premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is not rich is not funny or not curious. If alice is quiet or generous then someone is not generous or not rich and vice versa. Everyone who is both not brave and curious is kind and vice versa. Everyone who is both not curious and patient is either funny or rich. Everyone who is both happy and not patient is either happy or kind. Everyone who is not patient or not humble is patient and vice versa. Everyone who is wise or not strong is not patient and vice versa. Everyone who is happy or not wise is tall and vice versa. Everyone who is either not brave or not creative is both rich and not calm and vice versa. Everyone who is both quiet and rich is not calm or kind. If someone is either not kind or not rich then someone is either not brave or humble and vice versa. Everyone who is both not curious and strong is old or generous. Everyone who is rich or wise is either not humble or not funny. Everyone who is tall or not tall is either not creative or not patient and vice versa. If fred is happy or not curious then alice is either kind or not old. If susan is both curious and not funny then fred is both generous and wise and vice versa. Fred is both patient and calm. Fred is curious or humble. Fred is not old or not tall. Fred is both not old and funny. Someone is curious or not calm. Alice is not wise. Alice is either patient or not curious. | Alice is patient. | entailment | (![X]:(~rich(X)=>(~funny(X)|~curious(X))))&
(((quiet(alice)|generous(alice)))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((~brave(X)&curious(X))<=>kind(X)))&
(![X]:((~curious(X)&patient(X))=>(funny(X)<~>rich(X))))&
(![X]:((happy(X)&~patient(X))=>(happy(X)<~>kind(X))))&
(![X]:((~patient(X)|~humble(X))<=>patient(X)))&
(![X]:((wise(X)|~strong(X))<=>~patient(X)))&
(![X]:((happy(X)|~wise(X))<=>tall(X)))&
(![X]:((~brave(X)<~>~creative(X))<=>(rich(X)&~calm(X))))&
(![X]:((quiet(X)&rich(X))=>(~calm(X)|kind(X))))&
((?[X]:((~kind(X)<~>~rich(X))))<=>(?[X]:((~brave(X)<~>humble(X)))))&
(![X]:((~curious(X)&strong(X))=>(old(X)|generous(X))))&
(![X]:((rich(X)|wise(X))=>(~humble(X)<~>~funny(X))))&
(![X]:((tall(X)|~tall(X))<=>(~creative(X)<~>~patient(X))))&
(((happy(fred)|~curious(fred)))=>((kind(alice)<~>~old(alice))))&
(((curious(susan)&~funny(susan)))<=>((generous(fred)&wise(fred))))&
((patient(fred)&calm(fred)))&
((curious(fred)|humble(fred)))&
((~old(fred)|~tall(fred)))&
((~old(fred)&funny(fred)))&
(?[X]:((curious(X)|~calm(X))))&
(~wise(alice))&
((patient(alice)<~>~curious(alice))) | patient(alice) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1278157832322928422476366
% SZS output start Proof for 1278157832322928422476366
6. ! [X0] : ((~humble(X0) | ~patient(X0)) <=> patient(X0)) [input p5]
24. ~patient(alice) [input hypothesis]
47. ! [X0] : (((~humble(X0) | ~patient(X0)) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [nnf transformation 6]
48. ! [X0] : ((~humble(X0) | ~patient(X0) | ~patient(X0)) & (patient(X0) | (humble(X0) & patient(X0)))) [flattening 47]
81. patient(X0) | patient(X0) [cnf transformation 48]
134. ~patient(alice) [cnf transformation 24]
135. patient(X0) [duplicate literal removal 81]
257. $false [subsumption resolution 134,135]
% SZS output end Proof for 1278157832322928422476366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not strong is both not humble and funny and vice versa. Everyone who is both wise and not tall is not old or not generous. Everyone who is either not creative or humble is generous or not strong and vice versa. If john is either calm or not strong then someone is either wise or old. If someone is not strong or not curious then mary is not strong. If someone is both not happy and not old then someone is creative and vice versa. Everyone who is either not tall or not wise is either not generous or not funny and vice versa. If john is either rich or strong then lucy is calm and vice versa. If someone is tall or humble then someone is either not kind or old. If someone is not humble or strong then someone is either not wise or humble. Everyone who is not funny or not tall is either not strong or strong. Everyone who is not generous or not patient is patient and vice versa. Everyone who is not tall is kind and vice versa. Everyone who is either not tall or quiet is not kind or patient and vice versa. Everyone who is not brave is both funny and not old. If someone is curious or generous then alice is both not humble and not brave. Paul is both brave and rich. Susan is not tall or patient. Someone is not humble or tall. Fred is either not calm or not happy. Someone is either not kind or not brave. John is either brave or not brave. | Mary is patient. | entailment | (![X]:((humble(X)<~>~strong(X))<=>(~humble(X)&funny(X))))&
(![X]:((wise(X)&~tall(X))=>(~old(X)|~generous(X))))&
(![X]:((~creative(X)<~>humble(X))<=>(generous(X)|~strong(X))))&
(((calm(john)<~>~strong(john)))=>(?[X]:((wise(X)<~>old(X)))))&
((?[X]:((~strong(X)|~curious(X))))=>(~strong(mary)))&
((?[X]:((~happy(X)&~old(X))))<=>(?[X]:(creative(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(~generous(X)<~>~funny(X))))&
(((rich(john)<~>strong(john)))<=>(calm(lucy)))&
((?[X]:((tall(X)|humble(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
((?[X]:((~humble(X)|strong(X))))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~funny(X)|~tall(X))=>(~strong(X)<~>strong(X))))&
(![X]:((~generous(X)|~patient(X))<=>patient(X)))&
(![X]:(~tall(X)<=>kind(X)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~kind(X)|patient(X))))&
(![X]:(~brave(X)=>(funny(X)&~old(X))))&
((?[X]:((curious(X)|generous(X))))=>((~humble(alice)&~brave(alice))))&
((brave(paul)&rich(paul)))&
((~tall(susan)|patient(susan)))&
(?[X]:((~humble(X)|tall(X))))&
((~calm(fred)<~>~happy(fred)))&
(?[X]:((~kind(X)<~>~brave(X))))&
((brave(john)<~>~brave(john))) | patient(mary) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7584731029685872003954519
% SZS output start Proof for 7584731029685872003954519
12. ! [X0] : ((~patient(X0) | ~generous(X0)) <=> patient(X0)) [input p11]
23. ~patient(mary) [input hypothesis]
59. ! [X0] : (((~patient(X0) | ~generous(X0)) | ~patient(X0)) & (patient(X0) | (patient(X0) & generous(X0)))) [nnf transformation 12]
60. ! [X0] : ((~patient(X0) | ~generous(X0) | ~patient(X0)) & (patient(X0) | (patient(X0) & generous(X0)))) [flattening 59]
118. patient(X0) | patient(X0) [cnf transformation 60]
144. ~patient(mary) [cnf transformation 23]
145. patient(X0) [duplicate literal removal 118]
301. $false [subsumption resolution 144,145]
% SZS output end Proof for 7584731029685872003954519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or brave is funny. If susan is not curious or not old then someone is either curious or not old and vice versa. If mary is both tall and not happy then fred is strong and vice versa. Everyone who is either brave or curious is both not patient and brave and vice versa. If someone is quiet or brave then fred is not funny or not strong and vice versa. If susan is both not kind and funny then someone is both not funny and humble and vice versa. Everyone who is kind or quiet is not happy or happy. Everyone who is not patient is either brave or not curious. If john is not rich then susan is either not humble or not funny. If someone is old or wise then someone is not rich and vice versa. Everyone who is both generous and tall is both funny and not generous. Everyone who is not patient or not creative is both not rich and creative and vice versa. Everyone who is either not kind or patient is both strong and brave. If susan is not strong then fred is not generous and vice versa. If john is curious or brave then someone is either humble or generous and vice versa. Everyone who is not old or generous is both curious and not calm and vice versa. Someone is old. Someone is strong or patient. Alice is either not patient or not calm. Fred is not calm or not creative. Someone is both not kind and not curious. Someone is not calm. Someone is not generous or not patient. | Alice is not generous. | neutral | (![X]:((humble(X)|brave(X))=>funny(X)))&
(((~curious(susan)|~old(susan)))<=>(?[X]:((curious(X)<~>~old(X)))))&
(((tall(mary)&~happy(mary)))<=>(strong(fred)))&
(![X]:((brave(X)<~>curious(X))<=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)|brave(X))))<=>((~funny(fred)|~strong(fred))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((kind(X)|quiet(X))=>(~happy(X)|happy(X))))&
(![X]:(~patient(X)=>(brave(X)<~>~curious(X))))&
((~rich(john))=>((~humble(susan)<~>~funny(susan))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:(~rich(X))))&
(![X]:((generous(X)&tall(X))=>(funny(X)&~generous(X))))&
(![X]:((~patient(X)|~creative(X))<=>(~rich(X)&creative(X))))&
(![X]:((~kind(X)<~>patient(X))=>(strong(X)&brave(X))))&
((~strong(susan))<=>(~generous(fred)))&
(((curious(john)|brave(john)))<=>(?[X]:((humble(X)<~>generous(X)))))&
(![X]:((~old(X)|generous(X))<=>(curious(X)&~calm(X))))&
(?[X]:(old(X)))&
(?[X]:((strong(X)|patient(X))))&
((~patient(alice)<~>~calm(alice)))&
((~calm(fred)|~creative(fred)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~generous(X)|~patient(X)))) | ~generous(alice) | [] | null | 0 |
If paul is either not strong or kind then susan is both curious and not curious and vice versa.
If someone is not old then fred is both not happy and quiet and vice versa.
Everyone who is either strong or not calm is both humble and not generous and vice versa.
Everyone who is both not creative and generous is either tall or old.
If someone is not strong or generous then someone is both calm and curious.
Everyone who is both not strong and not tall is either not happy or not kind.
If john is either curious or quiet then susan is not old and vice versa.
Everyone who is not kind is both curious and not generous.
If mary is kind or wise then lucy is either patient or creative.
If someone is not humble then fred is both funny and not funny and vice versa.
If fred is curious then someone is creative and vice versa.
If someone is either kind or not funny then paul is curious and vice versa.
If john is either not strong or not generous then paul is wise or quiet.
Everyone who is both patient and brave is either rich or not patient.
Everyone who is happy is calm or brave.
If someone is either humble or funny then mary is either not patient or not old.
Fred is not calm.
Alice is not humble or generous.
Someone is not strong or not quiet.
Someone is not tall or strong.
Alice is either funny or not strong.
Lucy is not strong.
Someone is tall or not humble.
Someone is either calm or rich. | Lucy is humble. | entailment | (((~strong(paul)<~>kind(paul)))<=>((curious(susan)&~curious(susan))))&
((?[X]:(~old(X)))<=>((~happy(fred)&quiet(fred))))&
(![X]:((strong(X)<~>~calm(X))<=>(humble(X)&~generous(X))))&
(![X]:((~creative(X)&generous(X))=>(tall(X)<~>old(X))))&
((?[X]:((~strong(X)|generous(X))))=>(?[X]:((calm(X)&curious(X)))))&
(![X]:((~strong(X)&~tall(X))=>(~happy(X)<~>~kind(X))))&
(((curious(john)<~>quiet(john)))<=>(~old(susan)))&
(![X]:(~kind(X)=>(curious(X)&~generous(X))))&
(((kind(mary)|wise(mary)))=>((patient(lucy)<~>creative(lucy))))&
((?[X]:(~humble(X)))<=>((funny(fred)&~funny(fred))))&
((curious(fred))<=>(?[X]:(creative(X))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(curious(paul)))&
(((~strong(john)<~>~generous(john)))=>((wise(paul)|quiet(paul))))&
(![X]:((patient(X)&brave(X))=>(rich(X)<~>~patient(X))))&
(![X]:(happy(X)=>(calm(X)|brave(X))))&
((?[X]:((humble(X)<~>funny(X))))=>((~patient(mary)<~>~old(mary))))&
(~calm(fred))&
((~humble(alice)|generous(alice)))&
(?[X]:((~strong(X)|~quiet(X))))&
(?[X]:((~tall(X)|strong(X))))&
((funny(alice)<~>~strong(alice)))&
(~strong(lucy))&
(?[X]:((tall(X)|~humble(X))))&
(?[X]:((calm(X)<~>rich(X)))) | humble(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 901009117343548761638810
% SZS output start Proof for 901009117343548761638810
10. ? [X0] : ~humble(X0) <=> (~funny(fred) & funny(fred)) [input p9]
25. ~humble(lucy) [input hypothesis]
57. (? [X0] : ~humble(X0) | (funny(fred) | ~funny(fred))) & ((~funny(fred) & funny(fred)) | ! [X0] : humble(X0)) [nnf transformation 10]
58. (? [X0] : ~humble(X0) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ! [X0] : humble(X0)) [flattening 57]
59. (? [X0] : ~humble(X0) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ! [X1] : humble(X1)) [rectify 58]
60. ? [X0] : ~humble(X0) => ~humble(sK2) [choice axiom]
61. (~humble(sK2) | funny(fred) | ~funny(fred)) & ((~funny(fred) & funny(fred)) | ! [X1] : humble(X1)) [skolemisation 59,60]
116. funny(fred) | humble(X1) [cnf transformation 61]
117. ~funny(fred) | humble(X1) [cnf transformation 61]
144. ~humble(lucy) [cnf transformation 25]
235. 19 <=> ! [X1] : humble(X1) [avatar definition]
236. humble(X1) <- (19) [avatar component clause 235]
238. 20 <=> funny(fred) [avatar definition]
241. 19 | ~20 [avatar split clause 117,238,235]
242. 19 | 20 [avatar split clause 116,238,235]
372. $false <- (19) [resolution 236,144]
373. ~19 [avatar contradiction clause 372]
374. $false [avatar sat refutation 241,242,373]
% SZS output end Proof for 901009117343548761638810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not creative is generous or not patient and vice versa.
Everyone who is not wise is not quiet or calm.
Everyone who is both humble and funny is rich or not generous and vice versa.
Everyone who is not strong is both not wise and not quiet and vice versa.
Everyone who is either curious or calm is old or creative.
Everyone who is both humble and generous is wise or brave and vice versa.
If susan is rich or curious then paul is kind or humble and vice versa.
If fred is both rich and creative then paul is both brave and not patient and vice versa.
If someone is either not brave or kind then lucy is not wise or quiet and vice versa.
If john is strong then someone is either brave or not humble and vice versa.
If someone is either not tall or humble then someone is not patient or brave and vice versa.
Everyone who is both not curious and funny is brave.
Everyone who is both not quiet and not humble is both not humble and humble.
Everyone who is either generous or happy is not strong or not happy and vice versa.
If alice is not kind or tall then susan is brave or not funny and vice versa.
If lucy is not patient then someone is creative or generous and vice versa.
Someone is either kind or not happy.
Someone is not happy.
Someone is either calm or old.
Someone is either not kind or not humble.
Someone is either brave or strong.
Paul is either calm or strong.
Someone is old.
Susan is both creative and not strong. | Paul is not humble. | contradiction | (![X]:((strong(X)|~creative(X))<=>(generous(X)|~patient(X))))&
(![X]:(~wise(X)=>(~quiet(X)|calm(X))))&
(![X]:((humble(X)&funny(X))<=>(rich(X)|~generous(X))))&
(![X]:(~strong(X)<=>(~wise(X)&~quiet(X))))&
(![X]:((curious(X)<~>calm(X))=>(old(X)|creative(X))))&
(![X]:((humble(X)&generous(X))<=>(wise(X)|brave(X))))&
(((rich(susan)|curious(susan)))<=>((kind(paul)|humble(paul))))&
(((rich(fred)&creative(fred)))<=>((brave(paul)&~patient(paul))))&
((?[X]:((~brave(X)<~>kind(X))))<=>((~wise(lucy)|quiet(lucy))))&
((strong(john))<=>(?[X]:((brave(X)<~>~humble(X)))))&
((?[X]:((~tall(X)<~>humble(X))))<=>(?[X]:((~patient(X)|brave(X)))))&
(![X]:((~curious(X)&funny(X))=>brave(X)))&
(![X]:((~quiet(X)&~humble(X))=>(~humble(X)&humble(X))))&
(![X]:((generous(X)<~>happy(X))<=>(~strong(X)|~happy(X))))&
(((~kind(alice)|tall(alice)))<=>((brave(susan)|~funny(susan))))&
((~patient(lucy))<=>(?[X]:((creative(X)|generous(X)))))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:(~happy(X)))&
(?[X]:((calm(X)<~>old(X))))&
(?[X]:((~kind(X)<~>~humble(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((calm(paul)<~>strong(paul)))&
(?[X]:(old(X)))&
((creative(susan)&~strong(susan))) | ~humble(paul) | [
"p1",
"p3",
"p5",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8795384187606889708248796
% SZS output start Proof for 8795384187606889708248796
2. ! [X0] : (~wise(X0) => (calm(X0) | ~quiet(X0))) [input p1]
4. ! [X0] : (~strong(X0) <=> (~quiet(X0) & ~wise(X0))) [input p3]
6. ! [X0] : ((generous(X0) & humble(X0)) <=> (brave(X0) | wise(X0))) [input p5]
13. ! [X0] : ((~humble(X0) & ~quiet(X0)) => (humble(X0) & ~humble(X0))) [input p12]
22. calm(paul) <~> strong(paul) [input p21]
25. ~humble(paul) [input hypothesis]
27. ! [X0] : ((calm(X0) | ~quiet(X0)) | wise(X0)) [ennf transformation 2]
28. ! [X0] : (calm(X0) | ~quiet(X0) | wise(X0)) [flattening 27]
33. ! [X0] : ((humble(X0) & ~humble(X0)) | (humble(X0) | quiet(X0))) [ennf transformation 13]
34. ! [X0] : ((humble(X0) & ~humble(X0)) | humble(X0) | quiet(X0)) [flattening 33]
39. ! [X0] : ((~strong(X0) | (quiet(X0) | wise(X0))) & ((~quiet(X0) & ~wise(X0)) | strong(X0))) [nnf transformation 4]
40. ! [X0] : ((~strong(X0) | quiet(X0) | wise(X0)) & ((~quiet(X0) & ~wise(X0)) | strong(X0))) [flattening 39]
42. ! [X0] : (((generous(X0) & humble(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~generous(X0) | ~humble(X0)))) [nnf transformation 6]
43. ! [X0] : (((generous(X0) & humble(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~generous(X0) | ~humble(X0))) [flattening 42]
84. (~strong(paul) | ~calm(paul)) & (strong(paul) | calm(paul)) [nnf transformation 22]
91. ~quiet(X0) | calm(X0) | wise(X0) [cnf transformation 28]
98. ~quiet(X0) | strong(X0) [cnf transformation 40]
103. ~wise(X0) | humble(X0) [cnf transformation 43]
133. humble(X0) | humble(X0) | quiet(X0) [cnf transformation 34]
157. ~strong(paul) | ~calm(paul) [cnf transformation 84]
161. ~humble(paul) [cnf transformation 25]
164. humble(X0) | quiet(X0) [duplicate literal removal 133]
166. 1 <=> humble(paul) [avatar definition]
168. ~humble(paul) <- (~1) [avatar component clause 166]
370. 44 <=> calm(paul) [avatar definition]
372. ~calm(paul) <- (~44) [avatar component clause 370]
374. 45 <=> strong(paul) [avatar definition]
377. ~44 | ~45 [avatar split clause 157,374,370]
379. ~1 [avatar split clause 161,166]
399. quiet(paul) <- (~1) [resolution 164,168]
404. strong(paul) <- (~1) [resolution 399,98]
407. 45 | 1 [avatar split clause 404,166,374]
466. calm(paul) | wise(paul) <- (~1) [resolution 91,399]
469. wise(paul) <- (~1, ~44) [subsumption resolution 466,372]
657. humble(paul) <- (~1, ~44) [resolution 469,103]
659. $false <- (~1, ~44) [subsumption resolution 657,168]
660. 1 | 44 [avatar contradiction clause 659]
661. $false [avatar sat refutation 377,379,407,660]
% SZS output end Proof for 8795384187606889708248796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not rich and not patient then someone is brave and vice versa. Everyone who is not humble is creative. Everyone who is either wise or not rich is not generous. If someone is not patient then someone is either old or quiet. Everyone who is both not curious and not generous is not strong. Everyone who is both happy and generous is not strong and vice versa. Everyone who is rich or creative is not generous or humble and vice versa. If someone is either not strong or not quiet then someone is tall or not wise. Everyone who is strong or not happy is funny or not curious. If fred is both not humble and happy then someone is either not creative or strong. Everyone who is either not quiet or quiet is either kind or brave and vice versa. Everyone who is either brave or not quiet is kind or brave. If someone is both not old and not brave then someone is either curious or wise. Everyone who is curious is either not calm or creative. Everyone who is either wise or brave is not wise or not strong. Everyone who is either kind or wise is rich. Someone is either not calm or quiet. Lucy is either not wise or patient. Someone is not kind. Susan is not strong. Mary is rich. Mary is not brave. Alice is not strong. Fred is not tall or not humble. | Mary is not kind. | contradiction | (((~rich(fred)&~patient(fred)))<=>(?[X]:(brave(X))))&
(![X]:(~humble(X)=>creative(X)))&
(![X]:((wise(X)<~>~rich(X))=>~generous(X)))&
((?[X]:(~patient(X)))=>(?[X]:((old(X)<~>quiet(X)))))&
(![X]:((~curious(X)&~generous(X))=>~strong(X)))&
(![X]:((happy(X)&generous(X))<=>~strong(X)))&
(![X]:((rich(X)|creative(X))<=>(~generous(X)|humble(X))))&
((?[X]:((~strong(X)<~>~quiet(X))))=>(?[X]:((tall(X)|~wise(X)))))&
(![X]:((strong(X)|~happy(X))=>(funny(X)|~curious(X))))&
(((~humble(fred)&happy(fred)))=>(?[X]:((~creative(X)<~>strong(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(kind(X)<~>brave(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(kind(X)|brave(X))))&
((?[X]:((~old(X)&~brave(X))))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:(curious(X)=>(~calm(X)<~>creative(X))))&
(![X]:((wise(X)<~>brave(X))=>(~wise(X)|~strong(X))))&
(![X]:((kind(X)<~>wise(X))=>rich(X)))&
(?[X]:((~calm(X)<~>quiet(X))))&
((~wise(lucy)<~>patient(lucy)))&
(?[X]:(~kind(X)))&
(~strong(susan))&
(rich(mary))&
(~brave(mary))&
(~strong(alice))&
((~tall(fred)|~humble(fred))) | ~kind(mary) | [
"p10",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8202944980340955099788828
% SZS output start Proof for 8202944980340955099788828
11. ! [X0] : ((~quiet(X0) <~> quiet(X0)) <=> (kind(X0) <~> brave(X0))) [input p10]
22. ~brave(mary) [input p21]
25. ~kind(mary) [input hypothesis]
66. ! [X0] : ((((~quiet(X0) | quiet(X0)) & (quiet(X0) | ~quiet(X0))) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) & (((~brave(X0) | ~kind(X0)) & (brave(X0) | kind(X0))) | ((~quiet(X0) | ~quiet(X0)) & (quiet(X0) | quiet(X0))))) [nnf transformation 11]
101. brave(X0) | kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 66]
102. brave(X0) | kind(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 66]
126. ~brave(mary) [cnf transformation 22]
129. ~kind(mary) [cnf transformation 25]
132. brave(X0) | kind(X0) | quiet(X0) [duplicate literal removal 101]
133. brave(X0) | kind(X0) | ~quiet(X0) [duplicate literal removal 102]
204. kind(X0) | brave(X0) [subsumption resolution 132,133]
255. brave(mary) [resolution 204,129]
259. $false [subsumption resolution 255,126]
% SZS output end Proof for 8202944980340955099788828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or kind is either generous or not patient and vice versa.
If someone is generous or not humble then mary is both kind and not happy and vice versa.
If susan is either not tall or creative then someone is either not old or humble.
Everyone who is not generous or happy is not brave and vice versa.
If john is both generous and happy then someone is either quiet or not calm and vice versa.
Everyone who is either not generous or not funny is funny and vice versa.
Everyone who is curious or not old is rich and vice versa.
Everyone who is both not tall and not quiet is not humble and vice versa.
Everyone who is not tall or brave is either wise or not brave and vice versa.
Everyone who is either creative or not humble is both not humble and not wise.
Everyone who is both calm and not tall is patient and vice versa.
If someone is not happy or rich then someone is brave and vice versa.
If alice is not wise or rich then someone is either funny or not happy.
If lucy is either old or quiet then paul is not strong or not quiet.
If someone is both not happy and strong then someone is either not wise or not rich and vice versa.
Someone is not generous.
Mary is humble.
Mary is both humble and not brave.
Someone is either tall or not creative.
Someone is either curious or strong.
Lucy is not funny or generous. | John is not calm. | entailment | (![X]:((strong(X)<~>kind(X))<=>(generous(X)<~>~patient(X))))&
((?[X]:((generous(X)|~humble(X))))<=>((kind(mary)&~happy(mary))))&
(((~tall(susan)<~>creative(susan)))=>(?[X]:((~old(X)<~>humble(X)))))&
(![X]:((~generous(X)|happy(X))<=>~brave(X)))&
(((generous(john)&happy(john)))<=>(?[X]:((quiet(X)<~>~calm(X)))))&
(![X]:((~generous(X)<~>~funny(X))<=>funny(X)))&
(![X]:((curious(X)|~old(X))<=>rich(X)))&
(![X]:((~tall(X)&~quiet(X))<=>~humble(X)))&
(![X]:((~tall(X)|brave(X))<=>(wise(X)<~>~brave(X))))&
(![X]:((creative(X)<~>~humble(X))=>(~humble(X)&~wise(X))))&
(![X]:((calm(X)&~tall(X))<=>patient(X)))&
((?[X]:((~happy(X)|rich(X))))<=>(?[X]:(brave(X))))&
(((~wise(alice)|rich(alice)))=>(?[X]:((funny(X)<~>~happy(X)))))&
(((old(lucy)<~>quiet(lucy)))=>((~strong(paul)|~quiet(paul))))&
((?[X]:((~happy(X)&strong(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
(?[X]:(~generous(X)))&
(humble(mary))&
((humble(mary)&~brave(mary)))&
(?[X]:((tall(X)<~>~creative(X))))&
(?[X]:((curious(X)<~>strong(X))))&
((~funny(lucy)|generous(lucy))) | ~calm(john) | [
"p1",
"p3",
"p4",
"p5",
"p7",
"p8",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7513420340027735350794525
% SZS output start Proof for 7513420340027735350794525
2. ? [X0] : (~humble(X0) | generous(X0)) <=> (~happy(mary) & kind(mary)) [input p1]
4. ! [X0] : ((happy(X0) | ~generous(X0)) <=> ~brave(X0)) [input p3]
5. (happy(john) & generous(john)) <=> ? [X0] : (quiet(X0) <~> ~calm(X0)) [input p4]
6. ! [X0] : ((~generous(X0) <~> ~funny(X0)) <=> funny(X0)) [input p5]
8. ! [X0] : ((~quiet(X0) & ~tall(X0)) <=> ~humble(X0)) [input p7]
9. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (wise(X0) <~> ~brave(X0))) [input p8]
12. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X0] : brave(X0) [input p11]
15. ? [X0] : (strong(X0) & ~happy(X0)) <=> ? [X0] : (~wise(X0) <~> ~rich(X0)) [input p14]
22. calm(john) [input hypothesis]
23. ? [X0] : (rich(X0) | ~happy(X0)) <=> ? [X1] : brave(X1) [rectify 12]
24. ? [X0] : (strong(X0) & ~happy(X0)) <=> ? [X1] : (~wise(X1) <~> ~rich(X1)) [rectify 15]
31. (? [X0] : (~humble(X0) | generous(X0)) | (happy(mary) | ~kind(mary))) & ((~happy(mary) & kind(mary)) | ! [X0] : (humble(X0) & ~generous(X0))) [nnf transformation 2]
32. (? [X0] : (~humble(X0) | generous(X0)) | happy(mary) | ~kind(mary)) & ((~happy(mary) & kind(mary)) | ! [X0] : (humble(X0) & ~generous(X0))) [flattening 31]
33. (? [X0] : (~humble(X0) | generous(X0)) | happy(mary) | ~kind(mary)) & ((~happy(mary) & kind(mary)) | ! [X1] : (humble(X1) & ~generous(X1))) [rectify 32]
34. ? [X0] : (~humble(X0) | generous(X0)) => (~humble(sK0) | generous(sK0)) [choice axiom]
35. ((~humble(sK0) | generous(sK0)) | happy(mary) | ~kind(mary)) & ((~happy(mary) & kind(mary)) | ! [X1] : (humble(X1) & ~generous(X1))) [skolemisation 33,34]
39. ! [X0] : (((happy(X0) | ~generous(X0)) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [nnf transformation 4]
40. ! [X0] : ((happy(X0) | ~generous(X0) | brave(X0)) & (~brave(X0) | (~happy(X0) & generous(X0)))) [flattening 39]
41. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | (~happy(john) | ~generous(john))) [nnf transformation 5]
42. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (? [X0] : ((calm(X0) | ~quiet(X0)) & (~calm(X0) | quiet(X0))) | ~happy(john) | ~generous(john)) [flattening 41]
43. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (? [X1] : ((calm(X1) | ~quiet(X1)) & (~calm(X1) | quiet(X1))) | ~happy(john) | ~generous(john)) [rectify 42]
44. ? [X1] : ((calm(X1) | ~quiet(X1)) & (~calm(X1) | quiet(X1))) => ((calm(sK2) | ~quiet(sK2)) & (~calm(sK2) | quiet(sK2))) [choice axiom]
45. ((happy(john) & generous(john)) | ! [X0] : ((quiet(X0) | calm(X0)) & (~calm(X0) | ~quiet(X0)))) & (((calm(sK2) | ~quiet(sK2)) & (~calm(sK2) | quiet(sK2))) | ~happy(john) | ~generous(john)) [skolemisation 43,44]
46. ! [X0] : ((((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~funny(X0)) & (funny(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0))))) [nnf transformation 6]
49. ! [X0] : (((~quiet(X0) & ~tall(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) | tall(X0)))) [nnf transformation 8]
50. ! [X0] : (((~quiet(X0) & ~tall(X0)) | humble(X0)) & (~humble(X0) | quiet(X0) | tall(X0))) [flattening 49]
51. ! [X0] : (((brave(X0) | ~tall(X0)) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~brave(X0) & tall(X0)))) [nnf transformation 9]
52. ! [X0] : ((brave(X0) | ~tall(X0) | ((wise(X0) | brave(X0)) & (~brave(X0) | ~wise(X0)))) & (((brave(X0) | ~wise(X0)) & (~brave(X0) | wise(X0))) | (~brave(X0) & tall(X0)))) [flattening 51]
56. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X1] : brave(X1) | ! [X0] : (~rich(X0) & happy(X0))) [nnf transformation 23]
57. (? [X0] : (rich(X0) | ~happy(X0)) | ! [X1] : ~brave(X1)) & (? [X2] : brave(X2) | ! [X3] : (~rich(X3) & happy(X3))) [rectify 56]
58. ? [X0] : (rich(X0) | ~happy(X0)) => (rich(sK3) | ~happy(sK3)) [choice axiom]
59. ? [X2] : brave(X2) => brave(sK4) [choice axiom]
60. ((rich(sK3) | ~happy(sK3)) | ! [X1] : ~brave(X1)) & (brave(sK4) | ! [X3] : (~rich(X3) & happy(X3))) [skolemisation 57,59,58]
65. (? [X0] : (strong(X0) & ~happy(X0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (? [X1] : ((rich(X1) | wise(X1)) & (~rich(X1) | ~wise(X1))) | ! [X0] : (~strong(X0) | happy(X0))) [nnf transformation 24]
66. (? [X0] : (strong(X0) & ~happy(X0)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (? [X2] : ((rich(X2) | wise(X2)) & (~rich(X2) | ~wise(X2))) | ! [X3] : (~strong(X3) | happy(X3))) [rectify 65]
67. ? [X0] : (strong(X0) & ~happy(X0)) => (strong(sK6) & ~happy(sK6)) [choice axiom]
68. ? [X2] : ((rich(X2) | wise(X2)) & (~rich(X2) | ~wise(X2))) => ((rich(sK7) | wise(sK7)) & (~rich(sK7) | ~wise(sK7))) [choice axiom]
69. ((strong(sK6) & ~happy(sK6)) | ! [X1] : ((~wise(X1) | rich(X1)) & (~rich(X1) | wise(X1)))) & (((rich(sK7) | wise(sK7)) & (~rich(sK7) | ~wise(sK7))) | ! [X3] : (~strong(X3) | happy(X3))) [skolemisation 66,68,67]
89. ~happy(mary) | humble(X1) [cnf transformation 35]
95. ~brave(X0) | generous(X0) [cnf transformation 40]
100. generous(john) | ~calm(X0) | ~quiet(X0) [cnf transformation 45]
105. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 46]
106. ~funny(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 46]
111. ~humble(X0) | quiet(X0) | tall(X0) [cnf transformation 50]
119. brave(X0) | ~tall(X0) | wise(X0) | brave(X0) [cnf transformation 52]
127. brave(sK4) | happy(X3) [cnf transformation 60]
128. brave(sK4) | ~rich(X3) [cnf transformation 60]
129. rich(sK3) | ~happy(sK3) | ~brave(X1) [cnf transformation 60]
139. ~happy(sK6) | ~wise(X1) | rich(X1) [cnf transformation 69]
151. calm(john) [cnf transformation 22]
154. ~tall(X0) | brave(X0) | wise(X0) [duplicate literal removal 119]
155. funny(X0) | ~generous(X0) [duplicate literal removal 105]
156. ~funny(X0) | ~generous(X0) [duplicate literal removal 106]
162. 2 <=> happy(mary) [avatar definition]
163. ~happy(mary) <- (~2) [avatar component clause 162]
175. 5 <=> ! [X1] : humble(X1) [avatar definition]
176. humble(X1) <- (5) [avatar component clause 175]
177. 5 | ~2 [avatar split clause 89,162,175]
179. 6 <=> ! [X1] : ~generous(X1) [avatar definition]
180. ~generous(X1) <- (6) [avatar component clause 179]
213. 13 <=> ! [X0] : (~calm(X0) | ~quiet(X0)) [avatar definition]
214. ~calm(X0) | ~quiet(X0) <- (13) [avatar component clause 213]
217. 14 <=> generous(john) [avatar definition]
219. generous(john) <- (14) [avatar component clause 217]
221. 13 | 14 [avatar split clause 100,217,213]
232. ~generous(X0) [subsumption resolution 155,156]
233. 6 [avatar split clause 232,179]
235. 17 <=> ! [X1] : ~brave(X1) [avatar definition]
236. ~brave(X1) <- (17) [avatar component clause 235]
238. 18 <=> happy(sK3) [avatar definition]
240. ~happy(sK3) <- (~18) [avatar component clause 238]
242. 19 <=> rich(sK3) [avatar definition]
244. rich(sK3) <- (19) [avatar component clause 242]
245. 17 | ~18 | 19 [avatar split clause 129,242,238,235]
247. 20 <=> ! [X3] : ~rich(X3) [avatar definition]
248. ~rich(X3) <- (20) [avatar component clause 247]
250. 21 <=> brave(sK4) [avatar definition]
252. brave(sK4) <- (21) [avatar component clause 250]
253. 20 | 21 [avatar split clause 128,250,247]
255. 22 <=> ! [X3] : happy(X3) [avatar definition]
256. happy(X3) <- (22) [avatar component clause 255]
257. 22 | 21 [avatar split clause 127,250,255]
297. 31 <=> ! [X1] : (~wise(X1) | rich(X1)) [avatar definition]
298. ~wise(X1) | rich(X1) <- (31) [avatar component clause 297]
309. 34 <=> happy(sK6) [avatar definition]
311. ~happy(sK6) <- (~34) [avatar component clause 309]
312. 31 | ~34 [avatar split clause 139,309,297]
350. generous(sK4) <- (21) [resolution 95,252]
351. $false <- (6, 21) [subsumption resolution 350,180]
352. ~6 | ~21 [avatar contradiction clause 351]
354. $false <- (~18, 22) [resolution 256,240]
356. $false <- (22, ~34) [resolution 256,311]
357. ~22 | 34 [avatar contradiction clause 356]
359. 18 | ~22 [avatar contradiction clause 354]
361. ~wise(X1) <- (20, 31) [subsumption resolution 298,248]
373. ~quiet(john) <- (13) [resolution 214,151]
379. quiet(X0) | tall(X0) <- (5) [resolution 111,176]
392. tall(john) <- (5, 13) [resolution 379,373]
398. brave(john) | wise(john) <- (5, 13) [resolution 154,392]
402. wise(john) <- (5, 13, 17) [subsumption resolution 398,236]
403. $false <- (5, 13, 17, 20, 31) [subsumption resolution 402,361]
404. ~5 | ~13 | ~17 | ~20 | ~31 [avatar contradiction clause 403]
414. $false <- (6, 14) [subsumption resolution 219,180]
415. ~6 | ~14 [avatar contradiction clause 414]
416. $false <- (19, 20) [subsumption resolution 244,248]
417. ~19 | ~20 [avatar contradiction clause 416]
418. $false <- (~2, 22) [subsumption resolution 163,256]
419. 2 | ~22 [avatar contradiction clause 418]
420. $false [avatar sat refutation 177,221,233,245,253,257,312,352,357,359,404,415,417,419]
% SZS output end Proof for 7513420340027735350794525
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then paul is either wise or not patient and vice versa. If mary is either not brave or not patient then susan is not brave and vice versa. Everyone who is either not brave or quiet is wise or not quiet and vice versa. If someone is both not old and not curious then alice is both calm and not generous and vice versa. If paul is either not wise or not patient then susan is both old and not tall and vice versa. Everyone who is not calm is not brave and vice versa. If someone is not happy then fred is brave or not generous and vice versa. Everyone who is both old and creative is both generous and brave and vice versa. Everyone who is generous is not quiet or not generous. If someone is either brave or not humble then someone is either curious or funny and vice versa. Everyone who is both humble and kind is both rich and creative. Everyone who is curious is not funny and vice versa. If alice is both not generous and strong then john is both not tall and not quiet. If someone is brave or quiet then alice is either not strong or wise. If someone is both not happy and not quiet then someone is patient or not kind. If someone is both not strong and not wise then paul is either not calm or not happy and vice versa. Someone is kind. Fred is generous or not calm. John is not generous. Alice is not patient. Someone is quiet. Someone is humble or generous. | Alice is strong. | neutral | ((?[X]:(~calm(X)))<=>((wise(paul)<~>~patient(paul))))&
(((~brave(mary)<~>~patient(mary)))<=>(~brave(susan)))&
(![X]:((~brave(X)<~>quiet(X))<=>(wise(X)|~quiet(X))))&
((?[X]:((~old(X)&~curious(X))))<=>((calm(alice)&~generous(alice))))&
(((~wise(paul)<~>~patient(paul)))<=>((old(susan)&~tall(susan))))&
(![X]:(~calm(X)<=>~brave(X)))&
((?[X]:(~happy(X)))<=>((brave(fred)|~generous(fred))))&
(![X]:((old(X)&creative(X))<=>(generous(X)&brave(X))))&
(![X]:(generous(X)=>(~quiet(X)|~generous(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((humble(X)&kind(X))=>(rich(X)&creative(X))))&
(![X]:(curious(X)<=>~funny(X)))&
(((~generous(alice)&strong(alice)))=>((~tall(john)&~quiet(john))))&
((?[X]:((brave(X)|quiet(X))))=>((~strong(alice)<~>wise(alice))))&
((?[X]:((~happy(X)&~quiet(X))))=>(?[X]:((patient(X)|~kind(X)))))&
((?[X]:((~strong(X)&~wise(X))))<=>((~calm(paul)<~>~happy(paul))))&
(?[X]:(kind(X)))&
((generous(fred)|~calm(fred)))&
(~generous(john))&
(~patient(alice))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)|generous(X)))) | strong(alice) | [] | null | 0 |
Everyone who is curious or calm is both not happy and not wise and vice versa.
Everyone who is not rich or quiet is not rich or old.
Everyone who is both not old and patient is either not kind or generous.
If someone is tall or old then someone is either not funny or curious.
Everyone who is not strong or not calm is both calm and quiet.
If fred is both not curious and patient then lucy is either not brave or generous.
Everyone who is either rich or wise is curious.
If fred is patient or not humble then susan is both not curious and not funny and vice versa.
Everyone who is both generous and wise is not quiet or not generous and vice versa.
If someone is not calm or calm then mary is not strong and vice versa.
Everyone who is kind or not wise is either not wise or kind.
If fred is not generous then fred is either not tall or patient and vice versa.
Everyone who is not creative is happy.
If fred is rich or not generous then paul is not curious or tall.
If someone is either not rich or quiet then paul is either not generous or not quiet and vice versa.
Fred is tall.
Susan is either happy or quiet.
Alice is either calm or old.
Someone is strong or not quiet.
Someone is not happy or not calm. | Paul is not creative. | contradiction | (![X]:((curious(X)|calm(X))<=>(~happy(X)&~wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(~rich(X)|old(X))))&
(![X]:((~old(X)&patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((tall(X)|old(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~strong(X)|~calm(X))=>(calm(X)&quiet(X))))&
(((~curious(fred)&patient(fred)))=>((~brave(lucy)<~>generous(lucy))))&
(![X]:((rich(X)<~>wise(X))=>curious(X)))&
(((patient(fred)|~humble(fred)))<=>((~curious(susan)&~funny(susan))))&
(![X]:((generous(X)&wise(X))<=>(~quiet(X)|~generous(X))))&
((?[X]:((~calm(X)|calm(X))))<=>(~strong(mary)))&
(![X]:((kind(X)|~wise(X))=>(~wise(X)<~>kind(X))))&
((~generous(fred))<=>((~tall(fred)<~>patient(fred))))&
(![X]:(~creative(X)=>happy(X)))&
(((rich(fred)|~generous(fred)))=>((~curious(paul)|tall(paul))))&
((?[X]:((~rich(X)<~>quiet(X))))<=>((~generous(paul)<~>~quiet(paul))))&
(tall(fred))&
((happy(susan)<~>quiet(susan)))&
((calm(alice)<~>old(alice)))&
(?[X]:((strong(X)|~quiet(X))))&
(?[X]:((~happy(X)|~calm(X)))) | ~creative(paul) | [
"p0",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 120347431838463251412435
% SZS output start Proof for 120347431838463251412435
1. ! [X0] : ((calm(X0) | curious(X0)) <=> (~wise(X0) & ~happy(X0))) [input p0]
5. ! [X0] : ((~calm(X0) | ~strong(X0)) => (quiet(X0) & calm(X0))) [input p4]
13. ! [X0] : (~creative(X0) => happy(X0)) [input p12]
21. ~creative(paul) [input hypothesis]
28. ! [X0] : ((quiet(X0) & calm(X0)) | (calm(X0) & strong(X0))) [ennf transformation 5]
33. ! [X0] : (happy(X0) | creative(X0)) [ennf transformation 13]
36. ! [X0] : (((calm(X0) | curious(X0)) | (wise(X0) | happy(X0))) & ((~wise(X0) & ~happy(X0)) | (~calm(X0) & ~curious(X0)))) [nnf transformation 1]
37. ! [X0] : ((calm(X0) | curious(X0) | wise(X0) | happy(X0)) & ((~wise(X0) & ~happy(X0)) | (~calm(X0) & ~curious(X0)))) [flattening 36]
66. ~happy(X0) | ~calm(X0) [cnf transformation 37]
79. calm(X0) | calm(X0) [cnf transformation 28]
107. creative(X0) | happy(X0) [cnf transformation 33]
125. ~creative(paul) [cnf transformation 21]
130. calm(X0) [duplicate literal removal 79]
264. happy(paul) [resolution 107,125]
265. ~calm(paul) [resolution 264,66]
267. $false [subsumption resolution 265,130]
% SZS output end Proof for 120347431838463251412435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or old then alice is either patient or brave and vice versa.
Everyone who is creative is either not tall or old.
Everyone who is both kind and not funny is not kind or strong and vice versa.
Everyone who is wise or not strong is both creative and not quiet and vice versa.
If susan is both not wise and wise then someone is both not rich and not generous and vice versa.
Everyone who is strong is not old or rich.
Everyone who is kind or not generous is either not patient or not rich and vice versa.
Everyone who is not rich is not funny or tall.
Everyone who is kind is either happy or wise and vice versa.
Everyone who is quiet or not humble is either not creative or not happy and vice versa.
Everyone who is either not strong or not happy is humble.
Everyone who is patient or not kind is not humble or not rich and vice versa.
Everyone who is both not brave and tall is not tall or not calm and vice versa.
If fred is either calm or patient then alice is not strong.
Everyone who is both not brave and humble is quiet and vice versa.
If someone is patient then alice is both tall and not funny and vice versa.
Lucy is both not creative and not humble.
Paul is either patient or happy.
Paul is both creative and tall.
Someone is either not strong or not creative.
John is both old and tall.
Someone is tall.
Susan is either happy or not brave. | Paul is rich. | neutral | ((?[X]:((calm(X)|old(X))))<=>((patient(alice)<~>brave(alice))))&
(![X]:(creative(X)=>(~tall(X)<~>old(X))))&
(![X]:((kind(X)&~funny(X))<=>(~kind(X)|strong(X))))&
(![X]:((wise(X)|~strong(X))<=>(creative(X)&~quiet(X))))&
(((~wise(susan)&wise(susan)))<=>(?[X]:((~rich(X)&~generous(X)))))&
(![X]:(strong(X)=>(~old(X)|rich(X))))&
(![X]:((kind(X)|~generous(X))<=>(~patient(X)<~>~rich(X))))&
(![X]:(~rich(X)=>(~funny(X)|tall(X))))&
(![X]:(kind(X)<=>(happy(X)<~>wise(X))))&
(![X]:((quiet(X)|~humble(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:((~strong(X)<~>~happy(X))=>humble(X)))&
(![X]:((patient(X)|~kind(X))<=>(~humble(X)|~rich(X))))&
(![X]:((~brave(X)&tall(X))<=>(~tall(X)|~calm(X))))&
(((calm(fred)<~>patient(fred)))=>(~strong(alice)))&
(![X]:((~brave(X)&humble(X))<=>quiet(X)))&
((?[X]:(patient(X)))<=>((tall(alice)&~funny(alice))))&
((~creative(lucy)&~humble(lucy)))&
((patient(paul)<~>happy(paul)))&
((creative(paul)&tall(paul)))&
(?[X]:((~strong(X)<~>~creative(X))))&
((old(john)&tall(john)))&
(?[X]:(tall(X)))&
((happy(susan)<~>~brave(susan))) | rich(paul) | [] | null | 0 |
If susan is humble then someone is either not patient or not happy and vice versa.
If someone is both not patient and not kind then someone is either tall or not kind.
If someone is either not kind or not strong then mary is both not kind and not tall and vice versa.
Everyone who is both tall and not calm is both kind and not tall.
If paul is not strong then someone is not strong or curious.
If mary is brave then alice is both not generous and not happy and vice versa.
Everyone who is both creative and not quiet is strong.
Everyone who is not tall or quiet is humble.
Everyone who is both patient and rich is generous and vice versa.
Everyone who is humble is both happy and not generous.
If alice is not curious or brave then john is either not quiet or curious.
If lucy is either generous or not generous then susan is not old or not humble and vice versa.
If someone is generous or not strong then someone is not old.
Everyone who is quiet or patient is wise.
Everyone who is brave or tall is both rich and happy and vice versa.
If someone is strong then alice is not kind or not wise.
Paul is both not old and not humble.
Someone is either not happy or not rich.
Someone is curious.
Paul is not funny.
Susan is creative or tall.
Alice is either not wise or wise. | Lucy is happy. | entailment | ((humble(susan))<=>(?[X]:((~patient(X)<~>~happy(X)))))&
((?[X]:((~patient(X)&~kind(X))))=>(?[X]:((tall(X)<~>~kind(X)))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>((~kind(mary)&~tall(mary))))&
(![X]:((tall(X)&~calm(X))=>(kind(X)&~tall(X))))&
((~strong(paul))=>(?[X]:((~strong(X)|curious(X)))))&
((brave(mary))<=>((~generous(alice)&~happy(alice))))&
(![X]:((creative(X)&~quiet(X))=>strong(X)))&
(![X]:((~tall(X)|quiet(X))=>humble(X)))&
(![X]:((patient(X)&rich(X))<=>generous(X)))&
(![X]:(humble(X)=>(happy(X)&~generous(X))))&
(((~curious(alice)|brave(alice)))=>((~quiet(john)<~>curious(john))))&
(((generous(lucy)<~>~generous(lucy)))<=>((~old(susan)|~humble(susan))))&
((?[X]:((generous(X)|~strong(X))))=>(?[X]:(~old(X))))&
(![X]:((quiet(X)|patient(X))=>wise(X)))&
(![X]:((brave(X)|tall(X))<=>(rich(X)&happy(X))))&
((?[X]:(strong(X)))=>((~kind(alice)|~wise(alice))))&
((~old(paul)&~humble(paul)))&
(?[X]:((~happy(X)<~>~rich(X))))&
(?[X]:(curious(X)))&
(~funny(paul))&
((creative(susan)|tall(susan)))&
((~wise(alice)<~>wise(alice))) | happy(lucy) | [
"p7",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1743268819667013367160612
% SZS output start Proof for 1743268819667013367160612
8. ! [X0] : ((quiet(X0) | ~tall(X0)) => humble(X0)) [input p7]
10. ! [X0] : (humble(X0) => (~generous(X0) & happy(X0))) [input p9]
15. ! [X0] : ((tall(X0) | brave(X0)) <=> (happy(X0) & rich(X0))) [input p14]
23. ~happy(lucy) [input hypothesis]
32. ! [X0] : (humble(X0) | (~quiet(X0) & tall(X0))) [ennf transformation 8]
33. ! [X0] : ((~generous(X0) & happy(X0)) | ~humble(X0)) [ennf transformation 10]
64. ! [X0] : (((tall(X0) | brave(X0)) | (~happy(X0) | ~rich(X0))) & ((happy(X0) & rich(X0)) | (~tall(X0) & ~brave(X0)))) [nnf transformation 15]
65. ! [X0] : ((tall(X0) | brave(X0) | ~happy(X0) | ~rich(X0)) & ((happy(X0) & rich(X0)) | (~tall(X0) & ~brave(X0)))) [flattening 64]
89. tall(X0) | humble(X0) [cnf transformation 32]
94. ~humble(X0) | happy(X0) [cnf transformation 33]
113. ~tall(X0) | happy(X0) [cnf transformation 65]
124. ~happy(lucy) [cnf transformation 23]
303. happy(X0) | humble(X0) [resolution 113,89]
304. happy(X0) [subsumption resolution 303,94]
317. $false [resolution 304,124]
% SZS output end Proof for 1743268819667013367160612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and not old is either tall or not curious and vice versa.
Everyone who is humble or calm is strong.
Everyone who is either not strong or not curious is both not quiet and generous.
Everyone who is either not funny or patient is both not patient and not quiet.
If fred is not patient or not quiet then someone is either generous or not quiet and vice versa.
Everyone who is funny is not tall or not curious and vice versa.
If someone is either not funny or strong then paul is not curious.
Everyone who is not humble or kind is not tall.
Everyone who is strong is wise and vice versa.
Everyone who is both strong and not happy is not patient or happy.
If lucy is not old or patient then someone is not curious or not generous.
If someone is strong then fred is either strong or not rich.
If someone is not patient or rich then someone is not rich or not quiet.
Everyone who is either patient or not happy is generous and vice versa.
Everyone who is tall is either quiet or curious.
Everyone who is either not old or kind is funny or not rich.
Susan is not kind or not happy.
Someone is not happy.
Fred is strong.
Susan is either quiet or not curious.
Fred is either not humble or not brave.
Someone is strong or rich.
Susan is funny or happy.
Someone is both tall and not rich. | Fred is not tall. | entailment | (![X]:((happy(X)&~old(X))<=>(tall(X)<~>~curious(X))))&
(![X]:((humble(X)|calm(X))=>strong(X)))&
(![X]:((~strong(X)<~>~curious(X))=>(~quiet(X)&generous(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~patient(X)&~quiet(X))))&
(((~patient(fred)|~quiet(fred)))<=>(?[X]:((generous(X)<~>~quiet(X)))))&
(![X]:(funny(X)<=>(~tall(X)|~curious(X))))&
((?[X]:((~funny(X)<~>strong(X))))=>(~curious(paul)))&
(![X]:((~humble(X)|kind(X))=>~tall(X)))&
(![X]:(strong(X)<=>wise(X)))&
(![X]:((strong(X)&~happy(X))=>(~patient(X)|happy(X))))&
(((~old(lucy)|patient(lucy)))=>(?[X]:((~curious(X)|~generous(X)))))&
((?[X]:(strong(X)))=>((strong(fred)<~>~rich(fred))))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((patient(X)<~>~happy(X))<=>generous(X)))&
(![X]:(tall(X)=>(quiet(X)<~>curious(X))))&
(![X]:((~old(X)<~>kind(X))=>(funny(X)|~rich(X))))&
((~kind(susan)|~happy(susan)))&
(?[X]:(~happy(X)))&
(strong(fred))&
((quiet(susan)<~>~curious(susan)))&
((~humble(fred)<~>~brave(fred)))&
(?[X]:((strong(X)|rich(X))))&
((funny(susan)|happy(susan)))&
(?[X]:((tall(X)&~rich(X)))) | ~tall(fred) | [
"p0",
"p2",
"p5",
"p7",
"p11",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 868281729771394999849415
% SZS output start Proof for 868281729771394999849415
1. ! [X0] : ((~old(X0) & happy(X0)) <=> (tall(X0) <~> ~curious(X0))) [input p0]
3. ! [X0] : ((~strong(X0) <~> ~curious(X0)) => (generous(X0) & ~quiet(X0))) [input p2]
6. ! [X0] : (funny(X0) <=> (~curious(X0) | ~tall(X0))) [input p5]
8. ! [X0] : ((kind(X0) | ~humble(X0)) => ~tall(X0)) [input p7]
12. ? [X0] : strong(X0) => (strong(fred) <~> ~rich(fred)) [input p11]
15. ! [X0] : (tall(X0) => (quiet(X0) <~> curious(X0))) [input p14]
16. ! [X0] : ((~old(X0) <~> kind(X0)) => (~rich(X0) | funny(X0))) [input p15]
19. strong(fred) [input p18]
25. tall(fred) [input hypothesis]
29. ! [X0] : ((generous(X0) & ~quiet(X0)) | (~strong(X0) <=> ~curious(X0))) [ennf transformation 3]
32. ! [X0] : (~tall(X0) | (~kind(X0) & humble(X0))) [ennf transformation 8]
36. (strong(fred) <~> ~rich(fred)) | ! [X0] : ~strong(X0) [ennf transformation 12]
38. ! [X0] : ((quiet(X0) <~> curious(X0)) | ~tall(X0)) [ennf transformation 15]
39. ! [X0] : ((~rich(X0) | funny(X0)) | (~old(X0) <=> kind(X0))) [ennf transformation 16]
40. ! [X0] : (~rich(X0) | funny(X0) | (~old(X0) <=> kind(X0))) [flattening 39]
41. ! [X0] : (((~old(X0) & happy(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (old(X0) | ~happy(X0)))) [nnf transformation 1]
42. ! [X0] : (((~old(X0) & happy(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0)))) & (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | old(X0) | ~happy(X0))) [flattening 41]
43. ! [X0] : ((generous(X0) & ~quiet(X0)) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0)))) [nnf transformation 29]
50. ! [X0] : ((funny(X0) | (curious(X0) & tall(X0))) & ((~curious(X0) | ~tall(X0)) | ~funny(X0))) [nnf transformation 6]
51. ! [X0] : ((funny(X0) | (curious(X0) & tall(X0))) & (~curious(X0) | ~tall(X0) | ~funny(X0))) [flattening 50]
56. ((rich(fred) | ~strong(fred)) & (~rich(fred) | strong(fred))) | ! [X0] : ~strong(X0) [nnf transformation 36]
61. ! [X0] : (((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ~tall(X0)) [nnf transformation 38]
62. ! [X0] : (~rich(X0) | funny(X0) | ((~old(X0) | ~kind(X0)) & (kind(X0) | old(X0)))) [nnf transformation 40]
75. ~curious(X0) | ~old(X0) | ~tall(X0) [cnf transformation 42]
79. ~quiet(X0) | ~strong(X0) | curious(X0) [cnf transformation 43]
92. ~funny(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 51]
98. ~kind(X0) | ~tall(X0) [cnf transformation 32]
105. rich(fred) | ~strong(fred) | ~strong(X0) [cnf transformation 56]
112. ~tall(X0) | quiet(X0) | curious(X0) [cnf transformation 61]
114. ~rich(X0) | funny(X0) | kind(X0) | old(X0) [cnf transformation 62]
118. strong(fred) [cnf transformation 19]
127. tall(fred) [cnf transformation 25]
138. 3 <=> quiet(fred) [avatar definition]
139. quiet(fred) <- (3) [avatar component clause 138]
189. 14 <=> ! [X0] : ~strong(X0) [avatar definition]
190. ~strong(X0) <- (14) [avatar component clause 189]
192. 15 <=> strong(fred) [avatar definition]
193. strong(fred) <- (15) [avatar component clause 192]
196. 16 <=> rich(fred) [avatar definition]
198. rich(fred) <- (16) [avatar component clause 196]
199. 14 | ~15 | 16 [avatar split clause 105,196,192,189]
226. 15 [avatar split clause 118,192]
261. $false <- (14, 15) [resolution 193,190]
262. ~14 | ~15 [avatar contradiction clause 261]
355. quiet(fred) | curious(fred) [resolution 112,127]
384. 41 <=> curious(fred) [avatar definition]
385. ~curious(fred) <- (~41) [avatar component clause 384]
386. curious(fred) <- (41) [avatar component clause 384]
387. 41 | 3 [avatar split clause 355,138,384]
425. ~old(fred) | ~tall(fred) <- (41) [resolution 386,75]
427. ~old(fred) <- (41) [subsumption resolution 425,127]
436. funny(fred) | kind(fred) | old(fred) <- (16) [resolution 114,198]
438. funny(fred) | kind(fred) <- (16, 41) [subsumption resolution 436,427]
440. 47 <=> kind(fred) [avatar definition]
442. kind(fred) <- (47) [avatar component clause 440]
444. 48 <=> funny(fred) [avatar definition]
446. funny(fred) <- (48) [avatar component clause 444]
447. 47 | 48 | ~16 | ~41 [avatar split clause 438,384,196,444,440]
461. ~tall(fred) <- (47) [resolution 442,98]
462. $false <- (47) [subsumption resolution 461,127]
463. ~47 [avatar contradiction clause 462]
464. ~tall(fred) | ~curious(fred) <- (48) [resolution 446,92]
465. ~curious(fred) <- (48) [subsumption resolution 464,127]
468. ~41 | ~48 [avatar split clause 465,444,384]
477. ~strong(fred) | curious(fred) <- (3) [resolution 139,79]
479. curious(fred) <- (3, 15) [subsumption resolution 477,193]
480. $false <- (3, 15, ~41) [subsumption resolution 479,385]
481. ~3 | ~15 | 41 [avatar contradiction clause 480]
482. $false [avatar sat refutation 199,226,262,387,447,463,468,481]
% SZS output end Proof for 868281729771394999849415
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is patient and vice versa. Everyone who is quiet or patient is both creative and not funny. Everyone who is both calm and not curious is either wise or not kind and vice versa. Everyone who is generous is both quiet and funny. Everyone who is not old or not funny is not creative or happy. Everyone who is both not patient and not wise is both creative and brave and vice versa. If someone is not strong or not old then someone is generous. Everyone who is not patient is both not curious and not wise. If paul is either not rich or not wise then someone is either wise or not brave. Everyone who is not patient or generous is not kind. Everyone who is both not old and humble is both not kind and curious and vice versa. If someone is either not brave or happy then someone is calm or not generous. Everyone who is not patient is humble and vice versa. If someone is both not tall and not wise then fred is both brave and not rich and vice versa. If someone is not creative then someone is both quiet and not creative and vice versa. Everyone who is either not brave or happy is not generous. Alice is kind or tall. Someone is not curious or not generous. Mary is either humble or curious. John is both not kind and creative. Someone is either funny or not creative. | Alice is wise. | contradiction | (![X]:(~happy(X)<=>patient(X)))&
(![X]:((quiet(X)|patient(X))=>(creative(X)&~funny(X))))&
(![X]:((calm(X)&~curious(X))<=>(wise(X)<~>~kind(X))))&
(![X]:(generous(X)=>(quiet(X)&funny(X))))&
(![X]:((~old(X)|~funny(X))=>(~creative(X)|happy(X))))&
(![X]:((~patient(X)&~wise(X))<=>(creative(X)&brave(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:(generous(X))))&
(![X]:(~patient(X)=>(~curious(X)&~wise(X))))&
(((~rich(paul)<~>~wise(paul)))=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
(![X]:((~old(X)&humble(X))<=>(~kind(X)&curious(X))))&
((?[X]:((~brave(X)<~>happy(X))))=>(?[X]:((calm(X)|~generous(X)))))&
(![X]:(~patient(X)<=>humble(X)))&
((?[X]:((~tall(X)&~wise(X))))<=>((brave(fred)&~rich(fred))))&
((?[X]:(~creative(X)))<=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~brave(X)<~>happy(X))=>~generous(X)))&
((kind(alice)|tall(alice)))&
(?[X]:((~curious(X)|~generous(X))))&
((humble(mary)<~>curious(mary)))&
((~kind(john)&creative(john)))&
(?[X]:((funny(X)<~>~creative(X)))) | wise(alice) | [
"p0",
"p1",
"p4",
"p7",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4869624452311691913125742
% SZS output start Proof for 4869624452311691913125742
1. ! [X0] : (~happy(X0) <=> patient(X0)) [input p0]
2. ! [X0] : ((patient(X0) | quiet(X0)) => (~funny(X0) & creative(X0))) [input p1]
5. ! [X0] : ((~funny(X0) | ~old(X0)) => (happy(X0) | ~creative(X0))) [input p4]
8. ! [X0] : (~patient(X0) => (~wise(X0) & ~curious(X0))) [input p7]
15. ? [X0] : ~creative(X0) <=> ? [X0] : (~creative(X0) & quiet(X0)) [input p14]
22. wise(alice) [input hypothesis]
25. ? [X0] : ~creative(X0) <=> ? [X1] : (~creative(X1) & quiet(X1)) [rectify 15]
27. ! [X0] : ((~funny(X0) & creative(X0)) | (~patient(X0) & ~quiet(X0))) [ennf transformation 2]
29. ! [X0] : ((happy(X0) | ~creative(X0)) | (funny(X0) & old(X0))) [ennf transformation 5]
30. ! [X0] : (happy(X0) | ~creative(X0) | (funny(X0) & old(X0))) [flattening 29]
32. ! [X0] : ((~wise(X0) & ~curious(X0)) | patient(X0)) [ennf transformation 8]
37. ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))) [nnf transformation 1]
60. (? [X0] : ~creative(X0) | ! [X1] : (creative(X1) | ~quiet(X1))) & (? [X1] : (~creative(X1) & quiet(X1)) | ! [X0] : creative(X0)) [nnf transformation 25]
61. (? [X0] : ~creative(X0) | ! [X1] : (creative(X1) | ~quiet(X1))) & (? [X2] : (~creative(X2) & quiet(X2)) | ! [X3] : creative(X3)) [rectify 60]
62. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
63. ? [X2] : (~creative(X2) & quiet(X2)) => (~creative(sK5) & quiet(sK5)) [choice axiom]
64. (~creative(sK4) | ! [X1] : (creative(X1) | ~quiet(X1))) & ((~creative(sK5) & quiet(sK5)) | ! [X3] : creative(X3)) [skolemisation 61,63,62]
73. ~patient(X0) | ~happy(X0) [cnf transformation 37]
74. ~quiet(X0) | creative(X0) [cnf transformation 27]
77. ~funny(X0) | ~patient(X0) [cnf transformation 27]
87. ~creative(X0) | happy(X0) | funny(X0) [cnf transformation 30]
94. ~wise(X0) | patient(X0) [cnf transformation 32]
113. quiet(sK5) | creative(X3) [cnf transformation 64]
114. ~creative(sK5) | creative(X3) [cnf transformation 64]
126. wise(alice) [cnf transformation 22]
197. 16 <=> ! [X3] : creative(X3) [avatar definition]
198. creative(X3) <- (16) [avatar component clause 197]
200. 17 <=> creative(sK5) [avatar definition]
202. ~creative(sK5) <- (~17) [avatar component clause 200]
203. 16 | ~17 [avatar split clause 114,200,197]
205. 18 <=> quiet(sK5) [avatar definition]
207. quiet(sK5) <- (18) [avatar component clause 205]
208. 16 | 18 [avatar split clause 113,205,197]
250. creative(sK5) <- (18) [resolution 74,207]
251. $false <- (~17, 18) [subsumption resolution 250,202]
252. 17 | ~18 [avatar contradiction clause 251]
266. patient(alice) [resolution 94,126]
301. funny(X0) | happy(X0) <- (16) [resolution 87,198]
326. happy(X0) | ~patient(X0) <- (16) [resolution 301,77]
328. ~patient(X0) <- (16) [subsumption resolution 326,73]
330. $false <- (16) [resolution 328,266]
331. ~16 [avatar contradiction clause 330]
332. $false [avatar sat refutation 203,208,252,331]
% SZS output end Proof for 4869624452311691913125742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not brave or calm then alice is either not wise or funny.
Everyone who is strong is either not creative or not brave and vice versa.
Everyone who is not happy or not quiet is both not generous and humble.
If someone is not curious then someone is both happy and patient and vice versa.
If mary is wise then paul is not curious or strong.
If lucy is either not generous or wise then susan is either happy or patient.
If lucy is either patient or creative then mary is both calm and funny.
Everyone who is both not wise and not generous is both funny and not generous and vice versa.
If fred is not patient then lucy is not wise and vice versa.
Everyone who is both happy and funny is either rich or generous and vice versa.
If alice is either not kind or not creative then someone is not brave or wise.
Everyone who is either not creative or calm is either strong or tall and vice versa.
Everyone who is not patient is humble.
Everyone who is not quiet is not rich and vice versa.
Everyone who is wise or patient is humble and vice versa.
Everyone who is not happy is not curious or not calm.
Someone is not curious or not humble.
Lucy is both happy and kind.
Lucy is calm.
John is rich.
Paul is both kind and rich.
Someone is calm or not generous.
Fred is either calm or not calm. | Fred is humble. | entailment | (((~brave(mary)<~>calm(mary)))=>((~wise(alice)<~>funny(alice))))&
(![X]:(strong(X)<=>(~creative(X)<~>~brave(X))))&
(![X]:((~happy(X)|~quiet(X))=>(~generous(X)&humble(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((happy(X)&patient(X)))))&
((wise(mary))=>((~curious(paul)|strong(paul))))&
(((~generous(lucy)<~>wise(lucy)))=>((happy(susan)<~>patient(susan))))&
(((patient(lucy)<~>creative(lucy)))=>((calm(mary)&funny(mary))))&
(![X]:((~wise(X)&~generous(X))<=>(funny(X)&~generous(X))))&
((~patient(fred))<=>(~wise(lucy)))&
(![X]:((happy(X)&funny(X))<=>(rich(X)<~>generous(X))))&
(((~kind(alice)<~>~creative(alice)))=>(?[X]:((~brave(X)|wise(X)))))&
(![X]:((~creative(X)<~>calm(X))<=>(strong(X)<~>tall(X))))&
(![X]:(~patient(X)=>humble(X)))&
(![X]:(~quiet(X)<=>~rich(X)))&
(![X]:((wise(X)|patient(X))<=>humble(X)))&
(![X]:(~happy(X)=>(~curious(X)|~calm(X))))&
(?[X]:((~curious(X)|~humble(X))))&
((happy(lucy)&kind(lucy)))&
(calm(lucy))&
(rich(john))&
((kind(paul)&rich(paul)))&
(?[X]:((calm(X)|~generous(X))))&
((calm(fred)<~>~calm(fred))) | humble(fred) | [
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3799489941289406750374482
% SZS output start Proof for 3799489941289406750374482
13. ! [X0] : (~patient(X0) => humble(X0)) [input p12]
15. ! [X0] : ((patient(X0) | wise(X0)) <=> humble(X0)) [input p14]
24. ~humble(fred) [input hypothesis]
34. ! [X0] : (humble(X0) | patient(X0)) [ennf transformation 13]
56. ! [X0] : (((patient(X0) | wise(X0)) | ~humble(X0)) & (humble(X0) | (~patient(X0) & ~wise(X0)))) [nnf transformation 15]
57. ! [X0] : ((patient(X0) | wise(X0) | ~humble(X0)) & (humble(X0) | (~patient(X0) & ~wise(X0)))) [flattening 56]
109. humble(X0) | patient(X0) [cnf transformation 34]
112. humble(X0) | ~patient(X0) [cnf transformation 57]
125. ~humble(fred) [cnf transformation 24]
243. humble(X0) [subsumption resolution 112,109]
254. $false [subsumption resolution 125,243]
% SZS output end Proof for 3799489941289406750374482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not tall is not strong or old. Everyone who is either not generous or not brave is either not patient or calm. Everyone who is creative is either not generous or kind and vice versa. Everyone who is humble or not quiet is both not strong and not patient. Everyone who is both not old and quiet is not strong or happy and vice versa. If someone is both patient and not curious then paul is brave. If someone is not rich or wise then paul is strong or not tall. Everyone who is either not brave or not happy is creative or brave and vice versa. If someone is wise or happy then someone is not tall and vice versa. If someone is not creative or not strong then paul is either strong or kind and vice versa. If mary is both not humble and curious then someone is not brave or creative. If someone is calm then someone is humble. Everyone who is either not wise or not humble is not patient. Everyone who is either not funny or kind is either wise or curious. If someone is both not humble and not strong then someone is both not patient and not brave and vice versa. If someone is funny then mary is either patient or not curious and vice versa. Fred is tall or not quiet. Someone is either not tall or not humble. Someone is both not patient and generous. Someone is both wise and brave. Lucy is old or not happy. Fred is both rich and not patient. Fred is not brave. Someone is both not funny and old. | Mary is not quiet. | contradiction | (![X]:((~wise(X)|~tall(X))=>(~strong(X)|old(X))))&
(![X]:((~generous(X)<~>~brave(X))=>(~patient(X)<~>calm(X))))&
(![X]:(creative(X)<=>(~generous(X)<~>kind(X))))&
(![X]:((humble(X)|~quiet(X))=>(~strong(X)&~patient(X))))&
(![X]:((~old(X)&quiet(X))<=>(~strong(X)|happy(X))))&
((?[X]:((patient(X)&~curious(X))))=>(brave(paul)))&
((?[X]:((~rich(X)|wise(X))))=>((strong(paul)|~tall(paul))))&
(![X]:((~brave(X)<~>~happy(X))<=>(creative(X)|brave(X))))&
((?[X]:((wise(X)|happy(X))))<=>(?[X]:(~tall(X))))&
((?[X]:((~creative(X)|~strong(X))))<=>((strong(paul)<~>kind(paul))))&
(((~humble(mary)&curious(mary)))=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:(calm(X)))=>(?[X]:(humble(X))))&
(![X]:((~wise(X)<~>~humble(X))=>~patient(X)))&
(![X]:((~funny(X)<~>kind(X))=>(wise(X)<~>curious(X))))&
((?[X]:((~humble(X)&~strong(X))))<=>(?[X]:((~patient(X)&~brave(X)))))&
((?[X]:(funny(X)))<=>((patient(mary)<~>~curious(mary))))&
((tall(fred)|~quiet(fred)))&
(?[X]:((~tall(X)<~>~humble(X))))&
(?[X]:((~patient(X)&generous(X))))&
(?[X]:((wise(X)&brave(X))))&
((old(lucy)|~happy(lucy)))&
((rich(fred)&~patient(fred)))&
(~brave(fred))&
(?[X]:((~funny(X)&old(X)))) | ~quiet(mary) | [
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 223581361524713072373255
% SZS output start Proof for 223581361524713072373255
4. ! [X0] : ((~quiet(X0) | humble(X0)) => (~patient(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((quiet(X0) & ~old(X0)) <=> (happy(X0) | ~strong(X0))) [input p4]
25. ~quiet(mary) [input hypothesis]
34. ! [X0] : ((~patient(X0) & ~strong(X0)) | (quiet(X0) & ~humble(X0))) [ennf transformation 4]
45. ! [X0] : (((quiet(X0) & ~old(X0)) | (~happy(X0) & strong(X0))) & ((happy(X0) | ~strong(X0)) | (~quiet(X0) | old(X0)))) [nnf transformation 5]
46. ! [X0] : (((quiet(X0) & ~old(X0)) | (~happy(X0) & strong(X0))) & (happy(X0) | ~strong(X0) | ~quiet(X0) | old(X0))) [flattening 45]
94. ~strong(X0) | quiet(X0) [cnf transformation 34]
100. quiet(X0) | strong(X0) [cnf transformation 46]
147. ~quiet(mary) [cnf transformation 25]
150. quiet(X0) [subsumption resolution 100,94]
297. $false [subsumption resolution 147,150]
% SZS output end Proof for 223581361524713072373255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is not rich. Everyone who is both not strong and calm is kind or curious and vice versa. Everyone who is either not generous or not tall is both not patient and not calm. Everyone who is both tall and not humble is wise or quiet. Everyone who is both not tall and humble is quiet or not brave. If someone is either old or kind then someone is either not patient or rich. If susan is either not strong or not happy then someone is not brave or not patient and vice versa. If mary is both happy and funny then someone is both not kind and creative and vice versa. Everyone who is either calm or old is both not patient and patient and vice versa. Everyone who is not wise is patient. If alice is either patient or rich then someone is not curious and vice versa. Everyone who is both curious and not patient is tall. Everyone who is both not creative and curious is either not tall or not funny and vice versa. If someone is rich then someone is both not kind and patient. Everyone who is not old is both quiet and not wise. Everyone who is both generous and not quiet is not patient and vice versa. Someone is both funny and not creative. Someone is not funny or not patient. Lucy is both humble and tall. Fred is not patient. Someone is both not brave and not quiet. Someone is not strong. Paul is not humble. Alice is either not generous or not wise. | Paul is not generous. | neutral | (![X]:(~patient(X)=>~rich(X)))&
(![X]:((~strong(X)&calm(X))<=>(kind(X)|curious(X))))&
(![X]:((~generous(X)<~>~tall(X))=>(~patient(X)&~calm(X))))&
(![X]:((tall(X)&~humble(X))=>(wise(X)|quiet(X))))&
(![X]:((~tall(X)&humble(X))=>(quiet(X)|~brave(X))))&
((?[X]:((old(X)<~>kind(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
(((~strong(susan)<~>~happy(susan)))<=>(?[X]:((~brave(X)|~patient(X)))))&
(((happy(mary)&funny(mary)))<=>(?[X]:((~kind(X)&creative(X)))))&
(![X]:((calm(X)<~>old(X))<=>(~patient(X)&patient(X))))&
(![X]:(~wise(X)=>patient(X)))&
(((patient(alice)<~>rich(alice)))<=>(?[X]:(~curious(X))))&
(![X]:((curious(X)&~patient(X))=>tall(X)))&
(![X]:((~creative(X)&curious(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:(rich(X)))=>(?[X]:((~kind(X)&patient(X)))))&
(![X]:(~old(X)=>(quiet(X)&~wise(X))))&
(![X]:((generous(X)&~quiet(X))<=>~patient(X)))&
(?[X]:((funny(X)&~creative(X))))&
(?[X]:((~funny(X)|~patient(X))))&
((humble(lucy)&tall(lucy)))&
(~patient(fred))&
(?[X]:((~brave(X)&~quiet(X))))&
(?[X]:(~strong(X)))&
(~humble(paul))&
((~generous(alice)<~>~wise(alice))) | ~generous(paul) | [] | null | 0 |
Everyone who is both not happy and not generous is not kind or not quiet and vice versa.
Everyone who is either tall or not rich is either quiet or not brave and vice versa.
Everyone who is not curious or curious is either not generous or rich and vice versa.
Everyone who is either not tall or not quiet is both quiet and not quiet.
Everyone who is either not calm or not old is not happy and vice versa.
Everyone who is both not kind and not funny is strong or generous and vice versa.
If someone is not strong or not old then someone is both not brave and not humble.
If someone is either not wise or tall then someone is generous or not tall and vice versa.
If mary is both funny and curious then someone is quiet.
If someone is brave or not calm then paul is both brave and creative.
Everyone who is generous or strong is both not humble and curious and vice versa.
If someone is not quiet or not happy then paul is both calm and wise.
Everyone who is either not old or wise is not humble and vice versa.
If someone is creative then someone is patient.
If someone is either not humble or not generous then lucy is either patient or wise and vice versa.
Someone is not old or not patient.
Someone is either not rich or not tall.
Alice is either curious or old.
Lucy is not creative.
Fred is old or not creative. | Alice is not calm. | contradiction | (![X]:((~happy(X)&~generous(X))<=>(~kind(X)|~quiet(X))))&
(![X]:((tall(X)<~>~rich(X))<=>(quiet(X)<~>~brave(X))))&
(![X]:((~curious(X)|curious(X))<=>(~generous(X)<~>rich(X))))&
(![X]:((~tall(X)<~>~quiet(X))=>(quiet(X)&~quiet(X))))&
(![X]:((~calm(X)<~>~old(X))<=>~happy(X)))&
(![X]:((~kind(X)&~funny(X))<=>(strong(X)|generous(X))))&
((?[X]:((~strong(X)|~old(X))))=>(?[X]:((~brave(X)&~humble(X)))))&
((?[X]:((~wise(X)<~>tall(X))))<=>(?[X]:((generous(X)|~tall(X)))))&
(((funny(mary)&curious(mary)))=>(?[X]:(quiet(X))))&
((?[X]:((brave(X)|~calm(X))))=>((brave(paul)&creative(paul))))&
(![X]:((generous(X)|strong(X))<=>(~humble(X)&curious(X))))&
((?[X]:((~quiet(X)|~happy(X))))=>((calm(paul)&wise(paul))))&
(![X]:((~old(X)<~>wise(X))<=>~humble(X)))&
((?[X]:(creative(X)))=>(?[X]:(patient(X))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>((patient(lucy)<~>wise(lucy))))&
(?[X]:((~old(X)|~patient(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
((curious(alice)<~>old(alice)))&
(~creative(lucy))&
((old(fred)|~creative(fred))) | ~calm(alice) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4457534949822688068239205
% SZS output start Proof for 4457534949822688068239205
1. ! [X0] : ((~generous(X0) & ~happy(X0)) <=> (~quiet(X0) | ~kind(X0))) [input p0]
2. ! [X0] : ((tall(X0) <~> ~rich(X0)) <=> (quiet(X0) <~> ~brave(X0))) [input p1]
3. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (~generous(X0) <~> rich(X0))) [input p2]
4. ! [X0] : ((~tall(X0) <~> ~quiet(X0)) => (~quiet(X0) & quiet(X0))) [input p3]
6. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (generous(X0) | strong(X0))) [input p5]
10. ? [X0] : (~calm(X0) | brave(X0)) => (creative(paul) & brave(paul)) [input p9]
21. ~calm(alice) [input hypothesis]
25. ! [X0] : ((~quiet(X0) & quiet(X0)) | (~tall(X0) <=> ~quiet(X0))) [ennf transformation 4]
29. (creative(paul) & brave(paul)) | ! [X0] : (calm(X0) & ~brave(X0)) [ennf transformation 10]
32. ! [X0] : (((~generous(X0) & ~happy(X0)) | (quiet(X0) & kind(X0))) & ((~quiet(X0) | ~kind(X0)) | (generous(X0) | happy(X0)))) [nnf transformation 1]
33. ! [X0] : (((~generous(X0) & ~happy(X0)) | (quiet(X0) & kind(X0))) & (~quiet(X0) | ~kind(X0) | generous(X0) | happy(X0))) [flattening 32]
34. ! [X0] : ((((rich(X0) | ~tall(X0)) & (~rich(X0) | tall(X0))) | ((quiet(X0) | brave(X0)) & (~brave(X0) | ~quiet(X0)))) & (((brave(X0) | ~quiet(X0)) & (~brave(X0) | quiet(X0))) | ((tall(X0) | rich(X0)) & (~rich(X0) | ~tall(X0))))) [nnf transformation 2]
35. ! [X0] : (((curious(X0) | ~curious(X0)) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~curious(X0) & curious(X0)))) [nnf transformation 3]
36. ! [X0] : ((curious(X0) | ~curious(X0) | ((~generous(X0) | ~rich(X0)) & (rich(X0) | generous(X0)))) & (((~rich(X0) | generous(X0)) & (rich(X0) | ~generous(X0))) | (~curious(X0) & curious(X0)))) [flattening 35]
37. ! [X0] : ((~quiet(X0) & quiet(X0)) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) [nnf transformation 25]
39. ! [X0] : (((~funny(X0) & ~kind(X0)) | (~generous(X0) & ~strong(X0))) & ((generous(X0) | strong(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 6]
40. ! [X0] : (((~funny(X0) & ~kind(X0)) | (~generous(X0) & ~strong(X0))) & (generous(X0) | strong(X0) | funny(X0) | kind(X0))) [flattening 39]
70. ~generous(X0) | kind(X0) [cnf transformation 33]
73. ~brave(X0) | quiet(X0) | tall(X0) | rich(X0) [cnf transformation 34]
78. ~brave(X0) | ~tall(X0) | rich(X0) | ~quiet(X0) [cnf transformation 34]
82. ~rich(X0) | generous(X0) | curious(X0) [cnf transformation 36]
83. ~curious(X0) | generous(X0) | ~rich(X0) [cnf transformation 36]
87. quiet(X0) | ~tall(X0) | quiet(X0) [cnf transformation 37]
88. ~quiet(X0) | ~quiet(X0) | tall(X0) [cnf transformation 37]
96. ~kind(X0) | ~generous(X0) [cnf transformation 40]
111. brave(paul) | calm(X0) [cnf transformation 29]
143. ~calm(alice) [cnf transformation 21]
144. ~tall(X0) | quiet(X0) [duplicate literal removal 87]
145. ~quiet(X0) | tall(X0) [duplicate literal removal 88]
146. ~rich(X0) | generous(X0) [subsumption resolution 82,83]
148. ~generous(X0) [subsumption resolution 96,70]
209. 14 <=> ! [X0] : calm(X0) [avatar definition]
210. calm(X0) <- (14) [avatar component clause 209]
221. 17 <=> brave(paul) [avatar definition]
223. brave(paul) <- (17) [avatar component clause 221]
224. 14 | 17 [avatar split clause 111,221,209]
314. $false <- (14) [resolution 210,143]
315. ~14 [avatar contradiction clause 314]
466. quiet(paul) | tall(paul) | rich(paul) <- (17) [resolution 73,223]
467. tall(paul) | rich(paul) <- (17) [subsumption resolution 466,145]
469. 53 <=> rich(paul) [avatar definition]
470. ~rich(paul) <- (~53) [avatar component clause 469]
471. rich(paul) <- (53) [avatar component clause 469]
473. 54 <=> tall(paul) [avatar definition]
475. tall(paul) <- (54) [avatar component clause 473]
476. 53 | 54 | ~17 [avatar split clause 467,221,473,469]
484. generous(paul) <- (53) [resolution 471,146]
485. $false <- (53) [subsumption resolution 484,148]
486. ~53 [avatar contradiction clause 485]
488. quiet(paul) <- (54) [resolution 475,144]
489. ~tall(paul) | rich(paul) | ~quiet(paul) <- (17) [resolution 78,223]
490. rich(paul) | ~quiet(paul) <- (17, 54) [subsumption resolution 489,475]
491. ~quiet(paul) <- (17, ~53, 54) [subsumption resolution 490,470]
492. $false <- (17, ~53, 54) [subsumption resolution 491,488]
493. ~17 | 53 | ~54 [avatar contradiction clause 492]
494. $false [avatar sat refutation 224,315,476,486,493]
% SZS output end Proof for 4457534949822688068239205
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not funny and tall then mary is both not kind and happy and vice versa. If someone is not funny or happy then john is not rich or curious and vice versa. If mary is not kind or wise then someone is either wise or strong. Everyone who is not curious is rich and vice versa. If someone is brave then someone is not old. Everyone who is both not patient and rich is kind. Everyone who is either strong or not funny is either brave or not rich. Everyone who is calm is both not old and rich and vice versa. If someone is tall then someone is both brave and not old and vice versa. Everyone who is either not quiet or strong is old and vice versa. Everyone who is patient or not strong is not calm and vice versa. If someone is not curious or brave then lucy is not creative or curious and vice versa. If john is not rich or old then someone is not humble or brave. Everyone who is not happy or not humble is not happy. If someone is either not brave or not strong then lucy is either funny or humble and vice versa. If someone is generous or old then someone is either not generous or calm and vice versa. Fred is not rich. Someone is not curious. Someone is either wise or not funny. Paul is both not tall and not quiet. Lucy is both strong and not curious. Someone is not old or not brave. John is both curious and kind. | Fred is calm. | contradiction | (((~funny(lucy)&tall(lucy)))<=>((~kind(mary)&happy(mary))))&
((?[X]:((~funny(X)|happy(X))))<=>((~rich(john)|curious(john))))&
(((~kind(mary)|wise(mary)))=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:(~curious(X)<=>rich(X)))&
((?[X]:(brave(X)))=>(?[X]:(~old(X))))&
(![X]:((~patient(X)&rich(X))=>kind(X)))&
(![X]:((strong(X)<~>~funny(X))=>(brave(X)<~>~rich(X))))&
(![X]:(calm(X)<=>(~old(X)&rich(X))))&
((?[X]:(tall(X)))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~quiet(X)<~>strong(X))<=>old(X)))&
(![X]:((patient(X)|~strong(X))<=>~calm(X)))&
((?[X]:((~curious(X)|brave(X))))<=>((~creative(lucy)|curious(lucy))))&
(((~rich(john)|old(john)))=>(?[X]:((~humble(X)|brave(X)))))&
(![X]:((~happy(X)|~humble(X))=>~happy(X)))&
((?[X]:((~brave(X)<~>~strong(X))))<=>((funny(lucy)<~>humble(lucy))))&
((?[X]:((generous(X)|old(X))))<=>(?[X]:((~generous(X)<~>calm(X)))))&
(~rich(fred))&
(?[X]:(~curious(X)))&
(?[X]:((wise(X)<~>~funny(X))))&
((~tall(paul)&~quiet(paul)))&
((strong(lucy)&~curious(lucy)))&
(?[X]:((~old(X)|~brave(X))))&
((curious(john)&kind(john))) | calm(fred) | [
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7991470214816731192561700
% SZS output start Proof for 7991470214816731192561700
8. ! [X0] : (calm(X0) <=> (rich(X0) & ~old(X0))) [input p7]
17. ~rich(fred) [input p16]
24. calm(fred) [input hypothesis]
50. ! [X0] : ((calm(X0) | (~rich(X0) | old(X0))) & ((rich(X0) & ~old(X0)) | ~calm(X0))) [nnf transformation 8]
51. ! [X0] : ((calm(X0) | ~rich(X0) | old(X0)) & ((rich(X0) & ~old(X0)) | ~calm(X0))) [flattening 50]
104. ~calm(X0) | rich(X0) [cnf transformation 51]
138. ~rich(fred) [cnf transformation 17]
149. calm(fred) [cnf transformation 24]
366. rich(fred) [resolution 104,149]
367. $false [subsumption resolution 366,138]
% SZS output end Proof for 7991470214816731192561700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is kind or not humble is both not quiet and calm and vice versa.
If someone is both brave and calm then mary is patient or not generous and vice versa.
Everyone who is not old or not humble is not tall or happy and vice versa.
Everyone who is both curious and quiet is not brave.
Everyone who is not old is both not tall and not happy.
If someone is brave or not creative then susan is both brave and not kind and vice versa.
Everyone who is not calm or not humble is not tall and vice versa.
Everyone who is not funny or kind is either not patient or humble and vice versa.
If someone is either not patient or not creative then someone is humble and vice versa.
Everyone who is either not curious or curious is rich and vice versa.
Everyone who is either happy or not creative is both not brave and funny and vice versa.
If alice is not wise or calm then john is both not kind and old.
Everyone who is not patient is both not creative and not old.
Everyone who is both brave and not humble is not tall.
Everyone who is happy or curious is either not calm or old.
If fred is calm or not calm then alice is not tall.
Mary is either tall or generous.
Someone is either not rich or creative.
Someone is either tall or funny.
Someone is both not strong and not patient.
Mary is both brave and not calm.
Someone is either not generous or humble.
Fred is either creative or old.
Someone is not tall. | Fred is brave. | neutral | (![X]:((kind(X)|~humble(X))<=>(~quiet(X)&calm(X))))&
((?[X]:((brave(X)&calm(X))))<=>((patient(mary)|~generous(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~tall(X)|happy(X))))&
(![X]:((curious(X)&quiet(X))=>~brave(X)))&
(![X]:(~old(X)=>(~tall(X)&~happy(X))))&
((?[X]:((brave(X)|~creative(X))))<=>((brave(susan)&~kind(susan))))&
(![X]:((~calm(X)|~humble(X))<=>~tall(X)))&
(![X]:((~funny(X)|kind(X))<=>(~patient(X)<~>humble(X))))&
((?[X]:((~patient(X)<~>~creative(X))))<=>(?[X]:(humble(X))))&
(![X]:((~curious(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
(((calm(fred)|~calm(fred)))=>(~tall(alice)))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~strong(X)&~patient(X))))&
((brave(mary)&~calm(mary)))&
(?[X]:((~generous(X)<~>humble(X))))&
((creative(fred)<~>old(fred)))&
(?[X]:(~tall(X))) | brave(fred) | [] | null | 0 |
Everyone who is not funny is happy or generous. If susan is not wise then someone is funny and vice versa. Everyone who is either not old or not patient is both quiet and calm and vice versa. If someone is both not quiet and not wise then lucy is curious or patient and vice versa. Everyone who is wise or not funny is both brave and not creative. If someone is either tall or not humble then susan is rich. Everyone who is not rich is both generous and kind and vice versa. Everyone who is calm or quiet is both not funny and creative and vice versa. If someone is either quiet or not curious then someone is quiet or not patient. If someone is kind or not old then alice is happy. Everyone who is not calm or not old is either brave or rich and vice versa. If someone is not tall then someone is both kind and not curious and vice versa. If lucy is both wise and calm then fred is strong or humble. If someone is both not funny and funny then someone is both not brave and happy. If someone is calm or tall then someone is either quiet or not rich. Everyone who is either calm or patient is calm. Mary is either calm or not quiet. Mary is either happy or not humble. Mary is not funny or not curious. Someone is patient or not strong. Someone is not humble. John is not rich. Someone is strong. Someone is either wise or not old. | Alice is not old. | entailment | (![X]:(~funny(X)=>(happy(X)|generous(X))))&
((~wise(susan))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(quiet(X)&calm(X))))&
((?[X]:((~quiet(X)&~wise(X))))<=>((curious(lucy)|patient(lucy))))&
(![X]:((wise(X)|~funny(X))=>(brave(X)&~creative(X))))&
((?[X]:((tall(X)<~>~humble(X))))=>(rich(susan)))&
(![X]:(~rich(X)<=>(generous(X)&kind(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&creative(X))))&
((?[X]:((quiet(X)<~>~curious(X))))=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((kind(X)|~old(X))))=>(happy(alice)))&
(![X]:((~calm(X)|~old(X))<=>(brave(X)<~>rich(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((kind(X)&~curious(X)))))&
(((wise(lucy)&calm(lucy)))=>((strong(fred)|humble(fred))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~brave(X)&happy(X)))))&
((?[X]:((calm(X)|tall(X))))=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:((calm(X)<~>patient(X))=>calm(X)))&
((calm(mary)<~>~quiet(mary)))&
((happy(mary)<~>~humble(mary)))&
((~funny(mary)|~curious(mary)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:(~humble(X)))&
(~rich(john))&
(?[X]:(strong(X)))&
(?[X]:((wise(X)<~>~old(X)))) | ~old(alice) | [
"p2",
"p4",
"p7",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6364611851194637805390174
% SZS output start Proof for 6364611851194637805390174
3. ! [X0] : ((~old(X0) <~> ~patient(X0)) <=> (calm(X0) & quiet(X0))) [input p2]
5. ! [X0] : ((~funny(X0) | wise(X0)) => (~creative(X0) & brave(X0))) [input p4]
8. ! [X0] : ((quiet(X0) | calm(X0)) <=> (creative(X0) & ~funny(X0))) [input p7]
16. ! [X0] : ((calm(X0) <~> patient(X0)) => calm(X0)) [input p15]
25. old(alice) [input hypothesis]
32. ! [X0] : ((~creative(X0) & brave(X0)) | (funny(X0) & ~wise(X0))) [ennf transformation 5]
40. ! [X0] : (calm(X0) | (calm(X0) <=> patient(X0))) [ennf transformation 16]
45. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | (~calm(X0) | ~quiet(X0))) & ((calm(X0) & quiet(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [nnf transformation 3]
46. ! [X0] : ((((patient(X0) | old(X0)) & (~patient(X0) | ~old(X0))) | ~calm(X0) | ~quiet(X0)) & ((calm(X0) & quiet(X0)) | ((~old(X0) | patient(X0)) & (~patient(X0) | old(X0))))) [flattening 45]
55. ! [X0] : (((quiet(X0) | calm(X0)) | (~creative(X0) | funny(X0))) & ((creative(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 8]
56. ! [X0] : ((quiet(X0) | calm(X0) | ~creative(X0) | funny(X0)) & ((creative(X0) & ~funny(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 55]
75. ! [X0] : (calm(X0) | ((calm(X0) | ~patient(X0)) & (patient(X0) | ~calm(X0)))) [nnf transformation 40]
91. ~old(X0) | quiet(X0) | patient(X0) [cnf transformation 46]
104. ~creative(X0) | funny(X0) [cnf transformation 32]
110. ~calm(X0) | ~funny(X0) [cnf transformation 56]
111. ~quiet(X0) | ~funny(X0) [cnf transformation 56]
112. ~calm(X0) | creative(X0) [cnf transformation 56]
113. ~quiet(X0) | creative(X0) [cnf transformation 56]
136. calm(X0) | calm(X0) | ~patient(X0) [cnf transformation 75]
148. old(alice) [cnf transformation 25]
149. ~patient(X0) | calm(X0) [duplicate literal removal 136]
348. quiet(alice) | patient(alice) [resolution 91,148]
350. 42 <=> patient(alice) [avatar definition]
352. patient(alice) <- (42) [avatar component clause 350]
354. 43 <=> quiet(alice) [avatar definition]
356. quiet(alice) <- (43) [avatar component clause 354]
357. 42 | 43 [avatar split clause 348,354,350]
359. calm(alice) <- (42) [resolution 352,149]
361. creative(alice) <- (42) [resolution 359,112]
362. ~funny(alice) <- (42) [resolution 359,110]
364. funny(alice) <- (42) [resolution 361,104]
366. $false <- (42) [subsumption resolution 364,362]
367. ~42 [avatar contradiction clause 366]
392. creative(alice) <- (43) [resolution 356,113]
393. ~funny(alice) <- (43) [resolution 356,111]
518. funny(alice) <- (43) [resolution 392,104]
520. $false <- (43) [subsumption resolution 518,393]
521. ~43 [avatar contradiction clause 520]
522. $false [avatar sat refutation 357,367,521]
% SZS output end Proof for 6364611851194637805390174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is both creative and not generous and vice versa.
Everyone who is either brave or old is either funny or not quiet.
If fred is calm then john is either curious or not curious and vice versa.
Everyone who is curious or not humble is both not curious and not quiet.
If someone is either not old or not strong then someone is curious and vice versa.
Everyone who is rich or not wise is both happy and not rich.
If susan is funny or not old then someone is both patient and not rich and vice versa.
If someone is kind or brave then alice is not tall and vice versa.
Everyone who is both brave and not wise is either strong or quiet.
If someone is curious or tall then someone is not wise or curious and vice versa.
Everyone who is either not kind or quiet is not generous.
If susan is either not patient or not wise then someone is both not old and humble and vice versa.
Everyone who is humble is not rich.
Everyone who is either not creative or not strong is either creative or not funny.
If john is not old then someone is kind and vice versa.
Everyone who is not wise is either funny or not wise.
Susan is not kind.
Someone is both quiet and humble.
Someone is not strong or not quiet.
Lucy is either not creative or patient.
Someone is either humble or generous.
Someone is not rich.
Susan is creative or brave. | Susan is wise. | entailment | (![X]:(~patient(X)<=>(creative(X)&~generous(X))))&
(![X]:((brave(X)<~>old(X))=>(funny(X)<~>~quiet(X))))&
((calm(fred))<=>((curious(john)<~>~curious(john))))&
(![X]:((curious(X)|~humble(X))=>(~curious(X)&~quiet(X))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:(curious(X))))&
(![X]:((rich(X)|~wise(X))=>(happy(X)&~rich(X))))&
(((funny(susan)|~old(susan)))<=>(?[X]:((patient(X)&~rich(X)))))&
((?[X]:((kind(X)|brave(X))))<=>(~tall(alice)))&
(![X]:((brave(X)&~wise(X))=>(strong(X)<~>quiet(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~wise(X)|curious(X)))))&
(![X]:((~kind(X)<~>quiet(X))=>~generous(X)))&
(((~patient(susan)<~>~wise(susan)))<=>(?[X]:((~old(X)&humble(X)))))&
(![X]:(humble(X)=>~rich(X)))&
(![X]:((~creative(X)<~>~strong(X))=>(creative(X)<~>~funny(X))))&
((~old(john))<=>(?[X]:(kind(X))))&
(![X]:(~wise(X)=>(funny(X)<~>~wise(X))))&
(~kind(susan))&
(?[X]:((quiet(X)&humble(X))))&
(?[X]:((~strong(X)|~quiet(X))))&
((~creative(lucy)<~>patient(lucy)))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(~rich(X)))&
((creative(susan)|brave(susan))) | wise(susan) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p6",
"p8",
"p13",
"p15",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5025188055351189552642944
% SZS output start Proof for 5025188055351189552642944
1. ! [X0] : (~patient(X0) <=> (~generous(X0) & creative(X0))) [input p0]
2. ! [X0] : ((brave(X0) <~> old(X0)) => (funny(X0) <~> ~quiet(X0))) [input p1]
4. ! [X0] : ((~humble(X0) | curious(X0)) => (~quiet(X0) & ~curious(X0))) [input p3]
5. ? [X0] : (~old(X0) <~> ~strong(X0)) <=> ? [X0] : curious(X0) [input p4]
6. ! [X0] : ((~wise(X0) | rich(X0)) => (~rich(X0) & happy(X0))) [input p5]
7. (~old(susan) | funny(susan)) <=> ? [X0] : (~rich(X0) & patient(X0)) [input p6]
9. ! [X0] : ((~wise(X0) & brave(X0)) => (strong(X0) <~> quiet(X0))) [input p8]
14. ! [X0] : ((~creative(X0) <~> ~strong(X0)) => (creative(X0) <~> ~funny(X0))) [input p13]
16. ! [X0] : (~wise(X0) => (funny(X0) <~> ~wise(X0))) [input p15]
20. ~creative(lucy) <~> patient(lucy) [input p19]
23. brave(susan) | creative(susan) [input p22]
24. ~wise(susan) [input hypothesis]
25. ? [X0] : (~old(X0) <~> ~strong(X0)) <=> ? [X1] : curious(X1) [rectify 5]
27. ! [X0] : ((~wise(X0) | rich(X0)) => ~rich(X0)) [pure predicate removal 6]
28. ! [X0] : ((funny(X0) <~> ~quiet(X0)) | (brave(X0) <=> old(X0))) [ennf transformation 2]
29. ! [X0] : ((~quiet(X0) & ~curious(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 4]
30. ! [X0] : (~rich(X0) | (wise(X0) & ~rich(X0))) [ennf transformation 27]
31. ! [X0] : ((strong(X0) <~> quiet(X0)) | (wise(X0) | ~brave(X0))) [ennf transformation 9]
32. ! [X0] : ((strong(X0) <~> quiet(X0)) | wise(X0) | ~brave(X0)) [flattening 31]
35. ! [X0] : ((creative(X0) <~> ~funny(X0)) | (~creative(X0) <=> ~strong(X0))) [ennf transformation 14]
36. ! [X0] : ((funny(X0) <~> ~wise(X0)) | wise(X0)) [ennf transformation 16]
37. ! [X0] : ((~patient(X0) | (generous(X0) | ~creative(X0))) & ((~generous(X0) & creative(X0)) | patient(X0))) [nnf transformation 1]
38. ! [X0] : ((~patient(X0) | generous(X0) | ~creative(X0)) & ((~generous(X0) & creative(X0)) | patient(X0))) [flattening 37]
39. ! [X0] : (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0)))) [nnf transformation 28]
41. (? [X0] : ((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : ((~old(X0) | strong(X0)) & (~strong(X0) | old(X0)))) [nnf transformation 25]
42. (? [X0] : ((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : ((~old(X3) | strong(X3)) & (~strong(X3) | old(X3)))) [rectify 41]
43. ? [X0] : ((strong(X0) | old(X0)) & (~strong(X0) | ~old(X0))) => ((strong(sK0) | old(sK0)) & (~strong(sK0) | ~old(sK0))) [choice axiom]
44. ? [X2] : curious(X2) => curious(sK1) [choice axiom]
45. (((strong(sK0) | old(sK0)) & (~strong(sK0) | ~old(sK0))) | ! [X1] : ~curious(X1)) & (curious(sK1) | ! [X3] : ((~old(X3) | strong(X3)) & (~strong(X3) | old(X3)))) [skolemisation 42,44,43]
46. ((~old(susan) | funny(susan)) | ! [X0] : (rich(X0) | ~patient(X0))) & (? [X0] : (~rich(X0) & patient(X0)) | (old(susan) & ~funny(susan))) [nnf transformation 7]
47. (~old(susan) | funny(susan) | ! [X0] : (rich(X0) | ~patient(X0))) & (? [X0] : (~rich(X0) & patient(X0)) | (old(susan) & ~funny(susan))) [flattening 46]
48. (~old(susan) | funny(susan) | ! [X0] : (rich(X0) | ~patient(X0))) & (? [X1] : (~rich(X1) & patient(X1)) | (old(susan) & ~funny(susan))) [rectify 47]
49. ? [X1] : (~rich(X1) & patient(X1)) => (~rich(sK2) & patient(sK2)) [choice axiom]
50. (~old(susan) | funny(susan) | ! [X0] : (rich(X0) | ~patient(X0))) & ((~rich(sK2) & patient(sK2)) | (old(susan) & ~funny(susan))) [skolemisation 48,49]
55. ! [X0] : (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | wise(X0) | ~brave(X0)) [nnf transformation 32]
66. ! [X0] : (((funny(X0) | ~creative(X0)) & (~funny(X0) | creative(X0))) | ((~creative(X0) | strong(X0)) & (~strong(X0) | creative(X0)))) [nnf transformation 35]
71. ! [X0] : (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | wise(X0)) [nnf transformation 36]
76. (~patient(lucy) | creative(lucy)) & (patient(lucy) | ~creative(lucy)) [nnf transformation 20]
82. creative(X0) | patient(X0) [cnf transformation 38]
85. ~quiet(X0) | funny(X0) | old(X0) | ~brave(X0) [cnf transformation 39]
93. ~curious(X0) | ~curious(X0) [cnf transformation 29]
97. curious(sK1) | ~strong(X3) | old(X3) [cnf transformation 45]
101. ~rich(X0) | ~rich(X0) [cnf transformation 30]
107. ~old(susan) | funny(susan) | rich(X0) | ~patient(X0) [cnf transformation 50]
111. ~brave(X0) | strong(X0) | wise(X0) | quiet(X0) [cnf transformation 55]
129. funny(X0) | ~creative(X0) | ~creative(X0) | strong(X0) [cnf transformation 66]
133. wise(X0) | ~funny(X0) | wise(X0) [cnf transformation 71]
138. patient(lucy) | ~creative(lucy) [cnf transformation 76]
139. ~patient(lucy) | creative(lucy) [cnf transformation 76]
143. brave(susan) | creative(susan) [cnf transformation 23]
144. ~wise(susan) [cnf transformation 24]
145. ~funny(X0) | wise(X0) [duplicate literal removal 133]
147. ~creative(X0) | funny(X0) | strong(X0) [duplicate literal removal 129]
148. ~rich(X0) [duplicate literal removal 101]
149. ~curious(X0) [duplicate literal removal 93]
163. ~strong(X3) | old(X3) [subsumption resolution 97,149]
164. ~old(susan) | funny(susan) | ~patient(X0) [subsumption resolution 107,148]
166. 3 <=> ! [X0] : ~patient(X0) [avatar definition]
167. ~patient(X0) <- (3) [avatar component clause 166]
169. 4 <=> funny(susan) [avatar definition]
170. ~funny(susan) <- (~4) [avatar component clause 169]
171. funny(susan) <- (4) [avatar component clause 169]
173. 5 <=> old(susan) [avatar definition]
175. ~old(susan) <- (~5) [avatar component clause 173]
176. 3 | 4 | ~5 [avatar split clause 164,173,169,166]
230. 18 <=> wise(susan) [avatar definition]
231. ~wise(susan) <- (~18) [avatar component clause 230]
266. creative(lucy) [subsumption resolution 139,82]
267. patient(lucy) [subsumption resolution 138,266]
279. 27 <=> creative(susan) [avatar definition]
281. creative(susan) <- (27) [avatar component clause 279]
283. 28 <=> brave(susan) [avatar definition]
285. brave(susan) <- (28) [avatar component clause 283]
286. 27 | 28 [avatar split clause 143,283,279]
287. ~18 [avatar split clause 144,230]
292. $false <- (3) [resolution 267,167]
293. ~3 [avatar contradiction clause 292]
330. funny(susan) | strong(susan) <- (27) [resolution 147,281]
341. strong(susan) <- (~4, 27) [subsumption resolution 330,170]
345. old(susan) <- (~4, 27) [resolution 341,163]
346. $false <- (~4, ~5, 27) [subsumption resolution 345,175]
347. 4 | 5 | ~27 [avatar contradiction clause 346]
375. strong(susan) | wise(susan) | quiet(susan) <- (28) [resolution 111,285]
389. strong(susan) | quiet(susan) <- (~18, 28) [subsumption resolution 375,231]
391. 40 <=> quiet(susan) [avatar definition]
393. quiet(susan) <- (40) [avatar component clause 391]
395. 41 <=> strong(susan) [avatar definition]
397. strong(susan) <- (41) [avatar component clause 395]
398. 40 | 41 | 18 | ~28 [avatar split clause 389,283,230,395,391]
438. old(susan) <- (41) [resolution 397,163]
442. $false <- (~5, 41) [subsumption resolution 438,175]
443. 5 | ~41 [avatar contradiction clause 442]
445. funny(susan) | old(susan) | ~brave(susan) <- (40) [resolution 393,85]
451. funny(susan) | ~brave(susan) <- (~5, 40) [subsumption resolution 445,175]
452. funny(susan) <- (~5, 28, 40) [subsumption resolution 451,285]
453. 4 | 5 | ~28 | ~40 [avatar split clause 452,391,283,173,169]
456. wise(susan) <- (4) [resolution 171,145]
457. $false <- (4, ~18) [subsumption resolution 456,231]
458. ~4 | 18 [avatar contradiction clause 457]
459. $false [avatar sat refutation 176,286,287,293,347,398,443,453,458]
% SZS output end Proof for 5025188055351189552642944
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not humble or humble is not brave and vice versa. If someone is either strong or old then someone is not curious or kind and vice versa. If someone is brave then someone is both not calm and not brave. If fred is both not strong and not humble then someone is either brave or happy. Everyone who is kind is either kind or not happy and vice versa. If someone is both funny and happy then john is creative. Everyone who is patient or calm is either quiet or not rich. Everyone who is both not tall and not rich is either happy or not calm and vice versa. Everyone who is old is brave. If lucy is not creative or wise then paul is calm or not rich. Everyone who is not calm or not curious is old or not happy and vice versa. If someone is humble then john is both happy and not humble and vice versa. If someone is not tall then john is not funny and vice versa. If lucy is curious or kind then mary is not brave and vice versa. Someone is happy or rich. Someone is generous. Susan is kind or not kind. Someone is either calm or not kind. Someone is both not kind and not generous. Someone is not quiet or not patient. Someone is rich or calm. | Susan is not tall. | entailment | (![X]:((~humble(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((strong(X)<~>old(X))))<=>(?[X]:((~curious(X)|kind(X)))))&
((?[X]:(brave(X)))=>(?[X]:((~calm(X)&~brave(X)))))&
(((~strong(fred)&~humble(fred)))=>(?[X]:((brave(X)<~>happy(X)))))&
(![X]:(kind(X)<=>(kind(X)<~>~happy(X))))&
((?[X]:((funny(X)&happy(X))))=>(creative(john)))&
(![X]:((patient(X)|calm(X))=>(quiet(X)<~>~rich(X))))&
(![X]:((~tall(X)&~rich(X))<=>(happy(X)<~>~calm(X))))&
(![X]:(old(X)=>brave(X)))&
(((~creative(lucy)|wise(lucy)))=>((calm(paul)|~rich(paul))))&
(![X]:((~calm(X)|~curious(X))<=>(old(X)|~happy(X))))&
((?[X]:(humble(X)))<=>((happy(john)&~humble(john))))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(((curious(lucy)|kind(lucy)))<=>(~brave(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((calm(X)<~>~kind(X))))&
(?[X]:((~kind(X)&~generous(X))))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X)))) | ~tall(susan) | [
"p0",
"p4",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4776981963109949125393557
% SZS output start Proof for 4776981963109949125393557
1. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> ~brave(X0)) [input p0]
5. ! [X0] : (kind(X0) <=> (kind(X0) <~> ~happy(X0))) [input p4]
8. ! [X0] : ((~rich(X0) & ~tall(X0)) <=> (happy(X0) <~> ~calm(X0))) [input p7]
9. ! [X0] : (old(X0) => brave(X0)) [input p8]
11. ! [X0] : ((~curious(X0) | ~calm(X0)) <=> (~happy(X0) | old(X0))) [input p10]
22. tall(susan) [input hypothesis]
34. ! [X0] : (brave(X0) | ~old(X0)) [ennf transformation 9]
35. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | brave(X0)) & (~brave(X0) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 1]
47. ! [X0] : ((kind(X0) | ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0)))) & (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | ~kind(X0))) [nnf transformation 5]
49. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | (rich(X0) | tall(X0)))) [nnf transformation 8]
50. ! [X0] : (((~rich(X0) & ~tall(X0)) | ((happy(X0) | calm(X0)) & (~calm(X0) | ~happy(X0)))) & (((calm(X0) | ~happy(X0)) & (~calm(X0) | happy(X0))) | rich(X0) | tall(X0))) [flattening 49]
51. ! [X0] : (((~curious(X0) | ~calm(X0)) | (happy(X0) & ~old(X0))) & ((~happy(X0) | old(X0)) | (curious(X0) & calm(X0)))) [nnf transformation 11]
52. ! [X0] : ((~curious(X0) | ~calm(X0) | (happy(X0) & ~old(X0))) & (~happy(X0) | old(X0) | (curious(X0) & calm(X0)))) [flattening 51]
75. ~brave(X0) | humble(X0) | humble(X0) [cnf transformation 35]
76. ~brave(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 35]
90. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 47]
92. kind(X0) | kind(X0) | happy(X0) [cnf transformation 47]
97. ~tall(X0) | ~calm(X0) | ~happy(X0) [cnf transformation 50]
101. brave(X0) | ~old(X0) [cnf transformation 34]
102. ~happy(X0) | old(X0) | calm(X0) [cnf transformation 52]
122. tall(susan) [cnf transformation 22]
123. happy(X0) | ~kind(X0) [duplicate literal removal 90]
124. happy(X0) | kind(X0) [duplicate literal removal 92]
125. ~brave(X0) | humble(X0) [duplicate literal removal 75]
126. ~brave(X0) | ~humble(X0) [duplicate literal removal 76]
127. ~brave(X0) [subsumption resolution 125,126]
176. happy(X0) [subsumption resolution 123,124]
178. ~tall(X0) | ~calm(X0) [subsumption resolution 97,176]
180. ~old(X0) [subsumption resolution 101,127]
184. old(X0) | calm(X0) [subsumption resolution 102,176]
185. calm(X0) [subsumption resolution 184,180]
226. ~calm(susan) [resolution 178,122]
227. $false [subsumption resolution 226,185]
% SZS output end Proof for 4776981963109949125393557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or not generous then someone is not calm or not curious.
If someone is either not rich or humble then john is either patient or brave.
Everyone who is not creative or not old is not happy.
If someone is not brave then someone is not generous or brave and vice versa.
If lucy is brave then someone is not patient and vice versa.
Everyone who is happy or not humble is not patient or not happy.
If alice is both curious and not tall then someone is not quiet or not calm.
Everyone who is both funny and generous is not calm or quiet and vice versa.
Everyone who is rich is either quiet or patient and vice versa.
Everyone who is not rich is either not creative or not old and vice versa.
If fred is not happy then alice is both kind and not patient and vice versa.
Everyone who is calm is both happy and not brave and vice versa.
Everyone who is brave is either wise or strong and vice versa.
If someone is both not patient and not creative then someone is not wise.
If susan is not tall then alice is both strong and not curious.
Everyone who is not quiet or not old is either not old or kind.
Someone is both not brave and patient.
Fred is not kind or not funny.
Someone is not creative.
Someone is either not humble or not old.
John is not calm or kind.
Fred is either not old or brave.
Mary is either tall or not humble. | Fred is not funny. | contradiction | ((?[X]:((brave(X)<~>~generous(X))))=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((~rich(X)<~>humble(X))))=>((patient(john)<~>brave(john))))&
(![X]:((~creative(X)|~old(X))=>~happy(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~generous(X)|brave(X)))))&
((brave(lucy))<=>(?[X]:(~patient(X))))&
(![X]:((happy(X)|~humble(X))=>(~patient(X)|~happy(X))))&
(((curious(alice)&~tall(alice)))=>(?[X]:((~quiet(X)|~calm(X)))))&
(![X]:((funny(X)&generous(X))<=>(~calm(X)|quiet(X))))&
(![X]:(rich(X)<=>(quiet(X)<~>patient(X))))&
(![X]:(~rich(X)<=>(~creative(X)<~>~old(X))))&
((~happy(fred))<=>((kind(alice)&~patient(alice))))&
(![X]:(calm(X)<=>(happy(X)&~brave(X))))&
(![X]:(brave(X)<=>(wise(X)<~>strong(X))))&
((?[X]:((~patient(X)&~creative(X))))=>(?[X]:(~wise(X))))&
((~tall(susan))=>((strong(alice)&~curious(alice))))&
(![X]:((~quiet(X)|~old(X))=>(~old(X)<~>kind(X))))&
(?[X]:((~brave(X)&patient(X))))&
((~kind(fred)|~funny(fred)))&
(?[X]:(~creative(X)))&
(?[X]:((~humble(X)<~>~old(X))))&
((~calm(john)|kind(john)))&
((~old(fred)<~>brave(fred)))&
((tall(mary)<~>~humble(mary))) | ~funny(fred) | [
"p2",
"p7",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4105284759803304803796390
% SZS output start Proof for 4105284759803304803796390
3. ! [X0] : ((~old(X0) | ~creative(X0)) => ~happy(X0)) [input p2]
8. ! [X0] : ((generous(X0) & funny(X0)) <=> (quiet(X0) | ~calm(X0))) [input p7]
12. ! [X0] : (calm(X0) <=> (~brave(X0) & happy(X0))) [input p11]
22. ~old(fred) <~> brave(fred) [input p21]
24. ~funny(fred) [input hypothesis]
32. ! [X0] : (~happy(X0) | (old(X0) & creative(X0))) [ennf transformation 3]
48. ! [X0] : (((generous(X0) & funny(X0)) | (~quiet(X0) & calm(X0))) & ((quiet(X0) | ~calm(X0)) | (~generous(X0) | ~funny(X0)))) [nnf transformation 8]
49. ! [X0] : (((generous(X0) & funny(X0)) | (~quiet(X0) & calm(X0))) & (quiet(X0) | ~calm(X0) | ~generous(X0) | ~funny(X0))) [flattening 48]
54. ! [X0] : ((calm(X0) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | ~calm(X0))) [nnf transformation 12]
55. ! [X0] : ((calm(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | ~calm(X0))) [flattening 54]
68. (~brave(fred) | old(fred)) & (brave(fred) | ~old(fred)) [nnf transformation 22]
75. ~happy(X0) | old(X0) [cnf transformation 32]
84. funny(X0) | calm(X0) [cnf transformation 49]
99. ~calm(X0) | happy(X0) [cnf transformation 55]
100. ~calm(X0) | ~brave(X0) [cnf transformation 55]
119. brave(fred) | ~old(fred) [cnf transformation 68]
123. ~funny(fred) [cnf transformation 24]
190. 16 <=> happy(fred) [avatar definition]
191. happy(fred) <- (16) [avatar component clause 190]
218. 22 <=> funny(fred) [avatar definition]
220. ~funny(fred) <- (~22) [avatar component clause 218]
242. 27 <=> old(fred) [avatar definition]
246. 28 <=> brave(fred) [avatar definition]
247. brave(fred) <- (28) [avatar component clause 246]
250. ~27 | 28 [avatar split clause 119,246,242]
261. ~22 [avatar split clause 123,218]
264. calm(fred) <- (~22) [resolution 84,220]
266. happy(fred) <- (~22) [resolution 99,264]
270. 16 | 22 [avatar split clause 266,218,190]
271. old(fred) <- (16) [resolution 191,75]
275. 27 | ~16 [avatar split clause 271,190,242]
276. ~brave(fred) <- (~22) [resolution 100,264]
278. $false <- (~22, 28) [subsumption resolution 276,247]
279. 22 | ~28 [avatar contradiction clause 278]
280. $false [avatar sat refutation 250,261,270,275,279]
% SZS output end Proof for 4105284759803304803796390
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is curious or generous then someone is either generous or not old and vice versa.
If someone is both strong and humble then mary is happy.
Everyone who is funny or not creative is not curious or not creative.
Everyone who is not creative or not generous is either not old or not quiet and vice versa.
If mary is both brave and not kind then lucy is either not humble or kind and vice versa.
If mary is both not kind and not patient then john is quiet and vice versa.
If fred is both kind and patient then someone is either not humble or patient.
Everyone who is not curious or not quiet is both happy and curious.
Everyone who is either not curious or not quiet is both humble and not brave and vice versa.
If lucy is either brave or kind then someone is both generous and not brave.
If lucy is either not happy or not generous then someone is wise and vice versa.
Everyone who is strong is both not tall and not funny and vice versa.
Everyone who is generous or not rich is both not strong and tall.
Everyone who is both funny and generous is wise or not creative and vice versa.
Everyone who is both not wise and not creative is either rich or wise.
If someone is not generous then someone is both tall and not rich.
Someone is both not happy and curious.
Mary is both happy and kind.
Someone is not rich.
Someone is old.
Alice is not quiet.
Lucy is both curious and not humble.
Someone is either not strong or humble. | John is not happy. | contradiction | (((curious(fred)|generous(fred)))<=>(?[X]:((generous(X)<~>~old(X)))))&
((?[X]:((strong(X)&humble(X))))=>(happy(mary)))&
(![X]:((funny(X)|~creative(X))=>(~curious(X)|~creative(X))))&
(![X]:((~creative(X)|~generous(X))<=>(~old(X)<~>~quiet(X))))&
(((brave(mary)&~kind(mary)))<=>((~humble(lucy)<~>kind(lucy))))&
(((~kind(mary)&~patient(mary)))<=>(quiet(john)))&
(((kind(fred)&patient(fred)))=>(?[X]:((~humble(X)<~>patient(X)))))&
(![X]:((~curious(X)|~quiet(X))=>(happy(X)&curious(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(humble(X)&~brave(X))))&
(((brave(lucy)<~>kind(lucy)))=>(?[X]:((generous(X)&~brave(X)))))&
(((~happy(lucy)<~>~generous(lucy)))<=>(?[X]:(wise(X))))&
(![X]:(strong(X)<=>(~tall(X)&~funny(X))))&
(![X]:((generous(X)|~rich(X))=>(~strong(X)&tall(X))))&
(![X]:((funny(X)&generous(X))<=>(wise(X)|~creative(X))))&
(![X]:((~wise(X)&~creative(X))=>(rich(X)<~>wise(X))))&
((?[X]:(~generous(X)))=>(?[X]:((tall(X)&~rich(X)))))&
(?[X]:((~happy(X)&curious(X))))&
((happy(mary)&kind(mary)))&
(?[X]:(~rich(X)))&
(?[X]:(old(X)))&
(~quiet(alice))&
((curious(lucy)&~humble(lucy)))&
(?[X]:((~strong(X)<~>humble(X)))) | ~happy(john) | [
"p5",
"p7",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1163397422476950517132112
% SZS output start Proof for 1163397422476950517132112
6. (~patient(mary) & ~kind(mary)) <=> quiet(john) [input p5]
8. ! [X0] : ((~quiet(X0) | ~curious(X0)) => (curious(X0) & happy(X0))) [input p7]
18. kind(mary) & happy(mary) [input p17]
24. ~happy(john) [input hypothesis]
31. ! [X0] : ((curious(X0) & happy(X0)) | (quiet(X0) & curious(X0))) [ennf transformation 8]
46. ((~patient(mary) & ~kind(mary)) | ~quiet(john)) & (quiet(john) | (patient(mary) | kind(mary))) [nnf transformation 6]
47. ((~patient(mary) & ~kind(mary)) | ~quiet(john)) & (quiet(john) | patient(mary) | kind(mary)) [flattening 46]
99. ~kind(mary) | ~quiet(john) [cnf transformation 47]
104. quiet(X0) | happy(X0) [cnf transformation 31]
140. kind(mary) [cnf transformation 18]
148. ~happy(john) [cnf transformation 24]
196. 11 <=> kind(mary) [avatar definition]
210. 13 <=> quiet(john) [avatar definition]
212. ~quiet(john) <- (~13) [avatar component clause 210]
218. ~13 | ~11 [avatar split clause 99,196,210]
289. 11 [avatar split clause 140,196]
309. happy(john) <- (~13) [resolution 104,212]
310. $false <- (~13) [subsumption resolution 309,148]
311. 13 [avatar contradiction clause 310]
312. $false [avatar sat refutation 218,289,311]
% SZS output end Proof for 1163397422476950517132112
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or generous is either wise or creative and vice versa.
If someone is either creative or quiet then someone is both calm and not curious and vice versa.
Everyone who is both not old and not rich is either not strong or not creative.
Everyone who is old is wise.
If someone is not patient then someone is not old.
If someone is either wise or strong then fred is either not brave or funny and vice versa.
If susan is not calm then someone is quiet or not creative.
Everyone who is both wise and generous is not creative or brave and vice versa.
Everyone who is either not wise or tall is strong and vice versa.
If alice is curious then someone is wise or not quiet.
Everyone who is both tall and rich is not calm.
Everyone who is either quiet or calm is either not brave or not old.
If susan is either calm or not generous then someone is either funny or not rich and vice versa.
If someone is not rich then lucy is kind.
Everyone who is humble or not humble is not old or not happy and vice versa.
Everyone who is both not calm and not brave is either wise or tall.
Lucy is either not humble or tall.
Someone is creative.
John is both not brave and old.
Paul is either generous or humble.
Someone is strong.
Someone is both not funny and generous. | Lucy is brave. | neutral | (![X]:((happy(X)<~>generous(X))<=>(wise(X)<~>creative(X))))&
((?[X]:((creative(X)<~>quiet(X))))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((~old(X)&~rich(X))=>(~strong(X)<~>~creative(X))))&
(![X]:(old(X)=>wise(X)))&
((?[X]:(~patient(X)))=>(?[X]:(~old(X))))&
((?[X]:((wise(X)<~>strong(X))))<=>((~brave(fred)<~>funny(fred))))&
((~calm(susan))=>(?[X]:((quiet(X)|~creative(X)))))&
(![X]:((wise(X)&generous(X))<=>(~creative(X)|brave(X))))&
(![X]:((~wise(X)<~>tall(X))<=>strong(X)))&
((curious(alice))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:((tall(X)&rich(X))=>~calm(X)))&
(![X]:((quiet(X)<~>calm(X))=>(~brave(X)<~>~old(X))))&
(((calm(susan)<~>~generous(susan)))<=>(?[X]:((funny(X)<~>~rich(X)))))&
((?[X]:(~rich(X)))=>(kind(lucy)))&
(![X]:((humble(X)|~humble(X))<=>(~old(X)|~happy(X))))&
(![X]:((~calm(X)&~brave(X))=>(wise(X)<~>tall(X))))&
((~humble(lucy)<~>tall(lucy)))&
(?[X]:(creative(X)))&
((~brave(john)&old(john)))&
((generous(paul)<~>humble(paul)))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)&generous(X)))) | brave(lucy) | [] | null | 0 |
Everyone who is funny or not calm is brave and vice versa.
If fred is not calm or not tall then someone is curious or calm and vice versa.
If susan is either not creative or patient then paul is both not patient and not brave and vice versa.
Everyone who is either quiet or generous is not quiet.
Everyone who is happy is either funny or not wise.
If someone is not rich or not patient then paul is not brave.
Everyone who is either not happy or not creative is tall or patient and vice versa.
If someone is both creative and tall then mary is strong or old.
Everyone who is not patient or humble is either brave or not generous and vice versa.
Everyone who is not kind or brave is not rich or happy and vice versa.
Everyone who is not rich is both not curious and happy and vice versa.
If someone is either happy or curious then someone is both happy and not wise and vice versa.
Everyone who is not tall or happy is both humble and not generous.
Everyone who is either curious or brave is not tall or not wise and vice versa.
If lucy is either not old or calm then susan is tall.
Everyone who is either not patient or not humble is either not rich or funny.
John is not patient or not curious.
Susan is both not brave and not generous.
Someone is either not strong or not tall.
Someone is both not old and wise.
Someone is either not brave or brave.
Someone is not calm or not funny.
Paul is either not tall or not rich. | Mary is not funny. | entailment | (![X]:((funny(X)|~calm(X))<=>brave(X)))&
(((~calm(fred)|~tall(fred)))<=>(?[X]:((curious(X)|calm(X)))))&
(((~creative(susan)<~>patient(susan)))<=>((~patient(paul)&~brave(paul))))&
(![X]:((quiet(X)<~>generous(X))=>~quiet(X)))&
(![X]:(happy(X)=>(funny(X)<~>~wise(X))))&
((?[X]:((~rich(X)|~patient(X))))=>(~brave(paul)))&
(![X]:((~happy(X)<~>~creative(X))<=>(tall(X)|patient(X))))&
((?[X]:((creative(X)&tall(X))))=>((strong(mary)|old(mary))))&
(![X]:((~patient(X)|humble(X))<=>(brave(X)<~>~generous(X))))&
(![X]:((~kind(X)|brave(X))<=>(~rich(X)|happy(X))))&
(![X]:(~rich(X)<=>(~curious(X)&happy(X))))&
((?[X]:((happy(X)<~>curious(X))))<=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~tall(X)|happy(X))=>(humble(X)&~generous(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~tall(X)|~wise(X))))&
(((~old(lucy)<~>calm(lucy)))=>(tall(susan)))&
(![X]:((~patient(X)<~>~humble(X))=>(~rich(X)<~>funny(X))))&
((~patient(john)|~curious(john)))&
((~brave(susan)&~generous(susan)))&
(?[X]:((~strong(X)<~>~tall(X))))&
(?[X]:((~old(X)&wise(X))))&
(?[X]:((~brave(X)<~>brave(X))))&
(?[X]:((~calm(X)|~funny(X))))&
((~tall(paul)<~>~rich(paul))) | ~funny(mary) | [
"p0",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3237954390323187781314724
% SZS output start Proof for 3237954390323187781314724
1. ! [X0] : ((~calm(X0) | funny(X0)) <=> brave(X0)) [input p0]
9. ! [X0] : ((humble(X0) | ~patient(X0)) <=> (brave(X0) <~> ~generous(X0))) [input p8]
10. ! [X0] : ((brave(X0) | ~kind(X0)) <=> (happy(X0) | ~rich(X0))) [input p9]
11. ! [X0] : (~rich(X0) <=> (happy(X0) & ~curious(X0))) [input p10]
13. ! [X0] : ((happy(X0) | ~tall(X0)) => (~generous(X0) & humble(X0))) [input p12]
24. funny(mary) [input hypothesis]
31. ! [X0] : ((~generous(X0) & humble(X0)) | (~happy(X0) & tall(X0))) [ennf transformation 13]
34. ! [X0] : (((~calm(X0) | funny(X0)) | ~brave(X0)) & (brave(X0) | (calm(X0) & ~funny(X0)))) [nnf transformation 1]
35. ! [X0] : ((~calm(X0) | funny(X0) | ~brave(X0)) & (brave(X0) | (calm(X0) & ~funny(X0)))) [flattening 34]
47. ! [X0] : (((humble(X0) | ~patient(X0)) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) & (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | (~humble(X0) & patient(X0)))) [nnf transformation 9]
48. ! [X0] : ((humble(X0) | ~patient(X0) | ((brave(X0) | generous(X0)) & (~generous(X0) | ~brave(X0)))) & (((generous(X0) | ~brave(X0)) & (~generous(X0) | brave(X0))) | (~humble(X0) & patient(X0)))) [flattening 47]
49. ! [X0] : (((brave(X0) | ~kind(X0)) | (~happy(X0) & rich(X0))) & ((happy(X0) | ~rich(X0)) | (~brave(X0) & kind(X0)))) [nnf transformation 10]
50. ! [X0] : ((brave(X0) | ~kind(X0) | (~happy(X0) & rich(X0))) & (happy(X0) | ~rich(X0) | (~brave(X0) & kind(X0)))) [flattening 49]
51. ! [X0] : ((~rich(X0) | (~happy(X0) | curious(X0))) & ((happy(X0) & ~curious(X0)) | rich(X0))) [nnf transformation 11]
52. ! [X0] : ((~rich(X0) | ~happy(X0) | curious(X0)) & ((happy(X0) & ~curious(X0)) | rich(X0))) [flattening 51]
73. ~funny(X0) | brave(X0) [cnf transformation 35]
102. ~humble(X0) | ~brave(X0) | generous(X0) [cnf transformation 48]
106. ~rich(X0) | happy(X0) | ~brave(X0) [cnf transformation 50]
110. rich(X0) | happy(X0) [cnf transformation 52]
119. ~happy(X0) | humble(X0) [cnf transformation 31]
121. ~happy(X0) | ~generous(X0) [cnf transformation 31]
146. funny(mary) [cnf transformation 24]
299. brave(mary) [resolution 73,146]
360. 39 <=> generous(mary) [avatar definition]
361. ~generous(mary) <- (~39) [avatar component clause 360]
397. 43 <=> happy(mary) [avatar definition]
399. happy(mary) <- (43) [avatar component clause 397]
422. happy(X0) | ~brave(X0) | happy(X0) [resolution 106,110]
425. ~brave(X0) | happy(X0) [duplicate literal removal 422]
429. humble(mary) <- (43) [resolution 399,119]
430. ~generous(mary) <- (43) [resolution 399,121]
436. ~39 | ~43 [avatar split clause 430,397,360]
573. happy(mary) [resolution 425,299]
800. ~brave(mary) | generous(mary) <- (43) [resolution 429,102]
802. generous(mary) <- (43) [subsumption resolution 800,299]
803. $false <- (~39, 43) [subsumption resolution 802,361]
804. 39 | ~43 [avatar contradiction clause 803]
807. 43 [avatar split clause 573,397]
808. $false [avatar sat refutation 436,804,807]
% SZS output end Proof for 3237954390323187781314724
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative then someone is either generous or not strong and vice versa.
Everyone who is both not happy and not creative is either not happy or curious and vice versa.
Everyone who is not quiet or not curious is not creative or calm and vice versa.
Everyone who is both rich and curious is both not humble and generous and vice versa.
If someone is creative then someone is patient or not old and vice versa.
If paul is not wise or rich then paul is either old or not strong.
Everyone who is not happy or not patient is not happy and vice versa.
If someone is not patient or patient then paul is not generous and vice versa.
Everyone who is either not generous or kind is not quiet or old.
Everyone who is old or brave is not funny and vice versa.
If fred is both not happy and quiet then paul is either not creative or generous and vice versa.
Everyone who is happy or not rich is not wise.
If lucy is funny or not wise then paul is both not quiet and brave and vice versa.
Everyone who is either not funny or tall is strong or not patient.
Everyone who is both happy and not tall is not brave or tall and vice versa.
If someone is not wise then lucy is both not generous and old.
Someone is either not humble or quiet.
Someone is not humble or tall.
Lucy is not old.
Someone is both not patient and not quiet.
Someone is either not funny or not wise.
Someone is funny or quiet. | Lucy is brave. | entailment | ((~creative(alice))<=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~happy(X)&~creative(X))<=>(~happy(X)<~>curious(X))))&
(![X]:((~quiet(X)|~curious(X))<=>(~creative(X)|calm(X))))&
(![X]:((rich(X)&curious(X))<=>(~humble(X)&generous(X))))&
((?[X]:(creative(X)))<=>(?[X]:((patient(X)|~old(X)))))&
(((~wise(paul)|rich(paul)))=>((old(paul)<~>~strong(paul))))&
(![X]:((~happy(X)|~patient(X))<=>~happy(X)))&
((?[X]:((~patient(X)|patient(X))))<=>(~generous(paul)))&
(![X]:((~generous(X)<~>kind(X))=>(~quiet(X)|old(X))))&
(![X]:((old(X)|brave(X))<=>~funny(X)))&
(((~happy(fred)&quiet(fred)))<=>((~creative(paul)<~>generous(paul))))&
(![X]:((happy(X)|~rich(X))=>~wise(X)))&
(((funny(lucy)|~wise(lucy)))<=>((~quiet(paul)&brave(paul))))&
(![X]:((~funny(X)<~>tall(X))=>(strong(X)|~patient(X))))&
(![X]:((happy(X)&~tall(X))<=>(~brave(X)|tall(X))))&
((?[X]:(~wise(X)))=>((~generous(lucy)&old(lucy))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~humble(X)|tall(X))))&
(~old(lucy))&
(?[X]:((~patient(X)&~quiet(X))))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((funny(X)|quiet(X)))) | brave(lucy) | [
"p11",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3397364687357033464859859
% SZS output start Proof for 3397364687357033464859859
12. ! [X0] : ((~rich(X0) | happy(X0)) => ~wise(X0)) [input p11]
15. ! [X0] : ((~tall(X0) & happy(X0)) <=> (tall(X0) | ~brave(X0))) [input p14]
16. ? [X0] : ~wise(X0) => (old(lucy) & ~generous(lucy)) [input p15]
19. ~old(lucy) [input p18]
23. ~brave(lucy) [input hypothesis]
28. ! [X0] : (~wise(X0) | (rich(X0) & ~happy(X0))) [ennf transformation 12]
31. (old(lucy) & ~generous(lucy)) | ! [X0] : wise(X0) [ennf transformation 16]
62. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & ((tall(X0) | ~brave(X0)) | (tall(X0) | ~happy(X0)))) [nnf transformation 15]
63. ! [X0] : (((~tall(X0) & happy(X0)) | (~tall(X0) & brave(X0))) & (tall(X0) | ~brave(X0) | tall(X0) | ~happy(X0))) [flattening 62]
118. ~wise(X0) | ~happy(X0) [cnf transformation 28]
128. brave(X0) | happy(X0) [cnf transformation 63]
133. old(lucy) | wise(X0) [cnf transformation 31]
137. ~old(lucy) [cnf transformation 19]
143. ~brave(lucy) [cnf transformation 23]
265. 25 <=> ! [X0] : wise(X0) [avatar definition]
266. wise(X0) <- (25) [avatar component clause 265]
268. 26 <=> old(lucy) [avatar definition]
271. 25 | 26 [avatar split clause 133,268,265]
288. ~26 [avatar split clause 137,268]
322. ~happy(X0) <- (25) [resolution 118,266]
324. happy(lucy) [resolution 128,143]
326. $false <- (25) [subsumption resolution 324,322]
327. ~25 [avatar contradiction clause 326]
330. $false [avatar sat refutation 271,288,327]
% SZS output end Proof for 3397364687357033464859859
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and wise then lucy is not quiet. Everyone who is not funny or rich is both not happy and not curious. Everyone who is generous is both not happy and funny and vice versa. If someone is brave then someone is either not calm or funny and vice versa. If someone is either not wise or quiet then fred is curious or patient and vice versa. Everyone who is not brave is happy or kind and vice versa. If john is both not humble and not rich then lucy is not humble or calm. If someone is both funny and not old then lucy is either tall or not funny and vice versa. If fred is both not rich and quiet then alice is curious. Everyone who is calm or kind is both generous and not curious and vice versa. If someone is not wise or funny then someone is either not rich or not wise and vice versa. Everyone who is not wise is either not quiet or strong and vice versa. If mary is either not rich or tall then mary is either patient or old and vice versa. If fred is patient then someone is either strong or not patient and vice versa. If someone is happy or not calm then someone is either not kind or generous and vice versa. If lucy is both generous and not generous then someone is not humble or not patient and vice versa. Fred is either generous or not humble. Someone is strong. Alice is not strong. John is rich or not patient. Lucy is not calm or not kind. Someone is not quiet. | John is curious. | contradiction | ((?[X]:((curious(X)&wise(X))))=>(~quiet(lucy)))&
(![X]:((~funny(X)|rich(X))=>(~happy(X)&~curious(X))))&
(![X]:(generous(X)<=>(~happy(X)&funny(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~calm(X)<~>funny(X)))))&
((?[X]:((~wise(X)<~>quiet(X))))<=>((curious(fred)|patient(fred))))&
(![X]:(~brave(X)<=>(happy(X)|kind(X))))&
(((~humble(john)&~rich(john)))=>((~humble(lucy)|calm(lucy))))&
((?[X]:((funny(X)&~old(X))))<=>((tall(lucy)<~>~funny(lucy))))&
(((~rich(fred)&quiet(fred)))=>(curious(alice)))&
(![X]:((calm(X)|kind(X))<=>(generous(X)&~curious(X))))&
((?[X]:((~wise(X)|funny(X))))<=>(?[X]:((~rich(X)<~>~wise(X)))))&
(![X]:(~wise(X)<=>(~quiet(X)<~>strong(X))))&
(((~rich(mary)<~>tall(mary)))<=>((patient(mary)<~>old(mary))))&
((patient(fred))<=>(?[X]:((strong(X)<~>~patient(X)))))&
((?[X]:((happy(X)|~calm(X))))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(((generous(lucy)&~generous(lucy)))<=>(?[X]:((~humble(X)|~patient(X)))))&
((generous(fred)<~>~humble(fred)))&
(?[X]:(strong(X)))&
(~strong(alice))&
((rich(john)|~patient(john)))&
((~calm(lucy)|~kind(lucy)))&
(?[X]:(~quiet(X))) | curious(john) | [
"p1",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4918064297245165794998769
% SZS output start Proof for 4918064297245165794998769
2. ! [X0] : ((rich(X0) | ~funny(X0)) => (~curious(X0) & ~happy(X0))) [input p1]
16. (~generous(lucy) & generous(lucy)) <=> ? [X0] : (~patient(X0) | ~humble(X0)) [input p15]
20. ~patient(john) | rich(john) [input p19]
23. curious(john) [input hypothesis]
28. ! [X0] : ((~curious(X0) & ~happy(X0)) | (~rich(X0) & funny(X0))) [ennf transformation 2]
69. ((~generous(lucy) & generous(lucy)) | ! [X0] : (patient(X0) & humble(X0))) & (? [X0] : (~patient(X0) | ~humble(X0)) | (generous(lucy) | ~generous(lucy))) [nnf transformation 16]
70. ((~generous(lucy) & generous(lucy)) | ! [X0] : (patient(X0) & humble(X0))) & (? [X0] : (~patient(X0) | ~humble(X0)) | generous(lucy) | ~generous(lucy)) [flattening 69]
71. ((~generous(lucy) & generous(lucy)) | ! [X0] : (patient(X0) & humble(X0))) & (? [X1] : (~patient(X1) | ~humble(X1)) | generous(lucy) | ~generous(lucy)) [rectify 70]
72. ? [X1] : (~patient(X1) | ~humble(X1)) => (~patient(sK9) | ~humble(sK9)) [choice axiom]
73. ((~generous(lucy) & generous(lucy)) | ! [X0] : (patient(X0) & humble(X0))) & ((~patient(sK9) | ~humble(sK9)) | generous(lucy) | ~generous(lucy)) [skolemisation 71,72]
83. ~rich(X0) | ~curious(X0) [cnf transformation 28]
143. generous(lucy) | patient(X0) [cnf transformation 73]
145. ~generous(lucy) | patient(X0) [cnf transformation 73]
150. ~patient(john) | rich(john) [cnf transformation 20]
153. curious(john) [cnf transformation 23]
220. 16 <=> rich(john) [avatar definition]
222. rich(john) <- (16) [avatar component clause 220]
381. 51 <=> ! [X0] : patient(X0) [avatar definition]
382. patient(X0) <- (51) [avatar component clause 381]
384. 52 <=> generous(lucy) [avatar definition]
387. 51 | ~52 [avatar split clause 145,384,381]
392. 51 | 52 [avatar split clause 143,384,381]
405. 56 <=> patient(john) [avatar definition]
407. ~patient(john) <- (~56) [avatar component clause 405]
408. 16 | ~56 [avatar split clause 150,405,220]
427. $false <- (51, ~56) [resolution 407,382]
428. ~51 | 56 [avatar contradiction clause 427]
432. ~curious(john) <- (16) [resolution 83,222]
433. $false <- (16) [subsumption resolution 432,153]
434. ~16 [avatar contradiction clause 433]
435. $false [avatar sat refutation 387,392,408,428,434]
% SZS output end Proof for 4918064297245165794998769
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is either not calm or not rich.
If someone is either tall or not old then paul is both not quiet and funny.
Everyone who is either curious or old is both not kind and brave and vice versa.
If mary is either funny or strong then someone is both humble and not wise.
If someone is not rich then fred is either not creative or tall and vice versa.
If someone is either quiet or not quiet then someone is not wise or creative.
If mary is both patient and wise then lucy is either not kind or not humble and vice versa.
Everyone who is both wise and patient is both calm and brave.
Everyone who is both old and not tall is both tall and curious and vice versa.
Everyone who is both brave and not wise is both old and patient.
If someone is both not creative and not quiet then someone is not happy.
Everyone who is wise or not funny is either tall or calm and vice versa.
Everyone who is both not quiet and happy is old or not old and vice versa.
Everyone who is either funny or creative is not quiet or curious.
Everyone who is both not calm and happy is creative or not happy and vice versa.
If someone is not creative then mary is not funny or creative.
Someone is not old or not quiet.
Someone is not rich or wise.
Lucy is either happy or not strong.
Someone is either not patient or old.
Someone is not happy or not tall. | Fred is not brave. | neutral | (![X]:((humble(X)|~creative(X))=>(~calm(X)<~>~rich(X))))&
((?[X]:((tall(X)<~>~old(X))))=>((~quiet(paul)&funny(paul))))&
(![X]:((curious(X)<~>old(X))<=>(~kind(X)&brave(X))))&
(((funny(mary)<~>strong(mary)))=>(?[X]:((humble(X)&~wise(X)))))&
((?[X]:(~rich(X)))<=>((~creative(fred)<~>tall(fred))))&
((?[X]:((quiet(X)<~>~quiet(X))))=>(?[X]:((~wise(X)|creative(X)))))&
(((patient(mary)&wise(mary)))<=>((~kind(lucy)<~>~humble(lucy))))&
(![X]:((wise(X)&patient(X))=>(calm(X)&brave(X))))&
(![X]:((old(X)&~tall(X))<=>(tall(X)&curious(X))))&
(![X]:((brave(X)&~wise(X))=>(old(X)&patient(X))))&
((?[X]:((~creative(X)&~quiet(X))))=>(?[X]:(~happy(X))))&
(![X]:((wise(X)|~funny(X))<=>(tall(X)<~>calm(X))))&
(![X]:((~quiet(X)&happy(X))<=>(old(X)|~old(X))))&
(![X]:((funny(X)<~>creative(X))=>(~quiet(X)|curious(X))))&
(![X]:((~calm(X)&happy(X))<=>(creative(X)|~happy(X))))&
((?[X]:(~creative(X)))=>((~funny(mary)|creative(mary))))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((~rich(X)|wise(X))))&
((happy(lucy)<~>~strong(lucy)))&
(?[X]:((~patient(X)<~>old(X))))&
(?[X]:((~happy(X)|~tall(X)))) | ~brave(fred) | [] | null | 0 |
If fred is either not curious or curious then someone is both old and calm and vice versa.
Everyone who is either not rich or strong is patient.
If mary is either brave or happy then mary is either not wise or not patient.
Everyone who is not curious is funny and vice versa.
Everyone who is quiet is either funny or old and vice versa.
Everyone who is either not generous or wise is both not patient and brave.
If someone is either patient or wise then someone is both not happy and curious and vice versa.
If susan is either strong or kind then someone is either not tall or rich.
Everyone who is both not curious and quiet is both patient and not tall.
Everyone who is wise is either kind or not creative.
Everyone who is both not brave and kind is either kind or quiet and vice versa.
Everyone who is not patient or not kind is calm or strong and vice versa.
If someone is funny or not funny then susan is both generous and not tall.
Everyone who is funny is both not old and not funny and vice versa.
If someone is both not creative and not brave then someone is both old and not creative and vice versa.
If john is not generous then someone is either not curious or kind and vice versa.
Someone is not patient or happy.
Alice is both not tall and not happy.
Paul is not strong.
Someone is not patient or calm.
Susan is both not calm and rich.
Someone is not quiet or happy.
Paul is both not tall and quiet. | Fred is brave. | entailment | (((~curious(fred)<~>curious(fred)))<=>(?[X]:((old(X)&calm(X)))))&
(![X]:((~rich(X)<~>strong(X))=>patient(X)))&
(((brave(mary)<~>happy(mary)))=>((~wise(mary)<~>~patient(mary))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:(quiet(X)<=>(funny(X)<~>old(X))))&
(![X]:((~generous(X)<~>wise(X))=>(~patient(X)&brave(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((~happy(X)&curious(X)))))&
(((strong(susan)<~>kind(susan)))=>(?[X]:((~tall(X)<~>rich(X)))))&
(![X]:((~curious(X)&quiet(X))=>(patient(X)&~tall(X))))&
(![X]:(wise(X)=>(kind(X)<~>~creative(X))))&
(![X]:((~brave(X)&kind(X))<=>(kind(X)<~>quiet(X))))&
(![X]:((~patient(X)|~kind(X))<=>(calm(X)|strong(X))))&
((?[X]:((funny(X)|~funny(X))))=>((generous(susan)&~tall(susan))))&
(![X]:(funny(X)<=>(~old(X)&~funny(X))))&
((?[X]:((~creative(X)&~brave(X))))<=>(?[X]:((old(X)&~creative(X)))))&
((~generous(john))<=>(?[X]:((~curious(X)<~>kind(X)))))&
(?[X]:((~patient(X)|happy(X))))&
((~tall(alice)&~happy(alice)))&
(~strong(paul))&
(?[X]:((~patient(X)|calm(X))))&
((~calm(susan)&rich(susan)))&
(?[X]:((~quiet(X)|happy(X))))&
((~tall(paul)&quiet(paul))) | brave(fred) | [
"p3",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7078386311825729662786542
% SZS output start Proof for 7078386311825729662786542
4. ! [X0] : (~curious(X0) <=> funny(X0)) [input p3]
5. ! [X0] : (quiet(X0) <=> (funny(X0) <~> old(X0))) [input p4]
11. ! [X0] : ((kind(X0) & ~brave(X0)) <=> (kind(X0) <~> quiet(X0))) [input p10]
14. ! [X0] : (funny(X0) <=> (~funny(X0) & ~old(X0))) [input p13]
24. ~brave(fred) [input hypothesis]
41. ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0))) [nnf transformation 4]
42. ! [X0] : ((quiet(X0) | ((funny(X0) | ~old(X0)) & (old(X0) | ~funny(X0)))) & (((~old(X0) | ~funny(X0)) & (old(X0) | funny(X0))) | ~quiet(X0))) [nnf transformation 5]
53. ! [X0] : (((kind(X0) & ~brave(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) & (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | (~kind(X0) | brave(X0)))) [nnf transformation 11]
54. ! [X0] : (((kind(X0) & ~brave(X0)) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0)))) & (((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~kind(X0) | brave(X0))) [flattening 53]
57. ! [X0] : ((funny(X0) | (funny(X0) | old(X0))) & ((~funny(X0) & ~old(X0)) | ~funny(X0))) [nnf transformation 14]
58. ! [X0] : ((funny(X0) | funny(X0) | old(X0)) & ((~funny(X0) & ~old(X0)) | ~funny(X0))) [flattening 57]
86. funny(X0) | curious(X0) [cnf transformation 41]
87. ~funny(X0) | ~curious(X0) [cnf transformation 41]
91. ~old(X0) | funny(X0) | quiet(X0) [cnf transformation 42]
111. ~quiet(X0) | ~kind(X0) | ~kind(X0) | brave(X0) [cnf transformation 54]
115. kind(X0) | kind(X0) | ~quiet(X0) [cnf transformation 54]
125. ~funny(X0) | ~funny(X0) [cnf transformation 58]
126. funny(X0) | funny(X0) | old(X0) [cnf transformation 58]
145. ~brave(fred) [cnf transformation 24]
146. ~funny(X0) [duplicate literal removal 125]
147. funny(X0) | old(X0) [duplicate literal removal 126]
148. ~quiet(X0) | ~kind(X0) | brave(X0) [duplicate literal removal 111]
149. ~quiet(X0) | kind(X0) [duplicate literal removal 115]
241. ~quiet(X0) | brave(X0) [subsumption resolution 148,149]
251. 21 <=> ! [X0] : ~funny(X0) [avatar definition]
252. ~funny(X0) <- (21) [avatar component clause 251]
260. 21 [avatar split clause 146,251]
338. curious(X0) <- (21) [resolution 86,252]
347. old(X1) | ~curious(X1) [resolution 147,87]
349. old(X1) <- (21) [subsumption resolution 347,338]
394. funny(X0) | quiet(X0) <- (21) [resolution 91,349]
396. quiet(X0) <- (21) [subsumption resolution 394,252]
436. brave(X3) <- (21) [resolution 396,241]
441. $false <- (21) [resolution 436,145]
444. ~21 [avatar contradiction clause 441]
445. $false [avatar sat refutation 260,444]
% SZS output end Proof for 7078386311825729662786542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and tall then someone is not creative or not tall. Everyone who is not calm or not wise is either not kind or not brave. Everyone who is funny or not calm is both tall and brave and vice versa. Everyone who is not quiet or kind is both creative and not generous. If someone is either brave or happy then someone is either tall or strong. Everyone who is wise is both tall and not rich. Everyone who is both funny and old is strong or not quiet. Everyone who is either old or not humble is both not calm and not funny. If john is either not old or not humble then someone is either not tall or brave and vice versa. Everyone who is not quiet is either not rich or not humble. If alice is either not kind or not old then fred is either tall or not quiet. Everyone who is quiet is both wise and kind and vice versa. If someone is creative then fred is both not rich and not humble and vice versa. Everyone who is not old or kind is either not funny or not patient and vice versa. If someone is either not curious or humble then someone is not old or quiet. If alice is not kind or not happy then susan is not brave. Someone is either kind or generous. Someone is either not strong or humble. Alice is not patient or not happy. Someone is not old. John is not funny. Alice is either not happy or not tall. John is either not curious or happy. Someone is tall or curious. | Fred is not rich. | entailment | ((?[X]:((~quiet(X)&tall(X))))=>(?[X]:((~creative(X)|~tall(X)))))&
(![X]:((~calm(X)|~wise(X))=>(~kind(X)<~>~brave(X))))&
(![X]:((funny(X)|~calm(X))<=>(tall(X)&brave(X))))&
(![X]:((~quiet(X)|kind(X))=>(creative(X)&~generous(X))))&
((?[X]:((brave(X)<~>happy(X))))=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:(wise(X)=>(tall(X)&~rich(X))))&
(![X]:((funny(X)&old(X))=>(strong(X)|~quiet(X))))&
(![X]:((old(X)<~>~humble(X))=>(~calm(X)&~funny(X))))&
(((~old(john)<~>~humble(john)))<=>(?[X]:((~tall(X)<~>brave(X)))))&
(![X]:(~quiet(X)=>(~rich(X)<~>~humble(X))))&
(((~kind(alice)<~>~old(alice)))=>((tall(fred)<~>~quiet(fred))))&
(![X]:(quiet(X)<=>(wise(X)&kind(X))))&
((?[X]:(creative(X)))<=>((~rich(fred)&~humble(fred))))&
(![X]:((~old(X)|kind(X))<=>(~funny(X)<~>~patient(X))))&
((?[X]:((~curious(X)<~>humble(X))))=>(?[X]:((~old(X)|quiet(X)))))&
(((~kind(alice)|~happy(alice)))=>(~brave(susan)))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((~strong(X)<~>humble(X))))&
((~patient(alice)|~happy(alice)))&
(?[X]:(~old(X)))&
(~funny(john))&
((~happy(alice)<~>~tall(alice)))&
((~curious(john)<~>happy(john)))&
(?[X]:((tall(X)|curious(X)))) | ~rich(fred) | [
"p3",
"p5",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5121747705373896496289774
% SZS output start Proof for 5121747705373896496289774
4. ! [X0] : ((kind(X0) | ~quiet(X0)) => (~generous(X0) & creative(X0))) [input p3]
6. ! [X0] : (wise(X0) => (~rich(X0) & tall(X0))) [input p5]
12. ! [X0] : (quiet(X0) <=> (kind(X0) & wise(X0))) [input p11]
13. ? [X0] : creative(X0) <=> (~humble(fred) & ~rich(fred)) [input p12]
25. rich(fred) [input hypothesis]
31. ! [X0] : ((~generous(X0) & creative(X0)) | (~kind(X0) & quiet(X0))) [ennf transformation 4]
33. ! [X0] : ((~rich(X0) & tall(X0)) | ~wise(X0)) [ennf transformation 6]
58. ! [X0] : ((quiet(X0) | (~kind(X0) | ~wise(X0))) & ((kind(X0) & wise(X0)) | ~quiet(X0))) [nnf transformation 12]
59. ! [X0] : ((quiet(X0) | ~kind(X0) | ~wise(X0)) & ((kind(X0) & wise(X0)) | ~quiet(X0))) [flattening 58]
60. (? [X0] : creative(X0) | (humble(fred) | rich(fred))) & ((~humble(fred) & ~rich(fred)) | ! [X0] : ~creative(X0)) [nnf transformation 13]
61. (? [X0] : creative(X0) | humble(fred) | rich(fred)) & ((~humble(fred) & ~rich(fred)) | ! [X0] : ~creative(X0)) [flattening 60]
62. (? [X0] : creative(X0) | humble(fred) | rich(fred)) & ((~humble(fred) & ~rich(fred)) | ! [X1] : ~creative(X1)) [rectify 61]
63. ? [X0] : creative(X0) => creative(sK3) [choice axiom]
64. (creative(sK3) | humble(fred) | rich(fred)) & ((~humble(fred) & ~rich(fred)) | ! [X1] : ~creative(X1)) [skolemisation 62,63]
93. creative(X0) | quiet(X0) [cnf transformation 31]
102. ~rich(X0) | ~wise(X0) [cnf transformation 33]
122. ~quiet(X0) | wise(X0) [cnf transformation 59]
125. ~rich(fred) | ~creative(X1) [cnf transformation 64]
150. rich(fred) [cnf transformation 25]
232. 18 <=> rich(fred) [avatar definition]
234. rich(fred) <- (18) [avatar component clause 232]
245. 21 <=> ! [X1] : ~creative(X1) [avatar definition]
246. ~creative(X1) <- (21) [avatar component clause 245]
248. 21 | ~18 [avatar split clause 125,232,245]
324. 18 [avatar split clause 150,232]
327. quiet(X0) <- (21) [resolution 93,246]
333. ~wise(fred) <- (18) [resolution 102,234]
334. wise(X0) <- (21) [resolution 122,327]
336. $false <- (18, 21) [resolution 334,333]
337. ~18 | ~21 [avatar contradiction clause 336]
338. $false [avatar sat refutation 248,324,337]
% SZS output end Proof for 5121747705373896496289774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and not old is not generous.
If someone is both not generous and not quiet then someone is both not curious and brave.
If paul is rich or old then alice is either not brave or not kind and vice versa.
If someone is generous or not tall then fred is either calm or not strong and vice versa.
Everyone who is not wise or calm is wise and vice versa.
If someone is both brave and not strong then someone is either not happy or tall and vice versa.
Everyone who is either not brave or not patient is quiet.
Everyone who is wise is either not curious or tall and vice versa.
Everyone who is not wise is happy and vice versa.
Everyone who is happy is not quiet and vice versa.
If someone is brave or old then lucy is not old or wise and vice versa.
If john is funny or brave then mary is not happy or old and vice versa.
If someone is both not wise and not calm then alice is both not humble and not old.
If someone is either kind or patient then someone is not kind or tall.
If john is brave then paul is patient or quiet and vice versa.
If paul is either humble or brave then someone is either quiet or not happy and vice versa.
Someone is not curious.
Someone is either tall or not kind.
Alice is not old.
Someone is either wise or not creative.
Someone is not creative.
Fred is not rich.
Mary is not kind or rich. | Fred is strong. | entailment | (![X]:((~curious(X)&~old(X))=>~generous(X)))&
((?[X]:((~generous(X)&~quiet(X))))=>(?[X]:((~curious(X)&brave(X)))))&
(((rich(paul)|old(paul)))<=>((~brave(alice)<~>~kind(alice))))&
((?[X]:((generous(X)|~tall(X))))<=>((calm(fred)<~>~strong(fred))))&
(![X]:((~wise(X)|calm(X))<=>wise(X)))&
((?[X]:((brave(X)&~strong(X))))<=>(?[X]:((~happy(X)<~>tall(X)))))&
(![X]:((~brave(X)<~>~patient(X))=>quiet(X)))&
(![X]:(wise(X)<=>(~curious(X)<~>tall(X))))&
(![X]:(~wise(X)<=>happy(X)))&
(![X]:(happy(X)<=>~quiet(X)))&
((?[X]:((brave(X)|old(X))))<=>((~old(lucy)|wise(lucy))))&
(((funny(john)|brave(john)))<=>((~happy(mary)|old(mary))))&
((?[X]:((~wise(X)&~calm(X))))=>((~humble(alice)&~old(alice))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:((~kind(X)|tall(X)))))&
((brave(john))<=>((patient(paul)|quiet(paul))))&
(((humble(paul)<~>brave(paul)))<=>(?[X]:((quiet(X)<~>~happy(X)))))&
(?[X]:(~curious(X)))&
(?[X]:((tall(X)<~>~kind(X))))&
(~old(alice))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:(~creative(X)))&
(~rich(fred))&
((~kind(mary)|rich(mary))) | strong(fred) | [
"p3",
"p4",
"p7",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7160293405690824804867909
% SZS output start Proof for 7160293405690824804867909
4. ? [X0] : (~tall(X0) | generous(X0)) <=> (calm(fred) <~> ~strong(fred)) [input p3]
5. ! [X0] : ((calm(X0) | ~wise(X0)) <=> wise(X0)) [input p4]
8. ! [X0] : (wise(X0) <=> (~curious(X0) <~> tall(X0))) [input p7]
17. ? [X0] : ~curious(X0) [input p16]
24. ~strong(fred) [input hypothesis]
39. (? [X0] : (~tall(X0) | generous(X0)) | ((calm(fred) | strong(fred)) & (~strong(fred) | ~calm(fred)))) & (((strong(fred) | ~calm(fred)) & (~strong(fred) | calm(fred))) | ! [X0] : (tall(X0) & ~generous(X0))) [nnf transformation 4]
40. (? [X0] : (~tall(X0) | generous(X0)) | ((calm(fred) | strong(fred)) & (~strong(fred) | ~calm(fred)))) & (((strong(fred) | ~calm(fred)) & (~strong(fred) | calm(fred))) | ! [X1] : (tall(X1) & ~generous(X1))) [rectify 39]
41. ? [X0] : (~tall(X0) | generous(X0)) => (~tall(sK1) | generous(sK1)) [choice axiom]
42. ((~tall(sK1) | generous(sK1)) | ((calm(fred) | strong(fred)) & (~strong(fred) | ~calm(fred)))) & (((strong(fred) | ~calm(fred)) & (~strong(fred) | calm(fred))) | ! [X1] : (tall(X1) & ~generous(X1))) [skolemisation 40,41]
43. ! [X0] : (((calm(X0) | ~wise(X0)) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [nnf transformation 5]
44. ! [X0] : ((calm(X0) | ~wise(X0) | ~wise(X0)) & (wise(X0) | (~calm(X0) & wise(X0)))) [flattening 43]
51. ! [X0] : ((wise(X0) | ((~curious(X0) | ~tall(X0)) & (tall(X0) | curious(X0)))) & (((~tall(X0) | curious(X0)) & (tall(X0) | ~curious(X0))) | ~wise(X0))) [nnf transformation 8]
71. ? [X0] : ~curious(X0) => ~curious(sK7) [choice axiom]
72. ~curious(sK7) [skolemisation 17,71]
93. strong(fred) | ~calm(fred) | tall(X1) [cnf transformation 42]
96. wise(X0) | wise(X0) [cnf transformation 44]
98. calm(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 44]
108. ~tall(X0) | curious(X0) | ~wise(X0) [cnf transformation 51]
138. ~curious(sK7) [cnf transformation 72]
147. ~strong(fred) [cnf transformation 24]
148. wise(X0) [duplicate literal removal 96]
149. ~wise(X0) | calm(X0) [duplicate literal removal 98]
186. 8 <=> strong(fred) [avatar definition]
190. 9 <=> calm(fred) [avatar definition]
191. ~calm(fred) <- (~9) [avatar component clause 190]
204. 12 <=> ! [X1] : tall(X1) [avatar definition]
205. tall(X1) <- (12) [avatar component clause 204]
206. 12 | ~9 | 8 [avatar split clause 93,186,190,204]
244. ~tall(X0) | curious(X0) [subsumption resolution 108,148]
335. ~8 [avatar split clause 147,186]
342. calm(X0) [resolution 149,148]
344. $false <- (~9) [resolution 342,191]
346. 9 [avatar contradiction clause 344]
347. curious(X0) <- (12) [resolution 205,244]
361. $false <- (12) [resolution 347,138]
365. ~12 [avatar contradiction clause 361]
366. $false [avatar sat refutation 206,335,346,365]
% SZS output end Proof for 7160293405690824804867909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or not wise is brave and vice versa.
Everyone who is rich is quiet or kind.
If someone is either not funny or not strong then fred is not old and vice versa.
Everyone who is both generous and quiet is either humble or not humble.
If someone is both not tall and happy then lucy is not patient or quiet.
Everyone who is both not patient and not rich is strong.
Everyone who is both rich and strong is both not funny and wise and vice versa.
Everyone who is both not creative and humble is either not calm or funny.
Everyone who is not kind or not old is both not old and not happy.
Everyone who is old or generous is both calm and not quiet and vice versa.
Everyone who is not quiet is not kind.
Everyone who is not quiet or patient is either not calm or brave and vice versa.
If someone is rich then someone is either creative or generous and vice versa.
If lucy is not curious then someone is both wise and not strong and vice versa.
If someone is curious or not creative then someone is not wise or not funny and vice versa.
If someone is quiet or funny then someone is not quiet or tall and vice versa.
Lucy is either not quiet or not tall.
Fred is rich.
Alice is either not funny or wise.
Someone is both creative and rich.
Someone is either not brave or wise.
Someone is patient.
Alice is not wise.
Someone is both not brave and not old. | Alice is humble. | neutral | (![X]:((strong(X)|~wise(X))<=>brave(X)))&
(![X]:(rich(X)=>(quiet(X)|kind(X))))&
((?[X]:((~funny(X)<~>~strong(X))))<=>(~old(fred)))&
(![X]:((generous(X)&quiet(X))=>(humble(X)<~>~humble(X))))&
((?[X]:((~tall(X)&happy(X))))=>((~patient(lucy)|quiet(lucy))))&
(![X]:((~patient(X)&~rich(X))=>strong(X)))&
(![X]:((rich(X)&strong(X))<=>(~funny(X)&wise(X))))&
(![X]:((~creative(X)&humble(X))=>(~calm(X)<~>funny(X))))&
(![X]:((~kind(X)|~old(X))=>(~old(X)&~happy(X))))&
(![X]:((old(X)|generous(X))<=>(calm(X)&~quiet(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((~quiet(X)|patient(X))<=>(~calm(X)<~>brave(X))))&
((?[X]:(rich(X)))<=>(?[X]:((creative(X)<~>generous(X)))))&
((~curious(lucy))<=>(?[X]:((wise(X)&~strong(X)))))&
((?[X]:((curious(X)|~creative(X))))<=>(?[X]:((~wise(X)|~funny(X)))))&
((?[X]:((quiet(X)|funny(X))))<=>(?[X]:((~quiet(X)|tall(X)))))&
((~quiet(lucy)<~>~tall(lucy)))&
(rich(fred))&
((~funny(alice)<~>wise(alice)))&
(?[X]:((creative(X)&rich(X))))&
(?[X]:((~brave(X)<~>wise(X))))&
(?[X]:(patient(X)))&
(~wise(alice))&
(?[X]:((~brave(X)&~old(X)))) | humble(alice) | [] | null | 0 |
If susan is either not humble or not creative then someone is both strong and not strong.
Everyone who is not happy or not patient is both humble and creative.
If someone is brave then fred is either happy or kind and vice versa.
If someone is not generous or old then someone is rich or happy.
Everyone who is not kind or not strong is happy or not funny.
If someone is kind then paul is not quiet.
Everyone who is not rich is generous and vice versa.
Everyone who is either not funny or not patient is not strong or old and vice versa.
If susan is both wise and not strong then susan is wise or not rich.
If mary is either not creative or not strong then someone is both old and not curious.
Everyone who is both tall and creative is both old and not quiet.
Everyone who is both not happy and calm is both not wise and not kind.
Everyone who is not happy is not generous or not strong and vice versa.
Everyone who is both not old and generous is either brave or happy.
Everyone who is either not kind or not happy is not creative and vice versa.
Everyone who is not funny is not old or old.
Paul is either funny or creative.
Alice is not creative.
Fred is both funny and curious.
John is generous.
Alice is not old.
Mary is not funny.
Someone is not happy.
Someone is both funny and not old. | John is not rich. | entailment | (((~humble(susan)<~>~creative(susan)))=>(?[X]:((strong(X)&~strong(X)))))&
(![X]:((~happy(X)|~patient(X))=>(humble(X)&creative(X))))&
((?[X]:(brave(X)))<=>((happy(fred)<~>kind(fred))))&
((?[X]:((~generous(X)|old(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~kind(X)|~strong(X))=>(happy(X)|~funny(X))))&
((?[X]:(kind(X)))=>(~quiet(paul)))&
(![X]:(~rich(X)<=>generous(X)))&
(![X]:((~funny(X)<~>~patient(X))<=>(~strong(X)|old(X))))&
(((wise(susan)&~strong(susan)))=>((wise(susan)|~rich(susan))))&
(((~creative(mary)<~>~strong(mary)))=>(?[X]:((old(X)&~curious(X)))))&
(![X]:((tall(X)&creative(X))=>(old(X)&~quiet(X))))&
(![X]:((~happy(X)&calm(X))=>(~wise(X)&~kind(X))))&
(![X]:(~happy(X)<=>(~generous(X)|~strong(X))))&
(![X]:((~old(X)&generous(X))=>(brave(X)<~>happy(X))))&
(![X]:((~kind(X)<~>~happy(X))<=>~creative(X)))&
(![X]:(~funny(X)=>(~old(X)|old(X))))&
((funny(paul)<~>creative(paul)))&
(~creative(alice))&
((funny(fred)&curious(fred)))&
(generous(john))&
(~old(alice))&
(~funny(mary))&
(?[X]:(~happy(X)))&
(?[X]:((funny(X)&~old(X)))) | ~rich(john) | [
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3653233882511290095370080
% SZS output start Proof for 3653233882511290095370080
7. ! [X0] : (~rich(X0) <=> generous(X0)) [input p6]
20. generous(john) [input p19]
25. rich(john) [input hypothesis]
52. ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))) [nnf transformation 7]
84. ~rich(X0) | ~generous(X0) [cnf transformation 52]
111. generous(john) [cnf transformation 20]
117. rich(john) [cnf transformation 25]
206. ~generous(john) [resolution 84,117]
209. $false [subsumption resolution 206,111]
% SZS output end Proof for 3653233882511290095370080
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not patient is either wise or happy and vice versa.
Everyone who is creative or calm is not kind and vice versa.
Everyone who is either not tall or not curious is not creative or humble and vice versa.
Everyone who is not creative or not brave is not creative.
Everyone who is either patient or not rich is not calm or creative.
Everyone who is both not kind and not rich is either kind or humble and vice versa.
Everyone who is either creative or not humble is humble or patient and vice versa.
Everyone who is funny or not tall is not humble or patient and vice versa.
Everyone who is either not brave or not old is both not brave and kind.
If lucy is both quiet and not rich then fred is not funny.
Everyone who is not funny or rich is either not tall or wise and vice versa.
If mary is both not patient and humble then paul is either humble or happy and vice versa.
Everyone who is both not calm and not strong is both tall and not humble.
If fred is either not humble or rich then mary is either not brave or not old and vice versa.
If susan is wise then someone is either not rich or not tall.
If john is both tall and not generous then john is both not creative and humble and vice versa.
Someone is not tall or not strong.
Someone is not humble or not strong.
Lucy is either funny or not rich.
Lucy is both curious and rich.
Someone is either wise or not strong.
Someone is either patient or not curious.
Someone is old. | John is not strong. | neutral | (![X]:((quiet(X)|~patient(X))<=>(wise(X)<~>happy(X))))&
(![X]:((creative(X)|calm(X))<=>~kind(X)))&
(![X]:((~tall(X)<~>~curious(X))<=>(~creative(X)|humble(X))))&
(![X]:((~creative(X)|~brave(X))=>~creative(X)))&
(![X]:((patient(X)<~>~rich(X))=>(~calm(X)|creative(X))))&
(![X]:((~kind(X)&~rich(X))<=>(kind(X)<~>humble(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(humble(X)|patient(X))))&
(![X]:((funny(X)|~tall(X))<=>(~humble(X)|patient(X))))&
(![X]:((~brave(X)<~>~old(X))=>(~brave(X)&kind(X))))&
(((quiet(lucy)&~rich(lucy)))=>(~funny(fred)))&
(![X]:((~funny(X)|rich(X))<=>(~tall(X)<~>wise(X))))&
(((~patient(mary)&humble(mary)))<=>((humble(paul)<~>happy(paul))))&
(![X]:((~calm(X)&~strong(X))=>(tall(X)&~humble(X))))&
(((~humble(fred)<~>rich(fred)))<=>((~brave(mary)<~>~old(mary))))&
((wise(susan))=>(?[X]:((~rich(X)<~>~tall(X)))))&
(((tall(john)&~generous(john)))<=>((~creative(john)&humble(john))))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:((~humble(X)|~strong(X))))&
((funny(lucy)<~>~rich(lucy)))&
((curious(lucy)&rich(lucy)))&
(?[X]:((wise(X)<~>~strong(X))))&
(?[X]:((patient(X)<~>~curious(X))))&
(?[X]:(old(X))) | ~strong(john) | [] | null | 0 |
Everyone who is both not rich and strong is not creative.
If lucy is either not humble or not rich then susan is either not funny or brave.
Everyone who is both not generous and not calm is tall or strong.
Everyone who is not calm is old and vice versa.
If lucy is both strong and generous then paul is kind and vice versa.
Everyone who is both not brave and quiet is humble and vice versa.
Everyone who is not rich or calm is both wise and humble and vice versa.
If someone is either kind or not wise then paul is old or not kind.
If someone is either not rich or not strong then john is calm.
If someone is either not tall or not generous then someone is not kind or happy.
Everyone who is either creative or generous is either not patient or not strong and vice versa.
If mary is both tall and not patient then paul is both not patient and not wise and vice versa.
If alice is both not quiet and generous then someone is either rich or not rich.
Everyone who is not calm or not kind is not old and vice versa.
Everyone who is both patient and not happy is either old or generous.
If someone is quiet then alice is both not tall and generous.
Lucy is not wise or wise.
Paul is not old.
John is wise.
Paul is both tall and happy.
Someone is either rich or creative.
Fred is not curious or not humble. | John is not quiet. | contradiction | (![X]:((~rich(X)&strong(X))=>~creative(X)))&
(((~humble(lucy)<~>~rich(lucy)))=>((~funny(susan)<~>brave(susan))))&
(![X]:((~generous(X)&~calm(X))=>(tall(X)|strong(X))))&
(![X]:(~calm(X)<=>old(X)))&
(((strong(lucy)&generous(lucy)))<=>(kind(paul)))&
(![X]:((~brave(X)&quiet(X))<=>humble(X)))&
(![X]:((~rich(X)|calm(X))<=>(wise(X)&humble(X))))&
((?[X]:((kind(X)<~>~wise(X))))=>((old(paul)|~kind(paul))))&
((?[X]:((~rich(X)<~>~strong(X))))=>(calm(john)))&
((?[X]:((~tall(X)<~>~generous(X))))=>(?[X]:((~kind(X)|happy(X)))))&
(![X]:((creative(X)<~>generous(X))<=>(~patient(X)<~>~strong(X))))&
(((tall(mary)&~patient(mary)))<=>((~patient(paul)&~wise(paul))))&
(((~quiet(alice)&generous(alice)))=>(?[X]:((rich(X)<~>~rich(X)))))&
(![X]:((~calm(X)|~kind(X))<=>~old(X)))&
(![X]:((patient(X)&~happy(X))=>(old(X)<~>generous(X))))&
((?[X]:(quiet(X)))=>((~tall(alice)&generous(alice))))&
((~wise(lucy)|wise(lucy)))&
(~old(paul))&
(wise(john))&
((tall(paul)&happy(paul)))&
(?[X]:((rich(X)<~>creative(X))))&
((~curious(fred)|~humble(fred))) | ~quiet(john) | [
"p3",
"p5",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7166827359812557466326959
% SZS output start Proof for 7166827359812557466326959
4. ! [X0] : (~calm(X0) <=> old(X0)) [input p3]
6. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> humble(X0)) [input p5]
7. ! [X0] : ((calm(X0) | ~rich(X0)) <=> (humble(X0) & wise(X0))) [input p6]
14. ! [X0] : ((~kind(X0) | ~calm(X0)) <=> ~old(X0)) [input p13]
23. ~quiet(john) [input hypothesis]
41. ! [X0] : ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0))) [nnf transformation 4]
44. ! [X0] : (((quiet(X0) & ~brave(X0)) | ~humble(X0)) & (humble(X0) | (~quiet(X0) | brave(X0)))) [nnf transformation 6]
45. ! [X0] : (((quiet(X0) & ~brave(X0)) | ~humble(X0)) & (humble(X0) | ~quiet(X0) | brave(X0))) [flattening 44]
46. ! [X0] : (((calm(X0) | ~rich(X0)) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | (~calm(X0) & rich(X0)))) [nnf transformation 7]
47. ! [X0] : ((calm(X0) | ~rich(X0) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | (~calm(X0) & rich(X0)))) [flattening 46]
56. ! [X0] : (((~kind(X0) | ~calm(X0)) | old(X0)) & (~old(X0) | (kind(X0) & calm(X0)))) [nnf transformation 14]
57. ! [X0] : ((~kind(X0) | ~calm(X0) | old(X0)) & (~old(X0) | (kind(X0) & calm(X0)))) [flattening 56]
67. old(X0) | calm(X0) [cnf transformation 41]
68. ~old(X0) | ~calm(X0) [cnf transformation 41]
74. ~humble(X0) | quiet(X0) [cnf transformation 45]
78. ~calm(X0) | humble(X0) [cnf transformation 47]
98. ~old(X0) | calm(X0) [cnf transformation 57]
109. ~quiet(john) [cnf transformation 23]
161. 12 <=> calm(john) [avatar definition]
162. ~calm(john) <- (~12) [avatar component clause 161]
163. calm(john) <- (12) [avatar component clause 161]
190. ~old(X0) [subsumption resolution 98,68]
214. calm(X0) [resolution 67,190]
223. humble(john) <- (12) [resolution 78,163]
225. quiet(john) <- (12) [resolution 223,74]
226. $false <- (12) [subsumption resolution 225,109]
227. ~12 [avatar contradiction clause 226]
228. $false <- (~12) [subsumption resolution 162,214]
229. 12 [avatar contradiction clause 228]
231. $false [avatar sat refutation 227,229]
% SZS output end Proof for 7166827359812557466326959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or curious is not creative. Everyone who is both funny and kind is either not wise or not quiet. Everyone who is funny is not brave. If paul is not funny then mary is not kind or quiet. If someone is generous or happy then mary is both not wise and quiet and vice versa. Everyone who is patient is quiet and vice versa. Everyone who is tall or rich is either not funny or humble. Everyone who is humble is wise or happy. If someone is either generous or not calm then paul is both patient and not strong. Everyone who is old is either strong or not humble and vice versa. Everyone who is tall is both not brave and not curious. Everyone who is not old or creative is either tall or not humble. Everyone who is either not rich or tall is both generous and calm and vice versa. Everyone who is not wise is both calm and not tall. Everyone who is funny or creative is not tall and vice versa. Everyone who is happy is curious or kind. Paul is tall. Fred is both not funny and tall. Mary is calm. Someone is not creative or humble. Alice is patient or not humble. Fred is either brave or not funny. Someone is not rich. Mary is either not funny or brave. | Alice is not brave. | neutral | (![X]:((~rich(X)|curious(X))=>~creative(X)))&
(![X]:((funny(X)&kind(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:(funny(X)=>~brave(X)))&
((~funny(paul))=>((~kind(mary)|quiet(mary))))&
((?[X]:((generous(X)|happy(X))))<=>((~wise(mary)&quiet(mary))))&
(![X]:(patient(X)<=>quiet(X)))&
(![X]:((tall(X)|rich(X))=>(~funny(X)<~>humble(X))))&
(![X]:(humble(X)=>(wise(X)|happy(X))))&
((?[X]:((generous(X)<~>~calm(X))))=>((patient(paul)&~strong(paul))))&
(![X]:(old(X)<=>(strong(X)<~>~humble(X))))&
(![X]:(tall(X)=>(~brave(X)&~curious(X))))&
(![X]:((~old(X)|creative(X))=>(tall(X)<~>~humble(X))))&
(![X]:((~rich(X)<~>tall(X))<=>(generous(X)&calm(X))))&
(![X]:(~wise(X)=>(calm(X)&~tall(X))))&
(![X]:((funny(X)|creative(X))<=>~tall(X)))&
(![X]:(happy(X)=>(curious(X)|kind(X))))&
(tall(paul))&
((~funny(fred)&tall(fred)))&
(calm(mary))&
(?[X]:((~creative(X)|humble(X))))&
((patient(alice)|~humble(alice)))&
((brave(fred)<~>~funny(fred)))&
(?[X]:(~rich(X)))&
((~funny(mary)<~>brave(mary))) | ~brave(alice) | [] | null | 0 |
If someone is either strong or not happy then someone is both curious and strong and vice versa.
Everyone who is generous is both rich and humble.
If lucy is rich then someone is both not calm and not kind and vice versa.
If someone is not wise then someone is curious or not brave and vice versa.
Everyone who is not wise is both kind and quiet.
Everyone who is not quiet or not happy is calm or happy and vice versa.
Everyone who is both not strong and not tall is both strong and brave and vice versa.
If someone is tall or generous then susan is happy.
Everyone who is not happy is not patient or happy.
Everyone who is either wise or not patient is not quiet.
If someone is both not tall and patient then someone is both not old and not funny.
If someone is both not funny and kind then fred is both not quiet and not kind and vice versa.
Everyone who is not strong is happy or not generous and vice versa.
Everyone who is both quiet and humble is both not calm and not rich.
If john is either not generous or humble then susan is either not humble or not kind.
If paul is both strong and not kind then someone is generous.
Alice is not quiet or not kind.
Someone is either not creative or rich.
Someone is either brave or curious.
Alice is brave or calm.
Lucy is not quiet or not generous.
Alice is kind or not old.
Someone is tall. | Paul is strong. | contradiction | ((?[X]:((strong(X)<~>~happy(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(![X]:(generous(X)=>(rich(X)&humble(X))))&
((rich(lucy))<=>(?[X]:((~calm(X)&~kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((curious(X)|~brave(X)))))&
(![X]:(~wise(X)=>(kind(X)&quiet(X))))&
(![X]:((~quiet(X)|~happy(X))<=>(calm(X)|happy(X))))&
(![X]:((~strong(X)&~tall(X))<=>(strong(X)&brave(X))))&
((?[X]:((tall(X)|generous(X))))=>(happy(susan)))&
(![X]:(~happy(X)=>(~patient(X)|happy(X))))&
(![X]:((wise(X)<~>~patient(X))=>~quiet(X)))&
((?[X]:((~tall(X)&patient(X))))=>(?[X]:((~old(X)&~funny(X)))))&
((?[X]:((~funny(X)&kind(X))))<=>((~quiet(fred)&~kind(fred))))&
(![X]:(~strong(X)<=>(happy(X)|~generous(X))))&
(![X]:((quiet(X)&humble(X))=>(~calm(X)&~rich(X))))&
(((~generous(john)<~>humble(john)))=>((~humble(susan)<~>~kind(susan))))&
(((strong(paul)&~kind(paul)))=>(?[X]:(generous(X))))&
((~quiet(alice)|~kind(alice)))&
(?[X]:((~creative(X)<~>rich(X))))&
(?[X]:((brave(X)<~>curious(X))))&
((brave(alice)|calm(alice)))&
((~quiet(lucy)|~generous(lucy)))&
((kind(alice)|~old(alice)))&
(?[X]:(tall(X))) | strong(paul) | [
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1233303883666394402132751
% SZS output start Proof for 1233303883666394402132751
4. ? [X0] : ~wise(X0) <=> ? [X0] : (~brave(X0) | curious(X0)) [input p3]
5. ! [X0] : (~wise(X0) => (quiet(X0) & kind(X0))) [input p4]
6. ! [X0] : ((~happy(X0) | ~quiet(X0)) <=> (happy(X0) | calm(X0))) [input p5]
7. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (brave(X0) & strong(X0))) [input p6]
9. ! [X0] : (~happy(X0) => (happy(X0) | ~patient(X0))) [input p8]
10. ! [X0] : ((wise(X0) <~> ~patient(X0)) => ~quiet(X0)) [input p9]
24. strong(paul) [input hypothesis]
26. ? [X0] : ~wise(X0) <=> ? [X1] : (~brave(X1) | curious(X1)) [rectify 4]
31. ! [X0] : ((quiet(X0) & kind(X0)) | wise(X0)) [ennf transformation 5]
33. ! [X0] : ((happy(X0) | ~patient(X0)) | happy(X0)) [ennf transformation 9]
34. ! [X0] : (happy(X0) | ~patient(X0) | happy(X0)) [flattening 33]
35. ! [X0] : (~quiet(X0) | (wise(X0) <=> ~patient(X0))) [ennf transformation 10]
51. (? [X0] : ~wise(X0) | ! [X1] : (brave(X1) & ~curious(X1))) & (? [X1] : (~brave(X1) | curious(X1)) | ! [X0] : wise(X0)) [nnf transformation 26]
52. (? [X0] : ~wise(X0) | ! [X1] : (brave(X1) & ~curious(X1))) & (? [X2] : (~brave(X2) | curious(X2)) | ! [X3] : wise(X3)) [rectify 51]
53. ? [X0] : ~wise(X0) => ~wise(sK3) [choice axiom]
54. ? [X2] : (~brave(X2) | curious(X2)) => (~brave(sK4) | curious(sK4)) [choice axiom]
55. (~wise(sK3) | ! [X1] : (brave(X1) & ~curious(X1))) & ((~brave(sK4) | curious(sK4)) | ! [X3] : wise(X3)) [skolemisation 52,54,53]
56. ! [X0] : (((~happy(X0) | ~quiet(X0)) | (~happy(X0) & ~calm(X0))) & ((happy(X0) | calm(X0)) | (happy(X0) & quiet(X0)))) [nnf transformation 6]
57. ! [X0] : ((~happy(X0) | ~quiet(X0) | (~happy(X0) & ~calm(X0))) & (happy(X0) | calm(X0) | (happy(X0) & quiet(X0)))) [flattening 56]
58. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~brave(X0) | ~strong(X0))) & ((brave(X0) & strong(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 7]
59. ! [X0] : (((~tall(X0) & ~strong(X0)) | ~brave(X0) | ~strong(X0)) & ((brave(X0) & strong(X0)) | tall(X0) | strong(X0))) [flattening 58]
60. ! [X0] : (~quiet(X0) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0)))) [nnf transformation 35]
95. ~wise(sK3) | brave(X1) [cnf transformation 55]
97. quiet(X0) | wise(X0) [cnf transformation 31]
101. ~happy(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 57]
104. ~strong(X0) | ~brave(X0) | ~strong(X0) [cnf transformation 59]
108. happy(X0) | ~patient(X0) | happy(X0) [cnf transformation 34]
110. ~quiet(X0) | wise(X0) | patient(X0) [cnf transformation 60]
134. strong(paul) [cnf transformation 24]
135. ~patient(X0) | happy(X0) [duplicate literal removal 108]
137. ~brave(X0) | ~strong(X0) [duplicate literal removal 104]
139. ~quiet(X0) | ~happy(X0) [duplicate literal removal 101]
190. 12 <=> ! [X1] : brave(X1) [avatar definition]
191. brave(X1) <- (12) [avatar component clause 190]
193. 13 <=> wise(sK3) [avatar definition]
195. ~wise(sK3) <- (~13) [avatar component clause 193]
196. 12 | ~13 [avatar split clause 95,193,190]
202. 15 <=> ! [X3] : wise(X3) [avatar definition]
203. wise(X3) <- (15) [avatar component clause 202]
225. patient(X0) | wise(X0) [subsumption resolution 110,97]
283. 32 <=> strong(paul) [avatar definition]
284. strong(paul) <- (32) [avatar component clause 283]
342. 32 [avatar split clause 134,283]
351. ~happy(X0) | wise(X0) [resolution 139,97]
364. wise(X0) | happy(X0) [resolution 225,135]
365. wise(X0) [subsumption resolution 364,351]
366. 15 [avatar split clause 365,202]
367. $false <- (~13, 15) [resolution 203,195]
368. 13 | ~15 [avatar contradiction clause 367]
370. ~strong(X0) <- (12) [resolution 191,137]
379. $false <- (12, 32) [resolution 370,284]
382. ~12 | ~32 [avatar contradiction clause 379]
383. $false [avatar sat refutation 196,342,366,368,382]
% SZS output end Proof for 1233303883666394402132751
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is patient or not humble then someone is not brave or curious and vice versa.
If someone is creative then susan is either strong or calm and vice versa.
If someone is both not calm and rich then someone is not strong.
If alice is either rich or not humble then susan is not strong or not generous and vice versa.
If mary is both generous and kind then mary is happy or not calm.
If fred is creative then someone is both old and not rich and vice versa.
Everyone who is both creative and not curious is not strong or wise.
If lucy is either not humble or not tall then john is either not creative or not rich and vice versa.
Everyone who is not wise or not funny is either generous or patient and vice versa.
If someone is quiet or not calm then someone is either happy or not wise.
Everyone who is either humble or not strong is not funny or quiet.
If someone is either not tall or old then someone is not calm or not humble.
Everyone who is not quiet or not generous is not creative or wise and vice versa.
Everyone who is either generous or wise is either happy or strong.
Everyone who is quiet or kind is generous.
Everyone who is not wise or not calm is not quiet.
Paul is both humble and not curious.
Fred is either not rich or humble.
Someone is both wise and not rich.
Fred is either patient or quiet. | Susan is patient. | neutral | (((patient(lucy)|~humble(lucy)))<=>(?[X]:((~brave(X)|curious(X)))))&
((?[X]:(creative(X)))<=>((strong(susan)<~>calm(susan))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:(~strong(X))))&
(((rich(alice)<~>~humble(alice)))<=>((~strong(susan)|~generous(susan))))&
(((generous(mary)&kind(mary)))=>((happy(mary)|~calm(mary))))&
((creative(fred))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))&
(((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))&
(![X]:((quiet(X)|kind(X))=>generous(X)))&
(![X]:((~wise(X)|~calm(X))=>~quiet(X)))&
((humble(paul)&~curious(paul)))&
((~rich(fred)<~>humble(fred)))&
(?[X]:((wise(X)&~rich(X))))&
((patient(fred)<~>quiet(fred))) | patient(susan) | [] | null | 0 |
Everyone who is not strong or quiet is rich or strong and vice versa.
If fred is brave or generous then susan is either kind or rich.
Everyone who is old or tall is kind and vice versa.
Everyone who is both wise and not humble is kind and vice versa.
If john is funny or not curious then someone is both not calm and not patient.
Everyone who is not quiet or generous is either creative or tall and vice versa.
Everyone who is both kind and not happy is generous or happy and vice versa.
If lucy is either not creative or not happy then someone is quiet and vice versa.
Everyone who is funny is not humble and vice versa.
If someone is either not tall or funny then someone is not brave and vice versa.
Everyone who is either not kind or happy is not brave.
If someone is both curious and not quiet then someone is not strong and vice versa.
Everyone who is not quiet is both not tall and not kind.
Everyone who is tall is not curious or generous and vice versa.
Everyone who is not quiet or not creative is not tall.
If alice is not patient then someone is either kind or not tall.
Paul is not happy.
Susan is not funny or generous.
Someone is humble or not patient.
Someone is either not humble or quiet.
Someone is not tall or brave. | Susan is not humble. | contradiction | (![X]:((~strong(X)|quiet(X))<=>(rich(X)|strong(X))))&
(((brave(fred)|generous(fred)))=>((kind(susan)<~>rich(susan))))&
(![X]:((old(X)|tall(X))<=>kind(X)))&
(![X]:((wise(X)&~humble(X))<=>kind(X)))&
(((funny(john)|~curious(john)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(creative(X)<~>tall(X))))&
(![X]:((kind(X)&~happy(X))<=>(generous(X)|happy(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(funny(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>~brave(X)))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~kind(X))))&
(![X]:(tall(X)<=>(~curious(X)|generous(X))))&
(![X]:((~quiet(X)|~creative(X))=>~tall(X)))&
((~patient(alice))=>(?[X]:((kind(X)<~>~tall(X)))))&
(~happy(paul))&
((~funny(susan)|generous(susan)))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~tall(X)|brave(X)))) | ~humble(susan) | [
"p5",
"p8",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 67612277499109552488798
% SZS output start Proof for 67612277499109552488798
6. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (creative(X0) <~> tall(X0))) [input p5]
9. ! [X0] : (funny(X0) <=> ~humble(X0)) [input p8]
14. ! [X0] : (tall(X0) <=> (generous(X0) | ~curious(X0))) [input p13]
15. ! [X0] : ((~creative(X0) | ~quiet(X0)) => ~tall(X0)) [input p14]
18. generous(susan) | ~funny(susan) [input p17]
22. ~humble(susan) [input hypothesis]
30. ! [X0] : (~tall(X0) | (creative(X0) & quiet(X0))) [ennf transformation 15]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [nnf transformation 6]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [flattening 41]
49. ! [X0] : ((funny(X0) | humble(X0)) & (~humble(X0) | ~funny(X0))) [nnf transformation 9]
61. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | ~tall(X0))) [flattening 61]
92. ~creative(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 42]
105. funny(X0) | humble(X0) [cnf transformation 49]
119. ~generous(X0) | tall(X0) [cnf transformation 62]
121. ~tall(X0) | creative(X0) [cnf transformation 30]
125. generous(susan) | ~funny(susan) [cnf transformation 18]
130. ~humble(susan) [cnf transformation 22]
246. 25 <=> funny(susan) [avatar definition]
248. ~funny(susan) <- (~25) [avatar component clause 246]
250. 26 <=> generous(susan) [avatar definition]
252. generous(susan) <- (26) [avatar component clause 250]
253. ~25 | 26 [avatar split clause 125,250,246]
285. humble(susan) <- (~25) [resolution 105,248]
287. $false <- (~25) [subsumption resolution 285,130]
288. 25 [avatar contradiction clause 287]
297. tall(susan) <- (26) [resolution 119,252]
298. creative(susan) <- (26) [resolution 297,121]
312. ~tall(susan) | ~generous(susan) <- (26) [resolution 92,298]
315. ~generous(susan) <- (26) [subsumption resolution 312,297]
316. $false <- (26) [subsumption resolution 315,252]
317. ~26 [avatar contradiction clause 316]
318. $false [avatar sat refutation 253,288,317]
% SZS output end Proof for 67612277499109552488798
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both not humble and quiet then alice is both not humble and not generous.
Everyone who is rich is not rich.
Everyone who is generous is both not brave and calm and vice versa.
If someone is calm or creative then fred is either not curious or happy.
If fred is wise then someone is not humble or not wise.
Everyone who is not rich or kind is either wise or not humble and vice versa.
If someone is both not patient and not brave then lucy is both quiet and not brave and vice versa.
If alice is not old then fred is wise and vice versa.
If someone is both curious and humble then someone is either generous or brave and vice versa.
If someone is either not generous or quiet then alice is brave or quiet and vice versa.
Everyone who is either not brave or humble is not old and vice versa.
Everyone who is either old or not rich is not quiet and vice versa.
Everyone who is either wise or quiet is happy.
If lucy is either not happy or not quiet then fred is tall.
Everyone who is both patient and not funny is both not happy and quiet.
If lucy is either creative or tall then someone is not patient or patient and vice versa.
Fred is both funny and strong.
Mary is both brave and calm.
Someone is wise or creative.
Someone is brave.
Susan is both curious and funny.
Mary is curious or not patient.
Someone is both strong and wise.
John is both not kind and patient. | Alice is quiet. | neutral | (((~humble(lucy)&quiet(lucy)))=>((~humble(alice)&~generous(alice))))&
(![X]:(rich(X)=>~rich(X)))&
(![X]:(generous(X)<=>(~brave(X)&calm(X))))&
((?[X]:((calm(X)|creative(X))))=>((~curious(fred)<~>happy(fred))))&
((wise(fred))=>(?[X]:((~humble(X)|~wise(X)))))&
(![X]:((~rich(X)|kind(X))<=>(wise(X)<~>~humble(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>((quiet(lucy)&~brave(lucy))))&
((~old(alice))<=>(wise(fred)))&
((?[X]:((curious(X)&humble(X))))<=>(?[X]:((generous(X)<~>brave(X)))))&
((?[X]:((~generous(X)<~>quiet(X))))<=>((brave(alice)|quiet(alice))))&
(![X]:((~brave(X)<~>humble(X))<=>~old(X)))&
(![X]:((old(X)<~>~rich(X))<=>~quiet(X)))&
(![X]:((wise(X)<~>quiet(X))=>happy(X)))&
(((~happy(lucy)<~>~quiet(lucy)))=>(tall(fred)))&
(![X]:((patient(X)&~funny(X))=>(~happy(X)&quiet(X))))&
(((creative(lucy)<~>tall(lucy)))<=>(?[X]:((~patient(X)|patient(X)))))&
((funny(fred)&strong(fred)))&
((brave(mary)&calm(mary)))&
(?[X]:((wise(X)|creative(X))))&
(?[X]:(brave(X)))&
((curious(susan)&funny(susan)))&
((curious(mary)|~patient(mary)))&
(?[X]:((strong(X)&wise(X))))&
((~kind(john)&patient(john))) | quiet(alice) | [] | null | 0 |
Everyone who is both not calm and calm is quiet.
Everyone who is brave is either not humble or wise and vice versa.
If alice is tall or wise then someone is both curious and not strong and vice versa.
Everyone who is both not happy and not wise is not humble.
Everyone who is both creative and not tall is patient or not quiet.
If someone is not kind then someone is both kind and calm and vice versa.
If someone is not rich or not humble then paul is not creative or funny and vice versa.
If someone is wise then alice is calm or not generous and vice versa.
Everyone who is kind or humble is both tall and not generous.
If mary is either curious or not old then lucy is both brave and not brave.
If someone is not calm or generous then alice is generous or not humble and vice versa.
Everyone who is both not rich and humble is not strong.
Everyone who is both not happy and not brave is either curious or not humble.
If someone is both tall and not strong then lucy is either curious or not kind and vice versa.
If someone is either not creative or rich then susan is creative or not funny.
Everyone who is both not curious and happy is either creative or quiet.
John is kind or calm.
Lucy is both humble and tall.
Susan is both kind and wise.
Someone is both rich and not patient.
Someone is either not generous or brave.
Mary is both patient and curious.
Someone is either not tall or brave. | Lucy is not generous. | entailment | (![X]:((~calm(X)&calm(X))=>quiet(X)))&
(![X]:(brave(X)<=>(~humble(X)<~>wise(X))))&
(((tall(alice)|wise(alice)))<=>(?[X]:((curious(X)&~strong(X)))))&
(![X]:((~happy(X)&~wise(X))=>~humble(X)))&
(![X]:((creative(X)&~tall(X))=>(patient(X)|~quiet(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((kind(X)&calm(X)))))&
((?[X]:((~rich(X)|~humble(X))))<=>((~creative(paul)|funny(paul))))&
((?[X]:(wise(X)))<=>((calm(alice)|~generous(alice))))&
(![X]:((kind(X)|humble(X))=>(tall(X)&~generous(X))))&
(((curious(mary)<~>~old(mary)))=>((brave(lucy)&~brave(lucy))))&
((?[X]:((~calm(X)|generous(X))))<=>((generous(alice)|~humble(alice))))&
(![X]:((~rich(X)&humble(X))=>~strong(X)))&
(![X]:((~happy(X)&~brave(X))=>(curious(X)<~>~humble(X))))&
((?[X]:((tall(X)&~strong(X))))<=>((curious(lucy)<~>~kind(lucy))))&
((?[X]:((~creative(X)<~>rich(X))))=>((creative(susan)|~funny(susan))))&
(![X]:((~curious(X)&happy(X))=>(creative(X)<~>quiet(X))))&
((kind(john)|calm(john)))&
((humble(lucy)&tall(lucy)))&
((kind(susan)&wise(susan)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
((patient(mary)&curious(mary)))&
(?[X]:((~tall(X)<~>brave(X)))) | ~generous(lucy) | [
"p8",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6421128111311628818747957
% SZS output start Proof for 6421128111311628818747957
9. ! [X0] : ((humble(X0) | kind(X0)) => (~generous(X0) & tall(X0))) [input p8]
18. tall(lucy) & humble(lucy) [input p17]
24. generous(lucy) [input hypothesis]
32. ! [X0] : ((~generous(X0) & tall(X0)) | (~humble(X0) & ~kind(X0))) [ennf transformation 9]
109. ~generous(X0) | ~humble(X0) [cnf transformation 32]
132. humble(lucy) [cnf transformation 18]
144. generous(lucy) [cnf transformation 24]
352. ~humble(lucy) [resolution 109,144]
353. $false [subsumption resolution 352,132]
% SZS output end Proof for 6421128111311628818747957
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or happy is both not strong and not curious and vice versa.
Everyone who is both wise and strong is not humble or humble.
If someone is humble or curious then lucy is curious and vice versa.
If fred is not wise then someone is both not humble and old and vice versa.
Everyone who is both strong and not generous is not happy or not strong.
Everyone who is both not wise and wise is wise or not quiet.
Everyone who is both not humble and not tall is both calm and not funny and vice versa.
Everyone who is either curious or not quiet is either not old or calm and vice versa.
If someone is not strong or not creative then someone is humble and vice versa.
If fred is both calm and old then someone is not old or not humble.
Everyone who is either not humble or patient is not wise.
Everyone who is either not rich or not tall is tall or calm and vice versa.
Everyone who is both not happy and not wise is not calm and vice versa.
If someone is not patient then susan is both rich and not tall and vice versa.
Everyone who is tall is either not rich or quiet.
If someone is either wise or curious then someone is not funny or not curious.
Lucy is both not brave and not curious.
Someone is either not creative or tall.
Someone is curious or tall.
Someone is not calm.
Someone is not wise.
Someone is not rich. | Susan is not funny. | neutral | (![X]:((old(X)|happy(X))<=>(~strong(X)&~curious(X))))&
(![X]:((wise(X)&strong(X))=>(~humble(X)|humble(X))))&
((?[X]:((humble(X)|curious(X))))<=>(curious(lucy)))&
((~wise(fred))<=>(?[X]:((~humble(X)&old(X)))))&
(![X]:((strong(X)&~generous(X))=>(~happy(X)|~strong(X))))&
(![X]:((~wise(X)&wise(X))=>(wise(X)|~quiet(X))))&
(![X]:((~humble(X)&~tall(X))<=>(calm(X)&~funny(X))))&
(![X]:((curious(X)<~>~quiet(X))<=>(~old(X)<~>calm(X))))&
((?[X]:((~strong(X)|~creative(X))))<=>(?[X]:(humble(X))))&
(((calm(fred)&old(fred)))=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:((~humble(X)<~>patient(X))=>~wise(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(tall(X)|calm(X))))&
(![X]:((~happy(X)&~wise(X))<=>~calm(X)))&
((?[X]:(~patient(X)))<=>((rich(susan)&~tall(susan))))&
(![X]:(tall(X)=>(~rich(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>curious(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
((~brave(lucy)&~curious(lucy)))&
(?[X]:((~creative(X)<~>tall(X))))&
(?[X]:((curious(X)|tall(X))))&
(?[X]:(~calm(X)))&
(?[X]:(~wise(X)))&
(?[X]:(~rich(X))) | ~funny(susan) | [] | null | 0 |
If mary is calm then alice is either not kind or not rich. Everyone who is both generous and not tall is not curious and vice versa. If someone is humble or not creative then someone is both old and not old. Everyone who is old is both kind and strong. Everyone who is not generous or not creative is both not generous and brave. If someone is quiet then alice is either not humble or wise. Everyone who is either funny or rich is strong and vice versa. If lucy is not quiet then fred is both not creative and not strong. If someone is not strong then someone is not patient or not happy and vice versa. Everyone who is either generous or tall is both strong and creative and vice versa. If someone is kind or brave then alice is either not wise or rich and vice versa. If fred is not wise or not quiet then alice is both not creative and rich. If susan is wise or happy then someone is calm and vice versa. Everyone who is not calm is either quiet or patient. If someone is wise then mary is either not wise or not happy. If lucy is not old then someone is either old or not brave. Someone is either curious or brave. Mary is not strong. Fred is tall. Someone is either funny or not wise. Someone is either not old or not rich. Someone is not kind or calm. Someone is both creative and funny. Someone is strong or not old. | Fred is creative. | entailment | ((calm(mary))=>((~kind(alice)<~>~rich(alice))))&
(![X]:((generous(X)&~tall(X))<=>~curious(X)))&
((?[X]:((humble(X)|~creative(X))))=>(?[X]:((old(X)&~old(X)))))&
(![X]:(old(X)=>(kind(X)&strong(X))))&
(![X]:((~generous(X)|~creative(X))=>(~generous(X)&brave(X))))&
((?[X]:(quiet(X)))=>((~humble(alice)<~>wise(alice))))&
(![X]:((funny(X)<~>rich(X))<=>strong(X)))&
((~quiet(lucy))=>((~creative(fred)&~strong(fred))))&
((?[X]:(~strong(X)))<=>(?[X]:((~patient(X)|~happy(X)))))&
(![X]:((generous(X)<~>tall(X))<=>(strong(X)&creative(X))))&
((?[X]:((kind(X)|brave(X))))<=>((~wise(alice)<~>rich(alice))))&
(((~wise(fred)|~quiet(fred)))=>((~creative(alice)&rich(alice))))&
(((wise(susan)|happy(susan)))<=>(?[X]:(calm(X))))&
(![X]:(~calm(X)=>(quiet(X)<~>patient(X))))&
((?[X]:(wise(X)))=>((~wise(mary)<~>~happy(mary))))&
((~old(lucy))=>(?[X]:((old(X)<~>~brave(X)))))&
(?[X]:((curious(X)<~>brave(X))))&
(~strong(mary))&
(tall(fred))&
(?[X]:((funny(X)<~>~wise(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(?[X]:((~kind(X)|calm(X))))&
(?[X]:((creative(X)&funny(X))))&
(?[X]:((strong(X)|~old(X)))) | creative(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 5986325635453213639616243
% SZS output start Proof for 5986325635453213639616243
3. ? [X0] : (~creative(X0) | humble(X0)) => ? [X0] : (~old(X0) & old(X0)) [input p2]
25. ~creative(fred) [input hypothesis]
26. ? [X0] : (~creative(X0) | humble(X0)) => ? [X1] : (~old(X1) & old(X1)) [rectify 3]
29. ? [X1] : (~old(X1) & old(X1)) | ! [X0] : (creative(X0) & ~humble(X0)) [ennf transformation 26]
41. ? [X0] : (~old(X0) & old(X0)) | ! [X1] : (creative(X1) & ~humble(X1)) [rectify 29]
42. ? [X0] : (~old(X0) & old(X0)) => (~old(sK0) & old(sK0)) [choice axiom]
43. (~old(sK0) & old(sK0)) | ! [X1] : (creative(X1) & ~humble(X1)) [skolemisation 41,42]
88. old(sK0) | creative(X1) [cnf transformation 43]
90. ~old(sK0) | creative(X1) [cnf transformation 43]
145. ~creative(fred) [cnf transformation 25]
161. 4 <=> ! [X1] : creative(X1) [avatar definition]
162. creative(X1) <- (4) [avatar component clause 161]
164. 5 <=> old(sK0) [avatar definition]
167. 4 | ~5 [avatar split clause 90,164,161]
172. 4 | 5 [avatar split clause 88,164,161]
197. 12 <=> creative(fred) [avatar definition]
199. ~creative(fred) <- (~12) [avatar component clause 197]
347. ~12 [avatar split clause 145,197]
350. $false <- (4, ~12) [resolution 199,162]
351. ~4 | 12 [avatar contradiction clause 350]
352. $false [avatar sat refutation 167,172,347,351]
% SZS output end Proof for 5986325635453213639616243
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is strong or not funny and vice versa.
Everyone who is either not generous or kind is either not creative or not kind.
Everyone who is either tall or not calm is not generous or not tall.
Everyone who is curious is both curious and wise and vice versa.
Everyone who is humble is strong or old.
Everyone who is either not wise or not rich is either patient or not generous and vice versa.
If paul is not patient then susan is both not curious and not generous and vice versa.
Everyone who is both not brave and funny is both not creative and funny and vice versa.
Everyone who is patient or kind is wise.
Everyone who is brave or happy is either quiet or rich.
Everyone who is either not old or tall is either curious or tall.
Everyone who is wise or not curious is old and vice versa.
Everyone who is not humble is either strong or not creative.
Everyone who is not happy is either rich or not curious and vice versa.
Everyone who is not calm or funny is both not curious and not quiet.
If someone is both patient and strong then someone is either not tall or strong and vice versa.
Someone is either strong or not strong.
Someone is both not humble and rich.
Alice is both wise and not humble.
Someone is patient.
Someone is both happy and not curious.
Someone is both humble and patient. | Alice is brave. | contradiction | ((?[X]:(~old(X)))<=>(?[X]:((strong(X)|~funny(X)))))&
(![X]:((~generous(X)<~>kind(X))=>(~creative(X)<~>~kind(X))))&
(![X]:((tall(X)<~>~calm(X))=>(~generous(X)|~tall(X))))&
(![X]:(curious(X)<=>(curious(X)&wise(X))))&
(![X]:(humble(X)=>(strong(X)|old(X))))&
(![X]:((~wise(X)<~>~rich(X))<=>(patient(X)<~>~generous(X))))&
((~patient(paul))<=>((~curious(susan)&~generous(susan))))&
(![X]:((~brave(X)&funny(X))<=>(~creative(X)&funny(X))))&
(![X]:((patient(X)|kind(X))=>wise(X)))&
(![X]:((brave(X)|happy(X))=>(quiet(X)<~>rich(X))))&
(![X]:((~old(X)<~>tall(X))=>(curious(X)<~>tall(X))))&
(![X]:((wise(X)|~curious(X))<=>old(X)))&
(![X]:(~humble(X)=>(strong(X)<~>~creative(X))))&
(![X]:(~happy(X)<=>(rich(X)<~>~curious(X))))&
(![X]:((~calm(X)|funny(X))=>(~curious(X)&~quiet(X))))&
((?[X]:((patient(X)&strong(X))))<=>(?[X]:((~tall(X)<~>strong(X)))))&
(?[X]:((strong(X)<~>~strong(X))))&
(?[X]:((~humble(X)&rich(X))))&
((wise(alice)&~humble(alice)))&
(?[X]:(patient(X)))&
(?[X]:((happy(X)&~curious(X))))&
(?[X]:((humble(X)&patient(X)))) | brave(alice) | [
"p0",
"p3",
"p7",
"p11",
"p12",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6300806439877746138482727
% SZS output start Proof for 6300806439877746138482727
1. ? [X0] : ~old(X0) <=> ? [X0] : (~funny(X0) | strong(X0)) [input p0]
4. ! [X0] : (curious(X0) <=> (wise(X0) & curious(X0))) [input p3]
8. ! [X0] : ((funny(X0) & ~brave(X0)) <=> (funny(X0) & ~creative(X0))) [input p7]
12. ! [X0] : ((~curious(X0) | wise(X0)) <=> old(X0)) [input p11]
13. ! [X0] : (~humble(X0) => (strong(X0) <~> ~creative(X0))) [input p12]
19. ~humble(alice) & wise(alice) [input p18]
23. brave(alice) [input hypothesis]
24. ? [X0] : ~old(X0) <=> ? [X1] : (~funny(X1) | strong(X1)) [rectify 1]
34. ! [X0] : ((strong(X0) <~> ~creative(X0)) | humble(X0)) [ennf transformation 13]
36. (? [X0] : ~old(X0) | ! [X1] : (funny(X1) & ~strong(X1))) & (? [X1] : (~funny(X1) | strong(X1)) | ! [X0] : old(X0)) [nnf transformation 24]
37. (? [X0] : ~old(X0) | ! [X1] : (funny(X1) & ~strong(X1))) & (? [X2] : (~funny(X2) | strong(X2)) | ! [X3] : old(X3)) [rectify 36]
38. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
39. ? [X2] : (~funny(X2) | strong(X2)) => (~funny(sK1) | strong(sK1)) [choice axiom]
40. (~old(sK0) | ! [X1] : (funny(X1) & ~strong(X1))) & ((~funny(sK1) | strong(sK1)) | ! [X3] : old(X3)) [skolemisation 37,39,38]
43. ! [X0] : ((curious(X0) | (~wise(X0) | ~curious(X0))) & ((wise(X0) & curious(X0)) | ~curious(X0))) [nnf transformation 4]
44. ! [X0] : ((curious(X0) | ~wise(X0) | ~curious(X0)) & ((wise(X0) & curious(X0)) | ~curious(X0))) [flattening 43]
48. ! [X0] : (((funny(X0) & ~brave(X0)) | (~funny(X0) | creative(X0))) & ((funny(X0) & ~creative(X0)) | (~funny(X0) | brave(X0)))) [nnf transformation 8]
49. ! [X0] : (((funny(X0) & ~brave(X0)) | ~funny(X0) | creative(X0)) & ((funny(X0) & ~creative(X0)) | ~funny(X0) | brave(X0))) [flattening 48]
52. ! [X0] : (((~curious(X0) | wise(X0)) | ~old(X0)) & (old(X0) | (curious(X0) & ~wise(X0)))) [nnf transformation 12]
53. ! [X0] : ((~curious(X0) | wise(X0) | ~old(X0)) & (old(X0) | (curious(X0) & ~wise(X0)))) [flattening 52]
54. ! [X0] : (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | humble(X0)) [nnf transformation 34]
73. ~old(sK0) | ~strong(X1) [cnf transformation 40]
74. ~old(sK0) | funny(X1) [cnf transformation 40]
82. ~curious(X0) | wise(X0) [cnf transformation 44]
98. ~brave(X0) | ~funny(X0) | creative(X0) [cnf transformation 49]
110. ~wise(X0) | old(X0) [cnf transformation 53]
111. curious(X0) | old(X0) [cnf transformation 53]
113. ~creative(X0) | strong(X0) | humble(X0) [cnf transformation 54]
134. ~humble(alice) [cnf transformation 19]
140. brave(alice) [cnf transformation 23]
147. 1 <=> ! [X1] : funny(X1) [avatar definition]
148. funny(X1) <- (1) [avatar component clause 147]
150. 2 <=> old(sK0) [avatar definition]
152. ~old(sK0) <- (~2) [avatar component clause 150]
153. 1 | ~2 [avatar split clause 74,150,147]
155. 3 <=> ! [X1] : ~strong(X1) [avatar definition]
156. ~strong(X1) <- (3) [avatar component clause 155]
157. 3 | ~2 [avatar split clause 73,150,155]
159. 4 <=> ! [X3] : old(X3) [avatar definition]
160. old(X3) <- (4) [avatar component clause 159]
223. old(X0) | wise(X0) [resolution 111,82]
224. old(X0) [subsumption resolution 223,110]
225. 4 [avatar split clause 224,159]
226. $false <- (~2, 4) [resolution 160,152]
227. 2 | ~4 [avatar contradiction clause 226]
244. ~funny(alice) | creative(alice) [resolution 98,140]
245. creative(alice) <- (1) [subsumption resolution 244,148]
267. strong(alice) | humble(alice) <- (1) [resolution 113,245]
268. humble(alice) <- (1, 3) [subsumption resolution 267,156]
269. $false <- (1, 3) [subsumption resolution 268,134]
270. ~1 | ~3 [avatar contradiction clause 269]
271. $false [avatar sat refutation 153,157,225,227,270]
% SZS output end Proof for 6300806439877746138482727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either quiet or tall is both not quiet and kind.
Everyone who is not brave is not old.
If john is not strong then paul is brave or not tall and vice versa.
Everyone who is either happy or not calm is patient and vice versa.
If someone is both tall and humble then lucy is not humble or strong and vice versa.
Everyone who is funny or humble is kind.
If someone is either calm or not curious then someone is either tall or not calm.
Everyone who is either not humble or generous is quiet.
Everyone who is either old or not calm is both strong and not strong and vice versa.
Everyone who is calm is creative or not wise.
If paul is happy or humble then someone is not generous.
Everyone who is either strong or not quiet is both tall and not wise.
If fred is both not quiet and not brave then someone is not generous.
If alice is old or strong then someone is either not curious or not generous and vice versa.
Everyone who is not strong or not calm is either patient or wise and vice versa.
Everyone who is not calm is both not patient and not rich.
Someone is both not happy and not generous.
Someone is not kind.
Paul is both not old and not strong.
Someone is not old.
Someone is creative.
Susan is not wise.
Someone is both not generous and patient.
Someone is both not patient and tall. | Fred is not brave. | neutral | (![X]:((quiet(X)<~>tall(X))=>(~quiet(X)&kind(X))))&
(![X]:(~brave(X)=>~old(X)))&
((~strong(john))<=>((brave(paul)|~tall(paul))))&
(![X]:((happy(X)<~>~calm(X))<=>patient(X)))&
((?[X]:((tall(X)&humble(X))))<=>((~humble(lucy)|strong(lucy))))&
(![X]:((funny(X)|humble(X))=>kind(X)))&
((?[X]:((calm(X)<~>~curious(X))))=>(?[X]:((tall(X)<~>~calm(X)))))&
(![X]:((~humble(X)<~>generous(X))=>quiet(X)))&
(![X]:((old(X)<~>~calm(X))<=>(strong(X)&~strong(X))))&
(![X]:(calm(X)=>(creative(X)|~wise(X))))&
(((happy(paul)|humble(paul)))=>(?[X]:(~generous(X))))&
(![X]:((strong(X)<~>~quiet(X))=>(tall(X)&~wise(X))))&
(((~quiet(fred)&~brave(fred)))=>(?[X]:(~generous(X))))&
(((old(alice)|strong(alice)))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
(![X]:((~strong(X)|~calm(X))<=>(patient(X)<~>wise(X))))&
(![X]:(~calm(X)=>(~patient(X)&~rich(X))))&
(?[X]:((~happy(X)&~generous(X))))&
(?[X]:(~kind(X)))&
((~old(paul)&~strong(paul)))&
(?[X]:(~old(X)))&
(?[X]:(creative(X)))&
(~wise(susan))&
(?[X]:((~generous(X)&patient(X))))&
(?[X]:((~patient(X)&tall(X)))) | ~brave(fred) | [] | null | 0 |
Everyone who is not creative is either not tall or not humble and vice versa.
If someone is humble or not humble then someone is both humble and not funny and vice versa.
If mary is not brave or not strong then mary is both tall and not patient.
Everyone who is not rich is both not funny and funny and vice versa.
Everyone who is happy is either calm or kind.
If susan is not kind then alice is both patient and not humble and vice versa.
Everyone who is not creative is generous or creative and vice versa.
If lucy is either not creative or humble then mary is either not brave or not humble.
If john is not curious then someone is calm or not humble.
Everyone who is either kind or not generous is rich.
Everyone who is either not patient or not old is not generous and vice versa.
If someone is patient or not wise then someone is both not curious and not funny.
Everyone who is both curious and not calm is not patient and vice versa.
Everyone who is both quiet and calm is not humble and vice versa.
John is not brave.
Paul is both not happy and brave.
Mary is quiet.
John is both strong and not humble. | Paul is not strong. | neutral | (![X]:(~creative(X)<=>(~tall(X)<~>~humble(X))))&
((?[X]:((humble(X)|~humble(X))))<=>(?[X]:((humble(X)&~funny(X)))))&
(((~brave(mary)|~strong(mary)))=>((tall(mary)&~patient(mary))))&
(![X]:(~rich(X)<=>(~funny(X)&funny(X))))&
(![X]:(happy(X)=>(calm(X)<~>kind(X))))&
((~kind(susan))<=>((patient(alice)&~humble(alice))))&
(![X]:(~creative(X)<=>(generous(X)|creative(X))))&
(((~creative(lucy)<~>humble(lucy)))=>((~brave(mary)<~>~humble(mary))))&
((~curious(john))=>(?[X]:((calm(X)|~humble(X)))))&
(![X]:((kind(X)<~>~generous(X))=>rich(X)))&
(![X]:((~patient(X)<~>~old(X))<=>~generous(X)))&
((?[X]:((patient(X)|~wise(X))))=>(?[X]:((~curious(X)&~funny(X)))))&
(![X]:((curious(X)&~calm(X))<=>~patient(X)))&
(![X]:((quiet(X)&calm(X))<=>~humble(X)))&
(~brave(john))&
((~happy(paul)&brave(paul)))&
(quiet(mary))&
((strong(john)&~humble(john))) | ~strong(paul) | [] | null | 0 |
Everyone who is brave is not generous or quiet.
Everyone who is both not wise and funny is either strong or not tall and vice versa.
Everyone who is old is both not strong and brave and vice versa.
Everyone who is either calm or not rich is either kind or not calm and vice versa.
If susan is not generous or brave then mary is happy or not old.
Everyone who is not generous or generous is either not generous or not old and vice versa.
Everyone who is either not wise or brave is not creative.
Everyone who is rich or humble is both not funny and not creative.
If fred is not patient then fred is not brave or not wise and vice versa.
Everyone who is either kind or humble is kind or not old.
Everyone who is not curious is tall.
If someone is either not quiet or quiet then someone is not creative and vice versa.
Everyone who is not strong is either not rich or kind and vice versa.
If someone is not curious then lucy is both not patient and not brave and vice versa.
Everyone who is both patient and not calm is not patient.
If someone is both quiet and calm then someone is brave or old.
Susan is humble or not creative.
Lucy is either calm or not creative.
Someone is not brave.
John is either not old or tall.
Alice is either not patient or not wise.
Mary is both not funny and brave.
Paul is either not tall or quiet. | John is not strong. | entailment | (![X]:(brave(X)=>(~generous(X)|quiet(X))))&
(![X]:((~wise(X)&funny(X))<=>(strong(X)<~>~tall(X))))&
(![X]:(old(X)<=>(~strong(X)&brave(X))))&
(![X]:((calm(X)<~>~rich(X))<=>(kind(X)<~>~calm(X))))&
(((~generous(susan)|brave(susan)))=>((happy(mary)|~old(mary))))&
(![X]:((~generous(X)|generous(X))<=>(~generous(X)<~>~old(X))))&
(![X]:((~wise(X)<~>brave(X))=>~creative(X)))&
(![X]:((rich(X)|humble(X))=>(~funny(X)&~creative(X))))&
((~patient(fred))<=>((~brave(fred)|~wise(fred))))&
(![X]:((kind(X)<~>humble(X))=>(kind(X)|~old(X))))&
(![X]:(~curious(X)=>tall(X)))&
((?[X]:((~quiet(X)<~>quiet(X))))<=>(?[X]:(~creative(X))))&
(![X]:(~strong(X)<=>(~rich(X)<~>kind(X))))&
((?[X]:(~curious(X)))<=>((~patient(lucy)&~brave(lucy))))&
(![X]:((patient(X)&~calm(X))=>~patient(X)))&
((?[X]:((quiet(X)&calm(X))))=>(?[X]:((brave(X)|old(X)))))&
((humble(susan)|~creative(susan)))&
((calm(lucy)<~>~creative(lucy)))&
(?[X]:(~brave(X)))&
((~old(john)<~>tall(john)))&
((~patient(alice)<~>~wise(alice)))&
((~funny(mary)&brave(mary)))&
((~tall(paul)<~>quiet(paul))) | ~strong(john) | [
"p3",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5824500832569395836660646
% SZS output start Proof for 5824500832569395836660646
4. ! [X0] : ((calm(X0) <~> ~rich(X0)) <=> (kind(X0) <~> ~calm(X0))) [input p3]
13. ! [X0] : (~strong(X0) <=> (~rich(X0) <~> kind(X0))) [input p12]
24. strong(john) [input hypothesis]
42. ! [X0] : ((((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | ((kind(X0) | calm(X0)) & (~calm(X0) | ~kind(X0)))) & (((calm(X0) | ~kind(X0)) & (~calm(X0) | kind(X0))) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0))))) [nnf transformation 4]
54. ! [X0] : ((~strong(X0) | ((~rich(X0) | ~kind(X0)) & (kind(X0) | rich(X0)))) & (((~kind(X0) | rich(X0)) & (kind(X0) | ~rich(X0))) | strong(X0))) [nnf transformation 13]
79. ~calm(X0) | kind(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 42]
82. calm(X0) | ~kind(X0) | calm(X0) | rich(X0) [cnf transformation 42]
84. ~rich(X0) | calm(X0) | kind(X0) | calm(X0) [cnf transformation 42]
85. rich(X0) | ~calm(X0) | ~calm(X0) | ~kind(X0) [cnf transformation 42]
111. ~strong(X0) | kind(X0) | rich(X0) [cnf transformation 54]
112. ~strong(X0) | ~rich(X0) | ~kind(X0) [cnf transformation 54]
130. strong(john) [cnf transformation 24]
139. ~calm(X0) | kind(X0) | ~rich(X0) [duplicate literal removal 79]
140. calm(X0) | ~kind(X0) | rich(X0) [duplicate literal removal 82]
141. ~rich(X0) | calm(X0) | kind(X0) [duplicate literal removal 84]
142. rich(X0) | ~calm(X0) | ~kind(X0) [duplicate literal removal 85]
143. ~kind(X0) | rich(X0) [subsumption resolution 140,142]
144. kind(X0) | ~rich(X0) [subsumption resolution 139,141]
172. ~strong(X0) | ~kind(X0) [subsumption resolution 112,143]
173. ~strong(X0) | kind(X0) [subsumption resolution 111,144]
174. ~strong(X0) [subsumption resolution 173,172]
243. $false [subsumption resolution 130,174]
% SZS output end Proof for 5824500832569395836660646
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and quiet is not curious or strong and vice versa.
Everyone who is funny is kind or not funny and vice versa.
If someone is funny then someone is not strong or not tall and vice versa.
Everyone who is either old or not brave is both patient and humble and vice versa.
If someone is both not patient and funny then someone is both not kind and not patient and vice versa.
If someone is either not rich or not quiet then john is either not quiet or not old.
Everyone who is either not patient or not creative is wise and vice versa.
Everyone who is not quiet is both not patient and kind and vice versa.
If someone is both not rich and not generous then alice is not old and vice versa.
If susan is either old or brave then someone is both not kind and not calm and vice versa.
If lucy is humble then someone is either not strong or not humble.
Everyone who is either humble or not wise is either patient or not brave and vice versa.
If fred is either not happy or not humble then lucy is either not wise or curious and vice versa.
If someone is not old or generous then someone is both calm and funny.
If someone is not calm then mary is both not creative and calm.
Everyone who is both not calm and calm is not funny or not humble and vice versa.
Someone is not wise or not funny.
Fred is both rich and generous.
Someone is not calm.
Someone is generous.
Someone is not patient or humble. | Lucy is strong. | contradiction | (![X]:((~humble(X)&quiet(X))<=>(~curious(X)|strong(X))))&
(![X]:(funny(X)<=>(kind(X)|~funny(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~strong(X)|~tall(X)))))&
(![X]:((old(X)<~>~brave(X))<=>(patient(X)&humble(X))))&
((?[X]:((~patient(X)&funny(X))))<=>(?[X]:((~kind(X)&~patient(X)))))&
((?[X]:((~rich(X)<~>~quiet(X))))=>((~quiet(john)<~>~old(john))))&
(![X]:((~patient(X)<~>~creative(X))<=>wise(X)))&
(![X]:(~quiet(X)<=>(~patient(X)&kind(X))))&
((?[X]:((~rich(X)&~generous(X))))<=>(~old(alice)))&
(((old(susan)<~>brave(susan)))<=>(?[X]:((~kind(X)&~calm(X)))))&
((humble(lucy))=>(?[X]:((~strong(X)<~>~humble(X)))))&
(![X]:((humble(X)<~>~wise(X))<=>(patient(X)<~>~brave(X))))&
(((~happy(fred)<~>~humble(fred)))<=>((~wise(lucy)<~>curious(lucy))))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((calm(X)&funny(X)))))&
((?[X]:(~calm(X)))=>((~creative(mary)&calm(mary))))&
(![X]:((~calm(X)&calm(X))<=>(~funny(X)|~humble(X))))&
(?[X]:((~wise(X)|~funny(X))))&
((rich(fred)&generous(fred)))&
(?[X]:(~calm(X)))&
(?[X]:(generous(X)))&
(?[X]:((~patient(X)|humble(X)))) | strong(lucy) | [
"p0",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5223272895162440120798030
% SZS output start Proof for 5223272895162440120798030
1. ! [X0] : ((quiet(X0) & ~humble(X0)) <=> (strong(X0) | ~curious(X0))) [input p0]
16. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (~humble(X0) | ~funny(X0))) [input p15]
22. strong(lucy) [input hypothesis]
30. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~strong(X0) & curious(X0))) & ((strong(X0) | ~curious(X0)) | (~quiet(X0) | humble(X0)))) [nnf transformation 1]
31. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~strong(X0) & curious(X0))) & (strong(X0) | ~curious(X0) | ~quiet(X0) | humble(X0))) [flattening 30]
66. ! [X0] : (((calm(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) & ((~humble(X0) | ~funny(X0)) | (~calm(X0) | calm(X0)))) [nnf transformation 16]
67. ! [X0] : (((calm(X0) & ~calm(X0)) | (humble(X0) & funny(X0))) & (~humble(X0) | ~funny(X0) | ~calm(X0) | calm(X0))) [flattening 66]
78. ~strong(X0) | ~humble(X0) [cnf transformation 31]
143. ~calm(X0) | humble(X0) [cnf transformation 67]
145. calm(X0) | humble(X0) [cnf transformation 67]
152. strong(lucy) [cnf transformation 22]
295. humble(X0) [subsumption resolution 143,145]
304. ~humble(lucy) [resolution 78,152]
306. $false [subsumption resolution 304,295]
% SZS output end Proof for 5223272895162440120798030
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble is either wise or creative.
If alice is not brave or not kind then someone is not old or calm.
Everyone who is not kind is wise or not brave.
If mary is either not strong or not humble then mary is not generous or creative.
Everyone who is both not patient and old is not humble.
Everyone who is both brave and not quiet is calm and vice versa.
Everyone who is quiet or not curious is rich.
If someone is either wise or calm then someone is both not funny and not happy.
Everyone who is not humble is either calm or brave and vice versa.
Everyone who is not calm or calm is not strong or not wise.
Everyone who is both rich and happy is both not happy and not kind.
If john is both not brave and not strong then mary is both not rich and quiet.
If mary is not patient or not generous then someone is both not calm and not funny.
Everyone who is either humble or patient is not calm or patient and vice versa.
Everyone who is either not wise or not patient is both not humble and not tall and vice versa.
If someone is either not curious or calm then john is both not creative and calm.
Someone is curious.
Someone is either generous or old.
Mary is both not patient and not happy.
Fred is not funny or curious.
Someone is not generous.
Fred is either generous or not brave.
Someone is either not happy or brave.
Someone is either kind or not happy. | Mary is old. | contradiction | (![X]:(humble(X)=>(wise(X)<~>creative(X))))&
(((~brave(alice)|~kind(alice)))=>(?[X]:((~old(X)|calm(X)))))&
(![X]:(~kind(X)=>(wise(X)|~brave(X))))&
(((~strong(mary)<~>~humble(mary)))=>((~generous(mary)|creative(mary))))&
(![X]:((~patient(X)&old(X))=>~humble(X)))&
(![X]:((brave(X)&~quiet(X))<=>calm(X)))&
(![X]:((quiet(X)|~curious(X))=>rich(X)))&
((?[X]:((wise(X)<~>calm(X))))=>(?[X]:((~funny(X)&~happy(X)))))&
(![X]:(~humble(X)<=>(calm(X)<~>brave(X))))&
(![X]:((~calm(X)|calm(X))=>(~strong(X)|~wise(X))))&
(![X]:((rich(X)&happy(X))=>(~happy(X)&~kind(X))))&
(((~brave(john)&~strong(john)))=>((~rich(mary)&quiet(mary))))&
(((~patient(mary)|~generous(mary)))=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((humble(X)<~>patient(X))<=>(~calm(X)|patient(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~humble(X)&~tall(X))))&
((?[X]:((~curious(X)<~>calm(X))))=>((~creative(john)&calm(john))))&
(?[X]:(curious(X)))&
(?[X]:((generous(X)<~>old(X))))&
((~patient(mary)&~happy(mary)))&
((~funny(fred)|curious(fred)))&
(?[X]:(~generous(X)))&
((generous(fred)<~>~brave(fred)))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((kind(X)<~>~happy(X)))) | old(mary) | [
"p4",
"p5",
"p8",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 670235600143168859732113
% SZS output start Proof for 670235600143168859732113
5. ! [X0] : ((old(X0) & ~patient(X0)) => ~humble(X0)) [input p4]
6. ! [X0] : ((~quiet(X0) & brave(X0)) <=> calm(X0)) [input p5]
9. ! [X0] : (~humble(X0) <=> (calm(X0) <~> brave(X0))) [input p8]
14. ! [X0] : ((humble(X0) <~> patient(X0)) <=> (patient(X0) | ~calm(X0))) [input p13]
19. ~happy(mary) & ~patient(mary) [input p18]
25. old(mary) [input hypothesis]
36. ! [X0] : (~humble(X0) | (~old(X0) | patient(X0))) [ennf transformation 5]
37. ! [X0] : (~humble(X0) | ~old(X0) | patient(X0)) [flattening 36]
52. ! [X0] : (((~quiet(X0) & brave(X0)) | ~calm(X0)) & (calm(X0) | (quiet(X0) | ~brave(X0)))) [nnf transformation 6]
53. ! [X0] : (((~quiet(X0) & brave(X0)) | ~calm(X0)) & (calm(X0) | quiet(X0) | ~brave(X0))) [flattening 52]
58. ! [X0] : ((~humble(X0) | ((calm(X0) | ~brave(X0)) & (brave(X0) | ~calm(X0)))) & (((~brave(X0) | ~calm(X0)) & (brave(X0) | calm(X0))) | humble(X0))) [nnf transformation 9]
61. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [nnf transformation 14]
62. ! [X0] : ((((~patient(X0) | ~humble(X0)) & (patient(X0) | humble(X0))) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | ((humble(X0) | ~patient(X0)) & (patient(X0) | ~humble(X0))))) [flattening 61]
87. ~old(X0) | ~humble(X0) | patient(X0) [cnf transformation 37]
89. ~calm(X0) | brave(X0) [cnf transformation 53]
96. ~brave(X0) | ~calm(X0) | humble(X0) [cnf transformation 58]
109. patient(X0) | humble(X0) | calm(X0) [cnf transformation 62]
126. ~patient(mary) [cnf transformation 19]
135. old(mary) [cnf transformation 25]
158. 5 <=> humble(mary) [avatar definition]
160. humble(mary) <- (5) [avatar component clause 158]
187. ~calm(X0) | humble(X0) [subsumption resolution 96,89]
214. 17 <=> patient(mary) [avatar definition]
215. ~patient(mary) <- (~17) [avatar component clause 214]
218. patient(X0) | humble(X0) [subsumption resolution 109,187]
235. ~17 [avatar split clause 126,214]
268. humble(mary) <- (~17) [resolution 218,215]
270. 5 | 17 [avatar split clause 268,214,158]
330. ~humble(mary) | patient(mary) [resolution 87,135]
331. patient(mary) <- (5) [subsumption resolution 330,160]
332. $false <- (5, ~17) [subsumption resolution 331,215]
333. ~5 | 17 [avatar contradiction clause 332]
334. $false [avatar sat refutation 235,270,333]
% SZS output end Proof for 670235600143168859732113
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is curious.
If someone is not strong or wise then mary is both not happy and not creative.
If someone is either strong or rich then lucy is either strong or wise and vice versa.
Everyone who is not funny is rich or generous and vice versa.
If someone is quiet then someone is either wise or tall and vice versa.
Everyone who is both not funny and not patient is both kind and not strong and vice versa.
Everyone who is not kind or funny is either funny or not rich.
Everyone who is both old and not kind is both not humble and rich.
Everyone who is rich is not wise or quiet.
Everyone who is either rich or not generous is both not tall and not happy.
If fred is curious then mary is either wise or old.
Everyone who is both patient and brave is both generous and calm and vice versa.
If john is not curious or quiet then someone is strong.
If mary is both not kind and wise then alice is happy.
Everyone who is either not rich or not tall is not funny and vice versa.
If fred is either not tall or humble then john is both humble and not patient and vice versa.
Someone is not quiet.
Susan is either not curious or not brave.
Someone is not humble.
Mary is both rich and creative.
Fred is not rich.
Susan is either tall or happy.
Someone is not tall or not brave. | John is not patient. | contradiction | (![X]:(funny(X)=>curious(X)))&
((?[X]:((~strong(X)|wise(X))))=>((~happy(mary)&~creative(mary))))&
((?[X]:((strong(X)<~>rich(X))))<=>((strong(lucy)<~>wise(lucy))))&
(![X]:(~funny(X)<=>(rich(X)|generous(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((wise(X)<~>tall(X)))))&
(![X]:((~funny(X)&~patient(X))<=>(kind(X)&~strong(X))))&
(![X]:((~kind(X)|funny(X))=>(funny(X)<~>~rich(X))))&
(![X]:((old(X)&~kind(X))=>(~humble(X)&rich(X))))&
(![X]:(rich(X)=>(~wise(X)|quiet(X))))&
(![X]:((rich(X)<~>~generous(X))=>(~tall(X)&~happy(X))))&
((curious(fred))=>((wise(mary)<~>old(mary))))&
(![X]:((patient(X)&brave(X))<=>(generous(X)&calm(X))))&
(((~curious(john)|quiet(john)))=>(?[X]:(strong(X))))&
(((~kind(mary)&wise(mary)))=>(happy(alice)))&
(![X]:((~rich(X)<~>~tall(X))<=>~funny(X)))&
(((~tall(fred)<~>humble(fred)))<=>((humble(john)&~patient(john))))&
(?[X]:(~quiet(X)))&
((~curious(susan)<~>~brave(susan)))&
(?[X]:(~humble(X)))&
((rich(mary)&creative(mary)))&
(~rich(fred))&
((tall(susan)<~>happy(susan)))&
(?[X]:((~tall(X)|~brave(X)))) | ~patient(john) | [
"p1",
"p3",
"p5",
"p6",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8843487413394831400367801
% SZS output start Proof for 8843487413394831400367801
2. ? [X0] : (wise(X0) | ~strong(X0)) => (~creative(mary) & ~happy(mary)) [input p1]
4. ! [X0] : (~funny(X0) <=> (generous(X0) | rich(X0))) [input p3]
6. ! [X0] : ((~patient(X0) & ~funny(X0)) <=> (~strong(X0) & kind(X0))) [input p5]
7. ! [X0] : ((funny(X0) | ~kind(X0)) => (funny(X0) <~> ~rich(X0))) [input p6]
20. creative(mary) & rich(mary) [input p19]
24. ~patient(john) [input hypothesis]
27. (~creative(mary) & ~happy(mary)) | ! [X0] : (~wise(X0) & strong(X0)) [ennf transformation 2]
28. ! [X0] : ((funny(X0) <~> ~rich(X0)) | (~funny(X0) & kind(X0))) [ennf transformation 7]
42. ! [X0] : ((~funny(X0) | (~generous(X0) & ~rich(X0))) & ((generous(X0) | rich(X0)) | funny(X0))) [nnf transformation 4]
43. ! [X0] : ((~funny(X0) | (~generous(X0) & ~rich(X0))) & (generous(X0) | rich(X0) | funny(X0))) [flattening 42]
49. ! [X0] : (((~patient(X0) & ~funny(X0)) | (strong(X0) | ~kind(X0))) & ((~strong(X0) & kind(X0)) | (patient(X0) | funny(X0)))) [nnf transformation 6]
50. ! [X0] : (((~patient(X0) & ~funny(X0)) | strong(X0) | ~kind(X0)) & ((~strong(X0) & kind(X0)) | patient(X0) | funny(X0))) [flattening 49]
51. ! [X0] : (((rich(X0) | ~funny(X0)) & (~rich(X0) | funny(X0))) | (~funny(X0) & kind(X0))) [nnf transformation 28]
72. ~creative(mary) | strong(X0) [cnf transformation 27]
83. ~rich(X0) | ~funny(X0) [cnf transformation 43]
90. ~strong(X0) | patient(X0) | funny(X0) [cnf transformation 50]
96. rich(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 51]
128. creative(mary) [cnf transformation 20]
133. ~patient(john) [cnf transformation 24]
134. rich(X0) | ~funny(X0) [duplicate literal removal 96]
139. 2 <=> creative(mary) [avatar definition]
144. 3 <=> ! [X0] : strong(X0) [avatar definition]
145. strong(X0) <- (3) [avatar component clause 144]
146. 3 | ~2 [avatar split clause 72,139,144]
208. ~funny(X0) [subsumption resolution 134,83]
255. 26 <=> patient(john) [avatar definition]
256. ~patient(john) <- (~26) [avatar component clause 255]
282. 2 [avatar split clause 128,139]
302. ~26 [avatar split clause 133,255]
326. patient(X0) | funny(X0) <- (3) [resolution 90,145]
329. patient(X0) <- (3) [subsumption resolution 326,208]
330. $false <- (3, ~26) [resolution 329,256]
331. ~3 | 26 [avatar contradiction clause 330]
332. $false [avatar sat refutation 146,282,302,331]
% SZS output end Proof for 8843487413394831400367801
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and not kind is either quiet or happy and vice versa.
Everyone who is either patient or not calm is not kind or not curious and vice versa.
If alice is not calm or old then someone is either funny or not tall and vice versa.
If someone is calm or humble then someone is both funny and happy.
Everyone who is not generous is both brave and not kind and vice versa.
If lucy is rich or humble then someone is either happy or kind.
If someone is not brave or kind then lucy is either not funny or not strong and vice versa.
If john is not curious or not tall then mary is wise and vice versa.
If someone is generous then lucy is either generous or not strong.
If someone is not patient or not rich then lucy is both not generous and not humble.
Everyone who is either not patient or not kind is not quiet and vice versa.
Everyone who is both not strong and not generous is not happy or not kind and vice versa.
If someone is either not calm or not generous then someone is rich or wise and vice versa.
Everyone who is either kind or humble is either not patient or not old and vice versa.
Everyone who is old is either humble or not generous.
Everyone who is either not calm or kind is not happy and vice versa.
Someone is either tall or not rich.
John is quiet.
Someone is not creative.
Lucy is both happy and humble.
Someone is patient or not strong.
Someone is both not kind and not curious.
Lucy is wise or humble. | Lucy is strong. | entailment | (![X]:((~funny(X)&~kind(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((patient(X)<~>~calm(X))<=>(~kind(X)|~curious(X))))&
(((~calm(alice)|old(alice)))<=>(?[X]:((funny(X)<~>~tall(X)))))&
((?[X]:((calm(X)|humble(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(~generous(X)<=>(brave(X)&~kind(X))))&
(((rich(lucy)|humble(lucy)))=>(?[X]:((happy(X)<~>kind(X)))))&
((?[X]:((~brave(X)|kind(X))))<=>((~funny(lucy)<~>~strong(lucy))))&
(((~curious(john)|~tall(john)))<=>(wise(mary)))&
((?[X]:(generous(X)))=>((generous(lucy)<~>~strong(lucy))))&
((?[X]:((~patient(X)|~rich(X))))=>((~generous(lucy)&~humble(lucy))))&
(![X]:((~patient(X)<~>~kind(X))<=>~quiet(X)))&
(![X]:((~strong(X)&~generous(X))<=>(~happy(X)|~kind(X))))&
((?[X]:((~calm(X)<~>~generous(X))))<=>(?[X]:((rich(X)|wise(X)))))&
(![X]:((kind(X)<~>humble(X))<=>(~patient(X)<~>~old(X))))&
(![X]:(old(X)=>(humble(X)<~>~generous(X))))&
(![X]:((~calm(X)<~>kind(X))<=>~happy(X)))&
(?[X]:((tall(X)<~>~rich(X))))&
(quiet(john))&
(?[X]:(~creative(X)))&
((happy(lucy)&humble(lucy)))&
(?[X]:((patient(X)|~strong(X))))&
(?[X]:((~kind(X)&~curious(X))))&
((wise(lucy)|humble(lucy))) | strong(lucy) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"p10",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5090160748801695038911720
% SZS output start Proof for 5090160748801695038911720
1. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (quiet(X0) <~> happy(X0))) [input p0]
5. ! [X0] : (~generous(X0) <=> (~kind(X0) & brave(X0))) [input p4]
7. ? [X0] : (kind(X0) | ~brave(X0)) <=> (~funny(lucy) <~> ~strong(lucy)) [input p6]
9. ? [X0] : generous(X0) => (generous(lucy) <~> ~strong(lucy)) [input p8]
10. ? [X0] : (~rich(X0) | ~patient(X0)) => (~humble(lucy) & ~generous(lucy)) [input p9]
11. ! [X0] : ((~patient(X0) <~> ~kind(X0)) <=> ~quiet(X0)) [input p10]
18. quiet(john) [input p17]
20. humble(lucy) & happy(lucy) [input p19]
24. ~strong(lucy) [input hypothesis]
30. (generous(lucy) <~> ~strong(lucy)) | ! [X0] : ~generous(X0) [ennf transformation 9]
31. (~humble(lucy) & ~generous(lucy)) | ! [X0] : (rich(X0) & patient(X0)) [ennf transformation 10]
33. ! [X0] : (((~kind(X0) & ~funny(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | (kind(X0) | funny(X0)))) [nnf transformation 1]
34. ! [X0] : (((~kind(X0) & ~funny(X0)) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | kind(X0) | funny(X0))) [flattening 33]
45. ! [X0] : ((~generous(X0) | (kind(X0) | ~brave(X0))) & ((~kind(X0) & brave(X0)) | generous(X0))) [nnf transformation 5]
46. ! [X0] : ((~generous(X0) | kind(X0) | ~brave(X0)) & ((~kind(X0) & brave(X0)) | generous(X0))) [flattening 45]
50. (? [X0] : (kind(X0) | ~brave(X0)) | ((~funny(lucy) | strong(lucy)) & (~strong(lucy) | funny(lucy)))) & (((strong(lucy) | funny(lucy)) & (~strong(lucy) | ~funny(lucy))) | ! [X0] : (~kind(X0) & brave(X0))) [nnf transformation 7]
51. (? [X0] : (kind(X0) | ~brave(X0)) | ((~funny(lucy) | strong(lucy)) & (~strong(lucy) | funny(lucy)))) & (((strong(lucy) | funny(lucy)) & (~strong(lucy) | ~funny(lucy))) | ! [X1] : (~kind(X1) & brave(X1))) [rectify 50]
52. ? [X0] : (kind(X0) | ~brave(X0)) => (kind(sK3) | ~brave(sK3)) [choice axiom]
53. ((kind(sK3) | ~brave(sK3)) | ((~funny(lucy) | strong(lucy)) & (~strong(lucy) | funny(lucy)))) & (((strong(lucy) | funny(lucy)) & (~strong(lucy) | ~funny(lucy))) | ! [X1] : (~kind(X1) & brave(X1))) [skolemisation 51,52]
56. ((strong(lucy) | ~generous(lucy)) & (~strong(lucy) | generous(lucy))) | ! [X0] : ~generous(X0) [nnf transformation 30]
57. ! [X0] : ((((kind(X0) | patient(X0)) & (~kind(X0) | ~patient(X0))) | quiet(X0)) & (~quiet(X0) | ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))))) [nnf transformation 11]
78. ~happy(X0) | quiet(X0) | ~funny(X0) [cnf transformation 34]
98. ~kind(X0) | generous(X0) [cnf transformation 46]
107. strong(lucy) | funny(lucy) | ~kind(X1) [cnf transformation 53]
114. strong(lucy) | ~generous(lucy) | ~generous(X0) [cnf transformation 56]
117. ~humble(lucy) | patient(X0) [cnf transformation 31]
120. ~patient(X0) | ~quiet(X0) | kind(X0) [cnf transformation 57]
150. quiet(john) [cnf transformation 18]
151. happy(lucy) [cnf transformation 20]
152. humble(lucy) [cnf transformation 20]
157. ~strong(lucy) [cnf transformation 24]
205. 11 <=> humble(lucy) [avatar definition]
225. 15 <=> strong(lucy) [avatar definition]
229. 16 <=> funny(lucy) [avatar definition]
230. funny(lucy) <- (16) [avatar component clause 229]
243. 19 <=> ! [X1] : ~kind(X1) [avatar definition]
244. ~kind(X1) <- (19) [avatar component clause 243]
245. 19 | 16 | 15 [avatar split clause 107,225,229,243]
268. 24 <=> ! [X0] : ~generous(X0) [avatar definition]
269. ~generous(X0) <- (24) [avatar component clause 268]
271. 25 <=> generous(lucy) [avatar definition]
272. generous(lucy) <- (25) [avatar component clause 271]
274. 24 | ~25 | 15 [avatar split clause 114,225,271,268]
281. 27 <=> ! [X0] : patient(X0) [avatar definition]
282. patient(X0) <- (27) [avatar component clause 281]
283. 27 | ~11 [avatar split clause 117,205,281]
330. 11 [avatar split clause 152,205]
345. ~15 [avatar split clause 157,225]
367. quiet(lucy) | ~funny(lucy) [resolution 78,151]
371. quiet(lucy) <- (16) [subsumption resolution 367,230]
395. 47 <=> kind(john) [avatar definition]
396. kind(john) <- (47) [avatar component clause 395]
425. ~quiet(X0) | kind(X0) <- (27) [resolution 120,282]
485. kind(lucy) <- (16, 27) [resolution 425,371]
486. kind(john) <- (27) [resolution 425,150]
491. 47 | ~27 [avatar split clause 486,281,395]
521. generous(lucy) <- (16, 27) [resolution 485,98]
524. 25 | ~16 | ~27 [avatar split clause 521,281,229,271]
540. $false <- (19, 47) [resolution 244,396]
543. ~19 | ~47 [avatar contradiction clause 540]
570. $false <- (24, 25) [resolution 272,269]
574. ~24 | ~25 [avatar contradiction clause 570]
575. $false [avatar sat refutation 245,274,283,330,345,491,524,543,574]
% SZS output end Proof for 5090160748801695038911720
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is happy or kind then someone is humble or not rich and vice versa. Everyone who is both not quiet and funny is not brave or patient and vice versa. Everyone who is tall or rich is rich or quiet and vice versa. If alice is either not creative or humble then someone is either humble or old and vice versa. Everyone who is generous or not quiet is either happy or strong and vice versa. Everyone who is either not funny or not humble is strong or generous. Everyone who is not happy or not kind is either tall or not happy and vice versa. If someone is either not calm or not rich then lucy is both quiet and calm and vice versa. Everyone who is either not tall or funny is happy and vice versa. Everyone who is not strong or not kind is brave and vice versa. If someone is either funny or happy then fred is not funny or not generous and vice versa. If someone is not quiet or patient then mary is either tall or generous. Everyone who is either old or generous is not calm and vice versa. If alice is calm then someone is calm. Everyone who is both not quiet and calm is old or tall. Everyone who is both brave and not calm is both wise and calm and vice versa. Someone is not kind or not brave. Someone is tall or not kind. Someone is both not creative and old. Mary is not generous or creative. Someone is kind. Mary is either old or not tall. John is both not strong and not tall. John is either tall or not generous. | John is not patient. | entailment | (((happy(lucy)|kind(lucy)))<=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:((~quiet(X)&funny(X))<=>(~brave(X)|patient(X))))&
(![X]:((tall(X)|rich(X))<=>(rich(X)|quiet(X))))&
(((~creative(alice)<~>humble(alice)))<=>(?[X]:((humble(X)<~>old(X)))))&
(![X]:((generous(X)|~quiet(X))<=>(happy(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(strong(X)|generous(X))))&
(![X]:((~happy(X)|~kind(X))<=>(tall(X)<~>~happy(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((quiet(lucy)&calm(lucy))))&
(![X]:((~tall(X)<~>funny(X))<=>happy(X)))&
(![X]:((~strong(X)|~kind(X))<=>brave(X)))&
((?[X]:((funny(X)<~>happy(X))))<=>((~funny(fred)|~generous(fred))))&
((?[X]:((~quiet(X)|patient(X))))=>((tall(mary)<~>generous(mary))))&
(![X]:((old(X)<~>generous(X))<=>~calm(X)))&
((calm(alice))=>(?[X]:(calm(X))))&
(![X]:((~quiet(X)&calm(X))=>(old(X)|tall(X))))&
(![X]:((brave(X)&~calm(X))<=>(wise(X)&calm(X))))&
(?[X]:((~kind(X)|~brave(X))))&
(?[X]:((tall(X)|~kind(X))))&
(?[X]:((~creative(X)&old(X))))&
((~generous(mary)|creative(mary)))&
(?[X]:(kind(X)))&
((old(mary)<~>~tall(mary)))&
((~strong(john)&~tall(john)))&
((tall(john)<~>~generous(john))) | ~patient(john) | [
"p1",
"p4",
"p8",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6847567092193541710928179
% SZS output start Proof for 6847567092193541710928179
2. ! [X0] : ((funny(X0) & ~quiet(X0)) <=> (patient(X0) | ~brave(X0))) [input p1]
5. ! [X0] : ((~quiet(X0) | generous(X0)) <=> (happy(X0) <~> strong(X0))) [input p4]
9. ! [X0] : ((~tall(X0) <~> funny(X0)) <=> happy(X0)) [input p8]
23. ~tall(john) & ~strong(john) [input p22]
25. patient(john) [input hypothesis]
37. ! [X0] : (((funny(X0) & ~quiet(X0)) | (~patient(X0) & brave(X0))) & ((patient(X0) | ~brave(X0)) | (~funny(X0) | quiet(X0)))) [nnf transformation 2]
38. ! [X0] : (((funny(X0) & ~quiet(X0)) | (~patient(X0) & brave(X0))) & (patient(X0) | ~brave(X0) | ~funny(X0) | quiet(X0))) [flattening 37]
45. ! [X0] : (((~quiet(X0) | generous(X0)) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (quiet(X0) & ~generous(X0)))) [nnf transformation 5]
46. ! [X0] : ((~quiet(X0) | generous(X0) | ((happy(X0) | ~strong(X0)) & (strong(X0) | ~happy(X0)))) & (((~strong(X0) | ~happy(X0)) & (strong(X0) | happy(X0))) | (quiet(X0) & ~generous(X0)))) [flattening 45]
55. ! [X0] : ((((~funny(X0) | tall(X0)) & (funny(X0) | ~tall(X0))) | ~happy(X0)) & (happy(X0) | ((~tall(X0) | ~funny(X0)) & (funny(X0) | tall(X0))))) [nnf transformation 9]
85. ~patient(X0) | ~quiet(X0) [cnf transformation 38]
87. ~patient(X0) | funny(X0) [cnf transformation 38]
101. strong(X0) | happy(X0) | quiet(X0) [cnf transformation 46]
123. ~funny(X0) | tall(X0) | ~happy(X0) [cnf transformation 55]
155. ~strong(john) [cnf transformation 23]
156. ~tall(john) [cnf transformation 23]
159. patient(john) [cnf transformation 25]
338. ~quiet(john) [resolution 85,159]
343. funny(john) [resolution 87,159]
385. happy(john) | quiet(john) [resolution 101,155]
386. happy(john) [subsumption resolution 385,338]
412. tall(john) | ~happy(john) [resolution 123,343]
414. ~happy(john) [subsumption resolution 412,156]
415. $false [subsumption resolution 414,386]
% SZS output end Proof for 6847567092193541710928179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not calm is not happy or not kind and vice versa. Everyone who is either old or not curious is tall and vice versa. If someone is both patient and humble then lucy is both not tall and not kind and vice versa. Everyone who is not tall is both not humble and old and vice versa. Everyone who is either not calm or not old is not rich or not kind and vice versa. If susan is both not quiet and kind then susan is either strong or not brave. If someone is both generous and not happy then susan is both not quiet and humble. If someone is tall then paul is not curious or not creative. If someone is both strong and rich then someone is not tall or not humble. If someone is either old or brave then someone is wise. Everyone who is wise or not happy is both patient and quiet and vice versa. Everyone who is not funny or strong is kind. Everyone who is both brave and happy is quiet. If someone is both happy and not curious then john is either not rich or not strong. If someone is tall or not tall then susan is not calm. Everyone who is funny is both not kind and not brave. Someone is both funny and not quiet. Someone is creative or not strong. Mary is both not tall and quiet. Someone is either not creative or creative. Someone is strong. Lucy is both not curious and brave. Paul is either quiet or strong. | Paul is curious. | neutral | (![X]:((~tall(X)|~calm(X))<=>(~happy(X)|~kind(X))))&
(![X]:((old(X)<~>~curious(X))<=>tall(X)))&
((?[X]:((patient(X)&humble(X))))<=>((~tall(lucy)&~kind(lucy))))&
(![X]:(~tall(X)<=>(~humble(X)&old(X))))&
(![X]:((~calm(X)<~>~old(X))<=>(~rich(X)|~kind(X))))&
(((~quiet(susan)&kind(susan)))=>((strong(susan)<~>~brave(susan))))&
((?[X]:((generous(X)&~happy(X))))=>((~quiet(susan)&humble(susan))))&
((?[X]:(tall(X)))=>((~curious(paul)|~creative(paul))))&
((?[X]:((strong(X)&rich(X))))=>(?[X]:((~tall(X)|~humble(X)))))&
((?[X]:((old(X)<~>brave(X))))=>(?[X]:(wise(X))))&
(![X]:((wise(X)|~happy(X))<=>(patient(X)&quiet(X))))&
(![X]:((~funny(X)|strong(X))=>kind(X)))&
(![X]:((brave(X)&happy(X))=>quiet(X)))&
((?[X]:((happy(X)&~curious(X))))=>((~rich(john)<~>~strong(john))))&
((?[X]:((tall(X)|~tall(X))))=>(~calm(susan)))&
(![X]:(funny(X)=>(~kind(X)&~brave(X))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((creative(X)|~strong(X))))&
((~tall(mary)&quiet(mary)))&
(?[X]:((~creative(X)<~>creative(X))))&
(?[X]:(strong(X)))&
((~curious(lucy)&brave(lucy)))&
((quiet(paul)<~>strong(paul))) | curious(paul) | [] | null | 0 |
If john is patient then someone is not brave and vice versa.
Everyone who is wise or kind is both not quiet and curious and vice versa.
Everyone who is not old or not kind is not happy.
If someone is both not strong and not curious then paul is either not humble or not happy.
Everyone who is strong or curious is both brave and creative.
If lucy is either funny or tall then someone is either quiet or patient and vice versa.
Everyone who is patient is not humble and vice versa.
If john is tall then alice is either rich or not patient and vice versa.
Everyone who is calm is either not brave or funny and vice versa.
Everyone who is humble is either not curious or not quiet.
Everyone who is not patient is old or not quiet.
Everyone who is not humble is either not kind or not brave and vice versa.
If someone is either calm or not quiet then someone is generous or not humble and vice versa.
If alice is not old then susan is both quiet and not tall.
If mary is tall then lucy is both kind and not wise and vice versa.
Susan is both not quiet and not wise.
Paul is not funny.
John is humble or not rich.
Alice is humble or not kind.
Lucy is both not wise and patient.
Fred is both generous and not calm. | Susan is not brave. | contradiction | ((patient(john))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|kind(X))<=>(~quiet(X)&curious(X))))&
(![X]:((~old(X)|~kind(X))=>~happy(X)))&
((?[X]:((~strong(X)&~curious(X))))=>((~humble(paul)<~>~happy(paul))))&
(![X]:((strong(X)|curious(X))=>(brave(X)&creative(X))))&
(((funny(lucy)<~>tall(lucy)))<=>(?[X]:((quiet(X)<~>patient(X)))))&
(![X]:(patient(X)<=>~humble(X)))&
((tall(john))<=>((rich(alice)<~>~patient(alice))))&
(![X]:(calm(X)<=>(~brave(X)<~>funny(X))))&
(![X]:(humble(X)=>(~curious(X)<~>~quiet(X))))&
(![X]:(~patient(X)=>(old(X)|~quiet(X))))&
(![X]:(~humble(X)<=>(~kind(X)<~>~brave(X))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>(?[X]:((generous(X)|~humble(X)))))&
((~old(alice))=>((quiet(susan)&~tall(susan))))&
((tall(mary))<=>((kind(lucy)&~wise(lucy))))&
((~quiet(susan)&~wise(susan)))&
(~funny(paul))&
((humble(john)|~rich(john)))&
((humble(alice)|~kind(alice)))&
((~wise(lucy)&patient(lucy)))&
((generous(fred)&~calm(fred))) | ~brave(susan) | [
"p1",
"p4",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6512834988909888203974060
% SZS output start Proof for 6512834988909888203974060
2. ! [X0] : ((kind(X0) | wise(X0)) <=> (curious(X0) & ~quiet(X0))) [input p1]
5. ! [X0] : ((curious(X0) | strong(X0)) => (creative(X0) & brave(X0))) [input p4]
10. ! [X0] : (humble(X0) => (~curious(X0) <~> ~quiet(X0))) [input p9]
12. ! [X0] : (~humble(X0) <=> (~kind(X0) <~> ~brave(X0))) [input p11]
16. ~wise(susan) & ~quiet(susan) [input p15]
22. ~brave(susan) [input hypothesis]
24. ! [X0] : ((curious(X0) | strong(X0)) => brave(X0)) [pure predicate removal 5]
30. ! [X0] : (brave(X0) | (~curious(X0) & ~strong(X0))) [ennf transformation 24]
31. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) | ~humble(X0)) [ennf transformation 10]
36. ! [X0] : (((kind(X0) | wise(X0)) | (~curious(X0) | quiet(X0))) & ((curious(X0) & ~quiet(X0)) | (~kind(X0) & ~wise(X0)))) [nnf transformation 2]
37. ! [X0] : ((kind(X0) | wise(X0) | ~curious(X0) | quiet(X0)) & ((curious(X0) & ~quiet(X0)) | (~kind(X0) & ~wise(X0)))) [flattening 36]
46. ! [X0] : (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | ~humble(X0)) [nnf transformation 31]
47. ! [X0] : ((~humble(X0) | ((~kind(X0) | brave(X0)) & (~brave(X0) | kind(X0)))) & (((brave(X0) | kind(X0)) & (~brave(X0) | ~kind(X0))) | humble(X0))) [nnf transformation 12]
60. ~kind(X0) | curious(X0) [cnf transformation 37]
66. ~curious(X0) | brave(X0) [cnf transformation 30]
86. ~humble(X0) | curious(X0) | quiet(X0) [cnf transformation 46]
88. humble(X0) | kind(X0) | brave(X0) [cnf transformation 47]
100. ~quiet(susan) [cnf transformation 16]
109. ~brave(susan) [cnf transformation 22]
315. kind(X0) | brave(X0) | curious(X0) | quiet(X0) [resolution 88,86]
327. brave(X0) | curious(X0) | quiet(X0) [subsumption resolution 315,60]
328. quiet(X0) | brave(X0) [subsumption resolution 327,66]
358. brave(susan) [resolution 328,100]
360. $false [subsumption resolution 358,109]
% SZS output end Proof for 6512834988909888203974060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble and not rich is either not calm or not brave.
If someone is either creative or not old then paul is both wise and not calm.
If someone is patient then someone is not wise and vice versa.
Everyone who is not funny or humble is both not happy and not tall.
Everyone who is not rich or strong is either curious or patient and vice versa.
Everyone who is not kind or not creative is both humble and not kind and vice versa.
Everyone who is both not creative and not old is not wise and vice versa.
If john is both not patient and funny then someone is either creative or not calm.
Everyone who is either quiet or not rich is both rich and generous and vice versa.
Everyone who is generous or not rich is either tall or not patient and vice versa.
If someone is humble or tall then someone is not humble or not strong.
If fred is both not funny and generous then someone is patient or not humble and vice versa.
Everyone who is both tall and quiet is not funny or not curious and vice versa.
Everyone who is either generous or happy is either humble or not strong.
If someone is both not wise and rich then susan is not rich.
Someone is humble.
Lucy is either not rich or not wise.
Someone is either not brave or funny.
Someone is calm.
Someone is both not calm and not rich.
Someone is funny or not funny. | Fred is patient. | contradiction | (![X]:((humble(X)&~rich(X))=>(~calm(X)<~>~brave(X))))&
((?[X]:((creative(X)<~>~old(X))))=>((wise(paul)&~calm(paul))))&
((?[X]:(patient(X)))<=>(?[X]:(~wise(X))))&
(![X]:((~funny(X)|humble(X))=>(~happy(X)&~tall(X))))&
(![X]:((~rich(X)|strong(X))<=>(curious(X)<~>patient(X))))&
(![X]:((~kind(X)|~creative(X))<=>(humble(X)&~kind(X))))&
(![X]:((~creative(X)&~old(X))<=>~wise(X)))&
(((~patient(john)&funny(john)))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(![X]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((?[X]:((humble(X)|tall(X))))=>(?[X]:((~humble(X)|~strong(X)))))&
(((~funny(fred)&generous(fred)))<=>(?[X]:((patient(X)|~humble(X)))))&
(![X]:((tall(X)&quiet(X))<=>(~funny(X)|~curious(X))))&
(![X]:((generous(X)<~>happy(X))=>(humble(X)<~>~strong(X))))&
((?[X]:((~wise(X)&rich(X))))=>(~rich(susan)))&
(?[X]:(humble(X)))&
((~rich(lucy)<~>~wise(lucy)))&
(?[X]:((~brave(X)<~>funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((~calm(X)&~rich(X))))&
(?[X]:((funny(X)|~funny(X)))) | patient(fred) | [
"p3",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2107788762302426738497951
% SZS output start Proof for 2107788762302426738497951
4. ! [X0] : ((humble(X0) | ~funny(X0)) => (~tall(X0) & ~happy(X0))) [input p3]
12. (generous(fred) & ~funny(fred)) <=> ? [X0] : (~humble(X0) | patient(X0)) [input p11]
13. ! [X0] : ((quiet(X0) & tall(X0)) <=> (~curious(X0) | ~funny(X0))) [input p12]
22. patient(fred) [input hypothesis]
28. ! [X0] : ((~tall(X0) & ~happy(X0)) | (~humble(X0) & funny(X0))) [ennf transformation 4]
57. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & (? [X0] : (~humble(X0) | patient(X0)) | (~generous(fred) | funny(fred))) [nnf transformation 12]
58. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & (? [X0] : (~humble(X0) | patient(X0)) | ~generous(fred) | funny(fred)) [flattening 57]
59. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & (? [X1] : (~humble(X1) | patient(X1)) | ~generous(fred) | funny(fred)) [rectify 58]
60. ? [X1] : (~humble(X1) | patient(X1)) => (~humble(sK4) | patient(sK4)) [choice axiom]
61. ((generous(fred) & ~funny(fred)) | ! [X0] : (humble(X0) & ~patient(X0))) & ((~humble(sK4) | patient(sK4)) | ~generous(fred) | funny(fred)) [skolemisation 59,60]
62. ! [X0] : (((quiet(X0) & tall(X0)) | (curious(X0) & funny(X0))) & ((~curious(X0) | ~funny(X0)) | (~quiet(X0) | ~tall(X0)))) [nnf transformation 13]
63. ! [X0] : (((quiet(X0) & tall(X0)) | (curious(X0) & funny(X0))) & (~curious(X0) | ~funny(X0) | ~quiet(X0) | ~tall(X0))) [flattening 62]
87. ~tall(X0) | funny(X0) [cnf transformation 28]
120. ~funny(fred) | ~patient(X0) [cnf transformation 61]
125. tall(X0) | funny(X0) [cnf transformation 63]
143. patient(fred) [cnf transformation 22]
173. 7 <=> ! [X3] : ~patient(X3) [avatar definition]
174. ~patient(X3) <- (7) [avatar component clause 173]
224. 19 <=> funny(fred) [avatar definition]
226. ~funny(fred) <- (~19) [avatar component clause 224]
228. 7 | ~19 [avatar split clause 120,224,173]
238. funny(X0) [subsumption resolution 125,87]
265. $false <- (7) [resolution 174,143]
266. ~7 [avatar contradiction clause 265]
267. $false <- (~19) [subsumption resolution 226,238]
268. 19 [avatar contradiction clause 267]
271. $false [avatar sat refutation 228,266,268]
% SZS output end Proof for 2107788762302426738497951
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is 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. | John 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(john) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 387532513604165757262260
% SZS output start Proof for 387532513604165757262260
16. ! [X0] : ((happy(X0) | wise(X0)) <=> (~strong(X0) & ~happy(X0))) [input p15]
25. happy(john) [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(john) [cnf transformation 25]
153. ~happy(X0) [duplicate literal removal 135]
362. $false [subsumption resolution 152,153]
% SZS output end Proof for 387532513604165757262260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and not old then mary is either calm or not curious. If alice is not calm or not quiet then someone is either not calm or not happy. If mary is both tall and kind then john is either not humble or curious. Everyone who is not creative is either not funny or not tall and vice versa. Everyone who is either not creative or curious is either not creative or not funny. Everyone who is both not patient and not funny is both not humble and generous and vice versa. Everyone who is not happy or kind is either tall or humble. Everyone who is not rich or wise is either not patient or calm and vice versa. Everyone who is either patient or brave is either not happy or strong and vice versa. If someone is either not tall or curious then someone is either quiet or not humble and vice versa. Everyone who is strong is not quiet and vice versa. If alice is calm then fred is either not strong or tall and vice versa. Everyone who is either not creative or not happy is not patient and vice versa. Everyone who is either creative or not tall is both not old and not strong. Everyone who is not generous or kind is both old and kind and vice versa. Someone is either not wise or humble. Someone is either tall or not generous. Lucy is not rich. Alice is not rich. Someone is not wise. | Mary is humble. | neutral | ((?[X]:((tall(X)&~old(X))))=>((calm(mary)<~>~curious(mary))))&
(((~calm(alice)|~quiet(alice)))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(((tall(mary)&kind(mary)))=>((~humble(john)<~>curious(john))))&
(![X]:(~creative(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:((~creative(X)<~>curious(X))=>(~creative(X)<~>~funny(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~humble(X)&generous(X))))&
(![X]:((~happy(X)|kind(X))=>(tall(X)<~>humble(X))))&
(![X]:((~rich(X)|wise(X))<=>(~patient(X)<~>calm(X))))&
(![X]:((patient(X)<~>brave(X))<=>(~happy(X)<~>strong(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>(?[X]:((quiet(X)<~>~humble(X)))))&
(![X]:(strong(X)<=>~quiet(X)))&
((calm(alice))<=>((~strong(fred)<~>tall(fred))))&
(![X]:((~creative(X)<~>~happy(X))<=>~patient(X)))&
(![X]:((creative(X)<~>~tall(X))=>(~old(X)&~strong(X))))&
(![X]:((~generous(X)|kind(X))<=>(old(X)&kind(X))))&
(?[X]:((~wise(X)<~>humble(X))))&
(?[X]:((tall(X)<~>~generous(X))))&
(~rich(lucy))&
(~rich(alice))&
(?[X]:(~wise(X))) | humble(mary) | [] | null | 0 |
If someone is not strong then someone is both not wise and not old.
Everyone who is both not creative and not wise is quiet or patient and vice versa.
If someone is not generous then paul is not creative or brave.
Everyone who is brave or not humble is not rich or wise.
Everyone who is both strong and not funny is old or quiet and vice versa.
Everyone who is wise is both curious and not rich.
Everyone who is both old and humble is both quiet and not tall and vice versa.
Everyone who is either not humble or not happy is both not humble and strong and vice versa.
Everyone who is both patient and not curious is both not curious and patient.
Everyone who is strong is both old and wise and vice versa.
If john is both brave and not quiet then paul is not kind.
If someone is both quiet and not quiet then john is happy and vice versa.
Everyone who is either tall or not generous is either creative or kind.
If someone is both not curious and not calm then lucy is not strong and vice versa.
Everyone who is humble is not generous or calm and vice versa.
If someone is both not creative and not curious then someone is generous or not calm.
John is curious or creative.
Someone is both wise and kind.
Someone is not brave.
Someone is tall or not creative.
Someone is either calm or generous.
Alice is not humble.
Someone is either old or not rich. | Lucy is not strong. | neutral | ((?[X]:(~strong(X)))=>(?[X]:((~wise(X)&~old(X)))))&
(![X]:((~creative(X)&~wise(X))<=>(quiet(X)|patient(X))))&
((?[X]:(~generous(X)))=>((~creative(paul)|brave(paul))))&
(![X]:((brave(X)|~humble(X))=>(~rich(X)|wise(X))))&
(![X]:((strong(X)&~funny(X))<=>(old(X)|quiet(X))))&
(![X]:(wise(X)=>(curious(X)&~rich(X))))&
(![X]:((old(X)&humble(X))<=>(quiet(X)&~tall(X))))&
(![X]:((~humble(X)<~>~happy(X))<=>(~humble(X)&strong(X))))&
(![X]:((patient(X)&~curious(X))=>(~curious(X)&patient(X))))&
(![X]:(strong(X)<=>(old(X)&wise(X))))&
(((brave(john)&~quiet(john)))=>(~kind(paul)))&
((?[X]:((quiet(X)&~quiet(X))))<=>(happy(john)))&
(![X]:((tall(X)<~>~generous(X))=>(creative(X)<~>kind(X))))&
((?[X]:((~curious(X)&~calm(X))))<=>(~strong(lucy)))&
(![X]:(humble(X)<=>(~generous(X)|calm(X))))&
((?[X]:((~creative(X)&~curious(X))))=>(?[X]:((generous(X)|~calm(X)))))&
((curious(john)|creative(john)))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:(~brave(X)))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((calm(X)<~>generous(X))))&
(~humble(alice))&
(?[X]:((old(X)<~>~rich(X)))) | ~strong(lucy) | [] | null | 0 |
If someone is generous or not generous then john is either quiet or old.
If someone is either brave or tall then paul is either not rich or not patient and vice versa.
If someone is funny then someone is either not happy or rich and vice versa.
Everyone who is not kind is creative or not patient and vice versa.
Everyone who is both brave and curious is both not quiet and generous and vice versa.
If paul is both happy and funny then mary is not funny and vice versa.
Everyone who is either not old or generous is both calm and generous and vice versa.
Everyone who is either not patient or funny is not humble.
If paul is both curious and not kind then someone is not brave.
If someone is not patient then someone is both not brave and not old and vice versa.
If someone is both funny and not brave then paul is both kind and humble.
Everyone who is not strong is either creative or not strong and vice versa.
Everyone who is both strong and old is tall.
Everyone who is strong or not kind is either not funny or not tall and vice versa.
Everyone who is both not strong and tall is happy or kind and vice versa.
Everyone who is not quiet is not tall or generous and vice versa.
Susan is both happy and not strong.
Someone is either not quiet or tall.
Someone is not rich.
Susan is old.
Paul is not old.
Alice is both old and curious.
Paul is curious or not generous. | Susan is not patient. | contradiction | ((?[X]:((generous(X)|~generous(X))))=>((quiet(john)<~>old(john))))&
((?[X]:((brave(X)<~>tall(X))))<=>((~rich(paul)<~>~patient(paul))))&
((?[X]:(funny(X)))<=>(?[X]:((~happy(X)<~>rich(X)))))&
(![X]:(~kind(X)<=>(creative(X)|~patient(X))))&
(![X]:((brave(X)&curious(X))<=>(~quiet(X)&generous(X))))&
(((happy(paul)&funny(paul)))<=>(~funny(mary)))&
(![X]:((~old(X)<~>generous(X))<=>(calm(X)&generous(X))))&
(![X]:((~patient(X)<~>funny(X))=>~humble(X)))&
(((curious(paul)&~kind(paul)))=>(?[X]:(~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~brave(X)&~old(X)))))&
((?[X]:((funny(X)&~brave(X))))=>((kind(paul)&humble(paul))))&
(![X]:(~strong(X)<=>(creative(X)<~>~strong(X))))&
(![X]:((strong(X)&old(X))=>tall(X)))&
(![X]:((strong(X)|~kind(X))<=>(~funny(X)<~>~tall(X))))&
(![X]:((~strong(X)&tall(X))<=>(happy(X)|kind(X))))&
(![X]:(~quiet(X)<=>(~tall(X)|generous(X))))&
((happy(susan)&~strong(susan)))&
(?[X]:((~quiet(X)<~>tall(X))))&
(?[X]:(~rich(X)))&
(old(susan))&
(~old(paul))&
((old(alice)&curious(alice)))&
((curious(paul)|~generous(paul))) | ~patient(susan) | [
"p4",
"p6",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5218531737111056438155319
% SZS output start Proof for 5218531737111056438155319
5. ! [X0] : ((curious(X0) & brave(X0)) <=> (generous(X0) & ~quiet(X0))) [input p4]
7. ! [X0] : ((~old(X0) <~> generous(X0)) <=> (generous(X0) & calm(X0))) [input p6]
10. ? [X0] : ~patient(X0) <=> ? [X0] : (~old(X0) & ~brave(X0)) [input p9]
16. ! [X0] : (~quiet(X0) <=> (generous(X0) | ~tall(X0))) [input p15]
24. ~patient(susan) [input hypothesis]
26. ? [X0] : ~patient(X0) <=> ? [X1] : (~old(X1) & ~brave(X1)) [rectify 10]
46. ! [X0] : (((curious(X0) & brave(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (~curious(X0) | ~brave(X0)))) [nnf transformation 5]
47. ! [X0] : (((curious(X0) & brave(X0)) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | ~curious(X0) | ~brave(X0))) [flattening 46]
50. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [nnf transformation 7]
51. ! [X0] : ((((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0))))) [flattening 50]
55. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X1] : (~old(X1) & ~brave(X1)) | ! [X0] : patient(X0)) [nnf transformation 26]
56. (? [X0] : ~patient(X0) | ! [X1] : (old(X1) | brave(X1))) & (? [X2] : (~old(X2) & ~brave(X2)) | ! [X3] : patient(X3)) [rectify 55]
57. ? [X0] : ~patient(X0) => ~patient(sK4) [choice axiom]
58. ? [X2] : (~old(X2) & ~brave(X2)) => (~old(sK5) & ~brave(sK5)) [choice axiom]
59. (~patient(sK4) | ! [X1] : (old(X1) | brave(X1))) & ((~old(sK5) & ~brave(sK5)) | ! [X3] : patient(X3)) [skolemisation 56,58,57]
65. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & ((generous(X0) | ~tall(X0)) | quiet(X0))) [nnf transformation 16]
66. ! [X0] : ((~quiet(X0) | (~generous(X0) & tall(X0))) & (generous(X0) | ~tall(X0) | quiet(X0))) [flattening 65]
93. ~generous(X0) | brave(X0) | quiet(X0) [cnf transformation 47]
100. generous(X0) | generous(X0) | old(X0) [cnf transformation 51]
107. ~brave(sK5) | patient(X3) [cnf transformation 59]
108. ~old(sK5) | patient(X3) [cnf transformation 59]
130. ~quiet(X0) | ~generous(X0) [cnf transformation 66]
141. ~patient(susan) [cnf transformation 24]
144. old(X0) | generous(X0) [duplicate literal removal 100]
256. 25 <=> ! [X3] : patient(X3) [avatar definition]
257. patient(X3) <- (25) [avatar component clause 256]
259. 26 <=> old(sK5) [avatar definition]
261. ~old(sK5) <- (~26) [avatar component clause 259]
262. 25 | ~26 [avatar split clause 108,259,256]
264. 27 <=> brave(sK5) [avatar definition]
266. ~brave(sK5) <- (~27) [avatar component clause 264]
267. 25 | ~27 [avatar split clause 107,264,256]
294. generous(sK5) <- (~26) [resolution 144,261]
328. brave(sK5) | quiet(sK5) <- (~26) [resolution 93,294]
331. quiet(sK5) <- (~26, ~27) [subsumption resolution 328,266]
396. ~generous(sK5) <- (~26, ~27) [resolution 331,130]
398. $false <- (~26, ~27) [subsumption resolution 396,294]
399. 26 | 27 [avatar contradiction clause 398]
400. $false <- (25) [resolution 257,141]
404. ~25 [avatar contradiction clause 400]
406. $false [avatar sat refutation 262,267,399,404]
% SZS output end Proof for 5218531737111056438155319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or creative is old or wise.
Everyone who is humble or not humble is kind.
Everyone who is either not creative or not funny is not brave.
If mary is both not generous and brave then someone is brave or not calm and vice versa.
Everyone who is either generous or not generous is both not happy and not quiet and vice versa.
Everyone who is either curious or not quiet is happy.
Everyone who is both not funny and not patient is not funny.
If paul is not quiet then someone is humble or quiet.
If fred is both happy and not generous then someone is both strong and calm.
Everyone who is not strong is happy and vice versa.
Everyone who is not funny is humble.
Everyone who is either not funny or tall is either rich or calm and vice versa.
Everyone who is both old and not kind is either not generous or wise and vice versa.
Everyone who is funny is both humble and not happy and vice versa.
If paul is happy then someone is either curious or not patient and vice versa.
Mary is not patient or not rich.
Lucy is tall or not brave.
Fred is either not calm or not humble.
Someone is not old.
Someone is either old or not strong.
Someone is either not happy or patient. | Paul is wise. | neutral | (![X]:((~calm(X)<~>creative(X))=>(old(X)|wise(X))))&
(![X]:((humble(X)|~humble(X))=>kind(X)))&
(![X]:((~creative(X)<~>~funny(X))=>~brave(X)))&
(((~generous(mary)&brave(mary)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((generous(X)<~>~generous(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:((~funny(X)&~patient(X))=>~funny(X)))&
((~quiet(paul))=>(?[X]:((humble(X)|quiet(X)))))&
(((happy(fred)&~generous(fred)))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:(~funny(X)=>humble(X)))&
(![X]:((~funny(X)<~>tall(X))<=>(rich(X)<~>calm(X))))&
(![X]:((old(X)&~kind(X))<=>(~generous(X)<~>wise(X))))&
(![X]:(funny(X)<=>(humble(X)&~happy(X))))&
((happy(paul))<=>(?[X]:((curious(X)<~>~patient(X)))))&
((~patient(mary)|~rich(mary)))&
((tall(lucy)|~brave(lucy)))&
((~calm(fred)<~>~humble(fred)))&
(?[X]:(~old(X)))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:((~happy(X)<~>patient(X)))) | wise(paul) | [] | null | 0 |
Everyone who is strong is either old or patient. If mary is both not humble and brave then someone is both rich and not creative and vice versa. If john is not strong then lucy is not rich or tall. Everyone who is either humble or brave is either not strong or calm. If someone is not humble then susan is either not rich or creative and vice versa. Everyone who is both calm and not quiet is not calm or funny and vice versa. Everyone who is old is not generous or not humble and vice versa. Everyone who is not humble is either not curious or not happy. Everyone who is not tall is calm or creative and vice versa. Everyone who is not kind is both wise and not kind. If lucy is both old and not calm then someone is not generous or not quiet. Everyone who is brave is both not strong and not humble and vice versa. Everyone who is not calm or not brave is both curious and not old and vice versa. If someone is either not tall or curious then susan is not patient or wise and vice versa. Everyone who is both not kind and humble is calm. Everyone who is either humble or not tall is not kind or not wise. Paul is kind or quiet. Susan is patient. Susan is not wise. Alice is either generous or tall. Someone is either not calm or not tall. Someone is funny or not wise. | John is happy. | neutral | (![X]:(strong(X)=>(old(X)<~>patient(X))))&
(((~humble(mary)&brave(mary)))<=>(?[X]:((rich(X)&~creative(X)))))&
((~strong(john))=>((~rich(lucy)|tall(lucy))))&
(![X]:((humble(X)<~>brave(X))=>(~strong(X)<~>calm(X))))&
((?[X]:(~humble(X)))<=>((~rich(susan)<~>creative(susan))))&
(![X]:((calm(X)&~quiet(X))<=>(~calm(X)|funny(X))))&
(![X]:(old(X)<=>(~generous(X)|~humble(X))))&
(![X]:(~humble(X)=>(~curious(X)<~>~happy(X))))&
(![X]:(~tall(X)<=>(calm(X)|creative(X))))&
(![X]:(~kind(X)=>(wise(X)&~kind(X))))&
(((old(lucy)&~calm(lucy)))=>(?[X]:((~generous(X)|~quiet(X)))))&
(![X]:(brave(X)<=>(~strong(X)&~humble(X))))&
(![X]:((~calm(X)|~brave(X))<=>(curious(X)&~old(X))))&
((?[X]:((~tall(X)<~>curious(X))))<=>((~patient(susan)|wise(susan))))&
(![X]:((~kind(X)&humble(X))=>calm(X)))&
(![X]:((humble(X)<~>~tall(X))=>(~kind(X)|~wise(X))))&
((kind(paul)|quiet(paul)))&
(patient(susan))&
(~wise(susan))&
((generous(alice)<~>tall(alice)))&
(?[X]:((~calm(X)<~>~tall(X))))&
(?[X]:((funny(X)|~wise(X)))) | happy(john) | [] | null | 0 |
Everyone who is not calm is both not tall and not patient and vice versa.
If paul is brave then someone is wise or curious.
If susan is either generous or not patient then someone is either not quiet or not humble and vice versa.
If paul is both strong and not humble then someone is curious and vice versa.
If fred is patient or not creative then someone is not tall.
If someone is both tall and generous then someone is either not curious or humble and vice versa.
If john is not tall or humble then someone is either not generous or strong.
Everyone who is both strong and not generous is either creative or rich and vice versa.
Everyone who is both quiet and not kind is both not funny and funny and vice versa.
If someone is both not patient and generous then mary is both patient and not curious and vice versa.
Everyone who is not tall is not generous.
Everyone who is not generous is both not curious and tall and vice versa.
Everyone who is creative is either quiet or generous.
Everyone who is either not calm or humble is both not rich and not kind and vice versa.
Everyone who is both strong and wise is both not curious and not strong and vice versa.
Everyone who is quiet or patient is either tall or not tall and vice versa.
Someone is either not humble or not kind.
Someone is not rich or not creative.
Someone is both funny and wise.
Fred is tall.
Someone is not quiet or calm.
Someone is either strong or not patient.
Someone is not brave or not rich.
Someone is either not patient or wise. | Fred is creative. | entailment | (![X]:(~calm(X)<=>(~tall(X)&~patient(X))))&
((brave(paul))=>(?[X]:((wise(X)|curious(X)))))&
(((generous(susan)<~>~patient(susan)))<=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(((strong(paul)&~humble(paul)))<=>(?[X]:(curious(X))))&
(((patient(fred)|~creative(fred)))=>(?[X]:(~tall(X))))&
((?[X]:((tall(X)&generous(X))))<=>(?[X]:((~curious(X)<~>humble(X)))))&
(((~tall(john)|humble(john)))=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:((strong(X)&~generous(X))<=>(creative(X)<~>rich(X))))&
(![X]:((quiet(X)&~kind(X))<=>(~funny(X)&funny(X))))&
((?[X]:((~patient(X)&generous(X))))<=>((patient(mary)&~curious(mary))))&
(![X]:(~tall(X)=>~generous(X)))&
(![X]:(~generous(X)<=>(~curious(X)&tall(X))))&
(![X]:(creative(X)=>(quiet(X)<~>generous(X))))&
(![X]:((~calm(X)<~>humble(X))<=>(~rich(X)&~kind(X))))&
(![X]:((strong(X)&wise(X))<=>(~curious(X)&~strong(X))))&
(![X]:((quiet(X)|patient(X))<=>(tall(X)<~>~tall(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((~rich(X)|~creative(X))))&
(?[X]:((funny(X)&wise(X))))&
(tall(fred))&
(?[X]:((~quiet(X)|calm(X))))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((~brave(X)|~rich(X))))&
(?[X]:((~patient(X)<~>wise(X)))) | creative(fred) | [
"p4",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4290221172040715254155553
% SZS output start Proof for 4290221172040715254155553
5. (~creative(fred) | patient(fred)) => ? [X0] : ~tall(X0) [input p4]
11. ! [X0] : (~tall(X0) => ~generous(X0)) [input p10]
12. ! [X0] : (~generous(X0) <=> (tall(X0) & ~curious(X0))) [input p11]
25. ~creative(fred) [input hypothesis]
29. ? [X0] : ~tall(X0) | (creative(fred) & ~patient(fred)) [ennf transformation 5]
31. ! [X0] : (~generous(X0) | tall(X0)) [ennf transformation 11]
44. ? [X0] : ~tall(X0) => ~tall(sK2) [choice axiom]
45. ~tall(sK2) | (creative(fred) & ~patient(fred)) [skolemisation 29,44]
63. ! [X0] : ((~generous(X0) | (~tall(X0) | curious(X0))) & ((tall(X0) & ~curious(X0)) | generous(X0))) [nnf transformation 12]
64. ! [X0] : ((~generous(X0) | ~tall(X0) | curious(X0)) & ((tall(X0) & ~curious(X0)) | generous(X0))) [flattening 63]
102. ~tall(sK2) | creative(fred) [cnf transformation 45]
127. ~generous(X0) | tall(X0) [cnf transformation 31]
129. tall(X0) | generous(X0) [cnf transformation 64]
160. ~creative(fred) [cnf transformation 25]
214. 11 <=> creative(fred) [avatar definition]
218. 12 <=> tall(sK2) [avatar definition]
220. ~tall(sK2) <- (~12) [avatar component clause 218]
221. 11 | ~12 [avatar split clause 102,218,214]
303. tall(X0) [subsumption resolution 129,127]
353. ~11 [avatar split clause 160,214]
354. $false <- (~12) [subsumption resolution 220,303]
355. 12 [avatar contradiction clause 354]
356. $false [avatar sat refutation 221,353,355]
% SZS output end Proof for 4290221172040715254155553
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not happy and wise then someone is humble. Everyone who is creative is either old or curious and vice versa. Everyone who is both not patient and humble is either not funny or strong and vice versa. If john is either rich or not rich then alice is kind or not kind and vice versa. If someone is calm then someone is both not curious and tall. If susan is not quiet or not calm then paul is either not old or not generous. If someone is both brave and not kind then someone is both not kind and old. Everyone who is either strong or old is both not patient and not happy. Everyone who is either generous or not curious is both kind and not humble and vice versa. If someone is either funny or not brave then someone is curious and vice versa. Everyone who is both not creative and not patient is either curious or not curious and vice versa. Everyone who is not wise or brave is kind and vice versa. Everyone who is not patient is either calm or not quiet. If someone is either tall or curious then john is both rich and patient and vice versa. If someone is not patient then someone is both kind and rich and vice versa. If someone is either not old or curious then someone is both funny and happy. Alice is both strong and tall. Paul is calm or kind. Someone is not kind or curious. Mary is rich or generous. John is not tall. Mary is not rich. Lucy is strong or not humble. Someone is both not wise and rich. | Paul is not kind. | contradiction | ((?[X]:((~happy(X)&wise(X))))=>(?[X]:(humble(X))))&
(![X]:(creative(X)<=>(old(X)<~>curious(X))))&
(![X]:((~patient(X)&humble(X))<=>(~funny(X)<~>strong(X))))&
(((rich(john)<~>~rich(john)))<=>((kind(alice)|~kind(alice))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&tall(X)))))&
(((~quiet(susan)|~calm(susan)))=>((~old(paul)<~>~generous(paul))))&
((?[X]:((brave(X)&~kind(X))))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((strong(X)<~>old(X))=>(~patient(X)&~happy(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(kind(X)&~humble(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((~creative(X)&~patient(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~wise(X)|brave(X))<=>kind(X)))&
(![X]:(~patient(X)=>(calm(X)<~>~quiet(X))))&
((?[X]:((tall(X)<~>curious(X))))<=>((rich(john)&patient(john))))&
((?[X]:(~patient(X)))<=>(?[X]:((kind(X)&rich(X)))))&
((?[X]:((~old(X)<~>curious(X))))=>(?[X]:((funny(X)&happy(X)))))&
((strong(alice)&tall(alice)))&
((calm(paul)|kind(paul)))&
(?[X]:((~kind(X)|curious(X))))&
((rich(mary)|generous(mary)))&
(~tall(john))&
(~rich(mary))&
((strong(lucy)|~humble(lucy)))&
(?[X]:((~wise(X)&rich(X)))) | ~kind(paul) | [
"p4",
"p10",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6613429999864631022570636
% SZS output start Proof for 6613429999864631022570636
5. ? [X0] : calm(X0) => ? [X0] : (tall(X0) & ~curious(X0)) [input p4]
11. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p10]
14. ? [X0] : (tall(X0) <~> curious(X0)) <=> (patient(john) & rich(john)) [input p13]
18. kind(paul) | calm(paul) [input p17]
25. ~kind(paul) [input hypothesis]
27. ? [X0] : calm(X0) => ? [X1] : (tall(X1) & ~curious(X1)) [rectify 5]
33. ? [X1] : (tall(X1) & ~curious(X1)) | ! [X0] : ~calm(X0) [ennf transformation 27]
47. ? [X0] : (tall(X0) & ~curious(X0)) | ! [X1] : ~calm(X1) [rectify 33]
48. ? [X0] : (tall(X0) & ~curious(X0)) => (tall(sK1) & ~curious(sK1)) [choice axiom]
49. (tall(sK1) & ~curious(sK1)) | ! [X1] : ~calm(X1) [skolemisation 47,48]
62. ! [X0] : (((~patient(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (patient(X0) | creative(X0)))) [nnf transformation 11]
63. ! [X0] : (((~patient(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | patient(X0) | creative(X0))) [flattening 62]
67. (? [X0] : ((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | (~patient(john) | ~rich(john))) & ((patient(john) & rich(john)) | ! [X0] : ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0)))) [nnf transformation 14]
68. (? [X0] : ((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | ~patient(john) | ~rich(john)) & ((patient(john) & rich(john)) | ! [X0] : ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0)))) [flattening 67]
69. (? [X0] : ((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) | ~patient(john) | ~rich(john)) & ((patient(john) & rich(john)) | ! [X1] : ((tall(X1) | ~curious(X1)) & (curious(X1) | ~tall(X1)))) [rectify 68]
70. ? [X0] : ((~curious(X0) | ~tall(X0)) & (curious(X0) | tall(X0))) => ((~curious(sK5) | ~tall(sK5)) & (curious(sK5) | tall(sK5))) [choice axiom]
71. (((~curious(sK5) | ~tall(sK5)) & (curious(sK5) | tall(sK5))) | ~patient(john) | ~rich(john)) & ((patient(john) & rich(john)) | ! [X1] : ((tall(X1) | ~curious(X1)) & (curious(X1) | ~tall(X1)))) [skolemisation 69,70]
102. ~curious(sK1) | ~calm(X1) [cnf transformation 49]
103. tall(sK1) | ~calm(X1) [cnf transformation 49]
128. ~patient(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 63]
129. ~patient(X0) | curious(X0) | curious(X0) [cnf transformation 63]
137. patient(john) | curious(X1) | ~tall(X1) [cnf transformation 71]
150. kind(paul) | calm(paul) [cnf transformation 18]
158. ~kind(paul) [cnf transformation 25]
161. ~patient(X0) | ~curious(X0) [duplicate literal removal 128]
162. ~patient(X0) | curious(X0) [duplicate literal removal 129]
174. 3 <=> ! [X1] : ~calm(X1) [avatar definition]
175. ~calm(X1) <- (3) [avatar component clause 174]
177. 4 <=> tall(sK1) [avatar definition]
179. tall(sK1) <- (4) [avatar component clause 177]
180. 3 | 4 [avatar split clause 103,177,174]
182. 5 <=> curious(sK1) [avatar definition]
184. ~curious(sK1) <- (~5) [avatar component clause 182]
185. 3 | ~5 [avatar split clause 102,182,174]
244. ~patient(X0) [subsumption resolution 161,162]
250. ~tall(X1) | curious(X1) [subsumption resolution 137,244]
272. 23 <=> calm(paul) [avatar definition]
274. calm(paul) <- (23) [avatar component clause 272]
276. 24 <=> kind(paul) [avatar definition]
279. 23 | 24 [avatar split clause 150,276,272]
308. ~24 [avatar split clause 158,276]
309. $false <- (3, 23) [resolution 274,175]
310. ~3 | ~23 [avatar contradiction clause 309]
317. curious(sK1) <- (4) [resolution 250,179]
319. $false <- (4, ~5) [subsumption resolution 317,184]
320. ~4 | 5 [avatar contradiction clause 319]
321. $false [avatar sat refutation 180,185,279,308,310,320]
% SZS output end Proof for 6613429999864631022570636
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich then someone is kind or not generous.
Everyone who is both strong and curious is either strong or quiet.
Everyone who is not generous is wise and vice versa.
If someone is curious or funny then paul is kind.
If someone is not happy or kind then susan is both kind and curious.
If someone is not brave then someone is brave or old.
Everyone who is not strong or not brave is either wise or happy.
Everyone who is not wise or old is not wise or generous and vice versa.
If mary is not humble then someone is quiet.
If susan is kind then paul is kind and vice versa.
Everyone who is both not curious and rich is both old and not old and vice versa.
Everyone who is not brave or not kind is not wise or not rich.
Everyone who is both wise and old is calm or rich and vice versa.
If someone is not kind or not tall then someone is old or brave and vice versa.
If mary is quiet then someone is both funny and wise and vice versa.
Everyone who is both not calm and kind is humble or not old.
Fred is tall.
Someone is either kind or happy.
John is not strong.
Someone is not humble or generous.
Lucy is happy or strong.
Paul is old or not strong. | Lucy is not calm. | entailment | ((?[X]:(rich(X)))=>(?[X]:((kind(X)|~generous(X)))))&
(![X]:((strong(X)&curious(X))=>(strong(X)<~>quiet(X))))&
(![X]:(~generous(X)<=>wise(X)))&
((?[X]:((curious(X)|funny(X))))=>(kind(paul)))&
((?[X]:((~happy(X)|kind(X))))=>((kind(susan)&curious(susan))))&
((?[X]:(~brave(X)))=>(?[X]:((brave(X)|old(X)))))&
(![X]:((~strong(X)|~brave(X))=>(wise(X)<~>happy(X))))&
(![X]:((~wise(X)|old(X))<=>(~wise(X)|generous(X))))&
((~humble(mary))=>(?[X]:(quiet(X))))&
((kind(susan))<=>(kind(paul)))&
(![X]:((~curious(X)&rich(X))<=>(old(X)&~old(X))))&
(![X]:((~brave(X)|~kind(X))=>(~wise(X)|~rich(X))))&
(![X]:((wise(X)&old(X))<=>(calm(X)|rich(X))))&
((?[X]:((~kind(X)|~tall(X))))<=>(?[X]:((old(X)|brave(X)))))&
((quiet(mary))<=>(?[X]:((funny(X)&wise(X)))))&
(![X]:((~calm(X)&kind(X))=>(humble(X)|~old(X))))&
(tall(fred))&
(?[X]:((kind(X)<~>happy(X))))&
(~strong(john))&
(?[X]:((~humble(X)|generous(X))))&
((happy(lucy)|strong(lucy)))&
((old(paul)|~strong(paul))) | ~calm(lucy) | [
"p2",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1054537936424175635531942
% SZS output start Proof for 1054537936424175635531942
3. ! [X0] : (~generous(X0) <=> wise(X0)) [input p2]
8. ! [X0] : ((old(X0) | ~wise(X0)) <=> (generous(X0) | ~wise(X0))) [input p7]
13. ! [X0] : ((old(X0) & wise(X0)) <=> (rich(X0) | calm(X0))) [input p12]
23. calm(lucy) [input hypothesis]
43. ! [X0] : ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0))) [nnf transformation 3]
48. ! [X0] : (((old(X0) | ~wise(X0)) | (~generous(X0) & wise(X0))) & ((generous(X0) | ~wise(X0)) | (~old(X0) & wise(X0)))) [nnf transformation 8]
49. ! [X0] : ((old(X0) | ~wise(X0) | (~generous(X0) & wise(X0))) & (generous(X0) | ~wise(X0) | (~old(X0) & wise(X0)))) [flattening 48]
55. ! [X0] : (((old(X0) & wise(X0)) | (~rich(X0) & ~calm(X0))) & ((rich(X0) | calm(X0)) | (~old(X0) | ~wise(X0)))) [nnf transformation 13]
56. ! [X0] : (((old(X0) & wise(X0)) | (~rich(X0) & ~calm(X0))) & (rich(X0) | calm(X0) | ~old(X0) | ~wise(X0))) [flattening 55]
75. ~wise(X0) | ~generous(X0) [cnf transformation 43]
88. generous(X0) | ~wise(X0) | ~old(X0) [cnf transformation 49]
101. ~calm(X0) | wise(X0) [cnf transformation 56]
103. ~calm(X0) | old(X0) [cnf transformation 56]
120. calm(lucy) [cnf transformation 23]
176. ~old(X0) | ~wise(X0) [subsumption resolution 88,75]
283. wise(lucy) [resolution 101,120]
285. old(lucy) [resolution 103,120]
287. ~wise(lucy) [resolution 176,285]
288. $false [subsumption resolution 287,283]
% SZS output end Proof for 1054537936424175635531942
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not humble is both old and not tall. Everyone who is strong or old is both not wise and rich and vice versa. If lucy is either not tall or generous then john is either generous or happy. Everyone who is brave is not kind. Everyone who is either not patient or patient is either not old or old and vice versa. Everyone who is both old and funny is both not calm and old. Everyone who is not wise is not tall. Everyone who is not brave or strong is generous or not curious and vice versa. Everyone who is either wise or not funny is both not humble and not patient and vice versa. Everyone who is both not creative and creative is both not funny and wise and vice versa. If someone is tall or not curious then fred is wise and vice versa. If john is not patient then someone is both wise and happy. If someone is either not humble or not old then someone is both not tall and not creative. Everyone who is strong or patient is not calm. Everyone who is not creative is not happy or kind and vice versa. Someone is either tall or not brave. Susan is either calm or old. Someone is not quiet. Someone is both kind and not brave. Lucy is not rich or patient. Someone is rich. Fred is funny or not patient. Someone is strong or not brave. | Fred is curious. | entailment | (![X]:((kind(X)|~humble(X))=>(old(X)&~tall(X))))&
(![X]:((strong(X)|old(X))<=>(~wise(X)&rich(X))))&
(((~tall(lucy)<~>generous(lucy)))=>((generous(john)<~>happy(john))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((~patient(X)<~>patient(X))<=>(~old(X)<~>old(X))))&
(![X]:((old(X)&funny(X))=>(~calm(X)&old(X))))&
(![X]:(~wise(X)=>~tall(X)))&
(![X]:((~brave(X)|strong(X))<=>(generous(X)|~curious(X))))&
(![X]:((wise(X)<~>~funny(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~creative(X)&creative(X))<=>(~funny(X)&wise(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(wise(fred)))&
((~patient(john))=>(?[X]:((wise(X)&happy(X)))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((~tall(X)&~creative(X)))))&
(![X]:((strong(X)|patient(X))=>~calm(X)))&
(![X]:(~creative(X)<=>(~happy(X)|kind(X))))&
(?[X]:((tall(X)<~>~brave(X))))&
((calm(susan)<~>old(susan)))&
(?[X]:(~quiet(X)))&
(?[X]:((kind(X)&~brave(X))))&
((~rich(lucy)|patient(lucy)))&
(?[X]:(rich(X)))&
((funny(fred)|~patient(fred)))&
(?[X]:((strong(X)|~brave(X)))) | curious(fred) | [
"p0",
"p1",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 253737795507450429884564
% SZS output start Proof for 253737795507450429884564
1. ! [X0] : ((~humble(X0) | kind(X0)) => (~tall(X0) & old(X0))) [input p0]
2. ! [X0] : ((old(X0) | strong(X0)) <=> (rich(X0) & ~wise(X0))) [input p1]
9. ! [X0] : ((wise(X0) <~> ~funny(X0)) <=> (~patient(X0) & ~humble(X0))) [input p8]
10. ! [X0] : ((creative(X0) & ~creative(X0)) <=> (wise(X0) & ~funny(X0))) [input p9]
11. ? [X0] : (~curious(X0) | tall(X0)) <=> wise(fred) [input p10]
24. ~curious(fred) [input hypothesis]
27. ! [X0] : ((~tall(X0) & old(X0)) | (humble(X0) & ~kind(X0))) [ennf transformation 1]
36. ! [X0] : (((old(X0) | strong(X0)) | (~rich(X0) | wise(X0))) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [nnf transformation 2]
37. ! [X0] : ((old(X0) | strong(X0) | ~rich(X0) | wise(X0)) & ((rich(X0) & ~wise(X0)) | (~old(X0) & ~strong(X0)))) [flattening 36]
42. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | (patient(X0) | humble(X0))) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [nnf transformation 9]
43. ! [X0] : ((((funny(X0) | ~wise(X0)) & (~funny(X0) | wise(X0))) | patient(X0) | humble(X0)) & ((~patient(X0) & ~humble(X0)) | ((wise(X0) | funny(X0)) & (~funny(X0) | ~wise(X0))))) [flattening 42]
44. ! [X0] : (((creative(X0) & ~creative(X0)) | (~wise(X0) | funny(X0))) & ((wise(X0) & ~funny(X0)) | (~creative(X0) | creative(X0)))) [nnf transformation 10]
45. ! [X0] : (((creative(X0) & ~creative(X0)) | ~wise(X0) | funny(X0)) & ((wise(X0) & ~funny(X0)) | ~creative(X0) | creative(X0))) [flattening 44]
46. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X0] : (curious(X0) & ~tall(X0))) [nnf transformation 11]
47. (? [X0] : (~curious(X0) | tall(X0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [rectify 46]
48. ? [X0] : (~curious(X0) | tall(X0)) => (~curious(sK0) | tall(sK0)) [choice axiom]
49. ((~curious(sK0) | tall(sK0)) | ~wise(fred)) & (wise(fred) | ! [X1] : (curious(X1) & ~tall(X1))) [skolemisation 47,48]
69. old(X0) | humble(X0) [cnf transformation 27]
73. ~wise(X0) | ~old(X0) [cnf transformation 37]
97. ~funny(X0) | ~humble(X0) | ~wise(X0) [cnf transformation 43]
105. ~creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 45]
106. creative(X0) | ~wise(X0) | funny(X0) [cnf transformation 45]
108. wise(fred) | curious(X1) [cnf transformation 49]
131. ~curious(fred) [cnf transformation 24]
160. ~wise(X0) | funny(X0) [subsumption resolution 105,106]
162. 5 <=> wise(fred) [avatar definition]
163. wise(fred) <- (5) [avatar component clause 162]
175. 8 <=> ! [X1] : curious(X1) [avatar definition]
176. curious(X1) <- (8) [avatar component clause 175]
177. 8 | 5 [avatar split clause 108,162,175]
248. 23 <=> funny(fred) [avatar definition]
250. funny(fred) <- (23) [avatar component clause 248]
280. funny(fred) <- (5) [resolution 160,163]
282. 23 | ~5 [avatar split clause 280,162,248]
283. $false <- (8) [resolution 176,131]
286. ~8 [avatar contradiction clause 283]
288. ~old(fred) <- (5) [resolution 163,73]
293. humble(fred) <- (5) [resolution 288,69]
295. ~humble(fred) | ~wise(fred) <- (23) [resolution 97,250]
297. ~wise(fred) <- (5, 23) [subsumption resolution 295,293]
298. $false <- (5, 23) [subsumption resolution 297,163]
299. ~5 | ~23 [avatar contradiction clause 298]
303. $false [avatar sat refutation 177,282,286,299]
% SZS output end Proof for 253737795507450429884564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or brave is both not brave and not old and vice versa. If someone is humble or happy then mary is either tall or not creative. Everyone who is not brave or kind is not funny and vice versa. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Everyone who is either quiet or calm is both not wise and funny and vice versa. If someone is both humble and curious then someone is either humble or not creative and vice versa. Fred is either not generous or old. Alice is either patient or rich. Lucy is both tall and not curious. Someone is either not calm or generous. Susan is either not wise or rich. Someone is either not calm or funny. Someone is not tall. | Fred is happy. | neutral | (![X]:((~old(X)|brave(X))<=>(~brave(X)&~old(X))))&
((?[X]:((humble(X)|happy(X))))=>((tall(mary)<~>~creative(mary))))&
(![X]:((~brave(X)|kind(X))<=>~funny(X)))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
(?[X]:((~calm(X)<~>generous(X))))&
((~wise(susan)<~>rich(susan)))&
(?[X]:((~calm(X)<~>funny(X))))&
(?[X]:(~tall(X))) | happy(fred) | [] | null | 0 |
If someone is not curious or not rich then alice is both wise and not quiet. If someone is either creative or quiet then someone is both kind and not creative. If someone is not curious then john is old or calm and vice versa. If someone is tall then john is kind and vice versa. If susan is not brave then lucy is both patient and not quiet and vice versa. Everyone who is both not creative and curious is wise or not brave. If lucy is both not tall and not creative then mary is funny or not quiet and vice versa. Everyone who is both quiet and not strong is both not humble and not generous and vice versa. If someone is either funny or not wise then someone is both old and quiet and vice versa. Everyone who is both kind and creative is kind and vice versa. If fred is either not old or not happy then someone is either not calm or kind. Everyone who is both quiet and strong is not happy or quiet and vice versa. Everyone who is either not old or not funny is either strong or humble and vice versa. If paul is both not humble and not old then lucy is patient or not tall and vice versa. Everyone who is either kind or creative is either old or not tall and vice versa. Alice is happy. Someone is either not curious or brave. Someone is either not generous or not calm. Mary is wise. Someone is not brave or wise. Someone is brave or not quiet. Alice is generous or patient. | Susan is not generous. | neutral | ((?[X]:((~curious(X)|~rich(X))))=>((wise(alice)&~quiet(alice))))&
((?[X]:((creative(X)<~>quiet(X))))=>(?[X]:((kind(X)&~creative(X)))))&
((?[X]:(~curious(X)))<=>((old(john)|calm(john))))&
((?[X]:(tall(X)))<=>(kind(john)))&
((~brave(susan))<=>((patient(lucy)&~quiet(lucy))))&
(![X]:((~creative(X)&curious(X))=>(wise(X)|~brave(X))))&
(((~tall(lucy)&~creative(lucy)))<=>((funny(mary)|~quiet(mary))))&
(![X]:((quiet(X)&~strong(X))<=>(~humble(X)&~generous(X))))&
((?[X]:((funny(X)<~>~wise(X))))<=>(?[X]:((old(X)&quiet(X)))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(wise(mary))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | ~generous(susan) | [] | null | 0 |
Everyone who is both not happy and tall is either not kind or not curious and vice versa. If susan is quiet or rich then paul is either humble or not strong. If someone is patient or generous then alice is both generous and tall. If someone is either not curious or funny then someone is either not humble or not rich and vice versa. Everyone who is patient is both creative and not humble and vice versa. If someone is quiet then alice is brave or creative and vice versa. Everyone who is funny or not wise is wise and vice versa. Everyone who is either not kind or not tall is happy and vice versa. Everyone who is curious is either quiet or not funny. If someone is either not brave or humble then someone is patient or not creative. Everyone who is not generous or not humble is not old or not brave and vice versa. If someone is quiet or not calm then susan is not strong or not generous. Everyone who is both old and patient is either not patient or rich and vice versa. If lucy is not humble then mary is either not creative or calm. Everyone who is both rich and not humble is strong. Everyone who is either wise or funny is rich and vice versa. Someone is funny or tall. Mary is not quiet or funny. Someone is kind. Someone is both calm and not old. Someone is not generous. Someone is not curious. Alice is either not rich or not strong. Mary is patient. | Lucy is humble. | contradiction | (![X]:((~happy(X)&tall(X))<=>(~kind(X)<~>~curious(X))))&
(((quiet(susan)|rich(susan)))=>((humble(paul)<~>~strong(paul))))&
((?[X]:((patient(X)|generous(X))))=>((generous(alice)&tall(alice))))&
((?[X]:((~curious(X)<~>funny(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(![X]:(patient(X)<=>(creative(X)&~humble(X))))&
((?[X]:(quiet(X)))<=>((brave(alice)|creative(alice))))&
(![X]:((funny(X)|~wise(X))<=>wise(X)))&
(![X]:((~kind(X)<~>~tall(X))<=>happy(X)))&
(![X]:(curious(X)=>(quiet(X)<~>~funny(X))))&
((?[X]:((~brave(X)<~>humble(X))))=>(?[X]:((patient(X)|~creative(X)))))&
(![X]:((~generous(X)|~humble(X))<=>(~old(X)|~brave(X))))&
((?[X]:((quiet(X)|~calm(X))))=>((~strong(susan)|~generous(susan))))&
(![X]:((old(X)&patient(X))<=>(~patient(X)<~>rich(X))))&
((~humble(lucy))=>((~creative(mary)<~>calm(mary))))&
(![X]:((rich(X)&~humble(X))=>strong(X)))&
(![X]:((wise(X)<~>funny(X))<=>rich(X)))&
(?[X]:((funny(X)|tall(X))))&
((~quiet(mary)|funny(mary)))&
(?[X]:(kind(X)))&
(?[X]:((calm(X)&~old(X))))&
(?[X]:(~generous(X)))&
(?[X]:(~curious(X)))&
((~rich(alice)<~>~strong(alice)))&
(patient(mary)) | humble(lucy) | [
"p4",
"p6",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7702142726615375354824191
% SZS output start Proof for 7702142726615375354824191
5. ! [X0] : (patient(X0) <=> (~humble(X0) & creative(X0))) [input p4]
7. ! [X0] : ((~wise(X0) | funny(X0)) <=> wise(X0)) [input p6]
13. ! [X0] : ((patient(X0) & old(X0)) <=> (~patient(X0) <~> rich(X0))) [input p12]
16. ! [X0] : ((wise(X0) <~> funny(X0)) <=> rich(X0)) [input p15]
25. humble(lucy) [input hypothesis]
45. ! [X0] : ((patient(X0) | (humble(X0) | ~creative(X0))) & ((~humble(X0) & creative(X0)) | ~patient(X0))) [nnf transformation 5]
46. ! [X0] : ((patient(X0) | humble(X0) | ~creative(X0)) & ((~humble(X0) & creative(X0)) | ~patient(X0))) [flattening 45]
52. ! [X0] : (((~wise(X0) | funny(X0)) | ~wise(X0)) & (wise(X0) | (wise(X0) & ~funny(X0)))) [nnf transformation 7]
53. ! [X0] : ((~wise(X0) | funny(X0) | ~wise(X0)) & (wise(X0) | (wise(X0) & ~funny(X0)))) [flattening 52]
62. ! [X0] : (((patient(X0) & old(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~patient(X0) | ~old(X0)))) [nnf transformation 13]
63. ! [X0] : (((patient(X0) & old(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | ~patient(X0) | ~old(X0))) [flattening 62]
65. ! [X0] : ((((~funny(X0) | ~wise(X0)) & (funny(X0) | wise(X0))) | ~rich(X0)) & (rich(X0) | ((wise(X0) | ~funny(X0)) & (funny(X0) | ~wise(X0))))) [nnf transformation 16]
100. ~patient(X0) | ~humble(X0) [cnf transformation 46]
106. wise(X0) | wise(X0) [cnf transformation 53]
107. ~wise(X0) | funny(X0) | ~wise(X0) [cnf transformation 53]
126. patient(X0) | rich(X0) | patient(X0) [cnf transformation 63]
134. ~funny(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 65]
145. humble(lucy) [cnf transformation 25]
147. patient(X0) | rich(X0) [duplicate literal removal 126]
148. wise(X0) [duplicate literal removal 106]
149. ~wise(X0) | funny(X0) [duplicate literal removal 107]
189. 9 <=> ! [X1] : (~humble(X1) | rich(X1)) [avatar definition]
190. ~humble(X1) | rich(X1) <- (9) [avatar component clause 189]
273. 28 <=> humble(lucy) [avatar definition]
275. humble(lucy) <- (28) [avatar component clause 273]
286. ~funny(X0) | ~rich(X0) [subsumption resolution 134,148]
315. 28 [avatar split clause 145,273]
323. rich(X0) | ~humble(X0) [resolution 147,100]
325. 9 [avatar split clause 323,189]
326. funny(X0) [resolution 149,148]
330. rich(lucy) <- (9, 28) [resolution 190,275]
334. ~rich(X0) [resolution 286,326]
426. $false <- (9, 28) [resolution 334,330]
427. ~9 | ~28 [avatar contradiction clause 426]
430. $false [avatar sat refutation 315,325,427]
% SZS output end Proof for 7702142726615375354824191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not funny or not brave then someone is either not kind or strong.
If lucy is either not wise or creative then paul is not funny or brave.
If fred is kind then fred is either not curious or creative.
Everyone who is not old or kind is tall and vice versa.
Everyone who is either not funny or not curious is not calm or not strong and vice versa.
If someone is not rich then someone is strong or not old and vice versa.
Everyone who is old or not humble is curious or not funny.
If someone is both not wise and funny then someone is either strong or not generous and vice versa.
Everyone who is either calm or brave is strong or funny.
If someone is both generous and quiet then someone is not creative or not humble and vice versa.
If someone is both not brave and humble then someone is calm and vice versa.
If john is quiet then susan is not generous or not quiet and vice versa.
Everyone who is either not strong or funny is both not calm and strong and vice versa.
If someone is either not curious or not creative then lucy is either not patient or not old.
If someone is not humble then someone is curious.
Everyone who is not quiet or funny is not generous and vice versa.
Someone is both not generous and quiet.
Someone is either not quiet or not tall.
Someone is not old or not kind.
Alice is not brave.
Someone is either not rich or old.
Mary is either tall or not wise. | Alice is curious. | contradiction | (((~funny(john)<~>~brave(john)))=>(?[X]:((~kind(X)<~>strong(X)))))&
(((~wise(lucy)<~>creative(lucy)))=>((~funny(paul)|brave(paul))))&
((kind(fred))=>((~curious(fred)<~>creative(fred))))&
(![X]:((~old(X)|kind(X))<=>tall(X)))&
(![X]:((~funny(X)<~>~curious(X))<=>(~calm(X)|~strong(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((strong(X)|~old(X)))))&
(![X]:((old(X)|~humble(X))=>(curious(X)|~funny(X))))&
((?[X]:((~wise(X)&funny(X))))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((calm(X)<~>brave(X))=>(strong(X)|funny(X))))&
((?[X]:((generous(X)&quiet(X))))<=>(?[X]:((~creative(X)|~humble(X)))))&
((?[X]:((~brave(X)&humble(X))))<=>(?[X]:(calm(X))))&
((quiet(john))<=>((~generous(susan)|~quiet(susan))))&
(![X]:((~strong(X)<~>funny(X))<=>(~calm(X)&strong(X))))&
((?[X]:((~curious(X)<~>~creative(X))))=>((~patient(lucy)<~>~old(lucy))))&
((?[X]:(~humble(X)))=>(?[X]:(curious(X))))&
(![X]:((~quiet(X)|funny(X))<=>~generous(X)))&
(?[X]:((~generous(X)&quiet(X))))&
(?[X]:((~quiet(X)<~>~tall(X))))&
(?[X]:((~old(X)|~kind(X))))&
(~brave(alice))&
(?[X]:((~rich(X)<~>old(X))))&
((tall(mary)<~>~wise(mary))) | curious(alice) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2656793806427474732840516
% SZS output start Proof for 2656793806427474732840516
5. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> (~strong(X0) | ~calm(X0))) [input p4]
13. ! [X0] : ((~strong(X0) <~> funny(X0)) <=> (strong(X0) & ~calm(X0))) [input p12]
23. curious(alice) [input hypothesis]
46. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 5]
47. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [flattening 46]
71. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [nnf transformation 13]
72. ! [X0] : ((((~funny(X0) | strong(X0)) & (funny(X0) | ~strong(X0))) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))))) [flattening 71]
101. ~calm(X0) | ~strong(X0) | ~curious(X0) | funny(X0) [cnf transformation 47]
103. ~curious(X0) | ~funny(X0) | calm(X0) [cnf transformation 47]
104. ~curious(X0) | ~funny(X0) | strong(X0) [cnf transformation 47]
132. ~calm(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 72]
133. strong(X0) | funny(X0) | strong(X0) [cnf transformation 72]
135. funny(X0) | ~strong(X0) | ~strong(X0) | calm(X0) [cnf transformation 72]
155. curious(alice) [cnf transformation 23]
156. strong(X0) | funny(X0) [duplicate literal removal 133]
157. ~strong(X0) | funny(X0) | calm(X0) [duplicate literal removal 135]
408. ~funny(alice) | calm(alice) [resolution 103,155]
410. 53 <=> calm(alice) [avatar definition]
412. calm(alice) <- (53) [avatar component clause 410]
414. 54 <=> funny(alice) [avatar definition]
415. funny(alice) <- (54) [avatar component clause 414]
417. 53 | ~54 [avatar split clause 408,414,410]
418. ~funny(alice) | strong(alice) [resolution 104,155]
464. funny(X0) | calm(X0) | funny(X0) [resolution 157,156]
465. calm(X0) | funny(X0) [duplicate literal removal 464]
491. funny(X2) | ~strong(X2) | ~curious(X2) | funny(X2) [resolution 465,101]
493. funny(X2) | ~strong(X2) | ~curious(X2) [duplicate literal removal 491]
495. ~curious(X2) | funny(X2) [subsumption resolution 493,156]
496. funny(alice) [resolution 495,155]
501. 54 [avatar split clause 496,414]
502. strong(alice) [subsumption resolution 418,156]
506. ~strong(alice) | ~funny(alice) <- (53) [resolution 412,132]
507. ~funny(alice) <- (53) [subsumption resolution 506,502]
508. $false <- (53, 54) [subsumption resolution 507,415]
509. ~53 | ~54 [avatar contradiction clause 508]
510. $false [avatar sat refutation 417,501,509]
% SZS output end Proof for 2656793806427474732840516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both strong and humble is either curious or calm and vice versa. If lucy is not funny then someone is both strong and quiet. Everyone who is both curious and not tall is not calm. If someone is funny or not patient then john is old or not creative and vice versa. Everyone who is either not patient or happy is not curious and vice versa. Everyone who is not kind or not happy is not rich. If alice is either kind or not quiet then someone is either patient or not creative and vice versa. Everyone who is both rich and not brave is not old or wise and vice versa. If john is either old or not brave then someone is either calm or not tall and vice versa. Everyone who is old or not quiet is both wise and strong and vice versa. Everyone who is not happy is brave. Everyone who is either happy or patient is humble or calm and vice versa. If lucy is both not quiet and not generous then someone is curious or not funny and vice versa. If john is both funny and not rich then susan is creative. Everyone who is either not quiet or not calm is both old and rich and vice versa. If alice is not strong or not patient then someone is either not creative or not rich and vice versa. Someone is not generous or quiet. Lucy is both patient and not curious. Alice is either curious or not brave. Someone is not curious. Paul is both patient and old. | Alice is kind. | entailment | (![X]:((strong(X)&humble(X))<=>(curious(X)<~>calm(X))))&
((~funny(lucy))=>(?[X]:((strong(X)&quiet(X)))))&
(![X]:((curious(X)&~tall(X))=>~calm(X)))&
((?[X]:((funny(X)|~patient(X))))<=>((old(john)|~creative(john))))&
(![X]:((~patient(X)<~>happy(X))<=>~curious(X)))&
(![X]:((~kind(X)|~happy(X))=>~rich(X)))&
(((kind(alice)<~>~quiet(alice)))<=>(?[X]:((patient(X)<~>~creative(X)))))&
(![X]:((rich(X)&~brave(X))<=>(~old(X)|wise(X))))&
(((old(john)<~>~brave(john)))<=>(?[X]:((calm(X)<~>~tall(X)))))&
(![X]:((old(X)|~quiet(X))<=>(wise(X)&strong(X))))&
(![X]:(~happy(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))<=>(humble(X)|calm(X))))&
(((~quiet(lucy)&~generous(lucy)))<=>(?[X]:((curious(X)|~funny(X)))))&
(((funny(john)&~rich(john)))=>(creative(susan)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(old(X)&rich(X))))&
(((~strong(alice)|~patient(alice)))<=>(?[X]:((~creative(X)<~>~rich(X)))))&
(?[X]:((~generous(X)|quiet(X))))&
((patient(lucy)&~curious(lucy)))&
((curious(alice)<~>~brave(alice)))&
(?[X]:(~curious(X)))&
((patient(paul)&old(paul))) | kind(alice) | [
"p5",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2852825148373923121450928
% SZS output start Proof for 2852825148373923121450928
6. ! [X0] : ((~happy(X0) | ~kind(X0)) => ~rich(X0)) [input p5]
8. ! [X0] : ((~brave(X0) & rich(X0)) <=> (wise(X0) | ~old(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) | old(X0)) <=> (strong(X0) & wise(X0))) [input p9]
22. ~kind(alice) [input hypothesis]
26. ! [X0] : (~rich(X0) | (happy(X0) & kind(X0))) [ennf transformation 6]
44. ! [X0] : (((~brave(X0) & rich(X0)) | (~wise(X0) & old(X0))) & ((wise(X0) | ~old(X0)) | (brave(X0) | ~rich(X0)))) [nnf transformation 8]
45. ! [X0] : (((~brave(X0) & rich(X0)) | (~wise(X0) & old(X0))) & (wise(X0) | ~old(X0) | brave(X0) | ~rich(X0))) [flattening 44]
50. ! [X0] : (((~quiet(X0) | old(X0)) | (~strong(X0) | ~wise(X0))) & ((strong(X0) & wise(X0)) | (quiet(X0) & ~old(X0)))) [nnf transformation 10]
51. ! [X0] : ((~quiet(X0) | old(X0) | ~strong(X0) | ~wise(X0)) & ((strong(X0) & wise(X0)) | (quiet(X0) & ~old(X0)))) [flattening 50]
88. ~rich(X0) | kind(X0) [cnf transformation 26]
99. rich(X0) | old(X0) [cnf transformation 45]
100. ~wise(X0) | rich(X0) [cnf transformation 45]
111. ~old(X0) | wise(X0) [cnf transformation 51]
149. ~kind(alice) [cnf transformation 22]
194. 11 <=> kind(alice) [avatar definition]
196. ~kind(alice) <- (~11) [avatar component clause 194]
335. ~11 [avatar split clause 149,194]
337. kind(X1) | old(X1) [resolution 99,88]
355. old(alice) <- (~11) [resolution 337,196]
371. wise(alice) <- (~11) [resolution 355,111]
478. rich(alice) <- (~11) [resolution 371,100]
502. kind(alice) <- (~11) [resolution 478,88]
503. $false <- (~11) [subsumption resolution 502,196]
504. 11 [avatar contradiction clause 503]
505. $false [avatar sat refutation 335,504]
% SZS output end Proof for 2852825148373923121450928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then john is both not kind and patient and vice versa.
If mary is either not strong or curious then someone is both patient and not creative.
Everyone who is not brave or not funny is both not wise and rich and vice versa.
If someone is either not creative or happy then alice is not curious.
Everyone who is either not happy or quiet is old or not wise.
Everyone who is wise or rich is either wise or not humble.
If susan is not strong or not old then someone is both rich and curious and vice versa.
If alice is both not quiet and funny then someone is either not curious or curious and vice versa.
Everyone who is generous is both not quiet and not strong.
Everyone who is either not patient or tall is old or rich.
If someone is not rich or not patient then someone is both not brave and curious.
If someone is kind then susan is both quiet and kind.
If lucy is not kind or wise then someone is either kind or calm.
Everyone who is either curious or rich is both not curious and rich.
If someone is both old and strong then someone is generous or not kind.
Someone is strong.
Lucy is kind or not strong.
Someone is not happy or not kind.
Paul is not creative.
Someone is not kind.
Someone is not tall or old.
Mary is wise.
Paul is either not humble or not kind. | Paul is creative. | contradiction | ((?[X]:(~humble(X)))<=>((~kind(john)&patient(john))))&
(((~strong(mary)<~>curious(mary)))=>(?[X]:((patient(X)&~creative(X)))))&
(![X]:((~brave(X)|~funny(X))<=>(~wise(X)&rich(X))))&
((?[X]:((~creative(X)<~>happy(X))))=>(~curious(alice)))&
(![X]:((~happy(X)<~>quiet(X))=>(old(X)|~wise(X))))&
(![X]:((wise(X)|rich(X))=>(wise(X)<~>~humble(X))))&
(((~strong(susan)|~old(susan)))<=>(?[X]:((rich(X)&curious(X)))))&
(((~quiet(alice)&funny(alice)))<=>(?[X]:((~curious(X)<~>curious(X)))))&
(![X]:(generous(X)=>(~quiet(X)&~strong(X))))&
(![X]:((~patient(X)<~>tall(X))=>(old(X)|rich(X))))&
((?[X]:((~rich(X)|~patient(X))))=>(?[X]:((~brave(X)&curious(X)))))&
((?[X]:(kind(X)))=>((quiet(susan)&kind(susan))))&
(((~kind(lucy)|wise(lucy)))=>(?[X]:((kind(X)<~>calm(X)))))&
(![X]:((curious(X)<~>rich(X))=>(~curious(X)&rich(X))))&
((?[X]:((old(X)&strong(X))))=>(?[X]:((generous(X)|~kind(X)))))&
(?[X]:(strong(X)))&
((kind(lucy)|~strong(lucy)))&
(?[X]:((~happy(X)|~kind(X))))&
(~creative(paul))&
(?[X]:(~kind(X)))&
(?[X]:((~tall(X)|old(X))))&
(wise(mary))&
((~humble(paul)<~>~kind(paul))) | creative(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 733273119088913800494538
% SZS output start Proof for 733273119088913800494538
19. ~creative(paul) [input p18]
24. creative(paul) [input hypothesis]
136. ~creative(paul) [cnf transformation 19]
142. creative(paul) [cnf transformation 24]
338. $false [subsumption resolution 142,136]
% SZS output end Proof for 733273119088913800494538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is generous then alice is both tall and not happy and vice versa. Everyone who is not rich or generous is not old. Everyone who is either not humble or happy is not tall or old. If fred is both not rich and funny then paul is both not happy and strong and vice versa. If someone is not kind or curious then susan is wise. If susan is not calm or not patient then someone is either patient or not brave. Everyone who is either happy or not rich is happy and vice versa. Everyone who is both not rich and not funny is creative and vice versa. If someone is not quiet or rich then alice is kind and vice versa. Everyone who is curious is both not tall and not funny. If someone is both curious and not rich then susan is not brave or patient. If someone is both calm and wise then john is either not tall or creative and vice versa. If paul is both not calm and not rich then someone is not curious and vice versa. If someone is not happy or generous then susan is not tall or happy and vice versa. If someone is wise then susan is not happy or not tall. Everyone who is not wise or not brave is funny or kind and vice versa. Someone is wise. Someone is tall or not creative. Someone is not kind or humble. Someone is either strong or not humble. Susan is old or kind. Someone is funny or not happy. | John is creative. | contradiction | ((generous(fred))<=>((tall(alice)&~happy(alice))))&
(![X]:((~rich(X)|generous(X))=>~old(X)))&
(![X]:((~humble(X)<~>happy(X))=>(~tall(X)|old(X))))&
(((~rich(fred)&funny(fred)))<=>((~happy(paul)&strong(paul))))&
((?[X]:((~kind(X)|curious(X))))=>(wise(susan)))&
(((~calm(susan)|~patient(susan)))=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((happy(X)<~>~rich(X))<=>happy(X)))&
(![X]:((~rich(X)&~funny(X))<=>creative(X)))&
((?[X]:((~quiet(X)|rich(X))))<=>(kind(alice)))&
(![X]:(curious(X)=>(~tall(X)&~funny(X))))&
((?[X]:((curious(X)&~rich(X))))=>((~brave(susan)|patient(susan))))&
((?[X]:((calm(X)&wise(X))))<=>((~tall(john)<~>creative(john))))&
(((~calm(paul)&~rich(paul)))<=>(?[X]:(~curious(X))))&
((?[X]:((~happy(X)|generous(X))))<=>((~tall(susan)|happy(susan))))&
((?[X]:(wise(X)))=>((~happy(susan)|~tall(susan))))&
(![X]:((~wise(X)|~brave(X))<=>(funny(X)|kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((tall(X)|~creative(X))))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((strong(X)<~>~humble(X))))&
((old(susan)|kind(susan)))&
(?[X]:((funny(X)|~happy(X)))) | creative(john) | [
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3290171602612564084521621
% SZS output start Proof for 3290171602612564084521621
7. ! [X0] : ((happy(X0) <~> ~rich(X0)) <=> happy(X0)) [input p6]
8. ! [X0] : ((~funny(X0) & ~rich(X0)) <=> creative(X0)) [input p7]
23. creative(john) [input hypothesis]
42. ! [X0] : ((((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | ~happy(X0)) & (happy(X0) | ((happy(X0) | rich(X0)) & (~rich(X0) | ~happy(X0))))) [nnf transformation 7]
43. ! [X0] : (((~funny(X0) & ~rich(X0)) | ~creative(X0)) & (creative(X0) | (funny(X0) | rich(X0)))) [nnf transformation 8]
44. ! [X0] : (((~funny(X0) & ~rich(X0)) | ~creative(X0)) & (creative(X0) | funny(X0) | rich(X0))) [flattening 43]
94. happy(X0) | happy(X0) | rich(X0) [cnf transformation 42]
96. rich(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 42]
98. ~rich(X0) | ~creative(X0) [cnf transformation 44]
131. creative(john) [cnf transformation 23]
132. happy(X0) | rich(X0) [duplicate literal removal 94]
133. rich(X0) | ~happy(X0) [duplicate literal removal 96]
201. rich(X0) [subsumption resolution 132,133]
202. ~creative(X0) [subsumption resolution 98,201]
293. $false [subsumption resolution 131,202]
% SZS output end Proof for 3290171602612564084521621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not tall then someone is both not kind and not brave. If paul is not generous or not creative then someone is either patient or not quiet and vice versa. Everyone who is not kind or kind is either not rich or funny and vice versa. Everyone who is patient or creative is not funny and vice versa. Everyone who is kind is both not quiet and funny. If fred is creative or wise then someone is either brave or tall. If someone is both curious and not happy then someone is either not happy or not wise. If john is both creative and kind then someone is either humble or not kind and vice versa. If paul is tall or not patient then someone is both brave and not funny. If someone is both not brave and brave then someone is either not creative or not happy and vice versa. Everyone who is funny or creative is both happy and not rich. If paul is either funny or not creative then someone is not happy and vice versa. If susan is not humble then someone is both humble and not calm. Everyone who is either not strong or not wise is both not generous and not quiet and vice versa. If someone is either not funny or wise then susan is not creative and vice versa. Everyone who is both creative and patient is rich and vice versa. Lucy is both patient and not kind. Susan is happy or not old. Susan is both not calm and not wise. John is either funny or tall. Someone is calm. Mary is either not brave or not humble. Alice is tall. Someone is both not generous and not patient. | Paul is patient. | entailment | ((?[X]:((calm(X)<~>~tall(X))))=>(?[X]:((~kind(X)&~brave(X)))))&
(((~generous(paul)|~creative(paul)))<=>(?[X]:((patient(X)<~>~quiet(X)))))&
(![X]:((~kind(X)|kind(X))<=>(~rich(X)<~>funny(X))))&
(![X]:((patient(X)|creative(X))<=>~funny(X)))&
(![X]:(kind(X)=>(~quiet(X)&funny(X))))&
(((creative(fred)|wise(fred)))=>(?[X]:((brave(X)<~>tall(X)))))&
((?[X]:((curious(X)&~happy(X))))=>(?[X]:((~happy(X)<~>~wise(X)))))&
(((creative(john)&kind(john)))<=>(?[X]:((humble(X)<~>~kind(X)))))&
(((tall(paul)|~patient(paul)))=>(?[X]:((brave(X)&~funny(X)))))&
((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:((funny(X)|creative(X))=>(happy(X)&~rich(X))))&
(((funny(paul)<~>~creative(paul)))<=>(?[X]:(~happy(X))))&
((~humble(susan))=>(?[X]:((humble(X)&~calm(X)))))&
(![X]:((~strong(X)<~>~wise(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((~funny(X)<~>wise(X))))<=>(~creative(susan)))&
(![X]:((creative(X)&patient(X))<=>rich(X)))&
((patient(lucy)&~kind(lucy)))&
((happy(susan)|~old(susan)))&
((~calm(susan)&~wise(susan)))&
((funny(john)<~>tall(john)))&
(?[X]:(calm(X)))&
((~brave(mary)<~>~humble(mary)))&
(tall(alice))&
(?[X]:((~generous(X)&~patient(X)))) | patient(paul) | [
"p2",
"p3",
"p9",
"p10",
"p11",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8206222390639886699163511
% SZS output start Proof for 8206222390639886699163511
3. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (~rich(X0) <~> funny(X0))) [input p2]
4. ! [X0] : ((creative(X0) | patient(X0)) <=> ~funny(X0)) [input p3]
10. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X0] : (~creative(X0) <~> ~happy(X0)) [input p9]
11. ! [X0] : ((creative(X0) | funny(X0)) => (~rich(X0) & happy(X0))) [input p10]
12. (funny(paul) <~> ~creative(paul)) <=> ? [X0] : ~happy(X0) [input p11]
16. ! [X0] : ((patient(X0) & creative(X0)) <=> rich(X0)) [input p15]
17. ~kind(lucy) & patient(lucy) [input p16]
25. ~patient(paul) [input hypothesis]
28. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X1] : (~creative(X1) <~> ~happy(X1)) [rectify 10]
35. ! [X0] : ((~rich(X0) & happy(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 11]
46. ! [X0] : (((kind(X0) | ~kind(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~kind(X0) & kind(X0)))) [nnf transformation 3]
47. ! [X0] : ((kind(X0) | ~kind(X0) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~kind(X0) & kind(X0)))) [flattening 46]
48. ! [X0] : (((creative(X0) | patient(X0)) | funny(X0)) & (~funny(X0) | (~creative(X0) & ~patient(X0)))) [nnf transformation 4]
49. ! [X0] : ((creative(X0) | patient(X0) | funny(X0)) & (~funny(X0) | (~creative(X0) & ~patient(X0)))) [flattening 48]
60. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : ((~creative(X1) | happy(X1)) & (~happy(X1) | creative(X1)))) & (? [X1] : ((happy(X1) | creative(X1)) & (~happy(X1) | ~creative(X1))) | ! [X0] : (~brave(X0) | brave(X0))) [nnf transformation 28]
61. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : ((~creative(X1) | happy(X1)) & (~happy(X1) | creative(X1)))) & (? [X2] : ((happy(X2) | creative(X2)) & (~happy(X2) | ~creative(X2))) | ! [X3] : (~brave(X3) | brave(X3))) [rectify 60]
62. ? [X0] : (brave(X0) & ~brave(X0)) => (brave(sK5) & ~brave(sK5)) [choice axiom]
63. ? [X2] : ((happy(X2) | creative(X2)) & (~happy(X2) | ~creative(X2))) => ((happy(sK6) | creative(sK6)) & (~happy(sK6) | ~creative(sK6))) [choice axiom]
64. ((brave(sK5) & ~brave(sK5)) | ! [X1] : ((~creative(X1) | happy(X1)) & (~happy(X1) | creative(X1)))) & (((happy(sK6) | creative(sK6)) & (~happy(sK6) | ~creative(sK6))) | ! [X3] : (~brave(X3) | brave(X3))) [skolemisation 61,63,62]
65. (((creative(paul) | ~funny(paul)) & (~creative(paul) | funny(paul))) | ! [X0] : happy(X0)) & (? [X0] : ~happy(X0) | ((funny(paul) | creative(paul)) & (~creative(paul) | ~funny(paul)))) [nnf transformation 12]
66. (((creative(paul) | ~funny(paul)) & (~creative(paul) | funny(paul))) | ! [X0] : happy(X0)) & (? [X1] : ~happy(X1) | ((funny(paul) | creative(paul)) & (~creative(paul) | ~funny(paul)))) [rectify 65]
67. ? [X1] : ~happy(X1) => ~happy(sK7) [choice axiom]
68. (((creative(paul) | ~funny(paul)) & (~creative(paul) | funny(paul))) | ! [X0] : happy(X0)) & (~happy(sK7) | ((funny(paul) | creative(paul)) & (~creative(paul) | ~funny(paul)))) [skolemisation 66,67]
77. ! [X0] : (((patient(X0) & creative(X0)) | ~rich(X0)) & (rich(X0) | (~patient(X0) | ~creative(X0)))) [nnf transformation 16]
78. ! [X0] : (((patient(X0) & creative(X0)) | ~rich(X0)) & (rich(X0) | ~patient(X0) | ~creative(X0))) [flattening 77]
97. ~funny(X0) | rich(X0) | kind(X0) [cnf transformation 47]
98. ~funny(X0) | rich(X0) | ~kind(X0) [cnf transformation 47]
103. funny(X0) | patient(X0) | creative(X0) [cnf transformation 49]
122. ~brave(sK5) | ~happy(X1) | creative(X1) [cnf transformation 64]
124. brave(sK5) | ~happy(X1) | creative(X1) [cnf transformation 64]
128. ~rich(X0) | ~funny(X0) [cnf transformation 35]
129. ~rich(X0) | ~creative(X0) [cnf transformation 35]
132. ~creative(paul) | funny(paul) | happy(X0) [cnf transformation 68]
146. rich(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 78]
147. creative(X0) | ~rich(X0) [cnf transformation 78]
149. patient(lucy) [cnf transformation 17]
161. ~patient(paul) [cnf transformation 25]
188. 7 <=> creative(paul) [avatar definition]
208. ~funny(X0) | rich(X0) [subsumption resolution 97,98]
259. 21 <=> patient(paul) [avatar definition]
260. ~patient(paul) <- (~21) [avatar component clause 259]
282. 26 <=> brave(sK5) [avatar definition]
287. 27 <=> ! [X1] : (~happy(X1) | creative(X1)) [avatar definition]
288. ~happy(X1) | creative(X1) <- (27) [avatar component clause 287]
289. 27 | 26 [avatar split clause 124,282,287]
291. 27 | ~26 [avatar split clause 122,282,287]
292. ~funny(X0) [subsumption resolution 128,208]
294. ~creative(paul) | happy(X0) [subsumption resolution 132,292]
296. 28 <=> ! [X0] : happy(X0) [avatar definition]
297. happy(X0) <- (28) [avatar component clause 296]
298. 28 | ~7 [avatar split clause 294,188,296]
334. ~rich(X0) [subsumption resolution 147,129]
335. ~patient(X0) | ~creative(X0) [subsumption resolution 146,334]
347. ~21 [avatar split clause 161,259]
355. ~creative(lucy) [resolution 335,149]
357. patient(X1) | creative(X1) | rich(X1) [resolution 103,208]
362. patient(X1) | creative(X1) [subsumption resolution 357,334]
364. creative(paul) <- (~21) [resolution 362,260]
369. 7 | 21 [avatar split clause 364,259,188]
372. creative(X0) <- (27, 28) [resolution 297,288]
377. $false <- (27, 28) [resolution 372,355]
378. ~27 | ~28 [avatar contradiction clause 377]
381. $false [avatar sat refutation 289,291,298,347,369,378]
% SZS output end Proof for 8206222390639886699163511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both wise and not brave then susan is both not tall and wise. If lucy is not tall then someone is either funny or not creative and vice versa. Everyone who is rich or not humble is both not kind and not curious and vice versa. Everyone who is happy or curious is both not happy and not rich. Everyone who is not humble is not wise. Everyone who is both not humble and calm is either rich or calm. Everyone who is not tall is both funny and not tall. Everyone who is both humble and happy is both not calm and not kind. Everyone who is not quiet is both calm and strong and vice versa. Everyone who is both not wise and quiet is not strong and vice versa. If fred is either not patient or creative then someone is either strong or tall and vice versa. Everyone who is both strong and not calm is not patient or creative and vice versa. If john is happy or not happy then john is either not happy or creative and vice versa. Everyone who is quiet is either not patient or not creative and vice versa. Everyone who is either not wise or not humble is not patient or patient. If someone is not kind then lucy is not strong or not quiet. Someone is not tall. Someone is not tall or not wise. Someone is both patient and rich. Someone is humble. Alice is both kind and not brave. Lucy is either strong or old. | John is wise. | contradiction | ((?[X]:((wise(X)&~brave(X))))=>((~tall(susan)&wise(susan))))&
((~tall(lucy))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((rich(X)|~humble(X))<=>(~kind(X)&~curious(X))))&
(![X]:((happy(X)|curious(X))=>(~happy(X)&~rich(X))))&
(![X]:(~humble(X)=>~wise(X)))&
(![X]:((~humble(X)&calm(X))=>(rich(X)<~>calm(X))))&
(![X]:(~tall(X)=>(funny(X)&~tall(X))))&
(![X]:((humble(X)&happy(X))=>(~calm(X)&~kind(X))))&
(![X]:(~quiet(X)<=>(calm(X)&strong(X))))&
(![X]:((~wise(X)&quiet(X))<=>~strong(X)))&
(((~patient(fred)<~>creative(fred)))<=>(?[X]:((strong(X)<~>tall(X)))))&
(![X]:((strong(X)&~calm(X))<=>(~patient(X)|creative(X))))&
(((happy(john)|~happy(john)))<=>((~happy(john)<~>creative(john))))&
(![X]:(quiet(X)<=>(~patient(X)<~>~creative(X))))&
(![X]:((~wise(X)<~>~humble(X))=>(~patient(X)|patient(X))))&
((?[X]:(~kind(X)))=>((~strong(lucy)|~quiet(lucy))))&
(?[X]:(~tall(X)))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((patient(X)&rich(X))))&
(?[X]:(humble(X)))&
((kind(alice)&~brave(alice)))&
((strong(lucy)<~>old(lucy))) | wise(john) | [
"p3",
"p8",
"p9",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1665297180836305265833847
% SZS output start Proof for 1665297180836305265833847
4. ! [X0] : ((curious(X0) | happy(X0)) => (~rich(X0) & ~happy(X0))) [input p3]
9. ! [X0] : (~quiet(X0) <=> (strong(X0) & calm(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & ~wise(X0)) <=> ~strong(X0)) [input p9]
12. ! [X0] : ((~calm(X0) & strong(X0)) <=> (creative(X0) | ~patient(X0))) [input p11]
13. (~happy(john) | happy(john)) <=> (~happy(john) <~> creative(john)) [input p12]
14. ! [X0] : (quiet(X0) <=> (~patient(X0) <~> ~creative(X0))) [input p13]
23. wise(john) [input hypothesis]
25. ! [X0] : ((~rich(X0) & ~happy(X0)) | (~curious(X0) & ~happy(X0))) [ennf transformation 4]
43. ! [X0] : ((~quiet(X0) | (~strong(X0) | ~calm(X0))) & ((strong(X0) & calm(X0)) | quiet(X0))) [nnf transformation 9]
44. ! [X0] : ((~quiet(X0) | ~strong(X0) | ~calm(X0)) & ((strong(X0) & calm(X0)) | quiet(X0))) [flattening 43]
45. ! [X0] : (((quiet(X0) & ~wise(X0)) | strong(X0)) & (~strong(X0) | (~quiet(X0) | wise(X0)))) [nnf transformation 10]
46. ! [X0] : (((quiet(X0) & ~wise(X0)) | strong(X0)) & (~strong(X0) | ~quiet(X0) | wise(X0))) [flattening 45]
51. ! [X0] : (((~calm(X0) & strong(X0)) | (~creative(X0) & patient(X0))) & ((creative(X0) | ~patient(X0)) | (calm(X0) | ~strong(X0)))) [nnf transformation 12]
52. ! [X0] : (((~calm(X0) & strong(X0)) | (~creative(X0) & patient(X0))) & (creative(X0) | ~patient(X0) | calm(X0) | ~strong(X0))) [flattening 51]
53. ((~happy(john) | happy(john)) | ((~happy(john) | ~creative(john)) & (creative(john) | happy(john)))) & (((~creative(john) | happy(john)) & (creative(john) | ~happy(john))) | (happy(john) & ~happy(john))) [nnf transformation 13]
54. (~happy(john) | happy(john) | ((~happy(john) | ~creative(john)) & (creative(john) | happy(john)))) & (((~creative(john) | happy(john)) & (creative(john) | ~happy(john))) | (happy(john) & ~happy(john))) [flattening 53]
55. ! [X0] : ((quiet(X0) | ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0)))) & (((creative(X0) | patient(X0)) & (~creative(X0) | ~patient(X0))) | ~quiet(X0))) [nnf transformation 14]
77. ~happy(X0) | ~happy(X0) [cnf transformation 25]
88. quiet(X0) | calm(X0) [cnf transformation 44]
90. ~strong(X0) | ~quiet(X0) | ~calm(X0) [cnf transformation 44]
92. ~wise(X0) | strong(X0) [cnf transformation 46]
102. ~patient(X0) | creative(X0) | calm(X0) | ~strong(X0) [cnf transformation 52]
105. ~calm(X0) | patient(X0) [cnf transformation 52]
110. ~creative(john) | happy(john) | happy(john) [cnf transformation 54]
114. ~quiet(X0) | patient(X0) | creative(X0) [cnf transformation 55]
116. ~patient(X0) | quiet(X0) | creative(X0) [cnf transformation 55]
129. wise(john) [cnf transformation 23]
131. ~creative(john) | happy(john) [duplicate literal removal 110]
135. ~happy(X0) [duplicate literal removal 77]
201. ~creative(john) [subsumption resolution 131,135]
235. strong(john) [resolution 92,129]
268. ~quiet(john) | ~calm(john) [resolution 90,235]
279. 23 <=> calm(john) [avatar definition]
283. 24 <=> quiet(john) [avatar definition]
285. ~quiet(john) <- (~24) [avatar component clause 283]
286. ~23 | ~24 [avatar split clause 268,283,279]
305. patient(X0) | creative(X0) | calm(X0) [resolution 114,88]
306. patient(X0) | creative(X0) [subsumption resolution 305,105]
467. creative(X0) | creative(X0) | calm(X0) | ~strong(X0) [resolution 306,102]
468. creative(X1) | quiet(X1) | creative(X1) [resolution 306,116]
470. quiet(X1) | creative(X1) [duplicate literal removal 468]
471. ~strong(X0) | calm(X0) | creative(X0) [duplicate literal removal 467]
532. calm(john) | creative(john) [resolution 471,235]
538. calm(john) [subsumption resolution 532,201]
539. 23 [avatar split clause 538,279]
543. creative(john) <- (~24) [resolution 285,470]
546. $false <- (~24) [subsumption resolution 543,201]
547. 24 [avatar contradiction clause 546]
548. $false [avatar sat refutation 286,539,547]
% SZS output end Proof for 1665297180836305265833847
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not funny or curious then fred is creative or calm.
If someone is both happy and humble then fred is both not brave and rich.
If lucy is old then someone is curious or tall.
Everyone who is not funny is not rich or not funny and vice versa.
If paul is not curious then susan is wise.
Everyone who is both creative and not old is calm.
If lucy is either not generous or strong then someone is either not generous or calm and vice versa.
If someone is kind then someone is either not calm or patient.
If someone is patient then someone is calm and vice versa.
Everyone who is humble or not patient is both patient and brave and vice versa.
Everyone who is both not strong and not wise is both humble and calm.
Everyone who is either strong or not strong is happy or not strong and vice versa.
Everyone who is either not old or not quiet is both not humble and not old.
If someone is not happy then someone is not curious or not creative.
If john is not patient or not old then someone is not rich.
Susan is both not humble and old.
Someone is both rich and not funny.
Alice is not generous.
Someone is both not old and not wise.
Someone is not rich.
Mary is wise. | Paul is generous. | neutral | (((~funny(alice)<~>curious(alice)))=>((creative(fred)|calm(fred))))&
((?[X]:((happy(X)&humble(X))))=>((~brave(fred)&rich(fred))))&
((old(lucy))=>(?[X]:((curious(X)|tall(X)))))&
(![X]:(~funny(X)<=>(~rich(X)|~funny(X))))&
((~curious(paul))=>(wise(susan)))&
(![X]:((creative(X)&~old(X))=>calm(X)))&
(((~generous(lucy)<~>strong(lucy)))<=>(?[X]:((~generous(X)<~>calm(X)))))&
((?[X]:(kind(X)))=>(?[X]:((~calm(X)<~>patient(X)))))&
((?[X]:(patient(X)))<=>(?[X]:(calm(X))))&
(![X]:((humble(X)|~patient(X))<=>(patient(X)&brave(X))))&
(![X]:((~strong(X)&~wise(X))=>(humble(X)&calm(X))))&
(![X]:((strong(X)<~>~strong(X))<=>(happy(X)|~strong(X))))&
(![X]:((~old(X)<~>~quiet(X))=>(~humble(X)&~old(X))))&
((?[X]:(~happy(X)))=>(?[X]:((~curious(X)|~creative(X)))))&
(((~patient(john)|~old(john)))=>(?[X]:(~rich(X))))&
((~humble(susan)&old(susan)))&
(?[X]:((rich(X)&~funny(X))))&
(~generous(alice))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:(~rich(X)))&
(wise(mary)) | generous(paul) | [] | null | 0 |
If someone is kind then john is not kind or generous and vice versa. If someone is either quiet or creative then susan is curious and vice versa. Everyone who is brave is both not old and not curious and vice versa. Everyone who is patient or not creative is calm and vice versa. Everyone who is not strong is both humble and patient and vice versa. Everyone who is both not brave and not old is creative. If someone is not humble or funny then someone is both tall and not wise and vice versa. If someone is both not brave and not wise then alice is either not quiet or calm. Everyone who is quiet or humble is either not old or kind and vice versa. If alice is happy or not quiet then someone is either quiet or not quiet and vice versa. Everyone who is both strong and not calm is not quiet and vice versa. Everyone who is not brave or calm is not patient or humble. Everyone who is not kind or tall is both kind and not quiet. If someone is both not tall and patient then alice is rich and vice versa. Everyone who is both not generous and not brave is not calm and vice versa. Everyone who is not calm or not kind is both humble and strong. Someone is either strong or not generous. Paul is both creative and not brave. Alice is not curious or calm. Someone is not brave or quiet. John is either happy or wise. Mary is generous. | Mary is funny. | neutral | ((?[X]:(kind(X)))<=>((~kind(john)|generous(john))))&
((?[X]:((quiet(X)<~>creative(X))))<=>(curious(susan)))&
(![X]:(brave(X)<=>(~old(X)&~curious(X))))&
(![X]:((patient(X)|~creative(X))<=>calm(X)))&
(![X]:(~strong(X)<=>(humble(X)&patient(X))))&
(![X]:((~brave(X)&~old(X))=>creative(X)))&
((?[X]:((~humble(X)|funny(X))))<=>(?[X]:((tall(X)&~wise(X)))))&
((?[X]:((~brave(X)&~wise(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((quiet(X)|humble(X))<=>(~old(X)<~>kind(X))))&
(((happy(alice)|~quiet(alice)))<=>(?[X]:((quiet(X)<~>~quiet(X)))))&
(![X]:((strong(X)&~calm(X))<=>~quiet(X)))&
(![X]:((~brave(X)|calm(X))=>(~patient(X)|humble(X))))&
(![X]:((~kind(X)|tall(X))=>(kind(X)&~quiet(X))))&
((?[X]:((~tall(X)&patient(X))))<=>(rich(alice)))&
(![X]:((~generous(X)&~brave(X))<=>~calm(X)))&
(![X]:((~calm(X)|~kind(X))=>(humble(X)&strong(X))))&
(?[X]:((strong(X)<~>~generous(X))))&
((creative(paul)&~brave(paul)))&
((~curious(alice)|calm(alice)))&
(?[X]:((~brave(X)|quiet(X))))&
((happy(john)<~>wise(john)))&
(generous(mary)) | funny(mary) | [] | null | 0 |
Everyone who is brave is both kind and not patient and vice versa.
If paul is either wise or curious then mary is brave or not calm.
Everyone who is either old or funny is not happy or not generous and vice versa.
Everyone who is kind or not calm is either wise or not humble and vice versa.
Everyone who is both brave and humble is not patient or curious.
Everyone who is both not patient and creative is either humble or rich.
Everyone who is not wise or kind is happy or brave.
Everyone who is not curious is kind.
Everyone who is brave or not rich is both not patient and funny.
Everyone who is kind is either not strong or tall and vice versa.
Everyone who is either not humble or not rich is both not funny and old and vice versa.
Everyone who is not quiet or kind is both old and humble and vice versa.
If someone is either wise or not strong then someone is happy and vice versa.
Everyone who is not creative or kind is either not brave or not calm.
Everyone who is both not brave and quiet is not quiet or curious.
Everyone who is not curious or calm is not brave.
Someone is funny or not strong.
Someone is patient or brave.
Fred is both funny and humble.
Someone is both quiet and strong.
Fred is kind or not kind.
John is kind.
Someone is happy or not brave.
Mary is quiet. | Fred is not brave. | neutral | (![X]:(brave(X)<=>(kind(X)&~patient(X))))&
(((wise(paul)<~>curious(paul)))=>((brave(mary)|~calm(mary))))&
(![X]:((old(X)<~>funny(X))<=>(~happy(X)|~generous(X))))&
(![X]:((kind(X)|~calm(X))<=>(wise(X)<~>~humble(X))))&
(![X]:((brave(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~patient(X)&creative(X))=>(humble(X)<~>rich(X))))&
(![X]:((~wise(X)|kind(X))=>(happy(X)|brave(X))))&
(![X]:(~curious(X)=>kind(X)))&
(![X]:((brave(X)|~rich(X))=>(~patient(X)&funny(X))))&
(![X]:(kind(X)<=>(~strong(X)<~>tall(X))))&
(![X]:((~humble(X)<~>~rich(X))<=>(~funny(X)&old(X))))&
(![X]:((~quiet(X)|kind(X))<=>(old(X)&humble(X))))&
((?[X]:((wise(X)<~>~strong(X))))<=>(?[X]:(happy(X))))&
(![X]:((~creative(X)|kind(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((~brave(X)&quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:((~curious(X)|calm(X))=>~brave(X)))&
(?[X]:((funny(X)|~strong(X))))&
(?[X]:((patient(X)|brave(X))))&
((funny(fred)&humble(fred)))&
(?[X]:((quiet(X)&strong(X))))&
((kind(fred)|~kind(fred)))&
(kind(john))&
(?[X]:((happy(X)|~brave(X))))&
(quiet(mary)) | ~brave(fred) | [] | null | 0 |
If fred is tall then john is strong.
If someone is either not wise or calm then someone is brave.
If someone is both not kind and strong then someone is either not patient or generous and vice versa.
Everyone who is brave or not tall is both not generous and kind.
Everyone who is happy or not generous is not kind and vice versa.
If someone is either not strong or not patient then someone is quiet and vice versa.
Everyone who is either brave or not patient is not happy.
Everyone who is both rich and not calm is kind.
Everyone who is either rich or not curious is not wise or brave.
If someone is tall or not creative then someone is either rich or not old.
Everyone who is both not strong and not kind is both not curious and not funny and vice versa.
Everyone who is not humble or generous is either kind or not brave.
Everyone who is quiet is not calm and vice versa.
Everyone who is not curious is not kind or not wise and vice versa.
If john is not calm or not curious then someone is either calm or creative.
Lucy is either rich or not generous.
Someone is not brave.
Someone is either creative or not wise.
Susan is either calm or not patient.
Someone is either not patient or calm.
Lucy is either not funny or not quiet. | Susan is happy. | neutral | ((tall(fred))=>(strong(john)))&
((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:(brave(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(?[X]:((~patient(X)<~>generous(X)))))&
(![X]:((brave(X)|~tall(X))=>(~generous(X)&kind(X))))&
(![X]:((happy(X)|~generous(X))<=>~kind(X)))&
((?[X]:((~strong(X)<~>~patient(X))))<=>(?[X]:(quiet(X))))&
(![X]:((brave(X)<~>~patient(X))=>~happy(X)))&
(![X]:((rich(X)&~calm(X))=>kind(X)))&
(![X]:((rich(X)<~>~curious(X))=>(~wise(X)|brave(X))))&
((?[X]:((tall(X)|~creative(X))))=>(?[X]:((rich(X)<~>~old(X)))))&
(![X]:((~strong(X)&~kind(X))<=>(~curious(X)&~funny(X))))&
(![X]:((~humble(X)|generous(X))=>(kind(X)<~>~brave(X))))&
(![X]:(quiet(X)<=>~calm(X)))&
(![X]:(~curious(X)<=>(~kind(X)|~wise(X))))&
(((~calm(john)|~curious(john)))=>(?[X]:((calm(X)<~>creative(X)))))&
((rich(lucy)<~>~generous(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((creative(X)<~>~wise(X))))&
((calm(susan)<~>~patient(susan)))&
(?[X]:((~patient(X)<~>calm(X))))&
((~funny(lucy)<~>~quiet(lucy))) | happy(susan) | [] | null | 0 |
Everyone who is not tall is both patient and not rich and vice versa. Everyone who is both not funny and not humble is either not old or rich. Everyone who is either old or strong is either old or not brave. If paul is both happy and quiet then someone is creative and vice versa. If alice is both funny and not brave then someone is both creative and not creative and vice versa. If someone is not calm then someone is either calm or not wise. If someone is both happy and creative then someone is both wise and not rich. Everyone who is rich or not creative is either generous or not kind. Everyone who is not wise or not creative is either calm or not old. Everyone who is old or not humble is not quiet or not wise. Everyone who is either happy or generous is not funny. Everyone who is not brave or not happy is not brave. If someone is not wise or brave then lucy is humble. Everyone who is strong or generous is both not tall and calm. Everyone who is not brave or not generous is either patient or not calm and vice versa. Everyone who is both kind and tall is strong or not funny and vice versa. Someone is curious or not curious. Lucy is both not happy and not rich. Someone is not rich. Mary is not creative. Someone is generous. Someone is not happy. Someone is not tall or happy. Someone is either not generous or patient. | Paul is creative. | entailment | (![X]:(~tall(X)<=>(patient(X)&~rich(X))))&
(![X]:((~funny(X)&~humble(X))=>(~old(X)<~>rich(X))))&
(![X]:((old(X)<~>strong(X))=>(old(X)<~>~brave(X))))&
(((happy(paul)&quiet(paul)))<=>(?[X]:(creative(X))))&
(((funny(alice)&~brave(alice)))<=>(?[X]:((creative(X)&~creative(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((calm(X)<~>~wise(X)))))&
((?[X]:((happy(X)&creative(X))))=>(?[X]:((wise(X)&~rich(X)))))&
(![X]:((rich(X)|~creative(X))=>(generous(X)<~>~kind(X))))&
(![X]:((~wise(X)|~creative(X))=>(calm(X)<~>~old(X))))&
(![X]:((old(X)|~humble(X))=>(~quiet(X)|~wise(X))))&
(![X]:((happy(X)<~>generous(X))=>~funny(X)))&
(![X]:((~brave(X)|~happy(X))=>~brave(X)))&
((?[X]:((~wise(X)|brave(X))))=>(humble(lucy)))&
(![X]:((strong(X)|generous(X))=>(~tall(X)&calm(X))))&
(![X]:((~brave(X)|~generous(X))<=>(patient(X)<~>~calm(X))))&
(![X]:((kind(X)&tall(X))<=>(strong(X)|~funny(X))))&
(?[X]:((curious(X)|~curious(X))))&
((~happy(lucy)&~rich(lucy)))&
(?[X]:(~rich(X)))&
(~creative(mary))&
(?[X]:(generous(X)))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~generous(X)<~>patient(X)))) | creative(paul) | [
"p0",
"p2",
"p3",
"p7",
"p8",
"p10",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6688330867173087899124183
% SZS output start Proof for 6688330867173087899124183
1. ! [X0] : (~tall(X0) <=> (~rich(X0) & patient(X0))) [input p0]
3. ! [X0] : ((old(X0) <~> strong(X0)) => (old(X0) <~> ~brave(X0))) [input p2]
4. (quiet(paul) & happy(paul)) <=> ? [X0] : creative(X0) [input p3]
8. ! [X0] : ((~creative(X0) | rich(X0)) => (generous(X0) <~> ~kind(X0))) [input p7]
9. ! [X0] : ((~creative(X0) | ~wise(X0)) => (calm(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((happy(X0) <~> generous(X0)) => ~funny(X0)) [input p10]
14. ! [X0] : ((generous(X0) | strong(X0)) => (calm(X0) & ~tall(X0))) [input p13]
15. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> (patient(X0) <~> ~calm(X0))) [input p14]
16. ! [X0] : ((tall(X0) & kind(X0)) <=> (~funny(X0) | strong(X0))) [input p15]
21. ? [X0] : generous(X0) [input p20]
25. ~creative(paul) [input hypothesis]
31. ! [X0] : ((old(X0) <~> ~brave(X0)) | (old(X0) <=> strong(X0))) [ennf transformation 3]
34. ! [X0] : ((generous(X0) <~> ~kind(X0)) | (creative(X0) & ~rich(X0))) [ennf transformation 8]
35. ! [X0] : ((calm(X0) <~> ~old(X0)) | (creative(X0) & wise(X0))) [ennf transformation 9]
38. ! [X0] : (~funny(X0) | (happy(X0) <=> generous(X0))) [ennf transformation 11]
40. ! [X0] : ((calm(X0) & ~tall(X0)) | (~generous(X0) & ~strong(X0))) [ennf transformation 14]
41. ! [X0] : ((~tall(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | tall(X0))) [nnf transformation 1]
42. ! [X0] : ((~tall(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | tall(X0))) [flattening 41]
43. ! [X0] : (((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | ((old(X0) | ~strong(X0)) & (strong(X0) | ~old(X0)))) [nnf transformation 31]
44. ((quiet(paul) & happy(paul)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | (~quiet(paul) | ~happy(paul))) [nnf transformation 4]
45. ((quiet(paul) & happy(paul)) | ! [X0] : ~creative(X0)) & (? [X0] : creative(X0) | ~quiet(paul) | ~happy(paul)) [flattening 44]
46. ((quiet(paul) & happy(paul)) | ! [X0] : ~creative(X0)) & (? [X1] : creative(X1) | ~quiet(paul) | ~happy(paul)) [rectify 45]
47. ? [X1] : creative(X1) => creative(sK0) [choice axiom]
48. ((quiet(paul) & happy(paul)) | ! [X0] : ~creative(X0)) & (creative(sK0) | ~quiet(paul) | ~happy(paul)) [skolemisation 46,47]
61. ! [X0] : (((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | (creative(X0) & ~rich(X0))) [nnf transformation 34]
62. ! [X0] : (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (creative(X0) & wise(X0))) [nnf transformation 35]
63. ! [X0] : (~funny(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) [nnf transformation 38]
64. ! [X0] : (((~generous(X0) | ~brave(X0)) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0)))) & (((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (generous(X0) & brave(X0)))) [nnf transformation 15]
65. ! [X0] : ((~generous(X0) | ~brave(X0) | ((patient(X0) | calm(X0)) & (~calm(X0) | ~patient(X0)))) & (((calm(X0) | ~patient(X0)) & (~calm(X0) | patient(X0))) | (generous(X0) & brave(X0)))) [flattening 64]
66. ! [X0] : (((tall(X0) & kind(X0)) | (funny(X0) & ~strong(X0))) & ((~funny(X0) | strong(X0)) | (~tall(X0) | ~kind(X0)))) [nnf transformation 16]
67. ! [X0] : (((tall(X0) & kind(X0)) | (funny(X0) & ~strong(X0))) & (~funny(X0) | strong(X0) | ~tall(X0) | ~kind(X0))) [flattening 66]
72. ? [X0] : generous(X0) => generous(sK6) [choice axiom]
73. generous(sK6) [skolemisation 21,72]
81. patient(X0) | tall(X0) [cnf transformation 42]
86. brave(X0) | ~old(X0) | strong(X0) | ~old(X0) [cnf transformation 43]
89. happy(paul) | ~creative(X0) [cnf transformation 48]
100. ~kind(X0) | generous(X0) | creative(X0) [cnf transformation 61]
106. ~calm(X0) | old(X0) | creative(X0) [cnf transformation 62]
108. ~happy(X0) | generous(X0) | ~funny(X0) [cnf transformation 63]
112. ~strong(X0) | ~tall(X0) [cnf transformation 40]
113. ~generous(X0) | ~tall(X0) [cnf transformation 40]
115. ~generous(X0) | calm(X0) [cnf transformation 40]
120. ~generous(X0) | ~brave(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 65]
124. kind(X0) | funny(X0) [cnf transformation 67]
125. tall(X0) | ~strong(X0) [cnf transformation 67]
126. funny(X0) | tall(X0) [cnf transformation 67]
132. generous(sK6) [cnf transformation 73]
137. ~creative(paul) [cnf transformation 25]
139. ~old(X0) | brave(X0) | strong(X0) [duplicate literal removal 86]
141. 1 <=> ! [X0] : ~creative(X0) [avatar definition]
142. ~creative(X0) <- (1) [avatar component clause 141]
149. 3 <=> happy(paul) [avatar definition]
151. happy(paul) <- (3) [avatar component clause 149]
152. 1 | 3 [avatar split clause 89,149,141]
198. ~generous(X0) | ~brave(X0) | ~patient(X0) [subsumption resolution 120,115]
200. ~strong(X0) [subsumption resolution 125,112]
222. ~tall(sK6) [resolution 113,132]
223. calm(sK6) [resolution 115,132]
230. generous(X0) | creative(X0) | funny(X0) [resolution 100,124]
243. 20 <=> creative(sK6) [avatar definition]
245. creative(sK6) <- (20) [avatar component clause 243]
256. 22 <=> old(sK6) [avatar definition]
258. old(sK6) <- (22) [avatar component clause 256]
260. old(sK6) | creative(sK6) [resolution 106,223]
262. 20 | 22 [avatar split clause 260,256,243]
270. generous(paul) | ~funny(paul) <- (3) [resolution 108,151]
272. 24 <=> funny(paul) [avatar definition]
276. 25 <=> generous(paul) [avatar definition]
278. generous(paul) <- (25) [avatar component clause 276]
279. ~24 | 25 | ~3 [avatar split clause 270,149,276,272]
298. 28 <=> brave(sK6) [avatar definition]
302. 29 <=> patient(sK6) [avatar definition]
303. ~patient(sK6) <- (~29) [avatar component clause 302]
312. ~brave(sK6) | ~patient(sK6) [resolution 198,132]
315. brave(sK6) | strong(sK6) <- (22) [resolution 258,139]
328. creative(X5) | funny(X5) | ~tall(X5) [resolution 230,113]
339. creative(X5) | funny(X5) [subsumption resolution 328,126]
364. tall(sK6) <- (~29) [resolution 303,81]
365. $false <- (~29) [subsumption resolution 364,222]
366. 29 [avatar contradiction clause 365]
367. brave(sK6) <- (22) [subsumption resolution 315,200]
368. 28 | ~22 [avatar split clause 367,256,298]
369. ~29 | ~28 [avatar split clause 312,298,302]
382. funny(paul) [resolution 339,137]
386. 24 [avatar split clause 382,272]
387. ~brave(paul) | ~patient(paul) <- (25) [resolution 278,198]
394. 37 <=> patient(paul) [avatar definition]
396. ~patient(paul) <- (~37) [avatar component clause 394]
398. 38 <=> brave(paul) [avatar definition]
401. ~37 | ~38 | ~25 [avatar split clause 387,276,398,394]
411. $false <- (1, 20) [resolution 142,245]
413. ~1 | ~20 [avatar contradiction clause 411]
420. calm(paul) <- (25) [resolution 278,115]
421. ~tall(paul) <- (25) [resolution 278,113]
427. old(paul) | creative(paul) <- (25) [resolution 420,106]
429. old(paul) <- (25) [subsumption resolution 427,137]
452. brave(paul) | strong(paul) <- (25) [resolution 429,139]
459. brave(paul) <- (25) [subsumption resolution 452,200]
460. 38 | ~25 [avatar split clause 459,276,398]
462. tall(paul) <- (~37) [resolution 396,81]
463. $false <- (25, ~37) [subsumption resolution 462,421]
464. ~25 | 37 [avatar contradiction clause 463]
465. $false [avatar sat refutation 152,262,279,366,368,369,386,401,413,460,464]
% SZS output end Proof for 6688330867173087899124183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not curious is either brave or not kind.
Everyone who is either patient or not creative is both not wise and tall.
If someone is both not wise and not rich then lucy is calm or not wise and vice versa.
Everyone who is kind or patient is both not creative and quiet.
Everyone who is either not brave or happy is old or not humble and vice versa.
If someone is calm or creative then someone is either wise or not patient and vice versa.
Everyone who is creative is not happy or not curious and vice versa.
If susan is wise or tall then mary is not calm or not humble.
Everyone who is not strong is patient and vice versa.
Everyone who is rich or quiet is funny or patient.
Everyone who is both humble and creative is funny and vice versa.
Everyone who is both curious and wise is both wise and not strong and vice versa.
Everyone who is both calm and tall is rich and vice versa.
Everyone who is not rich is generous and vice versa.
If john is either not calm or not strong then someone is not rich.
If susan is both not old and curious then someone is humble and vice versa.
Someone is either not brave or calm.
Lucy is not rich or not humble.
Mary is not humble.
Someone is generous or not old.
Someone is either brave or wise.
John is tall.
Someone is either not curious or happy. | John is not humble. | neutral | (![X]:((quiet(X)&~curious(X))=>(brave(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~creative(X))=>(~wise(X)&tall(X))))&
((?[X]:((~wise(X)&~rich(X))))<=>((calm(lucy)|~wise(lucy))))&
(![X]:((kind(X)|patient(X))=>(~creative(X)&quiet(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(old(X)|~humble(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:((wise(X)<~>~patient(X)))))&
(![X]:(creative(X)<=>(~happy(X)|~curious(X))))&
(((wise(susan)|tall(susan)))=>((~calm(mary)|~humble(mary))))&
(![X]:(~strong(X)<=>patient(X)))&
(![X]:((rich(X)|quiet(X))=>(funny(X)|patient(X))))&
(![X]:((humble(X)&creative(X))<=>funny(X)))&
(![X]:((curious(X)&wise(X))<=>(wise(X)&~strong(X))))&
(![X]:((calm(X)&tall(X))<=>rich(X)))&
(![X]:(~rich(X)<=>generous(X)))&
(((~calm(john)<~>~strong(john)))=>(?[X]:(~rich(X))))&
(((~old(susan)&curious(susan)))<=>(?[X]:(humble(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
((~rich(lucy)|~humble(lucy)))&
(~humble(mary))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((brave(X)<~>wise(X))))&
(tall(john))&
(?[X]:((~curious(X)<~>happy(X)))) | ~humble(john) | [] | null | 0 |
If paul is both quiet and not old then someone is curious or not tall and vice versa.
If someone is strong or not curious then paul is both creative and old.
If susan is either not humble or not generous then fred is not wise or wise.
If someone is not brave then alice is not happy and vice versa.
Everyone who is not strong or not old is not creative.
Everyone who is either curious or creative is either not old or rich and vice versa.
Everyone who is both not creative and not tall is creative or patient.
Everyone who is calm or not calm is curious or happy.
Everyone who is kind is both happy and not calm.
If someone is both old and calm then mary is quiet and vice versa.
If someone is not old then alice is either kind or strong.
Everyone who is either not creative or not brave is wise and vice versa.
Everyone who is not humble is both happy and not brave and vice versa.
Everyone who is either not curious or humble is quiet or kind.
Everyone who is not creative is both not patient and happy and vice versa.
Someone is not quiet or strong.
Alice is both wise and not quiet.
Someone is both rich and not patient.
Someone is either calm or not wise.
John is both not calm and generous.
Alice is not rich or not old. | Susan is not strong. | neutral | (((quiet(paul)&~old(paul)))<=>(?[X]:((curious(X)|~tall(X)))))&
((?[X]:((strong(X)|~curious(X))))=>((creative(paul)&old(paul))))&
(((~humble(susan)<~>~generous(susan)))=>((~wise(fred)|wise(fred))))&
((?[X]:(~brave(X)))<=>(~happy(alice)))&
(![X]:((~strong(X)|~old(X))=>~creative(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~old(X)<~>rich(X))))&
(![X]:((~creative(X)&~tall(X))=>(creative(X)|patient(X))))&
(![X]:((calm(X)|~calm(X))=>(curious(X)|happy(X))))&
(![X]:(kind(X)=>(happy(X)&~calm(X))))&
((?[X]:((old(X)&calm(X))))<=>(quiet(mary)))&
((?[X]:(~old(X)))=>((kind(alice)<~>strong(alice))))&
(![X]:((~creative(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~humble(X)<=>(happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>humble(X))=>(quiet(X)|kind(X))))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((wise(alice)&~quiet(alice)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
((~calm(john)&generous(john)))&
((~rich(alice)|~old(alice))) | ~strong(susan) | [] | null | 0 |
Everyone who is both funny and not happy is not curious.
If someone is both not brave and happy then fred is not kind and vice versa.
Everyone who is either not tall or not rich is not old.
Everyone who is either rich or not rich is either creative or strong and vice versa.
If someone is both not quiet and rich then lucy is humble or not patient.
Everyone who is generous or not brave is both curious and not tall.
If someone is both not old and not patient then fred is generous or funny.
Everyone who is either strong or quiet is not funny or rich and vice versa.
If paul is curious then someone is creative or not generous.
Everyone who is not calm or not curious is quiet or strong and vice versa.
If lucy is not humble then susan is either strong or happy and vice versa.
Everyone who is quiet or tall is not brave.
Everyone who is not patient or strong is kind and vice versa.
If someone is funny or not creative then john is not patient or funny and vice versa.
If lucy is old or not kind then someone is happy.
If someone is both not humble and not patient then someone is both not kind and not old and vice versa.
Someone is both not happy and brave.
Lucy is either not calm or creative.
Paul is both calm and not quiet.
Someone is both curious and creative.
Someone is creative.
Susan is both humble and not patient.
John is not tall.
Paul is not patient or tall. | Lucy is funny. | neutral | (![X]:((funny(X)&~happy(X))=>~curious(X)))&
((?[X]:((~brave(X)&happy(X))))<=>(~kind(fred)))&
(![X]:((~tall(X)<~>~rich(X))=>~old(X)))&
(![X]:((rich(X)<~>~rich(X))<=>(creative(X)<~>strong(X))))&
((?[X]:((~quiet(X)&rich(X))))=>((humble(lucy)|~patient(lucy))))&
(![X]:((generous(X)|~brave(X))=>(curious(X)&~tall(X))))&
((?[X]:((~old(X)&~patient(X))))=>((generous(fred)|funny(fred))))&
(![X]:((strong(X)<~>quiet(X))<=>(~funny(X)|rich(X))))&
((curious(paul))=>(?[X]:((creative(X)|~generous(X)))))&
(![X]:((~calm(X)|~curious(X))<=>(quiet(X)|strong(X))))&
((~humble(lucy))<=>((strong(susan)<~>happy(susan))))&
(![X]:((quiet(X)|tall(X))=>~brave(X)))&
(![X]:((~patient(X)|strong(X))<=>kind(X)))&
((?[X]:((funny(X)|~creative(X))))<=>((~patient(john)|funny(john))))&
(((old(lucy)|~kind(lucy)))=>(?[X]:(happy(X))))&
((?[X]:((~humble(X)&~patient(X))))<=>(?[X]:((~kind(X)&~old(X)))))&
(?[X]:((~happy(X)&brave(X))))&
((~calm(lucy)<~>creative(lucy)))&
((calm(paul)&~quiet(paul)))&
(?[X]:((curious(X)&creative(X))))&
(?[X]:(creative(X)))&
((humble(susan)&~patient(susan)))&
(~tall(john))&
((~patient(paul)|tall(paul))) | funny(lucy) | [] | null | 0 |
If someone is either funny or not wise then someone is both wise and not humble.
Everyone who is both curious and humble is either strong or not calm.
If someone is not strong then someone is either calm or tall and vice versa.
Everyone who is both rich and not old is either not generous or patient and vice versa.
If mary is both humble and not wise then someone is quiet and vice versa.
Everyone who is quiet or calm is not brave.
If mary is both not creative and not curious then lucy is happy or not creative and vice versa.
If paul is both not wise and funny then susan is not old and vice versa.
Everyone who is wise or rich is both quiet and not brave and vice versa.
If paul is not tall or tall then someone is not rich or not strong.
If someone is not strong or not tall then susan is both not brave and rich.
Everyone who is both humble and quiet is both creative and not old and vice versa.
If someone is both wise and brave then someone is rich.
If fred is both not old and not strong then someone is generous or humble.
If someone is both curious and not funny then paul is either not rich or not tall and vice versa.
Everyone who is not tall or tall is not tall or not strong.
Fred is either not brave or not curious.
Someone is humble or not quiet.
Mary is not funny or not tall.
Fred is patient.
John is both not generous and old.
Fred is not patient or tall.
Fred is patient or old. | Susan is quiet. | entailment | ((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:((wise(X)&~humble(X)))))&
(![X]:((curious(X)&humble(X))=>(strong(X)<~>~calm(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((rich(X)&~old(X))<=>(~generous(X)<~>patient(X))))&
(((humble(mary)&~wise(mary)))<=>(?[X]:(quiet(X))))&
(![X]:((quiet(X)|calm(X))=>~brave(X)))&
(((~creative(mary)&~curious(mary)))<=>((happy(lucy)|~creative(lucy))))&
(((~wise(paul)&funny(paul)))<=>(~old(susan)))&
(![X]:((wise(X)|rich(X))<=>(quiet(X)&~brave(X))))&
(((~tall(paul)|tall(paul)))=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((~strong(X)|~tall(X))))=>((~brave(susan)&rich(susan))))&
(![X]:((humble(X)&quiet(X))<=>(creative(X)&~old(X))))&
((?[X]:((wise(X)&brave(X))))=>(?[X]:(rich(X))))&
(((~old(fred)&~strong(fred)))=>(?[X]:((generous(X)|humble(X)))))&
((?[X]:((curious(X)&~funny(X))))<=>((~rich(paul)<~>~tall(paul))))&
(![X]:((~tall(X)|tall(X))=>(~tall(X)|~strong(X))))&
((~brave(fred)<~>~curious(fred)))&
(?[X]:((humble(X)|~quiet(X))))&
((~funny(mary)|~tall(mary)))&
(patient(fred))&
((~generous(john)&old(john)))&
((~patient(fred)|tall(fred)))&
((patient(fred)|old(fred))) | quiet(susan) | [
"p8",
"p10",
"p15",
"p19",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6728549670919694123388700
% SZS output start Proof for 6728549670919694123388700
9. ! [X0] : ((rich(X0) | wise(X0)) <=> (~brave(X0) & quiet(X0))) [input p8]
11. ? [X0] : (~tall(X0) | ~strong(X0)) => (rich(susan) & ~brave(susan)) [input p10]
16. ! [X0] : ((tall(X0) | ~tall(X0)) => (~strong(X0) | ~tall(X0))) [input p15]
20. patient(fred) [input p19]
22. tall(fred) | ~patient(fred) [input p21]
24. ~quiet(susan) [input hypothesis]
33. (rich(susan) & ~brave(susan)) | ! [X0] : (tall(X0) & strong(X0)) [ennf transformation 11]
37. ! [X0] : ((~strong(X0) | ~tall(X0)) | (~tall(X0) & tall(X0))) [ennf transformation 16]
38. ! [X0] : (~strong(X0) | ~tall(X0) | (~tall(X0) & tall(X0))) [flattening 37]
60. ! [X0] : (((rich(X0) | wise(X0)) | (brave(X0) | ~quiet(X0))) & ((~brave(X0) & quiet(X0)) | (~rich(X0) & ~wise(X0)))) [nnf transformation 9]
61. ! [X0] : ((rich(X0) | wise(X0) | brave(X0) | ~quiet(X0)) & ((~brave(X0) & quiet(X0)) | (~rich(X0) & ~wise(X0)))) [flattening 60]
108. ~rich(X0) | quiet(X0) [cnf transformation 61]
116. rich(susan) | strong(X0) [cnf transformation 33]
131. ~strong(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 38]
136. patient(fred) [cnf transformation 20]
139. tall(fred) | ~patient(fred) [cnf transformation 22]
141. ~quiet(susan) [cnf transformation 24]
142. ~tall(X0) | ~strong(X0) [duplicate literal removal 131]
174. 8 <=> ! [X3] : strong(X3) [avatar definition]
175. strong(X3) <- (8) [avatar component clause 174]
259. 26 <=> rich(susan) [avatar definition]
261. rich(susan) <- (26) [avatar component clause 259]
263. 8 | 26 [avatar split clause 116,259,174]
336. tall(fred) [subsumption resolution 139,136]
347. quiet(susan) <- (26) [resolution 108,261]
348. $false <- (26) [subsumption resolution 347,141]
349. ~26 [avatar contradiction clause 348]
355. ~strong(fred) [resolution 142,336]
359. $false <- (8) [subsumption resolution 355,175]
360. ~8 [avatar contradiction clause 359]
363. $false [avatar sat refutation 263,349,360]
% SZS output end Proof for 6728549670919694123388700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If susan is curious or kind then someone is tall or brave.
If susan is either patient or curious then someone is both not humble and wise and vice versa.
If someone is both not creative and creative then lucy is either not curious or not generous.
Everyone who is either not humble or not tall is strong or not creative.
Everyone who is not funny or humble is either not strong or brave and vice versa.
Everyone who is not old or old is either old or brave and vice versa.
If someone is old or not happy then susan is not patient or not humble and vice versa.
If someone is curious or not wise then someone is not strong and vice versa.
If someone is not humble or not calm then john is funny and vice versa.
If paul is not humble or not generous then john is wise and vice versa.
If john is either not curious or not brave then someone is both quiet and strong and vice versa.
Everyone who is not brave is creative or not old and vice versa.
If someone is either old or not funny then john is either creative or old and vice versa.
If someone is either old or funny then someone is both kind and old and vice versa.
Everyone who is either happy or curious is both quiet and not strong.
Everyone who is not calm is both happy and humble.
John is both humble and quiet.
Someone is happy or not generous.
Someone is tall or not humble.
Paul is either kind or not humble.
Susan is either strong or happy. | Lucy is calm. | entailment | (((curious(susan)|kind(susan)))=>(?[X]:((tall(X)|brave(X)))))&
(((patient(susan)<~>curious(susan)))<=>(?[X]:((~humble(X)&wise(X)))))&
((?[X]:((~creative(X)&creative(X))))=>((~curious(lucy)<~>~generous(lucy))))&
(![X]:((~humble(X)<~>~tall(X))=>(strong(X)|~creative(X))))&
(![X]:((~funny(X)|humble(X))<=>(~strong(X)<~>brave(X))))&
(![X]:((~old(X)|old(X))<=>(old(X)<~>brave(X))))&
((?[X]:((old(X)|~happy(X))))<=>((~patient(susan)|~humble(susan))))&
((?[X]:((curious(X)|~wise(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~humble(X)|~calm(X))))<=>(funny(john)))&
(((~humble(paul)|~generous(paul)))<=>(wise(john)))&
(((~curious(john)<~>~brave(john)))<=>(?[X]:((quiet(X)&strong(X)))))&
(![X]:(~brave(X)<=>(creative(X)|~old(X))))&
((?[X]:((old(X)<~>~funny(X))))<=>((creative(john)<~>old(john))))&
((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((kind(X)&old(X)))))&
(![X]:((happy(X)<~>curious(X))=>(quiet(X)&~strong(X))))&
(![X]:(~calm(X)=>(happy(X)&humble(X))))&
((humble(john)&quiet(john)))&
(?[X]:((happy(X)|~generous(X))))&
(?[X]:((tall(X)|~humble(X))))&
((kind(paul)<~>~humble(paul)))&
((strong(susan)<~>happy(susan))) | calm(lucy) | [
"p5",
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3668213861092514593625441
% SZS output start Proof for 3668213861092514593625441
6. ! [X0] : ((old(X0) | ~old(X0)) <=> (old(X0) <~> brave(X0))) [input p5]
9. ? [X0] : (~calm(X0) | ~humble(X0)) <=> funny(john) [input p8]
12. ! [X0] : (~brave(X0) <=> (~old(X0) | creative(X0))) [input p11]
13. ? [X0] : (old(X0) <~> ~funny(X0)) <=> (creative(john) <~> old(john)) [input p12]
22. ~calm(lucy) [input hypothesis]
41. ! [X0] : (((old(X0) | ~old(X0)) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (~old(X0) & old(X0)))) [nnf transformation 6]
42. ! [X0] : ((old(X0) | ~old(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0)))) & (((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | (~old(X0) & old(X0)))) [flattening 41]
53. (? [X0] : (~calm(X0) | ~humble(X0)) | ~funny(john)) & (funny(john) | ! [X0] : (calm(X0) & humble(X0))) [nnf transformation 9]
54. (? [X0] : (~calm(X0) | ~humble(X0)) | ~funny(john)) & (funny(john) | ! [X1] : (calm(X1) & humble(X1))) [rectify 53]
55. ? [X0] : (~calm(X0) | ~humble(X0)) => (~calm(sK5) | ~humble(sK5)) [choice axiom]
56. ((~calm(sK5) | ~humble(sK5)) | ~funny(john)) & (funny(john) | ! [X1] : (calm(X1) & humble(X1))) [skolemisation 54,55]
63. ! [X0] : ((~brave(X0) | (old(X0) & ~creative(X0))) & ((~old(X0) | creative(X0)) | brave(X0))) [nnf transformation 12]
64. ! [X0] : ((~brave(X0) | (old(X0) & ~creative(X0))) & (~old(X0) | creative(X0) | brave(X0))) [flattening 63]
65. (? [X0] : ((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | ((creative(john) | ~old(john)) & (old(john) | ~creative(john)))) & (((~old(john) | ~creative(john)) & (old(john) | creative(john))) | ! [X0] : ((old(X0) | funny(X0)) & (~funny(X0) | ~old(X0)))) [nnf transformation 13]
66. (? [X0] : ((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) | ((creative(john) | ~old(john)) & (old(john) | ~creative(john)))) & (((~old(john) | ~creative(john)) & (old(john) | creative(john))) | ! [X1] : ((old(X1) | funny(X1)) & (~funny(X1) | ~old(X1)))) [rectify 65]
67. ? [X0] : ((funny(X0) | ~old(X0)) & (~funny(X0) | old(X0))) => ((funny(sK7) | ~old(sK7)) & (~funny(sK7) | old(sK7))) [choice axiom]
68. (((funny(sK7) | ~old(sK7)) & (~funny(sK7) | old(sK7))) | ((creative(john) | ~old(john)) & (old(john) | ~creative(john)))) & (((~old(john) | ~creative(john)) & (old(john) | creative(john))) | ! [X1] : ((old(X1) | funny(X1)) & (~funny(X1) | ~old(X1)))) [skolemisation 66,67]
99. brave(X0) | old(X0) | old(X0) [cnf transformation 42]
102. ~brave(X0) | ~old(X0) | ~old(X0) [cnf transformation 42]
113. funny(john) | calm(X1) [cnf transformation 56]
124. ~old(X0) | creative(X0) | brave(X0) [cnf transformation 64]
126. ~brave(X0) | old(X0) [cnf transformation 64]
129. ~old(john) | ~creative(john) | ~funny(X1) | ~old(X1) [cnf transformation 68]
155. ~calm(lucy) [cnf transformation 22]
156. old(X0) | brave(X0) [duplicate literal removal 99]
157. ~old(X0) | ~brave(X0) [duplicate literal removal 102]
246. 20 <=> funny(john) [avatar definition]
247. funny(john) <- (20) [avatar component clause 246]
259. 23 <=> ! [X1] : calm(X1) [avatar definition]
260. calm(X1) <- (23) [avatar component clause 259]
261. 23 | 20 [avatar split clause 113,246,259]
306. old(X0) [subsumption resolution 126,156]
307. creative(X0) | brave(X0) [subsumption resolution 124,306]
311. 33 <=> creative(john) [avatar definition]
312. ~creative(john) <- (~33) [avatar component clause 311]
319. ~creative(john) | ~funny(X1) | ~old(X1) [subsumption resolution 129,306]
320. ~creative(john) | ~funny(X1) [subsumption resolution 319,306]
322. 35 <=> ! [X1] : ~funny(X1) [avatar definition]
323. ~funny(X1) <- (35) [avatar component clause 322]
324. 35 | ~33 [avatar split clause 320,311,322]
383. ~brave(X1) [resolution 157,306]
386. brave(john) <- (~33) [resolution 307,312]
390. $false <- (~33) [subsumption resolution 386,383]
391. 33 [avatar contradiction clause 390]
398. $false <- (20, 35) [subsumption resolution 247,323]
399. ~20 | ~35 [avatar contradiction clause 398]
404. $false <- (23) [resolution 260,155]
405. ~23 [avatar contradiction clause 404]
406. $false [avatar sat refutation 261,324,391,399,405]
% SZS output end Proof for 3668213861092514593625441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is both not humble and not happy then someone is both funny and not old and vice versa. If mary is wise or not generous then john is old and vice versa. Everyone who is either rich or old is either not rich or strong and vice versa. Everyone who is both not brave and humble is not humble. If susan is both not happy and curious then paul is either calm or happy. Everyone who is patient is not tall and vice versa. Everyone who is both not brave and not happy is not patient and vice versa. Everyone who is tall is both not strong and not curious and vice versa. If fred is tall or happy then someone is both not creative and not quiet and vice versa. Everyone who is not happy or not calm is generous or not calm and vice versa. If someone is both not rich and rich then someone is both patient and tall. Everyone who is either not rich or old is either wise or not quiet. Everyone who is not humble or not curious is wise. Everyone who is either not brave or not patient is tall and vice versa. If someone is not generous then paul is not brave and vice versa. If someone is either patient or strong then alice is both not old and not quiet. Someone is either not creative or not old. Fred is either funny or tall. Lucy is both not calm and generous. Someone is either funny or patient. Someone is not funny or curious. Someone is not tall or humble. Lucy is not kind. Susan is either not patient or kind. | Alice is not strong. | contradiction | (((~humble(mary)&~happy(mary)))<=>(?[X]:((funny(X)&~old(X)))))&
(((wise(mary)|~generous(mary)))<=>(old(john)))&
(![X]:((rich(X)<~>old(X))<=>(~rich(X)<~>strong(X))))&
(![X]:((~brave(X)&humble(X))=>~humble(X)))&
(((~happy(susan)&curious(susan)))=>((calm(paul)<~>happy(paul))))&
(![X]:(patient(X)<=>~tall(X)))&
(![X]:((~brave(X)&~happy(X))<=>~patient(X)))&
(![X]:(tall(X)<=>(~strong(X)&~curious(X))))&
(((tall(fred)|happy(fred)))<=>(?[X]:((~creative(X)&~quiet(X)))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|~calm(X))))&
((?[X]:((~rich(X)&rich(X))))=>(?[X]:((patient(X)&tall(X)))))&
(![X]:((~rich(X)<~>old(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((~humble(X)|~curious(X))=>wise(X)))&
(![X]:((~brave(X)<~>~patient(X))<=>tall(X)))&
((?[X]:(~generous(X)))<=>(~brave(paul)))&
((?[X]:((patient(X)<~>strong(X))))=>((~old(alice)&~quiet(alice))))&
(?[X]:((~creative(X)<~>~old(X))))&
((funny(fred)<~>tall(fred)))&
((~calm(lucy)&generous(lucy)))&
(?[X]:((funny(X)<~>patient(X))))&
(?[X]:((~funny(X)|curious(X))))&
(?[X]:((~tall(X)|humble(X))))&
(~kind(lucy))&
((~patient(susan)<~>kind(susan))) | ~strong(alice) | [
"p2",
"p5",
"p6",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6204953519662546553947077
% SZS output start Proof for 6204953519662546553947077
3. ! [X0] : ((rich(X0) <~> old(X0)) <=> (~rich(X0) <~> strong(X0))) [input p2]
6. ! [X0] : (patient(X0) <=> ~tall(X0)) [input p5]
7. ! [X0] : ((~happy(X0) & ~brave(X0)) <=> ~patient(X0)) [input p6]
14. ! [X0] : ((~brave(X0) <~> ~patient(X0)) <=> tall(X0)) [input p13]
16. ? [X0] : (patient(X0) <~> strong(X0)) => (~quiet(alice) & ~old(alice)) [input p15]
25. ~strong(alice) [input hypothesis]
34. (~quiet(alice) & ~old(alice)) | ! [X0] : (patient(X0) <=> strong(X0)) [ennf transformation 16]
42. ! [X0] : ((((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | ((~rich(X0) | ~strong(X0)) & (strong(X0) | rich(X0)))) & (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0))))) [nnf transformation 3]
44. ! [X0] : ((patient(X0) | tall(X0)) & (~tall(X0) | ~patient(X0))) [nnf transformation 6]
45. ! [X0] : (((~happy(X0) & ~brave(X0)) | patient(X0)) & (~patient(X0) | (happy(X0) | brave(X0)))) [nnf transformation 7]
46. ! [X0] : (((~happy(X0) & ~brave(X0)) | patient(X0)) & (~patient(X0) | happy(X0) | brave(X0))) [flattening 45]
60. ! [X0] : ((((patient(X0) | brave(X0)) & (~patient(X0) | ~brave(X0))) | ~tall(X0)) & (tall(X0) | ((~brave(X0) | patient(X0)) & (~patient(X0) | brave(X0))))) [nnf transformation 14]
65. (~quiet(alice) & ~old(alice)) | ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 34]
85. strong(X0) | ~rich(X0) | old(X0) | ~rich(X0) [cnf transformation 42]
89. old(X0) | rich(X0) | strong(X0) | rich(X0) [cnf transformation 42]
96. ~tall(X0) | ~patient(X0) [cnf transformation 44]
97. tall(X0) | patient(X0) [cnf transformation 44]
99. ~brave(X0) | patient(X0) [cnf transformation 46]
124. patient(X0) | brave(X0) | ~tall(X0) [cnf transformation 60]
127. ~old(alice) | strong(X0) | ~patient(X0) [cnf transformation 65]
144. ~strong(alice) [cnf transformation 25]
146. strong(X0) | ~rich(X0) | old(X0) [duplicate literal removal 85]
148. old(X0) | rich(X0) | strong(X0) [duplicate literal removal 89]
189. strong(X0) | old(X0) [subsumption resolution 146,148]
232. patient(X0) | ~tall(X0) [subsumption resolution 124,99]
233. ~tall(X0) [subsumption resolution 232,96]
257. 23 <=> ! [X0] : (strong(X0) | ~patient(X0)) [avatar definition]
258. strong(X0) | ~patient(X0) <- (23) [avatar component clause 257]
261. 24 <=> old(alice) [avatar definition]
265. 23 | ~24 [avatar split clause 127,261,257]
307. patient(X1) [resolution 97,233]
315. old(alice) [resolution 189,144]
319. 24 [avatar split clause 315,261]
320. strong(X0) <- (23) [subsumption resolution 258,307]
321. $false <- (23) [resolution 320,144]
323. ~23 [avatar contradiction clause 321]
324. $false [avatar sat refutation 265,319,323]
% SZS output end Proof for 6204953519662546553947077
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not creative is either not brave or funny and vice versa. If someone is both brave and funny then alice is funny or not humble and vice versa. Everyone who is not happy or wise is either not calm or not tall and vice versa. If john is both not wise and funny then susan is either not strong or not kind and vice versa. If someone is generous or not kind then susan is not brave. Everyone who is brave is both brave and not curious and vice versa. If mary is both kind and not wise then fred is not kind and vice versa. If lucy is funny then john is both not strong and tall. If alice is happy or humble then john is not wise and vice versa. If someone is both tall and not funny then someone is not brave or rich. Everyone who is patient or strong is rich and vice versa. Everyone who is creative or not strong is both not calm and strong and vice versa. If fred is both not rich and not humble then susan is both not funny and quiet and vice versa. Everyone who is strong is tall or not funny. If someone is happy or generous then someone is either kind or not tall and vice versa. If lucy is not tall then mary is not patient and vice versa. Someone is not happy or humble. Someone is both humble and not curious. Alice is both tall and generous. Someone is not patient or happy. Susan is both not happy and strong. Paul is rich or not wise. | Susan is funny. | contradiction | (![X]:((strong(X)<~>~creative(X))<=>(~brave(X)<~>funny(X))))&
((?[X]:((brave(X)&funny(X))))<=>((funny(alice)|~humble(alice))))&
(![X]:((~happy(X)|wise(X))<=>(~calm(X)<~>~tall(X))))&
(((~wise(john)&funny(john)))<=>((~strong(susan)<~>~kind(susan))))&
((?[X]:((generous(X)|~kind(X))))=>(~brave(susan)))&
(![X]:(brave(X)<=>(brave(X)&~curious(X))))&
(((kind(mary)&~wise(mary)))<=>(~kind(fred)))&
((funny(lucy))=>((~strong(john)&tall(john))))&
(((happy(alice)|humble(alice)))<=>(~wise(john)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((?[X]:((happy(X)|generous(X))))<=>(?[X]:((kind(X)<~>~tall(X)))))&
((~tall(lucy))<=>(~patient(mary)))&
(?[X]:((~happy(X)|humble(X))))&
(?[X]:((humble(X)&~curious(X))))&
((tall(alice)&generous(alice)))&
(?[X]:((~patient(X)|happy(X))))&
((~happy(susan)&strong(susan)))&
((rich(paul)|~wise(paul))) | funny(susan) | [
"p0",
"p2",
"p4",
"p11",
"p13",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6543869925425217428489371
% SZS output start Proof for 6543869925425217428489371
1. ! [X0] : ((strong(X0) <~> ~creative(X0)) <=> (~brave(X0) <~> funny(X0))) [input p0]
3. ! [X0] : ((wise(X0) | ~happy(X0)) <=> (~calm(X0) <~> ~tall(X0))) [input p2]
5. ? [X0] : (~kind(X0) | generous(X0)) => ~brave(susan) [input p4]
12. ! [X0] : ((~strong(X0) | creative(X0)) <=> (strong(X0) & ~calm(X0))) [input p11]
14. ! [X0] : (strong(X0) => (~funny(X0) | tall(X0))) [input p13]
19. generous(alice) & tall(alice) [input p18]
21. strong(susan) & ~happy(susan) [input p20]
23. funny(susan) [input hypothesis]
26. ~brave(susan) | ! [X0] : (kind(X0) & ~generous(X0)) [ennf transformation 5]
29. ! [X0] : ((~funny(X0) | tall(X0)) | ~strong(X0)) [ennf transformation 14]
30. ! [X0] : (~funny(X0) | tall(X0) | ~strong(X0)) [flattening 29]
31. ! [X0] : ((((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | ((~brave(X0) | ~funny(X0)) & (funny(X0) | brave(X0)))) & (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | ((strong(X0) | creative(X0)) & (~creative(X0) | ~strong(X0))))) [nnf transformation 1]
37. ! [X0] : (((wise(X0) | ~happy(X0)) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~wise(X0) & happy(X0)))) [nnf transformation 3]
38. ! [X0] : ((wise(X0) | ~happy(X0) | ((~calm(X0) | tall(X0)) & (~tall(X0) | calm(X0)))) & (((tall(X0) | calm(X0)) & (~tall(X0) | ~calm(X0))) | (~wise(X0) & happy(X0)))) [flattening 37]
52. ! [X0] : (((~strong(X0) | creative(X0)) | (~strong(X0) | calm(X0))) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 12]
53. ! [X0] : ((~strong(X0) | creative(X0) | ~strong(X0) | calm(X0)) & ((strong(X0) & ~calm(X0)) | (strong(X0) & ~creative(X0)))) [flattening 52]
70. ~funny(X0) | brave(X0) | ~creative(X0) | ~strong(X0) [cnf transformation 31]
81. ~tall(X0) | ~calm(X0) | happy(X0) [cnf transformation 38]
93. ~brave(susan) | ~generous(X0) [cnf transformation 26]
113. strong(X0) | strong(X0) [cnf transformation 53]
114. ~strong(X0) | creative(X0) | ~strong(X0) | calm(X0) [cnf transformation 53]
119. ~funny(X0) | tall(X0) | ~strong(X0) [cnf transformation 30]
132. generous(alice) [cnf transformation 19]
134. ~happy(susan) [cnf transformation 21]
137. funny(susan) [cnf transformation 23]
138. strong(X0) [duplicate literal removal 113]
139. ~strong(X0) | creative(X0) | calm(X0) [duplicate literal removal 114]
190. 11 <=> brave(susan) [avatar definition]
195. 12 <=> ! [X0] : ~generous(X0) [avatar definition]
196. ~generous(X0) <- (12) [avatar component clause 195]
197. 12 | ~11 [avatar split clause 93,190,195]
247. 23 <=> funny(susan) [avatar definition]
249. funny(susan) <- (23) [avatar component clause 247]
266. ~funny(X0) | tall(X0) [subsumption resolution 119,138]
335. 23 [avatar split clause 137,247]
340. tall(susan) <- (23) [resolution 266,249]
356. ~calm(susan) | happy(susan) <- (23) [resolution 340,81]
362. 45 <=> calm(susan) [avatar definition]
364. ~calm(susan) <- (~45) [avatar component clause 362]
366. ~calm(susan) <- (23) [subsumption resolution 356,134]
367. ~45 | ~23 [avatar split clause 366,247,362]
424. calm(X0) | creative(X0) [resolution 139,138]
428. brave(susan) | ~creative(susan) | ~strong(susan) <- (23) [resolution 70,249]
436. creative(susan) <- (~45) [resolution 424,364]
442. brave(susan) | ~strong(susan) <- (23, ~45) [subsumption resolution 428,436]
443. brave(susan) <- (23, ~45) [subsumption resolution 442,138]
444. 11 | ~23 | 45 [avatar split clause 443,362,247,190]
449. $false <- (12) [resolution 196,132]
450. ~12 [avatar contradiction clause 449]
451. $false [avatar sat refutation 197,335,367,444,450]
% SZS output end Proof for 6543869925425217428489371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not strong or kind then someone is not kind and vice versa.
Everyone who is funny or generous is calm and vice versa.
Everyone who is either not calm or creative is both not humble and not tall.
If paul is both not curious and not old then mary is either not happy or not brave.
If someone is not calm then john is either not brave or not quiet and vice versa.
Everyone who is not quiet or not kind is not quiet or not happy and vice versa.
If someone is both curious and creative then someone is either generous or wise and vice versa.
If mary is tall then someone is humble or not wise and vice versa.
If someone is not brave then someone is generous or not curious and vice versa.
If alice is not happy then lucy is either not patient or not curious and vice versa.
Everyone who is both generous and not patient is both not brave and wise and vice versa.
Everyone who is either not brave or not generous is not strong or not generous and vice versa.
Everyone who is either quiet or not kind is both rich and not strong and vice versa.
Everyone who is either not funny or strong is either kind or curious and vice versa.
If lucy is not generous then alice is either strong or not happy.
If someone is not tall or creative then someone is old or not quiet.
Paul is either not tall or generous.
Someone is both not quiet and not wise.
Someone is either not happy or quiet.
Someone is both calm and rich.
Someone is funny or strong.
Someone is not wise.
Susan is not kind. | Paul is tall. | neutral | (((~strong(susan)|kind(susan)))<=>(?[X]:(~kind(X))))&
(![X]:((funny(X)|generous(X))<=>calm(X)))&
(![X]:((~calm(X)<~>creative(X))=>(~humble(X)&~tall(X))))&
(((~curious(paul)&~old(paul)))=>((~happy(mary)<~>~brave(mary))))&
((?[X]:(~calm(X)))<=>((~brave(john)<~>~quiet(john))))&
(![X]:((~quiet(X)|~kind(X))<=>(~quiet(X)|~happy(X))))&
((?[X]:((curious(X)&creative(X))))<=>(?[X]:((generous(X)<~>wise(X)))))&
((tall(mary))<=>(?[X]:((humble(X)|~wise(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((generous(X)|~curious(X)))))&
((~happy(alice))<=>((~patient(lucy)<~>~curious(lucy))))&
(![X]:((generous(X)&~patient(X))<=>(~brave(X)&wise(X))))&
(![X]:((~brave(X)<~>~generous(X))<=>(~strong(X)|~generous(X))))&
(![X]:((quiet(X)<~>~kind(X))<=>(rich(X)&~strong(X))))&
(![X]:((~funny(X)<~>strong(X))<=>(kind(X)<~>curious(X))))&
((~generous(lucy))=>((strong(alice)<~>~happy(alice))))&
((?[X]:((~tall(X)|creative(X))))=>(?[X]:((old(X)|~quiet(X)))))&
((~tall(paul)<~>generous(paul)))&
(?[X]:((~quiet(X)&~wise(X))))&
(?[X]:((~happy(X)<~>quiet(X))))&
(?[X]:((calm(X)&rich(X))))&
(?[X]:((funny(X)|strong(X))))&
(?[X]:(~wise(X)))&
(~kind(susan)) | tall(paul) | [] | null | 0 |
Everyone who is not patient is generous or not happy and vice versa.
Everyone who is not quiet is not brave and vice versa.
If john is both not curious and not tall then someone is not quiet or creative and vice versa.
Everyone who is rich or not curious is either not kind or happy and vice versa.
Everyone who is rich or not rich is either not old or not generous and vice versa.
If john is not quiet or strong then mary is both not curious and tall and vice versa.
Everyone who is generous or not brave is either wise or humble and vice versa.
If susan is both not curious and not happy then someone is both humble and not humble and vice versa.
If someone is both not patient and not happy then someone is not funny or not tall.
Everyone who is either brave or calm is not tall.
If someone is not humble then mary is both brave and patient.
If someone is old then paul is not happy or brave and vice versa.
Everyone who is either creative or not humble is both old and not humble and vice versa.
Everyone who is not humble is generous or wise and vice versa.
Someone is tall.
Someone is either curious or not rich.
Someone is funny or rich.
Mary is either generous or old.
Someone is either old or not patient.
Someone is not funny.
Paul is rich or tall.
Someone is not curious or funny. | Susan is not generous. | entailment | (![X]:(~patient(X)<=>(generous(X)|~happy(X))))&
(![X]:(~quiet(X)<=>~brave(X)))&
(((~curious(john)&~tall(john)))<=>(?[X]:((~quiet(X)|creative(X)))))&
(![X]:((rich(X)|~curious(X))<=>(~kind(X)<~>happy(X))))&
(![X]:((rich(X)|~rich(X))<=>(~old(X)<~>~generous(X))))&
(((~quiet(john)|strong(john)))<=>((~curious(mary)&tall(mary))))&
(![X]:((generous(X)|~brave(X))<=>(wise(X)<~>humble(X))))&
(((~curious(susan)&~happy(susan)))<=>(?[X]:((humble(X)&~humble(X)))))&
((?[X]:((~patient(X)&~happy(X))))=>(?[X]:((~funny(X)|~tall(X)))))&
(![X]:((brave(X)<~>calm(X))=>~tall(X)))&
((?[X]:(~humble(X)))=>((brave(mary)&patient(mary))))&
((?[X]:(old(X)))<=>((~happy(paul)|brave(paul))))&
(![X]:((creative(X)<~>~humble(X))<=>(old(X)&~humble(X))))&
(![X]:(~humble(X)<=>(generous(X)|wise(X))))&
(?[X]:(tall(X)))&
(?[X]:((curious(X)<~>~rich(X))))&
(?[X]:((funny(X)|rich(X))))&
((generous(mary)<~>old(mary)))&
(?[X]:((old(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
((rich(paul)|tall(paul)))&
(?[X]:((~curious(X)|funny(X)))) | ~generous(susan) | [
"p0",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4161851648259196845322144
% SZS output start Proof for 4161851648259196845322144
1. ! [X0] : (~patient(X0) <=> (~happy(X0) | generous(X0))) [input p0]
7. ! [X0] : ((~brave(X0) | generous(X0)) <=> (wise(X0) <~> humble(X0))) [input p6]
11. ? [X0] : ~humble(X0) => (patient(mary) & brave(mary)) [input p10]
14. ! [X0] : (~humble(X0) <=> (wise(X0) | generous(X0))) [input p13]
23. generous(susan) [input hypothesis]
27. (patient(mary) & brave(mary)) | ! [X0] : humble(X0) [ennf transformation 11]
28. ! [X0] : ((~patient(X0) | (happy(X0) & ~generous(X0))) & ((~happy(X0) | generous(X0)) | patient(X0))) [nnf transformation 1]
29. ! [X0] : ((~patient(X0) | (happy(X0) & ~generous(X0))) & (~happy(X0) | generous(X0) | patient(X0))) [flattening 28]
42. ! [X0] : (((~brave(X0) | generous(X0)) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (brave(X0) & ~generous(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | generous(X0) | ((wise(X0) | ~humble(X0)) & (humble(X0) | ~wise(X0)))) & (((~humble(X0) | ~wise(X0)) & (humble(X0) | wise(X0))) | (brave(X0) & ~generous(X0)))) [flattening 42]
60. ! [X0] : ((~humble(X0) | (~wise(X0) & ~generous(X0))) & ((wise(X0) | generous(X0)) | humble(X0))) [nnf transformation 14]
61. ! [X0] : ((~humble(X0) | (~wise(X0) & ~generous(X0))) & (wise(X0) | generous(X0) | humble(X0))) [flattening 60]
78. ~generous(X0) | ~patient(X0) [cnf transformation 29]
104. ~generous(X0) | wise(X0) | humble(X0) [cnf transformation 43]
108. ~wise(X0) | generous(X0) | humble(X0) | ~brave(X0) [cnf transformation 43]
109. ~humble(X0) | generous(X0) | wise(X0) | ~brave(X0) [cnf transformation 43]
117. brave(mary) | humble(X0) [cnf transformation 27]
118. patient(mary) | humble(X0) [cnf transformation 27]
128. wise(X0) | generous(X0) | humble(X0) [cnf transformation 61]
129. ~humble(X0) | ~generous(X0) [cnf transformation 61]
130. ~humble(X0) | ~wise(X0) [cnf transformation 61]
142. generous(susan) [cnf transformation 23]
223. 17 <=> ! [X0] : humble(X0) [avatar definition]
224. humble(X0) <- (17) [avatar component clause 223]
226. 18 <=> patient(mary) [avatar definition]
228. patient(mary) <- (18) [avatar component clause 226]
229. 17 | 18 [avatar split clause 118,226,223]
231. 19 <=> brave(mary) [avatar definition]
233. brave(mary) <- (19) [avatar component clause 231]
234. 17 | 19 [avatar split clause 117,231,223]
253. humble(X0) | wise(X0) [subsumption resolution 128,104]
302. ~generous(X0) <- (17) [resolution 129,224]
304. $false <- (17) [resolution 302,142]
305. ~17 [avatar contradiction clause 304]
315. ~generous(X2) | wise(X2) [resolution 253,129]
387. generous(X2) | wise(X2) | ~brave(X2) | wise(X2) [resolution 109,253]
388. generous(X2) | wise(X2) | ~brave(X2) [duplicate literal removal 387]
390. ~brave(X2) | wise(X2) [subsumption resolution 388,315]
393. wise(mary) <- (19) [resolution 390,233]
394. generous(mary) | humble(mary) | ~brave(mary) <- (19) [resolution 393,108]
395. generous(mary) | humble(mary) <- (19) [subsumption resolution 394,233]
397. 38 <=> humble(mary) [avatar definition]
399. humble(mary) <- (38) [avatar component clause 397]
401. 39 <=> generous(mary) [avatar definition]
403. generous(mary) <- (39) [avatar component clause 401]
404. 38 | 39 | ~19 [avatar split clause 395,231,401,397]
421. ~wise(mary) <- (38) [resolution 399,130]
426. $false <- (19, 38) [subsumption resolution 421,393]
427. ~19 | ~38 [avatar contradiction clause 426]
440. ~patient(mary) <- (39) [resolution 403,78]
442. $false <- (18, 39) [subsumption resolution 440,228]
443. ~18 | ~39 [avatar contradiction clause 442]
444. $false [avatar sat refutation 229,234,305,404,427,443]
% SZS output end Proof for 4161851648259196845322144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or kind is not old. If someone is happy then john is both not strong and not brave. If someone is creative or not calm then lucy is rich or calm and vice versa. If someone is strong then alice is either generous or not calm. If someone is not tall then someone is either not brave or quiet. If fred is either tall or humble then lucy is either not funny or kind. Everyone who is either old or not generous is patient. Everyone who is tall or rich is both not tall and rich and vice versa. Everyone who is not curious or rich is either funny or happy. If someone is funny or kind then someone is either not wise or humble and vice versa. Everyone who is happy is not old and vice versa. Everyone who is not happy is both generous and calm. Everyone who is old or rich is kind. Everyone who is funny is not creative or not kind. Everyone who is not humble or old is rich or not curious. If lucy is curious then fred is either strong or creative. Alice is either not curious or old. Someone is not generous. Someone is not tall. Fred is both not strong and not creative. John is either not old or curious. Fred is generous. | Lucy is not funny. | entailment | (![X]:((generous(X)|kind(X))=>~old(X)))&
((?[X]:(happy(X)))=>((~strong(john)&~brave(john))))&
((?[X]:((creative(X)|~calm(X))))<=>((rich(lucy)|calm(lucy))))&
((?[X]:(strong(X)))=>((generous(alice)<~>~calm(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((tall(fred)<~>humble(fred)))=>((~funny(lucy)<~>kind(lucy))))&
(![X]:((old(X)<~>~generous(X))=>patient(X)))&
(![X]:((tall(X)|rich(X))<=>(~tall(X)&rich(X))))&
(![X]:((~curious(X)|rich(X))=>(funny(X)<~>happy(X))))&
((?[X]:((funny(X)|kind(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:(happy(X)<=>~old(X)))&
(![X]:(~happy(X)=>(generous(X)&calm(X))))&
(![X]:((old(X)|rich(X))=>kind(X)))&
(![X]:(funny(X)=>(~creative(X)|~kind(X))))&
(![X]:((~humble(X)|old(X))=>(rich(X)|~curious(X))))&
((curious(lucy))=>((strong(fred)<~>creative(fred))))&
((~curious(alice)<~>old(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(~tall(X)))&
((~strong(fred)&~creative(fred)))&
((~old(john)<~>curious(john)))&
(generous(fred)) | ~funny(lucy) | [
"p0",
"p8",
"p10",
"p12",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2921562823886005553829285
% SZS output start Proof for 2921562823886005553829285
1. ! [X0] : ((kind(X0) | generous(X0)) => ~old(X0)) [input p0]
9. ! [X0] : ((rich(X0) | ~curious(X0)) => (funny(X0) <~> happy(X0))) [input p8]
11. ! [X0] : (happy(X0) <=> ~old(X0)) [input p10]
13. ! [X0] : ((rich(X0) | old(X0)) => kind(X0)) [input p12]
16. curious(lucy) => (strong(fred) <~> creative(fred)) [input p15]
20. ~creative(fred) & ~strong(fred) [input p19]
23. funny(lucy) [input hypothesis]
27. ! [X0] : (~old(X0) | (~kind(X0) & ~generous(X0))) [ennf transformation 1]
32. ! [X0] : ((funny(X0) <~> happy(X0)) | (~rich(X0) & curious(X0))) [ennf transformation 9]
34. ! [X0] : (kind(X0) | (~rich(X0) & ~old(X0))) [ennf transformation 13]
39. (strong(fred) <~> creative(fred)) | ~curious(lucy) [ennf transformation 16]
53. ! [X0] : (((~happy(X0) | ~funny(X0)) & (happy(X0) | funny(X0))) | (~rich(X0) & curious(X0))) [nnf transformation 32]
59. ! [X0] : ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0))) [nnf transformation 11]
60. ((~creative(fred) | ~strong(fred)) & (creative(fred) | strong(fred))) | ~curious(lucy) [nnf transformation 39]
68. ~old(X0) | ~kind(X0) [cnf transformation 27]
90. ~funny(X0) | ~happy(X0) | curious(X0) [cnf transformation 53]
99. happy(X0) | old(X0) [cnf transformation 59]
102. kind(X0) | ~old(X0) [cnf transformation 34]
107. creative(fred) | strong(fred) | ~curious(lucy) [cnf transformation 60]
113. ~strong(fred) [cnf transformation 20]
114. ~creative(fred) [cnf transformation 20]
118. funny(lucy) [cnf transformation 23]
195. 18 <=> funny(lucy) [avatar definition]
197. funny(lucy) <- (18) [avatar component clause 195]
241. ~old(X0) [subsumption resolution 102,68]
243. 28 <=> curious(lucy) [avatar definition]
245. ~curious(lucy) <- (~28) [avatar component clause 243]
247. 29 <=> strong(fred) [avatar definition]
251. 30 <=> creative(fred) [avatar definition]
255. ~28 | 29 | 30 [avatar split clause 107,251,247,243]
257. ~30 [avatar split clause 114,251]
258. ~29 [avatar split clause 113,247]
260. 18 [avatar split clause 118,195]
280. ~happy(lucy) | curious(lucy) <- (18) [resolution 90,197]
282. ~happy(lucy) <- (18, ~28) [subsumption resolution 280,245]
293. old(lucy) <- (18, ~28) [resolution 282,99]
294. $false <- (18, ~28) [subsumption resolution 293,241]
295. ~18 | 28 [avatar contradiction clause 294]
296. $false [avatar sat refutation 255,257,258,260,295]
% SZS output end Proof for 2921562823886005553829285
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If mary is creative or not funny then someone is either patient or not brave and vice versa. Everyone who is humble or not wise is not brave. If susan is not tall or not humble then alice is both generous and not rich and vice versa. Everyone who is not strong is both not humble and rich and vice versa. If mary is not quiet then mary is quiet or not rich. If paul is both not brave and creative then john is wise and vice versa. If someone is not funny then someone is not curious or old and vice versa. Everyone who is either not brave or strong is happy or not wise and vice versa. Everyone who is either happy or not curious is both not rich and kind. Everyone who is both not patient and creative is both not old and creative and vice versa. If someone is both humble and quiet then someone is not funny or tall and vice versa. Everyone who is either not strong or happy is not funny or not rich. Everyone who is either not happy or kind is both brave and rich. Alice is both not tall and calm. Someone is not wise or not quiet. Susan is either not humble or not creative. Lucy is not old. | Mary is rich. | neutral | (((creative(mary)|~funny(mary)))<=>(?[X]:((patient(X)<~>~brave(X)))))&
(![X]:((humble(X)|~wise(X))=>~brave(X)))&
(((~tall(susan)|~humble(susan)))<=>((generous(alice)&~rich(alice))))&
(![X]:(~strong(X)<=>(~humble(X)&rich(X))))&
((~quiet(mary))=>((quiet(mary)|~rich(mary))))&
(((~brave(paul)&creative(paul)))<=>(wise(john)))&
((?[X]:(~funny(X)))<=>(?[X]:((~curious(X)|old(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(happy(X)|~wise(X))))&
(![X]:((happy(X)<~>~curious(X))=>(~rich(X)&kind(X))))&
(![X]:((~patient(X)&creative(X))<=>(~old(X)&creative(X))))&
((?[X]:((humble(X)&quiet(X))))<=>(?[X]:((~funny(X)|tall(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~funny(X)|~rich(X))))&
(![X]:((~happy(X)<~>kind(X))=>(brave(X)&rich(X))))&
((~tall(alice)&calm(alice)))&
(?[X]:((~wise(X)|~quiet(X))))&
((~humble(susan)<~>~creative(susan)))&
(~old(lucy)) | rich(mary) | [] | null | 0 |
If someone is not kind or not wise then someone is both not humble and brave and vice versa.
Everyone who is not quiet is not calm and vice versa.
Everyone who is not generous is wise or not patient.
If someone is quiet or rich then someone is both calm and not humble and vice versa.
Everyone who is both not calm and not brave is brave and vice versa.
Everyone who is old is rich or generous and vice versa.
If someone is funny then someone is either not tall or curious.
If lucy is not quiet then someone is either strong or tall and vice versa.
If susan is either strong or not wise then someone is calm or tall.
Everyone who is either not quiet or not generous is not funny or not quiet and vice versa.
Everyone who is both quiet and wise is either not old or humble.
If someone is wise or brave then john is calm or strong.
If someone is humble or not tall then john is both kind and not humble.
If paul is either not creative or not brave then lucy is not quiet or not patient.
Everyone who is not old or funny is either not old or humble.
If someone is not humble then someone is not rich and vice versa.
Lucy is strong.
Someone is not rich.
Someone is not patient.
Someone is either not quiet or kind.
Lucy is either funny or not old.
Someone is either brave or rich.
Susan is old.
Fred is old or not brave. | Fred is not quiet. | contradiction | ((?[X]:((~kind(X)|~wise(X))))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:(~quiet(X)<=>~calm(X)))&
(![X]:(~generous(X)=>(wise(X)|~patient(X))))&
((?[X]:((quiet(X)|rich(X))))<=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:((~calm(X)&~brave(X))<=>brave(X)))&
(![X]:(old(X)<=>(rich(X)|generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((~quiet(lucy))<=>(?[X]:((strong(X)<~>tall(X)))))&
(((strong(susan)<~>~wise(susan)))=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~funny(X)|~quiet(X))))&
(![X]:((quiet(X)&wise(X))=>(~old(X)<~>humble(X))))&
((?[X]:((wise(X)|brave(X))))=>((calm(john)|strong(john))))&
((?[X]:((humble(X)|~tall(X))))=>((kind(john)&~humble(john))))&
(((~creative(paul)<~>~brave(paul)))=>((~quiet(lucy)|~patient(lucy))))&
(![X]:((~old(X)|funny(X))=>(~old(X)<~>humble(X))))&
((?[X]:(~humble(X)))<=>(?[X]:(~rich(X))))&
(strong(lucy))&
(?[X]:(~rich(X)))&
(?[X]:(~patient(X)))&
(?[X]:((~quiet(X)<~>kind(X))))&
((funny(lucy)<~>~old(lucy)))&
(?[X]:((brave(X)<~>rich(X))))&
(old(susan))&
((old(fred)|~brave(fred))) | ~quiet(fred) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 6812046043196780685610887
% SZS output start Proof for 6812046043196780685610887
2. ! [X0] : (~quiet(X0) <=> ~calm(X0)) [input p1]
5. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> brave(X0)) [input p4]
25. ~quiet(fred) [input hypothesis]
46. ! [X0] : ((~quiet(X0) | calm(X0)) & (~calm(X0) | quiet(X0))) [nnf transformation 2]
52. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | calm(X0)))) [nnf transformation 5]
53. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | calm(X0))) [flattening 52]
90. ~calm(X0) | quiet(X0) [cnf transformation 46]
97. brave(X0) | brave(X0) | calm(X0) [cnf transformation 53]
99. ~brave(X0) | ~brave(X0) [cnf transformation 53]
141. ~quiet(fred) [cnf transformation 25]
145. brave(X0) | calm(X0) [duplicate literal removal 97]
146. ~brave(X0) [duplicate literal removal 99]
207. calm(X0) [subsumption resolution 145,146]
323. quiet(X0) [resolution 90,207]
327. $false [resolution 323,141]
% SZS output end Proof for 6812046043196780685610887
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is generous.
If someone is strong then someone is both curious and not old and vice versa.
If paul is not tall or creative then susan is not old or not rich and vice versa.
If someone is both not funny and brave then someone is not kind.
Everyone who is not strong is not curious.
If someone is both rich and not humble then someone is both not funny and strong and vice versa.
Everyone who is not humble is tall and vice versa.
If someone is both not old and calm then someone is both strong and not happy.
If someone is not humble or not patient then fred is either not brave or not curious.
If lucy is both not funny and not tall then someone is kind or not tall and vice versa.
If lucy is not creative then fred is tall or not brave and vice versa.
If someone is both not generous and calm then someone is curious and vice versa.
If someone is funny then someone is both calm and not curious and vice versa.
Everyone who is both curious and not curious is not curious or not rich and vice versa.
Everyone who is either curious or not curious is either patient or brave and vice versa.
If someone is both not tall and humble then john is not funny and vice versa.
Lucy is either not patient or rich.
Someone is not brave.
Someone is both not brave and happy.
Someone is generous or creative.
Lucy is both generous and not quiet.
Paul is not funny.
John is creative or not wise.
Mary is either not curious or rich. | Fred is brave. | contradiction | (![X]:(~patient(X)=>generous(X)))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)&~old(X)))))&
(((~tall(paul)|creative(paul)))<=>((~old(susan)|~rich(susan))))&
((?[X]:((~funny(X)&brave(X))))=>(?[X]:(~kind(X))))&
(![X]:(~strong(X)=>~curious(X)))&
((?[X]:((rich(X)&~humble(X))))<=>(?[X]:((~funny(X)&strong(X)))))&
(![X]:(~humble(X)<=>tall(X)))&
((?[X]:((~old(X)&calm(X))))=>(?[X]:((strong(X)&~happy(X)))))&
((?[X]:((~humble(X)|~patient(X))))=>((~brave(fred)<~>~curious(fred))))&
(((~funny(lucy)&~tall(lucy)))<=>(?[X]:((kind(X)|~tall(X)))))&
((~creative(lucy))<=>((tall(fred)|~brave(fred))))&
((?[X]:((~generous(X)&calm(X))))<=>(?[X]:(curious(X))))&
((?[X]:(funny(X)))<=>(?[X]:((calm(X)&~curious(X)))))&
(![X]:((curious(X)&~curious(X))<=>(~curious(X)|~rich(X))))&
(![X]:((curious(X)<~>~curious(X))<=>(patient(X)<~>brave(X))))&
((?[X]:((~tall(X)&humble(X))))<=>(~funny(john)))&
((~patient(lucy)<~>rich(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:((generous(X)|creative(X))))&
((generous(lucy)&~quiet(lucy)))&
(~funny(paul))&
((creative(john)|~wise(john)))&
((~curious(mary)<~>rich(mary))) | brave(fred) | [
"p4",
"p5",
"p8",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8360092063407061118597602
% SZS output start Proof for 8360092063407061118597602
5. ! [X0] : (~strong(X0) => ~curious(X0)) [input p4]
6. ? [X0] : (~humble(X0) & rich(X0)) <=> ? [X0] : (strong(X0) & ~funny(X0)) [input p5]
9. ? [X0] : (~patient(X0) | ~humble(X0)) => (~brave(fred) <~> ~curious(fred)) [input p8]
13. ? [X0] : funny(X0) <=> ? [X0] : (~curious(X0) & calm(X0)) [input p12]
14. ! [X0] : ((~curious(X0) & curious(X0)) <=> (~rich(X0) | ~curious(X0))) [input p13]
25. brave(fred) [input hypothesis]
28. ? [X0] : (~humble(X0) & rich(X0)) <=> ? [X1] : (strong(X1) & ~funny(X1)) [rectify 6]
31. ? [X0] : funny(X0) <=> ? [X1] : (~curious(X1) & calm(X1)) [rectify 13]
36. ! [X0] : (~curious(X0) | strong(X0)) [ennf transformation 5]
38. (~brave(fred) <~> ~curious(fred)) | ! [X0] : (patient(X0) & humble(X0)) [ennf transformation 9]
49. (? [X0] : (~humble(X0) & rich(X0)) | ! [X1] : (~strong(X1) | funny(X1))) & (? [X1] : (strong(X1) & ~funny(X1)) | ! [X0] : (humble(X0) | ~rich(X0))) [nnf transformation 28]
50. (? [X0] : (~humble(X0) & rich(X0)) | ! [X1] : (~strong(X1) | funny(X1))) & (? [X2] : (strong(X2) & ~funny(X2)) | ! [X3] : (humble(X3) | ~rich(X3))) [rectify 49]
51. ? [X0] : (~humble(X0) & rich(X0)) => (~humble(sK3) & rich(sK3)) [choice axiom]
52. ? [X2] : (strong(X2) & ~funny(X2)) => (strong(sK4) & ~funny(sK4)) [choice axiom]
53. ((~humble(sK3) & rich(sK3)) | ! [X1] : (~strong(X1) | funny(X1))) & ((strong(sK4) & ~funny(sK4)) | ! [X3] : (humble(X3) | ~rich(X3))) [skolemisation 50,52,51]
58. ((curious(fred) | brave(fred)) & (~curious(fred) | ~brave(fred))) | ! [X0] : (patient(X0) & humble(X0)) [nnf transformation 38]
71. (? [X0] : funny(X0) | ! [X1] : (curious(X1) | ~calm(X1))) & (? [X1] : (~curious(X1) & calm(X1)) | ! [X0] : ~funny(X0)) [nnf transformation 31]
72. (? [X0] : funny(X0) | ! [X1] : (curious(X1) | ~calm(X1))) & (? [X2] : (~curious(X2) & calm(X2)) | ! [X3] : ~funny(X3)) [rectify 71]
73. ? [X0] : funny(X0) => funny(sK9) [choice axiom]
74. ? [X2] : (~curious(X2) & calm(X2)) => (~curious(sK10) & calm(sK10)) [choice axiom]
75. (funny(sK9) | ! [X1] : (curious(X1) | ~calm(X1))) & ((~curious(sK10) & calm(sK10)) | ! [X3] : ~funny(X3)) [skolemisation 72,74,73]
76. ! [X0] : (((~curious(X0) & curious(X0)) | (rich(X0) & curious(X0))) & ((~rich(X0) | ~curious(X0)) | (curious(X0) | ~curious(X0)))) [nnf transformation 14]
77. ! [X0] : (((~curious(X0) & curious(X0)) | (rich(X0) & curious(X0))) & (~rich(X0) | ~curious(X0) | curious(X0) | ~curious(X0))) [flattening 76]
100. ~curious(X0) | strong(X0) [cnf transformation 36]
104. ~humble(sK3) | ~strong(X1) | funny(X1) [cnf transformation 53]
109. ~curious(fred) | ~brave(fred) | humble(X0) [cnf transformation 58]
125. ~curious(sK10) | ~funny(X3) [cnf transformation 75]
128. curious(X0) | curious(X0) [cnf transformation 77]
153. brave(fred) [cnf transformation 25]
159. curious(X0) [duplicate literal removal 128]
169. 3 <=> ! [X3] : ~strong(X3) [avatar definition]
170. ~strong(X3) <- (3) [avatar component clause 169]
210. 12 <=> ! [X1] : (~strong(X1) | funny(X1)) [avatar definition]
211. ~strong(X1) | funny(X1) <- (12) [avatar component clause 210]
213. 13 <=> humble(sK3) [avatar definition]
215. ~humble(sK3) <- (~13) [avatar component clause 213]
216. 12 | ~13 [avatar split clause 104,213,210]
252. 22 <=> brave(fred) [avatar definition]
256. 23 <=> curious(fred) [avatar definition]
257. ~curious(fred) <- (~23) [avatar component clause 256]
261. 24 <=> ! [X0] : humble(X0) [avatar definition]
262. humble(X0) <- (24) [avatar component clause 261]
265. 24 | ~22 | ~23 [avatar split clause 109,256,252,261]
334. 40 <=> ! [X3] : ~funny(X3) [avatar definition]
335. ~funny(X3) <- (40) [avatar component clause 334]
337. 41 <=> curious(sK10) [avatar definition]
339. ~curious(sK10) <- (~41) [avatar component clause 337]
340. 40 | ~41 [avatar split clause 125,337,334]
375. 22 [avatar split clause 153,252]
378. $false <- (~23) [subsumption resolution 257,159]
379. 23 [avatar contradiction clause 378]
382. ~strong(X1) <- (12, 40) [subsumption resolution 211,335]
383. 3 | ~12 | ~40 [avatar split clause 382,334,210,169]
390. $false <- (~13, 24) [subsumption resolution 215,262]
391. 13 | ~24 [avatar contradiction clause 390]
392. $false <- (~41) [subsumption resolution 339,159]
393. 41 [avatar contradiction clause 392]
412. strong(X0) [resolution 100,159]
413. $false <- (3) [subsumption resolution 412,170]
414. ~3 [avatar contradiction clause 413]
415. $false [avatar sat refutation 216,265,340,375,379,383,391,393,414]
% SZS output end Proof for 8360092063407061118597602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not rich is funny or not curious. If fred is brave or not brave then john is both funny and old. Everyone who is wise or not generous is either not curious or not quiet and vice versa. Everyone who is not old is kind. Everyone who is not calm is not wise or quiet and vice versa. Everyone who is not kind is both wise and not rich and vice versa. Everyone who is either calm or curious is both not strong and not patient and vice versa. If susan is kind then someone is brave and vice versa. Everyone who is rich or kind is either not generous or wise and vice versa. If someone is both not brave and generous then someone is humble. Everyone who is either quiet or not generous is not brave or not patient and vice versa. If someone is both not tall and not rich then someone is curious. If someone is not happy or quiet then someone is both not generous and not happy and vice versa. Everyone who is calm or quiet is either not old or happy and vice versa. Everyone who is either funny or calm is both curious and not generous and vice versa. Everyone who is not humble or not kind is either old or not quiet and vice versa. Someone is both happy and creative. Someone is calm or not rich. Alice is quiet. Paul is not funny. John is rich. Someone is patient. Someone is not brave or happy. Alice is both old and not patient. | Paul is curious. | contradiction | (![X]:((creative(X)&~rich(X))=>(funny(X)|~curious(X))))&
(((brave(fred)|~brave(fred)))=>((funny(john)&old(john))))&
(![X]:((wise(X)|~generous(X))<=>(~curious(X)<~>~quiet(X))))&
(![X]:(~old(X)=>kind(X)))&
(![X]:(~calm(X)<=>(~wise(X)|quiet(X))))&
(![X]:(~kind(X)<=>(wise(X)&~rich(X))))&
(![X]:((calm(X)<~>curious(X))<=>(~strong(X)&~patient(X))))&
((kind(susan))<=>(?[X]:(brave(X))))&
(![X]:((rich(X)|kind(X))<=>(~generous(X)<~>wise(X))))&
((?[X]:((~brave(X)&generous(X))))=>(?[X]:(humble(X))))&
(![X]:((quiet(X)<~>~generous(X))<=>(~brave(X)|~patient(X))))&
((?[X]:((~tall(X)&~rich(X))))=>(?[X]:(curious(X))))&
((?[X]:((~happy(X)|quiet(X))))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~old(X)<~>happy(X))))&
(![X]:((funny(X)<~>calm(X))<=>(curious(X)&~generous(X))))&
(![X]:((~humble(X)|~kind(X))<=>(old(X)<~>~quiet(X))))&
(?[X]:((happy(X)&creative(X))))&
(?[X]:((calm(X)|~rich(X))))&
(quiet(alice))&
(~funny(paul))&
(rich(john))&
(?[X]:(patient(X)))&
(?[X]:((~brave(X)|happy(X))))&
((old(alice)&~patient(alice))) | curious(paul) | [
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p14",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5098448377813150259158767
% SZS output start Proof for 5098448377813150259158767
3. ! [X0] : ((~generous(X0) | wise(X0)) <=> (~curious(X0) <~> ~quiet(X0))) [input p2]
4. ! [X0] : (~old(X0) => kind(X0)) [input p3]
5. ! [X0] : (~calm(X0) <=> (quiet(X0) | ~wise(X0))) [input p4]
6. ! [X0] : (~kind(X0) <=> (~rich(X0) & wise(X0))) [input p5]
7. ! [X0] : ((calm(X0) <~> curious(X0)) <=> (~patient(X0) & ~strong(X0))) [input p6]
9. ! [X0] : ((kind(X0) | rich(X0)) <=> (~generous(X0) <~> wise(X0))) [input p8]
11. ! [X0] : ((quiet(X0) <~> ~generous(X0)) <=> (~patient(X0) | ~brave(X0))) [input p10]
15. ! [X0] : ((funny(X0) <~> calm(X0)) <=> (~generous(X0) & curious(X0))) [input p14]
16. ! [X0] : ((~kind(X0) | ~humble(X0)) <=> (old(X0) <~> ~quiet(X0))) [input p15]
20. ~funny(paul) [input p19]
25. curious(paul) [input hypothesis]
33. ! [X0] : (kind(X0) | old(X0)) [ennf transformation 4]
35. ! [X0] : (((~generous(X0) | wise(X0)) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (generous(X0) & ~wise(X0)))) [nnf transformation 3]
36. ! [X0] : ((~generous(X0) | wise(X0) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) & (((quiet(X0) | curious(X0)) & (~quiet(X0) | ~curious(X0))) | (generous(X0) & ~wise(X0)))) [flattening 35]
37. ! [X0] : ((~calm(X0) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | calm(X0))) [nnf transformation 5]
38. ! [X0] : ((~calm(X0) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | calm(X0))) [flattening 37]
39. ! [X0] : ((~kind(X0) | (rich(X0) | ~wise(X0))) & ((~rich(X0) & wise(X0)) | kind(X0))) [nnf transformation 6]
40. ! [X0] : ((~kind(X0) | rich(X0) | ~wise(X0)) & ((~rich(X0) & wise(X0)) | kind(X0))) [flattening 39]
41. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 7]
42. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [flattening 41]
47. ! [X0] : (((kind(X0) | rich(X0)) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (~kind(X0) & ~rich(X0)))) [nnf transformation 9]
48. ! [X0] : ((kind(X0) | rich(X0) | ((~generous(X0) | ~wise(X0)) & (wise(X0) | generous(X0)))) & (((~wise(X0) | generous(X0)) & (wise(X0) | ~generous(X0))) | (~kind(X0) & ~rich(X0)))) [flattening 47]
52. ! [X0] : ((((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | (patient(X0) & brave(X0))) & ((~patient(X0) | ~brave(X0)) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0))))) [nnf transformation 11]
53. ! [X0] : ((((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | (patient(X0) & brave(X0))) & (~patient(X0) | ~brave(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0))))) [flattening 52]
61. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~calm(X0) | ~funny(X0)) & (calm(X0) | funny(X0))) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | ((funny(X0) | ~calm(X0)) & (calm(X0) | ~funny(X0))))) [flattening 61]
63. ! [X0] : (((~kind(X0) | ~humble(X0)) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (kind(X0) & humble(X0)))) [nnf transformation 16]
64. ! [X0] : ((~kind(X0) | ~humble(X0) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) & (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (kind(X0) & humble(X0)))) [flattening 63]
78. ~quiet(X0) | ~curious(X0) | ~wise(X0) [cnf transformation 36]
84. kind(X0) | old(X0) [cnf transformation 33]
86. ~calm(X0) | wise(X0) [cnf transformation 38]
87. ~calm(X0) | ~quiet(X0) [cnf transformation 38]
88. kind(X0) | wise(X0) [cnf transformation 40]
89. ~rich(X0) | kind(X0) [cnf transformation 40]
94. ~patient(X0) | calm(X0) | ~curious(X0) [cnf transformation 42]
100. wise(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 48]
102. ~kind(X0) | generous(X0) | ~wise(X0) [cnf transformation 48]
104. kind(X0) | rich(X0) | ~generous(X0) | ~wise(X0) [cnf transformation 48]
109. ~generous(X0) | quiet(X0) | patient(X0) [cnf transformation 53]
126. ~calm(X0) | funny(X0) | ~generous(X0) [cnf transformation 62]
127. ~curious(X0) | funny(X0) | generous(X0) | calm(X0) [cnf transformation 62]
132. quiet(X0) | ~old(X0) | kind(X0) [cnf transformation 64]
139. ~funny(paul) [cnf transformation 20]
145. curious(paul) [cnf transformation 25]
175. kind(X0) | ~generous(X0) | ~wise(X0) [subsumption resolution 104,89]
176. ~generous(X0) | kind(X0) [subsumption resolution 175,88]
177. ~generous(X0) | wise(X0) [subsumption resolution 100,176]
217. kind(X0) | quiet(X0) [subsumption resolution 132,84]
291. ~wise(X0) | generous(X0) | quiet(X0) [resolution 102,217]
669. funny(paul) | generous(paul) | calm(paul) [resolution 127,145]
672. generous(paul) | calm(paul) [subsumption resolution 669,139]
674. 75 <=> calm(paul) [avatar definition]
675. ~calm(paul) <- (~75) [avatar component clause 674]
676. calm(paul) <- (75) [avatar component clause 674]
678. 76 <=> generous(paul) [avatar definition]
679. ~generous(paul) <- (~76) [avatar component clause 678]
680. generous(paul) <- (76) [avatar component clause 678]
681. 75 | 76 [avatar split clause 672,678,674]
755. wise(paul) <- (75) [resolution 676,86]
756. ~quiet(paul) <- (75) [resolution 676,87]
760. funny(paul) | ~generous(paul) <- (75) [resolution 676,126]
768. 87 <=> patient(paul) [avatar definition]
770. patient(paul) <- (87) [avatar component clause 768]
781. ~generous(paul) <- (75) [subsumption resolution 760,139]
782. ~76 | ~75 [avatar split clause 781,674,678]
990. generous(paul) | quiet(paul) <- (75) [resolution 755,291]
998. quiet(paul) <- (75, ~76) [subsumption resolution 990,679]
999. $false <- (75, ~76) [subsumption resolution 998,756]
1000. ~75 | 76 [avatar contradiction clause 999]
1006. quiet(paul) | patient(paul) <- (76) [resolution 680,109]
1008. wise(paul) <- (76) [resolution 680,177]
1012. 96 <=> quiet(paul) [avatar definition]
1014. quiet(paul) <- (96) [avatar component clause 1012]
1016. 97 <=> wise(paul) [avatar definition]
1018. wise(paul) <- (97) [avatar component clause 1016]
1020. 87 | 96 | ~76 [avatar split clause 1006,678,1012,768]
1026. 97 | ~76 [avatar split clause 1008,678,1016]
1034. calm(paul) | ~curious(paul) <- (87) [resolution 770,94]
1039. ~curious(paul) <- (~75, 87) [subsumption resolution 1034,675]
1040. $false <- (~75, 87) [subsumption resolution 1039,145]
1041. 75 | ~87 [avatar contradiction clause 1040]
1051. ~curious(paul) | ~wise(paul) <- (96) [resolution 1014,78]
1059. ~wise(paul) <- (96) [subsumption resolution 1051,145]
1060. $false <- (96, 97) [subsumption resolution 1059,1018]
1061. ~96 | ~97 [avatar contradiction clause 1060]
1063. $false [avatar sat refutation 681,782,1000,1020,1026,1041,1061]
% SZS output end Proof for 5098448377813150259158767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both brave and quiet then mary is not patient and vice versa.
If someone is not old then someone is strong and vice versa.
Everyone who is not funny or not wise is happy and vice versa.
Everyone who is not creative or old is either humble or not brave.
Everyone who is either not brave or not creative is either not humble or not wise.
If someone is not kind or creative then someone is both not rich and not patient.
Everyone who is either funny or happy is quiet or not strong.
Everyone who is either creative or not humble is not tall or not rich and vice versa.
Everyone who is not kind is humble.
If someone is creative or humble then mary is quiet.
If mary is not wise then mary is either not humble or old and vice versa.
If fred is both not happy and not kind then someone is either not wise or not humble and vice versa.
Everyone who is both not tall and kind is either not strong or patient and vice versa.
Everyone who is brave is either not rich or not kind.
If someone is both not rich and wise then mary is kind and vice versa.
If someone is not happy or tall then someone is both not rich and not happy.
Fred is not curious or not quiet.
Someone is both old and quiet.
Someone is either patient or not quiet.
Someone is not old or not wise.
Someone is not strong or not wise.
John is both humble and curious.
Mary is rich.
Someone is both funny and not creative. | Fred is happy. | neutral | (((brave(alice)&quiet(alice)))<=>(~patient(mary)))&
((?[X]:(~old(X)))<=>(?[X]:(strong(X))))&
(![X]:((~funny(X)|~wise(X))<=>happy(X)))&
(![X]:((~creative(X)|old(X))=>(humble(X)<~>~brave(X))))&
(![X]:((~brave(X)<~>~creative(X))=>(~humble(X)<~>~wise(X))))&
((?[X]:((~kind(X)|creative(X))))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:((funny(X)<~>happy(X))=>(quiet(X)|~strong(X))))&
(![X]:((creative(X)<~>~humble(X))<=>(~tall(X)|~rich(X))))&
(![X]:(~kind(X)=>humble(X)))&
((?[X]:((creative(X)|humble(X))))=>(quiet(mary)))&
((~wise(mary))<=>((~humble(mary)<~>old(mary))))&
(((~happy(fred)&~kind(fred)))<=>(?[X]:((~wise(X)<~>~humble(X)))))&
(![X]:((~tall(X)&kind(X))<=>(~strong(X)<~>patient(X))))&
(![X]:(brave(X)=>(~rich(X)<~>~kind(X))))&
((?[X]:((~rich(X)&wise(X))))<=>(kind(mary)))&
((?[X]:((~happy(X)|tall(X))))=>(?[X]:((~rich(X)&~happy(X)))))&
((~curious(fred)|~quiet(fred)))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((patient(X)<~>~quiet(X))))&
(?[X]:((~old(X)|~wise(X))))&
(?[X]:((~strong(X)|~wise(X))))&
((humble(john)&curious(john)))&
(rich(mary))&
(?[X]:((funny(X)&~creative(X)))) | happy(fred) | [] | null | 0 |
Everyone who is both not quiet and curious is either tall or quiet and vice versa.
Everyone who is not curious is not rich or wise.
Everyone who is funny or tall is tall and vice versa.
Everyone who is not old or not funny is both not humble and not quiet.
If lucy is humble then alice is either not generous or tall and vice versa.
If someone is both not calm and funny then someone is not funny or brave and vice versa.
If mary is tall or not humble then someone is either wise or funny.
If someone is both wise and funny then alice is old and vice versa.
If fred is either not curious or brave then someone is both patient and not old.
If john is either not strong or strong then lucy is either generous or rich.
Everyone who is not patient or not rich is tall or not tall.
If someone is not old then someone is both strong and not patient and vice versa.
Everyone who is either not happy or calm is rich and vice versa.
Everyone who is both funny and not generous is both patient and not calm.
If john is humble or not old then lucy is not funny.
Everyone who is either not funny or not tall is either not calm or patient.
John is either patient or rich.
Fred is rich.
Mary is calm.
Someone is either not brave or humble.
Someone is either funny or tall.
Susan is either not curious or strong.
Alice is both rich and brave.
Someone is wise. | Mary is not humble. | neutral | (![X]:((~quiet(X)&curious(X))<=>(tall(X)<~>quiet(X))))&
(![X]:(~curious(X)=>(~rich(X)|wise(X))))&
(![X]:((funny(X)|tall(X))<=>tall(X)))&
(![X]:((~old(X)|~funny(X))=>(~humble(X)&~quiet(X))))&
((humble(lucy))<=>((~generous(alice)<~>tall(alice))))&
((?[X]:((~calm(X)&funny(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(((tall(mary)|~humble(mary)))=>(?[X]:((wise(X)<~>funny(X)))))&
((?[X]:((wise(X)&funny(X))))<=>(old(alice)))&
(((~curious(fred)<~>brave(fred)))=>(?[X]:((patient(X)&~old(X)))))&
(((~strong(john)<~>strong(john)))=>((generous(lucy)<~>rich(lucy))))&
(![X]:((~patient(X)|~rich(X))=>(tall(X)|~tall(X))))&
((?[X]:(~old(X)))<=>(?[X]:((strong(X)&~patient(X)))))&
(![X]:((~happy(X)<~>calm(X))<=>rich(X)))&
(![X]:((funny(X)&~generous(X))=>(patient(X)&~calm(X))))&
(((humble(john)|~old(john)))=>(~funny(lucy)))&
(![X]:((~funny(X)<~>~tall(X))=>(~calm(X)<~>patient(X))))&
((patient(john)<~>rich(john)))&
(rich(fred))&
(calm(mary))&
(?[X]:((~brave(X)<~>humble(X))))&
(?[X]:((funny(X)<~>tall(X))))&
((~curious(susan)<~>strong(susan)))&
((rich(alice)&brave(alice)))&
(?[X]:(wise(X))) | ~humble(mary) | [] | null | 0 |
If susan is not rich then someone is either not strong or quiet.
If fred is not wise or calm then lucy is happy or wise and vice versa.
Everyone who is rich or humble is both curious and tall and vice versa.
Everyone who is both kind and patient is both not happy and funny and vice versa.
Everyone who is not brave or old is both brave and not strong and vice versa.
If john is both not creative and not tall then someone is either strong or quiet.
Everyone who is not humble is kind or curious.
Everyone who is patient or rich is not generous and vice versa.
Everyone who is not calm is both not happy and not old and vice versa.
If someone is both not strong and not creative then mary is either not curious or not quiet and vice versa.
Everyone who is either tall or old is not kind.
Everyone who is happy or not funny is either rich or quiet and vice versa.
Everyone who is humble is wise and vice versa.
If someone is curious or strong then someone is either humble or not humble and vice versa.
Everyone who is both strong and not generous is either tall or not patient.
If susan is both old and creative then lucy is both strong and not creative and vice versa.
Fred is not happy or kind.
Mary is not curious.
Lucy is either not brave or kind.
Mary is not patient.
John is wise or strong.
Someone is tall or not rich.
Someone is either not patient or generous.
Alice is either strong or not funny. | John is not creative. | neutral | ((~rich(susan))=>(?[X]:((~strong(X)<~>quiet(X)))))&
(((~wise(fred)|calm(fred)))<=>((happy(lucy)|wise(lucy))))&
(![X]:((rich(X)|humble(X))<=>(curious(X)&tall(X))))&
(![X]:((kind(X)&patient(X))<=>(~happy(X)&funny(X))))&
(![X]:((~brave(X)|old(X))<=>(brave(X)&~strong(X))))&
(((~creative(john)&~tall(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~humble(X)=>(kind(X)|curious(X))))&
(![X]:((patient(X)|rich(X))<=>~generous(X)))&
(![X]:(~calm(X)<=>(~happy(X)&~old(X))))&
((?[X]:((~strong(X)&~creative(X))))<=>((~curious(mary)<~>~quiet(mary))))&
(![X]:((tall(X)<~>old(X))=>~kind(X)))&
(![X]:((happy(X)|~funny(X))<=>(rich(X)<~>quiet(X))))&
(![X]:(humble(X)<=>wise(X)))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((strong(X)&~generous(X))=>(tall(X)<~>~patient(X))))&
(((old(susan)&creative(susan)))<=>((strong(lucy)&~creative(lucy))))&
((~happy(fred)|kind(fred)))&
(~curious(mary))&
((~brave(lucy)<~>kind(lucy)))&
(~patient(mary))&
((wise(john)|strong(john)))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((strong(alice)<~>~funny(alice))) | ~creative(john) | [] | null | 0 |
If someone is not humble or not quiet then john is humble or not curious and vice versa.
Everyone who is either old or not quiet is either not quiet or not creative.
Everyone who is not quiet or not creative is both strong and not wise and vice versa.
Everyone who is both not brave and kind is either not funny or not creative.
If mary is strong then someone is both not tall and not curious.
Everyone who is either not patient or calm is generous or not funny.
If someone is either quiet or not calm then someone is kind or rich.
Everyone who is not funny or not wise is both old and kind.
Everyone who is both strong and tall is not happy and vice versa.
If alice is both funny and not calm then lucy is both not humble and wise.
If someone is either brave or calm then susan is both not quiet and not wise.
If someone is either quiet or not generous then someone is not tall or quiet.
If someone is not creative then someone is both not funny and brave and vice versa.
Everyone who is not funny is both tall and not calm.
If mary is not generous then susan is not curious.
Everyone who is rich or generous is quiet.
Someone is funny.
Someone is curious or quiet.
Someone is kind.
Someone is both not strong and patient.
Susan is kind or not calm.
Mary is both quiet and not funny.
Susan is calm or not humble.
John is both happy and not quiet. | Susan is generous. | contradiction | ((?[X]:((~humble(X)|~quiet(X))))<=>((humble(john)|~curious(john))))&
(![X]:((old(X)<~>~quiet(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~creative(X))<=>(strong(X)&~wise(X))))&
(![X]:((~brave(X)&kind(X))=>(~funny(X)<~>~creative(X))))&
((strong(mary))=>(?[X]:((~tall(X)&~curious(X)))))&
(![X]:((~patient(X)<~>calm(X))=>(generous(X)|~funny(X))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~funny(X)|~wise(X))=>(old(X)&kind(X))))&
(![X]:((strong(X)&tall(X))<=>~happy(X)))&
(((funny(alice)&~calm(alice)))=>((~humble(lucy)&wise(lucy))))&
((?[X]:((brave(X)<~>calm(X))))=>((~quiet(susan)&~wise(susan))))&
((?[X]:((quiet(X)<~>~generous(X))))=>(?[X]:((~tall(X)|quiet(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((~funny(X)&brave(X)))))&
(![X]:(~funny(X)=>(tall(X)&~calm(X))))&
((~generous(mary))=>(~curious(susan)))&
(![X]:((rich(X)|generous(X))=>quiet(X)))&
(?[X]:(funny(X)))&
(?[X]:((curious(X)|quiet(X))))&
(?[X]:(kind(X)))&
(?[X]:((~strong(X)&patient(X))))&
((kind(susan)|~calm(susan)))&
((quiet(mary)&~funny(mary)))&
((calm(susan)|~humble(susan)))&
((happy(john)&~quiet(john))) | generous(susan) | [
"p1",
"p7",
"p10",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4146846372809303748982696
% SZS output start Proof for 4146846372809303748982696
2. ! [X0] : ((old(X0) <~> ~quiet(X0)) => (~quiet(X0) <~> ~creative(X0))) [input p1]
8. ! [X0] : ((~wise(X0) | ~funny(X0)) => (kind(X0) & old(X0))) [input p7]
11. ? [X0] : (brave(X0) <~> calm(X0)) => (~wise(susan) & ~quiet(susan)) [input p10]
13. ? [X0] : ~creative(X0) <=> ? [X0] : (brave(X0) & ~funny(X0)) [input p12]
14. ! [X0] : (~funny(X0) => (~calm(X0) & tall(X0))) [input p13]
16. ! [X0] : ((generous(X0) | rich(X0)) => quiet(X0)) [input p15]
22. ~funny(mary) & quiet(mary) [input p21]
25. generous(susan) [input hypothesis]
28. ? [X0] : ~creative(X0) <=> ? [X1] : (brave(X1) & ~funny(X1)) [rectify 13]
30. ! [X0] : ((~quiet(X0) <~> ~creative(X0)) | (old(X0) <=> ~quiet(X0))) [ennf transformation 2]
37. ! [X0] : ((kind(X0) & old(X0)) | (wise(X0) & funny(X0))) [ennf transformation 8]
42. (~wise(susan) & ~quiet(susan)) | ! [X0] : (brave(X0) <=> calm(X0)) [ennf transformation 11]
44. ! [X0] : ((~calm(X0) & tall(X0)) | funny(X0)) [ennf transformation 14]
46. ! [X0] : (quiet(X0) | (~generous(X0) & ~rich(X0))) [ennf transformation 16]
52. ! [X0] : (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ((old(X0) | quiet(X0)) & (~quiet(X0) | ~old(X0)))) [nnf transformation 30]
63. (~wise(susan) & ~quiet(susan)) | ! [X0] : ((brave(X0) | ~calm(X0)) & (calm(X0) | ~brave(X0))) [nnf transformation 42]
68. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X1] : (brave(X1) & ~funny(X1)) | ! [X0] : creative(X0)) [nnf transformation 28]
69. (? [X0] : ~creative(X0) | ! [X1] : (~brave(X1) | funny(X1))) & (? [X2] : (brave(X2) & ~funny(X2)) | ! [X3] : creative(X3)) [rectify 68]
70. ? [X0] : ~creative(X0) => ~creative(sK4) [choice axiom]
71. ? [X2] : (brave(X2) & ~funny(X2)) => (brave(sK5) & ~funny(sK5)) [choice axiom]
72. (~creative(sK4) | ! [X1] : (~brave(X1) | funny(X1))) & ((brave(sK5) & ~funny(sK5)) | ! [X3] : creative(X3)) [skolemisation 69,71,70]
85. ~creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 52]
102. funny(X0) | old(X0) [cnf transformation 37]
109. ~quiet(susan) | calm(X0) | ~brave(X0) [cnf transformation 63]
115. ~funny(sK5) | creative(X3) [cnf transformation 72]
116. brave(sK5) | creative(X3) [cnf transformation 72]
119. ~calm(X0) | funny(X0) [cnf transformation 44]
122. ~generous(X0) | quiet(X0) [cnf transformation 46]
129. quiet(mary) [cnf transformation 22]
130. ~funny(mary) [cnf transformation 22]
134. generous(susan) [cnf transformation 25]
135. ~creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 85]
220. 20 <=> ! [X0] : (calm(X0) | ~brave(X0)) [avatar definition]
221. ~brave(X0) | calm(X0) <- (20) [avatar component clause 220]
224. 21 <=> quiet(susan) [avatar definition]
228. 20 | ~21 [avatar split clause 109,224,220]
254. 28 <=> ! [X3] : creative(X3) [avatar definition]
255. creative(X3) <- (28) [avatar component clause 254]
257. 29 <=> brave(sK5) [avatar definition]
259. brave(sK5) <- (29) [avatar component clause 257]
260. 28 | 29 [avatar split clause 116,257,254]
262. 30 <=> funny(sK5) [avatar definition]
264. ~funny(sK5) <- (~30) [avatar component clause 262]
265. 28 | ~30 [avatar split clause 115,262,254]
304. old(mary) [resolution 102,130]
312. quiet(susan) [resolution 122,134]
315. 21 [avatar split clause 312,224]
330. ~old(X0) | ~quiet(X0) <- (28) [resolution 135,255]
427. ~quiet(mary) <- (28) [resolution 330,304]
430. $false <- (28) [subsumption resolution 427,129]
431. ~28 [avatar contradiction clause 430]
514. calm(sK5) <- (20, 29) [resolution 259,221]
552. funny(sK5) <- (20, 29) [resolution 514,119]
553. $false <- (20, 29, ~30) [subsumption resolution 552,264]
554. ~20 | ~29 | 30 [avatar contradiction clause 553]
555. $false [avatar sat refutation 228,260,265,315,431,554]
% SZS output end Proof for 4146846372809303748982696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both quiet and funny then alice is not funny. Everyone who is either not brave or happy is either not kind or old. Everyone who is either not funny or patient is both not old and not humble. Everyone who is both not old and not patient is not wise or not calm and vice versa. Everyone who is both happy and not calm is both wise and not humble and vice versa. If someone is either not wise or not rich then fred is funny. If someone is not generous or patient then paul is not strong. Everyone who is rich is not generous or generous and vice versa. Everyone who is both not kind and not generous is either brave or funny and vice versa. Everyone who is not rich is both not happy and generous. If someone is either not generous or quiet then someone is not tall. Everyone who is both not strong and patient is either humble or kind and vice versa. Everyone who is patient or not creative is both not wise and humble and vice versa. Everyone who is either not brave or happy is either rich or not happy and vice versa. If john is either brave or wise then someone is both not wise and not humble. Everyone who is not happy or humble is calm and vice versa. John is either rich or not funny. Lucy is not creative. Someone is not funny or not curious. John is rich or patient. Someone is not curious or not old. Lucy is either curious or not quiet. | Paul is happy. | neutral | (((quiet(fred)&funny(fred)))=>(~funny(alice)))&
(![X]:((~brave(X)<~>happy(X))=>(~kind(X)<~>old(X))))&
(![X]:((~funny(X)<~>patient(X))=>(~old(X)&~humble(X))))&
(![X]:((~old(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
(![X]:((happy(X)&~calm(X))<=>(wise(X)&~humble(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>(funny(fred)))&
((?[X]:((~generous(X)|patient(X))))=>(~strong(paul)))&
(![X]:(rich(X)<=>(~generous(X)|generous(X))))&
(![X]:((~kind(X)&~generous(X))<=>(brave(X)<~>funny(X))))&
(![X]:(~rich(X)=>(~happy(X)&generous(X))))&
((?[X]:((~generous(X)<~>quiet(X))))=>(?[X]:(~tall(X))))&
(![X]:((~strong(X)&patient(X))<=>(humble(X)<~>kind(X))))&
(![X]:((patient(X)|~creative(X))<=>(~wise(X)&humble(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(rich(X)<~>~happy(X))))&
(((brave(john)<~>wise(john)))=>(?[X]:((~wise(X)&~humble(X)))))&
(![X]:((~happy(X)|humble(X))<=>calm(X)))&
((rich(john)<~>~funny(john)))&
(~creative(lucy))&
(?[X]:((~funny(X)|~curious(X))))&
((rich(john)|patient(john)))&
(?[X]:((~curious(X)|~old(X))))&
((curious(lucy)<~>~quiet(lucy))) | happy(paul) | [] | null | 0 |
If susan is happy or not strong then someone is either not tall or not old and vice versa. Everyone who is creative is either not old or wise and vice versa. Everyone who is rich or humble is not quiet or rich and vice versa. If mary is generous then alice is brave and vice versa. Everyone who is brave or rich is either not tall or not curious and vice versa. Everyone who is either humble or not tall is funny and vice versa. Everyone who is funny or not funny is brave and vice versa. Everyone who is both creative and not calm is not brave or not strong. If lucy is both brave and humble then lucy is strong or patient. Everyone who is brave or not funny is both strong and not funny. If susan is both not old and curious then someone is kind or not wise and vice versa. Everyone who is tall or strong is curious or not rich and vice versa. Everyone who is not humble or rich is either wise or not creative. If fred is not kind or creative then someone is not curious or curious and vice versa. If mary is curious then john is either not generous or not humble and vice versa. John is not rich or tall. Someone is either kind or not happy. Someone is both humble and not patient. Someone is tall or curious. Someone is both not old and not wise. | John is not creative. | neutral | (((happy(susan)|~strong(susan)))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:(creative(X)<=>(~old(X)<~>wise(X))))&
(![X]:((rich(X)|humble(X))<=>(~quiet(X)|rich(X))))&
((generous(mary))<=>(brave(alice)))&
(![X]:((brave(X)|rich(X))<=>(~tall(X)<~>~curious(X))))&
(![X]:((humble(X)<~>~tall(X))<=>funny(X)))&
(![X]:((funny(X)|~funny(X))<=>brave(X)))&
(![X]:((creative(X)&~calm(X))=>(~brave(X)|~strong(X))))&
(((brave(lucy)&humble(lucy)))=>((strong(lucy)|patient(lucy))))&
(![X]:((brave(X)|~funny(X))=>(strong(X)&~funny(X))))&
(((~old(susan)&curious(susan)))<=>(?[X]:((kind(X)|~wise(X)))))&
(![X]:((tall(X)|strong(X))<=>(curious(X)|~rich(X))))&
(![X]:((~humble(X)|rich(X))=>(wise(X)<~>~creative(X))))&
(((~kind(fred)|creative(fred)))<=>(?[X]:((~curious(X)|curious(X)))))&
((curious(mary))<=>((~generous(john)<~>~humble(john))))&
((~rich(john)|tall(john)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((humble(X)&~patient(X))))&
(?[X]:((tall(X)|curious(X))))&
(?[X]:((~old(X)&~wise(X)))) | ~creative(john) | [] | null | 0 |
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