,318]
% SZS output end Proof for 641937276985492633334543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and not curious is not tall and vice versa.
Everyone who is old is either humble or not wise.
If someone is not kind then john is both rich and not curious and vice versa.
If someone is calm or not calm then lucy is both creative and not generous and vice versa.
If someone is not generous or not curious then fred is not wise and vice versa.
Everyone who is either not calm or not happy is not calm and vice versa.
If someone is not curious then someone is kind or not happy.
Everyone who is either not kind or not rich is tall and vice versa.
Everyone who is not generous or not rich is curious.
If john is either humble or kind then john is either not kind or not brave.
Everyone who is not patient is old or calm.
Everyone who is not generous or not brave is both old and kind.
Everyone who is not brave is not curious and vice versa.
If lucy is not creative or happy then someone is not calm.
If someone is not funny then someone is not quiet or calm and vice versa.
If mary is rich then paul is calm and vice versa.
Susan is curious.
Someone is either old or not tall.
Mary is both creative and patient.
Someone is either not rich or funny.
Someone is not old.
Paul is curious. | Mary is happy. | entailment | (![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(![X]:(old(X)=>(humble(X)<~>~wise(X))))&
((?[X]:(~kind(X)))<=>((rich(john)&~curious(john))))&
((?[X]:((calm(X)|~calm(X))))<=>((creative(lucy)&~generous(lucy))))&
((?[X]:((~generous(X)|~curious(X))))<=>(~wise(fred)))&
(![X]:((~calm(X)<~>~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((~kind(X)<~>~rich(X))<=>tall(X)))&
(![X]:((~generous(X)|~rich(X))=>curious(X)))&
(((humble(john)<~>kind(john)))=>((~kind(john)<~>~brave(john))))&
(![X]:(~patient(X)=>(old(X)|calm(X))))&
(![X]:((~generous(X)|~brave(X))=>(old(X)&kind(X))))&
(![X]:(~brave(X)<=>~curious(X)))&
(((~creative(lucy)|happy(lucy)))=>(?[X]:(~calm(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~quiet(X)|calm(X)))))&
((rich(mary))<=>(calm(paul)))&
(curious(susan))&
(?[X]:((old(X)<~>~tall(X))))&
((creative(mary)&patient(mary)))&
(?[X]:((~rich(X)<~>funny(X))))&
(?[X]:(~old(X)))&
(curious(paul)) | happy(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 6696261323401104504143521
% SZS output start Proof for 6696261323401104504143521
6. ! [X0] : ((~calm(X0) <~> ~happy(X0)) <=> ~calm(X0)) [input p5]
23. ~happy(mary) [input hypothesis]
51. ! [X0] : ((((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | happy(X0)) & (~happy(X0) | calm(X0))))) [nnf transformation 6]
91. ~calm(X0) | ~calm(X0) | happy(X0) [cnf transformation 51]
93. happy(X0) | calm(X0) | calm(X0) [cnf transformation 51]
126. ~happy(mary) [cnf transformation 23]
129. ~calm(X0) | happy(X0) [duplicate literal removal 91]
130. happy(X0) | calm(X0) [duplicate literal removal 93]
188. happy(X0) [subsumption resolution 129,130]
261. $false [subsumption resolution 126,188]
% SZS output end Proof for 6696261323401104504143521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not calm and curious then someone is not brave or not creative and vice versa.
Everyone who is either curious or brave is quiet and vice versa.
If someone is quiet then john is not brave and vice versa.
If alice is either patient or strong then mary is both not creative and not tall.
Everyone who is not strong is both tall and not creative.
If someone is kind then someone is not patient.
If someone is generous or not patient then someone is not creative or not funny.
Everyone who is happy or not strong is either not tall or calm.
Everyone who is not generous is both not kind and creative and vice versa.
Everyone who is tall is both not old and funny.
Everyone who is quiet is both tall and calm.
Everyone who is both generous and not happy is funny or not tall.
If someone is either curious or generous then susan is either patient or not brave and vice versa.
Everyone who is either brave or not tall is either strong or not curious and vice versa.
If lucy is not patient then lucy is brave or patient.
John is either funny or not brave.
Someone is either old or curious.
Someone is not humble.
Someone is not old.
Mary is kind or quiet.
Mary is strong.
Alice is happy. | Susan is funny. | entailment | (((~calm(susan)&curious(susan)))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((curious(X)<~>brave(X))<=>quiet(X)))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(((patient(alice)<~>strong(alice)))=>((~creative(mary)&~tall(mary))))&
(![X]:(~strong(X)=>(tall(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:(~patient(X))))&
((?[X]:((generous(X)|~patient(X))))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((happy(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:(~generous(X)<=>(~kind(X)&creative(X))))&
(![X]:(tall(X)=>(~old(X)&funny(X))))&
(![X]:(quiet(X)=>(tall(X)&calm(X))))&
(![X]:((generous(X)&~happy(X))=>(funny(X)|~tall(X))))&
((?[X]:((curious(X)<~>generous(X))))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((brave(X)<~>~tall(X))<=>(strong(X)<~>~curious(X))))&
((~patient(lucy))=>((brave(lucy)|patient(lucy))))&
((funny(john)<~>~brave(john)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~old(X)))&
((kind(mary)|quiet(mary)))&
(strong(mary))&
(happy(alice)) | funny(susan) | [
"p0",
"p1",
"p2",
"p4",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2709464165619989303141244
% SZS output start Proof for 2709464165619989303141244
1. (curious(susan) & ~calm(susan)) <=> ? [X0] : (~creative(X0) | ~brave(X0)) [input p0]
2. ! [X0] : ((curious(X0) <~> brave(X0)) <=> quiet(X0)) [input p1]
3. ? [X0] : quiet(X0) <=> ~brave(john) [input p2]
5. ! [X0] : (~strong(X0) => (~creative(X0) & tall(X0))) [input p4]
10. ! [X0] : (tall(X0) => (funny(X0) & ~old(X0))) [input p9]
11. ! [X0] : (quiet(X0) => (calm(X0) & tall(X0))) [input p10]
14. ! [X0] : ((brave(X0) <~> ~tall(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p13]
23. ~funny(susan) [input hypothesis]
28. ! [X0] : ((~creative(X0) & tall(X0)) | strong(X0)) [ennf transformation 5]
32. ! [X0] : ((funny(X0) & ~old(X0)) | ~tall(X0)) [ennf transformation 10]
33. ! [X0] : ((calm(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 11]
38. ((curious(susan) & ~calm(susan)) | ! [X0] : (creative(X0) & brave(X0))) & (? [X0] : (~creative(X0) | ~brave(X0)) | (~curious(susan) | calm(susan))) [nnf transformation 1]
39. ((curious(susan) & ~calm(susan)) | ! [X0] : (creative(X0) & brave(X0))) & (? [X0] : (~creative(X0) | ~brave(X0)) | ~curious(susan) | calm(susan)) [flattening 38]
40. ((curious(susan) & ~calm(susan)) | ! [X0] : (creative(X0) & brave(X0))) & (? [X1] : (~creative(X1) | ~brave(X1)) | ~curious(susan) | calm(susan)) [rectify 39]
41. ? [X1] : (~creative(X1) | ~brave(X1)) => (~creative(sK0) | ~brave(sK0)) [choice axiom]
42. ((curious(susan) & ~calm(susan)) | ! [X0] : (creative(X0) & brave(X0))) & ((~creative(sK0) | ~brave(sK0)) | ~curious(susan) | calm(susan)) [skolemisation 40,41]
43. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ~quiet(X0)) & (quiet(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 2]
44. (? [X0] : quiet(X0) | brave(john)) & (~brave(john) | ! [X0] : ~quiet(X0)) [nnf transformation 3]
45. (? [X0] : quiet(X0) | brave(john)) & (~brave(john) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
47. (quiet(sK1) | brave(john)) & (~brave(john) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
62. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [nnf transformation 14]
70. ~calm(susan) | brave(X0) [cnf transformation 42]
72. curious(susan) | brave(X0) [cnf transformation 42]
74. ~curious(X0) | brave(X0) | quiet(X0) [cnf transformation 43]
75. ~brave(X0) | curious(X0) | quiet(X0) [cnf transformation 43]
78. ~brave(john) | ~quiet(X1) [cnf transformation 47]
84. tall(X0) | strong(X0) [cnf transformation 28]
97. ~tall(X0) | funny(X0) [cnf transformation 32]
99. ~quiet(X0) | calm(X0) [cnf transformation 33]
115. tall(X0) | ~brave(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 62]
126. ~funny(susan) [cnf transformation 23]
132. 2 <=> curious(susan) [avatar definition]
134. curious(susan) <- (2) [avatar component clause 132]
137. 3 <=> ! [X0] : brave(X0) [avatar definition]
138. brave(X0) <- (3) [avatar component clause 137]
139. 3 | 2 [avatar split clause 72,132,137]
141. 4 <=> calm(susan) [avatar definition]
143. ~calm(susan) <- (~4) [avatar component clause 141]
145. 3 | ~4 [avatar split clause 70,141,137]
156. 7 <=> brave(john) [avatar definition]
157. ~brave(john) <- (~7) [avatar component clause 156]
165. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
166. ~quiet(X1) <- (9) [avatar component clause 165]
167. 9 | ~7 [avatar split clause 78,156,165]
214. 20 <=> brave(susan) [avatar definition]
215. ~brave(susan) <- (~20) [avatar component clause 214]
216. brave(susan) <- (20) [avatar component clause 214]
243. ~brave(X0) | tall(X0) | ~curious(X0) [subsumption resolution 115,84]
291. brave(susan) | quiet(susan) <- (2) [resolution 74,134]
293. quiet(susan) <- (2, ~20) [subsumption resolution 291,215]
303. calm(susan) <- (2, ~20) [resolution 293,99]
305. $false <- (2, ~4, ~20) [subsumption resolution 303,143]
306. ~2 | 4 | 20 [avatar contradiction clause 305]
311. $false <- (3, ~7) [resolution 138,157]
312. $false <- (3, ~20) [resolution 138,215]
313. ~3 | 20 [avatar contradiction clause 312]
314. ~3 | 7 [avatar contradiction clause 311]
326. curious(susan) | quiet(susan) <- (20) [resolution 75,216]
379. tall(susan) | ~curious(susan) <- (20) [resolution 243,216]
381. tall(susan) <- (2, 20) [subsumption resolution 379,134]
396. funny(susan) <- (2, 20) [resolution 381,97]
397. $false <- (2, 20) [subsumption resolution 396,126]
398. ~2 | ~20 [avatar contradiction clause 397]
405. 44 <=> quiet(susan) [avatar definition]
407. quiet(susan) <- (44) [avatar component clause 405]
408. 44 | 2 | ~20 [avatar split clause 326,214,132,405]
419. $false <- (9, 44) [subsumption resolution 407,166]
420. ~9 | ~44 [avatar contradiction clause 419]
421. $false [avatar sat refutation 139,145,167,306,313,314,398,408,420]
% SZS output end Proof for 2709464165619989303141244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and not generous is either not brave or not calm. Everyone who is both brave and creative is both not happy and brave. If alice is either not happy or not rich then someone is both wise and not tall. If someone is either not brave or funny then someone is patient. If someone is either not wise or rich then paul is either not old or curious. Everyone who is both not strong and rich is not rich or quiet. If someone is patient or not funny then paul is both not generous and quiet and vice versa. If paul is not generous then mary is old and vice versa. If someone is either not generous or not funny then someone is either not wise or not generous. If lucy is old or not happy then someone is patient or creative. Everyone who is calm or quiet is both rich and patient. Everyone who is not kind or not happy is both creative and old. If someone is both funny and old then someone is generous and vice versa. Everyone who is happy or quiet is both not patient and patient. Everyone who is both kind and patient is not patient or not creative. If someone is old then someone is not tall and vice versa. Someone is not generous or not tall. Susan is not patient. John is not kind or patient. Alice is either not old or not rich. Lucy is calm or humble. Someone is tall or not generous. Susan is funny. Lucy is brave or humble. | Mary is quiet. | contradiction | (![X]:((~creative(X)&~generous(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((brave(X)&creative(X))=>(~happy(X)&brave(X))))&
(((~happy(alice)<~>~rich(alice)))=>(?[X]:((wise(X)&~tall(X)))))&
((?[X]:((~brave(X)<~>funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((~wise(X)<~>rich(X))))=>((~old(paul)<~>curious(paul))))&
(![X]:((~strong(X)&rich(X))=>(~rich(X)|quiet(X))))&
((?[X]:((patient(X)|~funny(X))))<=>((~generous(paul)&quiet(paul))))&
((~generous(paul))<=>(old(mary)))&
((?[X]:((~generous(X)<~>~funny(X))))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(((old(lucy)|~happy(lucy)))=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((calm(X)|quiet(X))=>(rich(X)&patient(X))))&
(![X]:((~kind(X)|~happy(X))=>(creative(X)&old(X))))&
((?[X]:((funny(X)&old(X))))<=>(?[X]:(generous(X))))&
(![X]:((happy(X)|quiet(X))=>(~patient(X)&patient(X))))&
(![X]:((kind(X)&patient(X))=>(~patient(X)|~creative(X))))&
((?[X]:(old(X)))<=>(?[X]:(~tall(X))))&
(?[X]:((~generous(X)|~tall(X))))&
(~patient(susan))&
((~kind(john)|patient(john)))&
((~old(alice)<~>~rich(alice)))&
((calm(lucy)|humble(lucy)))&
(?[X]:((tall(X)|~generous(X))))&
(funny(susan))&
((brave(lucy)|humble(lucy))) | quiet(mary) | [
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5804093504297534858996475
% SZS output start Proof for 5804093504297534858996475
11. ! [X0] : ((quiet(X0) | calm(X0)) => (patient(X0) & rich(X0))) [input p10]
14. ! [X0] : ((quiet(X0) | happy(X0)) => (patient(X0) & ~patient(X0))) [input p13]
25. quiet(mary) [input hypothesis]
42. ! [X0] : ((patient(X0) & rich(X0)) | (~quiet(X0) & ~calm(X0))) [ennf transformation 11]
44. ! [X0] : ((patient(X0) & ~patient(X0)) | (~quiet(X0) & ~happy(X0))) [ennf transformation 14]
113. patient(X0) | ~quiet(X0) [cnf transformation 42]
122. ~patient(X0) | ~quiet(X0) [cnf transformation 44]
135. quiet(mary) [cnf transformation 25]
277. ~quiet(X0) [subsumption resolution 122,113]
328. $false [subsumption resolution 135,277]
% SZS output end Proof for 5804093504297534858996475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or tall then someone is not calm and vice versa.
If alice is both not strong and not rich then lucy is not kind or not brave and vice versa.
Everyone who is not curious or tall is both not humble and not curious and vice versa.
If someone is both not calm and calm then john is calm or creative and vice versa.
Everyone who is not humble is both not old and wise and vice versa.
Everyone who is either not strong or not tall is both happy and not wise.
If someone is either curious or not funny then someone is creative or happy.
Everyone who is not curious or not patient is both old and not funny.
If alice is funny then someone is both not quiet and humble.
Everyone who is not funny or not kind is either not quiet or not strong and vice versa.
If someone is either kind or wise then susan is rich or kind and vice versa.
Everyone who is both generous and not brave is not wise and vice versa.
If lucy is both rich and brave then someone is either calm or not brave and vice versa.
Everyone who is funny is both old and not creative.
Everyone who is both not old and wise is humble or wise and vice versa.
If john is both old and wise then fred is both rich and not tall.
Someone is calm or not curious.
Lucy is not strong or not curious.
Someone is happy or not patient.
Someone is both not strong and not old.
Someone is curious or patient. | Alice is not quiet. | contradiction | ((?[X]:((generous(X)|tall(X))))<=>(?[X]:(~calm(X))))&
(((~strong(alice)&~rich(alice)))<=>((~kind(lucy)|~brave(lucy))))&
(![X]:((~curious(X)|tall(X))<=>(~humble(X)&~curious(X))))&
((?[X]:((~calm(X)&calm(X))))<=>((calm(john)|creative(john))))&
(![X]:(~humble(X)<=>(~old(X)&wise(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(happy(X)&~wise(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:((~curious(X)|~patient(X))=>(old(X)&~funny(X))))&
((funny(alice))=>(?[X]:((~quiet(X)&humble(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(~quiet(X)<~>~strong(X))))&
((?[X]:((kind(X)<~>wise(X))))<=>((rich(susan)|kind(susan))))&
(![X]:((generous(X)&~brave(X))<=>~wise(X)))&
(((rich(lucy)&brave(lucy)))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:(funny(X)=>(old(X)&~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(humble(X)|wise(X))))&
(((old(john)&wise(john)))=>((rich(fred)&~tall(fred))))&
(?[X]:((calm(X)|~curious(X))))&
((~strong(lucy)|~curious(lucy)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~strong(X)&~old(X))))&
(?[X]:((curious(X)|patient(X)))) | ~quiet(alice) | [
"p2",
"p4",
"p5",
"p7",
"p8",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8585688078940810395689547
% SZS output start Proof for 8585688078940810395689547
3. ! [X0] : ((tall(X0) | ~curious(X0)) <=> (~curious(X0) & ~humble(X0))) [input p2]
5. ! [X0] : (~humble(X0) <=> (wise(X0) & ~old(X0))) [input p4]
6. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (~wise(X0) & happy(X0))) [input p5]
8. ! [X0] : ((~patient(X0) | ~curious(X0)) => (~funny(X0) & old(X0))) [input p7]
9. funny(alice) => ? [X0] : (humble(X0) & ~quiet(X0)) [input p8]
10. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (~quiet(X0) <~> ~strong(X0))) [input p9]
15. ! [X0] : ((wise(X0) & ~old(X0)) <=> (wise(X0) | humble(X0))) [input p14]
22. ~quiet(alice) [input hypothesis]
25. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => ~wise(X0)) [pure predicate removal 6]
29. ! [X0] : (~curious(X0) => (~funny(X0) & old(X0))) [pure predicate removal 8]
30. ! [X0] : (~wise(X0) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 25]
31. ! [X0] : ((~funny(X0) & old(X0)) | curious(X0)) [ennf transformation 29]
32. ? [X0] : (humble(X0) & ~quiet(X0)) | ~funny(alice) [ennf transformation 9]
43. ! [X0] : (((tall(X0) | ~curious(X0)) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | (~tall(X0) & curious(X0)))) [nnf transformation 3]
44. ! [X0] : ((tall(X0) | ~curious(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | (~tall(X0) & curious(X0)))) [flattening 43]
50. ! [X0] : ((~humble(X0) | (~wise(X0) | old(X0))) & ((wise(X0) & ~old(X0)) | humble(X0))) [nnf transformation 5]
51. ! [X0] : ((~humble(X0) | ~wise(X0) | old(X0)) & ((wise(X0) & ~old(X0)) | humble(X0))) [flattening 50]
52. ! [X0] : (~wise(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 30]
53. ? [X0] : (humble(X0) & ~quiet(X0)) => (humble(sK3) & ~quiet(sK3)) [choice axiom]
54. (humble(sK3) & ~quiet(sK3)) | ~funny(alice) [skolemisation 32,53]
55. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 10]
56. ! [X0] : ((~kind(X0) | ~funny(X0) | ((~quiet(X0) | strong(X0)) & (~strong(X0) | quiet(X0)))) & (((strong(X0) | quiet(X0)) & (~strong(X0) | ~quiet(X0))) | (kind(X0) & funny(X0)))) [flattening 55]
69. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & ((wise(X0) | humble(X0)) | (~wise(X0) | old(X0)))) [nnf transformation 15]
70. ! [X0] : (((wise(X0) & ~old(X0)) | (~wise(X0) & ~humble(X0))) & (wise(X0) | humble(X0) | ~wise(X0) | old(X0))) [flattening 69]
83. ~humble(X0) | curious(X0) [cnf transformation 44]
86. ~curious(X0) | ~tall(X0) [cnf transformation 44]
93. ~old(X0) | humble(X0) [cnf transformation 51]
94. wise(X0) | humble(X0) [cnf transformation 51]
95. ~wise(X0) | ~humble(X0) | old(X0) [cnf transformation 51]
97. ~wise(X0) | ~strong(X0) | tall(X0) [cnf transformation 52]
98. old(X0) | curious(X0) [cnf transformation 31]
101. humble(sK3) | ~funny(alice) [cnf transformation 54]
104. quiet(X0) | strong(X0) | funny(X0) [cnf transformation 56]
127. ~old(X0) | ~wise(X0) [cnf transformation 70]
128. wise(X0) | ~humble(X0) [cnf transformation 70]
136. ~quiet(alice) [cnf transformation 22]
150. 4 <=> ! [X3] : ~tall(X3) [avatar definition]
151. ~tall(X3) <- (4) [avatar component clause 150]
199. 14 <=> funny(alice) [avatar definition]
203. 15 <=> humble(sK3) [avatar definition]
205. humble(sK3) <- (15) [avatar component clause 203]
206. ~14 | 15 [avatar split clause 101,203,199]
264. wise(X0) [subsumption resolution 128,94]
265. ~old(X0) [subsumption resolution 127,264]
286. curious(X0) | humble(X0) [resolution 98,93]
288. curious(X0) [subsumption resolution 286,83]
291. ~tall(X0) [resolution 288,86]
294. 4 [avatar split clause 291,150]
300. ~humble(X2) | old(X2) [resolution 95,264]
302. ~humble(X2) [subsumption resolution 300,265]
307. ~strong(X1) | tall(X1) | humble(X1) [resolution 97,94]
310. ~strong(X1) | humble(X1) <- (4) [subsumption resolution 307,151]
311. ~strong(X1) <- (4) [subsumption resolution 310,302]
312. strong(alice) | funny(alice) [resolution 104,136]
319. funny(alice) <- (4) [subsumption resolution 312,311]
324. 14 | ~4 [avatar split clause 319,150,199]
325. $false <- (15) [subsumption resolution 205,302]
326. ~15 [avatar contradiction clause 325]
327. $false [avatar sat refutation 206,294,324,326]
% SZS output end Proof for 8585688078940810395689547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not calm or creative then paul is either quiet or humble and vice versa. If alice is not wise then susan is not old. If someone is either patient or old then someone is brave or not brave and vice versa. Everyone who is old is both not rich and funny. If mary is generous then mary is wise or not generous. Everyone who is both not rich and not happy is humble or not old and vice versa. Everyone who is both wise and not happy is not rich and vice versa. Everyone who is generous or not kind is either not happy or not wise. Everyone who is funny is either generous or not funny. Everyone who is creative or rich is either not wise or not quiet. Everyone who is not funny is either not funny or generous. Everyone who is not old is either brave or not kind and vice versa. If someone is either not tall or brave then paul is not calm or not tall and vice versa. Everyone who is both humble and happy is old and vice versa. If someone is tall then someone is wise or not old and vice versa. If someone is not curious or old then someone is either not wise or not rich and vice versa. Susan is patient. Mary is curious or not humble. Someone is not calm. Fred is either not brave or not tall. Someone is curious. Someone is either patient or happy. Someone is not generous or not old. | Paul is quiet. | neutral | (((~calm(paul)<~>creative(paul)))<=>((quiet(paul)<~>humble(paul))))&
((~wise(alice))=>(~old(susan)))&
((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:(old(X)=>(~rich(X)&funny(X))))&
((generous(mary))=>((wise(mary)|~generous(mary))))&
(![X]:((~rich(X)&~happy(X))<=>(humble(X)|~old(X))))&
(![X]:((wise(X)&~happy(X))<=>~rich(X)))&
(![X]:((generous(X)|~kind(X))=>(~happy(X)<~>~wise(X))))&
(![X]:(funny(X)=>(generous(X)<~>~funny(X))))&
(![X]:((creative(X)|rich(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:(~funny(X)=>(~funny(X)<~>generous(X))))&
(![X]:(~old(X)<=>(brave(X)<~>~kind(X))))&
((?[X]:((~tall(X)<~>brave(X))))<=>((~calm(paul)|~tall(paul))))&
(![X]:((humble(X)&happy(X))<=>old(X)))&
((?[X]:(tall(X)))<=>(?[X]:((wise(X)|~old(X)))))&
((?[X]:((~curious(X)|old(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(patient(susan))&
((curious(mary)|~humble(mary)))&
(?[X]:(~calm(X)))&
((~brave(fred)<~>~tall(fred)))&
(?[X]:(curious(X)))&
(?[X]:((patient(X)<~>happy(X))))&
(?[X]:((~generous(X)|~old(X)))) | quiet(paul) | [] | null | 0 |
Everyone who is strong or brave is humble. Everyone who is both not generous and not calm is both not humble and calm. Everyone who is both generous and not kind is not humble. If someone is both not creative and wise then someone is either tall or not curious and vice versa. Everyone who is both not rich and not humble is either not generous or not strong and vice versa. Everyone who is creative is either not wise or old and vice versa. Everyone who is strong or brave is wise and vice versa. Everyone who is calm is old or generous and vice versa. If alice is kind then someone is either brave or not funny and vice versa. Everyone who is not happy or patient is either patient or tall. Everyone who is not generous or wise is not wise and vice versa. Everyone who is patient is generous or old. Everyone who is either funny or not curious is either not creative or generous and vice versa. Everyone who is both not brave and not kind is both not happy and wise and vice versa. Everyone who is rich is happy or not old. Everyone who is calm or quiet is not patient and vice versa. Alice is both not strong and happy. Lucy is quiet. Someone is patient or not happy. Someone is not quiet. John is either not strong or tall. Lucy is either not curious or rich. Fred is either brave or not strong. | Fred is not calm. | contradiction | (![X]:((strong(X)|brave(X))=>humble(X)))&
(![X]:((~generous(X)&~calm(X))=>(~humble(X)&calm(X))))&
(![X]:((generous(X)&~kind(X))=>~humble(X)))&
((?[X]:((~creative(X)&wise(X))))<=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:((~rich(X)&~humble(X))<=>(~generous(X)<~>~strong(X))))&
(![X]:(creative(X)<=>(~wise(X)<~>old(X))))&
(![X]:((strong(X)|brave(X))<=>wise(X)))&
(![X]:(calm(X)<=>(old(X)|generous(X))))&
((kind(alice))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:((~happy(X)|patient(X))=>(patient(X)<~>tall(X))))&
(![X]:((~generous(X)|wise(X))<=>~wise(X)))&
(![X]:(patient(X)=>(generous(X)|old(X))))&
(![X]:((funny(X)<~>~curious(X))<=>(~creative(X)<~>generous(X))))&
(![X]:((~brave(X)&~kind(X))<=>(~happy(X)&wise(X))))&
(![X]:(rich(X)=>(happy(X)|~old(X))))&
(![X]:((calm(X)|quiet(X))<=>~patient(X)))&
((~strong(alice)&happy(alice)))&
(quiet(lucy))&
(?[X]:((patient(X)|~happy(X))))&
(?[X]:(~quiet(X)))&
((~strong(john)<~>tall(john)))&
((~curious(lucy)<~>rich(lucy)))&
((brave(fred)<~>~strong(fred))) | ~calm(fred) | [
"p1",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 110212552619188290967931
% SZS output start Proof for 110212552619188290967931
2. ! [X0] : ((~calm(X0) & ~generous(X0)) => (calm(X0) & ~humble(X0))) [input p1]
8. ! [X0] : (calm(X0) <=> (generous(X0) | old(X0))) [input p7]
24. ~calm(fred) [input hypothesis]
27. ! [X0] : ((calm(X0) & ~humble(X0)) | (calm(X0) | generous(X0))) [ennf transformation 2]
28. ! [X0] : ((calm(X0) & ~humble(X0)) | calm(X0) | generous(X0)) [flattening 27]
46. ! [X0] : ((calm(X0) | (~generous(X0) & ~old(X0))) & ((generous(X0) | old(X0)) | ~calm(X0))) [nnf transformation 8]
47. ! [X0] : ((calm(X0) | (~generous(X0) & ~old(X0))) & (generous(X0) | old(X0) | ~calm(X0))) [flattening 46]
70. calm(X0) | calm(X0) | generous(X0) [cnf transformation 28]
93. calm(X0) | ~generous(X0) [cnf transformation 47]
133. ~calm(fred) [cnf transformation 24]
137. calm(X0) | generous(X0) [duplicate literal removal 70]
171. calm(X0) [subsumption resolution 93,137]
228. $false [subsumption resolution 133,171]
% SZS output end Proof for 110212552619188290967931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and not creative then susan is both patient and not patient.
Everyone who is both not rich and not curious is not kind.
Everyone who is either not humble or patient is not rich or old and vice versa.
If someone is both not wise and not tall then someone is either not humble or not calm.
If someone is both wise and happy then paul is both funny and happy and vice versa.
Everyone who is humble or not creative is both not humble and old and vice versa.
Everyone who is both not kind and generous is both quiet and not kind.
Everyone who is either not humble or brave is strong or happy and vice versa.
Everyone who is both kind and generous is either not brave or humble.
Everyone who is wise or strong is either not humble or not tall.
Everyone who is not patient or happy is kind.
Everyone who is either not tall or not humble is rich and vice versa.
Everyone who is either not humble or funny is happy or rich.
If susan is not brave then susan is both not strong and happy and vice versa.
If fred is both brave and not generous then someone is both quiet and old and vice versa.
If someone is quiet then someone is not kind and vice versa.
Someone is either strong or not funny.
Someone is either not kind or calm.
Lucy is calm.
Someone is not happy.
Someone is generous.
Fred is creative or tall.
Lucy is both not funny and generous.
Someone is not tall. | Susan is not curious. | neutral | ((?[X]:((curious(X)&~creative(X))))=>((patient(susan)&~patient(susan))))&
(![X]:((~rich(X)&~curious(X))=>~kind(X)))&
(![X]:((~humble(X)<~>patient(X))<=>(~rich(X)|old(X))))&
((?[X]:((~wise(X)&~tall(X))))=>(?[X]:((~humble(X)<~>~calm(X)))))&
((?[X]:((wise(X)&happy(X))))<=>((funny(paul)&happy(paul))))&
(![X]:((humble(X)|~creative(X))<=>(~humble(X)&old(X))))&
(![X]:((~kind(X)&generous(X))=>(quiet(X)&~kind(X))))&
(![X]:((~humble(X)<~>brave(X))<=>(strong(X)|happy(X))))&
(![X]:((kind(X)&generous(X))=>(~brave(X)<~>humble(X))))&
(![X]:((wise(X)|strong(X))=>(~humble(X)<~>~tall(X))))&
(![X]:((~patient(X)|happy(X))=>kind(X)))&
(![X]:((~tall(X)<~>~humble(X))<=>rich(X)))&
(![X]:((~humble(X)<~>funny(X))=>(happy(X)|rich(X))))&
((~brave(susan))<=>((~strong(susan)&happy(susan))))&
(((brave(fred)&~generous(fred)))<=>(?[X]:((quiet(X)&old(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:(~kind(X))))&
(?[X]:((strong(X)<~>~funny(X))))&
(?[X]:((~kind(X)<~>calm(X))))&
(calm(lucy))&
(?[X]:(~happy(X)))&
(?[X]:(generous(X)))&
((creative(fred)|tall(fred)))&
((~funny(lucy)&generous(lucy)))&
(?[X]:(~tall(X))) | ~curious(susan) | [] | null | 0 |
Everyone who is not creative or not quiet is not brave.
If someone is not tall or not kind then someone is not kind or creative.
If someone is not funny then fred is not kind or strong.
If someone is both not patient and patient then someone is both not brave and not humble.
Everyone who is both wise and patient is both quiet and not happy and vice versa.
Everyone who is funny is either tall or rich and vice versa.
Everyone who is brave or not curious is not patient and vice versa.
Everyone who is not old or not strong is tall or curious and vice versa.
If someone is tall then someone is both not quiet and generous and vice versa.
If someone is both not strong and strong then someone is not calm or humble and vice versa.
Everyone who is both brave and not tall is either not wise or calm.
Everyone who is not curious or curious is both happy and not brave and vice versa.
Everyone who is either quiet or not patient is both not generous and not calm and vice versa.
Everyone who is happy or strong is both not patient and old.
Everyone who is either not brave or patient is either not rich or curious.
Someone is both calm and wise.
Lucy is rich or not tall.
Mary is wise or happy.
Someone is curious or old. | Fred is not strong. | contradiction | (![X]:((~creative(X)|~quiet(X))=>~brave(X)))&
((?[X]:((~tall(X)|~kind(X))))=>(?[X]:((~kind(X)|creative(X)))))&
((?[X]:(~funny(X)))=>((~kind(fred)|strong(fred))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((wise(X)&patient(X))<=>(quiet(X)&~happy(X))))&
(![X]:(funny(X)<=>(tall(X)<~>rich(X))))&
(![X]:((brave(X)|~curious(X))<=>~patient(X)))&
(![X]:((~old(X)|~strong(X))<=>(tall(X)|curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((~quiet(X)&generous(X)))))&
((?[X]:((~strong(X)&strong(X))))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((brave(X)&~tall(X))=>(~wise(X)<~>calm(X))))&
(![X]:((~curious(X)|curious(X))<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)<~>~patient(X))<=>(~generous(X)&~calm(X))))&
(![X]:((happy(X)|strong(X))=>(~patient(X)&old(X))))&
(![X]:((~brave(X)<~>patient(X))=>(~rich(X)<~>curious(X))))&
(?[X]:((calm(X)&wise(X))))&
((rich(lucy)|~tall(lucy)))&
((wise(mary)|happy(mary)))&
(?[X]:((curious(X)|old(X)))) | ~strong(fred) | [
"p6",
"p7",
"p8",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1728397348400032908784038
% SZS output start Proof for 1728397348400032908784038
7. ! [X0] : ((~curious(X0) | brave(X0)) <=> ~patient(X0)) [input p6]
8. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (curious(X0) | tall(X0))) [input p7]
9. ? [X0] : tall(X0) <=> ? [X0] : (generous(X0) & ~quiet(X0)) [input p8]
12. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~brave(X0) & happy(X0))) [input p11]
13. ! [X0] : ((quiet(X0) <~> ~patient(X0)) <=> (~calm(X0) & ~generous(X0))) [input p12]
14. ! [X0] : ((strong(X0) | happy(X0)) => (old(X0) & ~patient(X0))) [input p13]
20. ~strong(fred) [input hypothesis]
23. ? [X0] : tall(X0) <=> ? [X1] : (generous(X1) & ~quiet(X1)) [rectify 9]
34. ! [X0] : ((old(X0) & ~patient(X0)) | (~strong(X0) & ~happy(X0))) [ennf transformation 14]
41. ! [X0] : (((~curious(X0) | brave(X0)) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((~curious(X0) | brave(X0) | patient(X0)) & (~patient(X0) | (curious(X0) & ~brave(X0)))) [flattening 41]
43. ! [X0] : (((~strong(X0) | ~old(X0)) | (~curious(X0) & ~tall(X0))) & ((curious(X0) | tall(X0)) | (strong(X0) & old(X0)))) [nnf transformation 8]
44. ! [X0] : ((~strong(X0) | ~old(X0) | (~curious(X0) & ~tall(X0))) & (curious(X0) | tall(X0) | (strong(X0) & old(X0)))) [flattening 43]
45. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X1] : (generous(X1) & ~quiet(X1)) | ! [X0] : ~tall(X0)) [nnf transformation 23]
46. (? [X0] : tall(X0) | ! [X1] : (~generous(X1) | quiet(X1))) & (? [X2] : (generous(X2) & ~quiet(X2)) | ! [X3] : ~tall(X3)) [rectify 45]
47. ? [X0] : tall(X0) => tall(sK1) [choice axiom]
48. ? [X2] : (generous(X2) & ~quiet(X2)) => (generous(sK2) & ~quiet(sK2)) [choice axiom]
49. (tall(sK1) | ! [X1] : (~generous(X1) | quiet(X1))) & ((generous(sK2) & ~quiet(sK2)) | ! [X3] : ~tall(X3)) [skolemisation 46,48,47]
56. ! [X0] : (((curious(X0) | ~curious(X0)) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [nnf transformation 12]
57. ! [X0] : ((curious(X0) | ~curious(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | (~curious(X0) & curious(X0)))) [flattening 56]
58. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | (calm(X0) | generous(X0))) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [nnf transformation 13]
59. ! [X0] : ((((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | calm(X0) | generous(X0)) & ((~calm(X0) & ~generous(X0)) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0))))) [flattening 58]
74. ~curious(X0) | brave(X0) | patient(X0) [cnf transformation 42]
76. curious(X0) | tall(X0) | strong(X0) [cnf transformation 44]
79. ~quiet(sK2) | ~tall(X3) [cnf transformation 49]
80. generous(sK2) | ~tall(X3) [cnf transformation 49]
89. happy(X0) | curious(X0) [cnf transformation 57]
90. ~curious(X0) | happy(X0) [cnf transformation 57]
91. ~brave(X0) | curious(X0) [cnf transformation 57]
92. ~curious(X0) | ~brave(X0) [cnf transformation 57]
95. ~generous(X0) | quiet(X0) | patient(X0) [cnf transformation 59]
100. ~patient(X0) | ~happy(X0) [cnf transformation 34]
113. ~strong(fred) [cnf transformation 20]
123. 3 <=> ! [X3] : ~tall(X3) [avatar definition]
124. ~tall(X3) <- (3) [avatar component clause 123]
126. 4 <=> generous(sK2) [avatar definition]
128. generous(sK2) <- (4) [avatar component clause 126]
129. 3 | 4 [avatar split clause 80,126,123]
131. 5 <=> quiet(sK2) [avatar definition]
134. 3 | ~5 [avatar split clause 79,131,123]
149. ~brave(X0) [subsumption resolution 91,92]
150. happy(X0) [subsumption resolution 89,90]
152. ~patient(X0) [subsumption resolution 100,150]
166. tall(X0) | strong(X0) | brave(X0) | patient(X0) [resolution 76,74]
169. tall(X0) | strong(X0) | patient(X0) [subsumption resolution 166,149]
170. strong(X0) | tall(X0) [subsumption resolution 169,152]
171. tall(fred) [resolution 170,113]
180. quiet(sK2) | patient(sK2) <- (4) [resolution 95,128]
184. quiet(sK2) <- (4) [subsumption resolution 180,152]
185. 5 | ~4 [avatar split clause 184,126,131]
187. $false <- (3) [resolution 124,171]
188. ~3 [avatar contradiction clause 187]
190. $false [avatar sat refutation 129,134,185,188]
% SZS output end Proof for 1728397348400032908784038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not curious is kind and vice versa.
Everyone who is not strong is wise and vice versa.
If someone is not happy or not patient then someone is not creative.
If someone is brave then lucy is either happy or not kind.
If someone is both creative and not brave then someone is old or strong.
Everyone who is either funny or curious is both happy and rich and vice versa.
Everyone who is either not funny or not old is either strong or not strong and vice versa.
Everyone who is rich is both kind and funny and vice versa.
If mary is creative then mary is quiet or curious.
Everyone who is calm is not creative or wise.
Everyone who is both not kind and funny is not brave or not old and vice versa.
Everyone who is either calm or not humble is both not quiet and strong and vice versa.
If someone is not strong or calm then fred is both not happy and funny.
Everyone who is not calm or wise is both happy and not wise and vice versa.
If alice is both funny and tall then someone is either happy or not strong.
Someone is not happy or creative.
Someone is either generous or not patient.
Susan is brave or not funny.
John is not creative.
Someone is tall.
John is humble.
Someone is either happy or not generous. | John is not quiet. | contradiction | (![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:(~strong(X)<=>wise(X)))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:(brave(X)))=>((happy(lucy)<~>~kind(lucy))))&
((?[X]:((creative(X)&~brave(X))))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((funny(X)<~>curious(X))<=>(happy(X)&rich(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(rich(X)<=>(kind(X)&funny(X))))&
((creative(mary))=>((quiet(mary)|curious(mary))))&
(![X]:(calm(X)=>(~creative(X)|wise(X))))&
(![X]:((~kind(X)&funny(X))<=>(~brave(X)|~old(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(~quiet(X)&strong(X))))&
((?[X]:((~strong(X)|calm(X))))=>((~happy(fred)&funny(fred))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~wise(X))))&
(((funny(alice)&tall(alice)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((generous(X)<~>~patient(X))))&
((brave(susan)|~funny(susan)))&
(~creative(john))&
(?[X]:(tall(X)))&
(humble(john))&
(?[X]:((happy(X)<~>~generous(X)))) | ~quiet(john) | [
"p0",
"p1",
"p6",
"p10",
"p11",
"p12",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1589106623924172262446042
% SZS output start Proof for 1589106623924172262446042
1. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p0]
2. ! [X0] : (~strong(X0) <=> wise(X0)) [input p1]
7. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p6]
11. ! [X0] : ((funny(X0) & ~kind(X0)) <=> (~old(X0) | ~brave(X0))) [input p10]
12. ! [X0] : ((calm(X0) <~> ~humble(X0)) <=> (strong(X0) & ~quiet(X0))) [input p11]
13. ? [X0] : (calm(X0) | ~strong(X0)) => (funny(fred) & ~happy(fred)) [input p12]
14. ! [X0] : ((wise(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p13]
21. humble(john) [input p20]
23. ~quiet(john) [input hypothesis]
33. (funny(fred) & ~happy(fred)) | ! [X0] : (~calm(X0) & strong(X0)) [ennf transformation 13]
36. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 36]
38. ! [X0] : ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))) [nnf transformation 2]
48. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 7]
51. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | (~funny(X0) | kind(X0)))) [nnf transformation 11]
52. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | ~funny(X0) | kind(X0))) [flattening 51]
53. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | (~strong(X0) | quiet(X0))) & ((strong(X0) & ~quiet(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [nnf transformation 12]
54. ! [X0] : ((((humble(X0) | ~calm(X0)) & (~humble(X0) | calm(X0))) | ~strong(X0) | quiet(X0)) & ((strong(X0) & ~quiet(X0)) | ((calm(X0) | humble(X0)) & (~humble(X0) | ~calm(X0))))) [flattening 53]
55. ! [X0] : (((wise(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [flattening 55]
70. ~strong(X0) | kind(X0) [cnf transformation 37]
73. wise(X0) | strong(X0) [cnf transformation 38]
90. ~old(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 48]
91. ~old(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 48]
101. ~kind(X0) | old(X0) [cnf transformation 52]
108. ~humble(X0) | calm(X0) | ~strong(X0) | quiet(X0) [cnf transformation 54]
113. funny(fred) | ~calm(X0) [cnf transformation 33]
117. ~wise(X0) | ~wise(X0) [cnf transformation 56]
127. humble(john) [cnf transformation 21]
130. ~quiet(john) [cnf transformation 23]
131. ~wise(X0) [duplicate literal removal 117]
133. ~old(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 90]
134. ~funny(X0) | ~old(X0) | strong(X0) [duplicate literal removal 91]
175. ~funny(X0) | ~old(X0) [subsumption resolution 133,134]
190. 13 <=> ! [X0] : ~calm(X0) [avatar definition]
191. ~calm(X0) <- (13) [avatar component clause 190]
193. 14 <=> funny(fred) [avatar definition]
195. funny(fred) <- (14) [avatar component clause 193]
196. 13 | 14 [avatar split clause 113,193,190]
198. 15 <=> ! [X0] : strong(X0) [avatar definition]
199. strong(X0) <- (15) [avatar component clause 198]
256. strong(X0) [resolution 73,131]
257. 15 [avatar split clause 256,198]
258. kind(X0) <- (15) [resolution 199,70]
266. old(X0) <- (15) [resolution 101,258]
270. ~old(fred) <- (14) [resolution 175,195]
273. $false <- (14, 15) [subsumption resolution 270,266]
274. ~14 | ~15 [avatar contradiction clause 273]
311. calm(john) | ~strong(john) | quiet(john) [resolution 108,127]
314. ~strong(john) | quiet(john) <- (13) [subsumption resolution 311,191]
315. quiet(john) <- (13, 15) [subsumption resolution 314,199]
316. $false <- (13, 15) [subsumption resolution 315,130]
317. ~13 | ~15 [avatar contradiction clause 316]
318. $false [avatar sat refutation 196,257,274,317]
% SZS output end Proof for 1589106623924172262446042
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and strong then fred is either funny or not calm.
Everyone who is strong is both creative and not old.
Everyone who is either tall or not wise is brave or not patient and vice versa.
Everyone who is both not creative and not humble is both tall and brave.
Everyone who is both not calm and old is not funny or not strong and vice versa.
If someone is either not patient or wise then someone is not kind or calm.
If susan is not strong or not happy then someone is not kind.
Everyone who is either strong or not curious is not funny or happy.
If someone is both not funny and creative then someone is funny and vice versa.
If john is both old and not humble then someone is tall and vice versa.
Everyone who is either quiet or kind is not calm.
If john is not generous or calm then someone is both not brave and not kind and vice versa.
If susan is both kind and not funny then paul is tall and vice versa.
Everyone who is not funny or not tall is not creative and vice versa.
If someone is calm or not kind then someone is either quiet or brave and vice versa.
Everyone who is either not patient or not brave is generous and vice versa.
Someone is not calm.
Paul is kind or not funny.
Alice is either patient or tall.
Paul is not calm.
Susan is not quiet or not kind.
Someone is not generous.
Paul is not generous or not old. | Susan is not humble. | neutral | ((?[X]:((generous(X)&strong(X))))=>((funny(fred)<~>~calm(fred))))&
(![X]:(strong(X)=>(creative(X)&~old(X))))&
(![X]:((tall(X)<~>~wise(X))<=>(brave(X)|~patient(X))))&
(![X]:((~creative(X)&~humble(X))=>(tall(X)&brave(X))))&
(![X]:((~calm(X)&old(X))<=>(~funny(X)|~strong(X))))&
((?[X]:((~patient(X)<~>wise(X))))=>(?[X]:((~kind(X)|calm(X)))))&
(((~strong(susan)|~happy(susan)))=>(?[X]:(~kind(X))))&
(![X]:((strong(X)<~>~curious(X))=>(~funny(X)|happy(X))))&
((?[X]:((~funny(X)&creative(X))))<=>(?[X]:(funny(X))))&
(((old(john)&~humble(john)))<=>(?[X]:(tall(X))))&
(![X]:((quiet(X)<~>kind(X))=>~calm(X)))&
(((~generous(john)|calm(john)))<=>(?[X]:((~brave(X)&~kind(X)))))&
(((kind(susan)&~funny(susan)))<=>(tall(paul)))&
(![X]:((~funny(X)|~tall(X))<=>~creative(X)))&
((?[X]:((calm(X)|~kind(X))))<=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>generous(X)))&
(?[X]:(~calm(X)))&
((kind(paul)|~funny(paul)))&
((patient(alice)<~>tall(alice)))&
(~calm(paul))&
((~quiet(susan)|~kind(susan)))&
(?[X]:(~generous(X)))&
((~generous(paul)|~old(paul))) | ~humble(susan) | [] | null | 0 |
If john is either wise or not calm then susan is either happy or rich and vice versa. Everyone who is either not calm or not wise is both not humble and not wise and vice versa. If john is both not humble and happy then someone is rich or funny and vice versa. If someone is either not old or not quiet then lucy is not generous or funny. If someone is not kind or not tall then lucy is not kind or calm. If someone is either rich or brave then paul is not generous. Everyone who is strong or old is both calm and not patient. Everyone who is either creative or old is happy. Everyone who is generous or not wise is not creative or strong and vice versa. If someone is not strong then fred is not creative. If paul is both not tall and quiet then someone is quiet or not wise and vice versa. Everyone who is either humble or not wise is both not funny and wise and vice versa. Everyone who is either not strong or not tall is either funny or not patient. Everyone who is either calm or not generous is both calm and not old and vice versa. Everyone who is funny is not creative. If john is happy then someone is both funny and not calm. Someone is not tall or not quiet. Lucy is not calm or patient. John is not tall or humble. Mary is generous or curious. John is tall. Someone is kind or not wise. Paul is brave. | Susan is happy. | entailment | (((wise(john)<~>~calm(john)))<=>((happy(susan)<~>rich(susan))))&
(![X]:((~calm(X)<~>~wise(X))<=>(~humble(X)&~wise(X))))&
(((~humble(john)&happy(john)))<=>(?[X]:((rich(X)|funny(X)))))&
((?[X]:((~old(X)<~>~quiet(X))))=>((~generous(lucy)|funny(lucy))))&
((?[X]:((~kind(X)|~tall(X))))=>((~kind(lucy)|calm(lucy))))&
((?[X]:((rich(X)<~>brave(X))))=>(~generous(paul)))&
(![X]:((strong(X)|old(X))=>(calm(X)&~patient(X))))&
(![X]:((creative(X)<~>old(X))=>happy(X)))&
(![X]:((generous(X)|~wise(X))<=>(~creative(X)|strong(X))))&
((?[X]:(~strong(X)))=>(~creative(fred)))&
(((~tall(paul)&quiet(paul)))<=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:((humble(X)<~>~wise(X))<=>(~funny(X)&wise(X))))&
(![X]:((~strong(X)<~>~tall(X))=>(funny(X)<~>~patient(X))))&
(![X]:((calm(X)<~>~generous(X))<=>(calm(X)&~old(X))))&
(![X]:(funny(X)=>~creative(X)))&
((happy(john))=>(?[X]:((funny(X)&~calm(X)))))&
(?[X]:((~tall(X)|~quiet(X))))&
((~calm(lucy)|patient(lucy)))&
((~tall(john)|humble(john)))&
((generous(mary)|curious(mary)))&
(tall(john))&
(?[X]:((kind(X)|~wise(X))))&
(brave(paul)) | happy(susan) | [
"p0",
"p1",
"p2",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8043802344183318886661378
% SZS output start Proof for 8043802344183318886661378
1. (wise(john) <~> ~calm(john)) <=> (happy(susan) <~> rich(susan)) [input p0]
2. ! [X0] : ((~calm(X0) <~> ~wise(X0)) <=> (~wise(X0) & ~humble(X0))) [input p1]
3. (happy(john) & ~humble(john)) <=> ? [X0] : (funny(X0) | rich(X0)) [input p2]
19. humble(john) | ~tall(john) [input p18]
21. tall(john) [input p20]
24. ~happy(susan) [input hypothesis]
37. (((calm(john) | ~wise(john)) & (~calm(john) | wise(john))) | ((happy(susan) | ~rich(susan)) & (rich(susan) | ~happy(susan)))) & (((~rich(susan) | ~happy(susan)) & (rich(susan) | happy(susan))) | ((wise(john) | calm(john)) & (~calm(john) | ~wise(john)))) [nnf transformation 1]
38. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | (wise(X0) | humble(X0))) & ((~wise(X0) & ~humble(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [nnf transformation 2]
39. ! [X0] : ((((wise(X0) | calm(X0)) & (~wise(X0) | ~calm(X0))) | wise(X0) | humble(X0)) & ((~wise(X0) & ~humble(X0)) | ((~calm(X0) | wise(X0)) & (~wise(X0) | calm(X0))))) [flattening 38]
40. ((happy(john) & ~humble(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & (? [X0] : (funny(X0) | rich(X0)) | (~happy(john) | humble(john))) [nnf transformation 3]
41. ((happy(john) & ~humble(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & (? [X0] : (funny(X0) | rich(X0)) | ~happy(john) | humble(john)) [flattening 40]
42. ((happy(john) & ~humble(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & (? [X1] : (funny(X1) | rich(X1)) | ~happy(john) | humble(john)) [rectify 41]
43. ? [X1] : (funny(X1) | rich(X1)) => (funny(sK0) | rich(sK0)) [choice axiom]
44. ((happy(john) & ~humble(john)) | ! [X0] : (~funny(X0) & ~rich(X0))) & ((funny(sK0) | rich(sK0)) | ~happy(john) | humble(john)) [skolemisation 42,43]
66. rich(susan) | happy(susan) | ~calm(john) | ~wise(john) [cnf transformation 37]
67. rich(susan) | happy(susan) | wise(john) | calm(john) [cnf transformation 37]
75. ~humble(X0) | ~calm(X0) | wise(X0) [cnf transformation 39]
76. ~wise(X0) | ~wise(X0) | calm(X0) [cnf transformation 39]
81. ~humble(john) | ~rich(X0) [cnf transformation 44]
128. humble(john) | ~tall(john) [cnf transformation 19]
129. tall(john) [cnf transformation 21]
132. ~happy(susan) [cnf transformation 24]
137. ~wise(X0) | calm(X0) [duplicate literal removal 76]
140. 1 <=> rich(susan) [avatar definition]
141. rich(susan) <- (1) [avatar component clause 140]
144. 2 <=> happy(susan) [avatar definition]
148. 3 <=> wise(john) [avatar definition]
149. wise(john) <- (3) [avatar component clause 148]
150. ~wise(john) <- (~3) [avatar component clause 148]
152. 4 <=> calm(john) [avatar definition]
154. calm(john) <- (4) [avatar component clause 152]
161. 4 | 3 | 2 | 1 [avatar split clause 67,140,144,148,152]
162. ~3 | ~4 | 2 | 1 [avatar split clause 66,140,144,152,148]
172. 7 <=> ! [X0] : ~rich(X0) [avatar definition]
173. ~rich(X0) <- (7) [avatar component clause 172]
176. 8 <=> humble(john) [avatar definition]
177. humble(john) <- (8) [avatar component clause 176]
180. 7 | ~8 [avatar split clause 81,176,172]
297. 35 <=> tall(john) [avatar definition]
300. ~35 | 8 [avatar split clause 128,176,297]
301. 35 [avatar split clause 129,297]
311. ~2 [avatar split clause 132,144]
318. calm(john) <- (3) [resolution 137,149]
321. 4 | ~3 [avatar split clause 318,148,152]
322. $false <- (1, 7) [subsumption resolution 141,173]
323. ~1 | ~7 [avatar contradiction clause 322]
329. ~calm(john) | wise(john) <- (8) [resolution 75,177]
332. wise(john) <- (4, 8) [subsumption resolution 329,154]
333. $false <- (~3, 4, 8) [subsumption resolution 332,150]
334. 3 | ~4 | ~8 [avatar contradiction clause 333]
335. $false [avatar sat refutation 161,162,180,300,301,311,321,323,334]
% SZS output end Proof for 8043802344183318886661378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or rich is both curious and not old. Everyone who is generous or not kind is quiet. If paul is either funny or not kind then someone is either not curious or calm. Everyone who is both not old and not kind is both not creative and old and vice versa. Everyone who is both not wise and tall is not old. Everyone who is funny or not strong is not happy. Everyone who is patient or not kind is both not quiet and not generous and vice versa. Everyone who is generous is tall or happy and vice versa. If someone is curious or not rich then fred is both kind and not funny. Everyone who is not tall is not calm. Everyone who is not quiet or rich is brave or not strong. Everyone who is rich or not happy is either strong or generous and vice versa. If mary is strong or curious then john is creative or not tall and vice versa. Everyone who is not happy or old is tall. Everyone who is either calm or not brave is not patient or not creative and vice versa. Everyone who is either generous or not rich is both not creative and not funny. Susan is not funny. Someone is either not strong or creative. Fred is either not tall or not quiet. Alice is not brave. Someone is either not tall or quiet. Someone is not rich. Susan is either not strong or rich. | Fred is not strong. | contradiction | (![X]:((funny(X)|rich(X))=>(curious(X)&~old(X))))&
(![X]:((generous(X)|~kind(X))=>quiet(X)))&
(((funny(paul)<~>~kind(paul)))=>(?[X]:((~curious(X)<~>calm(X)))))&
(![X]:((~old(X)&~kind(X))<=>(~creative(X)&old(X))))&
(![X]:((~wise(X)&tall(X))=>~old(X)))&
(![X]:((funny(X)|~strong(X))=>~happy(X)))&
(![X]:((patient(X)|~kind(X))<=>(~quiet(X)&~generous(X))))&
(![X]:(generous(X)<=>(tall(X)|happy(X))))&
((?[X]:((curious(X)|~rich(X))))=>((kind(fred)&~funny(fred))))&
(![X]:(~tall(X)=>~calm(X)))&
(![X]:((~quiet(X)|rich(X))=>(brave(X)|~strong(X))))&
(![X]:((rich(X)|~happy(X))<=>(strong(X)<~>generous(X))))&
(((strong(mary)|curious(mary)))<=>((creative(john)|~tall(john))))&
(![X]:((~happy(X)|old(X))=>tall(X)))&
(![X]:((calm(X)<~>~brave(X))<=>(~patient(X)|~creative(X))))&
(![X]:((generous(X)<~>~rich(X))=>(~creative(X)&~funny(X))))&
(~funny(susan))&
(?[X]:((~strong(X)<~>creative(X))))&
((~tall(fred)<~>~quiet(fred)))&
(~brave(alice))&
(?[X]:((~tall(X)<~>quiet(X))))&
(?[X]:(~rich(X)))&
((~strong(susan)<~>rich(susan))) | ~strong(fred) | [
"p1",
"p5",
"p7",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6140417256946691487400415
% SZS output start Proof for 6140417256946691487400415
2. ! [X0] : ((~kind(X0) | generous(X0)) => quiet(X0)) [input p1]
6. ! [X0] : ((~strong(X0) | funny(X0)) => ~happy(X0)) [input p5]
8. ! [X0] : (generous(X0) <=> (happy(X0) | tall(X0))) [input p7]
14. ! [X0] : ((old(X0) | ~happy(X0)) => tall(X0)) [input p13]
19. ~tall(fred) <~> ~quiet(fred) [input p18]
24. ~strong(fred) [input hypothesis]
27. ! [X0] : (quiet(X0) | (kind(X0) & ~generous(X0))) [ennf transformation 2]
29. ! [X0] : (~happy(X0) | (strong(X0) & ~funny(X0))) [ennf transformation 6]
34. ! [X0] : (tall(X0) | (~old(X0) & happy(X0))) [ennf transformation 14]
43. ! [X0] : ((generous(X0) | (~happy(X0) & ~tall(X0))) & ((happy(X0) | tall(X0)) | ~generous(X0))) [nnf transformation 8]
44. ! [X0] : ((generous(X0) | (~happy(X0) & ~tall(X0))) & (happy(X0) | tall(X0) | ~generous(X0))) [flattening 43]
55. (quiet(fred) | tall(fred)) & (~quiet(fred) | ~tall(fred)) [nnf transformation 19]
66. ~generous(X0) | quiet(X0) [cnf transformation 27]
77. ~happy(X0) | strong(X0) [cnf transformation 29]
84. ~tall(X0) | generous(X0) [cnf transformation 44]
103. happy(X0) | tall(X0) [cnf transformation 34]
118. ~quiet(fred) | ~tall(fred) [cnf transformation 55]
126. ~strong(fred) [cnf transformation 24]
196. 14 <=> tall(fred) [avatar definition]
197. ~tall(fred) <- (~14) [avatar component clause 196]
198. tall(fred) <- (14) [avatar component clause 196]
200. 15 <=> quiet(fred) [avatar definition]
201. ~quiet(fred) <- (~15) [avatar component clause 200]
204. ~14 | ~15 [avatar split clause 118,200,196]
230. generous(fred) <- (14) [resolution 84,198]
234. quiet(fred) <- (14) [resolution 230,66]
235. $false <- (14, ~15) [subsumption resolution 234,201]
236. ~14 | 15 [avatar contradiction clause 235]
238. strong(X1) | tall(X1) [resolution 103,77]
252. tall(fred) [resolution 238,126]
256. $false <- (~14) [subsumption resolution 252,197]
257. 14 [avatar contradiction clause 256]
258. $false [avatar sat refutation 204,236,257]
% SZS output end Proof for 6140417256946691487400415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not rich or generous then fred is happy and vice versa. If someone is not happy then lucy is either tall or not generous and vice versa. Everyone who is kind or wise is generous and vice versa. If someone is not strong then lucy is either not old or not curious and vice versa. Everyone who is both curious and kind is curious or patient and vice versa. Everyone who is humble or creative is both strong and brave. If alice is wise then someone is not rich or not humble and vice versa. If lucy is both not calm and rich then someone is either kind or rich. Everyone who is strong is either not curious or old. Everyone who is creative is either not curious or not old and vice versa. Everyone who is tall or brave is either tall or rich and vice versa. Everyone who is both not old and not humble is brave and vice versa. If fred is both happy and strong then susan is not curious. Fred is not patient or not strong. Someone is both not tall and not calm. Someone is not calm. Someone is either not old or not tall. Paul is not funny or wise. Someone is not humble. | Fred is not strong. | contradiction | ((?[X]:((~rich(X)<~>generous(X))))<=>(happy(fred)))&
((?[X]:(~happy(X)))<=>((tall(lucy)<~>~generous(lucy))))&
(![X]:((kind(X)|wise(X))<=>generous(X)))&
((?[X]:(~strong(X)))<=>((~old(lucy)<~>~curious(lucy))))&
(![X]:((curious(X)&kind(X))<=>(curious(X)|patient(X))))&
(![X]:((humble(X)|creative(X))=>(strong(X)&brave(X))))&
((wise(alice))<=>(?[X]:((~rich(X)|~humble(X)))))&
(((~calm(lucy)&rich(lucy)))=>(?[X]:((kind(X)<~>rich(X)))))&
(![X]:(strong(X)=>(~curious(X)<~>old(X))))&
(![X]:(creative(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((tall(X)|brave(X))<=>(tall(X)<~>rich(X))))&
(![X]:((~old(X)&~humble(X))<=>brave(X)))&
(((happy(fred)&strong(fred)))=>(~curious(susan)))&
((~patient(fred)|~strong(fred)))&
(?[X]:((~tall(X)&~calm(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~old(X)<~>~tall(X))))&
((~funny(paul)|wise(paul)))&
(?[X]:(~humble(X))) | ~strong(fred) | [
"p3",
"p5",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5229130893228259057196720
% SZS output start Proof for 5229130893228259057196720
4. ? [X0] : ~strong(X0) <=> (~old(lucy) <~> ~curious(lucy)) [input p3]
6. ! [X0] : ((creative(X0) | humble(X0)) => (brave(X0) & strong(X0))) [input p5]
9. ! [X0] : (strong(X0) => (~curious(X0) <~> old(X0))) [input p8]
10. ! [X0] : (creative(X0) <=> (~curious(X0) <~> ~old(X0))) [input p9]
20. ~strong(fred) [input hypothesis]
21. ! [X0] : ((~curious(X0) <~> ~old(X0)) => creative(X0)) [unused predicate definition removal 10]
23. ! [X0] : ((brave(X0) & strong(X0)) | (~creative(X0) & ~humble(X0))) [ennf transformation 6]
26. ! [X0] : ((~curious(X0) <~> old(X0)) | ~strong(X0)) [ennf transformation 9]
27. ! [X0] : (creative(X0) | (~curious(X0) <=> ~old(X0))) [ennf transformation 21]
40. (? [X0] : ~strong(X0) | ((~old(lucy) | curious(lucy)) & (~curious(lucy) | old(lucy)))) & (((curious(lucy) | old(lucy)) & (~curious(lucy) | ~old(lucy))) | ! [X0] : strong(X0)) [nnf transformation 4]
41. (? [X0] : ~strong(X0) | ((~old(lucy) | curious(lucy)) & (~curious(lucy) | old(lucy)))) & (((curious(lucy) | old(lucy)) & (~curious(lucy) | ~old(lucy))) | ! [X1] : strong(X1)) [rectify 40]
42. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
43. (~strong(sK2) | ((~old(lucy) | curious(lucy)) & (~curious(lucy) | old(lucy)))) & (((curious(lucy) | old(lucy)) & (~curious(lucy) | ~old(lucy))) | ! [X1] : strong(X1)) [skolemisation 41,42]
53. ! [X0] : (((~old(X0) | curious(X0)) & (old(X0) | ~curious(X0))) | ~strong(X0)) [nnf transformation 26]
54. ! [X0] : (creative(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) [nnf transformation 27]
79. ~curious(lucy) | ~old(lucy) | strong(X1) [cnf transformation 43]
80. curious(lucy) | old(lucy) | strong(X1) [cnf transformation 43]
89. ~creative(X0) | strong(X0) [cnf transformation 23]
97. ~curious(X0) | old(X0) | ~strong(X0) [cnf transformation 53]
98. ~old(X0) | curious(X0) | ~strong(X0) [cnf transformation 53]
99. ~old(X0) | creative(X0) | curious(X0) [cnf transformation 54]
100. ~curious(X0) | creative(X0) | old(X0) [cnf transformation 54]
118. ~strong(fred) [cnf transformation 20]
163. 10 <=> curious(lucy) [avatar definition]
164. ~curious(lucy) <- (~10) [avatar component clause 163]
165. curious(lucy) <- (10) [avatar component clause 163]
167. 11 <=> old(lucy) [avatar definition]
168. old(lucy) <- (11) [avatar component clause 167]
169. ~old(lucy) <- (~11) [avatar component clause 167]
177. 13 <=> ! [X1] : strong(X1) [avatar definition]
178. strong(X1) <- (13) [avatar component clause 177]
179. 13 | 11 | 10 [avatar split clause 80,163,167,177]
180. 13 | ~11 | ~10 [avatar split clause 79,163,167,177]
223. 23 <=> strong(fred) [avatar definition]
225. ~strong(fred) <- (~23) [avatar component clause 223]
246. ~23 [avatar split clause 118,223]
261. old(lucy) | ~strong(lucy) <- (10) [resolution 97,165]
262. ~strong(lucy) <- (10, ~11) [subsumption resolution 261,169]
280. creative(lucy) | old(lucy) <- (10) [resolution 100,165]
281. creative(lucy) <- (10, ~11) [subsumption resolution 280,169]
284. strong(lucy) <- (10, ~11) [resolution 281,89]
285. $false <- (10, ~11) [subsumption resolution 284,262]
286. ~10 | 11 [avatar contradiction clause 285]
296. creative(lucy) | curious(lucy) <- (11) [resolution 168,99]
297. curious(lucy) | ~strong(lucy) <- (11) [resolution 168,98]
298. creative(lucy) <- (~10, 11) [subsumption resolution 296,164]
299. ~strong(lucy) <- (~10, 11) [subsumption resolution 297,164]
303. strong(lucy) <- (~10, 11) [resolution 298,89]
304. $false <- (~10, 11) [subsumption resolution 303,299]
305. 10 | ~11 [avatar contradiction clause 304]
319. $false <- (13, ~23) [resolution 178,225]
324. ~13 | 23 [avatar contradiction clause 319]
325. $false [avatar sat refutation 179,180,246,286,305,324]
% SZS output end Proof for 5229130893228259057196720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either not quiet or not tall then someone is rich or humble and vice versa.
If fred is either not brave or not kind then someone is both not tall and kind and vice versa.
If mary is not tall then paul is not strong and vice versa.
Everyone who is both not rich and not generous is either not kind or patient and vice versa.
Everyone who is both calm and humble is not humble or not wise and vice versa.
Everyone who is either old or not old is both funny and wise.
Everyone who is wise or not kind is not strong.
Everyone who is tall is strong or old and vice versa.
If fred is either creative or not patient then someone is strong or creative and vice versa.
Everyone who is either curious or not quiet is not kind or not happy and vice versa.
Everyone who is either not funny or not happy is both not creative and generous and vice versa.
Everyone who is not curious or not quiet is both not old and not kind.
If lucy is either not patient or brave then susan is tall or not rich and vice versa.
Everyone who is not funny is humble.
If fred is either not curious or not quiet then someone is either wise or not old.
Everyone who is not kind is either not calm or quiet.
Fred is not old.
Someone is not patient or humble.
Someone is brave or not happy.
Someone is either humble or not brave.
Someone is both funny and kind.
Alice is not brave. | Fred is not happy. | neutral | (((~quiet(susan)<~>~tall(susan)))<=>(?[X]:((rich(X)|humble(X)))))&
(((~brave(fred)<~>~kind(fred)))<=>(?[X]:((~tall(X)&kind(X)))))&
((~tall(mary))<=>(~strong(paul)))&
(![X]:((~rich(X)&~generous(X))<=>(~kind(X)<~>patient(X))))&
(![X]:((calm(X)&humble(X))<=>(~humble(X)|~wise(X))))&
(![X]:((old(X)<~>~old(X))=>(funny(X)&wise(X))))&
(![X]:((wise(X)|~kind(X))=>~strong(X)))&
(![X]:(tall(X)<=>(strong(X)|old(X))))&
(((creative(fred)<~>~patient(fred)))<=>(?[X]:((strong(X)|creative(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~kind(X)|~happy(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(~creative(X)&generous(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~old(X)&~kind(X))))&
(((~patient(lucy)<~>brave(lucy)))<=>((tall(susan)|~rich(susan))))&
(![X]:(~funny(X)=>humble(X)))&
(((~curious(fred)<~>~quiet(fred)))=>(?[X]:((wise(X)<~>~old(X)))))&
(![X]:(~kind(X)=>(~calm(X)<~>quiet(X))))&
(~old(fred))&
(?[X]:((~patient(X)|humble(X))))&
(?[X]:((brave(X)|~happy(X))))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((funny(X)&kind(X))))&
(~brave(alice)) | ~happy(fred) | [] | null | 0 |
If someone is not rich or curious then someone is both not brave and curious and vice versa.
Everyone who is both curious and not wise is either not wise or quiet.
If someone is either not humble or not kind then someone is either not rich or not tall.
Everyone who is funny or not rich is either quiet or not funny and vice versa.
Everyone who is rich is either generous or happy and vice versa.
Everyone who is both not kind and happy is both not generous and not curious and vice versa.
Everyone who is both not patient and not generous is not wise or curious and vice versa.
If someone is both patient and not strong then fred is either tall or old and vice versa.
If someone is both happy and not kind then someone is tall and vice versa.
If someone is either generous or not wise then john is either not old or humble.
If alice is both quiet and calm then someone is not old or not brave and vice versa.
If someone is either rich or not generous then someone is humble and vice versa.
Everyone who is not funny or not curious is both brave and not calm and vice versa.
If mary is both not quiet and not curious then someone is patient or calm and vice versa.
Everyone who is both old and quiet is either quiet or kind and vice versa.
Everyone who is wise or curious is either not humble or not funny.
John is generous.
Someone is both wise and not kind.
Susan is either not humble or not strong.
Someone is strong or tall.
Someone is curious or tall. | Susan is curious. | contradiction | ((?[X]:((~rich(X)|curious(X))))<=>(?[X]:((~brave(X)&curious(X)))))&
(![X]:((curious(X)&~wise(X))=>(~wise(X)<~>quiet(X))))&
((?[X]:((~humble(X)<~>~kind(X))))=>(?[X]:((~rich(X)<~>~tall(X)))))&
(![X]:((funny(X)|~rich(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:(rich(X)<=>(generous(X)<~>happy(X))))&
(![X]:((~kind(X)&happy(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~patient(X)&~generous(X))<=>(~wise(X)|curious(X))))&
((?[X]:((patient(X)&~strong(X))))<=>((tall(fred)<~>old(fred))))&
((?[X]:((happy(X)&~kind(X))))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)<~>~wise(X))))=>((~old(john)<~>humble(john))))&
(((quiet(alice)&calm(alice)))<=>(?[X]:((~old(X)|~brave(X)))))&
((?[X]:((rich(X)<~>~generous(X))))<=>(?[X]:(humble(X))))&
(![X]:((~funny(X)|~curious(X))<=>(brave(X)&~calm(X))))&
(((~quiet(mary)&~curious(mary)))<=>(?[X]:((patient(X)|calm(X)))))&
(![X]:((old(X)&quiet(X))<=>(quiet(X)<~>kind(X))))&
(![X]:((wise(X)|curious(X))=>(~humble(X)<~>~funny(X))))&
(generous(john))&
(?[X]:((wise(X)&~kind(X))))&
((~humble(susan)<~>~strong(susan)))&
(?[X]:((strong(X)|tall(X))))&
(?[X]:((curious(X)|tall(X)))) | curious(susan) | [
"p0",
"p3",
"p4",
"p5",
"p10",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 569059959624385967050419
% SZS output start Proof for 569059959624385967050419
1. ? [X0] : (curious(X0) | ~rich(X0)) <=> ? [X0] : (curious(X0) & ~brave(X0)) [input p0]
4. ! [X0] : ((~rich(X0) | funny(X0)) <=> (quiet(X0) <~> ~funny(X0))) [input p3]
5. ! [X0] : (rich(X0) <=> (generous(X0) <~> happy(X0))) [input p4]
6. ! [X0] : ((happy(X0) & ~kind(X0)) <=> (~curious(X0) & ~generous(X0))) [input p5]
11. (calm(alice) & quiet(alice)) <=> ? [X0] : (~brave(X0) | ~old(X0)) [input p10]
14. (~curious(mary) & ~quiet(mary)) <=> ? [X0] : (calm(X0) | patient(X0)) [input p13]
15. ! [X0] : ((quiet(X0) & old(X0)) <=> (quiet(X0) <~> kind(X0))) [input p14]
22. curious(susan) [input hypothesis]
23. ? [X0] : (curious(X0) | ~rich(X0)) <=> ? [X1] : (curious(X1) & ~brave(X1)) [rectify 1]
32. (? [X0] : (curious(X0) | ~rich(X0)) | ! [X1] : (~curious(X1) | brave(X1))) & (? [X1] : (curious(X1) & ~brave(X1)) | ! [X0] : (~curious(X0) & rich(X0))) [nnf transformation 23]
33. (? [X0] : (curious(X0) | ~rich(X0)) | ! [X1] : (~curious(X1) | brave(X1))) & (? [X2] : (curious(X2) & ~brave(X2)) | ! [X3] : (~curious(X3) & rich(X3))) [rectify 32]
34. ? [X0] : (curious(X0) | ~rich(X0)) => (curious(sK0) | ~rich(sK0)) [choice axiom]
35. ? [X2] : (curious(X2) & ~brave(X2)) => (curious(sK1) & ~brave(sK1)) [choice axiom]
36. ((curious(sK0) | ~rich(sK0)) | ! [X1] : (~curious(X1) | brave(X1))) & ((curious(sK1) & ~brave(sK1)) | ! [X3] : (~curious(X3) & rich(X3))) [skolemisation 33,35,34]
42. ! [X0] : (((~rich(X0) | funny(X0)) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (rich(X0) & ~funny(X0)))) [nnf transformation 4]
43. ! [X0] : ((~rich(X0) | funny(X0) | ((quiet(X0) | funny(X0)) & (~funny(X0) | ~quiet(X0)))) & (((funny(X0) | ~quiet(X0)) & (~funny(X0) | quiet(X0))) | (rich(X0) & ~funny(X0)))) [flattening 42]
44. ! [X0] : ((rich(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0)))) & (((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | ~rich(X0))) [nnf transformation 5]
45. ! [X0] : (((happy(X0) & ~kind(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (~happy(X0) | kind(X0)))) [nnf transformation 6]
46. ! [X0] : (((happy(X0) & ~kind(X0)) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | ~happy(X0) | kind(X0))) [flattening 45]
59. ((calm(alice) & quiet(alice)) | ! [X0] : (brave(X0) & old(X0))) & (? [X0] : (~brave(X0) | ~old(X0)) | (~calm(alice) | ~quiet(alice))) [nnf transformation 11]
60. ((calm(alice) & quiet(alice)) | ! [X0] : (brave(X0) & old(X0))) & (? [X0] : (~brave(X0) | ~old(X0)) | ~calm(alice) | ~quiet(alice)) [flattening 59]
61. ((calm(alice) & quiet(alice)) | ! [X0] : (brave(X0) & old(X0))) & (? [X1] : (~brave(X1) | ~old(X1)) | ~calm(alice) | ~quiet(alice)) [rectify 60]
62. ? [X1] : (~brave(X1) | ~old(X1)) => (~brave(sK6) | ~old(sK6)) [choice axiom]
63. ((calm(alice) & quiet(alice)) | ! [X0] : (brave(X0) & old(X0))) & ((~brave(sK6) | ~old(sK6)) | ~calm(alice) | ~quiet(alice)) [skolemisation 61,62]
71. ((~curious(mary) & ~quiet(mary)) | ! [X0] : (~calm(X0) & ~patient(X0))) & (? [X0] : (calm(X0) | patient(X0)) | (curious(mary) | quiet(mary))) [nnf transformation 14]
72. ((~curious(mary) & ~quiet(mary)) | ! [X0] : (~calm(X0) & ~patient(X0))) & (? [X0] : (calm(X0) | patient(X0)) | curious(mary) | quiet(mary)) [flattening 71]
73. ((~curious(mary) & ~quiet(mary)) | ! [X0] : (~calm(X0) & ~patient(X0))) & (? [X1] : (calm(X1) | patient(X1)) | curious(mary) | quiet(mary)) [rectify 72]
74. ? [X1] : (calm(X1) | patient(X1)) => (calm(sK9) | patient(sK9)) [choice axiom]
75. ((~curious(mary) & ~quiet(mary)) | ! [X0] : (~calm(X0) & ~patient(X0))) & ((calm(sK9) | patient(sK9)) | curious(mary) | quiet(mary)) [skolemisation 73,74]
76. ! [X0] : (((quiet(X0) & old(X0)) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (~quiet(X0) | ~old(X0)))) [nnf transformation 15]
77. ! [X0] : (((quiet(X0) & old(X0)) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | ~quiet(X0) | ~old(X0))) [flattening 76]
87. ~brave(sK1) | ~curious(X3) [cnf transformation 36]
97. ~funny(X0) | quiet(X0) | ~funny(X0) [cnf transformation 43]
102. ~rich(X0) | funny(X0) | quiet(X0) | funny(X0) [cnf transformation 43]
105. ~generous(X0) | happy(X0) | rich(X0) [cnf transformation 44]
106. ~happy(X0) | generous(X0) | rich(X0) [cnf transformation 44]
107. ~happy(X0) | ~generous(X0) | kind(X0) [cnf transformation 46]
110. happy(X0) | curious(X0) | generous(X0) [cnf transformation 46]
133. calm(alice) | brave(X0) [cnf transformation 63]
145. ~quiet(mary) | ~calm(X0) [cnf transformation 75]
147. ~curious(mary) | ~calm(X0) [cnf transformation 75]
153. quiet(X0) | quiet(X0) | ~kind(X0) [cnf transformation 77]
165. curious(susan) [cnf transformation 22]
167. ~kind(X0) | quiet(X0) [duplicate literal removal 153]
168. ~funny(X0) | quiet(X0) [duplicate literal removal 97]
169. ~rich(X0) | funny(X0) | quiet(X0) [duplicate literal removal 102]
184. 4 <=> ! [X3] : ~curious(X3) [avatar definition]
185. ~curious(X3) <- (4) [avatar component clause 184]
196. 7 <=> brave(sK1) [avatar definition]
198. ~brave(sK1) <- (~7) [avatar component clause 196]
199. 4 | ~7 [avatar split clause 87,196,184]
288. 26 <=> ! [X0] : brave(X0) [avatar definition]
289. brave(X0) <- (26) [avatar component clause 288]
291. 27 <=> calm(alice) [avatar definition]
293. calm(alice) <- (27) [avatar component clause 291]
294. 26 | 27 [avatar split clause 133,291,288]
340. 38 <=> ! [X0] : ~calm(X0) [avatar definition]
341. ~calm(X0) <- (38) [avatar component clause 340]
343. 39 <=> curious(mary) [avatar definition]
345. ~curious(mary) <- (~39) [avatar component clause 343]
346. 38 | ~39 [avatar split clause 147,343,340]
352. 41 <=> quiet(mary) [avatar definition]
354. ~quiet(mary) <- (~41) [avatar component clause 352]
355. 38 | ~41 [avatar split clause 145,352,340]
399. $false <- (~7, 26) [subsumption resolution 198,289]
400. 7 | ~26 [avatar contradiction clause 399]
401. $false <- (4) [resolution 185,165]
402. ~4 [avatar contradiction clause 401]
403. $false <- (27, 38) [subsumption resolution 293,341]
404. ~27 | ~38 [avatar contradiction clause 403]
485. curious(X2) | generous(X2) | generous(X2) | rich(X2) [resolution 110,106]
487. generous(X2) | curious(X2) | rich(X2) [duplicate literal removal 485]
703. curious(X0) | rich(X0) | happy(X0) | rich(X0) [resolution 487,105]
709. happy(X0) | rich(X0) | curious(X0) [duplicate literal removal 703]
860. rich(X1) | curious(X1) | ~generous(X1) | kind(X1) [resolution 709,107]
865. kind(X1) | curious(X1) | rich(X1) [subsumption resolution 860,487]
927. quiet(X1) | rich(X1) | curious(X1) [resolution 865,167]
1021. rich(mary) | curious(mary) <- (~41) [resolution 927,354]
1026. rich(mary) <- (~39, ~41) [subsumption resolution 1021,345]
1069. funny(mary) | quiet(mary) <- (~39, ~41) [resolution 1026,169]
1071. funny(mary) <- (~39, ~41) [subsumption resolution 1069,354]
1102. quiet(mary) <- (~39, ~41) [resolution 1071,168]
1112. $false <- (~39, ~41) [subsumption resolution 1102,354]
1113. 39 | 41 [avatar contradiction clause 1112]
1114. $false [avatar sat refutation 199,294,346,355,400,402,404,1113]
% SZS output end Proof for 569059959624385967050419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or generous then someone is either not creative or tall.
If someone is kind or creative then susan is wise and vice versa.
Everyone who is not creative or creative is either not patient or not strong.
Everyone who is creative or not strong is either not brave or not happy.
Everyone who is brave is happy and vice versa.
Everyone who is both not tall and not curious is humble or wise and vice versa.
If john is rich or not old then someone is both strong and not creative and vice versa.
Everyone who is either not calm or not quiet is either not wise or not old.
If lucy is either old or not rich then someone is tall.
Everyone who is either kind or wise is not humble or not generous.
Everyone who is humble or funny is both quiet and humble and vice versa.
Everyone who is humble is both not rich and not funny and vice versa.
Everyone who is not quiet or not curious is not rich or not kind and vice versa.
If someone is either wise or not happy then susan is both not happy and generous.
If john is both not old and funny then someone is not funny.
Everyone who is both not brave and old is not humble and vice versa.
Susan is both humble and not patient.
Someone is either quiet or not strong.
Someone is either not wise or curious.
Alice is either not brave or creative.
Alice is not curious. | Susan is rich. | contradiction | ((?[X]:((~brave(X)<~>generous(X))))=>(?[X]:((~creative(X)<~>tall(X)))))&
((?[X]:((kind(X)|creative(X))))<=>(wise(susan)))&
(![X]:((~creative(X)|creative(X))=>(~patient(X)<~>~strong(X))))&
(![X]:((creative(X)|~strong(X))=>(~brave(X)<~>~happy(X))))&
(![X]:(brave(X)<=>happy(X)))&
(![X]:((~tall(X)&~curious(X))<=>(humble(X)|wise(X))))&
(((rich(john)|~old(john)))<=>(?[X]:((strong(X)&~creative(X)))))&
(![X]:((~calm(X)<~>~quiet(X))=>(~wise(X)<~>~old(X))))&
(((old(lucy)<~>~rich(lucy)))=>(?[X]:(tall(X))))&
(![X]:((kind(X)<~>wise(X))=>(~humble(X)|~generous(X))))&
(![X]:((humble(X)|funny(X))<=>(quiet(X)&humble(X))))&
(![X]:(humble(X)<=>(~rich(X)&~funny(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(~rich(X)|~kind(X))))&
((?[X]:((wise(X)<~>~happy(X))))=>((~happy(susan)&generous(susan))))&
(((~old(john)&funny(john)))=>(?[X]:(~funny(X))))&
(![X]:((~brave(X)&old(X))<=>~humble(X)))&
((humble(susan)&~patient(susan)))&
(?[X]:((quiet(X)<~>~strong(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
((~brave(alice)<~>creative(alice)))&
(~curious(alice)) | rich(susan) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7103896227204284151390087
% SZS output start Proof for 7103896227204284151390087
12. ! [X0] : (humble(X0) <=> (~funny(X0) & ~rich(X0))) [input p11]
17. ~patient(susan) & humble(susan) [input p16]
22. rich(susan) [input hypothesis]
59. ! [X0] : ((humble(X0) | (funny(X0) | rich(X0))) & ((~funny(X0) & ~rich(X0)) | ~humble(X0))) [nnf transformation 12]
60. ! [X0] : ((humble(X0) | funny(X0) | rich(X0)) & ((~funny(X0) & ~rich(X0)) | ~humble(X0))) [flattening 59]
115. ~rich(X0) | ~humble(X0) [cnf transformation 60]
130. humble(susan) [cnf transformation 17]
139. rich(susan) [cnf transformation 22]
265. ~humble(susan) [resolution 115,139]
267. $false [subsumption resolution 265,130]
% SZS output end Proof for 7103896227204284151390087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is both brave and patient.
If someone is both quiet and not funny then john is tall.
Everyone who is calm is not old or wise.
Everyone who is not patient is either not brave or not calm and vice versa.
Everyone who is patient is both not patient and happy.
If someone is not calm or kind then paul is both not wise and not happy and vice versa.
If mary is brave then someone is not brave or generous and vice versa.
Everyone who is rich or not calm is both not generous and brave.
If susan is not creative then fred is either not happy or kind.
Everyone who is not brave or not happy is tall or kind.
Everyone who is not tall is not old and vice versa.
Everyone who is not kind or old is kind.
Everyone who is either calm or quiet is both happy and not creative.
If alice is either not wise or old then alice is not creative or curious.
If lucy is not generous or creative then someone is quiet or happy and vice versa.
Someone is either kind or creative.
Someone is both kind and strong.
Someone is not generous.
Alice is wise.
Someone is quiet or not quiet.
Someone is either funny or strong.
Alice is either brave or not generous.
Someone is not humble. | Susan is calm. | neutral | (![X]:(old(X)=>(brave(X)&patient(X))))&
((?[X]:((quiet(X)&~funny(X))))=>(tall(john)))&
(![X]:(calm(X)=>(~old(X)|wise(X))))&
(![X]:(~patient(X)<=>(~brave(X)<~>~calm(X))))&
(![X]:(patient(X)=>(~patient(X)&happy(X))))&
((?[X]:((~calm(X)|kind(X))))<=>((~wise(paul)&~happy(paul))))&
((brave(mary))<=>(?[X]:((~brave(X)|generous(X)))))&
(![X]:((rich(X)|~calm(X))=>(~generous(X)&brave(X))))&
((~creative(susan))=>((~happy(fred)<~>kind(fred))))&
(![X]:((~brave(X)|~happy(X))=>(tall(X)|kind(X))))&
(![X]:(~tall(X)<=>~old(X)))&
(![X]:((~kind(X)|old(X))=>kind(X)))&
(![X]:((calm(X)<~>quiet(X))=>(happy(X)&~creative(X))))&
(((~wise(alice)<~>old(alice)))=>((~creative(alice)|curious(alice))))&
(((~generous(lucy)|creative(lucy)))<=>(?[X]:((quiet(X)|happy(X)))))&
(?[X]:((kind(X)<~>creative(X))))&
(?[X]:((kind(X)&strong(X))))&
(?[X]:(~generous(X)))&
(wise(alice))&
(?[X]:((quiet(X)|~quiet(X))))&
(?[X]:((funny(X)<~>strong(X))))&
((brave(alice)<~>~generous(alice)))&
(?[X]:(~humble(X))) | calm(susan) | [] | null | 0 |
Everyone who is quiet or not quiet is quiet and vice versa.
If someone is either curious or not humble then fred is either strong or not happy.
Everyone who is both not rich and humble is creative.
If alice is either wise or not generous then someone is both wise and not kind and vice versa.
Everyone who is either not humble or not tall is patient or quiet.
Everyone who is either quiet or not funny is not tall.
Everyone who is either patient or not curious is either not tall or wise and vice versa.
Everyone who is both tall and curious is both happy and not kind and vice versa.
If lucy is strong or kind then someone is kind or not humble.
Everyone who is old is either quiet or not rich.
Everyone who is not strong is either curious or not tall.
If fred is not brave then someone is rich and vice versa.
Everyone who is both not creative and not funny is not old.
Everyone who is either kind or not happy is not brave.
If lucy is both patient and not old then alice is not kind and vice versa.
Everyone who is either funny or not kind is either not kind or not old and vice versa.
Someone is quiet or not brave.
Someone is rich.
Lucy is not tall.
Susan is not wise.
Alice is both not humble and strong.
Someone is both happy and not generous.
John is not kind or humble. | Alice is generous. | neutral | (![X]:((quiet(X)|~quiet(X))<=>quiet(X)))&
((?[X]:((curious(X)<~>~humble(X))))=>((strong(fred)<~>~happy(fred))))&
(![X]:((~rich(X)&humble(X))=>creative(X)))&
(((wise(alice)<~>~generous(alice)))<=>(?[X]:((wise(X)&~kind(X)))))&
(![X]:((~humble(X)<~>~tall(X))=>(patient(X)|quiet(X))))&
(![X]:((quiet(X)<~>~funny(X))=>~tall(X)))&
(![X]:((patient(X)<~>~curious(X))<=>(~tall(X)<~>wise(X))))&
(![X]:((tall(X)&curious(X))<=>(happy(X)&~kind(X))))&
(((strong(lucy)|kind(lucy)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:(old(X)=>(quiet(X)<~>~rich(X))))&
(![X]:(~strong(X)=>(curious(X)<~>~tall(X))))&
((~brave(fred))<=>(?[X]:(rich(X))))&
(![X]:((~creative(X)&~funny(X))=>~old(X)))&
(![X]:((kind(X)<~>~happy(X))=>~brave(X)))&
(((patient(lucy)&~old(lucy)))<=>(~kind(alice)))&
(![X]:((funny(X)<~>~kind(X))<=>(~kind(X)<~>~old(X))))&
(?[X]:((quiet(X)|~brave(X))))&
(?[X]:(rich(X)))&
(~tall(lucy))&
(~wise(susan))&
((~humble(alice)&strong(alice)))&
(?[X]:((happy(X)&~generous(X))))&
((~kind(john)|humble(john))) | generous(alice) | [] | null | 0 |
Everyone who is either not creative or not tall is curious or not curious. If someone is calm then someone is humble. Everyone who is either not strong or happy is tall or rich and vice versa. If someone is either happy or not patient then someone is both not strong and curious. Everyone who is not curious or not strong is not quiet and vice versa. If mary is both generous and humble then someone is happy or calm and vice versa. Everyone who is not strong is both patient and old and vice versa. If someone is humble or not curious then someone is either not kind or not rich. If mary is not creative or not tall then someone is strong or not calm and vice versa. Everyone who is either not creative or wise is strong or not humble. Everyone who is quiet is not strong. Everyone who is not humble is not funny and vice versa. If someone is both not humble and not generous then someone is either not calm or patient. Everyone who is tall or not funny is curious. Everyone who is old or not calm is either patient or not calm. If paul is both humble and strong then someone is either not patient or patient and vice versa. Alice is either curious or not curious. Someone is not old or kind. Fred is not rich or curious. John is either not strong or not old. Someone is either patient or not generous. Paul is both not tall and not brave. Someone is both happy and not kind. Someone is either not wise or rich. | Paul is strong. | entailment | (![X]:((~creative(X)<~>~tall(X))=>(curious(X)|~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:(humble(X))))&
(![X]:((~strong(X)<~>happy(X))<=>(tall(X)|rich(X))))&
((?[X]:((happy(X)<~>~patient(X))))=>(?[X]:((~strong(X)&curious(X)))))&
(![X]:((~curious(X)|~strong(X))<=>~quiet(X)))&
(((generous(mary)&humble(mary)))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:(~strong(X)<=>(patient(X)&old(X))))&
((?[X]:((humble(X)|~curious(X))))=>(?[X]:((~kind(X)<~>~rich(X)))))&
(((~creative(mary)|~tall(mary)))<=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((~creative(X)<~>wise(X))=>(strong(X)|~humble(X))))&
(![X]:(quiet(X)=>~strong(X)))&
(![X]:(~humble(X)<=>~funny(X)))&
((?[X]:((~humble(X)&~generous(X))))=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:((tall(X)|~funny(X))=>curious(X)))&
(![X]:((old(X)|~calm(X))=>(patient(X)<~>~calm(X))))&
(((humble(paul)&strong(paul)))<=>(?[X]:((~patient(X)<~>patient(X)))))&
((curious(alice)<~>~curious(alice)))&
(?[X]:((~old(X)|kind(X))))&
((~rich(fred)|curious(fred)))&
((~strong(john)<~>~old(john)))&
(?[X]:((patient(X)<~>~generous(X))))&
((~tall(paul)&~brave(paul)))&
(?[X]:((happy(X)&~kind(X))))&
(?[X]:((~wise(X)<~>rich(X)))) | strong(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8109914872798067238554524
% SZS output start Proof for 8109914872798067238554524
16. (strong(paul) & humble(paul)) <=> ? [X0] : (~patient(X0) <~> patient(X0)) [input p15]
25. ~strong(paul) [input hypothesis]
78. ((strong(paul) & humble(paul)) | ! [X0] : ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (? [X0] : ((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | (~strong(paul) | ~humble(paul))) [nnf transformation 16]
79. ((strong(paul) & humble(paul)) | ! [X0] : ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (? [X0] : ((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ~strong(paul) | ~humble(paul)) [flattening 78]
80. ((strong(paul) & humble(paul)) | ! [X0] : ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (? [X1] : ((~patient(X1) | patient(X1)) & (patient(X1) | ~patient(X1))) | ~strong(paul) | ~humble(paul)) [rectify 79]
81. ? [X1] : ((~patient(X1) | patient(X1)) & (patient(X1) | ~patient(X1))) => ((~patient(sK6) | patient(sK6)) & (patient(sK6) | ~patient(sK6))) [choice axiom]
82. ((strong(paul) & humble(paul)) | ! [X0] : ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(sK6) | patient(sK6)) & (patient(sK6) | ~patient(sK6))) | ~strong(paul) | ~humble(paul)) [skolemisation 80,81]
142. strong(paul) | patient(X0) | patient(X0) [cnf transformation 82]
143. strong(paul) | ~patient(X0) | ~patient(X0) [cnf transformation 82]
157. ~strong(paul) [cnf transformation 25]
160. strong(paul) | patient(X0) [duplicate literal removal 142]
161. strong(paul) | ~patient(X0) [duplicate literal removal 143]
271. 25 <=> ! [X0] : ~patient(X0) [avatar definition]
272. ~patient(X0) <- (25) [avatar component clause 271]
274. 26 <=> strong(paul) [avatar definition]
277. 25 | 26 [avatar split clause 161,274,271]
279. 27 <=> ! [X0] : patient(X0) [avatar definition]
280. patient(X0) <- (27) [avatar component clause 279]
281. 27 | 26 [avatar split clause 160,274,279]
335. ~26 [avatar split clause 157,274]
336. $false <- (25, 27) [subsumption resolution 272,280]
337. ~25 | ~27 [avatar contradiction clause 336]
340. $false [avatar sat refutation 277,281,335,337]
% SZS output end Proof for 8109914872798067238554524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not wise or patient then someone is not creative.
Everyone who is not old or not funny is either not strong or patient.
If mary is both not happy and happy then paul is both brave and quiet.
Everyone who is both tall and curious is not calm or not humble and vice versa.
Everyone who is either wise or not quiet is not creative or not brave and vice versa.
Everyone who is strong or not humble is humble.
Everyone who is calm is curious or not funny and vice versa.
Everyone who is rich or funny is both strong and tall.
If someone is both not rich and not calm then someone is both quiet and not strong and vice versa.
If lucy is generous or not generous then lucy is both not old and humble and vice versa.
Everyone who is kind is generous and vice versa.
If susan is not quiet or tall then paul is not patient and vice versa.
If mary is not quiet then someone is either tall or not funny and vice versa.
If someone is not wise or not tall then someone is strong or creative.
If someone is not strong then someone is curious or patient.
Someone is not kind.
Fred is either not generous or generous.
Someone is not old or not wise.
Alice is not patient or not creative.
Lucy is both curious and not quiet.
Susan is not tall or curious. | Lucy is not funny. | entailment | (((~wise(paul)<~>patient(paul)))=>(?[X]:(~creative(X))))&
(![X]:((~old(X)|~funny(X))=>(~strong(X)<~>patient(X))))&
(((~happy(mary)&happy(mary)))=>((brave(paul)&quiet(paul))))&
(![X]:((tall(X)&curious(X))<=>(~calm(X)|~humble(X))))&
(![X]:((wise(X)<~>~quiet(X))<=>(~creative(X)|~brave(X))))&
(![X]:((strong(X)|~humble(X))=>humble(X)))&
(![X]:(calm(X)<=>(curious(X)|~funny(X))))&
(![X]:((rich(X)|funny(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)&~calm(X))))<=>(?[X]:((quiet(X)&~strong(X)))))&
(((generous(lucy)|~generous(lucy)))<=>((~old(lucy)&humble(lucy))))&
(![X]:(kind(X)<=>generous(X)))&
(((~quiet(susan)|tall(susan)))<=>(~patient(paul)))&
((~quiet(mary))<=>(?[X]:((tall(X)<~>~funny(X)))))&
((?[X]:((~wise(X)|~tall(X))))=>(?[X]:((strong(X)|creative(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((curious(X)|patient(X)))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>generous(fred)))&
(?[X]:((~old(X)|~wise(X))))&
((~patient(alice)|~creative(alice)))&
((curious(lucy)&~quiet(lucy)))&
((~tall(susan)|curious(susan))) | ~funny(lucy) | [
"p3",
"p5",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 739306826869781540860617
% SZS output start Proof for 739306826869781540860617
4. ! [X0] : ((curious(X0) & tall(X0)) <=> (~humble(X0) | ~calm(X0))) [input p3]
6. ! [X0] : ((~humble(X0) | strong(X0)) => humble(X0)) [input p5]
7. ! [X0] : (calm(X0) <=> (~funny(X0) | curious(X0))) [input p6]
8. ! [X0] : ((funny(X0) | rich(X0)) => (tall(X0) & strong(X0))) [input p7]
20. ~quiet(lucy) & curious(lucy) [input p19]
22. funny(lucy) [input hypothesis]
31. ! [X0] : (humble(X0) | (humble(X0) & ~strong(X0))) [ennf transformation 6]
32. ! [X0] : ((tall(X0) & strong(X0)) | (~funny(X0) & ~rich(X0))) [ennf transformation 8]
40. ! [X0] : (((curious(X0) & tall(X0)) | (humble(X0) & calm(X0))) & ((~humble(X0) | ~calm(X0)) | (~curious(X0) | ~tall(X0)))) [nnf transformation 4]
41. ! [X0] : (((curious(X0) & tall(X0)) | (humble(X0) & calm(X0))) & (~humble(X0) | ~calm(X0) | ~curious(X0) | ~tall(X0))) [flattening 40]
44. ! [X0] : ((calm(X0) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | ~calm(X0))) [nnf transformation 7]
45. ! [X0] : ((calm(X0) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~calm(X0))) [flattening 44]
78. ~humble(X0) | ~calm(X0) | ~curious(X0) | ~tall(X0) [cnf transformation 41]
81. calm(X0) | curious(X0) [cnf transformation 41]
90. humble(X0) | humble(X0) [cnf transformation 31]
92. calm(X0) | ~curious(X0) [cnf transformation 45]
97. ~funny(X0) | tall(X0) [cnf transformation 32]
123. curious(lucy) [cnf transformation 20]
126. funny(lucy) [cnf transformation 22]
127. humble(X0) [duplicate literal removal 90]
142. calm(X0) [subsumption resolution 92,81]
238. tall(lucy) [resolution 97,126]
259. ~calm(X2) | ~curious(X2) | ~tall(X2) [resolution 78,127]
260. ~curious(X2) | ~tall(X2) [subsumption resolution 259,142]
261. ~tall(lucy) [resolution 260,123]
263. $false [subsumption resolution 261,238]
% SZS output end Proof for 739306826869781540860617
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and not brave then susan is either not tall or not generous and vice versa.
If lucy is both strong and not wise then someone is both humble and not quiet and vice versa.
Everyone who is not strong is kind and vice versa.
Everyone who is both not patient and not curious is not creative.
If paul is either funny or brave then lucy is either not humble or not funny and vice versa.
Everyone who is not brave is both not calm and not strong.
Everyone who is not happy or not calm is either not humble or patient and vice versa.
If alice is both not rich and tall then someone is either not tall or not funny.
Everyone who is either not patient or quiet is not calm and vice versa.
Everyone who is generous or not generous is either wise or funny and vice versa.
Everyone who is both not strong and not wise is not kind.
If mary is both patient and not happy then john is both not calm and rich and vice versa.
If mary is either not rich or not humble then fred is both not patient and generous and vice versa.
If mary is either not tall or old then someone is either not brave or not kind and vice versa.
Everyone who is not generous is not patient or kind.
If mary is either creative or not old then someone is either not calm or calm and vice versa.
Someone is not humble or brave.
Fred is happy.
John is strong.
Someone is not strong.
Fred is both generous and happy.
John is strong or quiet.
Alice is either not strong or not kind.
Mary is funny. | Mary is brave. | entailment | ((?[X]:((curious(X)&~brave(X))))<=>((~tall(susan)<~>~generous(susan))))&
(((strong(lucy)&~wise(lucy)))<=>(?[X]:((humble(X)&~quiet(X)))))&
(![X]:(~strong(X)<=>kind(X)))&
(![X]:((~patient(X)&~curious(X))=>~creative(X)))&
(((funny(paul)<~>brave(paul)))<=>((~humble(lucy)<~>~funny(lucy))))&
(![X]:(~brave(X)=>(~calm(X)&~strong(X))))&
(![X]:((~happy(X)|~calm(X))<=>(~humble(X)<~>patient(X))))&
(((~rich(alice)&tall(alice)))=>(?[X]:((~tall(X)<~>~funny(X)))))&
(![X]:((~patient(X)<~>quiet(X))<=>~calm(X)))&
(![X]:((generous(X)|~generous(X))<=>(wise(X)<~>funny(X))))&
(![X]:((~strong(X)&~wise(X))=>~kind(X)))&
(((patient(mary)&~happy(mary)))<=>((~calm(john)&rich(john))))&
(((~rich(mary)<~>~humble(mary)))<=>((~patient(fred)&generous(fred))))&
(((~tall(mary)<~>old(mary)))<=>(?[X]:((~brave(X)<~>~kind(X)))))&
(![X]:(~generous(X)=>(~patient(X)|kind(X))))&
(((creative(mary)<~>~old(mary)))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(?[X]:((~humble(X)|brave(X))))&
(happy(fred))&
(strong(john))&
(?[X]:(~strong(X)))&
((generous(fred)&happy(fred)))&
((strong(john)|quiet(john)))&
((~strong(alice)<~>~kind(alice)))&
(funny(mary)) | brave(mary) | [
"p2",
"p5",
"p9",
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 6343304520137124767616262
% SZS output start Proof for 6343304520137124767616262
3. ! [X0] : (~strong(X0) <=> kind(X0)) [input p2]
6. ! [X0] : (~brave(X0) => (~strong(X0) & ~calm(X0))) [input p5]
10. ! [X0] : ((~generous(X0) | generous(X0)) <=> (wise(X0) <~> funny(X0))) [input p9]
11. ! [X0] : ((~wise(X0) & ~strong(X0)) => ~kind(X0)) [input p10]
24. funny(mary) [input p23]
25. ~brave(mary) [input hypothesis]
28. ! [X0] : ((~strong(X0) & ~calm(X0)) | brave(X0)) [ennf transformation 6]
31. ! [X0] : (~kind(X0) | (wise(X0) | strong(X0))) [ennf transformation 11]
32. ! [X0] : (~kind(X0) | wise(X0) | strong(X0)) [flattening 31]
44. ! [X0] : ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))) [nnf transformation 3]
52. ! [X0] : (((~generous(X0) | generous(X0)) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (generous(X0) & ~generous(X0)))) [nnf transformation 10]
53. ! [X0] : ((~generous(X0) | generous(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0)))) & (((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | (generous(X0) & ~generous(X0)))) [flattening 52]
81. kind(X0) | strong(X0) [cnf transformation 44]
82. ~kind(X0) | ~strong(X0) [cnf transformation 44]
93. ~strong(X0) | brave(X0) [cnf transformation 28]
108. ~funny(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 53]
109. ~funny(X0) | ~wise(X0) | generous(X0) [cnf transformation 53]
112. ~kind(X0) | wise(X0) | strong(X0) [cnf transformation 32]
149. funny(mary) [cnf transformation 24]
150. ~brave(mary) [cnf transformation 25]
245. ~funny(X0) | ~wise(X0) [subsumption resolution 108,109]
247. ~kind(X0) | wise(X0) [subsumption resolution 112,82]
346. ~wise(mary) [resolution 245,149]
351. wise(X0) | strong(X0) [resolution 247,81]
367. strong(mary) [resolution 351,346]
368. brave(mary) [resolution 367,93]
369. $false [subsumption resolution 368,150]
% SZS output end Proof for 6343304520137124767616262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either brave or strong is either not strong or not rich.
Everyone who is tall is both not rich and happy.
Everyone who is not funny or strong is both creative and not brave.
Everyone who is not brave or not quiet is both not humble and not calm and vice versa.
If someone is either humble or not kind then someone is both not humble and rich and vice versa.
If someone is not strong or not calm then someone is not generous.
If fred is wise or quiet then john is wise.
If fred is creative or not rich then susan is either calm or not quiet.
Everyone who is either not rich or not humble is not tall or not quiet.
Everyone who is either tall or generous is not quiet and vice versa.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
Everyone who is kind is patient.
If mary is old then susan is not wise or not calm.
Everyone who is not generous is not kind and vice versa.
Someone is either not creative or not curious.
Someone is not kind or not creative.
John is curious.
Someone is both wise and happy.
Alice is either tall or funny. | Mary is not funny. | neutral | (![X]:((brave(X)<~>strong(X))=>(~strong(X)<~>~rich(X))))&
(![X]:(tall(X)=>(~rich(X)&happy(X))))&
(![X]:((~funny(X)|strong(X))=>(creative(X)&~brave(X))))&
(![X]:((~brave(X)|~quiet(X))<=>(~humble(X)&~calm(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>(?[X]:((~humble(X)&rich(X)))))&
((?[X]:((~strong(X)|~calm(X))))=>(?[X]:(~generous(X))))&
(((wise(fred)|quiet(fred)))=>(wise(john)))&
(((creative(fred)|~rich(fred)))=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((~kind(X)|~creative(X))))&
(curious(john))&
(?[X]:((wise(X)&happy(X))))&
((tall(alice)<~>funny(alice))) | ~funny(mary) | [] | null | 0 |
If someone is not kind then susan is not tall and vice versa.
If someone is both not happy and wise then lucy is not curious or not patient.
If john is wise or quiet then lucy is either not wise or not happy.
Everyone who is either wise or patient is kind or strong and vice versa.
If susan is kind or not patient then susan is calm or humble and vice versa.
Everyone who is either not wise or curious is brave or not quiet.
If someone is not generous or happy then lucy is both not kind and not curious and vice versa.
Everyone who is not generous is wise or not patient.
Everyone who is both old and calm is not curious or not old and vice versa.
Everyone who is not kind or not quiet is either calm or not wise and vice versa.
If someone is not quiet then someone is either not strong or humble and vice versa.
If alice is either not patient or funny then someone is curious or not strong and vice versa.
If fred is either creative or quiet then someone is happy and vice versa.
If paul is quiet or brave then paul is generous.
Everyone who is not happy or curious is not old or wise and vice versa.
Everyone who is quiet is both wise and brave and vice versa.
Someone is old.
Fred is both not happy and creative.
Someone is old or generous.
Lucy is happy or brave.
Alice is either not brave or not funny.
Susan is either curious or not wise.
Someone is either not rich or calm. | John is strong. | neutral | ((?[X]:(~kind(X)))<=>(~tall(susan)))&
((?[X]:((~happy(X)&wise(X))))=>((~curious(lucy)|~patient(lucy))))&
(((wise(john)|quiet(john)))=>((~wise(lucy)<~>~happy(lucy))))&
(![X]:((wise(X)<~>patient(X))<=>(kind(X)|strong(X))))&
(((kind(susan)|~patient(susan)))<=>((calm(susan)|humble(susan))))&
(![X]:((~wise(X)<~>curious(X))=>(brave(X)|~quiet(X))))&
((?[X]:((~generous(X)|happy(X))))<=>((~kind(lucy)&~curious(lucy))))&
(![X]:(~generous(X)=>(wise(X)|~patient(X))))&
(![X]:((old(X)&calm(X))<=>(~curious(X)|~old(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(calm(X)<~>~wise(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~strong(X)<~>humble(X)))))&
(((~patient(alice)<~>funny(alice)))<=>(?[X]:((curious(X)|~strong(X)))))&
(((creative(fred)<~>quiet(fred)))<=>(?[X]:(happy(X))))&
(((quiet(paul)|brave(paul)))=>(generous(paul)))&
(![X]:((~happy(X)|curious(X))<=>(~old(X)|wise(X))))&
(![X]:(quiet(X)<=>(wise(X)&brave(X))))&
(?[X]:(old(X)))&
((~happy(fred)&creative(fred)))&
(?[X]:((old(X)|generous(X))))&
((happy(lucy)|brave(lucy)))&
((~brave(alice)<~>~funny(alice)))&
((curious(susan)<~>~wise(susan)))&
(?[X]:((~rich(X)<~>calm(X)))) | strong(john) | [] | null | 0 |
If someone is both not patient and rich then someone is either creative or not tall and vice versa.
Everyone who is either funny or old is either kind or tall and vice versa.
Everyone who is both not rich and brave is either patient or creative and vice versa.
If paul is not strong or not generous then susan is not creative.
If alice is either tall or not humble then susan is patient and vice versa.
Everyone who is not creative is quiet.
If fred is not calm or not curious then john is not generous or patient.
Everyone who is not patient or not curious is not kind or not humble.
Everyone who is either not humble or not generous is both not creative and wise and vice versa.
Everyone who is not old or not strong is either creative or old.
Everyone who is not strong or not quiet is not humble and vice versa.
Everyone who is not generous or not happy is not old.
If someone is either not humble or quiet then paul is not generous.
Everyone who is quiet is either strong or not funny.
Everyone who is wise or rich is humble or funny.
Fred is funny.
John is both rich and quiet.
John is not strong or strong.
John is strong.
Someone is not happy or humble. | Susan is not rich. | neutral | ((?[X]:((~patient(X)&rich(X))))<=>(?[X]:((creative(X)<~>~tall(X)))))&
(![X]:((funny(X)<~>old(X))<=>(kind(X)<~>tall(X))))&
(![X]:((~rich(X)&brave(X))<=>(patient(X)<~>creative(X))))&
(((~strong(paul)|~generous(paul)))=>(~creative(susan)))&
(((tall(alice)<~>~humble(alice)))<=>(patient(susan)))&
(![X]:(~creative(X)=>quiet(X)))&
(((~calm(fred)|~curious(fred)))=>((~generous(john)|patient(john))))&
(![X]:((~patient(X)|~curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(~creative(X)&wise(X))))&
(![X]:((~old(X)|~strong(X))=>(creative(X)<~>old(X))))&
(![X]:((~strong(X)|~quiet(X))<=>~humble(X)))&
(![X]:((~generous(X)|~happy(X))=>~old(X)))&
((?[X]:((~humble(X)<~>quiet(X))))=>(~generous(paul)))&
(![X]:(quiet(X)=>(strong(X)<~>~funny(X))))&
(![X]:((wise(X)|rich(X))=>(humble(X)|funny(X))))&
(funny(fred))&
((rich(john)&quiet(john)))&
((~strong(john)|strong(john)))&
(strong(john))&
(?[X]:((~happy(X)|humble(X)))) | ~rich(susan) | [] | null | 0 |
Everyone who is both not funny and strong is both not wise and not quiet. Everyone who is both tall and wise is either not brave or tall. If someone is either not generous or tall then someone is brave or funny and vice versa. Everyone who is not patient is not creative. Everyone who is creative is both not happy and not old. If someone is either not brave or strong then paul is strong or patient and vice versa. Everyone who is patient or not funny is quiet and vice versa. Everyone who is humble is both patient and humble. If susan is either kind or not wise then paul is either generous or quiet. If someone is happy then someone is either rich or not patient and vice versa. Everyone who is quiet or not wise is not quiet and vice versa. Everyone who is rich is funny. If someone is rich or curious then someone is funny or tall and vice versa. Everyone who is both funny and not rich is both funny and kind. If someone is rich then susan is both not brave and creative. If fred is not strong or happy then someone is kind or curious. Someone is either creative or not tall. Susan is patient or not quiet. Someone is either not strong or humble. Someone is either not humble or not generous. Someone is kind. | Fred is brave. | neutral | (![X]:((~funny(X)&strong(X))=>(~wise(X)&~quiet(X))))&
(![X]:((tall(X)&wise(X))=>(~brave(X)<~>tall(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>(?[X]:((brave(X)|funny(X)))))&
(![X]:(~patient(X)=>~creative(X)))&
(![X]:(creative(X)=>(~happy(X)&~old(X))))&
((?[X]:((~brave(X)<~>strong(X))))<=>((strong(paul)|patient(paul))))&
(![X]:((patient(X)|~funny(X))<=>quiet(X)))&
(![X]:(humble(X)=>(patient(X)&humble(X))))&
(((kind(susan)<~>~wise(susan)))=>((generous(paul)<~>quiet(paul))))&
((?[X]:(happy(X)))<=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((quiet(X)|~wise(X))<=>~quiet(X)))&
(![X]:(rich(X)=>funny(X)))&
((?[X]:((rich(X)|curious(X))))<=>(?[X]:((funny(X)|tall(X)))))&
(![X]:((funny(X)&~rich(X))=>(funny(X)&kind(X))))&
((?[X]:(rich(X)))=>((~brave(susan)&creative(susan))))&
(((~strong(fred)|happy(fred)))=>(?[X]:((kind(X)|curious(X)))))&
(?[X]:((creative(X)<~>~tall(X))))&
((patient(susan)|~quiet(susan)))&
(?[X]:((~strong(X)<~>humble(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:(kind(X))) | brave(fred) | [] | null | 0 |
Everyone who is wise or not creative is either happy or not happy.
If someone is either not kind or not curious then paul is both not patient and not tall and vice versa.
If john is not quiet then alice is either old or not kind.
If susan is both wise and not patient then alice is old.
If someone is both strong and not strong then someone is kind or quiet and vice versa.
Everyone who is both not tall and not strong is not quiet or not curious and vice versa.
Everyone who is both not strong and quiet is both not strong and rich and vice versa.
Everyone who is not happy or calm is kind.
If someone is either generous or not calm then someone is either strong or not rich and vice versa.
If john is not happy or creative then paul is both rich and old and vice versa.
Everyone who is either wise or not rich is either not rich or calm.
Everyone who is either happy or not wise is not kind or not humble.
If someone is funny then mary is not wise or not quiet and vice versa.
Everyone who is either funny or creative is either creative or not brave and vice versa.
Everyone who is both not wise and not strong is generous or strong.
If susan is quiet or generous then someone is both kind and not old and vice versa.
Someone is not calm.
Someone is not old.
Someone is not patient.
Someone is generous.
Fred is not old. | Mary is not wise. | neutral | (![X]:((wise(X)|~creative(X))=>(happy(X)<~>~happy(X))))&
((?[X]:((~kind(X)<~>~curious(X))))<=>((~patient(paul)&~tall(paul))))&
((~quiet(john))=>((old(alice)<~>~kind(alice))))&
(((wise(susan)&~patient(susan)))=>(old(alice)))&
((?[X]:((strong(X)&~strong(X))))<=>(?[X]:((kind(X)|quiet(X)))))&
(![X]:((~tall(X)&~strong(X))<=>(~quiet(X)|~curious(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~strong(X)&rich(X))))&
(![X]:((~happy(X)|calm(X))=>kind(X)))&
((?[X]:((generous(X)<~>~calm(X))))<=>(?[X]:((strong(X)<~>~rich(X)))))&
(((~happy(john)|creative(john)))<=>((rich(paul)&old(paul))))&
(![X]:((wise(X)<~>~rich(X))=>(~rich(X)<~>calm(X))))&
(![X]:((happy(X)<~>~wise(X))=>(~kind(X)|~humble(X))))&
((?[X]:(funny(X)))<=>((~wise(mary)|~quiet(mary))))&
(![X]:((funny(X)<~>creative(X))<=>(creative(X)<~>~brave(X))))&
(![X]:((~wise(X)&~strong(X))=>(generous(X)|strong(X))))&
(((quiet(susan)|generous(susan)))<=>(?[X]:((kind(X)&~old(X)))))&
(?[X]:(~calm(X)))&
(?[X]:(~old(X)))&
(?[X]:(~patient(X)))&
(?[X]:(generous(X)))&
(~old(fred)) | ~wise(mary) | [] | null | 0 |
Everyone who is either kind or not wise is quiet. Everyone who is both funny and happy is both not calm and old and vice versa. Everyone who is either kind or not curious is either not kind or tall and vice versa. Everyone who is either not old or happy is wise. Everyone who is funny is not brave or rich. Everyone who is both not old and funny is not wise or patient. Everyone who is not generous is not calm and vice versa. Everyone who is kind is happy or not strong and vice versa. Everyone who is not generous is either happy or not tall. Everyone who is either tall or funny is strong. If john is either not funny or not creative then paul is calm. Everyone who is both not curious and tall is either not creative or tall. Everyone who is either brave or wise is not quiet and vice versa. Everyone who is either not kind or happy is not curious and vice versa. If someone is both brave and not strong then someone is both not generous and not strong. If someone is generous then someone is either generous or funny and vice versa. Paul is happy. Susan is not creative or not quiet. Alice is either not tall or quiet. Someone is tall or not happy. Paul is calm or not humble. Someone is either not curious or patient. Someone is wise or quiet. Someone is either funny or not calm. | Paul is tall. | contradiction | (![X]:((kind(X)<~>~wise(X))=>quiet(X)))&
(![X]:((funny(X)&happy(X))<=>(~calm(X)&old(X))))&
(![X]:((kind(X)<~>~curious(X))<=>(~kind(X)<~>tall(X))))&
(![X]:((~old(X)<~>happy(X))=>wise(X)))&
(![X]:(funny(X)=>(~brave(X)|rich(X))))&
(![X]:((~old(X)&funny(X))=>(~wise(X)|patient(X))))&
(![X]:(~generous(X)<=>~calm(X)))&
(![X]:(kind(X)<=>(happy(X)|~strong(X))))&
(![X]:(~generous(X)=>(happy(X)<~>~tall(X))))&
(![X]:((tall(X)<~>funny(X))=>strong(X)))&
(((~funny(john)<~>~creative(john)))=>(calm(paul)))&
(![X]:((~curious(X)&tall(X))=>(~creative(X)<~>tall(X))))&
(![X]:((brave(X)<~>wise(X))<=>~quiet(X)))&
(![X]:((~kind(X)<~>happy(X))<=>~curious(X)))&
((?[X]:((brave(X)&~strong(X))))=>(?[X]:((~generous(X)&~strong(X)))))&
((?[X]:(generous(X)))<=>(?[X]:((generous(X)<~>funny(X)))))&
(happy(paul))&
((~creative(susan)|~quiet(susan)))&
((~tall(alice)<~>quiet(alice)))&
(?[X]:((tall(X)|~happy(X))))&
((calm(paul)|~humble(paul)))&
(?[X]:((~curious(X)<~>patient(X))))&
(?[X]:((wise(X)|quiet(X))))&
(?[X]:((funny(X)<~>~calm(X)))) | tall(paul) | [
"p2",
"p7",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 324647744900256166983881
% SZS output start Proof for 324647744900256166983881
3. ! [X0] : ((kind(X0) <~> ~curious(X0)) <=> (~kind(X0) <~> tall(X0))) [input p2]
8. ! [X0] : (kind(X0) <=> (~strong(X0) | happy(X0))) [input p7]
14. ! [X0] : ((~kind(X0) <~> happy(X0)) <=> ~curious(X0)) [input p13]
17. happy(paul) [input p16]
25. tall(paul) [input hypothesis]
43. ! [X0] : ((((curious(X0) | ~kind(X0)) & (~curious(X0) | kind(X0))) | ((~kind(X0) | ~tall(X0)) & (tall(X0) | kind(X0)))) & (((~tall(X0) | kind(X0)) & (tall(X0) | ~kind(X0))) | ((kind(X0) | curious(X0)) & (~curious(X0) | ~kind(X0))))) [nnf transformation 3]
46. ! [X0] : ((kind(X0) | (strong(X0) & ~happy(X0))) & ((~strong(X0) | happy(X0)) | ~kind(X0))) [nnf transformation 8]
47. ! [X0] : ((kind(X0) | (strong(X0) & ~happy(X0))) & (~strong(X0) | happy(X0) | ~kind(X0))) [flattening 46]
53. ! [X0] : ((((~happy(X0) | kind(X0)) & (happy(X0) | ~kind(X0))) | curious(X0)) & (~curious(X0) | ((~kind(X0) | ~happy(X0)) & (happy(X0) | kind(X0))))) [nnf transformation 14]
82. ~tall(X0) | kind(X0) | kind(X0) | curious(X0) [cnf transformation 43]
86. curious(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0) [cnf transformation 43]
93. ~happy(X0) | kind(X0) [cnf transformation 47]
108. ~curious(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 53]
117. happy(paul) [cnf transformation 17]
127. tall(paul) [cnf transformation 25]
130. ~tall(X0) | kind(X0) | curious(X0) [duplicate literal removal 82]
132. curious(X0) | ~kind(X0) | ~tall(X0) [duplicate literal removal 86]
133. ~tall(X0) | curious(X0) [subsumption resolution 130,132]
149. ~curious(X0) | ~happy(X0) [subsumption resolution 108,93]
251. curious(paul) [resolution 133,127]
253. ~happy(paul) [resolution 149,251]
254. $false [subsumption resolution 253,117]
% SZS output end Proof for 324647744900256166983881
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and happy is strong. If someone is both not patient and rich then lucy is funny or not brave and vice versa. If john is quiet then susan is both not brave and not tall. Everyone who is quiet or not patient is both not rich and quiet and vice versa. Everyone who is both quiet and happy is not kind and vice versa. Everyone who is both happy and kind is kind or not tall and vice versa. Everyone who is patient or not old is rich and vice versa. Everyone who is not creative is not calm or brave. If someone is either happy or not funny then someone is both brave and not brave and vice versa. Everyone who is not kind is not patient. If john is either generous or old then someone is not funny. Everyone who is both not curious and curious is both wise and funny. Everyone who is both calm and happy is both not curious and not humble and vice versa. Everyone who is not humble is both not funny and quiet. Everyone who is both brave and not generous is either not tall or quiet and vice versa. Everyone who is old is either not quiet or not patient and vice versa. Lucy is both strong and generous. John is not quiet or old. Susan is both humble and rich. Paul is creative or not strong. Alice is strong or not quiet. Mary is either not calm or curious. | John is creative. | neutral | (![X]:((~happy(X)&happy(X))=>strong(X)))&
((?[X]:((~patient(X)&rich(X))))<=>((funny(lucy)|~brave(lucy))))&
((quiet(john))=>((~brave(susan)&~tall(susan))))&
(![X]:((quiet(X)|~patient(X))<=>(~rich(X)&quiet(X))))&
(![X]:((quiet(X)&happy(X))<=>~kind(X)))&
(![X]:((happy(X)&kind(X))<=>(kind(X)|~tall(X))))&
(![X]:((patient(X)|~old(X))<=>rich(X)))&
(![X]:(~creative(X)=>(~calm(X)|brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~brave(X)))))&
(![X]:(~kind(X)=>~patient(X)))&
(((generous(john)<~>old(john)))=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&curious(X))=>(wise(X)&funny(X))))&
(![X]:((calm(X)&happy(X))<=>(~curious(X)&~humble(X))))&
(![X]:(~humble(X)=>(~funny(X)&quiet(X))))&
(![X]:((brave(X)&~generous(X))<=>(~tall(X)<~>quiet(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>~patient(X))))&
((strong(lucy)&generous(lucy)))&
((~quiet(john)|old(john)))&
((humble(susan)&rich(susan)))&
((creative(paul)|~strong(paul)))&
((strong(alice)|~quiet(alice)))&
((~calm(mary)<~>curious(mary))) | creative(john) | [] | null | 0 |
Everyone who is both not calm and not funny is both wise and not creative and vice versa. If someone is both humble and happy then someone is not brave and vice versa. Everyone who is both humble and not brave is both old and patient. Everyone who is quiet is both generous and not creative. Everyone who is not creative is either not generous or not strong and vice versa. Everyone who is not patient is both not humble and quiet and vice versa. If someone is both not kind and creative then alice is either not strong or not rich and vice versa. If alice is quiet or not creative then john is kind. Everyone who is both not calm and not funny is wise or kind. If someone is either rich or calm then lucy is strong. If someone is humble or not funny then john is rich or kind. If mary is both brave and tall then paul is old or quiet. Everyone who is either brave or kind is either not strong or not brave and vice versa. Everyone who is wise is not patient or kind and vice versa. If someone is both generous and not tall then someone is not generous and vice versa. Someone is either brave or not brave. Someone is old. Susan is not quiet or happy. Paul is old or wise. Someone is not wise or not rich. Alice is either humble or tall. Mary is not humble. | Susan is generous. | neutral | (![X]:((~calm(X)&~funny(X))<=>(wise(X)&~creative(X))))&
((?[X]:((humble(X)&happy(X))))<=>(?[X]:(~brave(X))))&
(![X]:((humble(X)&~brave(X))=>(old(X)&patient(X))))&
(![X]:(quiet(X)=>(generous(X)&~creative(X))))&
(![X]:(~creative(X)<=>(~generous(X)<~>~strong(X))))&
(![X]:(~patient(X)<=>(~humble(X)&quiet(X))))&
((?[X]:((~kind(X)&creative(X))))<=>((~strong(alice)<~>~rich(alice))))&
(((quiet(alice)|~creative(alice)))=>(kind(john)))&
(![X]:((~calm(X)&~funny(X))=>(wise(X)|kind(X))))&
((?[X]:((rich(X)<~>calm(X))))=>(strong(lucy)))&
((?[X]:((humble(X)|~funny(X))))=>((rich(john)|kind(john))))&
(((brave(mary)&tall(mary)))=>((old(paul)|quiet(paul))))&
(![X]:((brave(X)<~>kind(X))<=>(~strong(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(~patient(X)|kind(X))))&
((?[X]:((generous(X)&~tall(X))))<=>(?[X]:(~generous(X))))&
(?[X]:((brave(X)<~>~brave(X))))&
(?[X]:(old(X)))&
((~quiet(susan)|happy(susan)))&
((old(paul)|wise(paul)))&
(?[X]:((~wise(X)|~rich(X))))&
((humble(alice)<~>tall(alice)))&
(~humble(mary)) | generous(susan) | [] | null | 0 |
Everyone who is not wise or old is both quiet and not patient and vice versa. Everyone who is both brave and patient is not generous or not happy and vice versa. Everyone who is either not tall or strong is tall or not funny. If someone is both humble and happy then susan is happy and vice versa. Everyone who is not strong is rich. If paul is tall then someone is not happy and vice versa. Everyone who is both not wise and curious is both not rich and generous. If someone is not calm then susan is both not old and tall. Everyone who is not funny is not creative and vice versa. Everyone who is not brave or not humble is not happy or calm and vice versa. If john is either not humble or wise then someone is not rich and vice versa. If lucy is both kind and tall then mary is both not calm and calm. Everyone who is either not wise or not strong is either not strong or not rich. If fred is quiet then someone is quiet or not creative and vice versa. Everyone who is not generous is both not kind and tall and vice versa. If someone is both patient and creative then paul is not patient or not strong. Mary is either not curious or kind. Paul is creative. Someone is both not kind and creative. Alice is both generous and not patient. Someone is humble or not curious. Someone is not rich or not curious. Paul is both kind and not wise. Someone is not funny. | Fred is creative. | neutral | (![X]:((~wise(X)|old(X))<=>(quiet(X)&~patient(X))))&
(![X]:((brave(X)&patient(X))<=>(~generous(X)|~happy(X))))&
(![X]:((~tall(X)<~>strong(X))=>(tall(X)|~funny(X))))&
((?[X]:((humble(X)&happy(X))))<=>(happy(susan)))&
(![X]:(~strong(X)=>rich(X)))&
((tall(paul))<=>(?[X]:(~happy(X))))&
(![X]:((~wise(X)&curious(X))=>(~rich(X)&generous(X))))&
((?[X]:(~calm(X)))=>((~old(susan)&tall(susan))))&
(![X]:(~funny(X)<=>~creative(X)))&
(![X]:((~brave(X)|~humble(X))<=>(~happy(X)|calm(X))))&
(((~humble(john)<~>wise(john)))<=>(?[X]:(~rich(X))))&
(((kind(lucy)&tall(lucy)))=>((~calm(mary)&calm(mary))))&
(![X]:((~wise(X)<~>~strong(X))=>(~strong(X)<~>~rich(X))))&
((quiet(fred))<=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:(~generous(X)<=>(~kind(X)&tall(X))))&
((?[X]:((patient(X)&creative(X))))=>((~patient(paul)|~strong(paul))))&
((~curious(mary)<~>kind(mary)))&
(creative(paul))&
(?[X]:((~kind(X)&creative(X))))&
((generous(alice)&~patient(alice)))&
(?[X]:((humble(X)|~curious(X))))&
(?[X]:((~rich(X)|~curious(X))))&
((kind(paul)&~wise(paul)))&
(?[X]:(~funny(X))) | creative(fred) | [] | null | 0 |
Everyone who is either not generous or not strong is funny and vice versa. Everyone who is not humble or rich is either strong or not tall. Everyone who is both not curious and brave is not kind or not curious and vice versa. Everyone who is kind is old. If john is quiet then someone is either not wise or brave and vice versa. If someone is either calm or not creative then someone is either wise or tall. If someone is humble or not rich then someone is either generous or quiet and vice versa. Everyone who is either happy or calm is either not old or not happy and vice versa. If someone is both funny and creative then fred is either not patient or not happy. Everyone who is not curious or not brave is either wise or not rich. If someone is curious then someone is happy or calm. Everyone who is not calm or happy is both wise and not rich. Everyone who is not old is kind and vice versa. Everyone who is both not old and not strong is quiet and vice versa. Everyone who is funny is quiet or not strong and vice versa. Everyone who is both creative and not wise is calm or not happy and vice versa. Someone is both old and creative. Susan is funny. Someone is not happy or tall. Paul is either brave or kind. Fred is not humble. Someone is generous. Lucy is either not funny or creative. | Lucy is funny. | entailment | (![X]:((~generous(X)<~>~strong(X))<=>funny(X)))&
(![X]:((~humble(X)|rich(X))=>(strong(X)<~>~tall(X))))&
(![X]:((~curious(X)&brave(X))<=>(~kind(X)|~curious(X))))&
(![X]:(kind(X)=>old(X)))&
((quiet(john))<=>(?[X]:((~wise(X)<~>brave(X)))))&
((?[X]:((calm(X)<~>~creative(X))))=>(?[X]:((wise(X)<~>tall(X)))))&
((?[X]:((humble(X)|~rich(X))))<=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:((happy(X)<~>calm(X))<=>(~old(X)<~>~happy(X))))&
((?[X]:((funny(X)&creative(X))))=>((~patient(fred)<~>~happy(fred))))&
(![X]:((~curious(X)|~brave(X))=>(wise(X)<~>~rich(X))))&
((?[X]:(curious(X)))=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~calm(X)|happy(X))=>(wise(X)&~rich(X))))&
(![X]:(~old(X)<=>kind(X)))&
(![X]:((~old(X)&~strong(X))<=>quiet(X)))&
(![X]:(funny(X)<=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)&~wise(X))<=>(calm(X)|~happy(X))))&
(?[X]:((old(X)&creative(X))))&
(funny(susan))&
(?[X]:((~happy(X)|tall(X))))&
((brave(paul)<~>kind(paul)))&
(~humble(fred))&
(?[X]:(generous(X)))&
((~funny(lucy)<~>creative(lucy))) | funny(lucy) | [
"p3",
"p7",
"p12",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4517287878744342343621610
% SZS output start Proof for 4517287878744342343621610
4. ! [X0] : (kind(X0) => old(X0)) [input p3]
8. ! [X0] : ((happy(X0) <~> calm(X0)) <=> (~old(X0) <~> ~happy(X0))) [input p7]
13. ! [X0] : (~old(X0) <=> kind(X0)) [input p12]
16. ! [X0] : ((~wise(X0) & creative(X0)) <=> (~happy(X0) | calm(X0))) [input p15]
23. ~funny(lucy) <~> creative(lucy) [input p22]
24. ~funny(lucy) [input hypothesis]
29. ! [X0] : (old(X0) | ~kind(X0)) [ennf transformation 4]
52. ! [X0] : ((((~calm(X0) | ~happy(X0)) & (calm(X0) | happy(X0))) | ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0)))) & (((happy(X0) | old(X0)) & (~happy(X0) | ~old(X0))) | ((happy(X0) | ~calm(X0)) & (calm(X0) | ~happy(X0))))) [nnf transformation 8]
58. ! [X0] : ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0))) [nnf transformation 13]
63. ! [X0] : (((~wise(X0) & creative(X0)) | (happy(X0) & ~calm(X0))) & ((~happy(X0) | calm(X0)) | (wise(X0) | ~creative(X0)))) [nnf transformation 16]
64. ! [X0] : (((~wise(X0) & creative(X0)) | (happy(X0) & ~calm(X0))) & (~happy(X0) | calm(X0) | wise(X0) | ~creative(X0))) [flattening 63]
72. (~creative(lucy) | funny(lucy)) & (creative(lucy) | ~funny(lucy)) [nnf transformation 23]
86. ~kind(X0) | old(X0) [cnf transformation 29]
101. ~happy(X0) | ~old(X0) | calm(X0) | ~happy(X0) [cnf transformation 52]
106. calm(X0) | happy(X0) | ~old(X0) | happy(X0) [cnf transformation 52]
120. kind(X0) | old(X0) [cnf transformation 58]
121. ~old(X0) | ~kind(X0) [cnf transformation 58]
129. ~calm(X0) | creative(X0) [cnf transformation 64]
142. ~creative(lucy) | funny(lucy) [cnf transformation 72]
143. ~funny(lucy) [cnf transformation 24]
144. ~happy(X0) | ~old(X0) | calm(X0) [duplicate literal removal 101]
146. calm(X0) | happy(X0) | ~old(X0) [duplicate literal removal 106]
223. ~old(X0) | calm(X0) [subsumption resolution 144,146]
249. ~kind(X0) [subsumption resolution 121,86]
250. old(X0) [subsumption resolution 120,249]
263. 26 <=> funny(lucy) [avatar definition]
267. 27 <=> creative(lucy) [avatar definition]
269. ~creative(lucy) <- (~27) [avatar component clause 267]
270. 26 | ~27 [avatar split clause 142,267,263]
272. ~26 [avatar split clause 143,263]
297. calm(X0) [resolution 223,250]
302. creative(X2) [resolution 297,129]
345. $false <- (~27) [resolution 302,269]
347. 27 [avatar contradiction clause 345]
348. $false [avatar sat refutation 270,272,347]
% SZS output end Proof for 4517287878744342343621610
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not generous or humble is not wise.
Everyone who is not funny or brave is generous.
If alice is either rich or not quiet then someone is not tall or curious.
If paul is strong then someone is curious or rich.
If susan is not wise or humble then mary is not generous or kind and vice versa.
If someone is patient or not strong then someone is either rich or not calm.
If paul is both not creative and old then someone is both not generous and not creative and vice versa.
If alice is either not patient or humble then susan is both not patient and wise.
Everyone who is not brave or tall is both brave and not generous.
If someone is not patient or not wise then someone is both not generous and wise.
If alice is either funny or not old then fred is either tall or quiet and vice versa.
Everyone who is either not quiet or old is either generous or not generous.
If fred is creative or humble then mary is both old and not creative and vice versa.
If someone is old or funny then someone is both calm and humble.
Everyone who is both not curious and patient is brave.
Everyone who is not wise is either brave or not kind.
Mary is either not kind or strong.
Someone is either creative or not calm.
Mary is either rich or not old.
Someone is both patient and brave.
Alice is generous.
Someone is not brave or generous. | Fred is not quiet. | contradiction | (![X]:((~generous(X)<~>humble(X))=>~wise(X)))&
(![X]:((~funny(X)|brave(X))=>generous(X)))&
(((rich(alice)<~>~quiet(alice)))=>(?[X]:((~tall(X)|curious(X)))))&
((strong(paul))=>(?[X]:((curious(X)|rich(X)))))&
(((~wise(susan)|humble(susan)))<=>((~generous(mary)|kind(mary))))&
((?[X]:((patient(X)|~strong(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
(((~creative(paul)&old(paul)))<=>(?[X]:((~generous(X)&~creative(X)))))&
(((~patient(alice)<~>humble(alice)))=>((~patient(susan)&wise(susan))))&
(![X]:((~brave(X)|tall(X))=>(brave(X)&~generous(X))))&
((?[X]:((~patient(X)|~wise(X))))=>(?[X]:((~generous(X)&wise(X)))))&
(((funny(alice)<~>~old(alice)))<=>((tall(fred)<~>quiet(fred))))&
(![X]:((~quiet(X)<~>old(X))=>(generous(X)<~>~generous(X))))&
(((creative(fred)|humble(fred)))<=>((old(mary)&~creative(mary))))&
((?[X]:((old(X)|funny(X))))=>(?[X]:((calm(X)&humble(X)))))&
(![X]:((~curious(X)&patient(X))=>brave(X)))&
(![X]:(~wise(X)=>(brave(X)<~>~kind(X))))&
((~kind(mary)<~>strong(mary)))&
(?[X]:((creative(X)<~>~calm(X))))&
((rich(mary)<~>~old(mary)))&
(?[X]:((patient(X)&brave(X))))&
(generous(alice))&
(?[X]:((~brave(X)|generous(X)))) | ~quiet(fred) | [
"p0",
"p1",
"p8",
"p9",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5445998311504890726212157
% SZS output start Proof for 5445998311504890726212157
1. ! [X0] : ((~generous(X0) <~> humble(X0)) => ~wise(X0)) [input p0]
2. ! [X0] : ((brave(X0) | ~funny(X0)) => generous(X0)) [input p1]
9. ! [X0] : ((tall(X0) | ~brave(X0)) => (~generous(X0) & brave(X0))) [input p8]
10. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X0] : (wise(X0) & ~generous(X0)) [input p9]
11. (funny(alice) <~> ~old(alice)) <=> (tall(fred) <~> quiet(fred)) [input p10]
14. ? [X0] : (funny(X0) | old(X0)) => ? [X0] : (humble(X0) & calm(X0)) [input p13]
23. ~quiet(fred) [input hypothesis]
25. ? [X0] : (~wise(X0) | ~patient(X0)) => ? [X1] : (wise(X1) & ~generous(X1)) [rectify 10]
26. ? [X0] : (funny(X0) | old(X0)) => ? [X1] : (humble(X1) & calm(X1)) [rectify 14]
30. ! [X0] : (~wise(X0) | (~generous(X0) <=> humble(X0))) [ennf transformation 1]
31. ! [X0] : (generous(X0) | (~brave(X0) & funny(X0))) [ennf transformation 2]
34. ! [X0] : ((~generous(X0) & brave(X0)) | (~tall(X0) & brave(X0))) [ennf transformation 9]
35. ? [X1] : (wise(X1) & ~generous(X1)) | ! [X0] : (wise(X0) & patient(X0)) [ennf transformation 25]
37. ? [X1] : (humble(X1) & calm(X1)) | ! [X0] : (~funny(X0) & ~old(X0)) [ennf transformation 26]
39. ! [X0] : (~wise(X0) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0)))) [nnf transformation 30]
52. ? [X0] : (wise(X0) & ~generous(X0)) | ! [X1] : (wise(X1) & patient(X1)) [rectify 35]
53. ? [X0] : (wise(X0) & ~generous(X0)) => (wise(sK2) & ~generous(sK2)) [choice axiom]
54. (wise(sK2) & ~generous(sK2)) | ! [X1] : (wise(X1) & patient(X1)) [skolemisation 52,53]
55. (((old(alice) | ~funny(alice)) & (~old(alice) | funny(alice))) | ((tall(fred) | ~quiet(fred)) & (quiet(fred) | ~tall(fred)))) & (((~quiet(fred) | ~tall(fred)) & (quiet(fred) | tall(fred))) | ((funny(alice) | old(alice)) & (~old(alice) | ~funny(alice)))) [nnf transformation 11]
59. ? [X0] : (humble(X0) & calm(X0)) | ! [X1] : (~funny(X1) & ~old(X1)) [rectify 37]
60. ? [X0] : (humble(X0) & calm(X0)) => (humble(sK3) & calm(sK3)) [choice axiom]
61. (humble(sK3) & calm(sK3)) | ! [X1] : (~funny(X1) & ~old(X1)) [skolemisation 59,60]
73. ~wise(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 39]
75. ~brave(X0) | generous(X0) [cnf transformation 31]
92. brave(X0) | brave(X0) [cnf transformation 34]
95. ~tall(X0) | ~generous(X0) [cnf transformation 34]
97. ~generous(sK2) | wise(X1) [cnf transformation 54]
101. quiet(fred) | tall(fred) | funny(alice) | old(alice) [cnf transformation 55]
119. humble(sK3) | ~old(X1) [cnf transformation 61]
120. humble(sK3) | ~funny(X1) [cnf transformation 61]
133. ~quiet(fred) [cnf transformation 23]
134. brave(X0) [duplicate literal removal 92]
213. 17 <=> ! [X1] : wise(X1) [avatar definition]
214. wise(X1) <- (17) [avatar component clause 213]
225. 20 <=> generous(sK2) [avatar definition]
227. ~generous(sK2) <- (~20) [avatar component clause 225]
228. 17 | ~20 [avatar split clause 97,225,213]
231. 21 <=> quiet(fred) [avatar definition]
235. 22 <=> tall(fred) [avatar definition]
237. tall(fred) <- (22) [avatar component clause 235]
239. 23 <=> funny(alice) [avatar definition]
240. funny(alice) <- (23) [avatar component clause 239]
243. 24 <=> old(alice) [avatar definition]
245. old(alice) <- (24) [avatar component clause 243]
252. 24 | 23 | 22 | 21 [avatar split clause 101,231,235,239,243]
276. 29 <=> ! [X1] : ~funny(X1) [avatar definition]
277. ~funny(X1) <- (29) [avatar component clause 276]
279. 30 <=> humble(sK3) [avatar definition]
281. humble(sK3) <- (30) [avatar component clause 279]
282. 29 | 30 [avatar split clause 120,279,276]
284. 31 <=> ! [X1] : ~old(X1) [avatar definition]
285. ~old(X1) <- (31) [avatar component clause 284]
286. 31 | 30 [avatar split clause 119,279,284]
316. ~21 [avatar split clause 133,231]
323. generous(X0) [resolution 75,134]
326. $false <- (~20) [resolution 323,227]
327. 20 [avatar contradiction clause 326]
335. ~generous(fred) <- (22) [resolution 95,237]
336. $false <- (22) [subsumption resolution 335,323]
337. ~22 [avatar contradiction clause 336]
346. ~generous(X0) | ~humble(X0) <- (17) [resolution 73,214]
351. ~humble(X0) <- (17) [subsumption resolution 346,323]
353. $false <- (17, 30) [resolution 351,281]
354. ~17 | ~30 [avatar contradiction clause 353]
356. $false <- (23, 29) [resolution 277,240]
357. ~23 | ~29 [avatar contradiction clause 356]
358. $false <- (24, 31) [subsumption resolution 245,285]
359. ~24 | ~31 [avatar contradiction clause 358]
360. $false [avatar sat refutation 228,252,282,286,316,327,337,354,357,359]
% SZS output end Proof for 5445998311504890726212157
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old and not rich is kind or brave.
Everyone who is quiet or patient is either humble or rich.
Everyone who is kind or brave is both not patient and funny.
Everyone who is either old or not strong is either not funny or patient and vice versa.
If someone is either curious or old then john is either not quiet or wise and vice versa.
If alice is both creative and not humble then paul is both rich and not old.
Everyone who is either not tall or not brave is both quiet and wise and vice versa.
If paul is both not calm and old then someone is both creative and not creative.
Everyone who is strong or not strong is not funny or quiet and vice versa.
Everyone who is not tall or funny is either generous or creative.
Everyone who is not kind or creative is either curious or strong.
Everyone who is both patient and not funny is not kind or creative.
If fred is both generous and rich then paul is either funny or wise and vice versa.
If alice is either old or not calm then john is curious.
Everyone who is both not wise and not funny is either funny or generous and vice versa.
If mary is funny then someone is either patient or not funny and vice versa.
Someone is either tall or not wise.
Paul is brave or not tall.
Alice is either creative or patient.
Someone is either old or not happy.
Lucy is not brave or rich.
Lucy is both not calm and not creative.
Someone is both not generous and curious.
Susan is not generous. | Susan is not kind. | entailment | (![X]:((old(X)&~rich(X))=>(kind(X)|brave(X))))&
(![X]:((quiet(X)|patient(X))=>(humble(X)<~>rich(X))))&
(![X]:((kind(X)|brave(X))=>(~patient(X)&funny(X))))&
(![X]:((old(X)<~>~strong(X))<=>(~funny(X)<~>patient(X))))&
((?[X]:((curious(X)<~>old(X))))<=>((~quiet(john)<~>wise(john))))&
(((creative(alice)&~humble(alice)))=>((rich(paul)&~old(paul))))&
(![X]:((~tall(X)<~>~brave(X))<=>(quiet(X)&wise(X))))&
(((~calm(paul)&old(paul)))=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((strong(X)|~strong(X))<=>(~funny(X)|quiet(X))))&
(![X]:((~tall(X)|funny(X))=>(generous(X)<~>creative(X))))&
(![X]:((~kind(X)|creative(X))=>(curious(X)<~>strong(X))))&
(![X]:((patient(X)&~funny(X))=>(~kind(X)|creative(X))))&
(((generous(fred)&rich(fred)))<=>((funny(paul)<~>wise(paul))))&
(((old(alice)<~>~calm(alice)))=>(curious(john)))&
(![X]:((~wise(X)&~funny(X))<=>(funny(X)<~>generous(X))))&
((funny(mary))<=>(?[X]:((patient(X)<~>~funny(X)))))&
(?[X]:((tall(X)<~>~wise(X))))&
((brave(paul)|~tall(paul)))&
((creative(alice)<~>patient(alice)))&
(?[X]:((old(X)<~>~happy(X))))&
((~brave(lucy)|rich(lucy)))&
((~calm(lucy)&~creative(lucy)))&
(?[X]:((~generous(X)&curious(X))))&
(~generous(susan)) | ~kind(susan) | [
"p2",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3910679125583946605772199
% SZS output start Proof for 3910679125583946605772199
3. ! [X0] : ((brave(X0) | kind(X0)) => (funny(X0) & ~patient(X0))) [input p2]
15. ! [X0] : ((~funny(X0) & ~wise(X0)) <=> (funny(X0) <~> generous(X0))) [input p14]
24. ~generous(susan) [input p23]
25. kind(susan) [input hypothesis]
29. ! [X0] : ((funny(X0) & ~patient(X0)) | (~brave(X0) & ~kind(X0))) [ennf transformation 3]
56. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | (funny(X0) | wise(X0)))) [nnf transformation 15]
57. ! [X0] : (((~funny(X0) & ~wise(X0)) | ((funny(X0) | ~generous(X0)) & (generous(X0) | ~funny(X0)))) & (((~generous(X0) | ~funny(X0)) & (generous(X0) | funny(X0))) | funny(X0) | wise(X0))) [flattening 56]
78. ~kind(X0) | funny(X0) [cnf transformation 29]
131. ~funny(X0) | generous(X0) | ~funny(X0) [cnf transformation 57]
149. ~generous(susan) [cnf transformation 24]
150. kind(susan) [cnf transformation 25]
152. ~funny(X0) | generous(X0) [duplicate literal removal 131]
315. funny(susan) [resolution 78,150]
317. generous(susan) [resolution 152,315]
318. $false [subsumption resolution 317,149]
% SZS output end Proof for 3910679125583946605772199
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and old then lucy is either not tall or calm. If john is either humble or not old then someone is both not curious and not generous. Everyone who is rich is either strong or not strong. Everyone who is either not calm or quiet is either not calm or humble and vice versa. Everyone who is not tall or not generous is both not patient and tall. Everyone who is curious or not tall is either not tall or kind and vice versa. Everyone who is both not strong and not calm is not funny or funny and vice versa. Everyone who is calm or not funny is not creative or not tall. Everyone who is not old is either brave or curious. Everyone who is happy is not patient. Everyone who is not tall is either not creative or curious and vice versa. If john is either not creative or not brave then paul is either tall or funny. Everyone who is curious is not old. If someone is either not happy or brave then alice is funny or tall. Everyone who is not old or calm is both strong and not funny. Everyone who is either happy or not curious is both generous and not old. Someone is brave or not humble. Someone is funny or not brave. Someone is happy. Someone is both quiet and funny. Someone is funny. Lucy is rich or old. | Paul is curious. | contradiction | ((?[X]:((calm(X)&old(X))))=>((~tall(lucy)<~>calm(lucy))))&
(((humble(john)<~>~old(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
(![X]:(rich(X)=>(strong(X)<~>~strong(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~generous(X))=>(~patient(X)&tall(X))))&
(![X]:((curious(X)|~tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((~strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
(![X]:((calm(X)|~funny(X))=>(~creative(X)|~tall(X))))&
(![X]:(~old(X)=>(brave(X)<~>curious(X))))&
(![X]:(happy(X)=>~patient(X)))&
(![X]:(~tall(X)<=>(~creative(X)<~>curious(X))))&
(((~creative(john)<~>~brave(john)))=>((tall(paul)<~>funny(paul))))&
(![X]:(curious(X)=>~old(X)))&
((?[X]:((~happy(X)<~>brave(X))))=>((funny(alice)|tall(alice))))&
(![X]:((~old(X)|calm(X))=>(strong(X)&~funny(X))))&
(![X]:((happy(X)<~>~curious(X))=>(generous(X)&~old(X))))&
(?[X]:((brave(X)|~humble(X))))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(funny(X)))&
((rich(lucy)|old(lucy))) | curious(paul) | [
"p6",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3649982876761159784372630
% SZS output start Proof for 3649982876761159784372630
7. ! [X0] : ((~calm(X0) & ~strong(X0)) <=> (funny(X0) | ~funny(X0))) [input p6]
13. ! [X0] : (curious(X0) => ~old(X0)) [input p12]
15. ! [X0] : ((calm(X0) | ~old(X0)) => (~funny(X0) & strong(X0))) [input p14]
23. curious(paul) [input hypothesis]
34. ! [X0] : (~old(X0) | ~curious(X0)) [ennf transformation 13]
37. ! [X0] : ((~funny(X0) & strong(X0)) | (~calm(X0) & old(X0))) [ennf transformation 15]
47. ! [X0] : (((~calm(X0) & ~strong(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (calm(X0) | strong(X0)))) [nnf transformation 7]
48. ! [X0] : (((~calm(X0) & ~strong(X0)) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | calm(X0) | strong(X0))) [flattening 47]
89. ~strong(X0) | funny(X0) [cnf transformation 48]
90. ~funny(X0) | ~strong(X0) [cnf transformation 48]
105. ~curious(X0) | ~old(X0) [cnf transformation 34]
108. strong(X0) | old(X0) [cnf transformation 37]
123. curious(paul) [cnf transformation 23]
169. ~strong(X0) [subsumption resolution 89,90]
189. old(X0) [subsumption resolution 108,169]
218. ~old(paul) [resolution 105,123]
219. $false [subsumption resolution 218,189]
% SZS output end Proof for 3649982876761159784372630
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is not calm.
Everyone who is calm is either calm or humble and vice versa.
If someone is not quiet then fred is wise or not calm and vice versa.
If someone is both kind and not rich then someone is either not funny or not rich.
If fred is both calm and wise then someone is not creative or not quiet.
Everyone who is brave or not wise is curious and vice versa.
Everyone who is either rich or not kind is not strong.
If lucy is not wise or funny then someone is curious.
If fred is either patient or not curious then someone is tall and vice versa.
If someone is not funny then someone is patient.
If someone is both rich and not wise then someone is not kind and vice versa.
Everyone who is not strong or brave is not patient and vice versa.
If fred is both not humble and strong then someone is not wise and vice versa.
Everyone who is either not strong or not humble is both tall and wise and vice versa.
If someone is both not generous and rich then paul is both not calm and not old and vice versa.
If someone is not brave or kind then someone is not humble or not curious.
Someone is either brave or funny.
Someone is quiet.
Someone is either not generous or not patient.
Alice is generous or not tall.
Someone is kind or not curious.
Paul is generous or patient. | Paul is rich. | neutral | (![X]:(tall(X)=>~calm(X)))&
(![X]:(calm(X)<=>(calm(X)<~>humble(X))))&
((?[X]:(~quiet(X)))<=>((wise(fred)|~calm(fred))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~funny(X)<~>~rich(X)))))&
(((calm(fred)&wise(fred)))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((brave(X)|~wise(X))<=>curious(X)))&
(![X]:((rich(X)<~>~kind(X))=>~strong(X)))&
(((~wise(lucy)|funny(lucy)))=>(?[X]:(curious(X))))&
(((patient(fred)<~>~curious(fred)))<=>(?[X]:(tall(X))))&
((?[X]:(~funny(X)))=>(?[X]:(patient(X))))&
((?[X]:((rich(X)&~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~strong(X)|brave(X))<=>~patient(X)))&
(((~humble(fred)&strong(fred)))<=>(?[X]:(~wise(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)&wise(X))))&
((?[X]:((~generous(X)&rich(X))))<=>((~calm(paul)&~old(paul))))&
((?[X]:((~brave(X)|kind(X))))=>(?[X]:((~humble(X)|~curious(X)))))&
(?[X]:((brave(X)<~>funny(X))))&
(?[X]:(quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
((generous(alice)|~tall(alice)))&
(?[X]:((kind(X)|~curious(X))))&
((generous(paul)|patient(paul))) | rich(paul) | [] | null | 0 |
If susan is either not humble or wise then someone is both strong and not rich and vice versa. Everyone who is not strong or funny is either not curious or not wise. If someone is both not generous and humble then someone is either funny or not old and vice versa. Everyone who is tall or not wise is quiet or not humble and vice versa. Everyone who is either curious or wise is not funny and vice versa. Everyone who is both patient and not tall is either not tall or not calm. If someone is both not funny and funny then john is quiet and vice versa. Everyone who is both not quiet and humble is not brave. If lucy is both not kind and rich then someone is not generous or not old. If someone is kind then alice is both not old and wise. If paul is not strong then someone is humble. If someone is creative or not creative then someone is both humble and calm and vice versa. If alice is funny then paul is either quiet or not humble and vice versa. Everyone who is both not strong and creative is both not tall and tall and vice versa. Everyone who is both not strong and quiet is both not funny and tall and vice versa. If fred is not kind or funny then someone is both curious and not kind and vice versa. Someone is kind or funny. Someone is both patient and creative. Alice is both happy and kind. Someone is either not old or rich. Someone is not curious. Fred is not generous or calm. Someone is both not brave and not generous. Someone is generous. | Fred is not calm. | neutral | (((~humble(susan)<~>wise(susan)))<=>(?[X]:((strong(X)&~rich(X)))))&
(![X]:((~strong(X)|funny(X))=>(~curious(X)<~>~wise(X))))&
((?[X]:((~generous(X)&humble(X))))<=>(?[X]:((funny(X)<~>~old(X)))))&
(![X]:((tall(X)|~wise(X))<=>(quiet(X)|~humble(X))))&
(![X]:((curious(X)<~>wise(X))<=>~funny(X)))&
(![X]:((patient(X)&~tall(X))=>(~tall(X)<~>~calm(X))))&
((?[X]:((~funny(X)&funny(X))))<=>(quiet(john)))&
(![X]:((~quiet(X)&humble(X))=>~brave(X)))&
(((~kind(lucy)&rich(lucy)))=>(?[X]:((~generous(X)|~old(X)))))&
((?[X]:(kind(X)))=>((~old(alice)&wise(alice))))&
((~strong(paul))=>(?[X]:(humble(X))))&
((?[X]:((creative(X)|~creative(X))))<=>(?[X]:((humble(X)&calm(X)))))&
((funny(alice))<=>((quiet(paul)<~>~humble(paul))))&
(![X]:((~strong(X)&creative(X))<=>(~tall(X)&tall(X))))&
(![X]:((~strong(X)&quiet(X))<=>(~funny(X)&tall(X))))&
(((~kind(fred)|funny(fred)))<=>(?[X]:((curious(X)&~kind(X)))))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((patient(X)&creative(X))))&
((happy(alice)&kind(alice)))&
(?[X]:((~old(X)<~>rich(X))))&
(?[X]:(~curious(X)))&
((~generous(fred)|calm(fred)))&
(?[X]:((~brave(X)&~generous(X))))&
(?[X]:(generous(X))) | ~calm(fred) | [] | null | 0 |
If john is both generous and old then mary is strong and vice versa.
If paul is both kind and brave then mary is calm.
If john is not happy then mary is both happy and not quiet.
If alice is both wise and not kind then alice is both happy and quiet and vice versa.
If someone is calm then someone is either quiet or wise and vice versa.
Everyone who is brave or not strong is both generous and not creative and vice versa.
If someone is calm then john is happy or patient and vice versa.
If someone is kind then someone is strong or not generous.
Everyone who is both not creative and humble is both not old and curious and vice versa.
If someone is not happy or not kind then john is both generous and not quiet.
Everyone who is not wise is not patient or happy.
Everyone who is curious or not strong is either not old or wise.
Everyone who is wise or not wise is both not curious and not wise.
Everyone who is not strong is not quiet or not rich and vice versa.
If paul is creative then someone is both rich and curious.
Everyone who is both not generous and old is patient or funny and vice versa.
Someone is both calm and generous.
Alice is both not generous and humble.
Someone is either creative or not rich.
Paul is both calm and generous.
Someone is tall or not happy.
Someone is either curious or funny.
Someone is either not kind or not calm. | Mary is not wise. | entailment | (((generous(john)&old(john)))<=>(strong(mary)))&
(((kind(paul)&brave(paul)))=>(calm(mary)))&
((~happy(john))=>((happy(mary)&~quiet(mary))))&
(((wise(alice)&~kind(alice)))<=>((happy(alice)&quiet(alice))))&
((?[X]:(calm(X)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((brave(X)|~strong(X))<=>(generous(X)&~creative(X))))&
((?[X]:(calm(X)))<=>((happy(john)|patient(john))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~rich(X))))&
((creative(paul))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~generous(X)&old(X))<=>(patient(X)|funny(X))))&
(?[X]:((calm(X)&generous(X))))&
((~generous(alice)&humble(alice)))&
(?[X]:((creative(X)<~>~rich(X))))&
((calm(paul)&generous(paul)))&
(?[X]:((tall(X)|~happy(X))))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~kind(X)<~>~calm(X)))) | ~wise(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3590313949197818255558335
% SZS output start Proof for 3590313949197818255558335
13. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p12]
24. wise(mary) [input hypothesis]
36. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 13]
115. ~wise(X0) | ~wise(X0) [cnf transformation 36]
139. wise(mary) [cnf transformation 24]
140. ~wise(X0) [duplicate literal removal 115]
285. $false [subsumption resolution 139,140]
% SZS output end Proof for 3590313949197818255558335
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not funny then paul is not tall or generous. If someone is both humble and calm then someone is either rich or humble and vice versa. Everyone who is generous is either not rich or not calm and vice versa. Everyone who is not quiet or tall is rich or brave and vice versa. If fred is both not funny and creative then someone is either not humble or not strong and vice versa. Everyone who is not tall is not brave and vice versa. Everyone who is either not tall or brave is both humble and not strong. Everyone who is either funny or not generous is not strong. If alice is both not old and not kind then someone is either strong or not patient and vice versa. If fred is either strong or not curious then someone is either generous or not funny. If mary is strong then someone is both strong and brave. Everyone who is creative is not curious or old. If someone is both not calm and not kind then alice is not creative or not humble and vice versa. Everyone who is not strong is not happy or not creative and vice versa. If paul is funny then mary is both brave and not wise. Everyone who is either not wise or not curious is not tall or rich and vice versa. Mary is either not humble or rich. John is both not happy and brave. Someone is either old or not calm. Someone is humble. Fred is not tall or not creative. Someone is not tall or not strong. Fred is both wise and not generous. Mary is both funny and not strong. | John is not tall. | contradiction | ((?[X]:((curious(X)|~funny(X))))=>((~tall(paul)|generous(paul))))&
((?[X]:((humble(X)&calm(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
(![X]:(generous(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((~quiet(X)|tall(X))<=>(rich(X)|brave(X))))&
(((~funny(fred)&creative(fred)))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:(~tall(X)<=>~brave(X)))&
(![X]:((~tall(X)<~>brave(X))=>(humble(X)&~strong(X))))&
(![X]:((funny(X)<~>~generous(X))=>~strong(X)))&
(((~old(alice)&~kind(alice)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(((strong(fred)<~>~curious(fred)))=>(?[X]:((generous(X)<~>~funny(X)))))&
((strong(mary))=>(?[X]:((strong(X)&brave(X)))))&
(![X]:(creative(X)=>(~curious(X)|old(X))))&
((?[X]:((~calm(X)&~kind(X))))<=>((~creative(alice)|~humble(alice))))&
(![X]:(~strong(X)<=>(~happy(X)|~creative(X))))&
((funny(paul))=>((brave(mary)&~wise(mary))))&
(![X]:((~wise(X)<~>~curious(X))<=>(~tall(X)|rich(X))))&
((~humble(mary)<~>rich(mary)))&
((~happy(john)&brave(john)))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:(humble(X)))&
((~tall(fred)|~creative(fred)))&
(?[X]:((~tall(X)|~strong(X))))&
((wise(fred)&~generous(fred)))&
((funny(mary)&~strong(mary))) | ~tall(john) | [
"p5",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1589222334543313474530852
% SZS output start Proof for 1589222334543313474530852
6. ! [X0] : (~tall(X0) <=> ~brave(X0)) [input p5]
18. brave(john) & ~happy(john) [input p17]
25. ~tall(john) [input hypothesis]
49. ! [X0] : ((~tall(X0) | brave(X0)) & (~brave(X0) | tall(X0))) [nnf transformation 6]
101. ~brave(X0) | tall(X0) [cnf transformation 49]
141. brave(john) [cnf transformation 18]
151. ~tall(john) [cnf transformation 25]
358. tall(john) [resolution 101,141]
359. $false [subsumption resolution 358,151]
% SZS output end Proof for 1589222334543313474530852
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious then susan is both not patient and quiet.
If john is not kind or brave then someone is either not patient or not curious and vice versa.
Everyone who is either patient or not curious is both not tall and brave.
Everyone who is both not rich and generous is either curious or patient.
If paul is not humble then fred is either not patient or not tall.
If john is not brave or humble then john is humble.
If someone is tall then someone is not patient or wise and vice versa.
If someone is both not brave and not patient then susan is quiet and vice versa.
If mary is not creative or calm then alice is not tall or funny and vice versa.
Everyone who is creative or old is generous and vice versa.
Everyone who is both not rich and tall is both not curious and not wise.
If mary is either calm or not wise then someone is either tall or old and vice versa.
If someone is not humble then someone is humble or not patient and vice versa.
If someone is kind then someone is both not brave and quiet.
Everyone who is both not old and curious is old or wise.
Everyone who is wise or happy is both not happy and not strong and vice versa.
Someone is both rich and wise.
Susan is not generous.
Susan is both not funny and not rich.
Someone is both not creative and tall.
Someone is not wise or tall.
Someone is not funny or generous.
Someone is either not happy or calm.
Lucy is either strong or wise. | Paul is not happy. | entailment | ((?[X]:(curious(X)))=>((~patient(susan)&quiet(susan))))&
(((~kind(john)|brave(john)))<=>(?[X]:((~patient(X)<~>~curious(X)))))&
(![X]:((patient(X)<~>~curious(X))=>(~tall(X)&brave(X))))&
(![X]:((~rich(X)&generous(X))=>(curious(X)<~>patient(X))))&
((~humble(paul))=>((~patient(fred)<~>~tall(fred))))&
(((~brave(john)|humble(john)))=>(humble(john)))&
((?[X]:(tall(X)))<=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((~brave(X)&~patient(X))))<=>(quiet(susan)))&
(((~creative(mary)|calm(mary)))<=>((~tall(alice)|funny(alice))))&
(![X]:((creative(X)|old(X))<=>generous(X)))&
(![X]:((~rich(X)&tall(X))=>(~curious(X)&~wise(X))))&
(((calm(mary)<~>~wise(mary)))<=>(?[X]:((tall(X)<~>old(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((humble(X)|~patient(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~brave(X)&quiet(X)))))&
(![X]:((~old(X)&curious(X))=>(old(X)|wise(X))))&
(![X]:((wise(X)|happy(X))<=>(~happy(X)&~strong(X))))&
(?[X]:((rich(X)&wise(X))))&
(~generous(susan))&
((~funny(susan)&~rich(susan)))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((~wise(X)|tall(X))))&
(?[X]:((~funny(X)|generous(X))))&
(?[X]:((~happy(X)<~>calm(X))))&
((strong(lucy)<~>wise(lucy))) | ~happy(paul) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8333864991570536737259905
% SZS output start Proof for 8333864991570536737259905
16. ! [X0] : ((happy(X0) | wise(X0)) <=> (~strong(X0) & ~happy(X0))) [input p15]
25. happy(paul) [input hypothesis]
73. ! [X0] : (((happy(X0) | wise(X0)) | (strong(X0) | happy(X0))) & ((~strong(X0) & ~happy(X0)) | (~happy(X0) & ~wise(X0)))) [nnf transformation 16]
74. ! [X0] : ((happy(X0) | wise(X0) | strong(X0) | happy(X0)) & ((~strong(X0) & ~happy(X0)) | (~happy(X0) & ~wise(X0)))) [flattening 73]
135. ~happy(X0) | ~happy(X0) [cnf transformation 74]
152. happy(paul) [cnf transformation 25]
153. ~happy(X0) [duplicate literal removal 135]
362. $false [subsumption resolution 152,153]
% SZS output end Proof for 8333864991570536737259905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not brave and old then mary is both old and strong and vice versa. Everyone who is not wise or not old is curious and vice versa. Everyone who is either calm or humble is both not generous and kind and vice versa. If someone is either brave or patient then someone is both not curious and not tall and vice versa. Everyone who is either not tall or not generous is humble and vice versa. If paul is patient then someone is both not tall and not generous and vice versa. Everyone who is both not tall and creative is humble or not wise and vice versa. Everyone who is not wise or kind is patient and vice versa. If mary is both tall and not rich then lucy is either creative or funny. If alice is both not brave and kind then someone is old. Everyone who is either not humble or not calm is quiet or not generous and vice versa. If john is both not tall and not calm then susan is not happy. Everyone who is not tall or not quiet is generous and vice versa. Everyone who is either not happy or generous is either happy or not strong. If fred is strong or not patient then fred is curious and vice versa. Someone is either strong or patient. Someone is either brave or creative. Someone is tall. Someone is not rich or calm. John is both not quiet and wise. Paul is either happy or humble. | Susan is happy. | neutral | ((?[X]:((~brave(X)&old(X))))<=>((old(mary)&strong(mary))))&
(![X]:((~wise(X)|~old(X))<=>curious(X)))&
(![X]:((calm(X)<~>humble(X))<=>(~generous(X)&kind(X))))&
((?[X]:((brave(X)<~>patient(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
(![X]:((~tall(X)<~>~generous(X))<=>humble(X)))&
((patient(paul))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~tall(X)&creative(X))<=>(humble(X)|~wise(X))))&
(![X]:((~wise(X)|kind(X))<=>patient(X)))&
(((tall(mary)&~rich(mary)))=>((creative(lucy)<~>funny(lucy))))&
(((~brave(alice)&kind(alice)))=>(?[X]:(old(X))))&
(![X]:((~humble(X)<~>~calm(X))<=>(quiet(X)|~generous(X))))&
(((~tall(john)&~calm(john)))=>(~happy(susan)))&
(![X]:((~tall(X)|~quiet(X))<=>generous(X)))&
(![X]:((~happy(X)<~>generous(X))=>(happy(X)<~>~strong(X))))&
(((strong(fred)|~patient(fred)))<=>(curious(fred)))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((brave(X)<~>creative(X))))&
(?[X]:(tall(X)))&
(?[X]:((~rich(X)|calm(X))))&
((~quiet(john)&wise(john)))&
((happy(paul)<~>humble(paul))) | happy(susan) | [] | null | 0 |
Everyone who is either not funny or not old is tall and vice versa.
If john is not tall then someone is either not calm or quiet.
Everyone who is not kind is not funny.
If lucy is either kind or quiet then someone is both generous and not patient.
Everyone who is not rich or not creative is not humble and vice versa.
If someone is both not creative and not generous then mary is not old or not kind and vice versa.
Everyone who is both not humble and brave is both wise and not quiet and vice versa.
Everyone who is either not happy or tall is either not tall or strong and vice versa.
If paul is both not calm and rich then someone is humble and vice versa.
Everyone who is tall is calm or brave.
Everyone who is not quiet or not humble is either generous or not humble and vice versa.
Everyone who is either not happy or not creative is wise or not curious and vice versa.
Everyone who is either rich or not funny is either curious or not curious and vice versa.
Everyone who is not strong or not generous is brave and vice versa.
Everyone who is not happy or tall is not rich or funny.
Everyone who is not funny is not calm and vice versa.
Someone is creative or patient.
Someone is wise or not creative.
Someone is both patient and not funny.
Someone is not wise or not calm.
Someone is not generous or quiet. | John is humble. | contradiction | (![X]:((~funny(X)<~>~old(X))<=>tall(X)))&
((~tall(john))=>(?[X]:((~calm(X)<~>quiet(X)))))&
(![X]:(~kind(X)=>~funny(X)))&
(((kind(lucy)<~>quiet(lucy)))=>(?[X]:((generous(X)&~patient(X)))))&
(![X]:((~rich(X)|~creative(X))<=>~humble(X)))&
((?[X]:((~creative(X)&~generous(X))))<=>((~old(mary)|~kind(mary))))&
(![X]:((~humble(X)&brave(X))<=>(wise(X)&~quiet(X))))&
(![X]:((~happy(X)<~>tall(X))<=>(~tall(X)<~>strong(X))))&
(((~calm(paul)&rich(paul)))<=>(?[X]:(humble(X))))&
(![X]:(tall(X)=>(calm(X)|brave(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(generous(X)<~>~humble(X))))&
(![X]:((~happy(X)<~>~creative(X))<=>(wise(X)|~curious(X))))&
(![X]:((rich(X)<~>~funny(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~strong(X)|~generous(X))<=>brave(X)))&
(![X]:((~happy(X)|tall(X))=>(~rich(X)|funny(X))))&
(![X]:(~funny(X)<=>~calm(X)))&
(?[X]:((creative(X)|patient(X))))&
(?[X]:((wise(X)|~creative(X))))&
(?[X]:((patient(X)&~funny(X))))&
(?[X]:((~wise(X)|~calm(X))))&
(?[X]:((~generous(X)|quiet(X)))) | humble(john) | [
"p8",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7551321862182612071722521
% SZS output start Proof for 7551321862182612071722521
9. (rich(paul) & ~calm(paul)) <=> ? [X0] : humble(X0) [input p8]
13. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p12]
16. ! [X0] : (~funny(X0) <=> ~calm(X0)) [input p15]
22. humble(john) [input hypothesis]
47. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~rich(paul) | calm(paul))) [nnf transformation 9]
48. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ~rich(paul) | calm(paul)) [flattening 47]
49. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ~rich(paul) | calm(paul)) [rectify 48]
50. ? [X1] : humble(X1) => humble(sK3) [choice axiom]
51. ((rich(paul) & ~calm(paul)) | ! [X0] : ~humble(X0)) & (humble(sK3) | ~rich(paul) | calm(paul)) [skolemisation 49,50]
56. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 13]
59. ! [X0] : ((~funny(X0) | calm(X0)) & (~calm(X0) | funny(X0))) [nnf transformation 16]
102. ~calm(paul) | ~humble(X0) [cnf transformation 51]
103. rich(paul) | ~humble(X0) [cnf transformation 51]
123. funny(X0) | ~rich(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 56]
124. funny(X0) | ~rich(X0) | curious(X0) | curious(X0) [cnf transformation 56]
131. ~funny(X0) | calm(X0) [cnf transformation 59]
138. humble(john) [cnf transformation 22]
141. funny(X0) | ~rich(X0) | ~curious(X0) [duplicate literal removal 123]
142. funny(X0) | ~rich(X0) | curious(X0) [duplicate literal removal 124]
210. 13 <=> ! [X0] : ~humble(X0) [avatar definition]
211. ~humble(X0) <- (13) [avatar component clause 210]
213. 14 <=> rich(paul) [avatar definition]
215. rich(paul) <- (14) [avatar component clause 213]
216. 13 | 14 [avatar split clause 103,213,210]
218. 15 <=> calm(paul) [avatar definition]
220. ~calm(paul) <- (~15) [avatar component clause 218]
221. 13 | ~15 [avatar split clause 102,218,210]
227. ~rich(X0) | funny(X0) [subsumption resolution 141,142]
265. $false <- (13) [resolution 211,138]
266. ~13 [avatar contradiction clause 265]
272. funny(paul) <- (14) [resolution 227,215]
276. calm(paul) <- (14) [resolution 272,131]
278. $false <- (14, ~15) [subsumption resolution 276,220]
279. ~14 | 15 [avatar contradiction clause 278]
280. $false [avatar sat refutation 216,221,266,279]
% SZS output end Proof for 7551321862182612071722521
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Fred is patient. | 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))) | patient(fred) | [
"p0",
"p1",
"p3",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3066855138691277160607204
% SZS output start Proof for 3066855138691277160607204
1. ! [X0] : ((creative(X0) | ~creative(X0)) <=> ~calm(X0)) [input p0]
2. ! [X0] : ((humble(X0) & patient(X0)) <=> creative(X0)) [input p1]
4. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (calm(X0) & quiet(X0))) [input p3]
15. ! [X0] : ((~curious(X0) | ~creative(X0)) <=> (~patient(X0) & ~strong(X0))) [input p14]
23. ~patient(fred) [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]
35. ! [X0] : (((humble(X0) & patient(X0)) | ~creative(X0)) & (creative(X0) | (~humble(X0) | ~patient(X0)))) [nnf transformation 2]
36. ! [X0] : (((humble(X0) & patient(X0)) | ~creative(X0)) & (creative(X0) | ~humble(X0) | ~patient(X0))) [flattening 35]
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]
62. ! [X0] : (((~curious(X0) | ~creative(X0)) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | (curious(X0) & creative(X0)))) [nnf transformation 15]
63. ! [X0] : ((~curious(X0) | ~creative(X0) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | (curious(X0) & creative(X0)))) [flattening 62]
72. ~calm(X0) | creative(X0) [cnf transformation 34]
73. ~calm(X0) | ~creative(X0) [cnf transformation 34]
76. ~creative(X0) | patient(X0) [cnf transformation 36]
83. calm(X0) | strong(X0) [cnf transformation 42]
116. ~strong(X0) | creative(X0) [cnf transformation 63]
132. ~patient(fred) [cnf transformation 23]
133. ~calm(X0) [subsumption resolution 72,73]
147. strong(X0) [subsumption resolution 83,133]
161. 6 <=> ! [X0] : creative(X0) [avatar definition]
162. creative(X0) <- (6) [avatar component clause 161]
223. creative(X0) [subsumption resolution 116,147]
224. 6 [avatar split clause 223,161]
249. patient(X0) <- (6) [resolution 76,162]
252. $false <- (6) [resolution 249,132]
255. ~6 [avatar contradiction clause 252]
256. $false [avatar sat refutation 224,255]
% SZS output end Proof for 3066855138691277160607204
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or not creative is not quiet. If lucy is either old or happy then mary is both strong and old and vice versa. If someone is generous or happy then fred is generous or not humble. Everyone who is either not calm or brave is not funny or curious and vice versa. Everyone who is either creative or wise is not rich or strong. If someone is quiet then someone is generous or not curious and vice versa. Everyone who is either brave or not old is either not strong or not funny and vice versa. If john is not old or brave then someone is either quiet or not quiet. Everyone who is not kind is not curious or not quiet and vice versa. If someone is tall then someone is both not old and kind. If fred is both not strong and not funny then someone is both not patient and old. Everyone who is either kind or not strong is either tall or strong and vice versa. Everyone who is either not strong or brave is not tall. Everyone who is not generous is both not brave and generous and vice versa. If someone is not calm then susan is either not curious or not creative and vice versa. Everyone who is both not strong and not quiet is both humble and happy and vice versa. Someone is strong. Fred is kind or not funny. Lucy is funny or wise. Someone is not creative or not brave. Someone is either happy or humble. | John is kind. | neutral | (![X]:((calm(X)<~>~creative(X))=>~quiet(X)))&
(((old(lucy)<~>happy(lucy)))<=>((strong(mary)&old(mary))))&
((?[X]:((generous(X)|happy(X))))=>((generous(fred)|~humble(fred))))&
(![X]:((~calm(X)<~>brave(X))<=>(~funny(X)|curious(X))))&
(![X]:((creative(X)<~>wise(X))=>(~rich(X)|strong(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((generous(X)|~curious(X)))))&
(![X]:((brave(X)<~>~old(X))<=>(~strong(X)<~>~funny(X))))&
(((~old(john)|brave(john)))=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:(~kind(X)<=>(~curious(X)|~quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:((~old(X)&kind(X)))))&
(((~strong(fred)&~funny(fred)))=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((kind(X)<~>~strong(X))<=>(tall(X)<~>strong(X))))&
(![X]:((~strong(X)<~>brave(X))=>~tall(X)))&
(![X]:(~generous(X)<=>(~brave(X)&generous(X))))&
((?[X]:(~calm(X)))<=>((~curious(susan)<~>~creative(susan))))&
(![X]:((~strong(X)&~quiet(X))<=>(humble(X)&happy(X))))&
(?[X]:(strong(X)))&
((kind(fred)|~funny(fred)))&
((funny(lucy)|wise(lucy)))&
(?[X]:((~creative(X)|~brave(X))))&
(?[X]:((happy(X)<~>humble(X)))) | kind(john) | [] | null | 0 |
Everyone who is not strong or not rich is both not humble and not patient and vice versa.
If mary is either not calm or not humble then someone is strong and vice versa.
Everyone who is rich or curious is either strong or brave and vice versa.
Everyone who is either not calm or not rich is humble or not happy and vice versa.
Everyone who is both not patient and kind is not strong or not creative.
Everyone who is either curious or tall is quiet.
If lucy is humble then fred is either not strong or not wise and vice versa.
Everyone who is strong or not humble is old.
If mary is not quiet then mary is not tall.
Everyone who is not creative is both old and not wise and vice versa.
If alice is both not rich and not quiet then someone is both not kind and not brave and vice versa.
Everyone who is both humble and not quiet is happy or not brave.
Everyone who is rich or wise is not curious or funny.
Everyone who is both not kind and creative is either wise or generous.
If someone is either not patient or quiet then lucy is either funny or happy.
If mary is both rich and not humble then susan is not generous or creative.
Someone is not creative.
Someone is old.
Someone is not curious or generous.
Someone is either not curious or not brave.
Someone is patient.
Mary is both curious and not humble.
Fred is humble. | Lucy is not tall. | neutral | (![X]:((~strong(X)|~rich(X))<=>(~humble(X)&~patient(X))))&
(((~calm(mary)<~>~humble(mary)))<=>(?[X]:(strong(X))))&
(![X]:((rich(X)|curious(X))<=>(strong(X)<~>brave(X))))&
(![X]:((~calm(X)<~>~rich(X))<=>(humble(X)|~happy(X))))&
(![X]:((~patient(X)&kind(X))=>(~strong(X)|~creative(X))))&
(![X]:((curious(X)<~>tall(X))=>quiet(X)))&
((humble(lucy))<=>((~strong(fred)<~>~wise(fred))))&
(![X]:((strong(X)|~humble(X))=>old(X)))&
((~quiet(mary))=>(~tall(mary)))&
(![X]:(~creative(X)<=>(old(X)&~wise(X))))&
(((~rich(alice)&~quiet(alice)))<=>(?[X]:((~kind(X)&~brave(X)))))&
(![X]:((humble(X)&~quiet(X))=>(happy(X)|~brave(X))))&
(![X]:((rich(X)|wise(X))=>(~curious(X)|funny(X))))&
(![X]:((~kind(X)&creative(X))=>(wise(X)<~>generous(X))))&
((?[X]:((~patient(X)<~>quiet(X))))=>((funny(lucy)<~>happy(lucy))))&
(((rich(mary)&~humble(mary)))=>((~generous(susan)|creative(susan))))&
(?[X]:(~creative(X)))&
(?[X]:(old(X)))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:(patient(X)))&
((curious(mary)&~humble(mary)))&
(humble(fred)) | ~tall(lucy) | [] | null | 0 |
Everyone who is strong or not kind is old.
If mary is either not brave or not quiet then someone is both not patient and not curious and vice versa.
Everyone who is not funny or not kind is creative.
Everyone who is both not rich and not tall is both curious and not wise and vice versa.
If someone is both quiet and kind then someone is either brave or creative and vice versa.
If someone is not curious or brave then someone is both calm and not happy and vice versa.
Everyone who is both not humble and not funny is either not tall or not kind.
If john is not wise then john is both not tall and not humble and vice versa.
If someone is either happy or not patient then someone is not patient or not strong and vice versa.
If alice is both not calm and happy then someone is not rich or not humble and vice versa.
Everyone who is humble is both not old and quiet and vice versa.
If mary is either strong or creative then john is both rich and not quiet and vice versa.
If mary is quiet or patient then someone is calm.
Everyone who is brave is not funny.
Everyone who is either wise or not rich is both strong and brave.
If someone is calm or not happy then someone is both humble and not kind and vice versa.
Someone is either generous or not tall.
Someone is both not old and not brave.
Someone is kind or not calm.
Someone is old.
Fred is either not patient or not kind.
Lucy is either old or not quiet.
Fred is tall. | John is happy. | entailment | (![X]:((strong(X)|~kind(X))=>old(X)))&
(((~brave(mary)<~>~quiet(mary)))<=>(?[X]:((~patient(X)&~curious(X)))))&
(![X]:((~funny(X)|~kind(X))=>creative(X)))&
(![X]:((~rich(X)&~tall(X))<=>(curious(X)&~wise(X))))&
((?[X]:((quiet(X)&kind(X))))<=>(?[X]:((brave(X)<~>creative(X)))))&
((?[X]:((~curious(X)|brave(X))))<=>(?[X]:((calm(X)&~happy(X)))))&
(![X]:((~humble(X)&~funny(X))=>(~tall(X)<~>~kind(X))))&
((~wise(john))<=>((~tall(john)&~humble(john))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(?[X]:((~patient(X)|~strong(X)))))&
(((~calm(alice)&happy(alice)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(humble(X)<=>(~old(X)&quiet(X))))&
(((strong(mary)<~>creative(mary)))<=>((rich(john)&~quiet(john))))&
(((quiet(mary)|patient(mary)))=>(?[X]:(calm(X))))&
(![X]:(brave(X)=>~funny(X)))&
(![X]:((wise(X)<~>~rich(X))=>(strong(X)&brave(X))))&
((?[X]:((calm(X)|~happy(X))))<=>(?[X]:((humble(X)&~kind(X)))))&
(?[X]:((generous(X)<~>~tall(X))))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((kind(X)|~calm(X))))&
(?[X]:(old(X)))&
((~patient(fred)<~>~kind(fred)))&
((old(lucy)<~>~quiet(lucy)))&
(tall(fred)) | happy(john) | [
"p0",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4715992044815160407963853
% SZS output start Proof for 4715992044815160407963853
1. ! [X0] : ((~kind(X0) | strong(X0)) => old(X0)) [input p0]
11. ! [X0] : (humble(X0) <=> (quiet(X0) & ~old(X0))) [input p10]
16. ? [X0] : (~happy(X0) | calm(X0)) <=> ? [X0] : (~kind(X0) & humble(X0)) [input p15]
24. ~happy(john) [input hypothesis]
28. ? [X0] : (~happy(X0) | calm(X0)) <=> ? [X1] : (~kind(X1) & humble(X1)) [rectify 16]
29. ! [X0] : (old(X0) | (kind(X0) & ~strong(X0))) [ennf transformation 1]
65. ! [X0] : ((humble(X0) | (~quiet(X0) | old(X0))) & ((quiet(X0) & ~old(X0)) | ~humble(X0))) [nnf transformation 11]
66. ! [X0] : ((humble(X0) | ~quiet(X0) | old(X0)) & ((quiet(X0) & ~old(X0)) | ~humble(X0))) [flattening 65]
72. (? [X0] : (~happy(X0) | calm(X0)) | ! [X1] : (kind(X1) | ~humble(X1))) & (? [X1] : (~kind(X1) & humble(X1)) | ! [X0] : (happy(X0) & ~calm(X0))) [nnf transformation 28]
73. (? [X0] : (~happy(X0) | calm(X0)) | ! [X1] : (kind(X1) | ~humble(X1))) & (? [X2] : (~kind(X2) & humble(X2)) | ! [X3] : (happy(X3) & ~calm(X3))) [rectify 72]
74. ? [X0] : (~happy(X0) | calm(X0)) => (~happy(sK9) | calm(sK9)) [choice axiom]
75. ? [X2] : (~kind(X2) & humble(X2)) => (~kind(sK10) & humble(sK10)) [choice axiom]
76. ((~happy(sK9) | calm(sK9)) | ! [X1] : (kind(X1) | ~humble(X1))) & ((~kind(sK10) & humble(sK10)) | ! [X3] : (happy(X3) & ~calm(X3))) [skolemisation 73,75,74]
89. old(X0) | kind(X0) [cnf transformation 29]
129. ~humble(X0) | ~old(X0) [cnf transformation 66]
146. humble(sK10) | happy(X3) [cnf transformation 76]
148. ~kind(sK10) | happy(X3) [cnf transformation 76]
161. ~happy(john) [cnf transformation 24]
369. 46 <=> ! [X3] : happy(X3) [avatar definition]
370. happy(X3) <- (46) [avatar component clause 369]
372. 47 <=> kind(sK10) [avatar definition]
374. ~kind(sK10) <- (~47) [avatar component clause 372]
375. 46 | ~47 [avatar split clause 148,372,369]
381. 49 <=> humble(sK10) [avatar definition]
383. humble(sK10) <- (49) [avatar component clause 381]
384. 46 | 49 [avatar split clause 146,381,369]
444. ~old(sK10) <- (49) [resolution 129,383]
447. kind(sK10) <- (49) [resolution 444,89]
448. $false <- (~47, 49) [subsumption resolution 447,374]
449. 47 | ~49 [avatar contradiction clause 448]
450. $false <- (46) [resolution 370,161]
451. ~46 [avatar contradiction clause 450]
452. $false [avatar sat refutation 375,384,449,451]
% SZS output end Proof for 4715992044815160407963853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both rich and not calm then someone is both not humble and calm.
Everyone who is not quiet or not happy is both not happy and not creative.
Everyone who is not kind or strong is either old or not patient.
Everyone who is generous is either not brave or generous and vice versa.
Everyone who is creative or not brave is not curious or patient and vice versa.
Everyone who is both strong and brave is not patient or not generous and vice versa.
Everyone who is either quiet or not old is humble or curious.
Everyone who is brave or old is creative and vice versa.
If someone is both not curious and rich then someone is not calm and vice versa.
Everyone who is not old is not wise or not patient.
If someone is not humble or happy then paul is not strong or not quiet.
Everyone who is both creative and not calm is old or humble and vice versa.
If fred is either not funny or happy then alice is either not wise or not kind and vice versa.
Everyone who is not calm is not happy and vice versa.
Everyone who is either not old or not calm is both not wise and calm.
Someone is not curious or wise.
Someone is both tall and quiet.
Someone is not old.
Someone is generous.
Susan is tall or generous.
Someone is strong or not strong. | Paul is kind. | entailment | (((rich(paul)&~calm(paul)))=>(?[X]:((~humble(X)&calm(X)))))&
(![X]:((~quiet(X)|~happy(X))=>(~happy(X)&~creative(X))))&
(![X]:((~kind(X)|strong(X))=>(old(X)<~>~patient(X))))&
(![X]:(generous(X)<=>(~brave(X)<~>generous(X))))&
(![X]:((creative(X)|~brave(X))<=>(~curious(X)|patient(X))))&
(![X]:((strong(X)&brave(X))<=>(~patient(X)|~generous(X))))&
(![X]:((quiet(X)<~>~old(X))=>(humble(X)|curious(X))))&
(![X]:((brave(X)|old(X))<=>creative(X)))&
((?[X]:((~curious(X)&rich(X))))<=>(?[X]:(~calm(X))))&
(![X]:(~old(X)=>(~wise(X)|~patient(X))))&
((?[X]:((~humble(X)|happy(X))))=>((~strong(paul)|~quiet(paul))))&
(![X]:((creative(X)&~calm(X))<=>(old(X)|humble(X))))&
(((~funny(fred)<~>happy(fred)))<=>((~wise(alice)<~>~kind(alice))))&
(![X]:(~calm(X)<=>~happy(X)))&
(![X]:((~old(X)<~>~calm(X))=>(~wise(X)&calm(X))))&
(?[X]:((~curious(X)|wise(X))))&
(?[X]:((tall(X)&quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:(generous(X)))&
((tall(susan)|generous(susan)))&
(?[X]:((strong(X)|~strong(X)))) | kind(paul) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p10",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7000899854556460676799560
% SZS output start Proof for 7000899854556460676799560
2. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~creative(X0) & ~happy(X0))) [input p1]
3. ! [X0] : ((strong(X0) | ~kind(X0)) => (old(X0) <~> ~patient(X0))) [input p2]
4. ! [X0] : (generous(X0) <=> (~brave(X0) <~> generous(X0))) [input p3]
6. ! [X0] : ((brave(X0) & strong(X0)) <=> (~generous(X0) | ~patient(X0))) [input p5]
8. ! [X0] : ((old(X0) | brave(X0)) <=> creative(X0)) [input p7]
11. ? [X0] : (happy(X0) | ~humble(X0)) => (~quiet(paul) | ~strong(paul)) [input p10]
12. ! [X0] : ((~calm(X0) & creative(X0)) <=> (humble(X0) | old(X0))) [input p11]
15. ! [X0] : ((~old(X0) <~> ~calm(X0)) => (calm(X0) & ~wise(X0))) [input p14]
22. ~kind(paul) [input hypothesis]
28. ! [X0] : ((~creative(X0) & ~happy(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 2]
29. ! [X0] : ((old(X0) <~> ~patient(X0)) | (~strong(X0) & kind(X0))) [ennf transformation 3]
34. (~quiet(paul) | ~strong(paul)) | ! [X0] : (~happy(X0) & humble(X0)) [ennf transformation 11]
35. ~quiet(paul) | ~strong(paul) | ! [X0] : (~happy(X0) & humble(X0)) [flattening 34]
36. ! [X0] : ((calm(X0) & ~wise(X0)) | (~old(X0) <=> ~calm(X0))) [ennf transformation 15]
39. ! [X0] : (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | (~strong(X0) & kind(X0))) [nnf transformation 29]
40. ! [X0] : ((generous(X0) | ((~brave(X0) | ~generous(X0)) & (generous(X0) | brave(X0)))) & (((~generous(X0) | brave(X0)) & (generous(X0) | ~brave(X0))) | ~generous(X0))) [nnf transformation 4]
43. ! [X0] : (((brave(X0) & strong(X0)) | (generous(X0) & patient(X0))) & ((~generous(X0) | ~patient(X0)) | (~brave(X0) | ~strong(X0)))) [nnf transformation 6]
44. ! [X0] : (((brave(X0) & strong(X0)) | (generous(X0) & patient(X0))) & (~generous(X0) | ~patient(X0) | ~brave(X0) | ~strong(X0))) [flattening 43]
46. ! [X0] : (((old(X0) | brave(X0)) | ~creative(X0)) & (creative(X0) | (~old(X0) & ~brave(X0)))) [nnf transformation 8]
47. ! [X0] : ((old(X0) | brave(X0) | ~creative(X0)) & (creative(X0) | (~old(X0) & ~brave(X0)))) [flattening 46]
53. ! [X0] : (((~calm(X0) & creative(X0)) | (~humble(X0) & ~old(X0))) & ((humble(X0) | old(X0)) | (calm(X0) | ~creative(X0)))) [nnf transformation 12]
54. ! [X0] : (((~calm(X0) & creative(X0)) | (~humble(X0) & ~old(X0))) & (humble(X0) | old(X0) | calm(X0) | ~creative(X0))) [flattening 53]
57. ! [X0] : ((calm(X0) & ~wise(X0)) | ((~old(X0) | calm(X0)) & (~calm(X0) | old(X0)))) [nnf transformation 36]
72. ~creative(X0) | quiet(X0) [cnf transformation 28]
73. ~creative(X0) | happy(X0) [cnf transformation 28]
74. ~patient(X0) | old(X0) | kind(X0) [cnf transformation 39]
79. ~generous(X0) | brave(X0) | ~generous(X0) [cnf transformation 40]
80. generous(X0) | generous(X0) | brave(X0) [cnf transformation 40]
87. patient(X0) | strong(X0) [cnf transformation 44]
93. creative(X0) | ~brave(X0) [cnf transformation 47]
101. ~quiet(paul) | ~strong(paul) | ~happy(X0) [cnf transformation 35]
105. ~old(X0) | ~calm(X0) [cnf transformation 54]
120. calm(X0) | ~old(X0) | calm(X0) [cnf transformation 57]
126. ~kind(paul) [cnf transformation 22]
127. calm(X0) | ~old(X0) [duplicate literal removal 120]
128. ~generous(X0) | brave(X0) [duplicate literal removal 79]
129. brave(X0) | generous(X0) [duplicate literal removal 80]
148. brave(X0) [subsumption resolution 128,129]
152. creative(X0) [subsumption resolution 93,148]
175. 10 <=> ! [X0] : ~happy(X0) [avatar definition]
176. ~happy(X0) <- (10) [avatar component clause 175]
178. 11 <=> strong(paul) [avatar definition]
180. ~strong(paul) <- (~11) [avatar component clause 178]
182. 12 <=> quiet(paul) [avatar definition]
184. ~quiet(paul) <- (~12) [avatar component clause 182]
185. 10 | ~11 | ~12 [avatar split clause 101,182,178,175]
215. ~old(X0) [subsumption resolution 127,105]
228. quiet(X0) [resolution 72,152]
229. happy(X0) [resolution 73,152]
243. old(X0) | kind(X0) | strong(X0) [resolution 74,87]
244. strong(X0) | kind(X0) [subsumption resolution 243,215]
246. kind(paul) <- (~11) [resolution 244,180]
247. $false <- (~11) [subsumption resolution 246,126]
248. 11 [avatar contradiction clause 247]
249. $false <- (~12) [subsumption resolution 184,228]
250. 12 [avatar contradiction clause 249]
251. $false <- (10) [subsumption resolution 176,229]
252. ~10 [avatar contradiction clause 251]
253. $false [avatar sat refutation 185,248,250,252]
% SZS output end Proof for 7000899854556460676799560
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not funny is patient and vice versa.
Everyone who is not old is not rich or not brave.
Everyone who is both not tall and rich is both rich and not tall and vice versa.
Everyone who is both strong and curious is both not brave and quiet.
Everyone who is both brave and creative is either brave or patient and vice versa.
Everyone who is kind or not kind is not funny and vice versa.
Everyone who is kind or not quiet is either not funny or not strong.
Everyone who is both not strong and kind is either not happy or not humble and vice versa.
If lucy is happy or tall then someone is both not wise and not humble.
If someone is either not tall or rich then john is generous or not calm.
Everyone who is both not brave and not quiet is wise or not kind.
Everyone who is both not quiet and wise is not kind or not quiet and vice versa.
Everyone who is strong is generous or wise and vice versa.
Everyone who is not kind is either humble or creative and vice versa.
If someone is both happy and not old then someone is humble or not wise.
Everyone who is kind is not old or not happy and vice versa.
Someone is both not patient and creative.
Paul is either not brave or patient.
Someone is curious or generous.
Someone is patient or not brave.
Someone is both patient and calm.
Mary is not kind.
Someone is either not creative or not rich.
Someone is either not brave or kind. | Paul is not brave. | neutral | (![X]:((~old(X)<~>~funny(X))<=>patient(X)))&
(![X]:(~old(X)=>(~rich(X)|~brave(X))))&
(![X]:((~tall(X)&rich(X))<=>(rich(X)&~tall(X))))&
(![X]:((strong(X)&curious(X))=>(~brave(X)&quiet(X))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>patient(X))))&
(![X]:((kind(X)|~kind(X))<=>~funny(X)))&
(![X]:((kind(X)|~quiet(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((~strong(X)&kind(X))<=>(~happy(X)<~>~humble(X))))&
(((happy(lucy)|tall(lucy)))=>(?[X]:((~wise(X)&~humble(X)))))&
((?[X]:((~tall(X)<~>rich(X))))=>((generous(john)|~calm(john))))&
(![X]:((~brave(X)&~quiet(X))=>(wise(X)|~kind(X))))&
(![X]:((~quiet(X)&wise(X))<=>(~kind(X)|~quiet(X))))&
(![X]:(strong(X)<=>(generous(X)|wise(X))))&
(![X]:(~kind(X)<=>(humble(X)<~>creative(X))))&
((?[X]:((happy(X)&~old(X))))=>(?[X]:((humble(X)|~wise(X)))))&
(![X]:(kind(X)<=>(~old(X)|~happy(X))))&
(?[X]:((~patient(X)&creative(X))))&
((~brave(paul)<~>patient(paul)))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:((patient(X)&calm(X))))&
(~kind(mary))&
(?[X]:((~creative(X)<~>~rich(X))))&
(?[X]:((~brave(X)<~>kind(X)))) | ~brave(paul) | [] | null | 0 |
If mary is either not curious or strong then someone is both calm and not kind and vice versa.
If fred is not wise or not patient then someone is both not funny and not happy and vice versa.
If someone is both not wise and calm then someone is both not calm and tall and vice versa.
Everyone who is old or not old is both patient and old and vice versa.
If susan is either wise or curious then someone is either not funny or not old and vice versa.
Everyone who is both humble and not humble is not kind or patient.
If someone is happy then lucy is both tall and not kind.
Everyone who is not tall is either strong or patient.
If someone is not tall then mary is both not generous and creative and vice versa.
Everyone who is both brave and not strong is either curious or tall and vice versa.
If someone is not humble or not creative then fred is either patient or generous and vice versa.
Everyone who is both not kind and not strong is either generous or not funny and vice versa.
If someone is not tall or old then susan is both not happy and curious.
If fred is either not brave or not creative then someone is curious and vice versa.
Everyone who is both quiet and old is kind.
If fred is either not calm or not tall then fred is kind or happy.
Susan is either not strong or not tall.
Someone is both not tall and quiet.
Paul is not kind or generous.
Someone is both not wise and not happy.
Lucy is not calm.
Someone is both curious and not kind.
Alice is calm. | Paul is generous. | neutral | (((~curious(mary)<~>strong(mary)))<=>(?[X]:((calm(X)&~kind(X)))))&
(((~wise(fred)|~patient(fred)))<=>(?[X]:((~funny(X)&~happy(X)))))&
((?[X]:((~wise(X)&calm(X))))<=>(?[X]:((~calm(X)&tall(X)))))&
(![X]:((old(X)|~old(X))<=>(patient(X)&old(X))))&
(((wise(susan)<~>curious(susan)))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((humble(X)&~humble(X))=>(~kind(X)|patient(X))))&
((?[X]:(happy(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:(~tall(X)=>(strong(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>((~generous(mary)&creative(mary))))&
(![X]:((brave(X)&~strong(X))<=>(curious(X)<~>tall(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((patient(fred)<~>generous(fred))))&
(![X]:((~kind(X)&~strong(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((~tall(X)|old(X))))=>((~happy(susan)&curious(susan))))&
(((~brave(fred)<~>~creative(fred)))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)&old(X))=>kind(X)))&
(((~calm(fred)<~>~tall(fred)))=>((kind(fred)|happy(fred))))&
((~strong(susan)<~>~tall(susan)))&
(?[X]:((~tall(X)&quiet(X))))&
((~kind(paul)|generous(paul)))&
(?[X]:((~wise(X)&~happy(X))))&
(~calm(lucy))&
(?[X]:((curious(X)&~kind(X))))&
(calm(alice)) | generous(paul) | [] | null | 0 |
Everyone who is not rich or creative is either humble or patient.
If someone is old then someone is not strong or not humble.
If someone is creative or not quiet then someone is tall.
Everyone who is generous or creative is humble.
Everyone who is not patient or not creative is both calm and not quiet and vice versa.
If susan is both not rich and not patient then someone is not creative or kind and vice versa.
If someone is both not curious and creative then someone is strong and vice versa.
Everyone who is both calm and rich is not generous.
Everyone who is either not generous or not tall is not calm.
If someone is generous then someone is funny.
Everyone who is rich is wise.
If someone is not generous then someone is not rich.
Everyone who is both rich and not generous is either strong or brave and vice versa.
If lucy is not wise or old then someone is brave or not strong and vice versa.
If someone is not patient then fred is both not quiet and calm.
If lucy is not brave or brave then fred is both old and brave and vice versa.
Mary is not rich.
Someone is either not creative or not tall.
Lucy is both calm and humble.
Fred is both old and rich.
Alice is either funny or patient.
John is not curious.
Someone is both not patient and not kind.
Lucy is quiet or not wise. | Alice is not quiet. | entailment | (![X]:((~rich(X)|creative(X))=>(humble(X)<~>patient(X))))&
((?[X]:(old(X)))=>(?[X]:((~strong(X)|~humble(X)))))&
((?[X]:((creative(X)|~quiet(X))))=>(?[X]:(tall(X))))&
(![X]:((generous(X)|creative(X))=>humble(X)))&
(![X]:((~patient(X)|~creative(X))<=>(calm(X)&~quiet(X))))&
(((~rich(susan)&~patient(susan)))<=>(?[X]:((~creative(X)|kind(X)))))&
((?[X]:((~curious(X)&creative(X))))<=>(?[X]:(strong(X))))&
(![X]:((calm(X)&rich(X))=>~generous(X)))&
(![X]:((~generous(X)<~>~tall(X))=>~calm(X)))&
((?[X]:(generous(X)))=>(?[X]:(funny(X))))&
(![X]:(rich(X)=>wise(X)))&
((?[X]:(~generous(X)))=>(?[X]:(~rich(X))))&
(![X]:((rich(X)&~generous(X))<=>(strong(X)<~>brave(X))))&
(((~wise(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~strong(X)))))&
((?[X]:(~patient(X)))=>((~quiet(fred)&calm(fred))))&
(((~brave(lucy)|brave(lucy)))<=>((old(fred)&brave(fred))))&
(~rich(mary))&
(?[X]:((~creative(X)<~>~tall(X))))&
((calm(lucy)&humble(lucy)))&
((old(fred)&rich(fred)))&
((funny(alice)<~>patient(alice)))&
(~curious(john))&
(?[X]:((~patient(X)&~kind(X))))&
((quiet(lucy)|~wise(lucy))) | ~quiet(alice) | [
"p0",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8330515734792056627522519
% SZS output start Proof for 8330515734792056627522519
1. ! [X0] : ((creative(X0) | ~rich(X0)) => (humble(X0) <~> patient(X0))) [input p0]
4. ! [X0] : ((creative(X0) | generous(X0)) => humble(X0)) [input p3]
5. ! [X0] : ((~creative(X0) | ~patient(X0)) <=> (~quiet(X0) & calm(X0))) [input p4]
25. quiet(alice) [input hypothesis]
31. ! [X0] : ((humble(X0) <~> patient(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 1]
34. ! [X0] : (humble(X0) | (~creative(X0) & ~generous(X0))) [ennf transformation 4]
42. ! [X0] : (((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~creative(X0) & rich(X0))) [nnf transformation 31]
49. ! [X0] : (((~creative(X0) | ~patient(X0)) | (quiet(X0) | ~calm(X0))) & ((~quiet(X0) & calm(X0)) | (creative(X0) & patient(X0)))) [nnf transformation 5]
50. ! [X0] : ((~creative(X0) | ~patient(X0) | quiet(X0) | ~calm(X0)) & ((~quiet(X0) & calm(X0)) | (creative(X0) & patient(X0)))) [flattening 49]
86. ~patient(X0) | ~humble(X0) | ~creative(X0) [cnf transformation 42]
91. ~creative(X0) | humble(X0) [cnf transformation 34]
94. ~quiet(X0) | patient(X0) [cnf transformation 50]
95. ~quiet(X0) | creative(X0) [cnf transformation 50]
141. quiet(alice) [cnf transformation 25]
301. 37 <=> patient(alice) [avatar definition]
302. patient(alice) <- (37) [avatar component clause 301]
321. patient(alice) [resolution 94,141]
324. 37 [avatar split clause 321,301]
325. creative(alice) [resolution 95,141]
346. humble(alice) [resolution 325,91]
352. ~humble(alice) | ~creative(alice) <- (37) [resolution 86,302]
353. ~creative(alice) <- (37) [subsumption resolution 352,346]
354. $false <- (37) [subsumption resolution 353,325]
355. ~37 [avatar contradiction clause 354]
356. $false [avatar sat refutation 324,355]
% SZS output end Proof for 8330515734792056627522519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not creative and vice versa.
If someone is either strong or not curious then someone is not kind.
If alice is quiet then paul is either not generous or tall and vice versa.
If alice is tall then someone is patient or not rich.
Everyone who is either tall or creative is both not funny and not rich and vice versa.
If someone is both not generous and generous then someone is both not happy and patient.
Everyone who is not curious or not old is brave and vice versa.
If paul is both rich and not brave then fred is strong or not generous.
If someone is either wise or not strong then lucy is both calm and not strong.
If someone is both not strong and funny then lucy is either not creative or wise and vice versa.
If fred is both wise and happy then john is not old or not brave.
Everyone who is not brave is happy or old.
Everyone who is not quiet is both creative and curious and vice versa.
If paul is strong then paul is both not calm and not curious and vice versa.
If john is not calm then someone is creative and vice versa.
Everyone who is rich or kind is both old and not kind and vice versa.
Someone is not funny or not happy.
John is funny or humble.
John is either strong or not tall.
Fred is strong.
Someone is both old and not creative.
Someone is humble.
Someone is both not curious and not calm.
John is either not brave or not strong. | John is brave. | entailment | (![X]:(~kind(X)<=>~creative(X)))&
((?[X]:((strong(X)<~>~curious(X))))=>(?[X]:(~kind(X))))&
((quiet(alice))<=>((~generous(paul)<~>tall(paul))))&
((tall(alice))=>(?[X]:((patient(X)|~rich(X)))))&
(![X]:((tall(X)<~>creative(X))<=>(~funny(X)&~rich(X))))&
((?[X]:((~generous(X)&generous(X))))=>(?[X]:((~happy(X)&patient(X)))))&
(![X]:((~curious(X)|~old(X))<=>brave(X)))&
(((rich(paul)&~brave(paul)))=>((strong(fred)|~generous(fred))))&
((?[X]:((wise(X)<~>~strong(X))))=>((calm(lucy)&~strong(lucy))))&
((?[X]:((~strong(X)&funny(X))))<=>((~creative(lucy)<~>wise(lucy))))&
(((wise(fred)&happy(fred)))=>((~old(john)|~brave(john))))&
(![X]:(~brave(X)=>(happy(X)|old(X))))&
(![X]:(~quiet(X)<=>(creative(X)&curious(X))))&
((strong(paul))<=>((~calm(paul)&~curious(paul))))&
((~calm(john))<=>(?[X]:(creative(X))))&
(![X]:((rich(X)|kind(X))<=>(old(X)&~kind(X))))&
(?[X]:((~funny(X)|~happy(X))))&
((funny(john)|humble(john)))&
((strong(john)<~>~tall(john)))&
(strong(fred))&
(?[X]:((old(X)&~creative(X))))&
(?[X]:(humble(X)))&
(?[X]:((~curious(X)&~calm(X))))&
((~brave(john)<~>~strong(john))) | brave(john) | [
"p0",
"p4",
"p6",
"p14",
"p15",
"p18",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1786401600337376441331035
% SZS output start Proof for 1786401600337376441331035
1. ! [X0] : (~kind(X0) <=> ~creative(X0)) [input p0]
5. ! [X0] : ((tall(X0) <~> creative(X0)) <=> (~rich(X0) & ~funny(X0))) [input p4]
7. ! [X0] : ((~old(X0) | ~curious(X0)) <=> brave(X0)) [input p6]
15. ~calm(john) <=> ? [X0] : creative(X0) [input p14]
16. ! [X0] : ((kind(X0) | rich(X0)) <=> (~kind(X0) & old(X0))) [input p15]
19. strong(john) <~> ~tall(john) [input p18]
24. ~brave(john) <~> ~strong(john) [input p23]
25. ~brave(john) [input hypothesis]
41. ! [X0] : ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))) [nnf transformation 1]
47. ! [X0] : ((((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0))))) [nnf transformation 5]
48. ! [X0] : ((((~creative(X0) | ~tall(X0)) & (creative(X0) | tall(X0))) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | ((tall(X0) | ~creative(X0)) & (creative(X0) | ~tall(X0))))) [flattening 47]
52. ! [X0] : (((~old(X0) | ~curious(X0)) | ~brave(X0)) & (brave(X0) | (old(X0) & curious(X0)))) [nnf transformation 7]
53. ! [X0] : ((~old(X0) | ~curious(X0) | ~brave(X0)) & (brave(X0) | (old(X0) & curious(X0)))) [flattening 52]
63. (~calm(john) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | calm(john)) [nnf transformation 15]
64. (~calm(john) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | calm(john)) [rectify 63]
65. ? [X1] : creative(X1) => creative(sK3) [choice axiom]
66. (~calm(john) | ! [X0] : ~creative(X0)) & (creative(sK3) | calm(john)) [skolemisation 64,65]
67. ! [X0] : (((kind(X0) | rich(X0)) | (kind(X0) | ~old(X0))) & ((~kind(X0) & old(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 16]
68. ! [X0] : ((kind(X0) | rich(X0) | kind(X0) | ~old(X0)) & ((~kind(X0) & old(X0)) | (~kind(X0) & ~rich(X0)))) [flattening 67]
71. (tall(john) | ~strong(john)) & (~tall(john) | strong(john)) [nnf transformation 19]
76. (strong(john) | brave(john)) & (~strong(john) | ~brave(john)) [nnf transformation 24]
77. ~creative(X0) | kind(X0) [cnf transformation 41]
87. ~rich(X0) | creative(X0) | ~tall(X0) [cnf transformation 48]
93. brave(X0) | old(X0) [cnf transformation 53]
114. creative(sK3) | calm(john) [cnf transformation 66]
115. ~calm(john) | ~creative(X0) [cnf transformation 66]
119. ~kind(X0) | ~kind(X0) [cnf transformation 68]
120. kind(X0) | rich(X0) | kind(X0) | ~old(X0) [cnf transformation 68]
123. tall(john) | ~strong(john) [cnf transformation 71]
130. strong(john) | brave(john) [cnf transformation 76]
131. ~brave(john) [cnf transformation 25]
132. ~kind(X0) [duplicate literal removal 119]
133. ~old(X0) | rich(X0) | kind(X0) [duplicate literal removal 120]
231. 22 <=> old(john) [avatar definition]
232. old(john) <- (22) [avatar component clause 231]
235. 23 <=> brave(john) [avatar definition]
237. ~brave(john) <- (~23) [avatar component clause 235]
255. 27 <=> ! [X0] : ~creative(X0) [avatar definition]
256. ~creative(X0) <- (27) [avatar component clause 255]
258. 28 <=> calm(john) [avatar definition]
261. 27 | ~28 [avatar split clause 115,258,255]
263. 29 <=> creative(sK3) [avatar definition]
265. creative(sK3) <- (29) [avatar component clause 263]
266. 28 | 29 [avatar split clause 114,263,258]
277. 32 <=> strong(john) [avatar definition]
281. 33 <=> tall(john) [avatar definition]
283. tall(john) <- (33) [avatar component clause 281]
284. ~32 | 33 [avatar split clause 123,281,277]
287. 23 | 32 [avatar split clause 130,277,235]
289. ~23 [avatar split clause 131,235]
291. old(john) <- (~23) [resolution 93,237]
292. 22 | 23 [avatar split clause 291,235,231]
307. rich(john) | kind(john) <- (22) [resolution 133,232]
309. rich(john) <- (22) [subsumption resolution 307,132]
332. creative(john) | ~tall(john) <- (22) [resolution 309,87]
334. ~tall(john) <- (22, 27) [subsumption resolution 332,256]
335. $false <- (22, 27, 33) [subsumption resolution 334,283]
336. ~22 | ~27 | ~33 [avatar contradiction clause 335]
366. kind(sK3) <- (29) [resolution 265,77]
367. $false <- (29) [subsumption resolution 366,132]
368. ~29 [avatar contradiction clause 367]
369. $false [avatar sat refutation 261,266,284,287,289,292,336,368]
% SZS output end Proof for 1786401600337376441331035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or curious is rich and vice versa.
Everyone who is strong or kind is both strong and rich and vice versa.
Everyone who is both not humble and not funny is not quiet or rich and vice versa.
If lucy is either brave or not old then alice is rich or not wise and vice versa.
Everyone who is not creative is not kind or not funny and vice versa.
Everyone who is curious or not calm is both rich and old.
Everyone who is happy or funny is not generous or humble.
Everyone who is not brave or not rich is either wise or happy.
Everyone who is rich or not quiet is either calm or not generous and vice versa.
Everyone who is either brave or not tall is both creative and not kind and vice versa.
Everyone who is patient is either strong or not creative and vice versa.
Everyone who is either tall or not funny is not old or not wise and vice versa.
If john is both generous and strong then someone is not rich and vice versa.
Everyone who is not humble is not calm or not creative.
If lucy is tall then someone is not wise or not patient and vice versa.
Someone is both not brave and not happy.
Mary is not strong.
Someone is both not funny and not brave.
Someone is calm or not funny.
Someone is not curious. | John is not calm. | contradiction | (![X]:((~patient(X)|curious(X))<=>rich(X)))&
(![X]:((strong(X)|kind(X))<=>(strong(X)&rich(X))))&
(![X]:((~humble(X)&~funny(X))<=>(~quiet(X)|rich(X))))&
(((brave(lucy)<~>~old(lucy)))<=>((rich(alice)|~wise(alice))))&
(![X]:(~creative(X)<=>(~kind(X)|~funny(X))))&
(![X]:((curious(X)|~calm(X))=>(rich(X)&old(X))))&
(![X]:((happy(X)|funny(X))=>(~generous(X)|humble(X))))&
(![X]:((~brave(X)|~rich(X))=>(wise(X)<~>happy(X))))&
(![X]:((rich(X)|~quiet(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((brave(X)<~>~tall(X))<=>(creative(X)&~kind(X))))&
(![X]:(patient(X)<=>(strong(X)<~>~creative(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(~old(X)|~wise(X))))&
(((generous(john)&strong(john)))<=>(?[X]:(~rich(X))))&
(![X]:(~humble(X)=>(~calm(X)|~creative(X))))&
((tall(lucy))<=>(?[X]:((~wise(X)|~patient(X)))))&
(?[X]:((~brave(X)&~happy(X))))&
(~strong(mary))&
(?[X]:((~funny(X)&~brave(X))))&
(?[X]:((calm(X)|~funny(X))))&
(?[X]:(~curious(X))) | ~calm(john) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p8",
"p9",
"p11",
"p12",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4545558966254619710873805
% SZS output start Proof for 4545558966254619710873805
1. ! [X0] : ((curious(X0) | ~patient(X0)) <=> rich(X0)) [input p0]
3. ! [X0] : ((~funny(X0) & ~humble(X0)) <=> (rich(X0) | ~quiet(X0))) [input p2]
4. (brave(lucy) <~> ~old(lucy)) <=> (~wise(alice) | rich(alice)) [input p3]
5. ! [X0] : (~creative(X0) <=> (~funny(X0) | ~kind(X0))) [input p4]
6. ! [X0] : ((~calm(X0) | curious(X0)) => (old(X0) & rich(X0))) [input p5]
9. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (calm(X0) <~> ~generous(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> ~tall(X0)) <=> (~kind(X0) & creative(X0))) [input p9]
12. ! [X0] : ((tall(X0) <~> ~funny(X0)) <=> (~wise(X0) | ~old(X0))) [input p11]
13. (strong(john) & generous(john)) <=> ? [X0] : ~rich(X0) [input p12]
15. tall(lucy) <=> ? [X0] : (~patient(X0) | ~wise(X0)) [input p14]
20. ? [X0] : ~curious(X0) [input p19]
21. ~calm(john) [input hypothesis]
22. ! [X0] : ((old(X0) & rich(X0)) | (calm(X0) & ~curious(X0))) [ennf transformation 6]
28. ! [X0] : (((curious(X0) | ~patient(X0)) | ~rich(X0)) & (rich(X0) | (~curious(X0) & patient(X0)))) [nnf transformation 1]
29. ! [X0] : ((curious(X0) | ~patient(X0) | ~rich(X0)) & (rich(X0) | (~curious(X0) & patient(X0)))) [flattening 28]
32. ! [X0] : (((~funny(X0) & ~humble(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (funny(X0) | humble(X0)))) [nnf transformation 3]
33. ! [X0] : (((~funny(X0) & ~humble(X0)) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | funny(X0) | humble(X0))) [flattening 32]
34. (((old(lucy) | ~brave(lucy)) & (~old(lucy) | brave(lucy))) | (wise(alice) & ~rich(alice))) & ((~wise(alice) | rich(alice)) | ((brave(lucy) | old(lucy)) & (~old(lucy) | ~brave(lucy)))) [nnf transformation 4]
35. (((old(lucy) | ~brave(lucy)) & (~old(lucy) | brave(lucy))) | (wise(alice) & ~rich(alice))) & (~wise(alice) | rich(alice) | ((brave(lucy) | old(lucy)) & (~old(lucy) | ~brave(lucy)))) [flattening 34]
36. ! [X0] : ((~creative(X0) | (funny(X0) & kind(X0))) & ((~funny(X0) | ~kind(X0)) | creative(X0))) [nnf transformation 5]
37. ! [X0] : ((~creative(X0) | (funny(X0) & kind(X0))) & (~funny(X0) | ~kind(X0) | creative(X0))) [flattening 36]
39. ! [X0] : (((~quiet(X0) | rich(X0)) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (quiet(X0) & ~rich(X0)))) [nnf transformation 9]
40. ! [X0] : ((~quiet(X0) | rich(X0) | ((calm(X0) | generous(X0)) & (~generous(X0) | ~calm(X0)))) & (((generous(X0) | ~calm(X0)) & (~generous(X0) | calm(X0))) | (quiet(X0) & ~rich(X0)))) [flattening 39]
41. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | (kind(X0) | ~creative(X0))) & ((~kind(X0) & creative(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [nnf transformation 10]
42. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | kind(X0) | ~creative(X0)) & ((~kind(X0) & creative(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [flattening 41]
44. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (wise(X0) & old(X0))) & ((~wise(X0) | ~old(X0)) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [nnf transformation 12]
45. ! [X0] : ((((funny(X0) | ~tall(X0)) & (~funny(X0) | tall(X0))) | (wise(X0) & old(X0))) & (~wise(X0) | ~old(X0) | ((tall(X0) | funny(X0)) & (~funny(X0) | ~tall(X0))))) [flattening 44]
46. ((strong(john) & generous(john)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (~strong(john) | ~generous(john))) [nnf transformation 13]
47. ((strong(john) & generous(john)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | ~strong(john) | ~generous(john)) [flattening 46]
48. ((strong(john) & generous(john)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | ~strong(john) | ~generous(john)) [rectify 47]
49. ? [X1] : ~rich(X1) => ~rich(sK0) [choice axiom]
50. ((strong(john) & generous(john)) | ! [X0] : rich(X0)) & (~rich(sK0) | ~strong(john) | ~generous(john)) [skolemisation 48,49]
51. (tall(lucy) | ! [X0] : (patient(X0) & wise(X0))) & (? [X0] : (~patient(X0) | ~wise(X0)) | ~tall(lucy)) [nnf transformation 15]
52. (tall(lucy) | ! [X0] : (patient(X0) & wise(X0))) & (? [X1] : (~patient(X1) | ~wise(X1)) | ~tall(lucy)) [rectify 51]
53. ? [X1] : (~patient(X1) | ~wise(X1)) => (~patient(sK1) | ~wise(sK1)) [choice axiom]
54. (tall(lucy) | ! [X0] : (patient(X0) & wise(X0))) & ((~patient(sK1) | ~wise(sK1)) | ~tall(lucy)) [skolemisation 52,53]
61. ? [X0] : ~curious(X0) => ~curious(sK5) [choice axiom]
62. ~curious(sK5) [skolemisation 20,61]
65. ~rich(X0) | ~patient(X0) | curious(X0) [cnf transformation 29]
75. ~funny(X0) | ~rich(X0) [cnf transformation 33]
78. ~old(lucy) | brave(lucy) | ~rich(alice) [cnf transformation 35]
83. ~creative(X0) | kind(X0) [cnf transformation 37]
86. calm(X0) | rich(X0) [cnf transformation 22]
95. ~generous(X0) | calm(X0) | ~rich(X0) [cnf transformation 40]
101. ~tall(X0) | creative(X0) | ~brave(X0) [cnf transformation 42]
103. ~tall(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 42]
115. ~tall(X0) | funny(X0) | old(X0) [cnf transformation 45]
118. generous(john) | rich(X0) [cnf transformation 50]
123. tall(lucy) | patient(X0) [cnf transformation 54]
130. ~curious(sK5) [cnf transformation 62]
131. ~calm(john) [cnf transformation 21]
137. 2 <=> brave(lucy) [avatar definition]
138. brave(lucy) <- (2) [avatar component clause 137]
141. 3 <=> old(lucy) [avatar definition]
142. ~old(lucy) <- (~3) [avatar component clause 141]
146. 4 <=> rich(alice) [avatar definition]
148. ~rich(alice) <- (~4) [avatar component clause 146]
151. ~4 | 2 | ~3 [avatar split clause 78,141,137,146]
155. ~generous(X0) | calm(X0) [subsumption resolution 95,86]
157. 5 <=> ! [X0] : rich(X0) [avatar definition]
158. rich(X0) <- (5) [avatar component clause 157]
165. 7 <=> generous(john) [avatar definition]
167. generous(john) <- (7) [avatar component clause 165]
168. 5 | 7 [avatar split clause 118,165,157]
175. 9 <=> ! [X0] : patient(X0) [avatar definition]
176. patient(X0) <- (9) [avatar component clause 175]
178. 10 <=> tall(lucy) [avatar definition]
180. tall(lucy) <- (10) [avatar component clause 178]
181. 9 | 10 [avatar split clause 123,178,175]
227. creative(lucy) | ~brave(lucy) <- (10) [resolution 101,180]
243. funny(lucy) | old(lucy) <- (10) [resolution 115,180]
245. funny(lucy) <- (~3, 10) [subsumption resolution 243,142]
250. ~rich(lucy) <- (~3, 10) [resolution 245,75]
253. 16 <=> creative(lucy) [avatar definition]
255. creative(lucy) <- (16) [avatar component clause 253]
257. 17 <=> kind(lucy) [avatar definition]
261. $false <- (~3, 5, 10) [subsumption resolution 250,158]
262. 3 | ~5 | ~10 [avatar contradiction clause 261]
277. calm(john) <- (7) [resolution 167,155]
293. $false <- (7) [subsumption resolution 277,131]
294. ~7 [avatar contradiction clause 293]
295. ~2 | 16 | ~10 [avatar split clause 227,178,253,137]
301. ~patient(X0) | curious(X0) <- (5) [resolution 158,65]
302. curious(X0) <- (5, 9) [subsumption resolution 301,176]
310. $false <- (~4, 5) [subsumption resolution 148,158]
311. 4 | ~5 [avatar contradiction clause 310]
321. $false <- (5, 9) [resolution 302,130]
324. ~5 | ~9 [avatar contradiction clause 321]
329. ~kind(lucy) | ~brave(lucy) <- (10) [resolution 180,103]
334. kind(lucy) <- (16) [resolution 255,83]
340. 17 | ~16 [avatar split clause 334,253,257]
341. ~kind(lucy) <- (2, 10) [subsumption resolution 329,138]
342. ~17 | ~2 | ~10 [avatar split clause 341,178,137,257]
343. $false [avatar sat refutation 151,168,181,262,294,295,311,324,340,342]
% SZS output end Proof for 4545558966254619710873805
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or creative is not curious or strong. If fred is rich then someone is happy and vice versa. Everyone who is wise or not quiet is either not happy or not calm. Everyone who is tall or not rich is either not creative or not kind and vice versa. If someone is not creative then fred is both calm and not curious. If someone is either calm or kind then someone is not generous or brave and vice versa. If alice is kind then mary is either happy or wise. Everyone who is generous is old. If someone is either humble or not creative then susan is generous and vice versa. Everyone who is creative or curious is curious. Everyone who is either not strong or not tall is both creative and not strong. Everyone who is funny or tall is either humble or kind and vice versa. Everyone who is both not tall and not wise is either not tall or not wise and vice versa. If someone is either not wise or calm then someone is either not curious or not old and vice versa. Everyone who is both not rich and not kind is curious and vice versa. Everyone who is both not old and old is humble. Someone is kind. Someone is not kind or tall. John is both not strong and curious. Susan is both not patient and humble. Paul is both humble and curious. Alice is not calm or not wise. Mary is either strong or generous. John is either not generous or not calm. | John is humble. | entailment | (![X]:((curious(X)<~>creative(X))=>(~curious(X)|strong(X))))&
((rich(fred))<=>(?[X]:(happy(X))))&
(![X]:((wise(X)|~quiet(X))=>(~happy(X)<~>~calm(X))))&
(![X]:((tall(X)|~rich(X))<=>(~creative(X)<~>~kind(X))))&
((?[X]:(~creative(X)))=>((calm(fred)&~curious(fred))))&
((?[X]:((calm(X)<~>kind(X))))<=>(?[X]:((~generous(X)|brave(X)))))&
((kind(alice))=>((happy(mary)<~>wise(mary))))&
(![X]:(generous(X)=>old(X)))&
((?[X]:((humble(X)<~>~creative(X))))<=>(generous(susan)))&
(![X]:((creative(X)|curious(X))=>curious(X)))&
(![X]:((~strong(X)<~>~tall(X))=>(creative(X)&~strong(X))))&
(![X]:((funny(X)|tall(X))<=>(humble(X)<~>kind(X))))&
(![X]:((~tall(X)&~wise(X))<=>(~tall(X)<~>~wise(X))))&
((?[X]:((~wise(X)<~>calm(X))))<=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((~rich(X)&~kind(X))<=>curious(X)))&
(![X]:((~old(X)&old(X))=>humble(X)))&
(?[X]:(kind(X)))&
(?[X]:((~kind(X)|tall(X))))&
((~strong(john)&curious(john)))&
((~patient(susan)&humble(susan)))&
((humble(paul)&curious(paul)))&
((~calm(alice)|~wise(alice)))&
((strong(mary)<~>generous(mary)))&
((~generous(john)<~>~calm(john))) | humble(john) | [
"p3",
"p10",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9022964509724570316410885
% SZS output start Proof for 9022964509724570316410885
4. ! [X0] : ((~rich(X0) | tall(X0)) <=> (~creative(X0) <~> ~kind(X0))) [input p3]
11. ! [X0] : ((~strong(X0) <~> ~tall(X0)) => (~strong(X0) & creative(X0))) [input p10]
12. ! [X0] : ((tall(X0) | funny(X0)) <=> (humble(X0) <~> kind(X0))) [input p11]
13. ! [X0] : ((~wise(X0) & ~tall(X0)) <=> (~tall(X0) <~> ~wise(X0))) [input p12]
19. curious(john) & ~strong(john) [input p18]
25. ~humble(john) [input hypothesis]
37. ! [X0] : ((~strong(X0) & creative(X0)) | (~strong(X0) <=> ~tall(X0))) [ennf transformation 11]
46. ! [X0] : (((~rich(X0) | tall(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (rich(X0) & ~tall(X0)))) [nnf transformation 4]
47. ! [X0] : ((~rich(X0) | tall(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (rich(X0) & ~tall(X0)))) [flattening 46]
58. ! [X0] : ((~strong(X0) & creative(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0)))) [nnf transformation 37]
59. ! [X0] : (((tall(X0) | funny(X0)) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) & (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~tall(X0) & ~funny(X0)))) [nnf transformation 12]
60. ! [X0] : ((tall(X0) | funny(X0) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) & (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | (~tall(X0) & ~funny(X0)))) [flattening 59]
61. ! [X0] : (((~wise(X0) & ~tall(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0)))) & (((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | (wise(X0) | tall(X0)))) [nnf transformation 13]
62. ! [X0] : (((~wise(X0) & ~tall(X0)) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0)))) & (((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | wise(X0) | tall(X0))) [flattening 61]
82. ~kind(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 47]
105. ~tall(X0) | creative(X0) | strong(X0) [cnf transformation 58]
110. ~tall(X0) | humble(X0) | kind(X0) [cnf transformation 60]
116. wise(X0) | tall(X0) | wise(X0) | tall(X0) [cnf transformation 62]
119. ~wise(X0) | ~wise(X0) | tall(X0) [cnf transformation 62]
135. ~strong(john) [cnf transformation 19]
145. ~humble(john) [cnf transformation 25]
146. wise(X0) | tall(X0) [duplicate literal removal 116]
148. ~wise(X0) | tall(X0) [duplicate literal removal 119]
247. tall(X0) [subsumption resolution 146,148]
347. strong(X0) | creative(X0) [resolution 105,247]
349. humble(X0) | kind(X0) [resolution 110,247]
350. creative(john) [resolution 347,135]
420. kind(john) [resolution 349,145]
429. ~creative(john) | ~tall(john) [resolution 420,82]
432. ~tall(john) [subsumption resolution 429,350]
433. $false [subsumption resolution 432,247]
% SZS output end Proof for 9022964509724570316410885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is either brave or not rich and vice versa.
Everyone who is old is not rich and vice versa.
If fred is patient then lucy is not curious or happy.
Everyone who is both not patient and rich is both creative and not humble and vice versa.
Everyone who is not old or rich is generous or not kind and vice versa.
Everyone who is either not brave or creative is not quiet or quiet and vice versa.
Everyone who is not happy is either generous or not generous.
If john is quiet then someone is either old or kind.
If alice is not kind then alice is either not happy or not generous.
Everyone who is funny is either not calm or not old and vice versa.
If mary is not calm or not brave then someone is both kind and creative and vice versa.
If someone is not generous or creative then john is happy or kind.
Everyone who is either not kind or not tall is either not kind or not generous.
Everyone who is either not rich or wise is calm.
If paul is either generous or kind then alice is either not calm or not tall.
Everyone who is both kind and wise is either generous or not funny and vice versa.
Someone is either not wise or humble.
Fred is either not calm or not brave.
Someone is either calm or rich.
Someone is not humble or not strong. | Paul is humble. | neutral | (![X]:(~creative(X)<=>(brave(X)<~>~rich(X))))&
(![X]:(old(X)<=>~rich(X)))&
((patient(fred))=>((~curious(lucy)|happy(lucy))))&
(![X]:((~patient(X)&rich(X))<=>(creative(X)&~humble(X))))&
(![X]:((~old(X)|rich(X))<=>(generous(X)|~kind(X))))&
(![X]:((~brave(X)<~>creative(X))<=>(~quiet(X)|quiet(X))))&
(![X]:(~happy(X)=>(generous(X)<~>~generous(X))))&
((quiet(john))=>(?[X]:((old(X)<~>kind(X)))))&
((~kind(alice))=>((~happy(alice)<~>~generous(alice))))&
(![X]:(funny(X)<=>(~calm(X)<~>~old(X))))&
(((~calm(mary)|~brave(mary)))<=>(?[X]:((kind(X)&creative(X)))))&
((?[X]:((~generous(X)|creative(X))))=>((happy(john)|kind(john))))&
(![X]:((~kind(X)<~>~tall(X))=>(~kind(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>wise(X))=>calm(X)))&
(((generous(paul)<~>kind(paul)))=>((~calm(alice)<~>~tall(alice))))&
(![X]:((kind(X)&wise(X))<=>(generous(X)<~>~funny(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
((~calm(fred)<~>~brave(fred)))&
(?[X]:((calm(X)<~>rich(X))))&
(?[X]:((~humble(X)|~strong(X)))) | humble(paul) | [] | null | 0 |
If someone is either not curious or brave then alice is both not patient and generous and vice versa. If someone is happy then lucy is not rich. Everyone who is both not strong and curious is both old and curious. If someone is either wise or creative then alice is funny or not wise and vice versa. If someone is both funny and not wise then paul is not funny or calm. If someone is humble then someone is not calm and vice versa. Everyone who is both creative and not strong is both not strong and old. Everyone who is either not curious or brave is quiet and vice versa. If lucy is not happy or wise then someone is old. If lucy is either not happy or creative then someone is not rich and vice versa. If someone is generous then mary is both not kind and not tall. Everyone who is happy is either not generous or not tall and vice versa. If someone is either not patient or kind then susan is not curious or not generous. If someone is not curious then someone is not funny or generous. Everyone who is either not creative or wise is both brave and not tall and vice versa. Everyone who is either not happy or patient is not old and vice versa. Fred is not wise. Fred is humble or not wise. Mary is not wise. Fred is both tall and happy. Paul is either wise or not funny. Someone is both not kind and not creative. Someone is both rich and patient. Lucy is both not patient and not strong. | Lucy is not strong. | entailment | ((?[X]:((~curious(X)<~>brave(X))))<=>((~patient(alice)&generous(alice))))&
((?[X]:(happy(X)))=>(~rich(lucy)))&
(![X]:((~strong(X)&curious(X))=>(old(X)&curious(X))))&
((?[X]:((wise(X)<~>creative(X))))<=>((funny(alice)|~wise(alice))))&
((?[X]:((funny(X)&~wise(X))))=>((~funny(paul)|calm(paul))))&
((?[X]:(humble(X)))<=>(?[X]:(~calm(X))))&
(![X]:((creative(X)&~strong(X))=>(~strong(X)&old(X))))&
(![X]:((~curious(X)<~>brave(X))<=>quiet(X)))&
(((~happy(lucy)|wise(lucy)))=>(?[X]:(old(X))))&
(((~happy(lucy)<~>creative(lucy)))<=>(?[X]:(~rich(X))))&
((?[X]:(generous(X)))=>((~kind(mary)&~tall(mary))))&
(![X]:(happy(X)<=>(~generous(X)<~>~tall(X))))&
((?[X]:((~patient(X)<~>kind(X))))=>((~curious(susan)|~generous(susan))))&
((?[X]:(~curious(X)))=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:((~creative(X)<~>wise(X))<=>(brave(X)&~tall(X))))&
(![X]:((~happy(X)<~>patient(X))<=>~old(X)))&
(~wise(fred))&
((humble(fred)|~wise(fred)))&
(~wise(mary))&
((tall(fred)&happy(fred)))&
((wise(paul)<~>~funny(paul)))&
(?[X]:((~kind(X)&~creative(X))))&
(?[X]:((rich(X)&patient(X))))&
((~patient(lucy)&~strong(lucy))) | ~strong(lucy) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5570168803412422838411946
% SZS output start Proof for 5570168803412422838411946
24. ~strong(lucy) & ~patient(lucy) [input p23]
25. strong(lucy) [input hypothesis]
131. ~strong(lucy) [cnf transformation 24]
132. strong(lucy) [cnf transformation 25]
301. $false [subsumption resolution 132,131]
% SZS output end Proof for 5570168803412422838411946
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not humble then paul is rich. Everyone who is curious or not kind is calm or not calm. Everyone who is not kind is either not quiet or funny and vice versa. Everyone who is either not creative or not kind is both creative and generous. Everyone who is not generous is rich and vice versa. Everyone who is not creative or not quiet is not curious or not generous and vice versa. Everyone who is rich is either calm or rich. Everyone who is not calm or not strong is not brave or strong and vice versa. Everyone who is rich is calm. Everyone who is not quiet or kind is either not calm or not kind. Everyone who is not patient is curious. If someone is either strong or not happy then mary is both happy and not curious and vice versa. If lucy is both generous and not funny then someone is either not wise or brave and vice versa. Everyone who is either not calm or calm is not rich or curious. If someone is not creative then someone is quiet or humble and vice versa. Someone is either kind or generous. John is either generous or calm. Fred is both not strong and not calm. Someone is both curious and old. Someone is old or not wise. Paul is either generous or not old. Fred is either not patient or not brave. | Lucy is not quiet. | neutral | ((?[X]:((~old(X)&~humble(X))))=>(rich(paul)))&
(![X]:((curious(X)|~kind(X))=>(calm(X)|~calm(X))))&
(![X]:(~kind(X)<=>(~quiet(X)<~>funny(X))))&
(![X]:((~creative(X)<~>~kind(X))=>(creative(X)&generous(X))))&
(![X]:(~generous(X)<=>rich(X)))&
(![X]:((~creative(X)|~quiet(X))<=>(~curious(X)|~generous(X))))&
(![X]:(rich(X)=>(calm(X)<~>rich(X))))&
(![X]:((~calm(X)|~strong(X))<=>(~brave(X)|strong(X))))&
(![X]:(rich(X)=>calm(X)))&
(![X]:((~quiet(X)|kind(X))=>(~calm(X)<~>~kind(X))))&
(![X]:(~patient(X)=>curious(X)))&
((?[X]:((strong(X)<~>~happy(X))))<=>((happy(mary)&~curious(mary))))&
(((generous(lucy)&~funny(lucy)))<=>(?[X]:((~wise(X)<~>brave(X)))))&
(![X]:((~calm(X)<~>calm(X))=>(~rich(X)|curious(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((quiet(X)|humble(X)))))&
(?[X]:((kind(X)<~>generous(X))))&
((generous(john)<~>calm(john)))&
((~strong(fred)&~calm(fred)))&
(?[X]:((curious(X)&old(X))))&
(?[X]:((old(X)|~wise(X))))&
((generous(paul)<~>~old(paul)))&
((~patient(fred)<~>~brave(fred))) | ~quiet(lucy) | [] | null | 0 |
Everyone who is either not rich or not creative is both not patient and calm and vice versa. Everyone who is not strong or not happy is brave and vice versa. Everyone who is curious or tall is creative and vice versa. Everyone who is either creative or funny is both not calm and patient and vice versa. Everyone who is not brave or kind is not generous. Everyone who is not creative is not brave or not kind and vice versa. Everyone who is either not quiet or calm is either not kind or not tall. Everyone who is both tall and brave is both not creative and not old and vice versa. Everyone who is either not funny or patient is either not tall or creative and vice versa. If alice is funny then someone is kind or curious. If john is not happy then paul is both not quiet and brave. If someone is quiet or not curious then mary is not brave and vice versa. If mary is both not wise and funny then someone is strong or generous and vice versa. If paul is not strong or kind then fred is not tall or generous and vice versa. Everyone who is both not rich and humble is not brave or not curious. Everyone who is not brave or not wise is quiet or wise. John is not creative. Alice is either patient or not curious. Someone is not rich or strong. Someone is both calm and strong. Alice is not wise. Someone is not tall or creative. Lucy is both curious and funny. Fred is both wise and not quiet. | Mary is tall. | contradiction | (![X]:((~rich(X)<~>~creative(X))<=>(~patient(X)&calm(X))))&
(![X]:((~strong(X)|~happy(X))<=>brave(X)))&
(![X]:((curious(X)|tall(X))<=>creative(X)))&
(![X]:((creative(X)<~>funny(X))<=>(~calm(X)&patient(X))))&
(![X]:((~brave(X)|kind(X))=>~generous(X)))&
(![X]:(~creative(X)<=>(~brave(X)|~kind(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~kind(X)<~>~tall(X))))&
(![X]:((tall(X)&brave(X))<=>(~creative(X)&~old(X))))&
(![X]:((~funny(X)<~>patient(X))<=>(~tall(X)<~>creative(X))))&
((funny(alice))=>(?[X]:((kind(X)|curious(X)))))&
((~happy(john))=>((~quiet(paul)&brave(paul))))&
((?[X]:((quiet(X)|~curious(X))))<=>(~brave(mary)))&
(((~wise(mary)&funny(mary)))<=>(?[X]:((strong(X)|generous(X)))))&
(((~strong(paul)|kind(paul)))<=>((~tall(fred)|generous(fred))))&
(![X]:((~rich(X)&humble(X))=>(~brave(X)|~curious(X))))&
(![X]:((~brave(X)|~wise(X))=>(quiet(X)|wise(X))))&
(~creative(john))&
((patient(alice)<~>~curious(alice)))&
(?[X]:((~rich(X)|strong(X))))&
(?[X]:((calm(X)&strong(X))))&
(~wise(alice))&
(?[X]:((~tall(X)|creative(X))))&
((curious(lucy)&funny(lucy)))&
((wise(fred)&~quiet(fred))) | tall(mary) | [
"p2",
"p5",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 760825028192809002814062
% SZS output start Proof for 760825028192809002814062
3. ! [X0] : ((tall(X0) | curious(X0)) <=> creative(X0)) [input p2]
6. ! [X0] : (~creative(X0) <=> (~kind(X0) | ~brave(X0))) [input p5]
12. ? [X0] : (~curious(X0) | quiet(X0)) <=> ~brave(mary) [input p11]
17. ~creative(john) [input p16]
25. tall(mary) [input hypothesis]
37. ! [X0] : (((tall(X0) | curious(X0)) | ~creative(X0)) & (creative(X0) | (~tall(X0) & ~curious(X0)))) [nnf transformation 3]
38. ! [X0] : ((tall(X0) | curious(X0) | ~creative(X0)) & (creative(X0) | (~tall(X0) & ~curious(X0)))) [flattening 37]
41. ! [X0] : ((~creative(X0) | (kind(X0) & brave(X0))) & ((~kind(X0) | ~brave(X0)) | creative(X0))) [nnf transformation 6]
42. ! [X0] : ((~creative(X0) | (kind(X0) & brave(X0))) & (~kind(X0) | ~brave(X0) | creative(X0))) [flattening 41]
49. (? [X0] : (~curious(X0) | quiet(X0)) | brave(mary)) & (~brave(mary) | ! [X0] : (curious(X0) & ~quiet(X0))) [nnf transformation 12]
50. (? [X0] : (~curious(X0) | quiet(X0)) | brave(mary)) & (~brave(mary) | ! [X1] : (curious(X1) & ~quiet(X1))) [rectify 49]
51. ? [X0] : (~curious(X0) | quiet(X0)) => (~curious(sK1) | quiet(sK1)) [choice axiom]
52. ((~curious(sK1) | quiet(sK1)) | brave(mary)) & (~brave(mary) | ! [X1] : (curious(X1) & ~quiet(X1))) [skolemisation 50,51]
76. ~curious(X0) | creative(X0) [cnf transformation 38]
77. ~tall(X0) | creative(X0) [cnf transformation 38]
88. ~creative(X0) | brave(X0) [cnf transformation 42]
110. ~brave(mary) | curious(X1) [cnf transformation 52]
123. ~creative(john) [cnf transformation 17]
135. tall(mary) [cnf transformation 25]
171. 7 <=> brave(mary) [avatar definition]
184. 10 <=> ! [X1] : curious(X1) [avatar definition]
185. curious(X1) <- (10) [avatar component clause 184]
186. 10 | ~7 [avatar split clause 110,171,184]
262. creative(mary) [resolution 77,135]
264. brave(mary) [resolution 88,262]
267. 7 [avatar split clause 264,171]
270. creative(X0) <- (10) [resolution 185,76]
275. $false <- (10) [resolution 270,123]
278. ~10 [avatar contradiction clause 275]
279. $false [avatar sat refutation 186,267,278]
% SZS output end Proof for 760825028192809002814062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and kind is not creative or strong and vice versa. If john is either not curious or not creative then someone is both not creative and curious. Everyone who is not funny is funny. If fred is not happy then someone is not quiet or calm. If alice is both quiet and not strong then paul is calm or not patient and vice versa. If mary is both generous and patient then fred is not happy and vice versa. If someone is either not tall or old then someone is calm and vice versa. If susan is not funny then mary is either not patient or humble. If john is either strong or kind then someone is both not calm and creative. If someone is rich or generous then someone is not tall. Everyone who is not curious is not kind. Everyone who is both brave and not calm is not strong and vice versa. Everyone who is quiet or wise is both not creative and not patient and vice versa. If fred is both tall and wise then lucy is both not quiet and not kind and vice versa. Everyone who is both brave and not brave is not patient or calm and vice versa. Alice is both not tall and patient. Susan is either old or not brave. Susan is both funny and strong. Mary is either creative or brave. Someone is both kind and creative. | Susan is not wise. | entailment | (![X]:((funny(X)&kind(X))<=>(~creative(X)|strong(X))))&
(((~curious(john)<~>~creative(john)))=>(?[X]:((~creative(X)&curious(X)))))&
(![X]:(~funny(X)=>funny(X)))&
((~happy(fred))=>(?[X]:((~quiet(X)|calm(X)))))&
(((quiet(alice)&~strong(alice)))<=>((calm(paul)|~patient(paul))))&
(((generous(mary)&patient(mary)))<=>(~happy(fred)))&
((?[X]:((~tall(X)<~>old(X))))<=>(?[X]:(calm(X))))&
((~funny(susan))=>((~patient(mary)<~>humble(mary))))&
(((strong(john)<~>kind(john)))=>(?[X]:((~calm(X)&creative(X)))))&
((?[X]:((rich(X)|generous(X))))=>(?[X]:(~tall(X))))&
(![X]:(~curious(X)=>~kind(X)))&
(![X]:((brave(X)&~calm(X))<=>~strong(X)))&
(![X]:((quiet(X)|wise(X))<=>(~creative(X)&~patient(X))))&
(((tall(fred)&wise(fred)))<=>((~quiet(lucy)&~kind(lucy))))&
(![X]:((brave(X)&~brave(X))<=>(~patient(X)|calm(X))))&
((~tall(alice)&patient(alice)))&
((old(susan)<~>~brave(susan)))&
((funny(susan)&strong(susan)))&
((creative(mary)<~>brave(mary)))&
(?[X]:((kind(X)&creative(X)))) | ~wise(susan) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5477102368618172076327408
% SZS output start Proof for 5477102368618172076327408
13. ! [X0] : ((wise(X0) | quiet(X0)) <=> (~patient(X0) & ~creative(X0))) [input p12]
15. ! [X0] : ((~brave(X0) & brave(X0)) <=> (calm(X0) | ~patient(X0))) [input p14]
21. wise(susan) [input hypothesis]
57. ! [X0] : (((wise(X0) | quiet(X0)) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | (~wise(X0) & ~quiet(X0)))) [nnf transformation 13]
58. ! [X0] : ((wise(X0) | quiet(X0) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | (~wise(X0) & ~quiet(X0)))) [flattening 57]
61. ! [X0] : (((~brave(X0) & brave(X0)) | (~calm(X0) & patient(X0))) & ((calm(X0) | ~patient(X0)) | (brave(X0) | ~brave(X0)))) [nnf transformation 15]
62. ! [X0] : (((~brave(X0) & brave(X0)) | (~calm(X0) & patient(X0))) & (calm(X0) | ~patient(X0) | brave(X0) | ~brave(X0))) [flattening 61]
104. ~wise(X0) | ~patient(X0) [cnf transformation 58]
111. brave(X0) | patient(X0) [cnf transformation 62]
113. ~brave(X0) | patient(X0) [cnf transformation 62]
125. wise(susan) [cnf transformation 21]
265. patient(X0) [subsumption resolution 111,113]
319. ~patient(susan) [resolution 104,125]
320. $false [subsumption resolution 319,265]
% SZS output end Proof for 5477102368618172076327408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and tall is brave or not wise and vice versa.
If someone is both not calm and rich then someone is both brave and not generous.
If someone is both not wise and not tall then john is both strong and humble and vice versa.
Everyone who is either patient or not patient is either not kind or tall and vice versa.
Everyone who is either not kind or calm is either not kind or kind and vice versa.
If mary is both not patient and not kind then someone is both not funny and creative.
Everyone who is either not funny or wise is either not kind or rich.
If someone is either generous or rich then someone is either not kind or curious and vice versa.
If lucy is not happy then someone is patient and vice versa.
Everyone who is calm is patient and vice versa.
If john is both curious and not tall then someone is calm.
Everyone who is calm or not rich is old and vice versa.
Everyone who is both patient and funny is both humble and not tall.
Everyone who is not happy or not strong is either curious or happy and vice versa.
Everyone who is both not calm and patient is either not quiet or tall.
If john is either wise or not happy then someone is both not creative and creative and vice versa.
Fred is creative or strong.
Someone is both not curious and not generous.
Someone is not quiet.
Fred is either not strong or not calm.
Someone is not quiet or not tall.
Someone is curious.
Someone is not curious. | John is not wise. | neutral | (![X]:((~creative(X)&tall(X))<=>(brave(X)|~wise(X))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((brave(X)&~generous(X)))))&
((?[X]:((~wise(X)&~tall(X))))<=>((strong(john)&humble(john))))&
(![X]:((patient(X)<~>~patient(X))<=>(~kind(X)<~>tall(X))))&
(![X]:((~kind(X)<~>calm(X))<=>(~kind(X)<~>kind(X))))&
(((~patient(mary)&~kind(mary)))=>(?[X]:((~funny(X)&creative(X)))))&
(![X]:((~funny(X)<~>wise(X))=>(~kind(X)<~>rich(X))))&
((?[X]:((generous(X)<~>rich(X))))<=>(?[X]:((~kind(X)<~>curious(X)))))&
((~happy(lucy))<=>(?[X]:(patient(X))))&
(![X]:(calm(X)<=>patient(X)))&
(((curious(john)&~tall(john)))=>(?[X]:(calm(X))))&
(![X]:((calm(X)|~rich(X))<=>old(X)))&
(![X]:((patient(X)&funny(X))=>(humble(X)&~tall(X))))&
(![X]:((~happy(X)|~strong(X))<=>(curious(X)<~>happy(X))))&
(![X]:((~calm(X)&patient(X))=>(~quiet(X)<~>tall(X))))&
(((wise(john)<~>~happy(john)))<=>(?[X]:((~creative(X)&creative(X)))))&
((creative(fred)|strong(fred)))&
(?[X]:((~curious(X)&~generous(X))))&
(?[X]:(~quiet(X)))&
((~strong(fred)<~>~calm(fred)))&
(?[X]:((~quiet(X)|~tall(X))))&
(?[X]:(curious(X)))&
(?[X]:(~curious(X))) | ~wise(john) | [] | null | 0 |
Everyone who is not humble is calm.
If someone is brave then alice is funny or not creative and vice versa.
Everyone who is generous is kind and vice versa.
Everyone who is both funny and brave is either not tall or not old.
If mary is not creative then someone is either humble or brave.
If mary is both not strong and happy then john is humble.
Everyone who is both not old and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Lucy is not old or tall.
Alice is not humble or kind.
Paul is both not quiet and not wise.
Paul is both not curious and not rich.
Paul is humble or not wise.
Someone is either not happy or not creative.
Alice is rich.
John is either not humble or kind. | Alice is not wise. | contradiction | (![X]:(~humble(X)=>calm(X)))&
((?[X]:(brave(X)))<=>((funny(alice)|~creative(alice))))&
(![X]:(generous(X)<=>kind(X)))&
(![X]:((funny(X)&brave(X))=>(~tall(X)<~>~old(X))))&
((~creative(mary))=>(?[X]:((humble(X)<~>brave(X)))))&
(((~strong(mary)&happy(mary)))=>(humble(john)))&
(![X]:((~old(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
((~old(lucy)|tall(lucy)))&
((~humble(alice)|kind(alice)))&
((~quiet(paul)&~wise(paul)))&
((~curious(paul)&~rich(paul)))&
((humble(paul)|~wise(paul)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(rich(alice))&
((~humble(john)<~>kind(john))) | ~wise(alice) | [
"p6",
"p8",
"p13",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4203333172144944232983263
% SZS output start Proof for 4203333172144944232983263
7. ! [X0] : ((creative(X0) & ~old(X0)) <=> ~wise(X0)) [input p6]
9. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p8]
14. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p13]
15. ! [X0] : (rich(X0) => ~kind(X0)) [input p14]
16. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p15]
23. rich(alice) [input p22]
25. ~wise(alice) [input hypothesis]
32. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 14]
33. ! [X0] : (~kind(X0) | ~rich(X0)) [ennf transformation 15]
43. ! [X0] : (((creative(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) | old(X0)))) [nnf transformation 7]
44. ! [X0] : (((creative(X0) & ~old(X0)) | wise(X0)) & (~wise(X0) | ~creative(X0) | old(X0))) [flattening 43]
46. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 9]
47. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 46]
57. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 16]
72. wise(X0) | creative(X0) [cnf transformation 44]
75. ~old(X0) | tall(X0) [cnf transformation 47]
76. ~curious(X0) | ~old(X0) [cnf transformation 47]
79. ~tall(X0) | curious(X0) | kind(X0) | old(X0) [cnf transformation 47]
99. tall(X0) | old(X0) [cnf transformation 32]
101. ~rich(X0) | ~kind(X0) [cnf transformation 33]
102. old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 57]
104. ~creative(X0) | curious(X0) | ~old(X0) [cnf transformation 57]
115. rich(alice) [cnf transformation 23]
118. ~wise(alice) [cnf transformation 25]
124. 1 <=> creative(alice) [avatar definition]
126. creative(alice) <- (1) [avatar component clause 124]
199. tall(X0) [subsumption resolution 99,75]
200. ~old(X0) | ~creative(X0) [subsumption resolution 104,76]
201. ~curious(X0) | ~creative(X0) [subsumption resolution 102,76]
207. 18 <=> kind(alice) [avatar definition]
208. ~kind(alice) <- (~18) [avatar component clause 207]
237. creative(alice) [resolution 72,118]
243. 1 [avatar split clause 237,124]
252. ~kind(alice) [resolution 101,115]
253. ~18 [avatar split clause 252,207]
289. curious(X0) | kind(X0) | old(X0) [resolution 79,199]
293. kind(X0) | old(X0) | ~creative(X0) [resolution 289,201]
305. ~creative(X0) | kind(X0) [subsumption resolution 293,200]
322. kind(alice) <- (1) [resolution 305,126]
325. $false <- (1, ~18) [subsumption resolution 322,208]
326. ~1 | 18 [avatar contradiction clause 325]
327. $false [avatar sat refutation 243,253,326]
% SZS output end Proof for 4203333172144944232983263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or not generous then someone is both quiet and not tall and vice versa.
Everyone who is both not rich and brave is calm or wise and vice versa.
Everyone who is either not rich or not patient is both not happy and strong.
If alice is tall then fred is not funny or creative and vice versa.
Everyone who is either not tall or not kind is quiet and vice versa.
Everyone who is strong is both patient and kind and vice versa.
If someone is both not creative and old then someone is quiet or not rich.
Everyone who is either not kind or not wise is either rich or curious and vice versa.
If someone is either rich or not humble then fred is old or not brave and vice versa.
If alice is either quiet or not calm then someone is rich or generous and vice versa.
If someone is both kind and not funny then someone is happy or not calm and vice versa.
If john is either quiet or not patient then someone is either kind or not old and vice versa.
If someone is not brave or brave then someone is not happy.
If someone is humble or not creative then fred is either not old or brave and vice versa.
Everyone who is both not tall and strong is either not wise or not tall.
Everyone who is not strong or funny is not brave and vice versa.
Alice is patient.
Lucy is not strong or not rich.
Someone is not calm.
Someone is both not curious and not old.
Susan is not patient or not creative.
Paul is quiet or creative.
John is quiet or humble.
Lucy is funny. | Alice is not rich. | neutral | ((?[X]:((~strong(X)<~>~generous(X))))<=>(?[X]:((quiet(X)&~tall(X)))))&
(![X]:((~rich(X)&brave(X))<=>(calm(X)|wise(X))))&
(![X]:((~rich(X)<~>~patient(X))=>(~happy(X)&strong(X))))&
((tall(alice))<=>((~funny(fred)|creative(fred))))&
(![X]:((~tall(X)<~>~kind(X))<=>quiet(X)))&
(![X]:(strong(X)<=>(patient(X)&kind(X))))&
((?[X]:((~creative(X)&old(X))))=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((~kind(X)<~>~wise(X))<=>(rich(X)<~>curious(X))))&
((?[X]:((rich(X)<~>~humble(X))))<=>((old(fred)|~brave(fred))))&
(((quiet(alice)<~>~calm(alice)))<=>(?[X]:((rich(X)|generous(X)))))&
((?[X]:((kind(X)&~funny(X))))<=>(?[X]:((happy(X)|~calm(X)))))&
(((quiet(john)<~>~patient(john)))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~happy(X))))&
((?[X]:((humble(X)|~creative(X))))<=>((~old(fred)<~>brave(fred))))&
(![X]:((~tall(X)&strong(X))=>(~wise(X)<~>~tall(X))))&
(![X]:((~strong(X)|funny(X))<=>~brave(X)))&
(patient(alice))&
((~strong(lucy)|~rich(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~curious(X)&~old(X))))&
((~patient(susan)|~creative(susan)))&
((quiet(paul)|creative(paul)))&
((quiet(john)|humble(john)))&
(funny(lucy)) | ~rich(alice) | [] | null | 0 |
Everyone who is either generous or tall is quiet or funny. Everyone who is not old is quiet. If susan is not happy then john is rich. If someone is strong then someone is both not happy and creative and vice versa. Everyone who is not patient is both quiet and not tall and vice versa. Everyone who is either not patient or not generous is happy or not happy and vice versa. If susan is both curious and patient then someone is either calm or not rich. Everyone who is both not happy and curious is both not tall and rich. Everyone who is brave or not patient is not funny and vice versa. Everyone who is tall is both not generous and not quiet. Everyone who is not creative is either kind or creative. Everyone who is either not calm or not tall is either not strong or not tall and vice versa. Everyone who is not brave or not patient is humble and vice versa. Everyone who is not brave or patient is creative or humble. Everyone who is either tall or not funny is either brave or funny and vice versa. Everyone who is either kind or quiet is quiet and vice versa. Someone is either quiet or funny. Fred is brave. Someone is either not creative or not old. Alice is both old and not calm. Mary is not old or not quiet. Someone is either not old or not brave. | John is brave. | neutral | (![X]:((generous(X)<~>tall(X))=>(quiet(X)|funny(X))))&
(![X]:(~old(X)=>quiet(X)))&
((~happy(susan))=>(rich(john)))&
((?[X]:(strong(X)))<=>(?[X]:((~happy(X)&creative(X)))))&
(![X]:(~patient(X)<=>(quiet(X)&~tall(X))))&
(![X]:((~patient(X)<~>~generous(X))<=>(happy(X)|~happy(X))))&
(((curious(susan)&patient(susan)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((~happy(X)&curious(X))=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~patient(X))<=>~funny(X)))&
(![X]:(tall(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~creative(X)=>(kind(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~strong(X)<~>~tall(X))))&
(![X]:((~brave(X)|~patient(X))<=>humble(X)))&
(![X]:((~brave(X)|patient(X))=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>quiet(X)))&
(?[X]:((quiet(X)<~>funny(X))))&
(brave(fred))&
(?[X]:((~creative(X)<~>~old(X))))&
((old(alice)&~calm(alice)))&
((~old(mary)|~quiet(mary)))&
(?[X]:((~old(X)<~>~brave(X)))) | brave(john) | [] | null | 0 |
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