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
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is both not quiet and not creative then alice is funny or old. Everyone who is either not strong or humble is not quiet and vice versa. Everyone who is either rich or not kind is both generous and funny and vice versa. Everyone who is quiet is not generous and vice versa. If someone is kind or tall then someone is either rich or humble and vice versa. If someone is either strong or rich then someone is both rich and calm and vice versa. If someone is either not humble or not strong then fred is not humble or rich and vice versa. Everyone who is not old or old is either tall or happy and vice versa. If susan is either curious or not curious then susan is either kind or not brave and vice versa. If susan is both not calm and not funny then john is not curious. If susan is either brave or not calm then lucy is both rich and quiet and vice versa. If someone is either creative or not wise then someone is happy. Everyone who is either not rich or creative is patient. Everyone who is both not wise and not generous is quiet or creative and vice versa. If someone is not rich or generous then fred is either calm or wise. Mary is not patient. Someone is both not calm and happy. Paul is both funny and not quiet. Someone is happy or not rich. Mary is not brave or not strong. Susan is not generous. Someone is both generous and not kind. | Paul is creative. | contradiction | ((?[X]:((~quiet(X)&~creative(X))))=>((funny(alice)|old(alice))))&
(![X]:((~strong(X)<~>humble(X))<=>~quiet(X)))&
(![X]:((rich(X)<~>~kind(X))<=>(generous(X)&funny(X))))&
(![X]:(quiet(X)<=>~generous(X)))&
((?[X]:((kind(X)|tall(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((?[X]:((strong(X)<~>rich(X))))<=>(?[X]:((rich(X)&calm(X)))))&
((?[X]:((~humble(X)<~>~strong(X))))<=>((~humble(fred)|rich(fred))))&
(![X]:((~old(X)|old(X))<=>(tall(X)<~>happy(X))))&
(((curious(susan)<~>~curious(susan)))<=>((kind(susan)<~>~brave(susan))))&
(((~calm(susan)&~funny(susan)))=>(~curious(john)))&
(((brave(susan)<~>~calm(susan)))<=>((rich(lucy)&quiet(lucy))))&
((?[X]:((creative(X)<~>~wise(X))))=>(?[X]:(happy(X))))&
(![X]:((~rich(X)<~>creative(X))=>patient(X)))&
(![X]:((~wise(X)&~generous(X))<=>(quiet(X)|creative(X))))&
((?[X]:((~rich(X)|generous(X))))=>((calm(fred)<~>wise(fred))))&
(~patient(mary))&
(?[X]:((~calm(X)&happy(X))))&
((funny(paul)&~quiet(paul)))&
(?[X]:((happy(X)|~rich(X))))&
((~brave(mary)|~strong(mary)))&
(~generous(susan))&
(?[X]:((generous(X)&~kind(X)))) | creative(paul) | [
"p3",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7368578420762193529412137
% SZS output start Proof for 7368578420762193529412137
4. ! [X0] : (quiet(X0) <=> ~generous(X0)) [input p3]
14. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> (creative(X0) | quiet(X0))) [input p13]
18. ~quiet(paul) & funny(paul) [input p17]
23. creative(paul) [input hypothesis]
37. ! [X0] : ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0))) [nnf transformation 4]
63. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~creative(X0) & ~quiet(X0))) & ((creative(X0) | quiet(X0)) | (generous(X0) | wise(X0)))) [nnf transformation 14]
64. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~creative(X0) & ~quiet(X0))) & (creative(X0) | quiet(X0) | generous(X0) | wise(X0))) [flattening 63]
84. generous(X0) | quiet(X0) [cnf transformation 37]
132. ~generous(X0) | ~creative(X0) [cnf transformation 64]
141. ~quiet(paul) [cnf transformation 18]
147. creative(paul) [cnf transformation 23]
355. ~creative(X0) | quiet(X0) [resolution 132,84]
420. quiet(paul) [resolution 355,147]
422. $false [subsumption resolution 420,141]
% SZS output end Proof for 7368578420762193529412137
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and generous then someone is either kind or not brave. If fred is wise or brave then someone is not curious or patient and vice versa. Everyone who is both not humble and not brave is not kind. Everyone who is both not wise and old is either not old or happy and vice versa. If someone is either curious or not calm then lucy is kind and vice versa. Everyone who is creative or not old is both tall and not patient and vice versa. Everyone who is either humble or not strong is not kind. If someone is either not old or humble then someone is not tall or not curious. If lucy is both happy and creative then someone is either not wise or not generous. If mary is not generous then someone is curious or not strong. Everyone who is either not old or not brave is both not funny and strong. Everyone who is brave or strong is both not brave and calm and vice versa. Everyone who is wise is not funny or quiet and vice versa. Everyone who is humble or not wise is wise. Everyone who is either not old or not calm is not curious. If john is either patient or not tall then alice is generous or not quiet and vice versa. Someone is both not brave and funny. Lucy is funny or strong. Paul is strong or not rich. Mary is old or wise. Someone is both not rich and not funny. Someone is rich or not humble. | Mary is generous. | neutral | ((?[X]:((strong(X)&generous(X))))=>(?[X]:((kind(X)<~>~brave(X)))))&
(((wise(fred)|brave(fred)))<=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((~humble(X)&~brave(X))=>~kind(X)))&
(![X]:((~wise(X)&old(X))<=>(~old(X)<~>happy(X))))&
((?[X]:((curious(X)<~>~calm(X))))<=>(kind(lucy)))&
(![X]:((creative(X)|~old(X))<=>(tall(X)&~patient(X))))&
(![X]:((humble(X)<~>~strong(X))=>~kind(X)))&
((?[X]:((~old(X)<~>humble(X))))=>(?[X]:((~tall(X)|~curious(X)))))&
(((happy(lucy)&creative(lucy)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
((~generous(mary))=>(?[X]:((curious(X)|~strong(X)))))&
(![X]:((~old(X)<~>~brave(X))=>(~funny(X)&strong(X))))&
(![X]:((brave(X)|strong(X))<=>(~brave(X)&calm(X))))&
(![X]:(wise(X)<=>(~funny(X)|quiet(X))))&
(![X]:((humble(X)|~wise(X))=>wise(X)))&
(![X]:((~old(X)<~>~calm(X))=>~curious(X)))&
(((patient(john)<~>~tall(john)))<=>((generous(alice)|~quiet(alice))))&
(?[X]:((~brave(X)&funny(X))))&
((funny(lucy)|strong(lucy)))&
((strong(paul)|~rich(paul)))&
((old(mary)|wise(mary)))&
(?[X]:((~rich(X)&~funny(X))))&
(?[X]:((rich(X)|~humble(X)))) | generous(mary) | [] | null | 0 |
If someone is either not creative or not happy then someone is not tall and vice versa.
Everyone who is both not strong and rich is wise or not wise and vice versa.
If someone is humble then someone is either patient or not curious and vice versa.
Everyone who is tall is not old or not tall.
If john is both old and rich then paul is either creative or not old and vice versa.
Everyone who is patient or generous is both not generous and not patient.
Everyone who is both tall and not kind is not strong or quiet and vice versa.
Everyone who is quiet or kind is both not tall and generous and vice versa.
If someone is either not happy or happy then alice is either not tall or not curious.
Everyone who is kind or patient is both not tall and generous and vice versa.
Everyone who is not calm or not brave is kind or creative and vice versa.
Everyone who is not humble or old is curious.
If alice is either not patient or creative then john is either rich or not creative.
Everyone who is not calm or strong is not curious.
If someone is either kind or curious then john is not generous and vice versa.
Someone is either not funny or not old.
Someone is not kind or not happy.
Lucy is both not humble and happy.
Someone is either funny or calm.
Alice is not quiet.
Someone is creative or funny.
Someone is either not rich or not wise. | John is quiet. | contradiction | ((?[X]:((~creative(X)<~>~happy(X))))<=>(?[X]:(~tall(X))))&
(![X]:((~strong(X)&rich(X))<=>(wise(X)|~wise(X))))&
((?[X]:(humble(X)))<=>(?[X]:((patient(X)<~>~curious(X)))))&
(![X]:(tall(X)=>(~old(X)|~tall(X))))&
(((old(john)&rich(john)))<=>((creative(paul)<~>~old(paul))))&
(![X]:((patient(X)|generous(X))=>(~generous(X)&~patient(X))))&
(![X]:((tall(X)&~kind(X))<=>(~strong(X)|quiet(X))))&
(![X]:((quiet(X)|kind(X))<=>(~tall(X)&generous(X))))&
((?[X]:((~happy(X)<~>happy(X))))=>((~tall(alice)<~>~curious(alice))))&
(![X]:((kind(X)|patient(X))<=>(~tall(X)&generous(X))))&
(![X]:((~calm(X)|~brave(X))<=>(kind(X)|creative(X))))&
(![X]:((~humble(X)|old(X))=>curious(X)))&
(((~patient(alice)<~>creative(alice)))=>((rich(john)<~>~creative(john))))&
(![X]:((~calm(X)|strong(X))=>~curious(X)))&
((?[X]:((kind(X)<~>curious(X))))<=>(~generous(john)))&
(?[X]:((~funny(X)<~>~old(X))))&
(?[X]:((~kind(X)|~happy(X))))&
((~humble(lucy)&happy(lucy)))&
(?[X]:((funny(X)<~>calm(X))))&
(~quiet(alice))&
(?[X]:((creative(X)|funny(X))))&
(?[X]:((~rich(X)<~>~wise(X)))) | quiet(john) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 493558650924512678423864
% SZS output start Proof for 493558650924512678423864
6. ! [X0] : ((generous(X0) | patient(X0)) => (~patient(X0) & ~generous(X0))) [input p5]
8. ! [X0] : ((kind(X0) | quiet(X0)) <=> (generous(X0) & ~tall(X0))) [input p7]
23. quiet(john) [input hypothesis]
28. ! [X0] : ((~patient(X0) & ~generous(X0)) | (~generous(X0) & ~patient(X0))) [ennf transformation 6]
49. ! [X0] : (((kind(X0) | quiet(X0)) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 8]
50. ! [X0] : ((kind(X0) | quiet(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | (~kind(X0) & ~quiet(X0)))) [flattening 49]
95. ~generous(X0) | ~generous(X0) [cnf transformation 28]
105. generous(X0) | ~quiet(X0) [cnf transformation 50]
144. quiet(john) [cnf transformation 23]
149. ~generous(X0) [duplicate literal removal 95]
225. ~quiet(X0) [subsumption resolution 105,149]
289. $false [subsumption resolution 144,225]
% SZS output end Proof for 493558650924512678423864
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or strong then someone is both brave and rich and vice versa.
Everyone who is either not wise or brave is either funny or patient and vice versa.
Everyone who is humble is not patient and vice versa.
If someone is either not creative or calm then someone is both old and happy.
If someone is either happy or not calm then someone is either strong or generous.
Everyone who is either funny or brave is funny.
Everyone who is not strong is both not generous and strong.
Everyone who is generous is either funny or not strong and vice versa.
Everyone who is curious or funny is not happy or quiet and vice versa.
Everyone who is either not creative or calm is not calm and vice versa.
Everyone who is both wise and tall is curious or not patient and vice versa.
Everyone who is quiet or creative is humble or curious and vice versa.
Everyone who is both happy and curious is rich and vice versa.
If alice is either not creative or patient then someone is either not brave or calm.
Everyone who is generous is creative.
If someone is not brave then someone is either old or brave.
Someone is both old and quiet.
Someone is quiet or not happy.
Someone is either wise or not tall.
Someone is wise.
Alice is both not humble and strong.
Someone is not kind.
Alice is generous or calm. | Alice is not quiet. | entailment | ((?[X]:((happy(X)<~>strong(X))))<=>(?[X]:((brave(X)&rich(X)))))&
(![X]:((~wise(X)<~>brave(X))<=>(funny(X)<~>patient(X))))&
(![X]:(humble(X)<=>~patient(X)))&
((?[X]:((~creative(X)<~>calm(X))))=>(?[X]:((old(X)&happy(X)))))&
((?[X]:((happy(X)<~>~calm(X))))=>(?[X]:((strong(X)<~>generous(X)))))&
(![X]:((funny(X)<~>brave(X))=>funny(X)))&
(![X]:(~strong(X)=>(~generous(X)&strong(X))))&
(![X]:(generous(X)<=>(funny(X)<~>~strong(X))))&
(![X]:((curious(X)|funny(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~creative(X)<~>calm(X))<=>~calm(X)))&
(![X]:((wise(X)&tall(X))<=>(curious(X)|~patient(X))))&
(![X]:((quiet(X)|creative(X))<=>(humble(X)|curious(X))))&
(![X]:((happy(X)&curious(X))<=>rich(X)))&
(((~creative(alice)<~>patient(alice)))=>(?[X]:((~brave(X)<~>calm(X)))))&
(![X]:(generous(X)=>creative(X)))&
((?[X]:(~brave(X)))=>(?[X]:((old(X)<~>brave(X)))))&
(?[X]:((old(X)&quiet(X))))&
(?[X]:((quiet(X)|~happy(X))))&
(?[X]:((wise(X)<~>~tall(X))))&
(?[X]:(wise(X)))&
((~humble(alice)&strong(alice)))&
(?[X]:(~kind(X)))&
((generous(alice)|calm(alice))) | ~quiet(alice) | [
"p1",
"p2",
"p5",
"p6",
"p7",
"p8",
"p9",
"p10",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 6154639429800561901641605
% SZS output start Proof for 6154639429800561901641605
2. ! [X0] : ((~wise(X0) <~> brave(X0)) <=> (funny(X0) <~> patient(X0))) [input p1]
3. ! [X0] : (humble(X0) <=> ~patient(X0)) [input p2]
6. ! [X0] : ((funny(X0) <~> brave(X0)) => funny(X0)) [input p5]
7. ! [X0] : (~strong(X0) => (strong(X0) & ~generous(X0))) [input p6]
8. ! [X0] : (generous(X0) <=> (funny(X0) <~> ~strong(X0))) [input p7]
9. ! [X0] : ((funny(X0) | curious(X0)) <=> (quiet(X0) | ~happy(X0))) [input p8]
10. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> ~calm(X0)) [input p9]
11. ! [X0] : ((tall(X0) & wise(X0)) <=> (~patient(X0) | curious(X0))) [input p10]
15. ! [X0] : (generous(X0) => creative(X0)) [input p14]
21. strong(alice) & ~humble(alice) [input p20]
24. quiet(alice) [input hypothesis]
32. ! [X0] : (funny(X0) | (funny(X0) <=> brave(X0))) [ennf transformation 6]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | strong(X0)) [ennf transformation 7]
35. ! [X0] : (creative(X0) | ~generous(X0)) [ennf transformation 15]
42. ! [X0] : ((((~brave(X0) | wise(X0)) & (brave(X0) | ~wise(X0))) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | ((~wise(X0) | ~brave(X0)) & (brave(X0) | wise(X0))))) [nnf transformation 2]
43. ! [X0] : ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))) [nnf transformation 3]
52. ! [X0] : (funny(X0) | ((funny(X0) | ~brave(X0)) & (brave(X0) | ~funny(X0)))) [nnf transformation 32]
53. ! [X0] : ((generous(X0) | ((funny(X0) | strong(X0)) & (~strong(X0) | ~funny(X0)))) & (((strong(X0) | ~funny(X0)) & (~strong(X0) | funny(X0))) | ~generous(X0))) [nnf transformation 8]
54. ! [X0] : (((funny(X0) | curious(X0)) | (~quiet(X0) & happy(X0))) & ((quiet(X0) | ~happy(X0)) | (~funny(X0) & ~curious(X0)))) [nnf transformation 9]
55. ! [X0] : ((funny(X0) | curious(X0) | (~quiet(X0) & happy(X0))) & (quiet(X0) | ~happy(X0) | (~funny(X0) & ~curious(X0)))) [flattening 54]
56. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | calm(X0)) & (~calm(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 10]
57. ! [X0] : (((tall(X0) & wise(X0)) | (patient(X0) & ~curious(X0))) & ((~patient(X0) | curious(X0)) | (~tall(X0) | ~wise(X0)))) [nnf transformation 11]
58. ! [X0] : (((tall(X0) & wise(X0)) | (patient(X0) & ~curious(X0))) & (~patient(X0) | curious(X0) | ~tall(X0) | ~wise(X0))) [flattening 57]
90. ~patient(X0) | ~wise(X0) | funny(X0) | brave(X0) [cnf transformation 42]
94. humble(X0) | patient(X0) [cnf transformation 43]
104. funny(X0) | funny(X0) | ~brave(X0) [cnf transformation 52]
106. strong(X0) | strong(X0) [cnf transformation 33]
109. generous(X0) | ~strong(X0) | ~funny(X0) [cnf transformation 53]
114. ~quiet(X0) | curious(X0) | funny(X0) [cnf transformation 55]
116. ~calm(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 56]
117. calm(X0) | ~creative(X0) | calm(X0) [cnf transformation 56]
120. ~curious(X0) | wise(X0) [cnf transformation 58]
135. creative(X0) | ~generous(X0) [cnf transformation 35]
144. ~humble(alice) [cnf transformation 21]
147. quiet(alice) [cnf transformation 24]
148. ~calm(X0) | ~creative(X0) [duplicate literal removal 116]
149. ~creative(X0) | calm(X0) [duplicate literal removal 117]
150. strong(X0) [duplicate literal removal 106]
151. ~brave(X0) | funny(X0) [duplicate literal removal 104]
219. ~funny(X0) | generous(X0) [subsumption resolution 109,150]
221. ~creative(X0) [subsumption resolution 148,149]
226. 16 <=> patient(alice) [avatar definition]
228. patient(alice) <- (16) [avatar component clause 226]
240. ~generous(X0) [subsumption resolution 135,221]
287. patient(alice) [resolution 94,144]
312. curious(alice) | funny(alice) [resolution 114,147]
316. 26 <=> funny(alice) [avatar definition]
317. ~funny(alice) <- (~26) [avatar component clause 316]
318. funny(alice) <- (26) [avatar component clause 316]
320. 27 <=> curious(alice) [avatar definition]
322. curious(alice) <- (27) [avatar component clause 320]
323. 26 | 27 [avatar split clause 312,320,316]
343. generous(alice) <- (26) [resolution 318,219]
344. $false <- (26) [subsumption resolution 343,240]
345. ~26 [avatar contradiction clause 344]
360. wise(alice) <- (27) [resolution 322,120]
391. ~wise(alice) | funny(alice) | brave(alice) <- (16) [resolution 90,228]
396. funny(alice) | brave(alice) <- (16, 27) [subsumption resolution 391,360]
397. brave(alice) <- (16, ~26, 27) [subsumption resolution 396,317]
398. funny(alice) <- (16, ~26, 27) [resolution 397,151]
399. $false <- (16, ~26, 27) [subsumption resolution 398,317]
400. ~16 | 26 | ~27 [avatar contradiction clause 399]
401. 16 [avatar split clause 287,226]
402. $false [avatar sat refutation 323,345,400,401]
% SZS output end Proof for 6154639429800561901641605
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient then someone is both strong and not strong and vice versa. If someone is calm or old then paul is not generous and vice versa. Everyone who is generous or creative is both curious and not kind. Everyone who is old is both not calm and not humble. Everyone who is tall or brave is happy or old. Everyone who is either not creative or not funny is not patient. Everyone who is either brave or not quiet is both not brave and strong. Everyone who is not brave is either wise or not old and vice versa. Everyone who is both not humble and not patient is either not wise or not funny and vice versa. If susan is not strong then someone is humble or not rich. Everyone who is not quiet is not brave or not curious and vice versa. If paul is either kind or not tall then mary is either not brave or tall and vice versa. Everyone who is tall is curious or old. Everyone who is not humble is either humble or happy and vice versa. If paul is curious or not strong then someone is not quiet and vice versa. If lucy is either not tall or not curious then fred is either not humble or not old. Lucy is not generous. Someone is generous. Paul is both not kind and not quiet. Fred is wise. Lucy is not brave. Someone is creative. Someone is funny. | Paul is not quiet. | entailment | ((?[X]:(patient(X)))<=>(?[X]:((strong(X)&~strong(X)))))&
((?[X]:((calm(X)|old(X))))<=>(~generous(paul)))&
(![X]:((generous(X)|creative(X))=>(curious(X)&~kind(X))))&
(![X]:(old(X)=>(~calm(X)&~humble(X))))&
(![X]:((tall(X)|brave(X))=>(happy(X)|old(X))))&
(![X]:((~creative(X)<~>~funny(X))=>~patient(X)))&
(![X]:((brave(X)<~>~quiet(X))=>(~brave(X)&strong(X))))&
(![X]:(~brave(X)<=>(wise(X)<~>~old(X))))&
(![X]:((~humble(X)&~patient(X))<=>(~wise(X)<~>~funny(X))))&
((~strong(susan))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:(~quiet(X)<=>(~brave(X)|~curious(X))))&
(((kind(paul)<~>~tall(paul)))<=>((~brave(mary)<~>tall(mary))))&
(![X]:(tall(X)=>(curious(X)|old(X))))&
(![X]:(~humble(X)<=>(humble(X)<~>happy(X))))&
(((curious(paul)|~strong(paul)))<=>(?[X]:(~quiet(X))))&
(((~tall(lucy)<~>~curious(lucy)))=>((~humble(fred)<~>~old(fred))))&
(~generous(lucy))&
(?[X]:(generous(X)))&
((~kind(paul)&~quiet(paul)))&
(wise(fred))&
(~brave(lucy))&
(?[X]:(creative(X)))&
(?[X]:(funny(X))) | ~quiet(paul) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3636001113827908381340184
% SZS output start Proof for 3636001113827908381340184
7. ! [X0] : ((brave(X0) <~> ~quiet(X0)) => (strong(X0) & ~brave(X0))) [input p6]
11. ! [X0] : (~quiet(X0) <=> (~curious(X0) | ~brave(X0))) [input p10]
24. quiet(paul) [input hypothesis]
32. ! [X0] : ((strong(X0) & ~brave(X0)) | (brave(X0) <=> ~quiet(X0))) [ennf transformation 7]
46. ! [X0] : ((strong(X0) & ~brave(X0)) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) [nnf transformation 32]
50. ! [X0] : ((~quiet(X0) | (curious(X0) & brave(X0))) & ((~curious(X0) | ~brave(X0)) | quiet(X0))) [nnf transformation 11]
51. ! [X0] : ((~quiet(X0) | (curious(X0) & brave(X0))) & (~curious(X0) | ~brave(X0) | quiet(X0))) [flattening 50]
82. ~brave(X0) | ~quiet(X0) | ~brave(X0) [cnf transformation 46]
97. ~quiet(X0) | brave(X0) [cnf transformation 51]
127. quiet(paul) [cnf transformation 24]
130. ~brave(X0) | ~quiet(X0) [duplicate literal removal 82]
161. ~quiet(X0) [subsumption resolution 97,130]
217. $false [subsumption resolution 127,161]
% SZS output end Proof for 3636001113827908381340184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not quiet is not tall or kind.
Everyone who is brave or not wise is not patient or funny.
Everyone who is both not funny and not happy is not funny.
Everyone who is not patient or not humble is both patient and not creative and vice versa.
If someone is not tall then someone is either not rich or rich and vice versa.
Everyone who is not kind or kind is not tall and vice versa.
If fred is either not curious or patient then john is not rich and vice versa.
Everyone who is either not creative or creative is both creative and curious and vice versa.
Everyone who is both strong and not curious is not patient or brave and vice versa.
If lucy is both not brave and rich then john is either quiet or not brave and vice versa.
Everyone who is both not quiet and tall is both not rich and generous.
Everyone who is both rich and humble is either not old or patient and vice versa.
If someone is patient or wise then lucy is either not old or not kind and vice versa.
If someone is either not calm or generous then someone is either old or creative.
Everyone who is either not funny or not creative is either not wise or quiet.
Everyone who is both not rich and not creative is both not calm and curious.
John is strong.
Someone is not tall or funny.
John is both not rich and calm.
Alice is both kind and old.
Someone is not funny or tall.
Mary is either not generous or calm.
Susan is brave or not generous. | Alice is not creative. | contradiction | (![X]:((~creative(X)<~>~quiet(X))=>(~tall(X)|kind(X))))&
(![X]:((brave(X)|~wise(X))=>(~patient(X)|funny(X))))&
(![X]:((~funny(X)&~happy(X))=>~funny(X)))&
(![X]:((~patient(X)|~humble(X))<=>(patient(X)&~creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~rich(X)<~>rich(X)))))&
(![X]:((~kind(X)|kind(X))<=>~tall(X)))&
(((~curious(fred)<~>patient(fred)))<=>(~rich(john)))&
(![X]:((~creative(X)<~>creative(X))<=>(creative(X)&curious(X))))&
(![X]:((strong(X)&~curious(X))<=>(~patient(X)|brave(X))))&
(((~brave(lucy)&rich(lucy)))<=>((quiet(john)<~>~brave(john))))&
(![X]:((~quiet(X)&tall(X))=>(~rich(X)&generous(X))))&
(![X]:((rich(X)&humble(X))<=>(~old(X)<~>patient(X))))&
((?[X]:((patient(X)|wise(X))))<=>((~old(lucy)<~>~kind(lucy))))&
((?[X]:((~calm(X)<~>generous(X))))=>(?[X]:((old(X)<~>creative(X)))))&
(![X]:((~funny(X)<~>~creative(X))=>(~wise(X)<~>quiet(X))))&
(![X]:((~rich(X)&~creative(X))=>(~calm(X)&curious(X))))&
(strong(john))&
(?[X]:((~tall(X)|funny(X))))&
((~rich(john)&calm(john)))&
((kind(alice)&old(alice)))&
(?[X]:((~funny(X)|tall(X))))&
((~generous(mary)<~>calm(mary)))&
((brave(susan)|~generous(susan))) | ~creative(alice) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1766880314148330280463331
% SZS output start Proof for 1766880314148330280463331
8. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (curious(X0) & creative(X0))) [input p7]
24. ~creative(alice) [input hypothesis]
49. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~curious(X0) | ~creative(X0))) & ((curious(X0) & creative(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 8]
50. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~curious(X0) | ~creative(X0)) & ((curious(X0) & creative(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 49]
91. creative(X0) | creative(X0) | creative(X0) [cnf transformation 50]
142. ~creative(alice) [cnf transformation 24]
143. creative(X0) [duplicate literal removal 91]
242. $false [subsumption resolution 142,143]
% SZS output end Proof for 1766880314148330280463331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not strong or brave then someone is both not wise and humble.
Everyone who is both not funny and strong is wise or quiet and vice versa.
If paul is brave or not tall then someone is brave or happy.
Everyone who is not curious is patient and vice versa.
Everyone who is not generous is curious and vice versa.
Everyone who is not strong or old is both funny and not tall.
Everyone who is not creative or not brave is both tall and curious and vice versa.
Everyone who is both funny and not patient is either rich or not calm and vice versa.
If someone is not generous or funny then someone is funny and vice versa.
Everyone who is either not old or not calm is not strong or strong and vice versa.
Everyone who is both curious and tall is both not patient and creative.
Everyone who is either not quiet or generous is rich or creative and vice versa.
Everyone who is either not patient or not rich is both quiet and calm.
Everyone who is either not brave or not wise is either not funny or curious.
Everyone who is funny is either not brave or wise and vice versa.
Everyone who is both patient and strong is strong and vice versa.
Lucy is not patient or not tall.
Fred is either humble or strong.
Susan is wise or quiet.
Lucy is either curious or not rich.
Fred is both not happy and not rich. | Paul is not curious. | entailment | ((?[X]:((~strong(X)<~>brave(X))))=>(?[X]:((~wise(X)&humble(X)))))&
(![X]:((~funny(X)&strong(X))<=>(wise(X)|quiet(X))))&
(((brave(paul)|~tall(paul)))=>(?[X]:((brave(X)|happy(X)))))&
(![X]:(~curious(X)<=>patient(X)))&
(![X]:(~generous(X)<=>curious(X)))&
(![X]:((~strong(X)|old(X))=>(funny(X)&~tall(X))))&
(![X]:((~creative(X)|~brave(X))<=>(tall(X)&curious(X))))&
(![X]:((funny(X)&~patient(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((~generous(X)|funny(X))))<=>(?[X]:(funny(X))))&
(![X]:((~old(X)<~>~calm(X))<=>(~strong(X)|strong(X))))&
(![X]:((curious(X)&tall(X))=>(~patient(X)&creative(X))))&
(![X]:((~quiet(X)<~>generous(X))<=>(rich(X)|creative(X))))&
(![X]:((~patient(X)<~>~rich(X))=>(quiet(X)&calm(X))))&
(![X]:((~brave(X)<~>~wise(X))=>(~funny(X)<~>curious(X))))&
(![X]:(funny(X)<=>(~brave(X)<~>wise(X))))&
(![X]:((patient(X)&strong(X))<=>strong(X)))&
((~patient(lucy)|~tall(lucy)))&
((humble(fred)<~>strong(fred)))&
((wise(susan)|quiet(susan)))&
((curious(lucy)<~>~rich(lucy)))&
((~happy(fred)&~rich(fred))) | ~curious(paul) | [
"p1",
"p3",
"p5",
"p6",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1017858689480535796298564
% SZS output start Proof for 1017858689480535796298564
2. ! [X0] : ((strong(X0) & ~funny(X0)) <=> (quiet(X0) | wise(X0))) [input p1]
4. ! [X0] : (~curious(X0) <=> patient(X0)) [input p3]
6. ! [X0] : ((old(X0) | ~strong(X0)) => (~tall(X0) & funny(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~creative(X0)) <=> (curious(X0) & tall(X0))) [input p6]
14. ! [X0] : ((~brave(X0) <~> ~wise(X0)) => (~funny(X0) <~> curious(X0))) [input p13]
15. ! [X0] : (funny(X0) <=> (~brave(X0) <~> wise(X0))) [input p14]
16. ! [X0] : ((strong(X0) & patient(X0)) <=> strong(X0)) [input p15]
22. curious(paul) [input hypothesis]
27. ! [X0] : ((~tall(X0) & funny(X0)) | (~old(X0) & strong(X0))) [ennf transformation 6]
31. ! [X0] : ((~funny(X0) <~> curious(X0)) | (~brave(X0) <=> ~wise(X0))) [ennf transformation 14]
36. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & ((quiet(X0) | wise(X0)) | (~strong(X0) | funny(X0)))) [nnf transformation 2]
37. ! [X0] : (((strong(X0) & ~funny(X0)) | (~quiet(X0) & ~wise(X0))) & (quiet(X0) | wise(X0) | ~strong(X0) | funny(X0))) [flattening 36]
40. ! [X0] : ((~curious(X0) | ~patient(X0)) & (patient(X0) | curious(X0))) [nnf transformation 4]
42. ! [X0] : (((~brave(X0) | ~creative(X0)) | (~curious(X0) | ~tall(X0))) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [nnf transformation 7]
43. ! [X0] : ((~brave(X0) | ~creative(X0) | ~curious(X0) | ~tall(X0)) & ((curious(X0) & tall(X0)) | (brave(X0) & creative(X0)))) [flattening 42]
56. ! [X0] : (((~curious(X0) | funny(X0)) & (curious(X0) | ~funny(X0))) | ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0)))) [nnf transformation 31]
57. ! [X0] : ((funny(X0) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0)))) & (((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | ~funny(X0))) [nnf transformation 15]
58. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | (~strong(X0) | ~patient(X0)))) [nnf transformation 16]
59. ! [X0] : (((strong(X0) & patient(X0)) | ~strong(X0)) & (strong(X0) | ~strong(X0) | ~patient(X0))) [flattening 58]
67. ~funny(X0) | ~wise(X0) [cnf transformation 37]
74. ~patient(X0) | ~curious(X0) [cnf transformation 40]
77. funny(X0) | strong(X0) [cnf transformation 27]
79. ~tall(X0) | strong(X0) [cnf transformation 27]
82. tall(X0) | brave(X0) [cnf transformation 43]
84. curious(X0) | brave(X0) [cnf transformation 43]
115. ~curious(X0) | funny(X0) | ~wise(X0) | brave(X0) [cnf transformation 56]
117. wise(X0) | ~brave(X0) | ~funny(X0) [cnf transformation 57]
120. funny(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 57]
122. ~strong(X0) | patient(X0) [cnf transformation 59]
132. curious(paul) [cnf transformation 22]
142. 3 <=> ! [X1] : (brave(X1) | strong(X1)) [avatar definition]
143. brave(X1) | strong(X1) <- (3) [avatar component clause 142]
196. funny(X0) | ~wise(X0) | brave(X0) [subsumption resolution 115,84]
197. ~wise(X0) | brave(X0) [subsumption resolution 196,67]
200. funny(X0) | ~wise(X0) [subsumption resolution 120,197]
201. ~wise(X0) [subsumption resolution 200,67]
203. ~funny(X0) | ~brave(X0) [subsumption resolution 117,201]
244. brave(X0) | strong(X0) [resolution 82,79]
245. 3 [avatar split clause 244,142]
271. ~brave(X1) | strong(X1) [resolution 203,77]
272. strong(X1) <- (3) [subsumption resolution 271,143]
277. patient(X0) <- (3) [resolution 272,122]
279. ~curious(X0) <- (3) [resolution 277,74]
284. $false <- (3) [resolution 279,132]
289. ~3 [avatar contradiction clause 284]
290. $false [avatar sat refutation 245,289]
% SZS output end Proof for 1017858689480535796298564
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not strong is either not brave or not old and vice versa.
Everyone who is humble is not calm.
Everyone who is happy or not strong is either calm or not old and vice versa.
Everyone who is both generous and not quiet is strong.
Everyone who is either rich or brave is both not kind and quiet and vice versa.
Everyone who is either calm or strong is strong or not humble.
If someone is either calm or happy then mary is not old.
Everyone who is both not humble and not strong is either not funny or creative.
Everyone who is tall is either old or not rich and vice versa.
If someone is not wise or rich then fred is not humble and vice versa.
If someone is either not brave or not funny then fred is both happy and not humble and vice versa.
Everyone who is not rich is rich or not brave and vice versa.
Everyone who is both old and not happy is brave.
Everyone who is wise is either not quiet or not brave and vice versa.
If someone is either old or not creative then lucy is not strong or quiet.
Everyone who is either not generous or brave is both not strong and funny.
Someone is generous.
Someone is strong.
Alice is both not quiet and humble.
Someone is not calm or strong.
Someone is either not brave or not humble.
Someone is both creative and not wise.
Paul is tall or happy. | Fred is strong. | contradiction | (![X]:((~calm(X)<~>~strong(X))<=>(~brave(X)<~>~old(X))))&
(![X]:(humble(X)=>~calm(X)))&
(![X]:((happy(X)|~strong(X))<=>(calm(X)<~>~old(X))))&
(![X]:((generous(X)&~quiet(X))=>strong(X)))&
(![X]:((rich(X)<~>brave(X))<=>(~kind(X)&quiet(X))))&
(![X]:((calm(X)<~>strong(X))=>(strong(X)|~humble(X))))&
((?[X]:((calm(X)<~>happy(X))))=>(~old(mary)))&
(![X]:((~humble(X)&~strong(X))=>(~funny(X)<~>creative(X))))&
(![X]:(tall(X)<=>(old(X)<~>~rich(X))))&
((?[X]:((~wise(X)|rich(X))))<=>(~humble(fred)))&
((?[X]:((~brave(X)<~>~funny(X))))<=>((happy(fred)&~humble(fred))))&
(![X]:(~rich(X)<=>(rich(X)|~brave(X))))&
(![X]:((old(X)&~happy(X))=>brave(X)))&
(![X]:(wise(X)<=>(~quiet(X)<~>~brave(X))))&
((?[X]:((old(X)<~>~creative(X))))=>((~strong(lucy)|quiet(lucy))))&
(![X]:((~generous(X)<~>brave(X))=>(~strong(X)&funny(X))))&
(?[X]:(generous(X)))&
(?[X]:(strong(X)))&
((~quiet(alice)&humble(alice)))&
(?[X]:((~calm(X)|strong(X))))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((creative(X)&~wise(X))))&
((tall(paul)|happy(paul))) | strong(fred) | [
"p0",
"p1",
"p2",
"p3",
"p10",
"p11",
"p12",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 9214238187328068246176565
% SZS output start Proof for 9214238187328068246176565
1. ! [X0] : ((~calm(X0) <~> ~strong(X0)) <=> (~brave(X0) <~> ~old(X0))) [input p0]
2. ! [X0] : (humble(X0) => ~calm(X0)) [input p1]
3. ! [X0] : ((~strong(X0) | happy(X0)) <=> (calm(X0) <~> ~old(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) & generous(X0)) => strong(X0)) [input p3]
11. ? [X0] : (~brave(X0) <~> ~funny(X0)) <=> (~humble(fred) & happy(fred)) [input p10]
12. ! [X0] : (~rich(X0) <=> (~brave(X0) | rich(X0))) [input p11]
13. ! [X0] : ((~happy(X0) & old(X0)) => brave(X0)) [input p12]
16. ! [X0] : ((~generous(X0) <~> brave(X0)) => (funny(X0) & ~strong(X0))) [input p15]
19. humble(alice) & ~quiet(alice) [input p18]
24. strong(fred) [input hypothesis]
26. ! [X0] : (~calm(X0) | ~humble(X0)) [ennf transformation 2]
27. ! [X0] : (strong(X0) | (quiet(X0) | ~generous(X0))) [ennf transformation 4]
28. ! [X0] : (strong(X0) | quiet(X0) | ~generous(X0)) [flattening 27]
35. ! [X0] : (brave(X0) | (happy(X0) | ~old(X0))) [ennf transformation 13]
36. ! [X0] : (brave(X0) | happy(X0) | ~old(X0)) [flattening 35]
39. ! [X0] : ((funny(X0) & ~strong(X0)) | (~generous(X0) <=> brave(X0))) [ennf transformation 16]
40. ! [X0] : ((((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ((~brave(X0) | old(X0)) & (~old(X0) | brave(X0)))) & (((old(X0) | brave(X0)) & (~old(X0) | ~brave(X0))) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0))))) [nnf transformation 1]
41. ! [X0] : (((~strong(X0) | happy(X0)) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (strong(X0) & ~happy(X0)))) [nnf transformation 3]
42. ! [X0] : ((~strong(X0) | happy(X0) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) & (((old(X0) | ~calm(X0)) & (~old(X0) | calm(X0))) | (strong(X0) & ~happy(X0)))) [flattening 41]
53. (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (humble(fred) | ~happy(fred))) & ((~humble(fred) & happy(fred)) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) [nnf transformation 11]
54. (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | humble(fred) | ~happy(fred)) & ((~humble(fred) & happy(fred)) | ! [X0] : ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) [flattening 53]
55. (? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | humble(fred) | ~happy(fred)) & ((~humble(fred) & happy(fred)) | ! [X1] : ((~brave(X1) | funny(X1)) & (~funny(X1) | brave(X1)))) [rectify 54]
56. ? [X0] : ((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) => ((funny(sK1) | brave(sK1)) & (~funny(sK1) | ~brave(sK1))) [choice axiom]
57. (((funny(sK1) | brave(sK1)) & (~funny(sK1) | ~brave(sK1))) | humble(fred) | ~happy(fred)) & ((~humble(fred) & happy(fred)) | ! [X1] : ((~brave(X1) | funny(X1)) & (~funny(X1) | brave(X1)))) [skolemisation 55,56]
58. ! [X0] : ((~rich(X0) | (brave(X0) & ~rich(X0))) & ((~brave(X0) | rich(X0)) | rich(X0))) [nnf transformation 12]
59. ! [X0] : ((~rich(X0) | (brave(X0) & ~rich(X0))) & (~brave(X0) | rich(X0) | rich(X0))) [flattening 58]
62. ! [X0] : ((funny(X0) & ~strong(X0)) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0)))) [nnf transformation 39]
76. ~strong(X0) | brave(X0) | old(X0) | calm(X0) [cnf transformation 40]
78. ~old(X0) | ~calm(X0) | ~strong(X0) | brave(X0) [cnf transformation 40]
82. ~humble(X0) | ~calm(X0) [cnf transformation 26]
83. ~happy(X0) | calm(X0) | ~old(X0) [cnf transformation 42]
85. ~happy(X0) | ~calm(X0) | old(X0) [cnf transformation 42]
89. ~generous(X0) | quiet(X0) | strong(X0) [cnf transformation 28]
107. happy(fred) | ~funny(X1) | brave(X1) [cnf transformation 57]
113. ~brave(X0) | rich(X0) | rich(X0) [cnf transformation 59]
114. ~rich(X0) | ~rich(X0) [cnf transformation 59]
116. ~old(X0) | happy(X0) | brave(X0) [cnf transformation 36]
125. funny(X0) | brave(X0) | generous(X0) [cnf transformation 62]
129. ~quiet(alice) [cnf transformation 19]
130. humble(alice) [cnf transformation 19]
137. strong(fred) [cnf transformation 24]
138. ~brave(X0) | rich(X0) [duplicate literal removal 113]
139. ~rich(X0) [duplicate literal removal 114]
167. 7 <=> ! [X1] : ~rich(X1) [avatar definition]
168. ~rich(X1) <- (7) [avatar component clause 167]
175. 9 <=> happy(fred) [avatar definition]
176. happy(fred) <- (9) [avatar component clause 175]
193. 13 <=> ! [X1] : (~funny(X1) | brave(X1)) [avatar definition]
194. ~funny(X1) | brave(X1) <- (13) [avatar component clause 193]
197. 13 | 9 [avatar split clause 107,175,193]
198. 7 [avatar split clause 139,167]
243. ~calm(alice) [resolution 82,130]
251. calm(fred) | ~old(fred) <- (9) [resolution 83,176]
253. 24 <=> old(fred) [avatar definition]
254. old(fred) <- (24) [avatar component clause 253]
257. 25 <=> calm(fred) [avatar definition]
259. calm(fred) <- (25) [avatar component clause 257]
260. ~24 | 25 | ~9 [avatar split clause 251,175,257,253]
261. ~calm(fred) | old(fred) <- (9) [resolution 85,176]
294. 31 <=> brave(fred) [avatar definition]
295. ~brave(fred) <- (~31) [avatar component clause 294]
296. brave(fred) <- (31) [avatar component clause 294]
317. brave(fred) | old(fred) | calm(fred) [resolution 76,137]
329. old(fred) | calm(fred) <- (~31) [subsumption resolution 317,295]
343. 25 | 24 | 31 [avatar split clause 329,294,253,257]
344. 24 | ~25 | ~9 [avatar split clause 261,175,257,253]
362. ~calm(fred) | ~strong(fred) | brave(fred) <- (24) [resolution 78,254]
363. ~strong(fred) | brave(fred) <- (24, 25) [subsumption resolution 362,259]
364. brave(fred) <- (24, 25) [subsumption resolution 363,137]
367. 31 | ~24 | ~25 [avatar split clause 364,257,253,294]
404. rich(fred) <- (31) [resolution 296,138]
416. $false <- (7, 31) [subsumption resolution 404,168]
417. ~7 | ~31 [avatar contradiction clause 416]
422. brave(X0) | brave(X0) | generous(X0) <- (13) [resolution 194,125]
423. generous(X0) | brave(X0) <- (13) [duplicate literal removal 422]
448. quiet(X2) | brave(X2) | strong(X2) <- (13) [resolution 423,89]
477. brave(alice) | strong(alice) <- (13) [resolution 448,129]
483. 48 <=> strong(alice) [avatar definition]
485. strong(alice) <- (48) [avatar component clause 483]
487. 49 <=> brave(alice) [avatar definition]
488. ~brave(alice) <- (~49) [avatar component clause 487]
489. brave(alice) <- (49) [avatar component clause 487]
490. 48 | 49 | ~13 [avatar split clause 477,193,487,483]
497. rich(alice) <- (49) [resolution 489,138]
500. 50 <=> old(alice) [avatar definition]
502. old(alice) <- (50) [avatar component clause 500]
508. $false <- (7, 49) [subsumption resolution 497,168]
509. ~7 | ~49 [avatar contradiction clause 508]
511. brave(alice) | old(alice) | calm(alice) <- (48) [resolution 485,76]
515. 51 <=> happy(alice) [avatar definition]
517. happy(alice) <- (51) [avatar component clause 515]
519. old(alice) | calm(alice) <- (48, ~49) [subsumption resolution 511,488]
520. old(alice) <- (48, ~49) [subsumption resolution 519,243]
521. 50 | ~48 | 49 [avatar split clause 520,487,483,500]
528. happy(alice) | brave(alice) <- (50) [resolution 502,116]
529. happy(alice) <- (~49, 50) [subsumption resolution 528,488]
530. 51 | 49 | ~50 [avatar split clause 529,500,487,515]
569. calm(alice) | ~old(alice) <- (51) [resolution 517,83]
570. ~old(alice) <- (51) [subsumption resolution 569,243]
571. $false <- (50, 51) [subsumption resolution 570,502]
572. ~50 | ~51 [avatar contradiction clause 571]
573. $false [avatar sat refutation 197,198,260,343,344,367,417,490,509,521,530,572]
% SZS output end Proof for 9214238187328068246176565
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient or not wise is old or funny. If lucy is either not strong or curious then someone is not brave or creative and vice versa. If susan is tall or rich then someone is not creative. If lucy is not curious or funny then lucy is rich and vice versa. Everyone who is both quiet and not patient is not wise. If someone is not generous or not funny then someone is either brave or kind. Everyone who is both not curious and wise is tall or not happy. Everyone who is not strong is not rich or kind and vice versa. Everyone who is either not curious or not happy is creative or not humble. Everyone who is both brave and humble is either not kind or strong. Everyone who is generous or not quiet is not funny. Everyone who is generous or not rich is tall or not calm. If john is either not old or not patient then someone is old or creative. If someone is either humble or calm then alice is old and vice versa. If mary is either patient or happy then someone is both not strong and not brave. If lucy is either humble or wise then lucy is tall or not happy and vice versa. Alice is not humble. Someone is generous or not humble. Someone is not humble or not strong. Someone is either wise or happy. Paul is either not strong or not creative. Someone is both not wise and brave. John is happy or not creative. Paul is not humble. | John is happy. | neutral | (![X]:((~patient(X)|~wise(X))=>(old(X)|funny(X))))&
(((~strong(lucy)<~>curious(lucy)))<=>(?[X]:((~brave(X)|creative(X)))))&
(((tall(susan)|rich(susan)))=>(?[X]:(~creative(X))))&
(((~curious(lucy)|funny(lucy)))<=>(rich(lucy)))&
(![X]:((quiet(X)&~patient(X))=>~wise(X)))&
((?[X]:((~generous(X)|~funny(X))))=>(?[X]:((brave(X)<~>kind(X)))))&
(![X]:((~curious(X)&wise(X))=>(tall(X)|~happy(X))))&
(![X]:(~strong(X)<=>(~rich(X)|kind(X))))&
(![X]:((~curious(X)<~>~happy(X))=>(creative(X)|~humble(X))))&
(![X]:((brave(X)&humble(X))=>(~kind(X)<~>strong(X))))&
(![X]:((generous(X)|~quiet(X))=>~funny(X)))&
(![X]:((generous(X)|~rich(X))=>(tall(X)|~calm(X))))&
(((~old(john)<~>~patient(john)))=>(?[X]:((old(X)|creative(X)))))&
((?[X]:((humble(X)<~>calm(X))))<=>(old(alice)))&
(((patient(mary)<~>happy(mary)))=>(?[X]:((~strong(X)&~brave(X)))))&
(((humble(lucy)<~>wise(lucy)))<=>((tall(lucy)|~happy(lucy))))&
(~humble(alice))&
(?[X]:((generous(X)|~humble(X))))&
(?[X]:((~humble(X)|~strong(X))))&
(?[X]:((wise(X)<~>happy(X))))&
((~strong(paul)<~>~creative(paul)))&
(?[X]:((~wise(X)&brave(X))))&
((happy(john)|~creative(john)))&
(~humble(paul)) | happy(john) | [] | null | 0 |
If paul is brave then someone is either humble or not tall and vice versa.
If alice is rich or wise then john is funny.
Everyone who is either not tall or quiet is creative and vice versa.
If someone is not creative then paul is not tall.
Everyone who is not wise or strong is either not generous or patient and vice versa.
Everyone who is not old is curious or not humble and vice versa.
If mary is either quiet or old then someone is both brave and generous.
If alice is both not generous and not rich then someone is either strong or not brave and vice versa.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is both not creative and wise is not brave or rich and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Everyone who is either not curious or happy is either humble or not generous.
If someone is not wise or brave then lucy is not humble and vice versa.
If someone is both strong and quiet then susan is calm and vice versa.
Someone is tall or not brave.
John is either calm or not strong.
Lucy is both not funny and wise.
Someone is not kind or not calm.
Someone is not humble or old.
Someone is not creative or tall.
Fred is not quiet or creative.
Alice is wise or not kind. | Mary is old. | contradiction | ((brave(paul))<=>(?[X]:((humble(X)<~>~tall(X)))))&
(((rich(alice)|wise(alice)))=>(funny(john)))&
(![X]:((~tall(X)<~>quiet(X))<=>creative(X)))&
((?[X]:(~creative(X)))=>(~tall(paul)))&
(![X]:((~wise(X)|strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~old(X)<=>(curious(X)|~humble(X))))&
(((quiet(mary)<~>old(mary)))=>(?[X]:((brave(X)&generous(X)))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~creative(X)&wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~humble(lucy)))&
((?[X]:((strong(X)&quiet(X))))<=>(calm(susan)))&
(?[X]:((tall(X)|~brave(X))))&
((calm(john)<~>~strong(john)))&
((~funny(lucy)&wise(lucy)))&
(?[X]:((~kind(X)|~calm(X))))&
(?[X]:((~humble(X)|old(X))))&
(?[X]:((~creative(X)|tall(X))))&
((~quiet(fred)|creative(fred)))&
((wise(alice)|~kind(alice))) | old(mary) | [
"p5",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4848914940272353993376985
% SZS output start Proof for 4848914940272353993376985
6. ! [X0] : (~old(X0) <=> (~humble(X0) | curious(X0))) [input p5]
10. ? [X0] : (rich(X0) & ~wise(X0)) <=> ? [X0] : humble(X0) [input p9]
12. ! [X0] : ((wise(X0) & ~creative(X0)) <=> (rich(X0) | ~brave(X0))) [input p11]
25. old(mary) [input hypothesis]
26. ? [X0] : (rich(X0) & ~wise(X0)) <=> ? [X1] : humble(X1) [rectify 10]
38. ! [X0] : ((~old(X0) | (humble(X0) & ~curious(X0))) & ((~humble(X0) | curious(X0)) | old(X0))) [nnf transformation 6]
39. ! [X0] : ((~old(X0) | (humble(X0) & ~curious(X0))) & (~humble(X0) | curious(X0) | old(X0))) [flattening 38]
50. (? [X0] : (rich(X0) & ~wise(X0)) | ! [X1] : ~humble(X1)) & (? [X1] : humble(X1) | ! [X0] : (~rich(X0) | wise(X0))) [nnf transformation 26]
51. (? [X0] : (rich(X0) & ~wise(X0)) | ! [X1] : ~humble(X1)) & (? [X2] : humble(X2) | ! [X3] : (~rich(X3) | wise(X3))) [rectify 50]
52. ? [X0] : (rich(X0) & ~wise(X0)) => (rich(sK3) & ~wise(sK3)) [choice axiom]
53. ? [X2] : humble(X2) => humble(sK4) [choice axiom]
54. ((rich(sK3) & ~wise(sK3)) | ! [X1] : ~humble(X1)) & (humble(sK4) | ! [X3] : (~rich(X3) | wise(X3))) [skolemisation 51,53,52]
56. ! [X0] : (((wise(X0) & ~creative(X0)) | (~rich(X0) & brave(X0))) & ((rich(X0) | ~brave(X0)) | (~wise(X0) | creative(X0)))) [nnf transformation 12]
57. ! [X0] : (((wise(X0) & ~creative(X0)) | (~rich(X0) & brave(X0))) & (rich(X0) | ~brave(X0) | ~wise(X0) | creative(X0))) [flattening 56]
97. ~old(X0) | humble(X0) [cnf transformation 39]
115. ~wise(sK3) | ~humble(X1) [cnf transformation 54]
116. rich(sK3) | ~humble(X1) [cnf transformation 54]
125. wise(X0) | ~rich(X0) [cnf transformation 57]
151. old(mary) [cnf transformation 25]
197. 11 <=> old(mary) [avatar definition]
198. old(mary) <- (11) [avatar component clause 197]
241. 20 <=> ! [X1] : ~humble(X1) [avatar definition]
242. ~humble(X1) <- (20) [avatar component clause 241]
244. 21 <=> rich(sK3) [avatar definition]
246. rich(sK3) <- (21) [avatar component clause 244]
247. 20 | 21 [avatar split clause 116,244,241]
249. 22 <=> wise(sK3) [avatar definition]
251. ~wise(sK3) <- (~22) [avatar component clause 249]
252. 20 | ~22 [avatar split clause 115,249,241]
254. 23 <=> ! [X3] : (~rich(X3) | wise(X3)) [avatar definition]
255. ~rich(X3) | wise(X3) <- (23) [avatar component clause 254]
261. 23 [avatar split clause 125,254]
354. 11 [avatar split clause 151,197]
355. humble(mary) <- (11) [resolution 97,198]
356. $false <- (11, 20) [subsumption resolution 355,242]
357. ~11 | ~20 [avatar contradiction clause 356]
363. wise(sK3) <- (21, 23) [resolution 255,246]
364. $false <- (21, ~22, 23) [subsumption resolution 363,251]
365. ~21 | 22 | ~23 [avatar contradiction clause 364]
366. $false [avatar sat refutation 247,252,261,354,357,365]
% SZS output end Proof for 4848914940272353993376985
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not patient is calm or tall.
Everyone who is both not rich and not humble is both generous and wise and vice versa.
Everyone who is generous is not curious and vice versa.
Everyone who is rich or brave is not happy and vice versa.
Everyone who is not quiet or not old is calm and vice versa.
If john is not wise or curious then someone is not patient.
If paul is strong or old then paul is not tall and vice versa.
If someone is wise or kind then someone is both quiet and calm and vice versa.
If lucy is both happy and wise then susan is quiet and vice versa.
If alice is curious or brave then someone is tall or not humble.
Everyone who is not old or not humble is funny and vice versa.
If someone is either funny or not humble then someone is either brave or not calm and vice versa.
Everyone who is funny or not old is both wise and not strong and vice versa.
Everyone who is either strong or not funny is either not tall or tall and vice versa.
If fred is not tall or tall then someone is not curious and vice versa.
If someone is both not curious and happy then someone is both not humble and not wise.
Mary is both not quiet and not strong.
Alice is kind or not tall.
Someone is either not tall or humble.
Mary is not wise.
Alice is not tall. | Lucy is generous. | neutral | (![X]:((patient(X)|~patient(X))=>(calm(X)|tall(X))))&
(![X]:((~rich(X)&~humble(X))<=>(generous(X)&wise(X))))&
(![X]:(generous(X)<=>~curious(X)))&
(![X]:((rich(X)|brave(X))<=>~happy(X)))&
(![X]:((~quiet(X)|~old(X))<=>calm(X)))&
(((~wise(john)|curious(john)))=>(?[X]:(~patient(X))))&
(((strong(paul)|old(paul)))<=>(~tall(paul)))&
((?[X]:((wise(X)|kind(X))))<=>(?[X]:((quiet(X)&calm(X)))))&
(((happy(lucy)&wise(lucy)))<=>(quiet(susan)))&
(((curious(alice)|brave(alice)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((~old(X)|~humble(X))<=>funny(X)))&
((?[X]:((funny(X)<~>~humble(X))))<=>(?[X]:((brave(X)<~>~calm(X)))))&
(![X]:((funny(X)|~old(X))<=>(wise(X)&~strong(X))))&
(![X]:((strong(X)<~>~funny(X))<=>(~tall(X)<~>tall(X))))&
(((~tall(fred)|tall(fred)))<=>(?[X]:(~curious(X))))&
((?[X]:((~curious(X)&happy(X))))=>(?[X]:((~humble(X)&~wise(X)))))&
((~quiet(mary)&~strong(mary)))&
((kind(alice)|~tall(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
(~wise(mary))&
(~tall(alice)) | generous(lucy) | [] | null | 0 |
If someone is generous then mary is patient or wise.
Everyone who is not quiet or generous is both not tall and not wise.
If someone is either not tall or not generous then someone is generous or not rich and vice versa.
If paul is both not patient and not calm then paul is either not patient or not wise.
If john is not calm then fred is not tall or rich.
If fred is both funny and brave then someone is either not calm or curious and vice versa.
If paul is either curious or not generous then someone is not quiet.
If lucy is not creative then fred is both creative and not patient.
Everyone who is curious or not creative is either humble or patient.
If someone is both not patient and humble then susan is both happy and not humble.
If lucy is brave then someone is either not brave or not tall and vice versa.
If john is both kind and not kind then john is generous or calm.
If someone is both not happy and not wise then john is both not calm and creative and vice versa.
Everyone who is not kind or kind is not tall and vice versa.
If john is both not patient and not creative then john is happy and vice versa.
If fred is both not happy and not strong then mary is not generous or not creative.
Susan is not happy or not creative.
Mary is both not old and not calm.
Fred is either not happy or quiet.
Alice is not tall.
Someone is generous.
Lucy is creative.
Someone is either not calm or not creative.
Mary is kind. | Lucy is creative. | entailment | ((?[X]:(generous(X)))=>((patient(mary)|wise(mary))))&
(![X]:((~quiet(X)|generous(X))=>(~tall(X)&~wise(X))))&
((?[X]:((~tall(X)<~>~generous(X))))<=>(?[X]:((generous(X)|~rich(X)))))&
(((~patient(paul)&~calm(paul)))=>((~patient(paul)<~>~wise(paul))))&
((~calm(john))=>((~tall(fred)|rich(fred))))&
(((funny(fred)&brave(fred)))<=>(?[X]:((~calm(X)<~>curious(X)))))&
(((curious(paul)<~>~generous(paul)))=>(?[X]:(~quiet(X))))&
((~creative(lucy))=>((creative(fred)&~patient(fred))))&
(![X]:((curious(X)|~creative(X))=>(humble(X)<~>patient(X))))&
((?[X]:((~patient(X)&humble(X))))=>((happy(susan)&~humble(susan))))&
((brave(lucy))<=>(?[X]:((~brave(X)<~>~tall(X)))))&
(((kind(john)&~kind(john)))=>((generous(john)|calm(john))))&
((?[X]:((~happy(X)&~wise(X))))<=>((~calm(john)&creative(john))))&
(![X]:((~kind(X)|kind(X))<=>~tall(X)))&
(((~patient(john)&~creative(john)))<=>(happy(john)))&
(((~happy(fred)&~strong(fred)))=>((~generous(mary)|~creative(mary))))&
((~happy(susan)|~creative(susan)))&
((~old(mary)&~calm(mary)))&
((~happy(fred)<~>quiet(fred)))&
(~tall(alice))&
(?[X]:(generous(X)))&
(creative(lucy))&
(?[X]:((~calm(X)<~>~creative(X))))&
(kind(mary)) | creative(lucy) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4892918367838278328424632
% SZS output start Proof for 4892918367838278328424632
22. creative(lucy) [input p21]
25. ~creative(lucy) [input hypothesis]
127. creative(lucy) [cnf transformation 22]
131. ~creative(lucy) [cnf transformation 25]
242. 25 <=> creative(lucy) [avatar definition]
337. 25 [avatar split clause 127,242]
348. ~25 [avatar split clause 131,242]
349. $false [avatar sat refutation 337,348]
% SZS output end Proof for 4892918367838278328424632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If john is both generous and quiet then someone is not strong or kind and vice versa.
Everyone who is both not curious and not humble is humble and vice versa.
Everyone who is wise is not tall.
If someone is either quiet or not strong then someone is either tall or quiet.
Everyone who is not happy is both creative and not rich.
If someone is calm then someone is both strong and funny and vice versa.
If john is not rich then paul is either not happy or kind.
If alice is not rich then susan is creative or generous.
If john is both not happy and generous then someone is either not happy or brave.
If lucy is both not calm and strong then someone is either humble or tall.
If someone is either not strong or tall then lucy is both not old and not humble and vice versa.
If fred is kind then someone is either not creative or not brave.
Everyone who is kind or tall is both not curious and funny and vice versa.
Everyone who is either humble or quiet is both humble and not kind and vice versa.
If susan is both not humble and not generous then alice is either creative or wise and vice versa.
If someone is patient then someone is either not old or not generous.
Someone is both calm and not funny.
Paul is curious or not strong.
Mary is either brave or wise.
Alice is either brave or curious.
Paul is both calm and funny.
Someone is not tall.
John is funny or not generous. | Paul is not calm. | contradiction | (((generous(john)&quiet(john)))<=>(?[X]:((~strong(X)|kind(X)))))&
(![X]:((~curious(X)&~humble(X))<=>humble(X)))&
(![X]:(wise(X)=>~tall(X)))&
((?[X]:((quiet(X)<~>~strong(X))))=>(?[X]:((tall(X)<~>quiet(X)))))&
(![X]:(~happy(X)=>(creative(X)&~rich(X))))&
((?[X]:(calm(X)))<=>(?[X]:((strong(X)&funny(X)))))&
((~rich(john))=>((~happy(paul)<~>kind(paul))))&
((~rich(alice))=>((creative(susan)|generous(susan))))&
(((~happy(john)&generous(john)))=>(?[X]:((~happy(X)<~>brave(X)))))&
(((~calm(lucy)&strong(lucy)))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((~old(lucy)&~humble(lucy))))&
((kind(fred))=>(?[X]:((~creative(X)<~>~brave(X)))))&
(![X]:((kind(X)|tall(X))<=>(~curious(X)&funny(X))))&
(![X]:((humble(X)<~>quiet(X))<=>(humble(X)&~kind(X))))&
(((~humble(susan)&~generous(susan)))<=>((creative(alice)<~>wise(alice))))&
((?[X]:(patient(X)))=>(?[X]:((~old(X)<~>~generous(X)))))&
(?[X]:((calm(X)&~funny(X))))&
((curious(paul)|~strong(paul)))&
((brave(mary)<~>wise(mary)))&
((brave(alice)<~>curious(alice)))&
((calm(paul)&funny(paul)))&
(?[X]:(~tall(X)))&
((funny(john)|~generous(john))) | ~calm(paul) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9004776520967024652913735
% SZS output start Proof for 9004776520967024652913735
21. funny(paul) & calm(paul) [input p20]
24. ~calm(paul) [input hypothesis]
140. calm(paul) [cnf transformation 21]
144. ~calm(paul) [cnf transformation 24]
344. $false [subsumption resolution 144,140]
% SZS output end Proof for 9004776520967024652913735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not strong or patient is not creative or happy and vice versa. If john is not humble or not wise then someone is calm. Everyone who is not wise is either humble or funny and vice versa. If someone is either strong or not curious then fred is both not old and patient. Everyone who is not old is brave or not creative and vice versa. Everyone who is rich is quiet and vice versa. If paul is funny then someone is either not calm or not generous. Everyone who is either not strong or quiet is both not generous and rich. If lucy is wise or not tall then lucy is old and vice versa. If someone is strong then john is not creative. If someone is both quiet and curious then someone is either not funny or tall and vice versa. If john is both quiet and not humble then someone is both brave and not happy. If john is either not wise or not tall then someone is tall and vice versa. If mary is not happy or not wise then fred is patient. Everyone who is strong is both not brave and strong and vice versa. If someone is not brave or not patient then someone is both not quiet and funny and vice versa. John is either not happy or not old. Paul is wise or happy. Susan is either generous or quiet. John is not generous or not wise. Someone is both tall and not brave. Someone is either generous or not creative. Someone is either not strong or not old. | John is old. | contradiction | (![X]:((~strong(X)<~>patient(X))<=>(~creative(X)|happy(X))))&
(((~humble(john)|~wise(john)))=>(?[X]:(calm(X))))&
(![X]:(~wise(X)<=>(humble(X)<~>funny(X))))&
((?[X]:((strong(X)<~>~curious(X))))=>((~old(fred)&patient(fred))))&
(![X]:(~old(X)<=>(brave(X)|~creative(X))))&
(![X]:(rich(X)<=>quiet(X)))&
((funny(paul))=>(?[X]:((~calm(X)<~>~generous(X)))))&
(![X]:((~strong(X)<~>quiet(X))=>(~generous(X)&rich(X))))&
(((wise(lucy)|~tall(lucy)))<=>(old(lucy)))&
((?[X]:(strong(X)))=>(~creative(john)))&
((?[X]:((quiet(X)&curious(X))))<=>(?[X]:((~funny(X)<~>tall(X)))))&
(((quiet(john)&~humble(john)))=>(?[X]:((brave(X)&~happy(X)))))&
(((~wise(john)<~>~tall(john)))<=>(?[X]:(tall(X))))&
(((~happy(mary)|~wise(mary)))=>(patient(fred)))&
(![X]:(strong(X)<=>(~brave(X)&strong(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(?[X]:((~quiet(X)&funny(X)))))&
((~happy(john)<~>~old(john)))&
((wise(paul)|happy(paul)))&
((generous(susan)<~>quiet(susan)))&
((~generous(john)|~wise(john)))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:((generous(X)<~>~creative(X))))&
(?[X]:((~strong(X)<~>~old(X)))) | old(john) | [
"p4",
"p5",
"p7",
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 187207523547381038658470
% SZS output start Proof for 187207523547381038658470
5. ! [X0] : (~old(X0) <=> (~creative(X0) | brave(X0))) [input p4]
6. ! [X0] : (rich(X0) <=> quiet(X0)) [input p5]
8. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (rich(X0) & ~generous(X0))) [input p7]
10. ? [X0] : strong(X0) => ~creative(john) [input p9]
16. ? [X0] : (~patient(X0) | ~brave(X0)) <=> ? [X0] : (funny(X0) & ~quiet(X0)) [input p15]
21. ? [X0] : (~brave(X0) & tall(X0)) [input p20]
24. old(john) [input hypothesis]
26. ? [X0] : (~patient(X0) | ~brave(X0)) <=> ? [X1] : (funny(X1) & ~quiet(X1)) [rectify 16]
27. ! [X0] : (rich(X0) => quiet(X0)) [unused predicate definition removal 6]
30. ! [X0] : (quiet(X0) | ~rich(X0)) [ennf transformation 27]
32. ! [X0] : ((rich(X0) & ~generous(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 8]
33. ~creative(john) | ! [X0] : ~strong(X0) [ennf transformation 10]
43. ! [X0] : ((~old(X0) | (creative(X0) & ~brave(X0))) & ((~creative(X0) | brave(X0)) | old(X0))) [nnf transformation 5]
44. ! [X0] : ((~old(X0) | (creative(X0) & ~brave(X0))) & (~creative(X0) | brave(X0) | old(X0))) [flattening 43]
48. ! [X0] : ((rich(X0) & ~generous(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 32]
64. (? [X0] : (~patient(X0) | ~brave(X0)) | ! [X1] : (~funny(X1) | quiet(X1))) & (? [X1] : (funny(X1) & ~quiet(X1)) | ! [X0] : (patient(X0) & brave(X0))) [nnf transformation 26]
65. (? [X0] : (~patient(X0) | ~brave(X0)) | ! [X1] : (~funny(X1) | quiet(X1))) & (? [X2] : (funny(X2) & ~quiet(X2)) | ! [X3] : (patient(X3) & brave(X3))) [rectify 64]
66. ? [X0] : (~patient(X0) | ~brave(X0)) => (~patient(sK6) | ~brave(sK6)) [choice axiom]
67. ? [X2] : (funny(X2) & ~quiet(X2)) => (funny(sK7) & ~quiet(sK7)) [choice axiom]
68. ((~patient(sK6) | ~brave(sK6)) | ! [X1] : (~funny(X1) | quiet(X1))) & ((funny(sK7) & ~quiet(sK7)) | ! [X3] : (patient(X3) & brave(X3))) [skolemisation 65,67,66]
71. ? [X0] : (~brave(X0) & tall(X0)) => (~brave(sK8) & tall(sK8)) [choice axiom]
72. ~brave(sK8) & tall(sK8) [skolemisation 21,71]
97. ~old(X0) | creative(X0) [cnf transformation 44]
98. ~rich(X0) | quiet(X0) [cnf transformation 30]
103. rich(X0) | quiet(X0) | strong(X0) [cnf transformation 48]
108. ~creative(john) | ~strong(X0) [cnf transformation 33]
126. ~quiet(sK7) | brave(X3) [cnf transformation 68]
138. ~brave(sK8) [cnf transformation 72]
143. old(john) [cnf transformation 24]
190. quiet(X0) | strong(X0) [subsumption resolution 103,98]
207. 14 <=> ! [X0] : ~strong(X0) [avatar definition]
208. ~strong(X0) <- (14) [avatar component clause 207]
210. 15 <=> creative(john) [avatar definition]
213. 14 | ~15 [avatar split clause 108,210,207]
305. 36 <=> ! [X3] : brave(X3) [avatar definition]
306. brave(X3) <- (36) [avatar component clause 305]
309. 37 <=> quiet(sK7) [avatar definition]
311. ~quiet(sK7) <- (~37) [avatar component clause 309]
313. 36 | ~37 [avatar split clause 126,309,305]
319. 39 <=> old(john) [avatar definition]
321. old(john) <- (39) [avatar component clause 319]
368. 39 [avatar split clause 143,319]
375. creative(john) <- (39) [resolution 97,321]
378. 15 | ~39 [avatar split clause 375,319,210]
383. strong(sK7) <- (~37) [resolution 190,311]
387. $false <- (14, ~37) [subsumption resolution 383,208]
388. ~14 | 37 [avatar contradiction clause 387]
395. $false <- (36) [resolution 306,138]
398. ~36 [avatar contradiction clause 395]
399. $false [avatar sat refutation 213,313,368,378,388,398]
% SZS output end Proof for 187207523547381038658470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then mary is either not kind or not curious.
Everyone who is tall is calm and vice versa.
Everyone who is funny is either rich or quiet and vice versa.
Everyone who is not calm is patient and vice versa.
If john is curious or not wise then someone is either patient or rich and vice versa.
Everyone who is both not old and not calm is not quiet.
If susan is both happy and humble then someone is calm or funny.
If mary is both old and patient then someone is happy or quiet.
Everyone who is old is either not humble or not generous.
Everyone who is not tall is not brave or kind and vice versa.
Everyone who is either not kind or happy is generous.
If someone is both brave and not old then someone is either not patient or calm.
If lucy is old or not creative then alice is tall and vice versa.
Everyone who is either calm or quiet is either not brave or rich and vice versa.
Everyone who is not generous or not brave is not rich and vice versa.
Everyone who is both not brave and old is both funny and happy and vice versa.
Someone is not creative.
Someone is both kind and wise.
Susan is either not creative or not curious.
Someone is quiet.
Someone is either not old or tall.
Someone is old.
Mary is either not quiet or not wise. | Lucy is not old. | contradiction | ((?[X]:(old(X)))=>((~kind(mary)<~>~curious(mary))))&
(![X]:(tall(X)<=>calm(X)))&
(![X]:(funny(X)<=>(rich(X)<~>quiet(X))))&
(![X]:(~calm(X)<=>patient(X)))&
(((curious(john)|~wise(john)))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((~old(X)&~calm(X))=>~quiet(X)))&
(((happy(susan)&humble(susan)))=>(?[X]:((calm(X)|funny(X)))))&
(((old(mary)&patient(mary)))=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:(old(X)=>(~humble(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>(~brave(X)|kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>generous(X)))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((~patient(X)<~>calm(X)))))&
(((old(lucy)|~creative(lucy)))<=>(tall(alice)))&
(![X]:((calm(X)<~>quiet(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((~generous(X)|~brave(X))<=>~rich(X)))&
(![X]:((~brave(X)&old(X))<=>(funny(X)&happy(X))))&
(?[X]:(~creative(X)))&
(?[X]:((kind(X)&wise(X))))&
((~creative(susan)<~>~curious(susan)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>tall(X))))&
(?[X]:(old(X)))&
((~quiet(mary)<~>~wise(mary))) | ~old(lucy) | [
"p1",
"p3",
"p5",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 891530469900020208974981
% SZS output start Proof for 891530469900020208974981
2. ! [X0] : (tall(X0) <=> calm(X0)) [input p1]
4. ! [X0] : (~calm(X0) <=> patient(X0)) [input p3]
6. ! [X0] : ((~calm(X0) & ~old(X0)) => ~quiet(X0)) [input p5]
10. ! [X0] : (~tall(X0) <=> (kind(X0) | ~brave(X0))) [input p9]
12. ? [X0] : (~old(X0) & brave(X0)) => ? [X0] : (~patient(X0) <~> calm(X0)) [input p11]
14. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> (~brave(X0) <~> rich(X0))) [input p13]
15. ! [X0] : ((~brave(X0) | ~generous(X0)) <=> ~rich(X0)) [input p14]
24. ~old(lucy) [input hypothesis]
25. ? [X0] : (~old(X0) & brave(X0)) => ? [X1] : (~patient(X1) <~> calm(X1)) [rectify 12]
27. ! [X0] : (~quiet(X0) | (calm(X0) | old(X0))) [ennf transformation 6]
28. ! [X0] : (~quiet(X0) | calm(X0) | old(X0)) [flattening 27]
35. ? [X1] : (~patient(X1) <~> calm(X1)) | ! [X0] : (old(X0) | ~brave(X0)) [ennf transformation 25]
37. ! [X0] : ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0))) [nnf transformation 2]
39. ! [X0] : ((~calm(X0) | ~patient(X0)) & (patient(X0) | calm(X0))) [nnf transformation 4]
50. ! [X0] : ((~tall(X0) | (~kind(X0) & brave(X0))) & ((kind(X0) | ~brave(X0)) | tall(X0))) [nnf transformation 10]
51. ! [X0] : ((~tall(X0) | (~kind(X0) & brave(X0))) & (kind(X0) | ~brave(X0) | tall(X0))) [flattening 50]
53. ? [X1] : ((~calm(X1) | patient(X1)) & (calm(X1) | ~patient(X1))) | ! [X0] : (old(X0) | ~brave(X0)) [nnf transformation 35]
54. ? [X0] : ((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) | ! [X1] : (old(X1) | ~brave(X1)) [rectify 53]
55. ? [X0] : ((~calm(X0) | patient(X0)) & (calm(X0) | ~patient(X0))) => ((~calm(sK3) | patient(sK3)) & (calm(sK3) | ~patient(sK3))) [choice axiom]
56. ((~calm(sK3) | patient(sK3)) & (calm(sK3) | ~patient(sK3))) | ! [X1] : (old(X1) | ~brave(X1)) [skolemisation 54,55]
59. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0)))) & (((~rich(X0) | brave(X0)) & (rich(X0) | ~brave(X0))) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 14]
60. ! [X0] : (((~brave(X0) | ~generous(X0)) | rich(X0)) & (~rich(X0) | (brave(X0) & generous(X0)))) [nnf transformation 15]
61. ! [X0] : ((~brave(X0) | ~generous(X0) | rich(X0)) & (~rich(X0) | (brave(X0) & generous(X0)))) [flattening 60]
80. ~calm(X0) | tall(X0) [cnf transformation 37]
85. patient(X0) | calm(X0) [cnf transformation 39]
86. ~patient(X0) | ~calm(X0) [cnf transformation 39]
93. ~quiet(X0) | calm(X0) | old(X0) [cnf transformation 28]
99. ~tall(X0) | brave(X0) [cnf transformation 51]
103. calm(sK3) | ~patient(sK3) | old(X1) | ~brave(X1) [cnf transformation 56]
104. ~calm(sK3) | patient(sK3) | old(X1) | ~brave(X1) [cnf transformation 56]
112. brave(X0) | calm(X0) | rich(X0) | quiet(X0) [cnf transformation 59]
117. ~rich(X0) | brave(X0) [cnf transformation 61]
134. ~old(lucy) [cnf transformation 24]
210. patient(sK3) | old(X1) | ~brave(X1) [subsumption resolution 104,85]
212. 18 <=> ! [X1] : (old(X1) | ~brave(X1)) [avatar definition]
213. ~brave(X1) | old(X1) <- (18) [avatar component clause 212]
215. 19 <=> patient(sK3) [avatar definition]
218. 18 | 19 [avatar split clause 210,215,212]
219. ~patient(sK3) | old(X1) | ~brave(X1) [subsumption resolution 103,86]
220. 18 | ~19 [avatar split clause 219,215,212]
226. 21 <=> old(lucy) [avatar definition]
227. ~old(lucy) <- (~21) [avatar component clause 226]
266. ~21 [avatar split clause 134,226]
504. calm(X5) | rich(X5) | quiet(X5) | old(X5) <- (18) [resolution 112,213]
509. rich(X5) | calm(X5) | old(X5) <- (18) [subsumption resolution 504,93]
573. calm(X3) | old(X3) | brave(X3) <- (18) [resolution 509,117]
579. calm(X3) | old(X3) <- (18) [subsumption resolution 573,213]
760. tall(X0) | old(X0) <- (18) [resolution 579,80]
861. old(X1) | brave(X1) <- (18) [resolution 760,99]
866. old(X1) <- (18) [subsumption resolution 861,213]
896. $false <- (18, ~21) [resolution 866,227]
899. ~18 | 21 [avatar contradiction clause 896]
900. $false [avatar sat refutation 218,220,266,899]
% SZS output end Proof for 891530469900020208974981
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise is either not strong or tall and vice versa.
If mary is not funny or calm then lucy is humble or wise and vice versa.
Everyone who is quiet is generous or not quiet and vice versa.
If someone is not creative or not curious then fred is either not rich or brave and vice versa.
Everyone who is old is not generous or kind and vice versa.
If someone is either funny or rich then lucy is not humble and vice versa.
If someone is both not tall and not brave then alice is both happy and wise and vice versa.
If someone is not creative then susan is curious and vice versa.
Everyone who is not tall is not happy.
Everyone who is both generous and old is either curious or not quiet and vice versa.
Everyone who is both not wise and not kind is either patient or not curious and vice versa.
Everyone who is either strong or not creative is either funny or old.
If someone is either not wise or creative then someone is not tall or strong and vice versa.
Everyone who is both curious and not calm is not calm or strong and vice versa.
If someone is either brave or not strong then someone is old or happy.
If someone is brave or not calm then mary is both brave and not strong.
Someone is generous.
Someone is either not humble or not happy.
Fred is either not funny or tall.
Someone is either curious or rich.
Lucy is tall.
Alice is either happy or not rich.
Someone is wise or not rich.
Someone is both not happy and curious. | Fred is generous. | entailment | (![X]:(wise(X)<=>(~strong(X)<~>tall(X))))&
(((~funny(mary)|calm(mary)))<=>((humble(lucy)|wise(lucy))))&
(![X]:(quiet(X)<=>(generous(X)|~quiet(X))))&
((?[X]:((~creative(X)|~curious(X))))<=>((~rich(fred)<~>brave(fred))))&
(![X]:(old(X)<=>(~generous(X)|kind(X))))&
((?[X]:((funny(X)<~>rich(X))))<=>(~humble(lucy)))&
((?[X]:((~tall(X)&~brave(X))))<=>((happy(alice)&wise(alice))))&
((?[X]:(~creative(X)))<=>(curious(susan)))&
(![X]:(~tall(X)=>~happy(X)))&
(![X]:((generous(X)&old(X))<=>(curious(X)<~>~quiet(X))))&
(![X]:((~wise(X)&~kind(X))<=>(patient(X)<~>~curious(X))))&
(![X]:((strong(X)<~>~creative(X))=>(funny(X)<~>old(X))))&
((?[X]:((~wise(X)<~>creative(X))))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((curious(X)&~calm(X))<=>(~calm(X)|strong(X))))&
((?[X]:((brave(X)<~>~strong(X))))=>(?[X]:((old(X)|happy(X)))))&
((?[X]:((brave(X)|~calm(X))))=>((brave(mary)&~strong(mary))))&
(?[X]:(generous(X)))&
(?[X]:((~humble(X)<~>~happy(X))))&
((~funny(fred)<~>tall(fred)))&
(?[X]:((curious(X)<~>rich(X))))&
(tall(lucy))&
((happy(alice)<~>~rich(alice)))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((~happy(X)&curious(X)))) | generous(fred) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 697804414418595365714376
% SZS output start Proof for 697804414418595365714376
3. ! [X0] : (quiet(X0) <=> (~quiet(X0) | generous(X0))) [input p2]
25. ~generous(fred) [input hypothesis]
35. ! [X0] : ((quiet(X0) | (quiet(X0) & ~generous(X0))) & ((~quiet(X0) | generous(X0)) | ~quiet(X0))) [nnf transformation 3]
36. ! [X0] : ((quiet(X0) | (quiet(X0) & ~generous(X0))) & (~quiet(X0) | generous(X0) | ~quiet(X0))) [flattening 35]
94. ~quiet(X0) | generous(X0) | ~quiet(X0) [cnf transformation 36]
96. quiet(X0) | quiet(X0) [cnf transformation 36]
163. ~generous(fred) [cnf transformation 25]
164. ~quiet(X0) | generous(X0) [duplicate literal removal 94]
165. quiet(X0) [duplicate literal removal 96]
186. generous(X0) [subsumption resolution 164,165]
383. $false [subsumption resolution 163,186]
% SZS output end Proof for 697804414418595365714376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is either not old or patient.
If alice is both happy and funny then someone is either calm or not happy and vice versa.
Everyone who is generous is not patient or happy.
Everyone who is kind is not patient or tall and vice versa.
Everyone who is both not kind and not tall is generous or rich and vice versa.
Everyone who is not calm or patient is either not kind or generous.
If someone is not humble or not generous then someone is not strong and vice versa.
If someone is either funny or not calm then mary is both not humble and not strong and vice versa.
Everyone who is either not rich or funny is either tall or generous.
Everyone who is creative or not strong is both tall and old and vice versa.
If paul is either happy or not funny then someone is either tall or not strong and vice versa.
Everyone who is either not patient or happy is rich and vice versa.
Everyone who is both rich and not strong is happy.
If someone is old then mary is either not quiet or not wise and vice versa.
If someone is both tall and kind then someone is either not strong or strong and vice versa.
Everyone who is not kind or not old is both not brave and not strong and vice versa.
Lucy is either not rich or strong.
Lucy is not happy or calm.
Fred is both not generous and not wise.
Susan is not old or creative.
Someone is not old or tall.
Alice is either not humble or not creative.
Someone is either not creative or calm. | Lucy is patient. | contradiction | ((?[X]:(~curious(X)))=>(?[X]:((~old(X)<~>patient(X)))))&
(((happy(alice)&funny(alice)))<=>(?[X]:((calm(X)<~>~happy(X)))))&
(![X]:(generous(X)=>(~patient(X)|happy(X))))&
(![X]:(kind(X)<=>(~patient(X)|tall(X))))&
(![X]:((~kind(X)&~tall(X))<=>(generous(X)|rich(X))))&
(![X]:((~calm(X)|patient(X))=>(~kind(X)<~>generous(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((funny(X)<~>~calm(X))))<=>((~humble(mary)&~strong(mary))))&
(![X]:((~rich(X)<~>funny(X))=>(tall(X)<~>generous(X))))&
(![X]:((creative(X)|~strong(X))<=>(tall(X)&old(X))))&
(((happy(paul)<~>~funny(paul)))<=>(?[X]:((tall(X)<~>~strong(X)))))&
(![X]:((~patient(X)<~>happy(X))<=>rich(X)))&
(![X]:((rich(X)&~strong(X))=>happy(X)))&
((?[X]:(old(X)))<=>((~quiet(mary)<~>~wise(mary))))&
((?[X]:((tall(X)&kind(X))))<=>(?[X]:((~strong(X)<~>strong(X)))))&
(![X]:((~kind(X)|~old(X))<=>(~brave(X)&~strong(X))))&
((~rich(lucy)<~>strong(lucy)))&
((~happy(lucy)|calm(lucy)))&
((~generous(fred)&~wise(fred)))&
((~old(susan)|creative(susan)))&
(?[X]:((~old(X)|tall(X))))&
((~humble(alice)<~>~creative(alice)))&
(?[X]:((~creative(X)<~>calm(X)))) | patient(lucy) | [
"p3",
"p4",
"p5",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1095264022152325946191678
% SZS output start Proof for 1095264022152325946191678
4. ! [X0] : (kind(X0) <=> (tall(X0) | ~patient(X0))) [input p3]
5. ! [X0] : ((~tall(X0) & ~kind(X0)) <=> (rich(X0) | generous(X0))) [input p4]
6. ! [X0] : ((patient(X0) | ~calm(X0)) => (~kind(X0) <~> generous(X0))) [input p5]
10. ! [X0] : ((~strong(X0) | creative(X0)) <=> (old(X0) & tall(X0))) [input p9]
16. ! [X0] : ((~old(X0) | ~kind(X0)) <=> (~strong(X0) & ~brave(X0))) [input p15]
24. patient(lucy) [input hypothesis]
31. ! [X0] : ((~kind(X0) <~> generous(X0)) | (~patient(X0) & calm(X0))) [ennf transformation 6]
40. ! [X0] : ((kind(X0) | (~tall(X0) & patient(X0))) & ((tall(X0) | ~patient(X0)) | ~kind(X0))) [nnf transformation 4]
41. ! [X0] : ((kind(X0) | (~tall(X0) & patient(X0))) & (tall(X0) | ~patient(X0) | ~kind(X0))) [flattening 40]
42. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~rich(X0) & ~generous(X0))) & ((rich(X0) | generous(X0)) | (tall(X0) | kind(X0)))) [nnf transformation 5]
43. ! [X0] : (((~tall(X0) & ~kind(X0)) | (~rich(X0) & ~generous(X0))) & (rich(X0) | generous(X0) | tall(X0) | kind(X0))) [flattening 42]
44. ! [X0] : (((~generous(X0) | kind(X0)) & (generous(X0) | ~kind(X0))) | (~patient(X0) & calm(X0))) [nnf transformation 31]
56. ! [X0] : (((~strong(X0) | creative(X0)) | (~old(X0) | ~tall(X0))) & ((old(X0) & tall(X0)) | (strong(X0) & ~creative(X0)))) [nnf transformation 10]
57. ! [X0] : ((~strong(X0) | creative(X0) | ~old(X0) | ~tall(X0)) & ((old(X0) & tall(X0)) | (strong(X0) & ~creative(X0)))) [flattening 56]
72. ! [X0] : (((~old(X0) | ~kind(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (old(X0) & kind(X0)))) [nnf transformation 16]
73. ! [X0] : ((~old(X0) | ~kind(X0) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | (old(X0) & kind(X0)))) [flattening 72]
89. kind(X0) | patient(X0) [cnf transformation 41]
90. ~tall(X0) | kind(X0) [cnf transformation 41]
92. ~kind(X0) | ~generous(X0) [cnf transformation 43]
97. generous(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 44]
99. ~generous(X0) | kind(X0) | ~patient(X0) [cnf transformation 44]
114. strong(X0) | tall(X0) [cnf transformation 57]
143. ~strong(X0) | kind(X0) [cnf transformation 73]
157. patient(lucy) [cnf transformation 24]
191. ~generous(X0) | kind(X0) [subsumption resolution 99,89]
192. ~generous(X0) [subsumption resolution 191,92]
193. ~kind(X0) | ~patient(X0) [subsumption resolution 97,192]
365. kind(X1) | tall(X1) [resolution 143,114]
378. kind(X1) [subsumption resolution 365,90]
418. ~patient(X2) [resolution 378,193]
465. $false [resolution 418,157]
% SZS output end Proof for 1095264022152325946191678
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not old then someone is not curious or creative and vice versa. Everyone who is not quiet or not patient is both brave and not generous and vice versa. Everyone who is old is either old or not happy and vice versa. If someone is not humble or old then mary is both curious and brave and vice versa. If susan is either not rich or not wise then someone is not rich and vice versa. Everyone who is tall or funny is old or quiet. If lucy is not kind then someone is not creative or curious and vice versa. Everyone who is either not strong or not rich is either not brave or not patient and vice versa. If someone is either not funny or kind then someone is kind and vice versa. If alice is not patient or old then alice is both curious and creative. Everyone who is not patient is both tall and patient. Everyone who is not kind or kind is either not strong or patient and vice versa. Everyone who is not creative or strong is either not strong or not humble and vice versa. If someone is either strong or humble then mary is either humble or not wise and vice versa. If someone is both generous and not patient then john is both not wise and funny. If someone is either patient or creative then someone is either humble or wise. Lucy is calm. Someone is either not old or not kind. Someone is both not kind and calm. Susan is humble or wise. Alice is not wise or not brave. Someone is both wise and creative. Fred is not humble or generous. | Fred is not strong. | contradiction | ((?[X]:((happy(X)&~old(X))))<=>(?[X]:((~curious(X)|creative(X)))))&
(![X]:((~quiet(X)|~patient(X))<=>(brave(X)&~generous(X))))&
(![X]:(old(X)<=>(old(X)<~>~happy(X))))&
((?[X]:((~humble(X)|old(X))))<=>((curious(mary)&brave(mary))))&
(((~rich(susan)<~>~wise(susan)))<=>(?[X]:(~rich(X))))&
(![X]:((tall(X)|funny(X))=>(old(X)|quiet(X))))&
((~kind(lucy))<=>(?[X]:((~creative(X)|curious(X)))))&
(![X]:((~strong(X)<~>~rich(X))<=>(~brave(X)<~>~patient(X))))&
((?[X]:((~funny(X)<~>kind(X))))<=>(?[X]:(kind(X))))&
(((~patient(alice)|old(alice)))=>((curious(alice)&creative(alice))))&
(![X]:(~patient(X)=>(tall(X)&patient(X))))&
(![X]:((~kind(X)|kind(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((~creative(X)|strong(X))<=>(~strong(X)<~>~humble(X))))&
((?[X]:((strong(X)<~>humble(X))))<=>((humble(mary)<~>~wise(mary))))&
((?[X]:((generous(X)&~patient(X))))=>((~wise(john)&funny(john))))&
((?[X]:((patient(X)<~>creative(X))))=>(?[X]:((humble(X)<~>wise(X)))))&
(calm(lucy))&
(?[X]:((~old(X)<~>~kind(X))))&
(?[X]:((~kind(X)&calm(X))))&
((humble(susan)|wise(susan)))&
((~wise(alice)|~brave(alice)))&
(?[X]:((wise(X)&creative(X))))&
((~humble(fred)|generous(fred))) | ~strong(fred) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 684664092621467692773602
% SZS output start Proof for 684664092621467692773602
11. ! [X0] : (~patient(X0) => (patient(X0) & tall(X0))) [input p10]
12. ! [X0] : ((kind(X0) | ~kind(X0)) <=> (~strong(X0) <~> patient(X0))) [input p11]
24. ~strong(fred) [input hypothesis]
33. ! [X0] : ((patient(X0) & tall(X0)) | patient(X0)) [ennf transformation 11]
63. ! [X0] : (((kind(X0) | ~kind(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~kind(X0) & kind(X0)))) [nnf transformation 12]
64. ! [X0] : ((kind(X0) | ~kind(X0) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~kind(X0) & kind(X0)))) [flattening 63]
127. patient(X0) | patient(X0) [cnf transformation 33]
130. ~patient(X0) | strong(X0) | kind(X0) [cnf transformation 64]
131. ~patient(X0) | strong(X0) | ~kind(X0) [cnf transformation 64]
162. ~strong(fred) [cnf transformation 24]
165. patient(X0) [duplicate literal removal 127]
315. strong(X0) | ~kind(X0) [subsumption resolution 131,165]
316. strong(X0) | kind(X0) [subsumption resolution 130,165]
317. strong(X0) [subsumption resolution 316,315]
350. $false [subsumption resolution 162,317]
% SZS output end Proof for 684664092621467692773602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both happy and not happy.
If susan is both curious and patient then someone is either calm or not rich.
Everyone who is both not happy and curious is both not tall and rich.
Everyone who is brave or not patient is not funny and vice versa.
Everyone who is tall is both not generous and not quiet.
Everyone who is not creative is either kind or creative.
Everyone who is either not calm or not tall is either not strong or not tall and vice versa.
Everyone who is not brave or not patient is humble and vice versa.
Everyone who is not brave or patient is creative or humble.
Everyone who is either tall or not funny is either brave or funny and vice versa.
Everyone who is either kind or quiet is quiet and vice versa.
Everyone who is quiet or funny is not creative and vice versa.
Everyone who is both not wise and tall is both not curious and not patient and vice versa.
Everyone who is tall or not old is not quiet or not old.
Everyone who is both not kind and not old is either not humble or not rich and vice versa.
If someone is kind or humble then alice is quiet.
Someone is either curious or not brave.
Susan is happy.
Someone is both not rich and not curious.
Someone is not happy or tall.
Susan is both happy and calm.
Someone is not calm or patient. | Susan is not funny. | entailment | (![X]:(~strong(X)=>(happy(X)&~happy(X))))&
(((curious(susan)&patient(susan)))=>(?[X]:((calm(X)<~>~rich(X)))))&
(![X]:((~happy(X)&curious(X))=>(~tall(X)&rich(X))))&
(![X]:((brave(X)|~patient(X))<=>~funny(X)))&
(![X]:(tall(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~creative(X)=>(kind(X)<~>creative(X))))&
(![X]:((~calm(X)<~>~tall(X))<=>(~strong(X)<~>~tall(X))))&
(![X]:((~brave(X)|~patient(X))<=>humble(X)))&
(![X]:((~brave(X)|patient(X))=>(creative(X)|humble(X))))&
(![X]:((tall(X)<~>~funny(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)<~>quiet(X))<=>quiet(X)))&
(![X]:((quiet(X)|funny(X))<=>~creative(X)))&
(![X]:((~wise(X)&tall(X))<=>(~curious(X)&~patient(X))))&
(![X]:((tall(X)|~old(X))=>(~quiet(X)|~old(X))))&
(![X]:((~kind(X)&~old(X))<=>(~humble(X)<~>~rich(X))))&
((?[X]:((kind(X)|humble(X))))=>(quiet(alice)))&
(?[X]:((curious(X)<~>~brave(X))))&
(happy(susan))&
(?[X]:((~rich(X)&~curious(X))))&
(?[X]:((~happy(X)|tall(X))))&
((happy(susan)&calm(susan)))&
(?[X]:((~calm(X)|patient(X)))) | ~funny(susan) | [
"p3",
"p5",
"p7",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 54612088101067598960296
% SZS output start Proof for 54612088101067598960296
4. ! [X0] : ((~patient(X0) | brave(X0)) <=> ~funny(X0)) [input p3]
6. ! [X0] : (~creative(X0) => (kind(X0) <~> creative(X0))) [input p5]
8. ! [X0] : ((~patient(X0) | ~brave(X0)) <=> humble(X0)) [input p7]
11. ! [X0] : ((kind(X0) <~> quiet(X0)) <=> quiet(X0)) [input p10]
12. ! [X0] : ((funny(X0) | quiet(X0)) <=> ~creative(X0)) [input p11]
16. ? [X0] : (humble(X0) | kind(X0)) => quiet(alice) [input p15]
23. funny(susan) [input hypothesis]
31. ! [X0] : ((kind(X0) <~> creative(X0)) | creative(X0)) [ennf transformation 6]
36. quiet(alice) | ! [X0] : (~humble(X0) & ~kind(X0)) [ennf transformation 16]
40. ! [X0] : (((~patient(X0) | brave(X0)) | funny(X0)) & (~funny(X0) | (patient(X0) & ~brave(X0)))) [nnf transformation 4]
41. ! [X0] : ((~patient(X0) | brave(X0) | funny(X0)) & (~funny(X0) | (patient(X0) & ~brave(X0)))) [flattening 40]
42. ! [X0] : (((~creative(X0) | ~kind(X0)) & (creative(X0) | kind(X0))) | creative(X0)) [nnf transformation 31]
44. ! [X0] : (((~patient(X0) | ~brave(X0)) | ~humble(X0)) & (humble(X0) | (patient(X0) & brave(X0)))) [nnf transformation 8]
45. ! [X0] : ((~patient(X0) | ~brave(X0) | ~humble(X0)) & (humble(X0) | (patient(X0) & brave(X0)))) [flattening 44]
47. ! [X0] : ((((~quiet(X0) | ~kind(X0)) & (quiet(X0) | kind(X0))) | ~quiet(X0)) & (quiet(X0) | ((kind(X0) | ~quiet(X0)) & (quiet(X0) | ~kind(X0))))) [nnf transformation 11]
48. ! [X0] : (((funny(X0) | quiet(X0)) | creative(X0)) & (~creative(X0) | (~funny(X0) & ~quiet(X0)))) [nnf transformation 12]
49. ! [X0] : ((funny(X0) | quiet(X0) | creative(X0)) & (~creative(X0) | (~funny(X0) & ~quiet(X0)))) [flattening 48]
69. ~funny(X0) | ~brave(X0) [cnf transformation 41]
73. creative(X0) | kind(X0) | creative(X0) [cnf transformation 42]
83. humble(X0) | brave(X0) [cnf transformation 45]
99. ~quiet(X0) | ~kind(X0) | ~quiet(X0) [cnf transformation 47]
100. ~creative(X0) | ~quiet(X0) [cnf transformation 49]
116. quiet(alice) | ~humble(X0) [cnf transformation 36]
126. funny(susan) [cnf transformation 23]
128. ~kind(X0) | ~quiet(X0) [duplicate literal removal 99]
137. kind(X0) | creative(X0) [duplicate literal removal 73]
168. 5 <=> ! [X0] : ~humble(X0) [avatar definition]
169. ~humble(X0) <- (5) [avatar component clause 168]
171. 6 <=> quiet(alice) [avatar definition]
173. quiet(alice) <- (6) [avatar component clause 171]
174. 5 | 6 [avatar split clause 116,171,168]
196. ~brave(susan) [resolution 69,126]
199. brave(X0) <- (5) [resolution 83,169]
201. $false <- (5) [resolution 199,196]
202. ~5 [avatar contradiction clause 201]
205. creative(X0) | ~quiet(X0) [resolution 137,128]
207. ~quiet(X0) [subsumption resolution 205,100]
211. $false <- (6) [resolution 207,173]
212. ~6 [avatar contradiction clause 211]
213. $false [avatar sat refutation 174,202,212]
% SZS output end Proof for 54612088101067598960296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not old and not wise then someone is both not old and not curious and vice versa.
Everyone who is not brave or quiet is either not old or not rich and vice versa.
Everyone who is both tall and not rich is not old and vice versa.
If mary is either not creative or wise then someone is either humble or creative.
Everyone who is both not curious and happy is not tall and vice versa.
Everyone who is both creative and not funny is not quiet or not wise and vice versa.
If someone is both old and not wise then someone is either rich or not creative.
Everyone who is not rich or not kind is either not old or curious and vice versa.
Everyone who is both not tall and not curious is not kind or not calm.
Everyone who is not calm is either not patient or not strong.
If alice is patient or funny then someone is either not patient or strong.
If lucy is both patient and not generous then someone is funny or kind.
Everyone who is not brave or not wise is not old and vice versa.
If mary is both not kind and funny then paul is both not tall and generous.
If someone is strong then someone is humble and vice versa.
Everyone who is either quiet or not generous is not happy or kind.
Someone is both happy and creative.
Lucy is either wise or not happy.
Someone is not kind.
Mary is humble.
Someone is not humble.
Mary is not curious. | Paul is funny. | contradiction | ((?[X]:((~old(X)&~wise(X))))<=>(?[X]:((~old(X)&~curious(X)))))&
(![X]:((~brave(X)|quiet(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((tall(X)&~rich(X))<=>~old(X)))&
(((~creative(mary)<~>wise(mary)))=>(?[X]:((humble(X)<~>creative(X)))))&
(![X]:((~curious(X)&happy(X))<=>~tall(X)))&
(![X]:((creative(X)&~funny(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((old(X)&~wise(X))))=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((~rich(X)|~kind(X))<=>(~old(X)<~>curious(X))))&
(![X]:((~tall(X)&~curious(X))=>(~kind(X)|~calm(X))))&
(![X]:(~calm(X)=>(~patient(X)<~>~strong(X))))&
(((patient(alice)|funny(alice)))=>(?[X]:((~patient(X)<~>strong(X)))))&
(((patient(lucy)&~generous(lucy)))=>(?[X]:((funny(X)|kind(X)))))&
(![X]:((~brave(X)|~wise(X))<=>~old(X)))&
(((~kind(mary)&funny(mary)))=>((~tall(paul)&generous(paul))))&
((?[X]:(strong(X)))<=>(?[X]:(humble(X))))&
(![X]:((quiet(X)<~>~generous(X))=>(~happy(X)|kind(X))))&
(?[X]:((happy(X)&creative(X))))&
((wise(lucy)<~>~happy(lucy)))&
(?[X]:(~kind(X)))&
(humble(mary))&
(?[X]:(~humble(X)))&
(~curious(mary)) | funny(paul) | [
"p1",
"p2",
"p4",
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4607215985000332693402327
% SZS output start Proof for 4607215985000332693402327
2. ! [X0] : ((quiet(X0) | ~brave(X0)) <=> (~old(X0) <~> ~rich(X0))) [input p1]
3. ! [X0] : ((~rich(X0) & tall(X0)) <=> ~old(X0)) [input p2]
5. ! [X0] : ((happy(X0) & ~curious(X0)) <=> ~tall(X0)) [input p4]
6. ! [X0] : ((~funny(X0) & creative(X0)) <=> (~wise(X0) | ~quiet(X0))) [input p5]
8. ! [X0] : ((~kind(X0) | ~rich(X0)) <=> (~old(X0) <~> curious(X0))) [input p7]
23. funny(paul) [input hypothesis]
44. ! [X0] : (((quiet(X0) | ~brave(X0)) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) & (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~quiet(X0) & brave(X0)))) [nnf transformation 2]
45. ! [X0] : ((quiet(X0) | ~brave(X0) | ((~old(X0) | rich(X0)) & (~rich(X0) | old(X0)))) & (((rich(X0) | old(X0)) & (~rich(X0) | ~old(X0))) | (~quiet(X0) & brave(X0)))) [flattening 44]
46. ! [X0] : (((~rich(X0) & tall(X0)) | old(X0)) & (~old(X0) | (rich(X0) | ~tall(X0)))) [nnf transformation 3]
47. ! [X0] : (((~rich(X0) & tall(X0)) | old(X0)) & (~old(X0) | rich(X0) | ~tall(X0))) [flattening 46]
51. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | (~happy(X0) | curious(X0)))) [nnf transformation 5]
52. ! [X0] : (((happy(X0) & ~curious(X0)) | tall(X0)) & (~tall(X0) | ~happy(X0) | curious(X0))) [flattening 51]
53. ! [X0] : (((~funny(X0) & creative(X0)) | (wise(X0) & quiet(X0))) & ((~wise(X0) | ~quiet(X0)) | (funny(X0) | ~creative(X0)))) [nnf transformation 6]
54. ! [X0] : (((~funny(X0) & creative(X0)) | (wise(X0) & quiet(X0))) & (~wise(X0) | ~quiet(X0) | funny(X0) | ~creative(X0))) [flattening 53]
59. ! [X0] : (((~kind(X0) | ~rich(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (kind(X0) & rich(X0)))) [nnf transformation 8]
60. ! [X0] : ((~kind(X0) | ~rich(X0) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (kind(X0) & rich(X0)))) [flattening 59]
87. ~rich(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 45]
89. ~quiet(X0) | old(X0) | rich(X0) [cnf transformation 45]
92. ~tall(X0) | rich(X0) | ~old(X0) [cnf transformation 47]
94. ~rich(X0) | old(X0) [cnf transformation 47]
100. ~curious(X0) | tall(X0) [cnf transformation 52]
105. ~funny(X0) | quiet(X0) [cnf transformation 54]
109. ~old(X0) | curious(X0) | rich(X0) [cnf transformation 60]
140. funny(paul) [cnf transformation 23]
255. 25 <=> tall(paul) [avatar definition]
256. tall(paul) <- (25) [avatar component clause 255]
294. quiet(paul) [resolution 105,140]
304. old(paul) | rich(paul) [resolution 89,294]
307. old(paul) [subsumption resolution 304,94]
347. curious(paul) | rich(paul) [resolution 307,109]
351. 38 <=> rich(paul) [avatar definition]
352. ~rich(paul) <- (~38) [avatar component clause 351]
353. rich(paul) <- (38) [avatar component clause 351]
355. 39 <=> curious(paul) [avatar definition]
357. curious(paul) <- (39) [avatar component clause 355]
358. 38 | 39 [avatar split clause 347,355,351]
420. ~old(paul) | ~quiet(paul) <- (38) [resolution 353,87]
423. ~quiet(paul) <- (38) [subsumption resolution 420,307]
424. $false <- (38) [subsumption resolution 423,294]
425. ~38 [avatar contradiction clause 424]
470. tall(paul) <- (39) [resolution 357,100]
471. 25 | ~39 [avatar split clause 470,355,255]
472. rich(paul) | ~old(paul) <- (25) [resolution 256,92]
473. ~old(paul) <- (25, ~38) [subsumption resolution 472,352]
474. $false <- (25, ~38) [subsumption resolution 473,307]
475. ~25 | 38 [avatar contradiction clause 474]
476. $false [avatar sat refutation 358,425,471,475]
% SZS output end Proof for 4607215985000332693402327
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not curious and calm is both humble and patient and vice versa. If someone is not rich or brave then lucy is both old and wise. Everyone who is not humble is generous or tall. Everyone who is curious is both humble and rich and vice versa. If someone is both not patient and strong then john is strong and vice versa. If susan is calm or not kind then fred is both creative and not happy and vice versa. If fred is both not quiet and kind then someone is both wise and funny and vice versa. If someone is either not brave or not curious then someone is both rich and calm and vice versa. Everyone who is wise is both not humble and old and vice versa. If someone is generous then paul is not quiet or strong. If someone is kind or patient then lucy is either brave or not old. If someone is both not quiet and quiet then mary is creative and vice versa. If fred is not humble then fred is either creative or not strong. Everyone who is happy is either funny or kind. If someone is quiet then john is not brave and vice versa. Everyone who is not kind or strong is either kind or calm and vice versa. Someone is calm or not rich. Alice is calm or quiet. Lucy is happy. Fred is both patient and brave. Paul is not strong. Paul is brave or generous. Susan is not old or quiet. Mary is both not wise and not happy. | Fred is happy. | neutral | (![X]:((~curious(X)&calm(X))<=>(humble(X)&patient(X))))&
((?[X]:((~rich(X)|brave(X))))=>((old(lucy)&wise(lucy))))&
(![X]:(~humble(X)=>(generous(X)|tall(X))))&
(![X]:(curious(X)<=>(humble(X)&rich(X))))&
((?[X]:((~patient(X)&strong(X))))<=>(strong(john)))&
(((calm(susan)|~kind(susan)))<=>((creative(fred)&~happy(fred))))&
(((~quiet(fred)&kind(fred)))<=>(?[X]:((wise(X)&funny(X)))))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((rich(X)&calm(X)))))&
(![X]:(wise(X)<=>(~humble(X)&old(X))))&
((?[X]:(generous(X)))=>((~quiet(paul)|strong(paul))))&
((?[X]:((kind(X)|patient(X))))=>((brave(lucy)<~>~old(lucy))))&
((?[X]:((~quiet(X)&quiet(X))))<=>(creative(mary)))&
((~humble(fred))=>((creative(fred)<~>~strong(fred))))&
(![X]:(happy(X)=>(funny(X)<~>kind(X))))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(![X]:((~kind(X)|strong(X))<=>(kind(X)<~>calm(X))))&
(?[X]:((calm(X)|~rich(X))))&
((calm(alice)|quiet(alice)))&
(happy(lucy))&
((patient(fred)&brave(fred)))&
(~strong(paul))&
((brave(paul)|generous(paul)))&
((~old(susan)|quiet(susan)))&
((~wise(mary)&~happy(mary))) | happy(fred) | [] | null | 0 |
Everyone who is either not strong or not happy is either not curious or not patient and vice versa. If someone is funny or old then someone is both strong and not old and vice versa. Everyone who is funny is both not wise and funny and vice versa. If alice is both not patient and not happy then mary is happy or not quiet. If someone is not happy then someone is either strong or creative and vice versa. Everyone who is creative or not creative is both not old and curious and vice versa. Everyone who is either not funny or old is not generous and vice versa. If mary is either old or not old then john is both calm and not creative. Everyone who is both patient and not happy is either not calm or patient and vice versa. If someone is either not kind or old then paul is both curious and not patient. If someone is both happy and tall then susan is either brave or strong. If someone is humble or not creative then john is not quiet and vice versa. If paul is not strong then john is generous or not tall and vice versa. If fred is either not rich or not curious then mary is either funny or not old and vice versa. Everyone who is either tall or not brave is both wise and quiet and vice versa. Everyone who is not patient or funny is both not funny and not calm. Someone is kind or tall. Someone is kind or not patient. Someone is both not strong and not generous. Fred is patient or not kind. Someone is kind or strong. Lucy is not creative. | Lucy is tall. | neutral | (![X]:((~strong(X)<~>~happy(X))<=>(~curious(X)<~>~patient(X))))&
((?[X]:((funny(X)|old(X))))<=>(?[X]:((strong(X)&~old(X)))))&
(![X]:(funny(X)<=>(~wise(X)&funny(X))))&
(((~patient(alice)&~happy(alice)))=>((happy(mary)|~quiet(mary))))&
((?[X]:(~happy(X)))<=>(?[X]:((strong(X)<~>creative(X)))))&
(![X]:((creative(X)|~creative(X))<=>(~old(X)&curious(X))))&
(![X]:((~funny(X)<~>old(X))<=>~generous(X)))&
(((old(mary)<~>~old(mary)))=>((calm(john)&~creative(john))))&
(![X]:((patient(X)&~happy(X))<=>(~calm(X)<~>patient(X))))&
((?[X]:((~kind(X)<~>old(X))))=>((curious(paul)&~patient(paul))))&
((?[X]:((happy(X)&tall(X))))=>((brave(susan)<~>strong(susan))))&
((?[X]:((humble(X)|~creative(X))))<=>(~quiet(john)))&
((~strong(paul))<=>((generous(john)|~tall(john))))&
(((~rich(fred)<~>~curious(fred)))<=>((funny(mary)<~>~old(mary))))&
(![X]:((tall(X)<~>~brave(X))<=>(wise(X)&quiet(X))))&
(![X]:((~patient(X)|funny(X))=>(~funny(X)&~calm(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:((kind(X)|~patient(X))))&
(?[X]:((~strong(X)&~generous(X))))&
((patient(fred)|~kind(fred)))&
(?[X]:((kind(X)|strong(X))))&
(~creative(lucy)) | tall(lucy) | [] | null | 0 |
Everyone who is not brave or kind is both not happy and tall and vice versa. Everyone who is either old or tall is curious and vice versa. If someone is not old then someone is either patient or happy and vice versa. If mary is both rich and old then someone is happy and vice versa. Everyone who is both wise and kind is not strong or not creative. Everyone who is quiet or patient is not strong or tall. If someone is patient then someone is either not wise or not humble. If paul is both not funny and quiet then someone is not patient or funny. Everyone who is either not calm or strong is wise. Everyone who is both not quiet and not happy is strong. Everyone who is either generous or not patient is not curious. If someone is not tall or tall then john is either patient or old and vice versa. If someone is generous then alice is not creative and vice versa. If mary is rich or not tall then mary is either rich or wise and vice versa. If alice is both not quiet and happy then john is both not strong and not old and vice versa. Everyone who is creative is either humble or not calm. Someone is not patient or curious. Someone is funny or not creative. Someone is kind. Someone is not kind or brave. Someone is not kind or rich. Susan is not tall. Someone is either not curious or not calm. Someone is either calm or not strong. | Susan is kind. | contradiction | (![X]:((~brave(X)|kind(X))<=>(~happy(X)&tall(X))))&
(![X]:((old(X)<~>tall(X))<=>curious(X)))&
((?[X]:(~old(X)))<=>(?[X]:((patient(X)<~>happy(X)))))&
(((rich(mary)&old(mary)))<=>(?[X]:(happy(X))))&
(![X]:((wise(X)&kind(X))=>(~strong(X)|~creative(X))))&
(![X]:((quiet(X)|patient(X))=>(~strong(X)|tall(X))))&
((?[X]:(patient(X)))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(((~funny(paul)&quiet(paul)))=>(?[X]:((~patient(X)|funny(X)))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
(![X]:((~quiet(X)&~happy(X))=>strong(X)))&
(![X]:((generous(X)<~>~patient(X))=>~curious(X)))&
((?[X]:((~tall(X)|tall(X))))<=>((patient(john)<~>old(john))))&
((?[X]:(generous(X)))<=>(~creative(alice)))&
(((rich(mary)|~tall(mary)))<=>((rich(mary)<~>wise(mary))))&
(((~quiet(alice)&happy(alice)))<=>((~strong(john)&~old(john))))&
(![X]:(creative(X)=>(humble(X)<~>~calm(X))))&
(?[X]:((~patient(X)|curious(X))))&
(?[X]:((funny(X)|~creative(X))))&
(?[X]:(kind(X)))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((~kind(X)|rich(X))))&
(~tall(susan))&
(?[X]:((~curious(X)<~>~calm(X))))&
(?[X]:((calm(X)<~>~strong(X)))) | kind(susan) | [
"p0",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 267681273412072101946173
% SZS output start Proof for 267681273412072101946173
1. ! [X0] : ((kind(X0) | ~brave(X0)) <=> (tall(X0) & ~happy(X0))) [input p0]
22. ~tall(susan) [input p21]
25. kind(susan) [input hypothesis]
40. ! [X0] : (((kind(X0) | ~brave(X0)) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | (~kind(X0) & brave(X0)))) [nnf transformation 1]
41. ! [X0] : ((kind(X0) | ~brave(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | (~kind(X0) & brave(X0)))) [flattening 40]
89. ~kind(X0) | tall(X0) [cnf transformation 41]
136. ~tall(susan) [cnf transformation 22]
141. kind(susan) [cnf transformation 25]
312. tall(susan) [resolution 89,141]
313. $false [subsumption resolution 312,136]
% SZS output end Proof for 267681273412072101946173
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is calm and vice versa.
Everyone who is not strong is either creative or not kind and vice versa.
If someone is not happy or not funny then someone is either brave or funny.
If someone is not patient then fred is either patient or brave.
Everyone who is both not happy and not quiet is both not funny and rich and vice versa.
Everyone who is both calm and not tall is patient or strong and vice versa.
Everyone who is both funny and tall is humble or not patient and vice versa.
If lucy is tall then mary is rich or old.
If paul is tall then someone is either creative or not happy and vice versa.
If someone is not kind then someone is both not strong and wise.
Everyone who is patient is both brave and generous.
If someone is either creative or old then someone is either not rich or not strong and vice versa.
Everyone who is generous is both not calm and calm.
Everyone who is either kind or old is either not quiet or brave.
Everyone who is not rich or patient is either creative or old.
Everyone who is either not generous or funny is not tall or not creative.
Someone is calm.
Fred is not wise.
Someone is either not brave or wise.
Lucy is not funny or not rich.
Someone is both funny and creative.
Alice is not curious or generous.
John is both not calm and funny.
Lucy is either humble or not calm. | Alice is not patient. | entailment | ((?[X]:(~strong(X)))<=>(?[X]:(calm(X))))&
(![X]:(~strong(X)<=>(creative(X)<~>~kind(X))))&
((?[X]:((~happy(X)|~funny(X))))=>(?[X]:((brave(X)<~>funny(X)))))&
((?[X]:(~patient(X)))=>((patient(fred)<~>brave(fred))))&
(![X]:((~happy(X)&~quiet(X))<=>(~funny(X)&rich(X))))&
(![X]:((calm(X)&~tall(X))<=>(patient(X)|strong(X))))&
(![X]:((funny(X)&tall(X))<=>(humble(X)|~patient(X))))&
((tall(lucy))=>((rich(mary)|old(mary))))&
((tall(paul))<=>(?[X]:((creative(X)<~>~happy(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~strong(X)&wise(X)))))&
(![X]:(patient(X)=>(brave(X)&generous(X))))&
((?[X]:((creative(X)<~>old(X))))<=>(?[X]:((~rich(X)<~>~strong(X)))))&
(![X]:(generous(X)=>(~calm(X)&calm(X))))&
(![X]:((kind(X)<~>old(X))=>(~quiet(X)<~>brave(X))))&
(![X]:((~rich(X)|patient(X))=>(creative(X)<~>old(X))))&
(![X]:((~generous(X)<~>funny(X))=>(~tall(X)|~creative(X))))&
(?[X]:(calm(X)))&
(~wise(fred))&
(?[X]:((~brave(X)<~>wise(X))))&
((~funny(lucy)|~rich(lucy)))&
(?[X]:((funny(X)&creative(X))))&
((~curious(alice)|generous(alice)))&
((~calm(john)&funny(john)))&
((humble(lucy)<~>~calm(lucy))) | ~patient(alice) | [
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5931706121261113537360674
% SZS output start Proof for 5931706121261113537360674
11. ! [X0] : (patient(X0) => (generous(X0) & brave(X0))) [input p10]
13. ! [X0] : (generous(X0) => (calm(X0) & ~calm(X0))) [input p12]
25. patient(alice) [input hypothesis]
36. ! [X0] : ((generous(X0) & brave(X0)) | ~patient(X0)) [ennf transformation 11]
37. ! [X0] : ((calm(X0) & ~calm(X0)) | ~generous(X0)) [ennf transformation 13]
116. ~patient(X0) | generous(X0) [cnf transformation 36]
125. ~calm(X0) | ~generous(X0) [cnf transformation 37]
126. calm(X0) | ~generous(X0) [cnf transformation 37]
148. patient(alice) [cnf transformation 25]
280. ~generous(X0) [subsumption resolution 125,126]
339. generous(alice) [resolution 116,148]
341. $false [subsumption resolution 339,280]
% SZS output end Proof for 5931706121261113537360674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not tall or not patient is both old and creative. If someone is happy then someone is both creative and not creative and vice versa. If someone is not creative or not funny then fred is not creative. Everyone who is both not rich and old is not happy. Everyone who is either funny or brave is either not kind or rich and vice versa. Everyone who is either old or happy is not strong or not old and vice versa. If paul is kind or not brave then someone is both not funny and not tall. If alice is either strong or not funny then someone is either curious or not brave. Everyone who is both not happy and not calm is both not kind and not old. Everyone who is not calm or not curious is curious or not brave. Everyone who is both not old and not strong is not tall and vice versa. Everyone who is humble or brave is not funny or old and vice versa. Everyone who is rich or generous is funny and vice versa. Everyone who is not creative is calm or not tall. If susan is generous or not curious then someone is both not strong and generous and vice versa. Someone is not humble. Someone is not creative. Someone is rich. Someone is kind or not brave. Susan is strong or not funny. Someone is either not generous or not brave. | Fred is patient. | entailment | (![X]:((~tall(X)<~>~patient(X))=>(old(X)&creative(X))))&
((?[X]:(happy(X)))<=>(?[X]:((creative(X)&~creative(X)))))&
((?[X]:((~creative(X)|~funny(X))))=>(~creative(fred)))&
(![X]:((~rich(X)&old(X))=>~happy(X)))&
(![X]:((funny(X)<~>brave(X))<=>(~kind(X)<~>rich(X))))&
(![X]:((old(X)<~>happy(X))<=>(~strong(X)|~old(X))))&
(((kind(paul)|~brave(paul)))=>(?[X]:((~funny(X)&~tall(X)))))&
(((strong(alice)<~>~funny(alice)))=>(?[X]:((curious(X)<~>~brave(X)))))&
(![X]:((~happy(X)&~calm(X))=>(~kind(X)&~old(X))))&
(![X]:((~calm(X)|~curious(X))=>(curious(X)|~brave(X))))&
(![X]:((~old(X)&~strong(X))<=>~tall(X)))&
(![X]:((humble(X)|brave(X))<=>(~funny(X)|old(X))))&
(![X]:((rich(X)|generous(X))<=>funny(X)))&
(![X]:(~creative(X)=>(calm(X)|~tall(X))))&
(((generous(susan)|~curious(susan)))<=>(?[X]:((~strong(X)&generous(X)))))&
(?[X]:(~humble(X)))&
(?[X]:(~creative(X)))&
(?[X]:(rich(X)))&
(?[X]:((kind(X)|~brave(X))))&
((strong(susan)|~funny(susan)))&
(?[X]:((~generous(X)<~>~brave(X)))) | patient(fred) | [
"p0",
"p1",
"p2",
"p5",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8821362501147896213729194
% SZS output start Proof for 8821362501147896213729194
1. ! [X0] : ((~tall(X0) <~> ~patient(X0)) => (creative(X0) & old(X0))) [input p0]
2. ? [X0] : happy(X0) <=> ? [X0] : (~creative(X0) & creative(X0)) [input p1]
3. ? [X0] : (~funny(X0) | ~creative(X0)) => ~creative(fred) [input p2]
6. ! [X0] : ((old(X0) <~> happy(X0)) <=> (~old(X0) | ~strong(X0))) [input p5]
11. ! [X0] : ((~strong(X0) & ~old(X0)) <=> ~tall(X0)) [input p10]
17. ? [X0] : ~creative(X0) [input p16]
22. ~patient(fred) [input hypothesis]
23. ? [X0] : happy(X0) <=> ? [X1] : (~creative(X1) & creative(X1)) [rectify 2]
27. ! [X0] : ((creative(X0) & old(X0)) | (~tall(X0) <=> ~patient(X0))) [ennf transformation 1]
28. ~creative(fred) | ! [X0] : (funny(X0) & creative(X0)) [ennf transformation 3]
35. ! [X0] : ((creative(X0) & old(X0)) | ((~tall(X0) | patient(X0)) & (~patient(X0) | tall(X0)))) [nnf transformation 27]
36. (? [X0] : happy(X0) | ! [X1] : (creative(X1) | ~creative(X1))) & (? [X1] : (~creative(X1) & creative(X1)) | ! [X0] : ~happy(X0)) [nnf transformation 23]
37. (? [X0] : happy(X0) | ! [X1] : (creative(X1) | ~creative(X1))) & (? [X2] : (~creative(X2) & creative(X2)) | ! [X3] : ~happy(X3)) [rectify 36]
38. ? [X0] : happy(X0) => happy(sK0) [choice axiom]
39. ? [X2] : (~creative(X2) & creative(X2)) => (~creative(sK1) & creative(sK1)) [choice axiom]
40. (happy(sK0) | ! [X1] : (creative(X1) | ~creative(X1))) & ((~creative(sK1) & creative(sK1)) | ! [X3] : ~happy(X3)) [skolemisation 37,39,38]
42. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (old(X0) & strong(X0))) & ((~old(X0) | ~strong(X0)) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~happy(X0) | ~old(X0)) & (happy(X0) | old(X0))) | (old(X0) & strong(X0))) & (~old(X0) | ~strong(X0) | ((old(X0) | ~happy(X0)) & (happy(X0) | ~old(X0))))) [flattening 42]
49. ! [X0] : (((~strong(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | (strong(X0) | old(X0)))) [nnf transformation 11]
50. ! [X0] : (((~strong(X0) & ~old(X0)) | tall(X0)) & (~tall(X0) | strong(X0) | old(X0))) [flattening 49]
62. ? [X0] : ~creative(X0) => ~creative(sK6) [choice axiom]
63. ~creative(sK6) [skolemisation 17,62]
74. ~tall(X0) | creative(X0) | patient(X0) [cnf transformation 35]
75. creative(sK1) | ~happy(X3) [cnf transformation 40]
76. ~creative(sK1) | ~happy(X3) [cnf transformation 40]
78. ~creative(fred) | creative(X0) [cnf transformation 28]
92. happy(X0) | old(X0) | old(X0) [cnf transformation 43]
105. ~old(X0) | tall(X0) [cnf transformation 50]
120. ~creative(sK6) [cnf transformation 63]
126. ~patient(fred) [cnf transformation 22]
129. happy(X0) | old(X0) [duplicate literal removal 92]
131. 1 <=> ! [X3] : ~happy(X3) [avatar definition]
132. ~happy(X3) <- (1) [avatar component clause 131]
134. 2 <=> creative(sK1) [avatar definition]
137. 1 | ~2 [avatar split clause 76,134,131]
138. 1 | 2 [avatar split clause 75,134,131]
143. 4 <=> creative(fred) [avatar definition]
145. ~creative(fred) <- (~4) [avatar component clause 143]
148. 5 <=> ! [X0] : creative(X0) [avatar definition]
149. creative(X0) <- (5) [avatar component clause 148]
150. 5 | ~4 [avatar split clause 78,143,148]
246. old(X0) <- (1) [resolution 129,132]
247. tall(X0) <- (1) [resolution 246,105]
252. creative(X0) | patient(X0) <- (1) [resolution 74,247]
255. patient(fred) <- (1, ~4) [resolution 252,145]
256. $false <- (1, ~4) [subsumption resolution 255,126]
257. ~1 | 4 [avatar contradiction clause 256]
262. $false <- (5) [resolution 149,120]
263. ~5 [avatar contradiction clause 262]
264. $false [avatar sat refutation 137,138,150,257,263]
% SZS output end Proof for 8821362501147896213729194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is old and vice versa.
If mary is both rich and not funny then lucy is calm or not calm.
Everyone who is both not calm and patient is not happy.
Everyone who is not funny or wise is both not kind and rich.
Everyone who is either tall or not creative is either patient or brave.
Everyone who is curious is either not kind or not tall and vice versa.
Everyone who is not curious is both strong and humble and vice versa.
Everyone who is rich is not patient and vice versa.
If someone is both tall and not quiet then someone is not creative or not strong and vice versa.
Everyone who is both calm and not quiet is creative.
Everyone who is not quiet or not creative is not tall and vice versa.
Everyone who is both tall and rich is both not generous and not happy.
Everyone who is both generous and tall is patient and vice versa.
If lucy is both not rich and wise then someone is both kind and quiet.
If someone is both tall and not brave then someone is both not old and creative and vice versa.
Everyone who is humble is not patient or not funny and vice versa.
Someone is both happy and not funny.
Mary is either not tall or not kind.
Someone is both strong and wise.
Someone is rich or strong.
Lucy is both calm and old.
John is both rich and old.
Someone is not rich or creative. | John is not generous. | entailment | (![X]:(tall(X)<=>old(X)))&
(((rich(mary)&~funny(mary)))=>((calm(lucy)|~calm(lucy))))&
(![X]:((~calm(X)&patient(X))=>~happy(X)))&
(![X]:((~funny(X)|wise(X))=>(~kind(X)&rich(X))))&
(![X]:((tall(X)<~>~creative(X))=>(patient(X)<~>brave(X))))&
(![X]:(curious(X)<=>(~kind(X)<~>~tall(X))))&
(![X]:(~curious(X)<=>(strong(X)&humble(X))))&
(![X]:(rich(X)<=>~patient(X)))&
((?[X]:((tall(X)&~quiet(X))))<=>(?[X]:((~creative(X)|~strong(X)))))&
(![X]:((calm(X)&~quiet(X))=>creative(X)))&
(![X]:((~quiet(X)|~creative(X))<=>~tall(X)))&
(![X]:((tall(X)&rich(X))=>(~generous(X)&~happy(X))))&
(![X]:((generous(X)&tall(X))<=>patient(X)))&
(((~rich(lucy)&wise(lucy)))=>(?[X]:((kind(X)&quiet(X)))))&
((?[X]:((tall(X)&~brave(X))))<=>(?[X]:((~old(X)&creative(X)))))&
(![X]:(humble(X)<=>(~patient(X)|~funny(X))))&
(?[X]:((happy(X)&~funny(X))))&
((~tall(mary)<~>~kind(mary)))&
(?[X]:((strong(X)&wise(X))))&
(?[X]:((rich(X)|strong(X))))&
((calm(lucy)&old(lucy)))&
((rich(john)&old(john)))&
(?[X]:((~rich(X)|creative(X)))) | ~generous(john) | [
"p0",
"p11",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 767907170992347203828054
% SZS output start Proof for 767907170992347203828054
1. ! [X0] : (tall(X0) <=> old(X0)) [input p0]
12. ! [X0] : ((rich(X0) & tall(X0)) => (~happy(X0) & ~generous(X0))) [input p11]
22. old(john) & rich(john) [input p21]
24. generous(john) [input hypothesis]
35. ! [X0] : ((~happy(X0) & ~generous(X0)) | (~rich(X0) | ~tall(X0))) [ennf transformation 12]
36. ! [X0] : ((~happy(X0) & ~generous(X0)) | ~rich(X0) | ~tall(X0)) [flattening 35]
39. ! [X0] : ((tall(X0) | ~old(X0)) & (old(X0) | ~tall(X0))) [nnf transformation 1]
73. ~old(X0) | tall(X0) [cnf transformation 39]
102. ~generous(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 36]
125. rich(john) [cnf transformation 22]
126. old(john) [cnf transformation 22]
128. generous(john) [cnf transformation 24]
217. tall(john) [resolution 73,126]
312. ~rich(john) | ~tall(john) [resolution 102,128]
313. ~tall(john) [subsumption resolution 312,125]
314. $false [subsumption resolution 313,217]
% SZS output end Proof for 767907170992347203828054
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both kind and calm.
Everyone who is both not rich and rich is old or tall.
Everyone who is not funny is both curious and not patient and vice versa.
Everyone who is not humble or patient is wise and vice versa.
Everyone who is not kind is both wise and patient and vice versa.
Everyone who is not funny is either not brave or brave and vice versa.
If someone is both kind and wise then fred is both not humble and not wise.
If someone is both not rich and generous then someone is happy or old and vice versa.
If someone is not old then alice is not kind or quiet and vice versa.
Everyone who is funny is both humble and creative.
Everyone who is kind is not quiet and vice versa.
Everyone who is either rich or not brave is either wise or not quiet and vice versa.
Someone is kind.
Fred is both happy and not tall.
Alice is not strong or not kind.
Someone is either tall or not brave.
Fred is either not funny or not curious.
Someone is not curious or curious.
John is not creative or rich. | Alice is not rich. | neutral | (![X]:(calm(X)=>(kind(X)&calm(X))))&
(![X]:((~rich(X)&rich(X))=>(old(X)|tall(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
(![X]:((~humble(X)|patient(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(wise(X)&patient(X))))&
(![X]:(~funny(X)<=>(~brave(X)<~>brave(X))))&
((?[X]:((kind(X)&wise(X))))=>((~humble(fred)&~wise(fred))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:(~old(X)))<=>((~kind(alice)|quiet(alice))))&
(![X]:(funny(X)=>(humble(X)&creative(X))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:((rich(X)<~>~brave(X))<=>(wise(X)<~>~quiet(X))))&
(?[X]:(kind(X)))&
((happy(fred)&~tall(fred)))&
((~strong(alice)|~kind(alice)))&
(?[X]:((tall(X)<~>~brave(X))))&
((~funny(fred)<~>~curious(fred)))&
(?[X]:((~curious(X)|curious(X))))&
((~creative(john)|rich(john))) | ~rich(alice) | [] | null | 0 |
Everyone who is either not humble or not strong is generous. If alice is humble then someone is not quiet or not strong and vice versa. If someone is wise or not strong then someone is either creative or brave. Everyone who is kind or rich is not curious or not calm. Everyone who is not old or not kind is both kind and not curious. If lucy is not patient or not strong then someone is either rich or strong. If someone is either not happy or calm then someone is not tall and vice versa. If lucy is not funny then lucy is not calm or patient and vice versa. Everyone who is either not calm or not patient is not calm and vice versa. Everyone who is both not kind and not strong is not brave. Everyone who is not generous is not curious or funny. If someone is happy or humble then someone is both tall and quiet and vice versa. Everyone who is either quiet or brave is both not wise and tall. Everyone who is both not funny and not curious is humble. Everyone who is either strong or funny is both not old and kind. If someone is either wise or not brave then lucy is both not tall and humble and vice versa. Someone is both calm and happy. Fred is not brave. Someone is both not strong and calm. Alice is both quiet and generous. Paul is both not humble and not strong. Fred is not brave or old. | Alice is not strong. | neutral | (![X]:((~humble(X)<~>~strong(X))=>generous(X)))&
((humble(alice))<=>(?[X]:((~quiet(X)|~strong(X)))))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((creative(X)<~>brave(X)))))&
(![X]:((kind(X)|rich(X))=>(~curious(X)|~calm(X))))&
(![X]:((~old(X)|~kind(X))=>(kind(X)&~curious(X))))&
(((~patient(lucy)|~strong(lucy)))=>(?[X]:((rich(X)<~>strong(X)))))&
((?[X]:((~happy(X)<~>calm(X))))<=>(?[X]:(~tall(X))))&
((~funny(lucy))<=>((~calm(lucy)|patient(lucy))))&
(![X]:((~calm(X)<~>~patient(X))<=>~calm(X)))&
(![X]:((~kind(X)&~strong(X))=>~brave(X)))&
(![X]:(~generous(X)=>(~curious(X)|funny(X))))&
((?[X]:((happy(X)|humble(X))))<=>(?[X]:((tall(X)&quiet(X)))))&
(![X]:((quiet(X)<~>brave(X))=>(~wise(X)&tall(X))))&
(![X]:((~funny(X)&~curious(X))=>humble(X)))&
(![X]:((strong(X)<~>funny(X))=>(~old(X)&kind(X))))&
((?[X]:((wise(X)<~>~brave(X))))<=>((~tall(lucy)&humble(lucy))))&
(?[X]:((calm(X)&happy(X))))&
(~brave(fred))&
(?[X]:((~strong(X)&calm(X))))&
((quiet(alice)&generous(alice)))&
((~humble(paul)&~strong(paul)))&
((~brave(fred)|old(fred))) | ~strong(alice) | [] | null | 0 |
If susan is both not curious and calm then mary is old or funny and vice versa.
Everyone who is tall or not brave is either not old or not brave.
If someone is not funny or creative then susan is not strong or not creative.
If paul is wise then someone is not wise and vice versa.
If lucy is rich then fred is not generous or not tall and vice versa.
Everyone who is both brave and not funny is either brave or tall.
Everyone who is both rich and not quiet is not curious or not strong.
Everyone who is either not humble or not patient is strong or not curious.
Everyone who is both tall and not patient is not rich and vice versa.
Everyone who is tall is not generous and vice versa.
Everyone who is either tall or not tall is not humble.
If alice is humble or not creative then lucy is both patient and not happy.
Everyone who is funny is either not humble or quiet.
Everyone who is wise or not patient is either kind or patient and vice versa.
Everyone who is both happy and tall is creative or not creative and vice versa.
If someone is both wise and not kind then someone is both not kind and not funny.
Someone is old or not curious.
Mary is either not curious or not quiet.
Someone is tall.
Lucy is not curious or curious.
Paul is not humble.
Susan is patient or not creative.
Someone is either not generous or rich. | Mary is curious. | neutral | (((~curious(susan)&calm(susan)))<=>((old(mary)|funny(mary))))&
(![X]:((tall(X)|~brave(X))=>(~old(X)<~>~brave(X))))&
((?[X]:((~funny(X)|creative(X))))=>((~strong(susan)|~creative(susan))))&
((wise(paul))<=>(?[X]:(~wise(X))))&
((rich(lucy))<=>((~generous(fred)|~tall(fred))))&
(![X]:((brave(X)&~funny(X))=>(brave(X)<~>tall(X))))&
(![X]:((rich(X)&~quiet(X))=>(~curious(X)|~strong(X))))&
(![X]:((~humble(X)<~>~patient(X))=>(strong(X)|~curious(X))))&
(![X]:((tall(X)&~patient(X))<=>~rich(X)))&
(![X]:(tall(X)<=>~generous(X)))&
(![X]:((tall(X)<~>~tall(X))=>~humble(X)))&
(((humble(alice)|~creative(alice)))=>((patient(lucy)&~happy(lucy))))&
(![X]:(funny(X)=>(~humble(X)<~>quiet(X))))&
(![X]:((wise(X)|~patient(X))<=>(kind(X)<~>patient(X))))&
(![X]:((happy(X)&tall(X))<=>(creative(X)|~creative(X))))&
((?[X]:((wise(X)&~kind(X))))=>(?[X]:((~kind(X)&~funny(X)))))&
(?[X]:((old(X)|~curious(X))))&
((~curious(mary)<~>~quiet(mary)))&
(?[X]:(tall(X)))&
((~curious(lucy)|curious(lucy)))&
(~humble(paul))&
((patient(susan)|~creative(susan)))&
(?[X]:((~generous(X)<~>rich(X)))) | curious(mary) | [] | null | 0 |
If lucy is both funny and creative then mary is both kind and not creative and vice versa.
If john is tall then someone is not calm or not brave and vice versa.
If paul is either creative or not creative then john is not quiet and vice versa.
Everyone who is not patient is both not humble and not old.
If mary is either not creative or not strong then lucy is not strong.
If paul is calm or not kind then lucy is both brave and tall and vice versa.
If someone is either not funny or humble then someone is not old.
Everyone who is happy or not quiet is both funny and wise and vice versa.
If susan is brave or not happy then alice is creative.
Everyone who is funny or rich is both not old and strong and vice versa.
Everyone who is rich is not strong and vice versa.
Everyone who is tall is both not creative and calm and vice versa.
If fred is both not rich and curious then paul is either funny or not patient.
If john is both not calm and not generous then paul is either not calm or not strong.
Everyone who is brave or not rich is not creative or wise and vice versa.
Everyone who is not patient is both not humble and quiet and vice versa.
Mary is rich or not funny.
Someone is both generous and funny.
John is both calm and humble.
Someone is both not wise and kind.
Susan is humble or not funny.
John is wise.
Someone is not brave or not happy.
Susan is not creative. | Mary is tall. | contradiction | (((funny(lucy)&creative(lucy)))<=>((kind(mary)&~creative(mary))))&
((tall(john))<=>(?[X]:((~calm(X)|~brave(X)))))&
(((creative(paul)<~>~creative(paul)))<=>(~quiet(john)))&
(![X]:(~patient(X)=>(~humble(X)&~old(X))))&
(((~creative(mary)<~>~strong(mary)))=>(~strong(lucy)))&
(((calm(paul)|~kind(paul)))<=>((brave(lucy)&tall(lucy))))&
((?[X]:((~funny(X)<~>humble(X))))=>(?[X]:(~old(X))))&
(![X]:((happy(X)|~quiet(X))<=>(funny(X)&wise(X))))&
(((brave(susan)|~happy(susan)))=>(creative(alice)))&
(![X]:((funny(X)|rich(X))<=>(~old(X)&strong(X))))&
(![X]:(rich(X)<=>~strong(X)))&
(![X]:(tall(X)<=>(~creative(X)&calm(X))))&
(((~rich(fred)&curious(fred)))=>((funny(paul)<~>~patient(paul))))&
(((~calm(john)&~generous(john)))=>((~calm(paul)<~>~strong(paul))))&
(![X]:((brave(X)|~rich(X))<=>(~creative(X)|wise(X))))&
(![X]:(~patient(X)<=>(~humble(X)&quiet(X))))&
((rich(mary)|~funny(mary)))&
(?[X]:((generous(X)&funny(X))))&
((calm(john)&humble(john)))&
(?[X]:((~wise(X)&kind(X))))&
((humble(susan)|~funny(susan)))&
(wise(john))&
(?[X]:((~brave(X)|~happy(X))))&
(~creative(susan)) | tall(mary) | [
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 63634755318040856726142
% SZS output start Proof for 63634755318040856726142
5. (~creative(mary) <~> ~strong(mary)) => ~strong(lucy) [input p4]
10. ! [X0] : ((rich(X0) | funny(X0)) <=> (strong(X0) & ~old(X0))) [input p9]
11. ! [X0] : (rich(X0) <=> ~strong(X0)) [input p10]
12. ! [X0] : (tall(X0) <=> (calm(X0) & ~creative(X0))) [input p11]
25. tall(mary) [input hypothesis]
32. ~strong(lucy) | (~creative(mary) <=> ~strong(mary)) [ennf transformation 5]
44. ~strong(lucy) | ((~creative(mary) | strong(mary)) & (~strong(mary) | creative(mary))) [nnf transformation 32]
53. ! [X0] : (((rich(X0) | funny(X0)) | (~strong(X0) | old(X0))) & ((strong(X0) & ~old(X0)) | (~rich(X0) & ~funny(X0)))) [nnf transformation 10]
54. ! [X0] : ((rich(X0) | funny(X0) | ~strong(X0) | old(X0)) & ((strong(X0) & ~old(X0)) | (~rich(X0) & ~funny(X0)))) [flattening 53]
55. ! [X0] : ((rich(X0) | strong(X0)) & (~strong(X0) | ~rich(X0))) [nnf transformation 11]
56. ! [X0] : ((tall(X0) | (~calm(X0) | creative(X0))) & ((calm(X0) & ~creative(X0)) | ~tall(X0))) [nnf transformation 12]
57. ! [X0] : ((tall(X0) | ~calm(X0) | creative(X0)) & ((calm(X0) & ~creative(X0)) | ~tall(X0))) [flattening 56]
79. ~strong(lucy) | ~strong(mary) | creative(mary) [cnf transformation 44]
98. ~rich(X0) | strong(X0) [cnf transformation 54]
101. rich(X0) | strong(X0) [cnf transformation 55]
102. ~tall(X0) | ~creative(X0) [cnf transformation 57]
120. tall(mary) [cnf transformation 25]
128. 2 <=> creative(mary) [avatar definition]
130. creative(mary) <- (2) [avatar component clause 128]
175. 12 <=> strong(mary) [avatar definition]
176. ~strong(mary) <- (~12) [avatar component clause 175]
179. 13 <=> strong(lucy) [avatar definition]
181. ~strong(lucy) <- (~13) [avatar component clause 179]
183. 2 | ~12 | ~13 [avatar split clause 79,179,175,128]
231. strong(X0) [subsumption resolution 101,98]
253. $false <- (~13) [subsumption resolution 181,231]
254. 13 [avatar contradiction clause 253]
255. $false <- (~12) [subsumption resolution 176,231]
256. 12 [avatar contradiction clause 255]
265. ~creative(mary) [resolution 102,120]
268. $false <- (2) [subsumption resolution 265,130]
269. ~2 [avatar contradiction clause 268]
270. $false [avatar sat refutation 183,254,256,269]
% SZS output end Proof for 63634755318040856726142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not quiet is either creative or old and vice versa.
Everyone who is either brave or quiet is generous and vice versa.
Everyone who is both not funny and not rich is not strong or not kind and vice versa.
Everyone who is either not patient or humble is not funny or not strong and vice versa.
If alice is curious then susan is not strong and vice versa.
Everyone who is either brave or not happy is not brave or rich and vice versa.
If fred is both not patient and not happy then alice is both creative and not quiet and vice versa.
If someone is both not generous and not wise then someone is not curious.
Everyone who is funny or strong is not old or humble and vice versa.
Everyone who is old or not rich is both not tall and kind and vice versa.
If someone is not creative then lucy is either not creative or not rich.
Everyone who is brave or not wise is rich and vice versa.
Everyone who is not curious is both not old and not calm.
Everyone who is either old or not rich is brave.
If fred is not old then alice is both curious and creative and vice versa.
If someone is either not tall or quiet then fred is both not wise and creative and vice versa.
Alice is not funny or kind.
Someone is curious or not happy.
Someone is either not funny or funny.
Someone is not calm or old.
Someone is happy.
Paul is either not calm or creative.
Someone is calm or patient.
Someone is both old and not humble. | Paul is kind. | entailment | (![X]:((~strong(X)<~>~quiet(X))<=>(creative(X)<~>old(X))))&
(![X]:((brave(X)<~>quiet(X))<=>generous(X)))&
(![X]:((~funny(X)&~rich(X))<=>(~strong(X)|~kind(X))))&
(![X]:((~patient(X)<~>humble(X))<=>(~funny(X)|~strong(X))))&
((curious(alice))<=>(~strong(susan)))&
(![X]:((brave(X)<~>~happy(X))<=>(~brave(X)|rich(X))))&
(((~patient(fred)&~happy(fred)))<=>((creative(alice)&~quiet(alice))))&
((?[X]:((~generous(X)&~wise(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)|strong(X))<=>(~old(X)|humble(X))))&
(![X]:((old(X)|~rich(X))<=>(~tall(X)&kind(X))))&
((?[X]:(~creative(X)))=>((~creative(lucy)<~>~rich(lucy))))&
(![X]:((brave(X)|~wise(X))<=>rich(X)))&
(![X]:(~curious(X)=>(~old(X)&~calm(X))))&
(![X]:((old(X)<~>~rich(X))=>brave(X)))&
((~old(fred))<=>((curious(alice)&creative(alice))))&
((?[X]:((~tall(X)<~>quiet(X))))<=>((~wise(fred)&creative(fred))))&
((~funny(alice)|kind(alice)))&
(?[X]:((curious(X)|~happy(X))))&
(?[X]:((~funny(X)<~>funny(X))))&
(?[X]:((~calm(X)|old(X))))&
(?[X]:(happy(X)))&
((~calm(paul)<~>creative(paul)))&
(?[X]:((calm(X)|patient(X))))&
(?[X]:((old(X)&~humble(X)))) | kind(paul) | [
"p2",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8840138792087835495370786
% SZS output start Proof for 8840138792087835495370786
3. ! [X0] : ((~rich(X0) & ~funny(X0)) <=> (~kind(X0) | ~strong(X0))) [input p2]
10. ! [X0] : ((~rich(X0) | old(X0)) <=> (kind(X0) & ~tall(X0))) [input p9]
25. ~kind(paul) [input hypothesis]
35. ! [X0] : (((~rich(X0) & ~funny(X0)) | (kind(X0) & strong(X0))) & ((~kind(X0) | ~strong(X0)) | (rich(X0) | funny(X0)))) [nnf transformation 3]
36. ! [X0] : (((~rich(X0) & ~funny(X0)) | (kind(X0) & strong(X0))) & (~kind(X0) | ~strong(X0) | rich(X0) | funny(X0))) [flattening 35]
49. ! [X0] : (((~rich(X0) | old(X0)) | (~kind(X0) | tall(X0))) & ((kind(X0) & ~tall(X0)) | (rich(X0) & ~old(X0)))) [nnf transformation 10]
50. ! [X0] : ((~rich(X0) | old(X0) | ~kind(X0) | tall(X0)) & ((kind(X0) & ~tall(X0)) | (rich(X0) & ~old(X0)))) [flattening 49]
90. ~rich(X0) | kind(X0) [cnf transformation 36]
117. kind(X0) | rich(X0) [cnf transformation 50]
148. ~kind(paul) [cnf transformation 25]
195. kind(X0) [subsumption resolution 117,90]
282. $false [subsumption resolution 148,195]
% SZS output end Proof for 8840138792087835495370786
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or happy is not generous or old.
Everyone who is either funny or strong is happy.
Everyone who is strong is either quiet or wise.
Everyone who is either not wise or calm is both kind and brave and vice versa.
Everyone who is kind or not creative is both kind and not wise.
Everyone who is creative or not happy is both patient and curious and vice versa.
Everyone who is either not tall or funny is both generous and not old.
If someone is not quiet then someone is either not brave or quiet and vice versa.
If mary is both not patient and brave then someone is both not strong and not creative and vice versa.
Everyone who is both not strong and quiet is not calm or quiet.
If someone is either not curious or not creative then john is calm and vice versa.
Everyone who is both not tall and not curious is not brave and vice versa.
If susan is both calm and not calm then paul is both not creative and not brave.
Everyone who is both not quiet and rich is brave or not brave and vice versa.
Everyone who is not wise or patient is old or not humble and vice versa.
Everyone who is either not happy or not generous is old.
Paul is either calm or not generous.
Susan is either calm or not generous.
Susan is strong or humble.
Someone is both kind and generous.
Someone is wise or not generous.
Paul is both not quiet and not tall. | Paul is kind. | neutral | (![X]:((~old(X)|happy(X))=>(~generous(X)|old(X))))&
(![X]:((funny(X)<~>strong(X))=>happy(X)))&
(![X]:(strong(X)=>(quiet(X)<~>wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(kind(X)&brave(X))))&
(![X]:((kind(X)|~creative(X))=>(kind(X)&~wise(X))))&
(![X]:((creative(X)|~happy(X))<=>(patient(X)&curious(X))))&
(![X]:((~tall(X)<~>funny(X))=>(generous(X)&~old(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(((~patient(mary)&brave(mary)))<=>(?[X]:((~strong(X)&~creative(X)))))&
(![X]:((~strong(X)&quiet(X))=>(~calm(X)|quiet(X))))&
((?[X]:((~curious(X)<~>~creative(X))))<=>(calm(john)))&
(![X]:((~tall(X)&~curious(X))<=>~brave(X)))&
(((calm(susan)&~calm(susan)))=>((~creative(paul)&~brave(paul))))&
(![X]:((~quiet(X)&rich(X))<=>(brave(X)|~brave(X))))&
(![X]:((~wise(X)|patient(X))<=>(old(X)|~humble(X))))&
(![X]:((~happy(X)<~>~generous(X))=>old(X)))&
((calm(paul)<~>~generous(paul)))&
((calm(susan)<~>~generous(susan)))&
((strong(susan)|humble(susan)))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((wise(X)|~generous(X))))&
((~quiet(paul)&~tall(paul))) | kind(paul) | [] | null | 0 |
If john is not brave then john is not kind or happy and vice versa.
Everyone who is kind or not tall is not strong or funny and vice versa.
Everyone who is both humble and not kind is kind and vice versa.
Everyone who is patient is creative or not generous.
Everyone who is brave or old is either not brave or not rich and vice versa.
Everyone who is not kind is both not funny and not old and vice versa.
Everyone who is not quiet is not patient or not kind.
Everyone who is both not calm and not brave is both wise and rich and vice versa.
Everyone who is both wise and happy is not creative.
Everyone who is either strong or not old is either brave or strong.
Everyone who is tall is not creative or wise.
Everyone who is not happy or creative is not curious or wise.
Everyone who is either not creative or calm is either patient or not generous and vice versa.
If fred is not generous or creative then alice is old and vice versa.
Everyone who is either generous or rich is rich or generous.
Someone is either not patient or not kind.
Lucy is either rich or not curious.
Fred is not curious or not creative.
Someone is not funny or brave.
Someone is either not quiet or not calm.
Someone is quiet. | Fred is calm. | entailment | ((~brave(john))<=>((~kind(john)|happy(john))))&
(![X]:((kind(X)|~tall(X))<=>(~strong(X)|funny(X))))&
(![X]:((humble(X)&~kind(X))<=>kind(X)))&
(![X]:(patient(X)=>(creative(X)|~generous(X))))&
(![X]:((brave(X)|old(X))<=>(~brave(X)<~>~rich(X))))&
(![X]:(~kind(X)<=>(~funny(X)&~old(X))))&
(![X]:(~quiet(X)=>(~patient(X)|~kind(X))))&
(![X]:((~calm(X)&~brave(X))<=>(wise(X)&rich(X))))&
(![X]:((wise(X)&happy(X))=>~creative(X)))&
(![X]:((strong(X)<~>~old(X))=>(brave(X)<~>strong(X))))&
(![X]:(tall(X)=>(~creative(X)|wise(X))))&
(![X]:((~happy(X)|creative(X))=>(~curious(X)|wise(X))))&
(![X]:((~creative(X)<~>calm(X))<=>(patient(X)<~>~generous(X))))&
(((~generous(fred)|creative(fred)))<=>(old(alice)))&
(![X]:((generous(X)<~>rich(X))=>(rich(X)|generous(X))))&
(?[X]:((~patient(X)<~>~kind(X))))&
((rich(lucy)<~>~curious(lucy)))&
((~curious(fred)|~creative(fred)))&
(?[X]:((~funny(X)|brave(X))))&
(?[X]:((~quiet(X)<~>~calm(X))))&
(?[X]:(quiet(X))) | calm(fred) | [
"p2",
"p3",
"p5",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5894003563110220882364295
% SZS output start Proof for 5894003563110220882364295
3. ! [X0] : ((~kind(X0) & humble(X0)) <=> kind(X0)) [input p2]
4. ! [X0] : (patient(X0) => (~generous(X0) | creative(X0))) [input p3]
6. ! [X0] : (~kind(X0) <=> (~old(X0) & ~funny(X0))) [input p5]
13. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> (patient(X0) <~> ~generous(X0))) [input p12]
14. (creative(fred) | ~generous(fred)) <=> old(alice) [input p13]
22. ~calm(fred) [input hypothesis]
23. ! [X0] : ((~generous(X0) | creative(X0)) | ~patient(X0)) [ennf transformation 4]
24. ! [X0] : (~generous(X0) | creative(X0) | ~patient(X0)) [flattening 23]
40. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | (kind(X0) | ~humble(X0)))) [nnf transformation 3]
41. ! [X0] : (((~kind(X0) & humble(X0)) | ~kind(X0)) & (kind(X0) | kind(X0) | ~humble(X0))) [flattening 40]
44. ! [X0] : ((~kind(X0) | (old(X0) | funny(X0))) & ((~old(X0) & ~funny(X0)) | kind(X0))) [nnf transformation 6]
45. ! [X0] : ((~kind(X0) | old(X0) | funny(X0)) & ((~old(X0) & ~funny(X0)) | kind(X0))) [flattening 44]
49. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ((patient(X0) | generous(X0)) & (~generous(X0) | ~patient(X0)))) & (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 13]
50. ((creative(fred) | ~generous(fred)) | ~old(alice)) & (old(alice) | (~creative(fred) & generous(fred))) [nnf transformation 14]
51. (creative(fred) | ~generous(fred) | ~old(alice)) & (old(alice) | (~creative(fred) & generous(fred))) [flattening 50]
73. ~kind(X0) | ~kind(X0) [cnf transformation 41]
74. ~generous(X0) | creative(X0) | ~patient(X0) [cnf transformation 24]
82. ~old(X0) | kind(X0) [cnf transformation 45]
97. ~generous(X0) | patient(X0) | calm(X0) | creative(X0) [cnf transformation 49]
101. calm(X0) | ~creative(X0) | ~generous(X0) | ~patient(X0) [cnf transformation 49]
105. old(alice) | generous(fred) [cnf transformation 51]
106. old(alice) | ~creative(fred) [cnf transformation 51]
119. ~calm(fred) [cnf transformation 22]
127. ~kind(X0) [duplicate literal removal 73]
144. ~old(X0) [subsumption resolution 82,127]
147. ~generous(X0) | calm(X0) | ~patient(X0) [subsumption resolution 101,74]
149. ~generous(X0) | calm(X0) | creative(X0) [subsumption resolution 97,147]
150. ~creative(fred) [subsumption resolution 106,144]
151. generous(fred) [subsumption resolution 105,144]
219. calm(fred) | creative(fred) [resolution 149,151]
220. creative(fred) [subsumption resolution 219,119]
221. $false [subsumption resolution 220,150]
% SZS output end Proof for 5894003563110220882364295
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not wise or calm then someone is patient or curious. Everyone who is not calm or not tall is either rich or not patient and vice versa. If someone is not kind then someone is both creative and not creative and vice versa. Everyone who is wise or rich is not strong or not creative. If mary is either kind or not calm then lucy is creative. If someone is not funny or not wise then someone is not creative or kind. Everyone who is happy or not patient is patient or not generous and vice versa. Everyone who is both strong and not kind is not funny or rich. Everyone who is either not patient or creative is either not funny or patient and vice versa. If fred is happy then john is both calm and not humble and vice versa. Everyone who is both rich and not funny is both patient and not creative and vice versa. Everyone who is both not tall and funny is quiet and vice versa. If fred is either not tall or not brave then someone is both strong and not quiet. Everyone who is tall is not wise. Everyone who is both strong and not kind is not happy and vice versa. Everyone who is not strong is not funny. Someone is either not creative or wise. Mary is either patient or not creative. John is either not rich or not generous. Someone is both not humble and patient. Someone is kind. John is not brave. Alice is either not funny or generous. Someone is happy or rich. | Alice is not brave. | neutral | ((?[X]:((~wise(X)<~>calm(X))))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((~calm(X)|~tall(X))<=>(rich(X)<~>~patient(X))))&
((?[X]:(~kind(X)))<=>(?[X]:((creative(X)&~creative(X)))))&
(![X]:((wise(X)|rich(X))=>(~strong(X)|~creative(X))))&
(((kind(mary)<~>~calm(mary)))=>(creative(lucy)))&
((?[X]:((~funny(X)|~wise(X))))=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((happy(X)|~patient(X))<=>(patient(X)|~generous(X))))&
(![X]:((strong(X)&~kind(X))=>(~funny(X)|rich(X))))&
(![X]:((~patient(X)<~>creative(X))<=>(~funny(X)<~>patient(X))))&
((happy(fred))<=>((calm(john)&~humble(john))))&
(![X]:((rich(X)&~funny(X))<=>(patient(X)&~creative(X))))&
(![X]:((~tall(X)&funny(X))<=>quiet(X)))&
(((~tall(fred)<~>~brave(fred)))=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:(tall(X)=>~wise(X)))&
(![X]:((strong(X)&~kind(X))<=>~happy(X)))&
(![X]:(~strong(X)=>~funny(X)))&
(?[X]:((~creative(X)<~>wise(X))))&
((patient(mary)<~>~creative(mary)))&
((~rich(john)<~>~generous(john)))&
(?[X]:((~humble(X)&patient(X))))&
(?[X]:(kind(X)))&
(~brave(john))&
((~funny(alice)<~>generous(alice)))&
(?[X]:((happy(X)|rich(X)))) | ~brave(alice) | [] | null | 0 |
Everyone who is not creative is rich.
If alice is either not wise or not patient then susan is both brave and kind and vice versa.
If someone is both wise and funny then someone is both not calm and generous.
If lucy is both not funny and curious then susan is either not wise or generous and vice versa.
Everyone who is either brave or not funny is not kind or creative and vice versa.
If fred is either kind or not calm then john is either not old or not curious and vice versa.
Everyone who is not humble is not calm.
Everyone who is funny is either not kind or generous and vice versa.
If fred is either patient or not humble then mary is old and vice versa.
Everyone who is brave is not old.
If john is calm then fred is happy and vice versa.
If alice is not brave or curious then someone is patient and vice versa.
Everyone who is either not calm or kind is either not curious or not patient.
Everyone who is either patient or not old is both patient and not patient.
Everyone who is not funny is both happy and not calm.
If someone is either not kind or kind then someone is both strong and not old and vice versa.
Lucy is either not old or not generous.
John is both brave and not generous.
Susan is calm or humble.
Someone is not strong or not rich.
Someone is not rich.
Someone is either kind or not happy.
Mary is either happy or not patient.
John is kind or not quiet. | Alice is not wise. | neutral | (![X]:(~creative(X)=>rich(X)))&
(((~wise(alice)<~>~patient(alice)))<=>((brave(susan)&kind(susan))))&
((?[X]:((wise(X)&funny(X))))=>(?[X]:((~calm(X)&generous(X)))))&
(((~funny(lucy)&curious(lucy)))<=>((~wise(susan)<~>generous(susan))))&
(![X]:((brave(X)<~>~funny(X))<=>(~kind(X)|creative(X))))&
(((kind(fred)<~>~calm(fred)))<=>((~old(john)<~>~curious(john))))&
(![X]:(~humble(X)=>~calm(X)))&
(![X]:(funny(X)<=>(~kind(X)<~>generous(X))))&
(((patient(fred)<~>~humble(fred)))<=>(old(mary)))&
(![X]:(brave(X)=>~old(X)))&
((calm(john))<=>(happy(fred)))&
(((~brave(alice)|curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~calm(X)<~>kind(X))=>(~curious(X)<~>~patient(X))))&
(![X]:((patient(X)<~>~old(X))=>(patient(X)&~patient(X))))&
(![X]:(~funny(X)=>(happy(X)&~calm(X))))&
((?[X]:((~kind(X)<~>kind(X))))<=>(?[X]:((strong(X)&~old(X)))))&
((~old(lucy)<~>~generous(lucy)))&
((brave(john)&~generous(john)))&
((calm(susan)|humble(susan)))&
(?[X]:((~strong(X)|~rich(X))))&
(?[X]:(~rich(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
((happy(mary)<~>~patient(mary)))&
((kind(john)|~quiet(john))) | ~wise(alice) | [] | null | 0 |
Everyone who is either happy or not kind is either not tall or patient and vice versa.
If mary is either not patient or tall then lucy is either not generous or not creative.
If someone is either not generous or wise then someone is strong.
Everyone who is curious is not kind.
Everyone who is curious or not curious is both not quiet and kind.
Everyone who is strong or not happy is both wise and funny.
Everyone who is both not kind and generous is not old or calm.
If someone is not creative or wise then lucy is both funny and rich.
If someone is not calm or not patient then someone is quiet or not tall and vice versa.
Everyone who is old is quiet or funny and vice versa.
Everyone who is either strong or not calm is either patient or not strong.
If susan is both strong and not brave then lucy is either not tall or not kind.
Everyone who is not brave is not generous and vice versa.
If someone is not generous or not happy then fred is strong or not tall and vice versa.
Everyone who is both wise and not curious is rich or not old and vice versa.
Lucy is generous.
Someone is both patient and not rich.
Someone is not strong. | Mary is generous. | neutral | (![X]:((happy(X)<~>~kind(X))<=>(~tall(X)<~>patient(X))))&
(((~patient(mary)<~>tall(mary)))=>((~generous(lucy)<~>~creative(lucy))))&
((?[X]:((~generous(X)<~>wise(X))))=>(?[X]:(strong(X))))&
(![X]:(curious(X)=>~kind(X)))&
(![X]:((curious(X)|~curious(X))=>(~quiet(X)&kind(X))))&
(![X]:((strong(X)|~happy(X))=>(wise(X)&funny(X))))&
(![X]:((~kind(X)&generous(X))=>(~old(X)|calm(X))))&
((?[X]:((~creative(X)|wise(X))))=>((funny(lucy)&rich(lucy))))&
((?[X]:((~calm(X)|~patient(X))))<=>(?[X]:((quiet(X)|~tall(X)))))&
(![X]:(old(X)<=>(quiet(X)|funny(X))))&
(![X]:((strong(X)<~>~calm(X))=>(patient(X)<~>~strong(X))))&
(((strong(susan)&~brave(susan)))=>((~tall(lucy)<~>~kind(lucy))))&
(![X]:(~brave(X)<=>~generous(X)))&
((?[X]:((~generous(X)|~happy(X))))<=>((strong(fred)|~tall(fred))))&
(![X]:((wise(X)&~curious(X))<=>(rich(X)|~old(X))))&
(generous(lucy))&
(?[X]:((patient(X)&~rich(X))))&
(?[X]:(~strong(X))) | generous(mary) | [] | null | 0 |
If someone is not kind then someone is not happy or calm.
Everyone who is either not generous or not tall is either quiet or not patient.
Everyone who is both not calm and not rich is quiet.
If paul is tall then someone is either not creative or not happy and vice versa.
Everyone who is not funny is either not funny or not quiet and vice versa.
If lucy is quiet or wise then someone is either not patient or not old and vice versa.
If someone is wise then someone is calm or not wise and vice versa.
If someone is funny or not wise then someone is both generous and creative.
Everyone who is either not strong or calm is both not old and not kind.
If lucy is rich then someone is both not creative and not strong.
If lucy is not happy or brave then someone is not old or not tall and vice versa.
If someone is tall then someone is generous and vice versa.
Everyone who is calm is either not tall or not creative.
If someone is not tall then someone is both not old and not generous.
Everyone who is not tall is funny or not curious.
If alice is patient then someone is both patient and calm.
Someone is both not kind and rich.
Someone is not rich or not tall.
Mary is kind or not tall.
Someone is not happy or not generous.
Someone is either not old or not wise.
Someone is both strong and not kind.
John is both not rich and creative.
Lucy is either happy or not strong. | Lucy is not funny. | neutral | ((?[X]:(~kind(X)))=>(?[X]:((~happy(X)|calm(X)))))&
(![X]:((~generous(X)<~>~tall(X))=>(quiet(X)<~>~patient(X))))&
(![X]:((~calm(X)&~rich(X))=>quiet(X)))&
((tall(paul))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:(~funny(X)<=>(~funny(X)<~>~quiet(X))))&
(((quiet(lucy)|wise(lucy)))<=>(?[X]:((~patient(X)<~>~old(X)))))&
((?[X]:(wise(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
((?[X]:((funny(X)|~wise(X))))=>(?[X]:((generous(X)&creative(X)))))&
(![X]:((~strong(X)<~>calm(X))=>(~old(X)&~kind(X))))&
((rich(lucy))=>(?[X]:((~creative(X)&~strong(X)))))&
(((~happy(lucy)|brave(lucy)))<=>(?[X]:((~old(X)|~tall(X)))))&
((?[X]:(tall(X)))<=>(?[X]:(generous(X))))&
(![X]:(calm(X)=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:(~tall(X)=>(funny(X)|~curious(X))))&
((patient(alice))=>(?[X]:((patient(X)&calm(X)))))&
(?[X]:((~kind(X)&rich(X))))&
(?[X]:((~rich(X)|~tall(X))))&
((kind(mary)|~tall(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
(?[X]:((~old(X)<~>~wise(X))))&
(?[X]:((strong(X)&~kind(X))))&
((~rich(john)&creative(john)))&
((happy(lucy)<~>~strong(lucy))) | ~funny(lucy) | [] | null | 0 |
If someone is both not generous and not humble then someone is old or calm and vice versa. Everyone who is either tall or not humble is both not happy and rich. If someone is not funny or brave then john is both brave and kind. If someone is both patient and quiet then alice is both kind and tall. If someone is quiet or not funny then fred is strong or generous. If someone is not funny then mary is either quiet or generous. If john is either not funny or not kind then someone is curious or tall and vice versa. Everyone who is funny or wise is either strong or not strong and vice versa. If someone is either calm or curious then mary is both not rich and brave and vice versa. If someone is either not creative or not wise then someone is both not rich and not tall. If paul is not happy or creative then someone is either not happy or not quiet and vice versa. If susan is either quiet or not funny then paul is patient or kind. If someone is rich then susan is not humble and vice versa. Everyone who is not wise or humble is not humble and vice versa. Everyone who is not calm or not happy is both generous and tall and vice versa. Everyone who is either not old or funny is old and vice versa. Someone is not generous or happy. Someone is not kind. Paul is either kind or old. Someone is generous. Someone is not old. Alice is wise or not generous. | Susan is creative. | contradiction | ((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((old(X)|calm(X)))))&
(![X]:((tall(X)<~>~humble(X))=>(~happy(X)&rich(X))))&
((?[X]:((~funny(X)|brave(X))))=>((brave(john)&kind(john))))&
((?[X]:((patient(X)&quiet(X))))=>((kind(alice)&tall(alice))))&
((?[X]:((quiet(X)|~funny(X))))=>((strong(fred)|generous(fred))))&
((?[X]:(~funny(X)))=>((quiet(mary)<~>generous(mary))))&
(((~funny(john)<~>~kind(john)))<=>(?[X]:((curious(X)|tall(X)))))&
(![X]:((funny(X)|wise(X))<=>(strong(X)<~>~strong(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>((~rich(mary)&brave(mary))))&
((?[X]:((~creative(X)<~>~wise(X))))=>(?[X]:((~rich(X)&~tall(X)))))&
(((~happy(paul)|creative(paul)))<=>(?[X]:((~happy(X)<~>~quiet(X)))))&
(((quiet(susan)<~>~funny(susan)))=>((patient(paul)|kind(paul))))&
((?[X]:(rich(X)))<=>(~humble(susan)))&
(![X]:((~wise(X)|humble(X))<=>~humble(X)))&
(![X]:((~calm(X)|~happy(X))<=>(generous(X)&tall(X))))&
(![X]:((~old(X)<~>funny(X))<=>old(X)))&
(?[X]:((~generous(X)|happy(X))))&
(?[X]:(~kind(X)))&
((kind(paul)<~>old(paul)))&
(?[X]:(generous(X)))&
(?[X]:(~old(X)))&
((wise(alice)|~generous(alice))) | creative(susan) | [
"p1",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 240676845077375227274513
% SZS output start Proof for 240676845077375227274513
2. ! [X0] : ((tall(X0) <~> ~humble(X0)) => (rich(X0) & ~happy(X0))) [input p1]
10. ? [X0] : (~creative(X0) <~> ~wise(X0)) => ? [X0] : (~tall(X0) & ~rich(X0)) [input p9]
14. ! [X0] : ((humble(X0) | ~wise(X0)) <=> ~humble(X0)) [input p13]
15. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (tall(X0) & generous(X0))) [input p14]
23. creative(susan) [input hypothesis]
25. ? [X0] : (~creative(X0) <~> ~wise(X0)) => ? [X1] : (~tall(X1) & ~rich(X1)) [rectify 10]
26. ! [X0] : ((rich(X0) & ~happy(X0)) | (tall(X0) <=> ~humble(X0))) [ennf transformation 2]
32. ? [X1] : (~tall(X1) & ~rich(X1)) | ! [X0] : (~creative(X0) <=> ~wise(X0)) [ennf transformation 25]
40. ! [X0] : ((rich(X0) & ~happy(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0)))) [nnf transformation 26]
53. ? [X1] : (~tall(X1) & ~rich(X1)) | ! [X0] : ((~creative(X0) | wise(X0)) & (~wise(X0) | creative(X0))) [nnf transformation 32]
54. ? [X0] : (~tall(X0) & ~rich(X0)) | ! [X1] : ((~creative(X1) | wise(X1)) & (~wise(X1) | creative(X1))) [rectify 53]
55. ? [X0] : (~tall(X0) & ~rich(X0)) => (~tall(sK4) & ~rich(sK4)) [choice axiom]
56. (~tall(sK4) & ~rich(sK4)) | ! [X1] : ((~creative(X1) | wise(X1)) & (~wise(X1) | creative(X1))) [skolemisation 54,55]
67. ! [X0] : (((humble(X0) | ~wise(X0)) | humble(X0)) & (~humble(X0) | (~humble(X0) & wise(X0)))) [nnf transformation 14]
68. ! [X0] : ((humble(X0) | ~wise(X0) | humble(X0)) & (~humble(X0) | (~humble(X0) & wise(X0)))) [flattening 67]
69. ! [X0] : (((~happy(X0) | ~calm(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 15]
70. ! [X0] : ((~happy(X0) | ~calm(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (happy(X0) & calm(X0)))) [flattening 69]
87. ~happy(X0) | tall(X0) | humble(X0) [cnf transformation 40]
121. ~tall(sK4) | ~creative(X1) | wise(X1) [cnf transformation 56]
133. ~humble(X0) | ~humble(X0) [cnf transformation 68]
134. humble(X0) | ~wise(X0) | humble(X0) [cnf transformation 68]
138. happy(X0) | tall(X0) [cnf transformation 70]
151. creative(susan) [cnf transformation 23]
154. ~humble(X0) [duplicate literal removal 133]
155. ~wise(X0) | humble(X0) [duplicate literal removal 134]
296. 31 <=> ! [X1] : (~creative(X1) | wise(X1)) [avatar definition]
297. ~creative(X1) | wise(X1) <- (31) [avatar component clause 296]
299. 32 <=> tall(sK4) [avatar definition]
301. ~tall(sK4) <- (~32) [avatar component clause 299]
302. 31 | ~32 [avatar split clause 121,299,296]
426. wise(susan) <- (31) [resolution 297,151]
429. humble(susan) <- (31) [resolution 426,155]
430. $false <- (31) [subsumption resolution 429,154]
431. ~31 [avatar contradiction clause 430]
450. tall(X0) | humble(X0) | tall(X0) [resolution 87,138]
452. tall(X0) | humble(X0) [duplicate literal removal 450]
465. tall(X0) [subsumption resolution 452,154]
466. $false <- (~32) [subsumption resolution 301,465]
467. 32 [avatar contradiction clause 466]
468. $false [avatar sat refutation 302,431,467]
% SZS output end Proof for 240676845077375227274513
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not funny then lucy is strong and vice versa. If john is not wise or humble then fred is both wise and creative and vice versa. If fred is generous then mary is not wise or not funny. If fred is both wise and not funny then paul is both not humble and old. Everyone who is either patient or not patient is both creative and funny and vice versa. If susan is both not kind and old then susan is not old. Everyone who is not kind is not wise or funny and vice versa. Everyone who is not kind or rich is either not quiet or calm. If lucy is humble then alice is curious and vice versa. Everyone who is not generous or patient is not creative and vice versa. Everyone who is both rich and strong is both generous and not curious. Everyone who is humble is not patient or not humble. Everyone who is not humble or tall is both funny and wise. If someone is patient or not quiet then paul is not patient or strong and vice versa. Everyone who is not happy or not patient is not strong and vice versa. Someone is both curious and not old. Fred is not strong. Alice is either not generous or calm. Fred is tall. Alice is generous. Someone is funny or not patient. Someone is not patient. | Fred is not happy. | neutral | ((~funny(alice))<=>(strong(lucy)))&
(((~wise(john)|humble(john)))<=>((wise(fred)&creative(fred))))&
((generous(fred))=>((~wise(mary)|~funny(mary))))&
(((wise(fred)&~funny(fred)))=>((~humble(paul)&old(paul))))&
(![X]:((patient(X)<~>~patient(X))<=>(creative(X)&funny(X))))&
(((~kind(susan)&old(susan)))=>(~old(susan)))&
(![X]:(~kind(X)<=>(~wise(X)|funny(X))))&
(![X]:((~kind(X)|rich(X))=>(~quiet(X)<~>calm(X))))&
((humble(lucy))<=>(curious(alice)))&
(![X]:((~generous(X)|patient(X))<=>~creative(X)))&
(![X]:((rich(X)&strong(X))=>(generous(X)&~curious(X))))&
(![X]:(humble(X)=>(~patient(X)|~humble(X))))&
(![X]:((~humble(X)|tall(X))=>(funny(X)&wise(X))))&
((?[X]:((patient(X)|~quiet(X))))<=>((~patient(paul)|strong(paul))))&
(![X]:((~happy(X)|~patient(X))<=>~strong(X)))&
(?[X]:((curious(X)&~old(X))))&
(~strong(fred))&
((~generous(alice)<~>calm(alice)))&
(tall(fred))&
(generous(alice))&
(?[X]:((funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | ~happy(fred) | [] | null | 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 8206222390639886699202884
% SZS output start Proof for 8206222390639886699202884
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 8206222390639886699202884
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not quiet is both not tall and not kind and vice versa.
Everyone who is creative is both not humble and curious and vice versa.
Everyone who is humble is either quiet or happy and vice versa.
Everyone who is strong is both creative and not quiet.
Everyone who is strong is both generous and not generous.
Everyone who is both strong and not creative is either not brave or old.
If someone is not quiet then someone is both not creative and not brave.
Everyone who is either not calm or not creative is either quiet or kind and vice versa.
If paul is not wise then paul is either not funny or wise and vice versa.
Everyone who is either kind or humble is either not strong or humble.
If someone is not happy or tall then john is brave or not creative.
Everyone who is not rich or happy is not happy.
If someone is not quiet then paul is both not strong and not patient and vice versa.
If someone is funny then susan is both not calm and not funny and vice versa.
If someone is not kind then someone is kind.
Everyone who is both not wise and creative is both not brave and tall and vice versa.
Someone is not calm.
Fred is not generous or not tall.
Someone is patient or not patient.
Alice is either creative or calm.
Lucy is both not wise and not funny.
Someone is kind.
Someone is not brave or not tall.
Mary is both rich and not generous. | Paul is patient. | contradiction | (![X]:((generous(X)&~quiet(X))<=>(~tall(X)&~kind(X))))&
(![X]:(creative(X)<=>(~humble(X)&curious(X))))&
(![X]:(humble(X)<=>(quiet(X)<~>happy(X))))&
(![X]:(strong(X)=>(creative(X)&~quiet(X))))&
(![X]:(strong(X)=>(generous(X)&~generous(X))))&
(![X]:((strong(X)&~creative(X))=>(~brave(X)<~>old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:((~calm(X)<~>~creative(X))<=>(quiet(X)<~>kind(X))))&
((~wise(paul))<=>((~funny(paul)<~>wise(paul))))&
(![X]:((kind(X)<~>humble(X))=>(~strong(X)<~>humble(X))))&
((?[X]:((~happy(X)|tall(X))))=>((brave(john)|~creative(john))))&
(![X]:((~rich(X)|happy(X))=>~happy(X)))&
((?[X]:(~quiet(X)))<=>((~strong(paul)&~patient(paul))))&
((?[X]:(funny(X)))<=>((~calm(susan)&~funny(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(kind(X))))&
(![X]:((~wise(X)&creative(X))<=>(~brave(X)&tall(X))))&
(?[X]:(~calm(X)))&
((~generous(fred)|~tall(fred)))&
(?[X]:((patient(X)|~patient(X))))&
((creative(alice)<~>calm(alice)))&
((~wise(lucy)&~funny(lucy)))&
(?[X]:(kind(X)))&
(?[X]:((~brave(X)|~tall(X))))&
((rich(mary)&~generous(mary))) | patient(paul) | [
"p1",
"p2",
"p4",
"p7",
"p9",
"p11",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 8586884850582957910121727
% SZS output start Proof for 8586884850582957910121727
2. ! [X0] : (creative(X0) <=> (curious(X0) & ~humble(X0))) [input p1]
3. ! [X0] : (humble(X0) <=> (quiet(X0) <~> happy(X0))) [input p2]
5. ! [X0] : (strong(X0) => (~generous(X0) & generous(X0))) [input p4]
8. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (quiet(X0) <~> kind(X0))) [input p7]
10. ! [X0] : ((kind(X0) <~> humble(X0)) => (~strong(X0) <~> humble(X0))) [input p9]
12. ! [X0] : ((happy(X0) | ~rich(X0)) => ~happy(X0)) [input p11]
13. ? [X0] : ~quiet(X0) <=> (~patient(paul) & ~strong(paul)) [input p12]
20. creative(alice) <~> calm(alice) [input p19]
25. patient(paul) [input hypothesis]
29. ! [X0] : (happy(X0) => ~happy(X0)) [pure predicate removal 12]
31. ! [X0] : ((~generous(X0) & generous(X0)) | ~strong(X0)) [ennf transformation 5]
35. ! [X0] : ((~strong(X0) <~> humble(X0)) | (kind(X0) <=> humble(X0))) [ennf transformation 10]
38. ! [X0] : (~happy(X0) | ~happy(X0)) [ennf transformation 29]
42. ! [X0] : ((creative(X0) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | ~creative(X0))) [nnf transformation 2]
43. ! [X0] : ((creative(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | ~creative(X0))) [flattening 42]
44. ! [X0] : ((humble(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0)))) & (((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ~humble(X0))) [nnf transformation 3]
49. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 8]
51. ! [X0] : (((~humble(X0) | strong(X0)) & (humble(X0) | ~strong(X0))) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) [nnf transformation 35]
52. (? [X0] : ~quiet(X0) | (patient(paul) | strong(paul))) & ((~patient(paul) & ~strong(paul)) | ! [X0] : quiet(X0)) [nnf transformation 13]
53. (? [X0] : ~quiet(X0) | patient(paul) | strong(paul)) & ((~patient(paul) & ~strong(paul)) | ! [X0] : quiet(X0)) [flattening 52]
54. (? [X0] : ~quiet(X0) | patient(paul) | strong(paul)) & ((~patient(paul) & ~strong(paul)) | ! [X1] : quiet(X1)) [rectify 53]
55. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
56. (~quiet(sK1) | patient(paul) | strong(paul)) & ((~patient(paul) & ~strong(paul)) | ! [X1] : quiet(X1)) [skolemisation 54,55]
71. (~calm(alice) | ~creative(alice)) & (calm(alice) | creative(alice)) [nnf transformation 20]
80. ~humble(X0) | ~creative(X0) [cnf transformation 43]
85. ~quiet(X0) | happy(X0) | humble(X0) [cnf transformation 44]
89. generous(X0) | ~strong(X0) [cnf transformation 31]
90. ~strong(X0) | ~generous(X0) [cnf transformation 31]
98. ~calm(X0) | ~quiet(X0) | ~kind(X0) | creative(X0) [cnf transformation 49]
110. ~humble(X0) | strong(X0) | kind(X0) | ~humble(X0) [cnf transformation 51]
113. ~happy(X0) | ~happy(X0) [cnf transformation 38]
115. ~patient(paul) | quiet(X1) [cnf transformation 56]
128. calm(alice) | creative(alice) [cnf transformation 71]
135. patient(paul) [cnf transformation 25]
136. ~happy(X0) [duplicate literal removal 113]
138. ~humble(X0) | strong(X0) | kind(X0) [duplicate literal removal 110]
141. ~strong(X0) [subsumption resolution 89,90]
143. 1 <=> ! [X1] : quiet(X1) [avatar definition]
144. quiet(X1) <- (1) [avatar component clause 143]
165. ~humble(X0) | kind(X0) [subsumption resolution 138,141]
184. 10 <=> patient(paul) [avatar definition]
192. 1 | ~10 [avatar split clause 115,184,143]
212. 16 <=> ! [X1] : kind(X1) [avatar definition]
213. kind(X1) <- (16) [avatar component clause 212]
229. 20 <=> creative(alice) [avatar definition]
230. creative(alice) <- (20) [avatar component clause 229]
233. 21 <=> calm(alice) [avatar definition]
234. calm(alice) <- (21) [avatar component clause 233]
237. 20 | 21 [avatar split clause 128,233,229]
247. 10 [avatar split clause 135,184]
254. happy(X0) | humble(X0) <- (1) [resolution 85,144]
255. humble(X0) <- (1) [subsumption resolution 254,136]
257. kind(X1) <- (1) [resolution 255,165]
258. ~creative(X2) <- (1) [resolution 255,80]
259. $false <- (1, 20) [resolution 258,230]
260. ~1 | ~20 [avatar contradiction clause 259]
262. ~quiet(alice) | ~kind(alice) | creative(alice) <- (21) [resolution 98,234]
263. ~kind(alice) | creative(alice) <- (1, 21) [subsumption resolution 262,144]
264. creative(alice) <- (1, 16, 21) [subsumption resolution 263,213]
265. $false <- (1, 16, 21) [subsumption resolution 264,258]
266. ~1 | ~16 | ~21 [avatar contradiction clause 265]
268. 16 | ~1 [avatar split clause 257,143,212]
269. $false [avatar sat refutation 192,237,247,260,266,268]
% SZS output end Proof for 8586884850582957910121727
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or quiet is either not tall or not kind.
Everyone who is both not humble and rich is both wise and not tall and vice versa.
If someone is tall or not curious then fred is both not wise and kind and vice versa.
Everyone who is kind is either quiet or humble and vice versa.
If john is either humble or quiet then alice is both creative and not old and vice versa.
Everyone who is either brave or not patient is old or wise.
Everyone who is patient is not strong or not brave and vice versa.
Everyone who is both wise and happy is not old or kind and vice versa.
Everyone who is either not old or not curious is not wise or not funny and vice versa.
If someone is either not strong or not funny then alice is not kind or humble and vice versa.
Everyone who is either not funny or not generous is both funny and brave.
If lucy is not curious or old then someone is brave or not brave and vice versa.
Everyone who is either not happy or tall is both kind and not funny and vice versa.
If mary is not calm then someone is either not patient or curious and vice versa.
Everyone who is rich or funny is not quiet or old and vice versa.
Someone is not calm or happy.
Someone is either rich or brave.
John is creative or rich.
Lucy is not calm or patient. | Fred is not kind. | neutral | (![X]:((~calm(X)<~>quiet(X))=>(~tall(X)<~>~kind(X))))&
(![X]:((~humble(X)&rich(X))<=>(wise(X)&~tall(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((~wise(fred)&kind(fred))))&
(![X]:(kind(X)<=>(quiet(X)<~>humble(X))))&
(((humble(john)<~>quiet(john)))<=>((creative(alice)&~old(alice))))&
(![X]:((brave(X)<~>~patient(X))=>(old(X)|wise(X))))&
(![X]:(patient(X)<=>(~strong(X)|~brave(X))))&
(![X]:((wise(X)&happy(X))<=>(~old(X)|kind(X))))&
(![X]:((~old(X)<~>~curious(X))<=>(~wise(X)|~funny(X))))&
((?[X]:((~strong(X)<~>~funny(X))))<=>((~kind(alice)|humble(alice))))&
(![X]:((~funny(X)<~>~generous(X))=>(funny(X)&brave(X))))&
(((~curious(lucy)|old(lucy)))<=>(?[X]:((brave(X)|~brave(X)))))&
(![X]:((~happy(X)<~>tall(X))<=>(kind(X)&~funny(X))))&
((~calm(mary))<=>(?[X]:((~patient(X)<~>curious(X)))))&
(![X]:((rich(X)|funny(X))<=>(~quiet(X)|old(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:((rich(X)<~>brave(X))))&
((creative(john)|rich(john)))&
((~calm(lucy)|patient(lucy))) | ~kind(fred) | [] | null | 0 |
Everyone who is curious or generous is not generous and vice versa.
If susan is not quiet then alice is both wise and not humble and vice versa.
If john is both funny and not humble then john is creative and vice versa.
Everyone who is not brave or not generous is both not funny and not brave and vice versa.
If someone is either not humble or not old then lucy is both not calm and rich.
If paul is both funny and curious then john is both not creative and quiet.
Everyone who is tall or calm is not wise.
Everyone who is either not patient or not wise is either not creative or not patient.
Everyone who is funny or not humble is brave and vice versa.
Everyone who is both not wise and not quiet is not generous or funny.
Everyone who is happy or generous is either not curious or generous and vice versa.
If someone is not generous then john is either not patient or creative.
Everyone who is either creative or generous is creative or not tall.
Everyone who is either not kind or not wise is either not generous or old and vice versa.
If someone is not rich or creative then paul is not patient and vice versa.
Everyone who is not calm is both not old and not rich and vice versa.
Someone is both not funny and not tall.
Susan is both curious and not strong.
Someone is both not strong and not generous.
Fred is either happy or strong.
Someone is either not rich or not happy. | Fred is not wise. | entailment | (![X]:((curious(X)|generous(X))<=>~generous(X)))&
((~quiet(susan))<=>((wise(alice)&~humble(alice))))&
(((funny(john)&~humble(john)))<=>(creative(john)))&
(![X]:((~brave(X)|~generous(X))<=>(~funny(X)&~brave(X))))&
((?[X]:((~humble(X)<~>~old(X))))=>((~calm(lucy)&rich(lucy))))&
(((funny(paul)&curious(paul)))=>((~creative(john)&quiet(john))))&
(![X]:((tall(X)|calm(X))=>~wise(X)))&
(![X]:((~patient(X)<~>~wise(X))=>(~creative(X)<~>~patient(X))))&
(![X]:((funny(X)|~humble(X))<=>brave(X)))&
(![X]:((~wise(X)&~quiet(X))=>(~generous(X)|funny(X))))&
(![X]:((happy(X)|generous(X))<=>(~curious(X)<~>generous(X))))&
((?[X]:(~generous(X)))=>((~patient(john)<~>creative(john))))&
(![X]:((creative(X)<~>generous(X))=>(creative(X)|~tall(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>(~generous(X)<~>old(X))))&
((?[X]:((~rich(X)|creative(X))))<=>(~patient(paul)))&
(![X]:(~calm(X)<=>(~old(X)&~rich(X))))&
(?[X]:((~funny(X)&~tall(X))))&
((curious(susan)&~strong(susan)))&
(?[X]:((~strong(X)&~generous(X))))&
((happy(fred)<~>strong(fred)))&
(?[X]:((~rich(X)<~>~happy(X)))) | ~wise(fred) | [
"p0",
"p3",
"p4",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1257819822538130638284886
% SZS output start Proof for 1257819822538130638284886
1. ! [X0] : ((generous(X0) | curious(X0)) <=> ~generous(X0)) [input p0]
4. ! [X0] : ((~generous(X0) | ~brave(X0)) <=> (~brave(X0) & ~funny(X0))) [input p3]
5. ? [X0] : (~humble(X0) <~> ~old(X0)) => (rich(lucy) & ~calm(lucy)) [input p4]
7. ! [X0] : ((calm(X0) | tall(X0)) => ~wise(X0)) [input p6]
9. ! [X0] : ((~humble(X0) | funny(X0)) <=> brave(X0)) [input p8]
16. ! [X0] : (~calm(X0) <=> (~rich(X0) & ~old(X0))) [input p15]
22. wise(fred) [input hypothesis]
23. ! [X0] : (~calm(X0) => (~rich(X0) & ~old(X0))) [unused predicate definition removal 16]
24. ! [X0] : (calm(X0) => ~wise(X0)) [pure predicate removal 7]
27. (rich(lucy) & ~calm(lucy)) | ! [X0] : (~humble(X0) <=> ~old(X0)) [ennf transformation 5]
30. ! [X0] : (~wise(X0) | ~calm(X0)) [ennf transformation 24]
35. ! [X0] : ((~rich(X0) & ~old(X0)) | calm(X0)) [ennf transformation 23]
36. ! [X0] : (((generous(X0) | curious(X0)) | generous(X0)) & (~generous(X0) | (~generous(X0) & ~curious(X0)))) [nnf transformation 1]
37. ! [X0] : ((generous(X0) | curious(X0) | generous(X0)) & (~generous(X0) | (~generous(X0) & ~curious(X0)))) [flattening 36]
42. ! [X0] : (((~generous(X0) | ~brave(X0)) | (brave(X0) | funny(X0))) & ((~brave(X0) & ~funny(X0)) | (generous(X0) & brave(X0)))) [nnf transformation 4]
43. ! [X0] : ((~generous(X0) | ~brave(X0) | brave(X0) | funny(X0)) & ((~brave(X0) & ~funny(X0)) | (generous(X0) & brave(X0)))) [flattening 42]
44. (rich(lucy) & ~calm(lucy)) | ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 27]
46. ! [X0] : (((~humble(X0) | funny(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) & ~funny(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | funny(X0) | ~brave(X0)) & (brave(X0) | (humble(X0) & ~funny(X0)))) [flattening 46]
65. ~generous(X0) | ~generous(X0) [cnf transformation 37]
76. ~brave(X0) | generous(X0) [cnf transformation 43]
79. ~calm(lucy) | ~humble(X0) | old(X0) [cnf transformation 44]
81. rich(lucy) | ~humble(X0) | old(X0) [cnf transformation 44]
84. ~calm(X0) | ~wise(X0) [cnf transformation 30]
90. brave(X0) | humble(X0) [cnf transformation 47]
112. ~old(X0) | calm(X0) [cnf transformation 35]
113. ~rich(X0) | calm(X0) [cnf transformation 35]
123. wise(fred) [cnf transformation 22]
128. ~generous(X0) [duplicate literal removal 65]
160. ~brave(X0) [subsumption resolution 76,128]
163. 7 <=> ! [X0] : (~humble(X0) | old(X0)) [avatar definition]
164. ~humble(X0) | old(X0) <- (7) [avatar component clause 163]
166. 8 <=> rich(lucy) [avatar definition]
168. rich(lucy) <- (8) [avatar component clause 166]
169. 7 | 8 [avatar split clause 81,166,163]
175. 10 <=> calm(lucy) [avatar definition]
177. ~calm(lucy) <- (~10) [avatar component clause 175]
178. 7 | ~10 [avatar split clause 79,175,163]
180. humble(X0) [subsumption resolution 90,160]
235. calm(lucy) <- (8) [resolution 113,168]
237. $false <- (8, ~10) [subsumption resolution 235,177]
238. ~8 | 10 [avatar contradiction clause 237]
239. old(X0) <- (7) [subsumption resolution 164,180]
240. calm(X0) <- (7) [resolution 239,112]
247. ~wise(X0) <- (7) [resolution 240,84]
262. $false <- (7) [resolution 247,123]
263. ~7 [avatar contradiction clause 262]
264. $false [avatar sat refutation 169,178,238,263]
% SZS output end Proof for 1257819822538130638284886
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative is both funny and patient.
Everyone who is calm is either not humble or happy and vice versa.
If lucy is either kind or tall then someone is both brave and strong.
If someone is happy or strong then someone is not brave.
Everyone who is either not rich or not old is curious or not tall.
Everyone who is either not curious or tall is tall and vice versa.
Everyone who is both kind and old is either tall or not funny.
Everyone who is both happy and calm is either not humble or wise and vice versa.
If mary is both quiet and not funny then mary is both not creative and calm and vice versa.
If susan is both wise and not tall then someone is both not tall and strong.
Everyone who is not brave or not generous is either not tall or humble.
Everyone who is both not strong and creative is both not generous and creative.
If someone is both curious and not brave then alice is both happy and generous.
Everyone who is not generous or not strong is generous and vice versa.
Everyone who is not curious is either not quiet or patient.
Everyone who is not wise is curious or not rich and vice versa.
Someone is both funny and tall.
Lucy is either not calm or not quiet. | Lucy is old. | neutral | (![X]:(~creative(X)=>(funny(X)&patient(X))))&
(![X]:(calm(X)<=>(~humble(X)<~>happy(X))))&
(((kind(lucy)<~>tall(lucy)))=>(?[X]:((brave(X)&strong(X)))))&
((?[X]:((happy(X)|strong(X))))=>(?[X]:(~brave(X))))&
(![X]:((~rich(X)<~>~old(X))=>(curious(X)|~tall(X))))&
(![X]:((~curious(X)<~>tall(X))<=>tall(X)))&
(![X]:((kind(X)&old(X))=>(tall(X)<~>~funny(X))))&
(![X]:((happy(X)&calm(X))<=>(~humble(X)<~>wise(X))))&
(((quiet(mary)&~funny(mary)))<=>((~creative(mary)&calm(mary))))&
(((wise(susan)&~tall(susan)))=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~brave(X)|~generous(X))=>(~tall(X)<~>humble(X))))&
(![X]:((~strong(X)&creative(X))=>(~generous(X)&creative(X))))&
((?[X]:((curious(X)&~brave(X))))=>((happy(alice)&generous(alice))))&
(![X]:((~generous(X)|~strong(X))<=>generous(X)))&
(![X]:(~curious(X)=>(~quiet(X)<~>patient(X))))&
(![X]:(~wise(X)<=>(curious(X)|~rich(X))))&
(?[X]:((funny(X)&tall(X))))&
((~calm(lucy)<~>~quiet(lucy))) | old(lucy) | [] | null | 0 |
Everyone who is both not happy and not brave is either creative or patient.
Everyone who is either brave or patient is either not humble or curious and vice versa.
Everyone who is both not humble and humble is not wise or not rich and vice versa.
Everyone who is either happy or not generous is old.
Everyone who is calm is both not brave and not tall and vice versa.
If fred is not funny then someone is both not patient and not quiet and vice versa.
If john is not creative then alice is both not quiet and not brave.
Everyone who is happy is not humble or not creative.
Everyone who is both not strong and kind is not calm and vice versa.
If john is both not tall and old then fred is rich or wise and vice versa.
If someone is not generous then someone is creative or patient.
Everyone who is both not rich and happy is calm and vice versa.
If someone is not patient or rich then someone is both not brave and not happy.
Everyone who is both not patient and curious is funny and vice versa.
Someone is not generous.
Someone is either old or not curious.
Someone is not patient or creative.
Someone is both not patient and not old.
John is both humble and happy.
Someone is either not rich or not strong.
Paul is creative. | John is not brave. | contradiction | (![X]:((~happy(X)&~brave(X))=>(creative(X)<~>patient(X))))&
(![X]:((brave(X)<~>patient(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((~humble(X)&humble(X))<=>(~wise(X)|~rich(X))))&
(![X]:((happy(X)<~>~generous(X))=>old(X)))&
(![X]:(calm(X)<=>(~brave(X)&~tall(X))))&
((~funny(fred))<=>(?[X]:((~patient(X)&~quiet(X)))))&
((~creative(john))=>((~quiet(alice)&~brave(alice))))&
(![X]:(happy(X)=>(~humble(X)|~creative(X))))&
(![X]:((~strong(X)&kind(X))<=>~calm(X)))&
(((~tall(john)&old(john)))<=>((rich(fred)|wise(fred))))&
((?[X]:(~generous(X)))=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~rich(X)&happy(X))<=>calm(X)))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((~brave(X)&~happy(X)))))&
(![X]:((~patient(X)&curious(X))<=>funny(X)))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)<~>~curious(X))))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((~patient(X)&~old(X))))&
((humble(john)&happy(john)))&
(?[X]:((~rich(X)<~>~strong(X))))&
(creative(paul)) | ~brave(john) | [
"p2",
"p4",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 1480968116012194613244099
% SZS output start Proof for 1480968116012194613244099
3. ! [X0] : ((humble(X0) & ~humble(X0)) <=> (~rich(X0) | ~wise(X0))) [input p2]
5. ! [X0] : (calm(X0) <=> (~tall(X0) & ~brave(X0))) [input p4]
10. (old(john) & ~tall(john)) <=> (wise(fred) | rich(fred)) [input p9]
12. ! [X0] : ((happy(X0) & ~rich(X0)) <=> calm(X0)) [input p11]
22. ~brave(john) [input hypothesis]
35. ! [X0] : (((humble(X0) & ~humble(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (~humble(X0) | humble(X0)))) [nnf transformation 3]
36. ! [X0] : (((humble(X0) & ~humble(X0)) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | ~humble(X0) | humble(X0))) [flattening 35]
38. ! [X0] : ((calm(X0) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ~calm(X0))) [nnf transformation 5]
39. ! [X0] : ((calm(X0) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ~calm(X0))) [flattening 38]
46. ((old(john) & ~tall(john)) | (~wise(fred) & ~rich(fred))) & ((wise(fred) | rich(fred)) | (~old(john) | tall(john))) [nnf transformation 10]
47. ((old(john) & ~tall(john)) | (~wise(fred) & ~rich(fred))) & (wise(fred) | rich(fred) | ~old(john) | tall(john)) [flattening 46]
51. ! [X0] : (((happy(X0) & ~rich(X0)) | ~calm(X0)) & (calm(X0) | (~happy(X0) | rich(X0)))) [nnf transformation 12]
52. ! [X0] : (((happy(X0) & ~rich(X0)) | ~calm(X0)) & (calm(X0) | ~happy(X0) | rich(X0))) [flattening 51]
81. ~humble(X0) | wise(X0) [cnf transformation 36]
82. ~humble(X0) | rich(X0) [cnf transformation 36]
83. wise(X0) | humble(X0) [cnf transformation 36]
84. rich(X0) | humble(X0) [cnf transformation 36]
89. tall(X0) | calm(X0) | brave(X0) [cnf transformation 39]
101. ~tall(john) | ~wise(fred) [cnf transformation 47]
106. ~rich(X0) | ~calm(X0) [cnf transformation 52]
126. ~brave(john) [cnf transformation 22]
127. rich(X0) [subsumption resolution 82,84]
128. wise(X0) [subsumption resolution 81,83]
162. ~tall(john) [subsumption resolution 101,128]
175. ~calm(X0) [subsumption resolution 106,127]
223. calm(john) | brave(john) [resolution 89,162]
225. brave(john) [subsumption resolution 223,175]
226. $false [subsumption resolution 225,126]
% SZS output end Proof for 1480968116012194613244099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If fred is calm or not strong then mary is not quiet.
If someone is not brave then mary is funny and vice versa.
If someone is kind or not humble then fred is both not creative and curious and vice versa.
Everyone who is both happy and not happy is either calm or not curious.
Everyone who is funny or not kind is either not humble or not quiet.
Everyone who is either not humble or wise is calm.
Everyone who is both not calm and rich is either not tall or strong and vice versa.
Everyone who is strong is both not tall and not generous.
If alice is both quiet and old then someone is rich.
Everyone who is tall is either not funny or calm and vice versa.
Everyone who is both not kind and not calm is patient or quiet.
Everyone who is funny or kind is either not generous or not kind and vice versa.
If someone is both generous and old then someone is funny and vice versa.
If someone is both not rich and not funny then paul is quiet or old.
Everyone who is calm or not tall is either not brave or not calm and vice versa.
Everyone who is both not tall and not brave is strong.
Paul is not curious or not patient.
Someone is not brave or happy.
Someone is both calm and not wise.
Lucy is not calm.
Lucy is either not rich or strong.
Alice is both calm and quiet.
Someone is creative or not happy.
Someone is both not old and tall. | Lucy is not generous. | entailment | (((calm(fred)|~strong(fred)))=>(~quiet(mary)))&
((?[X]:(~brave(X)))<=>(funny(mary)))&
((?[X]:((kind(X)|~humble(X))))<=>((~creative(fred)&curious(fred))))&
(![X]:((happy(X)&~happy(X))=>(calm(X)<~>~curious(X))))&
(![X]:((funny(X)|~kind(X))=>(~humble(X)<~>~quiet(X))))&
(![X]:((~humble(X)<~>wise(X))=>calm(X)))&
(![X]:((~calm(X)&rich(X))<=>(~tall(X)<~>strong(X))))&
(![X]:(strong(X)=>(~tall(X)&~generous(X))))&
(((quiet(alice)&old(alice)))=>(?[X]:(rich(X))))&
(![X]:(tall(X)<=>(~funny(X)<~>calm(X))))&
(![X]:((~kind(X)&~calm(X))=>(patient(X)|quiet(X))))&
(![X]:((funny(X)|kind(X))<=>(~generous(X)<~>~kind(X))))&
((?[X]:((generous(X)&old(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~rich(X)&~funny(X))))=>((quiet(paul)|old(paul))))&
(![X]:((calm(X)|~tall(X))<=>(~brave(X)<~>~calm(X))))&
(![X]:((~tall(X)&~brave(X))=>strong(X)))&
((~curious(paul)|~patient(paul)))&
(?[X]:((~brave(X)|happy(X))))&
(?[X]:((calm(X)&~wise(X))))&
(~calm(lucy))&
((~rich(lucy)<~>strong(lucy)))&
((calm(alice)&quiet(alice)))&
(?[X]:((creative(X)|~happy(X))))&
(?[X]:((~old(X)&tall(X)))) | ~generous(lucy) | [
"p6",
"p7",
"p9",
"p11",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 525315609936403338348692
% SZS output start Proof for 525315609936403338348692
7. ! [X0] : ((rich(X0) & ~calm(X0)) <=> (~tall(X0) <~> strong(X0))) [input p6]
8. ! [X0] : (strong(X0) => (~generous(X0) & ~tall(X0))) [input p7]
10. ! [X0] : (tall(X0) <=> (~funny(X0) <~> calm(X0))) [input p9]
12. ! [X0] : ((kind(X0) | funny(X0)) <=> (~generous(X0) <~> ~kind(X0))) [input p11]
15. ! [X0] : ((~tall(X0) | calm(X0)) <=> (~brave(X0) <~> ~calm(X0))) [input p14]
20. ~calm(lucy) [input p19]
21. ~rich(lucy) <~> strong(lucy) [input p20]
25. generous(lucy) [input hypothesis]
32. ! [X0] : ((~generous(X0) & ~tall(X0)) | ~strong(X0)) [ennf transformation 8]
53. ! [X0] : (((rich(X0) & ~calm(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) & (((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | (~rich(X0) | calm(X0)))) [nnf transformation 7]
54. ! [X0] : (((rich(X0) & ~calm(X0)) | ((~tall(X0) | ~strong(X0)) & (strong(X0) | tall(X0)))) & (((~strong(X0) | tall(X0)) & (strong(X0) | ~tall(X0))) | ~rich(X0) | calm(X0))) [flattening 53]
57. ! [X0] : ((tall(X0) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0)))) & (((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | ~tall(X0))) [nnf transformation 10]
58. ! [X0] : (((kind(X0) | funny(X0)) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~kind(X0) & ~funny(X0)))) [nnf transformation 12]
59. ! [X0] : ((kind(X0) | funny(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) & (((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | (~kind(X0) & ~funny(X0)))) [flattening 58]
65. ! [X0] : (((~tall(X0) | calm(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (tall(X0) & ~calm(X0)))) [nnf transformation 15]
66. ! [X0] : ((~tall(X0) | calm(X0) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0)))) & (((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (tall(X0) & ~calm(X0)))) [flattening 65]
71. (~strong(lucy) | rich(lucy)) & (strong(lucy) | ~rich(lucy)) [nnf transformation 21]
97. tall(X0) | strong(X0) | rich(X0) [cnf transformation 54]
100. ~generous(X0) | ~strong(X0) [cnf transformation 32]
102. ~tall(X0) | ~funny(X0) | calm(X0) [cnf transformation 57]
108. ~kind(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 59]
112. kind(X0) | funny(X0) | ~generous(X0) | kind(X0) [cnf transformation 59]
117. ~calm(X0) | ~brave(X0) | ~calm(X0) [cnf transformation 66]
120. tall(X0) | brave(X0) | calm(X0) [cnf transformation 66]
122. ~tall(X0) | calm(X0) | ~brave(X0) | calm(X0) [cnf transformation 66]
128. ~calm(lucy) [cnf transformation 20]
129. strong(lucy) | ~rich(lucy) [cnf transformation 71]
136. generous(lucy) [cnf transformation 25]
137. ~brave(X0) | ~calm(X0) [duplicate literal removal 117]
138. ~tall(X0) | calm(X0) | ~brave(X0) [duplicate literal removal 122]
139. ~generous(X0) | ~kind(X0) [duplicate literal removal 108]
140. ~generous(X0) | funny(X0) | kind(X0) [duplicate literal removal 112]
260. 28 <=> rich(lucy) [avatar definition]
264. 29 <=> strong(lucy) [avatar definition]
268. ~28 | 29 [avatar split clause 129,264,260]
284. ~strong(lucy) [resolution 100,136]
286. ~kind(lucy) [resolution 139,136]
459. brave(X1) | calm(X1) | ~funny(X1) | calm(X1) [resolution 120,102]
464. ~funny(X1) | calm(X1) | brave(X1) [duplicate literal removal 459]
475. calm(X3) | ~brave(X3) | strong(X3) | rich(X3) [resolution 138,97]
481. ~brave(X3) | strong(X3) | rich(X3) [subsumption resolution 475,137]
483. funny(lucy) | kind(lucy) [resolution 140,136]
485. funny(lucy) [subsumption resolution 483,286]
558. calm(lucy) | brave(lucy) [resolution 464,485]
562. brave(lucy) [subsumption resolution 558,128]
630. strong(lucy) | rich(lucy) [resolution 562,481]
637. 28 | 29 [avatar split clause 630,264,260]
638. ~29 [avatar split clause 284,264]
639. $false [avatar sat refutation 268,637,638]
% SZS output end Proof for 525315609936403338348692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not happy or humble then john is not rich.
Everyone who is creative or not strong is not generous or not kind and vice versa.
Everyone who is both generous and tall is quiet and vice versa.
Everyone who is not calm or not strong is not kind or funny.
Everyone who is not happy is either not wise or kind and vice versa.
If someone is quiet then john is both not strong and quiet.
If someone is tall or happy then john is not creative.
Everyone who is not calm is both wise and not quiet and vice versa.
Everyone who is not patient is not old or wise.
If lucy is either not humble or not brave then john is either not generous or tall and vice versa.
Everyone who is both rich and not curious is not old or not wise and vice versa.
If someone is either not generous or wise then someone is both funny and strong and vice versa.
Everyone who is funny is wise.
If someone is either quiet or not strong then lucy is either not old or creative and vice versa.
If paul is either not happy or not curious then lucy is either curious or not brave and vice versa.
If fred is tall or not curious then fred is funny.
Fred is both not old and not calm.
Someone is either kind or not patient.
Someone is not creative.
Someone is curious.
Susan is both not rich and not tall.
Susan is either not patient or old.
John is both not generous and strong.
Susan is both not humble and wise. | Lucy is old. | neutral | (((~happy(john)<~>humble(john)))=>(~rich(john)))&
(![X]:((creative(X)|~strong(X))<=>(~generous(X)|~kind(X))))&
(![X]:((generous(X)&tall(X))<=>quiet(X)))&
(![X]:((~calm(X)|~strong(X))=>(~kind(X)|funny(X))))&
(![X]:(~happy(X)<=>(~wise(X)<~>kind(X))))&
((?[X]:(quiet(X)))=>((~strong(john)&quiet(john))))&
((?[X]:((tall(X)|happy(X))))=>(~creative(john)))&
(![X]:(~calm(X)<=>(wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>(~old(X)|wise(X))))&
(((~humble(lucy)<~>~brave(lucy)))<=>((~generous(john)<~>tall(john))))&
(![X]:((rich(X)&~curious(X))<=>(~old(X)|~wise(X))))&
((?[X]:((~generous(X)<~>wise(X))))<=>(?[X]:((funny(X)&strong(X)))))&
(![X]:(funny(X)=>wise(X)))&
((?[X]:((quiet(X)<~>~strong(X))))<=>((~old(lucy)<~>creative(lucy))))&
(((~happy(paul)<~>~curious(paul)))<=>((curious(lucy)<~>~brave(lucy))))&
(((tall(fred)|~curious(fred)))=>(funny(fred)))&
((~old(fred)&~calm(fred)))&
(?[X]:((kind(X)<~>~patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:(curious(X)))&
((~rich(susan)&~tall(susan)))&
((~patient(susan)<~>old(susan)))&
((~generous(john)&strong(john)))&
((~humble(susan)&wise(susan))) | old(lucy) | [] | null | 0 |
Everyone who is not funny is rich or old and vice versa. Everyone who is either strong or rich is both generous and quiet and vice versa. If john is either not happy or calm then someone is not brave or not creative. Everyone who is old is not happy or brave. If someone is both rich and curious then john is quiet or happy. If john is both not patient and happy then susan is either not creative or not calm. Everyone who is either not strong or not brave is not happy. Everyone who is both not generous and not strong is rich and vice versa. If someone is both not quiet and rich then fred is not brave or not quiet and vice versa. If fred is both not funny and creative then fred is funny and vice versa. Everyone who is tall is either patient or rich and vice versa. Everyone who is either not rich or creative is not tall or humble. Everyone who is kind is either funny or not curious. Everyone who is both rich and not quiet is kind and vice versa. If mary is not calm then alice is either not strong or old and vice versa. Susan is not creative. Alice is not calm. Alice is either not strong or not wise. Lucy is both not old and funny. Someone is creative or not curious. Someone is rich or not creative. | Lucy is patient. | neutral | (![X]:(~funny(X)<=>(rich(X)|old(X))))&
(![X]:((strong(X)<~>rich(X))<=>(generous(X)&quiet(X))))&
(((~happy(john)<~>calm(john)))=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:(old(X)=>(~happy(X)|brave(X))))&
((?[X]:((rich(X)&curious(X))))=>((quiet(john)|happy(john))))&
(((~patient(john)&happy(john)))=>((~creative(susan)<~>~calm(susan))))&
(![X]:((~strong(X)<~>~brave(X))=>~happy(X)))&
(![X]:((~generous(X)&~strong(X))<=>rich(X)))&
((?[X]:((~quiet(X)&rich(X))))<=>((~brave(fred)|~quiet(fred))))&
(((~funny(fred)&creative(fred)))<=>(funny(fred)))&
(![X]:(tall(X)<=>(patient(X)<~>rich(X))))&
(![X]:((~rich(X)<~>creative(X))=>(~tall(X)|humble(X))))&
(![X]:(kind(X)=>(funny(X)<~>~curious(X))))&
(![X]:((rich(X)&~quiet(X))<=>kind(X)))&
((~calm(mary))<=>((~strong(alice)<~>old(alice))))&
(~creative(susan))&
(~calm(alice))&
((~strong(alice)<~>~wise(alice)))&
((~old(lucy)&funny(lucy)))&
(?[X]:((creative(X)|~curious(X))))&
(?[X]:((rich(X)|~creative(X)))) | patient(lucy) | [] | null | 0 |
If someone is either wise or not happy then someone is not funny and vice versa.
If paul is not patient or not brave then lucy is either not curious or curious.
If someone is not calm then someone is kind or not quiet and vice versa.
Everyone who is either quiet or not calm is either quiet or calm.
Everyone who is not quiet is either calm or not humble and vice versa.
If john is curious or not quiet then someone is patient or kind.
If someone is not quiet or rich then someone is either curious or quiet.
Everyone who is both not calm and creative is both not humble and not curious and vice versa.
If someone is either brave or not happy then susan is quiet or not tall and vice versa.
Everyone who is either not happy or not strong is creative and vice versa.
Everyone who is both rich and not curious is not old and vice versa.
If someone is old then susan is both not happy and not old and vice versa.
If john is either not patient or not rich then someone is not curious and vice versa.
Everyone who is tall is either not humble or not old.
Everyone who is either not kind or not funny is both humble and curious and vice versa.
Everyone who is both funny and not creative is brave.
Someone is either not quiet or patient.
Someone is either happy or not generous.
Someone is both not patient and humble.
Fred is either not creative or not happy.
Someone is creative or generous.
Susan is rich.
Someone is either strong or not humble.
Paul is both kind and patient. | Paul is patient. | entailment | ((?[X]:((wise(X)<~>~happy(X))))<=>(?[X]:(~funny(X))))&
(((~patient(paul)|~brave(paul)))=>((~curious(lucy)<~>curious(lucy))))&
((?[X]:(~calm(X)))<=>(?[X]:((kind(X)|~quiet(X)))))&
(![X]:((quiet(X)<~>~calm(X))=>(quiet(X)<~>calm(X))))&
(![X]:(~quiet(X)<=>(calm(X)<~>~humble(X))))&
(((curious(john)|~quiet(john)))=>(?[X]:((patient(X)|kind(X)))))&
((?[X]:((~quiet(X)|rich(X))))=>(?[X]:((curious(X)<~>quiet(X)))))&
(![X]:((~calm(X)&creative(X))<=>(~humble(X)&~curious(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((quiet(susan)|~tall(susan))))&
(![X]:((~happy(X)<~>~strong(X))<=>creative(X)))&
(![X]:((rich(X)&~curious(X))<=>~old(X)))&
((?[X]:(old(X)))<=>((~happy(susan)&~old(susan))))&
(((~patient(john)<~>~rich(john)))<=>(?[X]:(~curious(X))))&
(![X]:(tall(X)=>(~humble(X)<~>~old(X))))&
(![X]:((~kind(X)<~>~funny(X))<=>(humble(X)&curious(X))))&
(![X]:((funny(X)&~creative(X))=>brave(X)))&
(?[X]:((~quiet(X)<~>patient(X))))&
(?[X]:((happy(X)<~>~generous(X))))&
(?[X]:((~patient(X)&humble(X))))&
((~creative(fred)<~>~happy(fred)))&
(?[X]:((creative(X)|generous(X))))&
(rich(susan))&
(?[X]:((strong(X)<~>~humble(X))))&
((kind(paul)&patient(paul))) | patient(paul) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8088762309535528075141441
% SZS output start Proof for 8088762309535528075141441
24. patient(paul) & kind(paul) [input p23]
25. ~patient(paul) [input hypothesis]
162. patient(paul) [cnf transformation 24]
163. ~patient(paul) [cnf transformation 25]
360. $false [subsumption resolution 163,162]
% SZS output end Proof for 8088762309535528075141441
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or generous then mary is happy or quiet. If someone is either not curious or not patient then someone is kind. If lucy is happy or old then someone is happy or quiet and vice versa. If someone is both kind and not quiet then someone is either old or happy and vice versa. If john is wise then someone is not strong or creative and vice versa. If john is strong or not strong then alice is not tall and vice versa. If someone is either not brave or old then someone is not funny. If someone is brave or rich then paul is humble and vice versa. If paul is both not calm and not strong then someone is either not patient or old and vice versa. Everyone who is not calm is not old and vice versa. Everyone who is not humble is either calm or old. Everyone who is not generous or not quiet is both not humble and not funny and vice versa. If someone is curious or tall then someone is both not happy and humble and vice versa. If someone is both calm and patient then someone is rich or not old. Someone is either strong or not calm. Alice is either calm or generous. Lucy is either calm or not generous. Alice is curious or wise. | Paul is humble. | entailment | ((?[X]:((~happy(X)|generous(X))))=>((happy(mary)|quiet(mary))))&
((?[X]:((~curious(X)<~>~patient(X))))=>(?[X]:(kind(X))))&
(((happy(lucy)|old(lucy)))<=>(?[X]:((happy(X)|quiet(X)))))&
((?[X]:((kind(X)&~quiet(X))))<=>(?[X]:((old(X)<~>happy(X)))))&
((wise(john))<=>(?[X]:((~strong(X)|creative(X)))))&
(((strong(john)|~strong(john)))<=>(~tall(alice)))&
((?[X]:((~brave(X)<~>old(X))))=>(?[X]:(~funny(X))))&
((?[X]:((brave(X)|rich(X))))<=>(humble(paul)))&
(((~calm(paul)&~strong(paul)))<=>(?[X]:((~patient(X)<~>old(X)))))&
(![X]:(~calm(X)<=>~old(X)))&
(![X]:(~humble(X)=>(calm(X)<~>old(X))))&
(![X]:((~generous(X)|~quiet(X))<=>(~humble(X)&~funny(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~happy(X)&humble(X)))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:((rich(X)|~old(X)))))&
(?[X]:((strong(X)<~>~calm(X))))&
((calm(alice)<~>generous(alice)))&
((calm(lucy)<~>~generous(lucy)))&
((curious(alice)|wise(alice))) | humble(paul) | [
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7735721857451134427211799
% SZS output start Proof for 7735721857451134427211799
10. ! [X0] : (~calm(X0) <=> ~old(X0)) [input p9]
11. ! [X0] : (~humble(X0) => (calm(X0) <~> old(X0))) [input p10]
19. ~humble(paul) [input hypothesis]
29. ! [X0] : ((calm(X0) <~> old(X0)) | humble(X0)) [ennf transformation 11]
64. ! [X0] : ((~calm(X0) | old(X0)) & (~old(X0) | calm(X0))) [nnf transformation 10]
65. ! [X0] : (((~old(X0) | ~calm(X0)) & (old(X0) | calm(X0))) | humble(X0)) [nnf transformation 29]
112. ~old(X0) | calm(X0) [cnf transformation 64]
113. ~calm(X0) | old(X0) [cnf transformation 64]
114. old(X0) | calm(X0) | humble(X0) [cnf transformation 65]
115. ~old(X0) | ~calm(X0) | humble(X0) [cnf transformation 65]
134. ~humble(paul) [cnf transformation 19]
264. 31 <=> humble(paul) [avatar definition]
266. ~humble(paul) <- (~31) [avatar component clause 264]
297. 39 <=> calm(paul) [avatar definition]
298. calm(paul) <- (39) [avatar component clause 297]
312. ~calm(X0) | humble(X0) [subsumption resolution 115,113]
313. humble(X0) | old(X0) [subsumption resolution 114,312]
395. ~31 [avatar split clause 134,264]
430. old(paul) <- (~31) [resolution 313,266]
445. calm(paul) <- (~31) [resolution 430,112]
448. 39 | 31 [avatar split clause 445,264,297]
449. humble(paul) <- (39) [resolution 298,312]
451. $false <- (~31, 39) [subsumption resolution 449,266]
452. 31 | ~39 [avatar contradiction clause 451]
453. $false [avatar sat refutation 395,448,452]
% SZS output end Proof for 7735721857451134427211799
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not kind or quiet is either tall or not old.
If someone is quiet or calm then alice is both wise and not quiet.
If someone is not tall then someone is quiet or not calm.
If someone is not quiet then someone is kind or not calm.
Everyone who is not patient is generous and vice versa.
Everyone who is both strong and not strong is wise or brave and vice versa.
If someone is both humble and happy then john is both not patient and not creative.
Everyone who is not brave is either not curious or patient and vice versa.
Everyone who is not kind or happy is not wise or not rich and vice versa.
Everyone who is both funny and kind is not tall or kind.
If someone is both old and not old then susan is not brave or not strong.
If susan is happy or brave then alice is patient.
Everyone who is patient or creative is both not patient and generous.
Everyone who is not curious or rich is both tall and creative and vice versa.
Everyone who is both kind and humble is not curious.
John is kind.
Paul is not brave.
Someone is either humble or generous.
Someone is kind.
Alice is both not rich and humble.
Fred is funny or not old.
Someone is either funny or quiet. | Susan is not strong. | neutral | (![X]:((~kind(X)<~>quiet(X))=>(tall(X)<~>~old(X))))&
((?[X]:((quiet(X)|calm(X))))=>((wise(alice)&~quiet(alice))))&
((?[X]:(~tall(X)))=>(?[X]:((quiet(X)|~calm(X)))))&
((?[X]:(~quiet(X)))=>(?[X]:((kind(X)|~calm(X)))))&
(![X]:(~patient(X)<=>generous(X)))&
(![X]:((strong(X)&~strong(X))<=>(wise(X)|brave(X))))&
((?[X]:((humble(X)&happy(X))))=>((~patient(john)&~creative(john))))&
(![X]:(~brave(X)<=>(~curious(X)<~>patient(X))))&
(![X]:((~kind(X)|happy(X))<=>(~wise(X)|~rich(X))))&
(![X]:((funny(X)&kind(X))=>(~tall(X)|kind(X))))&
((?[X]:((old(X)&~old(X))))=>((~brave(susan)|~strong(susan))))&
(((happy(susan)|brave(susan)))=>(patient(alice)))&
(![X]:((patient(X)|creative(X))=>(~patient(X)&generous(X))))&
(![X]:((~curious(X)|rich(X))<=>(tall(X)&creative(X))))&
(![X]:((kind(X)&humble(X))=>~curious(X)))&
(kind(john))&
(~brave(paul))&
(?[X]:((humble(X)<~>generous(X))))&
(?[X]:(kind(X)))&
((~rich(alice)&humble(alice)))&
((funny(fred)|~old(fred)))&
(?[X]:((funny(X)<~>quiet(X)))) | ~strong(susan) | [] | null | 0 |
Everyone who is both rich and not strong is either brave or humble.
Everyone who is either old or not tall is curious and vice versa.
Everyone who is either not wise or not happy is not quiet or quiet.
If someone is either not humble or not rich then mary is both patient and not wise and vice versa.
If mary is not strong or not tall then someone is not rich or not humble and vice versa.
Everyone who is quiet is both quiet and not brave.
If someone is both tall and funny then someone is both brave and not rich.
If someone is both wise and generous then someone is funny.
If someone is not generous or generous then fred is both brave and not kind and vice versa.
Everyone who is either not old or generous is tall or not happy and vice versa.
Everyone who is both not old and not tall is either not wise or old and vice versa.
If alice is both not funny and not curious then alice is both humble and kind and vice versa.
Everyone who is both not creative and not patient is not curious or not creative and vice versa.
Everyone who is either humble or not tall is not tall and vice versa.
If someone is curious or rich then someone is strong.
If someone is either strong or brave then susan is not kind.
Someone is either not old or not calm.
Someone is either tall or generous.
Someone is both happy and quiet.
Someone is old.
Someone is not creative or calm.
Someone is not tall.
Mary is not strong or quiet.
Someone is both quiet and strong. | Fred is not quiet. | entailment | (![X]:((rich(X)&~strong(X))=>(brave(X)<~>humble(X))))&
(![X]:((old(X)<~>~tall(X))<=>curious(X)))&
(![X]:((~wise(X)<~>~happy(X))=>(~quiet(X)|quiet(X))))&
((?[X]:((~humble(X)<~>~rich(X))))<=>((patient(mary)&~wise(mary))))&
(((~strong(mary)|~tall(mary)))<=>(?[X]:((~rich(X)|~humble(X)))))&
(![X]:(quiet(X)=>(quiet(X)&~brave(X))))&
((?[X]:((tall(X)&funny(X))))=>(?[X]:((brave(X)&~rich(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:(funny(X))))&
((?[X]:((~generous(X)|generous(X))))<=>((brave(fred)&~kind(fred))))&
(![X]:((~old(X)<~>generous(X))<=>(tall(X)|~happy(X))))&
(![X]:((~old(X)&~tall(X))<=>(~wise(X)<~>old(X))))&
(((~funny(alice)&~curious(alice)))<=>((humble(alice)&kind(alice))))&
(![X]:((~creative(X)&~patient(X))<=>(~curious(X)|~creative(X))))&
(![X]:((humble(X)<~>~tall(X))<=>~tall(X)))&
((?[X]:((curious(X)|rich(X))))=>(?[X]:(strong(X))))&
((?[X]:((strong(X)<~>brave(X))))=>(~kind(susan)))&
(?[X]:((~old(X)<~>~calm(X))))&
(?[X]:((tall(X)<~>generous(X))))&
(?[X]:((happy(X)&quiet(X))))&
(?[X]:(old(X)))&
(?[X]:((~creative(X)|calm(X))))&
(?[X]:(~tall(X)))&
((~strong(mary)|quiet(mary)))&
(?[X]:((quiet(X)&strong(X)))) | ~quiet(fred) | [
"p5",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4064891349936469302850272
% SZS output start Proof for 4064891349936469302850272
6. ! [X0] : (quiet(X0) => (~brave(X0) & quiet(X0))) [input p5]
9. ? [X0] : (generous(X0) | ~generous(X0)) <=> (~kind(fred) & brave(fred)) [input p8]
25. quiet(fred) [input hypothesis]
33. ! [X0] : ((~brave(X0) & quiet(X0)) | ~quiet(X0)) [ennf transformation 6]
57. (? [X0] : (generous(X0) | ~generous(X0)) | (kind(fred) | ~brave(fred))) & ((~kind(fred) & brave(fred)) | ! [X0] : (~generous(X0) & generous(X0))) [nnf transformation 9]
58. (? [X0] : (generous(X0) | ~generous(X0)) | kind(fred) | ~brave(fred)) & ((~kind(fred) & brave(fred)) | ! [X0] : (~generous(X0) & generous(X0))) [flattening 57]
59. (? [X0] : (generous(X0) | ~generous(X0)) | kind(fred) | ~brave(fred)) & ((~kind(fred) & brave(fred)) | ! [X1] : (~generous(X1) & generous(X1))) [rectify 58]
60. ? [X0] : (generous(X0) | ~generous(X0)) => (generous(sK4) | ~generous(sK4)) [choice axiom]
61. ((generous(sK4) | ~generous(sK4)) | kind(fred) | ~brave(fred)) & ((~kind(fred) & brave(fred)) | ! [X1] : (~generous(X1) & generous(X1))) [skolemisation 59,60]
110. ~quiet(X0) | ~brave(X0) [cnf transformation 33]
114. brave(fred) | generous(X1) [cnf transformation 61]
115. brave(fred) | ~generous(X1) [cnf transformation 61]
160. quiet(fred) [cnf transformation 25]
241. 18 <=> ! [X1] : ~generous(X1) [avatar definition]
242. ~generous(X1) <- (18) [avatar component clause 241]
249. 20 <=> ! [X1] : generous(X1) [avatar definition]
250. generous(X1) <- (20) [avatar component clause 249]
253. 21 <=> brave(fred) [avatar definition]
255. brave(fred) <- (21) [avatar component clause 253]
256. 18 | 21 [avatar split clause 115,253,241]
257. 20 | 21 [avatar split clause 114,253,249]
340. $false <- (18, 20) [subsumption resolution 242,250]
341. ~18 | ~20 [avatar contradiction clause 340]
349. ~brave(fred) [resolution 110,160]
350. $false <- (21) [subsumption resolution 349,255]
351. ~21 [avatar contradiction clause 350]
352. $false [avatar sat refutation 256,257,341,351]
% SZS output end Proof for 4064891349936469302850272
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both kind and calm.
Everyone who is both not rich and rich is old or tall.
Everyone who is not funny is both curious and not patient and vice versa.
Everyone who is not humble or patient is wise and vice versa.
Everyone who is not kind is both wise and patient and vice versa.
Everyone who is not funny is either not brave or brave and vice versa.
If someone is both kind and wise then fred is both not humble and not wise.
If someone is both not rich and generous then someone is happy or old and vice versa.
If someone is not old then alice is not kind or quiet and vice versa.
Everyone who is funny is both humble and creative.
Everyone who is kind is not quiet and vice versa.
Everyone who is either rich or not brave is either wise or not quiet and vice versa.
Someone is kind.
Fred is both happy and not tall.
Alice is not strong or not kind.
Someone is either tall or not brave.
Fred is either not funny or not curious.
Someone is not curious or curious.
John is not creative or rich. | Alice is rich. | neutral | (![X]:(calm(X)=>(kind(X)&calm(X))))&
(![X]:((~rich(X)&rich(X))=>(old(X)|tall(X))))&
(![X]:(~funny(X)<=>(curious(X)&~patient(X))))&
(![X]:((~humble(X)|patient(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(wise(X)&patient(X))))&
(![X]:(~funny(X)<=>(~brave(X)<~>brave(X))))&
((?[X]:((kind(X)&wise(X))))=>((~humble(fred)&~wise(fred))))&
((?[X]:((~rich(X)&generous(X))))<=>(?[X]:((happy(X)|old(X)))))&
((?[X]:(~old(X)))<=>((~kind(alice)|quiet(alice))))&
(![X]:(funny(X)=>(humble(X)&creative(X))))&
(![X]:(kind(X)<=>~quiet(X)))&
(![X]:((rich(X)<~>~brave(X))<=>(wise(X)<~>~quiet(X))))&
(?[X]:(kind(X)))&
((happy(fred)&~tall(fred)))&
((~strong(alice)|~kind(alice)))&
(?[X]:((tall(X)<~>~brave(X))))&
((~funny(fred)<~>~curious(fred)))&
(?[X]:((~curious(X)|curious(X))))&
((~creative(john)|rich(john))) | rich(alice) | [] | null | 0 |
Everyone who is humble is curious or not old and vice versa.
Everyone who is both not wise and patient is both not calm and not brave and vice versa.
If someone is either not wise or calm then someone is not happy or not humble and vice versa.
If john is not tall then someone is patient and vice versa.
If paul is patient then someone is not tall.
If mary is old then someone is old and vice versa.
Everyone who is either brave or calm is both kind and not strong.
Everyone who is either not strong or tall is either not happy or not calm.
If fred is either not funny or patient then someone is not tall or not brave and vice versa.
Everyone who is either not humble or brave is both kind and strong.
If someone is not patient or not humble then paul is either wise or funny.
If someone is both wise and tall then alice is kind or humble and vice versa.
If someone is not patient or patient then mary is either quiet or old.
If lucy is not patient or happy then lucy is either not strong or wise and vice versa.
If alice is both not brave and not wise then someone is not tall or strong and vice versa.
Everyone who is both old and brave is generous.
Fred is either strong or not calm.
Someone is rich.
Someone is either not strong or brave.
John is both not calm and quiet.
Someone is both not generous and kind.
Someone is not patient.
Paul is strong.
Someone is both old and humble. | Paul is not strong. | contradiction | (![X]:(humble(X)<=>(curious(X)|~old(X))))&
(![X]:((~wise(X)&patient(X))<=>(~calm(X)&~brave(X))))&
((?[X]:((~wise(X)<~>calm(X))))<=>(?[X]:((~happy(X)|~humble(X)))))&
((~tall(john))<=>(?[X]:(patient(X))))&
((patient(paul))=>(?[X]:(~tall(X))))&
((old(mary))<=>(?[X]:(old(X))))&
(![X]:((brave(X)<~>calm(X))=>(kind(X)&~strong(X))))&
(![X]:((~strong(X)<~>tall(X))=>(~happy(X)<~>~calm(X))))&
(((~funny(fred)<~>patient(fred)))<=>(?[X]:((~tall(X)|~brave(X)))))&
(![X]:((~humble(X)<~>brave(X))=>(kind(X)&strong(X))))&
((?[X]:((~patient(X)|~humble(X))))=>((wise(paul)<~>funny(paul))))&
((?[X]:((wise(X)&tall(X))))<=>((kind(alice)|humble(alice))))&
((?[X]:((~patient(X)|patient(X))))=>((quiet(mary)<~>old(mary))))&
(((~patient(lucy)|happy(lucy)))<=>((~strong(lucy)<~>wise(lucy))))&
(((~brave(alice)&~wise(alice)))<=>(?[X]:((~tall(X)|strong(X)))))&
(![X]:((old(X)&brave(X))=>generous(X)))&
((strong(fred)<~>~calm(fred)))&
(?[X]:(rich(X)))&
(?[X]:((~strong(X)<~>brave(X))))&
((~calm(john)&quiet(john)))&
(?[X]:((~generous(X)&kind(X))))&
(?[X]:(~patient(X)))&
(strong(paul))&
(?[X]:((old(X)&humble(X)))) | ~strong(paul) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7657626303130804816287317
% SZS output start Proof for 7657626303130804816287317
23. strong(paul) [input p22]
25. ~strong(paul) [input hypothesis]
156. strong(paul) [cnf transformation 23]
159. ~strong(paul) [cnf transformation 25]
370. $false [subsumption resolution 159,156]
% SZS output end Proof for 7657626303130804816287317
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not curious is quiet. Everyone who is old is either not generous or not happy and vice versa. If mary is both calm and not strong then alice is both not old and not wise. If someone is not quiet or strong then someone is patient or humble and vice versa. Everyone who is creative is not funny. Everyone who is calm is both wise and not kind and vice versa. If lucy is both generous and not kind then someone is either strong or not brave. Everyone who is funny or not old is either happy or strong and vice versa. If john is tall then paul is either generous or tall and vice versa. Everyone who is both rich and tall is both curious and not rich and vice versa. Everyone who is both patient and happy is not old. Everyone who is not rich or calm is strong and vice versa. Everyone who is either patient or humble is both not rich and quiet and vice versa. If john is not calm or not rich then someone is curious. Everyone who is both creative and old is both not calm and not strong and vice versa. If someone is creative then someone is either not generous or creative and vice versa. Someone is humble. Susan is either not old or not creative. Fred is either not wise or not creative. Fred is creative or not rich. Lucy is not curious or not patient. Someone is not funny. John is not quiet. | Fred is rich. | neutral | (![X]:((strong(X)&~curious(X))=>quiet(X)))&
(![X]:(old(X)<=>(~generous(X)<~>~happy(X))))&
(((calm(mary)&~strong(mary)))=>((~old(alice)&~wise(alice))))&
((?[X]:((~quiet(X)|strong(X))))<=>(?[X]:((patient(X)|humble(X)))))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:(calm(X)<=>(wise(X)&~kind(X))))&
(((generous(lucy)&~kind(lucy)))=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((funny(X)|~old(X))<=>(happy(X)<~>strong(X))))&
((tall(john))<=>((generous(paul)<~>tall(paul))))&
(![X]:((rich(X)&tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((patient(X)&happy(X))=>~old(X)))&
(![X]:((~rich(X)|calm(X))<=>strong(X)))&
(![X]:((patient(X)<~>humble(X))<=>(~rich(X)&quiet(X))))&
(((~calm(john)|~rich(john)))=>(?[X]:(curious(X))))&
(![X]:((creative(X)&old(X))<=>(~calm(X)&~strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~generous(X)<~>creative(X)))))&
(?[X]:(humble(X)))&
((~old(susan)<~>~creative(susan)))&
((~wise(fred)<~>~creative(fred)))&
((creative(fred)|~rich(fred)))&
((~curious(lucy)|~patient(lucy)))&
(?[X]:(~funny(X)))&
(~quiet(john)) | rich(fred) | [] | null | 0 |
Everyone who is either not tall or kind is not old or strong. Everyone who is both not humble and not creative is not patient or old. If susan is both not old and not tall then someone is both not happy and old. Everyone who is patient or rich is not patient and vice versa. If mary is not generous or patient then someone is either quiet or funny. Everyone who is not generous or strong is rich or not old. If alice is either not funny or happy then someone is either brave or not wise and vice versa. If someone is not rich then alice is not brave and vice versa. Everyone who is either not creative or quiet is humble or not patient. Everyone who is not old is both not brave and old and vice versa. Everyone who is either patient or tall is both curious and not rich and vice versa. Everyone who is both calm and patient is either not calm or patient. Everyone who is either not happy or kind is calm. Everyone who is wise or generous is not strong or curious and vice versa. Everyone who is either not old or old is not strong. Someone is not funny or strong. Someone is both creative and not calm. John is not tall or brave. Someone is both not creative and not generous. Susan is not happy. Alice is both not creative and kind. | John is quiet. | neutral | (![X]:((~tall(X)<~>kind(X))=>(~old(X)|strong(X))))&
(![X]:((~humble(X)&~creative(X))=>(~patient(X)|old(X))))&
(((~old(susan)&~tall(susan)))=>(?[X]:((~happy(X)&old(X)))))&
(![X]:((patient(X)|rich(X))<=>~patient(X)))&
(((~generous(mary)|patient(mary)))=>(?[X]:((quiet(X)<~>funny(X)))))&
(![X]:((~generous(X)|strong(X))=>(rich(X)|~old(X))))&
(((~funny(alice)<~>happy(alice)))<=>(?[X]:((brave(X)<~>~wise(X)))))&
((?[X]:(~rich(X)))<=>(~brave(alice)))&
(![X]:((~creative(X)<~>quiet(X))=>(humble(X)|~patient(X))))&
(![X]:(~old(X)<=>(~brave(X)&old(X))))&
(![X]:((patient(X)<~>tall(X))<=>(curious(X)&~rich(X))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>patient(X))))&
(![X]:((~happy(X)<~>kind(X))=>calm(X)))&
(![X]:((wise(X)|generous(X))<=>(~strong(X)|curious(X))))&
(![X]:((~old(X)<~>old(X))=>~strong(X)))&
(?[X]:((~funny(X)|strong(X))))&
(?[X]:((creative(X)&~calm(X))))&
((~tall(john)|brave(john)))&
(?[X]:((~creative(X)&~generous(X))))&
(~happy(susan))&
((~creative(alice)&kind(alice))) | quiet(john) | [] | null | 0 |
Everyone who is either not generous or not funny is brave and vice versa.
If someone is kind or not rich then mary is not kind or calm.
Everyone who is not curious or not rich is not strong and vice versa.
Everyone who is not quiet is not happy and vice versa.
Everyone who is kind or patient is either happy or not funny.
Everyone who is both not quiet and brave is either not funny or not strong and vice versa.
Everyone who is kind is not generous or generous and vice versa.
If someone is either not creative or funny then someone is not humble or not strong and vice versa.
If paul is calm or creative then someone is both kind and not tall and vice versa.
If alice is patient then lucy is brave or patient and vice versa.
Everyone who is either not funny or brave is either happy or not strong.
Everyone who is not funny or not creative is curious or not happy and vice versa.
Everyone who is calm is both brave and quiet and vice versa.
If paul is not curious or humble then alice is generous.
Everyone who is not curious or tall is not tall or strong and vice versa.
If someone is not patient then someone is quiet.
Alice is both old and quiet.
Paul is either not strong or not calm.
Lucy is not humble or kind.
Someone is not humble.
Fred is both funny and not brave.
Alice is both brave and wise. | Alice is not strong. | contradiction | (![X]:((~generous(X)<~>~funny(X))<=>brave(X)))&
((?[X]:((kind(X)|~rich(X))))=>((~kind(mary)|calm(mary))))&
(![X]:((~curious(X)|~rich(X))<=>~strong(X)))&
(![X]:(~quiet(X)<=>~happy(X)))&
(![X]:((kind(X)|patient(X))=>(happy(X)<~>~funny(X))))&
(![X]:((~quiet(X)&brave(X))<=>(~funny(X)<~>~strong(X))))&
(![X]:(kind(X)<=>(~generous(X)|generous(X))))&
((?[X]:((~creative(X)<~>funny(X))))<=>(?[X]:((~humble(X)|~strong(X)))))&
(((calm(paul)|creative(paul)))<=>(?[X]:((kind(X)&~tall(X)))))&
((patient(alice))<=>((brave(lucy)|patient(lucy))))&
(![X]:((~funny(X)<~>brave(X))=>(happy(X)<~>~strong(X))))&
(![X]:((~funny(X)|~creative(X))<=>(curious(X)|~happy(X))))&
(![X]:(calm(X)<=>(brave(X)&quiet(X))))&
(((~curious(paul)|humble(paul)))=>(generous(alice)))&
(![X]:((~curious(X)|tall(X))<=>(~tall(X)|strong(X))))&
((?[X]:(~patient(X)))=>(?[X]:(quiet(X))))&
((old(alice)&quiet(alice)))&
((~strong(paul)<~>~calm(paul)))&
((~humble(lucy)|kind(lucy)))&
(?[X]:(~humble(X)))&
((funny(fred)&~brave(fred)))&
((brave(alice)&wise(alice))) | ~strong(alice) | [
"p3",
"p4",
"p5",
"p6",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 760592655837569848138073
% SZS output start Proof for 760592655837569848138073
4. ! [X0] : (~quiet(X0) <=> ~happy(X0)) [input p3]
5. ! [X0] : ((patient(X0) | kind(X0)) => (happy(X0) <~> ~funny(X0))) [input p4]
6. ! [X0] : ((brave(X0) & ~quiet(X0)) <=> (~funny(X0) <~> ~strong(X0))) [input p5]
7. ! [X0] : (kind(X0) <=> (generous(X0) | ~generous(X0))) [input p6]
17. quiet(alice) & old(alice) [input p16]
23. ~strong(alice) [input hypothesis]
27. quiet(alice) [pure predicate removal 17]
30. ! [X0] : ((happy(X0) <~> ~funny(X0)) | (~patient(X0) & ~kind(X0))) [ennf transformation 5]
37. ! [X0] : ((~quiet(X0) | happy(X0)) & (~happy(X0) | quiet(X0))) [nnf transformation 4]
38. ! [X0] : (((funny(X0) | ~happy(X0)) & (~funny(X0) | happy(X0))) | (~patient(X0) & ~kind(X0))) [nnf transformation 30]
39. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | (~brave(X0) | quiet(X0)))) [nnf transformation 6]
40. ! [X0] : (((brave(X0) & ~quiet(X0)) | ((~funny(X0) | strong(X0)) & (~strong(X0) | funny(X0)))) & (((strong(X0) | funny(X0)) & (~strong(X0) | ~funny(X0))) | ~brave(X0) | quiet(X0))) [flattening 39]
41. ! [X0] : ((kind(X0) | (~generous(X0) & generous(X0))) & ((generous(X0) | ~generous(X0)) | ~kind(X0))) [nnf transformation 7]
42. ! [X0] : ((kind(X0) | (~generous(X0) & generous(X0))) & (generous(X0) | ~generous(X0) | ~kind(X0))) [flattening 41]
78. ~quiet(X0) | happy(X0) [cnf transformation 37]
81. ~happy(X0) | funny(X0) | ~kind(X0) [cnf transformation 38]
86. ~quiet(X0) | ~funny(X0) | strong(X0) [cnf transformation 40]
90. kind(X0) | generous(X0) [cnf transformation 42]
91. ~generous(X0) | kind(X0) [cnf transformation 42]
124. quiet(alice) [cnf transformation 27]
132. ~strong(alice) [cnf transformation 23]
151. kind(X0) [subsumption resolution 90,91]
257. happy(alice) [resolution 78,124]
317. funny(alice) | ~kind(alice) [resolution 81,257]
322. funny(alice) [subsumption resolution 317,151]
329. ~funny(alice) | strong(alice) [resolution 86,124]
331. strong(alice) [subsumption resolution 329,322]
332. $false [subsumption resolution 331,132]
% SZS output end Proof for 760592655837569848138073
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong is not tall or not kind and vice versa.
If someone is not quiet then someone is either not creative or not quiet.
Everyone who is tall or not funny is both brave and not generous and vice versa.
If lucy is both not strong and not quiet then someone is not kind and vice versa.
If someone is not strong then someone is either funny or not brave and vice versa.
If mary is not funny then fred is both strong and tall.
Everyone who is patient or not patient is both not old and generous.
If susan is both strong and happy then alice is both kind and not strong and vice versa.
If someone is not happy or patient then someone is either not patient or rich and vice versa.
If someone is both tall and calm then someone is not calm or humble.
If mary is both brave and funny then someone is not funny or rich and vice versa.
Everyone who is both not old and patient is either not rich or strong.
If someone is both rich and tall then someone is either humble or rich.
If lucy is creative or not happy then someone is calm or happy and vice versa.
Someone is either not humble or happy.
Susan is either strong or not strong.
Someone is humble.
Alice is kind.
Paul is either not creative or quiet. | Lucy is not patient. | entailment | (![X]:(strong(X)<=>(~tall(X)|~kind(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~creative(X)<~>~quiet(X)))))&
(![X]:((tall(X)|~funny(X))<=>(brave(X)&~generous(X))))&
(((~strong(lucy)&~quiet(lucy)))<=>(?[X]:(~kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
((~funny(mary))=>((strong(fred)&tall(fred))))&
(![X]:((patient(X)|~patient(X))=>(~old(X)&generous(X))))&
(((strong(susan)&happy(susan)))<=>((kind(alice)&~strong(alice))))&
((?[X]:((~happy(X)|patient(X))))<=>(?[X]:((~patient(X)<~>rich(X)))))&
((?[X]:((tall(X)&calm(X))))=>(?[X]:((~calm(X)|humble(X)))))&
(((brave(mary)&funny(mary)))<=>(?[X]:((~funny(X)|rich(X)))))&
(![X]:((~old(X)&patient(X))=>(~rich(X)<~>strong(X))))&
((?[X]:((rich(X)&tall(X))))=>(?[X]:((humble(X)<~>rich(X)))))&
(((creative(lucy)|~happy(lucy)))<=>(?[X]:((calm(X)|happy(X)))))&
(?[X]:((~humble(X)<~>happy(X))))&
((strong(susan)<~>~strong(susan)))&
(?[X]:(humble(X)))&
(kind(alice))&
((~creative(paul)<~>quiet(paul))) | ~patient(lucy) | [
"p0",
"p2",
"p4",
"p6",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3536580136605100329553022
% SZS output start Proof for 3536580136605100329553022
1. ! [X0] : (strong(X0) <=> (~kind(X0) | ~tall(X0))) [input p0]
3. ! [X0] : ((~funny(X0) | tall(X0)) <=> (~generous(X0) & brave(X0))) [input p2]
5. ? [X0] : ~strong(X0) <=> ? [X0] : (funny(X0) <~> ~brave(X0)) [input p4]
7. ! [X0] : ((~patient(X0) | patient(X0)) => (generous(X0) & ~old(X0))) [input p6]
11. (funny(mary) & brave(mary)) <=> ? [X0] : (rich(X0) | ~funny(X0)) [input p10]
12. ! [X0] : ((patient(X0) & ~old(X0)) => (~rich(X0) <~> strong(X0))) [input p11]
20. patient(lucy) [input hypothesis]
22. ? [X0] : ~strong(X0) <=> ? [X1] : (funny(X1) <~> ~brave(X1)) [rectify 5]
28. ! [X0] : ((generous(X0) & ~old(X0)) | (patient(X0) & ~patient(X0))) [ennf transformation 7]
30. ! [X0] : ((~rich(X0) <~> strong(X0)) | (~patient(X0) | old(X0))) [ennf transformation 12]
31. ! [X0] : ((~rich(X0) <~> strong(X0)) | ~patient(X0) | old(X0)) [flattening 30]
33. ! [X0] : ((strong(X0) | (kind(X0) & tall(X0))) & ((~kind(X0) | ~tall(X0)) | ~strong(X0))) [nnf transformation 1]
34. ! [X0] : ((strong(X0) | (kind(X0) & tall(X0))) & (~kind(X0) | ~tall(X0) | ~strong(X0))) [flattening 33]
39. ! [X0] : (((~funny(X0) | tall(X0)) | (generous(X0) | ~brave(X0))) & ((~generous(X0) & brave(X0)) | (funny(X0) & ~tall(X0)))) [nnf transformation 3]
40. ! [X0] : ((~funny(X0) | tall(X0) | generous(X0) | ~brave(X0)) & ((~generous(X0) & brave(X0)) | (funny(X0) & ~tall(X0)))) [flattening 39]
46. (? [X0] : ~strong(X0) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1)))) & (? [X1] : ((brave(X1) | ~funny(X1)) & (~brave(X1) | funny(X1))) | ! [X0] : strong(X0)) [nnf transformation 22]
47. (? [X0] : ~strong(X0) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1)))) & (? [X2] : ((brave(X2) | ~funny(X2)) & (~brave(X2) | funny(X2))) | ! [X3] : strong(X3)) [rectify 46]
48. ? [X0] : ~strong(X0) => ~strong(sK2) [choice axiom]
49. ? [X2] : ((brave(X2) | ~funny(X2)) & (~brave(X2) | funny(X2))) => ((brave(sK3) | ~funny(sK3)) & (~brave(sK3) | funny(sK3))) [choice axiom]
50. (~strong(sK2) | ! [X1] : ((funny(X1) | brave(X1)) & (~brave(X1) | ~funny(X1)))) & (((brave(sK3) | ~funny(sK3)) & (~brave(sK3) | funny(sK3))) | ! [X3] : strong(X3)) [skolemisation 47,49,48]
61. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X0] : (rich(X0) | ~funny(X0)) | (~funny(mary) | ~brave(mary))) [nnf transformation 11]
62. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X0] : (rich(X0) | ~funny(X0)) | ~funny(mary) | ~brave(mary)) [flattening 61]
63. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & (? [X1] : (rich(X1) | ~funny(X1)) | ~funny(mary) | ~brave(mary)) [rectify 62]
64. ? [X1] : (rich(X1) | ~funny(X1)) => (rich(sK7) | ~funny(sK7)) [choice axiom]
65. ((funny(mary) & brave(mary)) | ! [X0] : (~rich(X0) & funny(X0))) & ((rich(sK7) | ~funny(sK7)) | ~funny(mary) | ~brave(mary)) [skolemisation 63,64]
66. ! [X0] : (((~strong(X0) | rich(X0)) & (strong(X0) | ~rich(X0))) | ~patient(X0) | old(X0)) [nnf transformation 31]
84. tall(X0) | strong(X0) [cnf transformation 34]
90. ~generous(X0) | ~tall(X0) [cnf transformation 40]
91. ~generous(X0) | funny(X0) [cnf transformation 40]
98. ~strong(sK2) | ~brave(X1) | ~funny(X1) [cnf transformation 50]
102. ~old(X0) | ~patient(X0) [cnf transformation 28]
103. ~old(X0) | patient(X0) [cnf transformation 28]
104. generous(X0) | ~patient(X0) [cnf transformation 28]
105. patient(X0) | generous(X0) [cnf transformation 28]
119. brave(mary) | ~rich(X0) [cnf transformation 65]
123. ~strong(X0) | rich(X0) | ~patient(X0) | old(X0) [cnf transformation 66]
138. patient(lucy) [cnf transformation 20]
171. 8 <=> ! [X1] : (~brave(X1) | ~funny(X1)) [avatar definition]
172. ~brave(X1) | ~funny(X1) <- (8) [avatar component clause 171]
174. 9 <=> strong(sK2) [avatar definition]
176. ~strong(sK2) <- (~9) [avatar component clause 174]
177. 8 | ~9 [avatar split clause 98,174,171]
180. 10 <=> ! [X3] : strong(X3) [avatar definition]
181. strong(X3) <- (10) [avatar component clause 180]
207. generous(X0) [subsumption resolution 104,105]
208. ~old(X0) [subsumption resolution 102,103]
278. 31 <=> ! [X0] : ~rich(X0) [avatar definition]
279. ~rich(X0) <- (31) [avatar component clause 278]
282. 32 <=> ! [X0] : funny(X0) [avatar definition]
283. funny(X0) <- (32) [avatar component clause 282]
286. 33 <=> brave(mary) [avatar definition]
288. brave(mary) <- (33) [avatar component clause 286]
289. 31 | 33 [avatar split clause 119,286,278]
300. ~patient(X0) | rich(X0) | ~strong(X0) [subsumption resolution 123,208]
362. $false <- (~9, 10) [subsumption resolution 176,181]
363. 9 | ~10 [avatar contradiction clause 362]
376. ~tall(X0) [resolution 90,207]
377. funny(X0) [resolution 91,207]
378. 32 [avatar split clause 377,282]
384. strong(X0) [resolution 376,84]
390. rich(lucy) | ~strong(lucy) [resolution 300,138]
392. ~strong(lucy) <- (31) [subsumption resolution 390,279]
393. $false <- (10, 31) [subsumption resolution 392,181]
394. ~10 | ~31 [avatar contradiction clause 393]
396. ~funny(mary) <- (8, 33) [resolution 288,172]
397. $false <- (8, 32, 33) [subsumption resolution 396,283]
398. ~8 | ~32 | ~33 [avatar contradiction clause 397]
404. 10 [avatar split clause 384,180]
405. $false [avatar sat refutation 177,289,363,378,394,398,404]
% SZS output end Proof for 3536580136605100329553022
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either calm or not curious then john is either not old or tall and vice versa.
Everyone who is rich or not creative is either not quiet or not funny and vice versa.
Everyone who is not creative is both generous and kind.
If alice is brave then mary is not funny.
Everyone who is not rich is either brave or not happy.
If someone is curious or not old then paul is happy or patient and vice versa.
Everyone who is wise or rich is not creative.
If john is not patient then someone is either funny or not wise.
If john is both not wise and not curious then someone is not strong and vice versa.
Everyone who is not old is not funny and vice versa.
If paul is either creative or patient then susan is either not old or curious and vice versa.
If paul is either happy or creative then someone is funny or humble and vice versa.
If someone is either not curious or not quiet then someone is not humble.
Everyone who is either brave or quiet is not generous.
If fred is both not creative and not funny then mary is either not brave or not creative and vice versa.
Everyone who is not rich or happy is strong and vice versa.
Someone is either generous or tall.
Mary is both not curious and not creative.
Someone is not quiet.
Fred is not calm or strong.
Fred is not tall or not brave.
Someone is patient.
Someone is wise.
Alice is happy. | Mary is creative. | contradiction | ((?[X]:((calm(X)<~>~curious(X))))<=>((~old(john)<~>tall(john))))&
(![X]:((rich(X)|~creative(X))<=>(~quiet(X)<~>~funny(X))))&
(![X]:(~creative(X)=>(generous(X)&kind(X))))&
((brave(alice))=>(~funny(mary)))&
(![X]:(~rich(X)=>(brave(X)<~>~happy(X))))&
((?[X]:((curious(X)|~old(X))))<=>((happy(paul)|patient(paul))))&
(![X]:((wise(X)|rich(X))=>~creative(X)))&
((~patient(john))=>(?[X]:((funny(X)<~>~wise(X)))))&
(((~wise(john)&~curious(john)))<=>(?[X]:(~strong(X))))&
(![X]:(~old(X)<=>~funny(X)))&
(((creative(paul)<~>patient(paul)))<=>((~old(susan)<~>curious(susan))))&
(((happy(paul)<~>creative(paul)))<=>(?[X]:((funny(X)|humble(X)))))&
((?[X]:((~curious(X)<~>~quiet(X))))=>(?[X]:(~humble(X))))&
(![X]:((brave(X)<~>quiet(X))=>~generous(X)))&
(((~creative(fred)&~funny(fred)))<=>((~brave(mary)<~>~creative(mary))))&
(![X]:((~rich(X)|happy(X))<=>strong(X)))&
(?[X]:((generous(X)<~>tall(X))))&
((~curious(mary)&~creative(mary)))&
(?[X]:(~quiet(X)))&
((~calm(fred)|strong(fred)))&
((~tall(fred)|~brave(fred)))&
(?[X]:(patient(X)))&
(?[X]:(wise(X)))&
(happy(alice)) | creative(mary) | [
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1679739988889294772541845
% SZS output start Proof for 1679739988889294772541845
18. ~creative(mary) & ~curious(mary) [input p17]
25. creative(mary) [input hypothesis]
140. ~creative(mary) [cnf transformation 18]
147. creative(mary) [cnf transformation 25]
298. 32 <=> creative(mary) [avatar definition]
329. ~32 [avatar split clause 140,298]
348. 32 [avatar split clause 147,298]
349. $false [avatar sat refutation 329,348]
% SZS output end Proof for 1679739988889294772541845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not strong and not patient then someone is curious and vice versa. If alice is not brave then fred is happy and vice versa. If someone is not creative or quiet then paul is either not old or not brave. Everyone who is not happy is both not quiet and quiet and vice versa. If someone is both not quiet and old then fred is funny or not quiet and vice versa. If someone is kind or not brave then someone is not brave or not tall and vice versa. Everyone who is not generous is brave. If alice is funny or happy then someone is both curious and generous and vice versa. If someone is both not quiet and humble then someone is either wise or funny. If paul is tall then paul is not quiet and vice versa. Everyone who is both not patient and strong is not wise or rich and vice versa. If someone is humble or brave then someone is both not quiet and kind and vice versa. If someone is tall or funny then someone is either not old or not funny and vice versa. If fred is both not rich and happy then someone is not patient or not humble and vice versa. Everyone who is not quiet is not strong or not tall. If alice is tall then mary is not tall and vice versa. Someone is not tall or happy. Someone is not curious or curious. Someone is not generous or not strong. John is both rich and strong. Someone is both not strong and humble. Fred is either tall or not creative. Lucy is either brave or not tall. | John is not creative. | neutral | ((?[X]:((~strong(X)&~patient(X))))<=>(?[X]:(curious(X))))&
((~brave(alice))<=>(happy(fred)))&
((?[X]:((~creative(X)|quiet(X))))=>((~old(paul)<~>~brave(paul))))&
(![X]:(~happy(X)<=>(~quiet(X)&quiet(X))))&
((?[X]:((~quiet(X)&old(X))))<=>((funny(fred)|~quiet(fred))))&
((?[X]:((kind(X)|~brave(X))))<=>(?[X]:((~brave(X)|~tall(X)))))&
(![X]:(~generous(X)=>brave(X)))&
(((funny(alice)|happy(alice)))<=>(?[X]:((curious(X)&generous(X)))))&
((?[X]:((~quiet(X)&humble(X))))=>(?[X]:((wise(X)<~>funny(X)))))&
((tall(paul))<=>(~quiet(paul)))&
(![X]:((~patient(X)&strong(X))<=>(~wise(X)|rich(X))))&
((?[X]:((humble(X)|brave(X))))<=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((~old(X)<~>~funny(X)))))&
(((~rich(fred)&happy(fred)))<=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:(~quiet(X)=>(~strong(X)|~tall(X))))&
((tall(alice))<=>(~tall(mary)))&
(?[X]:((~tall(X)|happy(X))))&
(?[X]:((~curious(X)|curious(X))))&
(?[X]:((~generous(X)|~strong(X))))&
((rich(john)&strong(john)))&
(?[X]:((~strong(X)&humble(X))))&
((tall(fred)<~>~creative(fred)))&
((brave(lucy)<~>~tall(lucy))) | ~creative(john) | [] | null | 0 |
Everyone who is both not happy and not generous is tall and vice versa.
If john is both not brave and not quiet then susan is either old or not kind.
Everyone who is not tall is both not strong and creative.
If someone is happy or not brave then someone is strong or not wise and vice versa.
If someone is wise or not happy then someone is both brave and not happy.
If mary is either kind or not strong then mary is not funny or old.
If fred is both not generous and creative then someone is either not wise or not kind.
Everyone who is not patient or not creative is both not humble and humble and vice versa.
Everyone who is either kind or humble is both not funny and generous.
Everyone who is both creative and not old is either not wise or not patient.
If someone is not tall then alice is both not wise and not happy.
Everyone who is not curious is either not generous or not happy.
Everyone who is not humble is either not creative or strong.
Everyone who is both not brave and strong is either not quiet or not wise and vice versa.
If fred is humble then alice is calm or not tall and vice versa.
If someone is both not curious and old then someone is both not calm and humble.
Lucy is either not humble or not creative.
Someone is both funny and happy.
Alice is creative.
Someone is both not old and not brave.
Someone is either not humble or not kind.
Someone is either wise or not curious.
Someone is funny or rich. | Mary is quiet. | neutral | (![X]:((~happy(X)&~generous(X))<=>tall(X)))&
(((~brave(john)&~quiet(john)))=>((old(susan)<~>~kind(susan))))&
(![X]:(~tall(X)=>(~strong(X)&creative(X))))&
((?[X]:((happy(X)|~brave(X))))<=>(?[X]:((strong(X)|~wise(X)))))&
((?[X]:((wise(X)|~happy(X))))=>(?[X]:((brave(X)&~happy(X)))))&
(((kind(mary)<~>~strong(mary)))=>((~funny(mary)|old(mary))))&
(((~generous(fred)&creative(fred)))=>(?[X]:((~wise(X)<~>~kind(X)))))&
(![X]:((~patient(X)|~creative(X))<=>(~humble(X)&humble(X))))&
(![X]:((kind(X)<~>humble(X))=>(~funny(X)&generous(X))))&
(![X]:((creative(X)&~old(X))=>(~wise(X)<~>~patient(X))))&
((?[X]:(~tall(X)))=>((~wise(alice)&~happy(alice))))&
(![X]:(~curious(X)=>(~generous(X)<~>~happy(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>strong(X))))&
(![X]:((~brave(X)&strong(X))<=>(~quiet(X)<~>~wise(X))))&
((humble(fred))<=>((calm(alice)|~tall(alice))))&
((?[X]:((~curious(X)&old(X))))=>(?[X]:((~calm(X)&humble(X)))))&
((~humble(lucy)<~>~creative(lucy)))&
(?[X]:((funny(X)&happy(X))))&
(creative(alice))&
(?[X]:((~old(X)&~brave(X))))&
(?[X]:((~humble(X)<~>~kind(X))))&
(?[X]:((wise(X)<~>~curious(X))))&
(?[X]:((funny(X)|rich(X)))) | quiet(mary) | [] | null | 0 |
If someone is not creative then someone is not kind.
If susan is rich then someone is either funny or brave.
If mary is both strong and not happy then mary is not rich and vice versa.
If someone is either not brave or not strong then someone is not humble and vice versa.
Everyone who is not calm or not patient is either quiet or not curious.
Everyone who is old is not calm and vice versa.
Everyone who is patient is not happy and vice versa.
If mary is humble or old then alice is not kind or not generous and vice versa.
If paul is brave or not funny then someone is not rich or not strong and vice versa.
If someone is wise or funny then someone is either not funny or rich and vice versa.
Everyone who is either creative or not brave is calm or not rich and vice versa.
Everyone who is either strong or not curious is either brave or not rich and vice versa.
If someone is not generous or old then susan is not happy and vice versa.
If someone is old or tall then lucy is not happy or not wise and vice versa.
Everyone who is old is either quiet or brave.
Everyone who is old is either patient or brave.
Someone is both creative and happy.
Someone is either humble or not generous.
John is either calm or wise.
Fred is either old or not funny.
Susan is both patient and calm.
Someone is both curious and tall.
Someone is patient or old.
Someone is not wise or not tall. | Paul is kind. | neutral | ((?[X]:(~creative(X)))=>(?[X]:(~kind(X))))&
((rich(susan))=>(?[X]:((funny(X)<~>brave(X)))))&
(((strong(mary)&~happy(mary)))<=>(~rich(mary)))&
((?[X]:((~brave(X)<~>~strong(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~calm(X)|~patient(X))=>(quiet(X)<~>~curious(X))))&
(![X]:(old(X)<=>~calm(X)))&
(![X]:(patient(X)<=>~happy(X)))&
(((humble(mary)|old(mary)))<=>((~kind(alice)|~generous(alice))))&
(((brave(paul)|~funny(paul)))<=>(?[X]:((~rich(X)|~strong(X)))))&
((?[X]:((wise(X)|funny(X))))<=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((creative(X)<~>~brave(X))<=>(calm(X)|~rich(X))))&
(![X]:((strong(X)<~>~curious(X))<=>(brave(X)<~>~rich(X))))&
((?[X]:((~generous(X)|old(X))))<=>(~happy(susan)))&
((?[X]:((old(X)|tall(X))))<=>((~happy(lucy)|~wise(lucy))))&
(![X]:(old(X)=>(quiet(X)<~>brave(X))))&
(![X]:(old(X)=>(patient(X)<~>brave(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((humble(X)<~>~generous(X))))&
((calm(john)<~>wise(john)))&
((old(fred)<~>~funny(fred)))&
((patient(susan)&calm(susan)))&
(?[X]:((curious(X)&tall(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:((~wise(X)|~tall(X)))) | kind(paul) | [] | null | 0 |
Everyone who is either wise or strong is calm or curious and vice versa. If someone is strong then paul is quiet. Everyone who is both not creative and not happy is not old and vice versa. If someone is rich or old then susan is patient. Everyone who is both not old and curious is funny. Everyone who is funny is either not funny or funny and vice versa. If susan is wise then someone is not rich or creative and vice versa. Everyone who is curious or calm is both wise and old and vice versa. Everyone who is either not old or old is either strong or generous and vice versa. If mary is either not curious or brave then paul is not old. If someone is both old and funny then alice is both strong and not curious. If lucy is both not calm and not patient then someone is both creative and not old and vice versa. Everyone who is kind or tall is both not tall and old and vice versa. Everyone who is quiet is both calm and not funny. Someone is wise or not curious. Alice is rich. Paul is not kind. Alice is either creative or patient. John is both brave and not tall. Alice is either humble or brave. | Alice is kind. | contradiction | (![X]:((wise(X)<~>strong(X))<=>(calm(X)|curious(X))))&
((?[X]:(strong(X)))=>(quiet(paul)))&
(![X]:((~creative(X)&~happy(X))<=>~old(X)))&
((?[X]:((rich(X)|old(X))))=>(patient(susan)))&
(![X]:((~old(X)&curious(X))=>funny(X)))&
(![X]:(funny(X)<=>(~funny(X)<~>funny(X))))&
((wise(susan))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:((curious(X)|calm(X))<=>(wise(X)&old(X))))&
(![X]:((~old(X)<~>old(X))<=>(strong(X)<~>generous(X))))&
(((~curious(mary)<~>brave(mary)))=>(~old(paul)))&
((?[X]:((old(X)&funny(X))))=>((strong(alice)&~curious(alice))))&
(((~calm(lucy)&~patient(lucy)))<=>(?[X]:((creative(X)&~old(X)))))&
(![X]:((kind(X)|tall(X))<=>(~tall(X)&old(X))))&
(![X]:(quiet(X)=>(calm(X)&~funny(X))))&
(?[X]:((wise(X)|~curious(X))))&
(rich(alice))&
(~kind(paul))&
((creative(alice)<~>patient(alice)))&
((brave(john)&~tall(john)))&
((humble(alice)<~>brave(alice))) | kind(alice) | [
"p1",
"p5",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7395907455281156297552557
% SZS output start Proof for 7395907455281156297552557
2. ? [X0] : strong(X0) => quiet(paul) [input p1]
6. ! [X0] : (funny(X0) <=> (~funny(X0) <~> funny(X0))) [input p5]
11. ? [X0] : (funny(X0) & old(X0)) => (~curious(alice) & strong(alice)) [input p10]
13. ! [X0] : ((tall(X0) | kind(X0)) <=> (old(X0) & ~tall(X0))) [input p12]
14. ! [X0] : (quiet(X0) => (~funny(X0) & calm(X0))) [input p13]
21. kind(alice) [input hypothesis]
22. quiet(paul) | ! [X0] : ~strong(X0) [ennf transformation 2]
27. (~curious(alice) & strong(alice)) | ! [X0] : (~funny(X0) | ~old(X0)) [ennf transformation 11]
28. ! [X0] : ((~funny(X0) & calm(X0)) | ~quiet(X0)) [ennf transformation 14]
33. ! [X0] : ((funny(X0) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) & (((~funny(X0) | funny(X0)) & (funny(X0) | ~funny(X0))) | ~funny(X0))) [nnf transformation 6]
47. ! [X0] : (((tall(X0) | kind(X0)) | (~old(X0) | tall(X0))) & ((old(X0) & ~tall(X0)) | (~tall(X0) & ~kind(X0)))) [nnf transformation 13]
48. ! [X0] : ((tall(X0) | kind(X0) | ~old(X0) | tall(X0)) & ((old(X0) & ~tall(X0)) | (~tall(X0) & ~kind(X0)))) [flattening 47]
59. quiet(paul) | ~strong(X0) [cnf transformation 22]
68. funny(X0) | funny(X0) | funny(X0) [cnf transformation 33]
88. strong(alice) | ~funny(X0) | ~old(X0) [cnf transformation 27]
96. ~kind(X0) | old(X0) [cnf transformation 48]
100. ~funny(X0) | ~quiet(X0) [cnf transformation 28]
110. kind(alice) [cnf transformation 21]
119. funny(X0) [duplicate literal removal 68]
122. 1 <=> ! [X0] : ~strong(X0) [avatar definition]
123. ~strong(X0) <- (1) [avatar component clause 122]
125. 2 <=> quiet(paul) [avatar definition]
127. quiet(paul) <- (2) [avatar component clause 125]
128. 1 | 2 [avatar split clause 59,125,122]
130. 3 <=> ! [X0] : ~old(X0) [avatar definition]
131. ~old(X0) <- (3) [avatar component clause 130]
184. strong(alice) | ~old(X0) [subsumption resolution 88,119]
186. 15 <=> strong(alice) [avatar definition]
188. strong(alice) <- (15) [avatar component clause 186]
189. 3 | 15 [avatar split clause 184,186,130]
208. ~quiet(X0) [subsumption resolution 100,119]
229. $false <- (2) [subsumption resolution 127,208]
230. ~2 [avatar contradiction clause 229]
238. old(alice) [resolution 96,110]
239. $false <- (3) [subsumption resolution 238,131]
240. ~3 [avatar contradiction clause 239]
241. $false <- (1, 15) [subsumption resolution 188,123]
242. ~1 | ~15 [avatar contradiction clause 241]
243. $false [avatar sat refutation 128,189,230,240,242]
% SZS output end Proof for 7395907455281156297552557
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or brave is quiet and vice versa.
If alice is either not strong or happy then someone is not kind.
Everyone who is either not tall or not brave is both not wise and not calm.
Everyone who is strong is not quiet or wise.
Everyone who is both not wise and not creative is both not patient and old.
If someone is patient then john is both calm and not kind.
Everyone who is creative is either funny or generous.
If someone is either old or not patient then lucy is not rich.
If mary is either not strong or quiet then john is kind.
If someone is creative then someone is both funny and rich.
Everyone who is not patient is quiet.
Everyone who is brave or not curious is both creative and not tall.
Everyone who is either not quiet or kind is either not humble or not creative and vice versa.
Everyone who is both not calm and brave is either quiet or wise and vice versa.
Everyone who is brave or not creative is strong and vice versa.
Everyone who is calm or happy is creative or curious.
Someone is funny or kind.
Someone is not patient.
Lucy is either strong or not brave.
Someone is kind or creative.
Someone is not patient or not humble. | Mary is not creative. | contradiction | (![X]:((~strong(X)|brave(X))<=>quiet(X)))&
(((~strong(alice)<~>happy(alice)))=>(?[X]:(~kind(X))))&
(![X]:((~tall(X)<~>~brave(X))=>(~wise(X)&~calm(X))))&
(![X]:(strong(X)=>(~quiet(X)|wise(X))))&
(![X]:((~wise(X)&~creative(X))=>(~patient(X)&old(X))))&
((?[X]:(patient(X)))=>((calm(john)&~kind(john))))&
(![X]:(creative(X)=>(funny(X)<~>generous(X))))&
((?[X]:((old(X)<~>~patient(X))))=>(~rich(lucy)))&
(((~strong(mary)<~>quiet(mary)))=>(kind(john)))&
((?[X]:(creative(X)))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:(~patient(X)=>quiet(X)))&
(![X]:((brave(X)|~curious(X))=>(creative(X)&~tall(X))))&
(![X]:((~quiet(X)<~>kind(X))<=>(~humble(X)<~>~creative(X))))&
(![X]:((~calm(X)&brave(X))<=>(quiet(X)<~>wise(X))))&
(![X]:((brave(X)|~creative(X))<=>strong(X)))&
(![X]:((calm(X)|happy(X))=>(creative(X)|curious(X))))&
(?[X]:((funny(X)|kind(X))))&
(?[X]:(~patient(X)))&
((strong(lucy)<~>~brave(lucy)))&
(?[X]:((kind(X)|creative(X))))&
(?[X]:((~patient(X)|~humble(X)))) | ~creative(mary) | [
"p0",
"p4",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8913104441295432424886389
% SZS output start Proof for 8913104441295432424886389
1. ! [X0] : ((brave(X0) | ~strong(X0)) <=> quiet(X0)) [input p0]
5. ! [X0] : ((~creative(X0) & ~wise(X0)) => (old(X0) & ~patient(X0))) [input p4]
11. ! [X0] : (~patient(X0) => quiet(X0)) [input p10]
12. ! [X0] : ((~curious(X0) | brave(X0)) => (~tall(X0) & creative(X0))) [input p11]
14. ! [X0] : ((brave(X0) & ~calm(X0)) <=> (quiet(X0) <~> wise(X0))) [input p13]
15. ! [X0] : ((~creative(X0) | brave(X0)) <=> strong(X0)) [input p14]
22. ~creative(mary) [input hypothesis]
25. ! [X0] : (brave(X0) => (~tall(X0) & creative(X0))) [pure predicate removal 12]
30. ! [X0] : ((old(X0) & ~patient(X0)) | (creative(X0) | wise(X0))) [ennf transformation 5]
31. ! [X0] : ((old(X0) & ~patient(X0)) | creative(X0) | wise(X0)) [flattening 30]
37. ! [X0] : (quiet(X0) | patient(X0)) [ennf transformation 11]
38. ! [X0] : ((~tall(X0) & creative(X0)) | ~brave(X0)) [ennf transformation 25]
39. ! [X0] : (((brave(X0) | ~strong(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & strong(X0)))) [nnf transformation 1]
40. ! [X0] : ((brave(X0) | ~strong(X0) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) & strong(X0)))) [flattening 39]
52. ! [X0] : (((brave(X0) & ~calm(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~brave(X0) | calm(X0)))) [nnf transformation 14]
53. ! [X0] : (((brave(X0) & ~calm(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) & (((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | ~brave(X0) | calm(X0))) [flattening 52]
54. ! [X0] : (((~creative(X0) | brave(X0)) | ~strong(X0)) & (strong(X0) | (creative(X0) & ~brave(X0)))) [nnf transformation 15]
55. ! [X0] : ((~creative(X0) | brave(X0) | ~strong(X0)) & (strong(X0) | (creative(X0) & ~brave(X0)))) [flattening 54]
66. ~brave(X0) | quiet(X0) [cnf transformation 40]
67. ~quiet(X0) | ~strong(X0) | brave(X0) [cnf transformation 40]
75. ~patient(X0) | creative(X0) | wise(X0) [cnf transformation 31]
87. patient(X0) | quiet(X0) [cnf transformation 37]
88. ~brave(X0) | creative(X0) [cnf transformation 38]
103. brave(X0) | quiet(X0) | ~wise(X0) [cnf transformation 53]
105. creative(X0) | strong(X0) [cnf transformation 55]
113. ~creative(mary) [cnf transformation 22]
154. 10 <=> quiet(mary) [avatar definition]
155. quiet(mary) <- (10) [avatar component clause 154]
158. 11 <=> strong(mary) [avatar definition]
159. strong(mary) <- (11) [avatar component clause 158]
160. ~strong(mary) <- (~11) [avatar component clause 158]
175. ~wise(X0) | quiet(X0) [subsumption resolution 103,66]
215. strong(mary) [resolution 105,113]
217. $false <- (~11) [subsumption resolution 215,160]
218. 11 [avatar contradiction clause 217]
242. creative(X0) | wise(X0) | quiet(X0) [resolution 75,87]
243. creative(X0) | quiet(X0) [subsumption resolution 242,175]
244. quiet(mary) [resolution 243,113]
247. 10 [avatar split clause 244,154]
250. ~strong(mary) | brave(mary) <- (10) [resolution 155,67]
252. brave(mary) <- (10, 11) [subsumption resolution 250,159]
262. creative(mary) <- (10, 11) [resolution 252,88]
264. $false <- (10, 11) [subsumption resolution 262,113]
265. ~10 | ~11 [avatar contradiction clause 264]
266. $false [avatar sat refutation 218,247,265]
% SZS output end Proof for 8913104441295432424886389
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then susan is not creative or calm and vice versa.
If fred is both not rich and not generous then someone is both humble and not patient and vice versa.
Everyone who is old or not generous is not wise or not rich and vice versa.
Everyone who is both kind and not funny is not kind or tall.
Everyone who is patient or not patient is not rich or not quiet and vice versa.
Everyone who is not wise or not patient is both patient and not rich and vice versa.
If fred is not curious then someone is not humble and vice versa.
If someone is both not curious and brave then someone is both kind and strong and vice versa.
Everyone who is not calm is both not old and not generous and vice versa.
Everyone who is both not old and quiet is both generous and not tall.
If someone is not rich or patient then susan is either not generous or not rich and vice versa.
Everyone who is both generous and brave is both wise and curious.
If someone is not calm then someone is not calm or calm and vice versa.
Everyone who is either humble or not old is both old and not quiet and vice versa.
If someone is both not tall and curious then alice is old or humble.
Everyone who is both creative and not calm is both humble and not old.
Someone is either wise or not generous.
Alice is both not humble and not rich.
Someone is not humble.
Someone is both not rich and not tall.
Alice is either tall or not curious.
Paul is either strong or generous. | Susan is brave. | contradiction | ((?[X]:(~creative(X)))<=>((~creative(susan)|calm(susan))))&
(((~rich(fred)&~generous(fred)))<=>(?[X]:((humble(X)&~patient(X)))))&
(![X]:((old(X)|~generous(X))<=>(~wise(X)|~rich(X))))&
(![X]:((kind(X)&~funny(X))=>(~kind(X)|tall(X))))&
(![X]:((patient(X)|~patient(X))<=>(~rich(X)|~quiet(X))))&
(![X]:((~wise(X)|~patient(X))<=>(patient(X)&~rich(X))))&
((~curious(fred))<=>(?[X]:(~humble(X))))&
((?[X]:((~curious(X)&brave(X))))<=>(?[X]:((kind(X)&strong(X)))))&
(![X]:(~calm(X)<=>(~old(X)&~generous(X))))&
(![X]:((~old(X)&quiet(X))=>(generous(X)&~tall(X))))&
((?[X]:((~rich(X)|patient(X))))<=>((~generous(susan)<~>~rich(susan))))&
(![X]:((generous(X)&brave(X))=>(wise(X)&curious(X))))&
((?[X]:(~calm(X)))<=>(?[X]:((~calm(X)|calm(X)))))&
(![X]:((humble(X)<~>~old(X))<=>(old(X)&~quiet(X))))&
((?[X]:((~tall(X)&curious(X))))=>((old(alice)|humble(alice))))&
(![X]:((creative(X)&~calm(X))=>(humble(X)&~old(X))))&
(?[X]:((wise(X)<~>~generous(X))))&
((~humble(alice)&~rich(alice)))&
(?[X]:(~humble(X)))&
(?[X]:((~rich(X)&~tall(X))))&
((tall(alice)<~>~curious(alice)))&
((strong(paul)<~>generous(paul))) | brave(susan) | [
"p2",
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4105057364867120374855184
% SZS output start Proof for 4105057364867120374855184
3. ! [X0] : ((~generous(X0) | old(X0)) <=> (~rich(X0) | ~wise(X0))) [input p2]
6. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (~rich(X0) & patient(X0))) [input p5]
11. ? [X0] : (patient(X0) | ~rich(X0)) <=> (~generous(susan) <~> ~rich(susan)) [input p10]
12. ! [X0] : ((brave(X0) & generous(X0)) => (curious(X0) & wise(X0))) [input p11]
23. brave(susan) [input hypothesis]
29. ! [X0] : ((curious(X0) & wise(X0)) | (~brave(X0) | ~generous(X0))) [ennf transformation 12]
30. ! [X0] : ((curious(X0) & wise(X0)) | ~brave(X0) | ~generous(X0)) [flattening 29]
45. ! [X0] : (((~generous(X0) | old(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (generous(X0) & ~old(X0)))) [nnf transformation 3]
46. ! [X0] : ((~generous(X0) | old(X0) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | (generous(X0) & ~old(X0)))) [flattening 45]
49. ! [X0] : (((~patient(X0) | ~wise(X0)) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | (patient(X0) & wise(X0)))) [nnf transformation 6]
50. ! [X0] : ((~patient(X0) | ~wise(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | (patient(X0) & wise(X0)))) [flattening 49]
62. (? [X0] : (patient(X0) | ~rich(X0)) | ((~generous(susan) | rich(susan)) & (~rich(susan) | generous(susan)))) & (((rich(susan) | generous(susan)) & (~rich(susan) | ~generous(susan))) | ! [X0] : (~patient(X0) & rich(X0))) [nnf transformation 11]
63. (? [X0] : (patient(X0) | ~rich(X0)) | ((~generous(susan) | rich(susan)) & (~rich(susan) | generous(susan)))) & (((rich(susan) | generous(susan)) & (~rich(susan) | ~generous(susan))) | ! [X1] : (~patient(X1) & rich(X1))) [rectify 62]
64. ? [X0] : (patient(X0) | ~rich(X0)) => (patient(sK5) | ~rich(sK5)) [choice axiom]
65. ((patient(sK5) | ~rich(sK5)) | ((~generous(susan) | rich(susan)) & (~rich(susan) | generous(susan)))) & (((rich(susan) | generous(susan)) & (~rich(susan) | ~generous(susan))) | ! [X1] : (~patient(X1) & rich(X1))) [skolemisation 63,64]
90. ~wise(X0) | ~rich(X0) | generous(X0) [cnf transformation 46]
98. patient(X0) | patient(X0) [cnf transformation 50]
99. ~rich(X0) | wise(X0) [cnf transformation 50]
101. ~patient(X0) | ~wise(X0) | rich(X0) | ~patient(X0) [cnf transformation 50]
114. ~rich(susan) | ~generous(susan) | ~patient(X1) [cnf transformation 65]
116. rich(susan) | generous(susan) | ~patient(X1) [cnf transformation 65]
119. ~brave(X0) | wise(X0) | ~generous(X0) [cnf transformation 30]
144. brave(susan) [cnf transformation 23]
147. patient(X0) [duplicate literal removal 98]
148. ~wise(X0) | ~patient(X0) | rich(X0) [duplicate literal removal 101]
230. rich(susan) | generous(susan) [subsumption resolution 116,147]
232. 19 <=> generous(susan) [avatar definition]
233. ~generous(susan) <- (~19) [avatar component clause 232]
234. generous(susan) <- (19) [avatar component clause 232]
236. 20 <=> rich(susan) [avatar definition]
237. ~rich(susan) <- (~20) [avatar component clause 236]
238. rich(susan) <- (20) [avatar component clause 236]
239. 19 | 20 [avatar split clause 230,236,232]
244. ~rich(susan) | ~generous(susan) [subsumption resolution 114,147]
245. ~19 | ~20 [avatar split clause 244,236,232]
293. wise(susan) <- (20) [resolution 238,99]
300. ~rich(susan) | generous(susan) <- (20) [resolution 90,293]
301. generous(susan) <- (20) [subsumption resolution 300,238]
302. $false <- (~19, 20) [subsumption resolution 301,233]
303. 19 | ~20 [avatar contradiction clause 302]
317. 33 <=> wise(susan) [avatar definition]
319. wise(susan) <- (33) [avatar component clause 317]
346. wise(susan) | ~generous(susan) [resolution 119,144]
398. ~patient(susan) | rich(susan) <- (33) [resolution 148,319]
402. rich(susan) <- (33) [subsumption resolution 398,147]
403. $false <- (~20, 33) [subsumption resolution 402,237]
404. 20 | ~33 [avatar contradiction clause 403]
405. wise(susan) <- (19) [subsumption resolution 346,234]
406. 33 | ~19 [avatar split clause 405,232,317]
407. $false [avatar sat refutation 239,245,303,404,406]
% SZS output end Proof for 4105057364867120374855184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is either curious or tall.
If someone is both happy and not happy then paul is not quiet and vice versa.
Everyone who is not old or not strong is both not quiet and not humble and vice versa.
If lucy is both quiet and not creative then john is not curious and vice versa.
If someone is not generous then someone is both rich and calm and vice versa.
Everyone who is both not humble and calm is either not quiet or creative and vice versa.
If someone is either not patient or not humble then mary is either not old or not patient and vice versa.
Everyone who is rich or funny is not wise and vice versa.
Everyone who is not old is not creative and vice versa.
Everyone who is not funny or not calm is either creative or kind.
Everyone who is calm or curious is either not old or kind and vice versa.
If lucy is curious or humble then alice is kind or not calm and vice versa.
If someone is not humble or rich then susan is funny and vice versa.
Everyone who is either not humble or not calm is not rich and vice versa.
If paul is either not funny or not curious then someone is creative.
If someone is not old or kind then fred is not rich and vice versa.
Someone is quiet.
Someone is not curious or not patient.
Someone is not curious.
Someone is both creative and patient.
Someone is patient.
Someone is either not generous or funny.
Someone is either generous or not calm.
Paul is not happy or quiet. | Paul is creative. | entailment | (![X]:(patient(X)=>(curious(X)<~>tall(X))))&
((?[X]:((happy(X)&~happy(X))))<=>(~quiet(paul)))&
(![X]:((~old(X)|~strong(X))<=>(~quiet(X)&~humble(X))))&
(((quiet(lucy)&~creative(lucy)))<=>(~curious(john)))&
((?[X]:(~generous(X)))<=>(?[X]:((rich(X)&calm(X)))))&
(![X]:((~humble(X)&calm(X))<=>(~quiet(X)<~>creative(X))))&
((?[X]:((~patient(X)<~>~humble(X))))<=>((~old(mary)<~>~patient(mary))))&
(![X]:((rich(X)|funny(X))<=>~wise(X)))&
(![X]:(~old(X)<=>~creative(X)))&
(![X]:((~funny(X)|~calm(X))=>(creative(X)<~>kind(X))))&
(![X]:((calm(X)|curious(X))<=>(~old(X)<~>kind(X))))&
(((curious(lucy)|humble(lucy)))<=>((kind(alice)|~calm(alice))))&
((?[X]:((~humble(X)|rich(X))))<=>(funny(susan)))&
(![X]:((~humble(X)<~>~calm(X))<=>~rich(X)))&
(((~funny(paul)<~>~curious(paul)))=>(?[X]:(creative(X))))&
((?[X]:((~old(X)|kind(X))))<=>(~rich(fred)))&
(?[X]:(quiet(X)))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((creative(X)&patient(X))))&
(?[X]:(patient(X)))&
(?[X]:((~generous(X)<~>funny(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
((~happy(paul)|quiet(paul))) | creative(paul) | [
"p1",
"p2",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 69949156862277682967776
% SZS output start Proof for 69949156862277682967776
2. ? [X0] : (~happy(X0) & happy(X0)) <=> ~quiet(paul) [input p1]
3. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (~humble(X0) & ~quiet(X0))) [input p2]
9. ! [X0] : (~old(X0) <=> ~creative(X0)) [input p8]
25. ~creative(paul) [input hypothesis]
31. (? [X0] : (~happy(X0) & happy(X0)) | quiet(paul)) & (~quiet(paul) | ! [X0] : (happy(X0) | ~happy(X0))) [nnf transformation 2]
32. (? [X0] : (~happy(X0) & happy(X0)) | quiet(paul)) & (~quiet(paul) | ! [X1] : (happy(X1) | ~happy(X1))) [rectify 31]
33. ? [X0] : (~happy(X0) & happy(X0)) => (~happy(sK0) & happy(sK0)) [choice axiom]
34. ((~happy(sK0) & happy(sK0)) | quiet(paul)) & (~quiet(paul) | ! [X1] : (happy(X1) | ~happy(X1))) [skolemisation 32,33]
35. ! [X0] : (((~strong(X0) | ~old(X0)) | (humble(X0) | quiet(X0))) & ((~humble(X0) & ~quiet(X0)) | (strong(X0) & old(X0)))) [nnf transformation 3]
36. ! [X0] : ((~strong(X0) | ~old(X0) | humble(X0) | quiet(X0)) & ((~humble(X0) & ~quiet(X0)) | (strong(X0) & old(X0)))) [flattening 35]
50. ! [X0] : ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0))) [nnf transformation 9]
87. happy(sK0) | quiet(paul) [cnf transformation 34]
88. ~happy(sK0) | quiet(paul) [cnf transformation 34]
89. ~quiet(X0) | old(X0) [cnf transformation 36]
115. ~old(X0) | creative(X0) [cnf transformation 50]
153. ~creative(paul) [cnf transformation 25]
155. 1 <=> quiet(paul) [avatar definition]
157. quiet(paul) <- (1) [avatar component clause 155]
159. 2 <=> happy(sK0) [avatar definition]
162. 1 | ~2 [avatar split clause 88,159,155]
163. 1 | 2 [avatar split clause 87,159,155]
347. old(paul) <- (1) [resolution 89,157]
352. creative(paul) <- (1) [resolution 115,347]
354. $false <- (1) [subsumption resolution 352,153]
355. ~1 [avatar contradiction clause 354]
356. $false [avatar sat refutation 162,163,355]
% SZS output end Proof for 69949156862277682967776
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not rich or wise is either not strong or wise and vice versa.
If paul is either not happy or not tall then susan is not happy or not strong and vice versa.
Everyone who is both wise and not creative is creative or generous and vice versa.
If susan is either quiet or not strong then alice is not kind or not brave.
Everyone who is either not quiet or not creative is both generous and not tall and vice versa.
Everyone who is rich is both curious and not curious and vice versa.
Everyone who is calm or patient is generous or wise.
Everyone who is tall or creative is both generous and rich and vice versa.
If paul is humble then someone is generous or brave.
Everyone who is both not tall and happy is curious and vice versa.
Everyone who is calm is not funny.
If someone is either strong or curious then lucy is generous and vice versa.
If fred is either strong or curious then someone is not generous or patient.
If alice is either happy or curious then alice is either calm or not rich.
If someone is brave or not generous then paul is not wise.
Susan is funny or quiet.
Someone is either strong or brave.
Someone is not generous or calm.
Someone is not generous or rich.
John is not patient or funny.
Alice is not wise.
Someone is not old or old. | Fred is not old. | neutral | (![X]:((~rich(X)<~>wise(X))<=>(~strong(X)<~>wise(X))))&
(((~happy(paul)<~>~tall(paul)))<=>((~happy(susan)|~strong(susan))))&
(![X]:((wise(X)&~creative(X))<=>(creative(X)|generous(X))))&
(((quiet(susan)<~>~strong(susan)))=>((~kind(alice)|~brave(alice))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(generous(X)&~tall(X))))&
(![X]:(rich(X)<=>(curious(X)&~curious(X))))&
(![X]:((calm(X)|patient(X))=>(generous(X)|wise(X))))&
(![X]:((tall(X)|creative(X))<=>(generous(X)&rich(X))))&
((humble(paul))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:((~tall(X)&happy(X))<=>curious(X)))&
(![X]:(calm(X)=>~funny(X)))&
((?[X]:((strong(X)<~>curious(X))))<=>(generous(lucy)))&
(((strong(fred)<~>curious(fred)))=>(?[X]:((~generous(X)|patient(X)))))&
(((happy(alice)<~>curious(alice)))=>((calm(alice)<~>~rich(alice))))&
((?[X]:((brave(X)|~generous(X))))=>(~wise(paul)))&
((funny(susan)|quiet(susan)))&
(?[X]:((strong(X)<~>brave(X))))&
(?[X]:((~generous(X)|calm(X))))&
(?[X]:((~generous(X)|rich(X))))&
((~patient(john)|funny(john)))&
(~wise(alice))&
(?[X]:((~old(X)|old(X)))) | ~old(fred) | [] | null | 0 |
If alice is either not rich or tall then someone is both funny and creative and vice versa. Everyone who is both not funny and not wise is either not funny or creative and vice versa. If paul is either not calm or tall then fred is both creative and quiet. If lucy is either humble or not curious then susan is either not brave or rich and vice versa. Everyone who is both not patient and old is both tall and humble. Everyone who is strong is not quiet. Everyone who is either creative or not kind is both calm and not happy and vice versa. Everyone who is brave is not humble. Everyone who is either not old or not patient is both not calm and not quiet and vice versa. If susan is both happy and not brave then someone is either not funny or not wise and vice versa. Everyone who is quiet is rich and vice versa. If fred is happy or not happy then susan is not patient or not rich and vice versa. If someone is either patient or not tall then alice is curious or not old. Everyone who is either old or not old is old or not old and vice versa. Everyone who is humble is both not humble and not happy and vice versa. Someone is both not calm and not strong. Susan is not curious or not creative. John is not rich. Fred is not humble or not tall. Paul is not tall. Alice is either not creative or not tall. Lucy is both not calm and strong. Mary is kind. | Paul is creative. | neutral | (((~rich(alice)<~>tall(alice)))<=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~funny(X)&~wise(X))<=>(~funny(X)<~>creative(X))))&
(((~calm(paul)<~>tall(paul)))=>((creative(fred)&quiet(fred))))&
(((humble(lucy)<~>~curious(lucy)))<=>((~brave(susan)<~>rich(susan))))&
(![X]:((~patient(X)&old(X))=>(tall(X)&humble(X))))&
(![X]:(strong(X)=>~quiet(X)))&
(![X]:((creative(X)<~>~kind(X))<=>(calm(X)&~happy(X))))&
(![X]:(brave(X)=>~humble(X)))&
(![X]:((~old(X)<~>~patient(X))<=>(~calm(X)&~quiet(X))))&
(((happy(susan)&~brave(susan)))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
(![X]:(quiet(X)<=>rich(X)))&
(((happy(fred)|~happy(fred)))<=>((~patient(susan)|~rich(susan))))&
((?[X]:((patient(X)<~>~tall(X))))=>((curious(alice)|~old(alice))))&
(![X]:((old(X)<~>~old(X))<=>(old(X)|~old(X))))&
(![X]:(humble(X)<=>(~humble(X)&~happy(X))))&
(?[X]:((~calm(X)&~strong(X))))&
((~curious(susan)|~creative(susan)))&
(~rich(john))&
((~humble(fred)|~tall(fred)))&
(~tall(paul))&
((~creative(alice)<~>~tall(alice)))&
((~calm(lucy)&strong(lucy)))&
(kind(mary)) | creative(paul) | [] | null | 0 |
If mary is both not quiet and not tall then mary is both not calm and not patient and vice versa.
Everyone who is creative is not wise or not humble and vice versa.
If someone is not humble or not brave then susan is curious or not old and vice versa.
If someone is happy or not brave then susan is not strong.
Everyone who is both curious and funny is humble and vice versa.
Everyone who is either not brave or creative is not creative or not tall and vice versa.
If fred is creative or not generous then john is not creative.
If fred is either calm or not calm then someone is not kind or patient and vice versa.
Everyone who is rich is not brave and vice versa.
If someone is not rich or not curious then someone is not quiet and vice versa.
Everyone who is both funny and generous is happy.
If susan is wise then lucy is both kind and not patient.
Everyone who is both generous and not humble is both not happy and calm.
If lucy is creative or not rich then someone is both brave and not funny.
Everyone who is either creative or not wise is not old and vice versa.
Someone is not funny.
Susan is both generous and not humble.
John is either not patient or not old.
Someone is not tall or not generous.
Paul is both rich and kind.
Susan is either not creative or not old. | Susan is brave. | neutral | (((~quiet(mary)&~tall(mary)))<=>((~calm(mary)&~patient(mary))))&
(![X]:(creative(X)<=>(~wise(X)|~humble(X))))&
((?[X]:((~humble(X)|~brave(X))))<=>((curious(susan)|~old(susan))))&
((?[X]:((happy(X)|~brave(X))))=>(~strong(susan)))&
(![X]:((curious(X)&funny(X))<=>humble(X)))&
(![X]:((~brave(X)<~>creative(X))<=>(~creative(X)|~tall(X))))&
(((creative(fred)|~generous(fred)))=>(~creative(john)))&
(((calm(fred)<~>~calm(fred)))<=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:(rich(X)<=>~brave(X)))&
((?[X]:((~rich(X)|~curious(X))))<=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)&generous(X))=>happy(X)))&
((wise(susan))=>((kind(lucy)&~patient(lucy))))&
(![X]:((generous(X)&~humble(X))=>(~happy(X)&calm(X))))&
(((creative(lucy)|~rich(lucy)))=>(?[X]:((brave(X)&~funny(X)))))&
(![X]:((creative(X)<~>~wise(X))<=>~old(X)))&
(?[X]:(~funny(X)))&
((generous(susan)&~humble(susan)))&
((~patient(john)<~>~old(john)))&
(?[X]:((~tall(X)|~generous(X))))&
((rich(paul)&kind(paul)))&
((~creative(susan)<~>~old(susan))) | brave(susan) | [] | null | 0 |
Everyone who is either wise or calm is wise and vice versa.
If alice is not rich or not generous then susan is either old or not creative and vice versa.
Everyone who is both funny and humble is creative or funny and vice versa.
Everyone who is strong or not humble is either rich or not strong.
Everyone who is both calm and quiet is not brave and vice versa.
If alice is both happy and strong then fred is both not quiet and quiet.
Everyone who is not kind or not creative is not rich.
Everyone who is both curious and not generous is either strong or not quiet and vice versa.
If fred is either not happy or not kind then someone is both humble and not generous and vice versa.
Everyone who is curious is wise.
Everyone who is both not quiet and not kind is not tall or not strong and vice versa.
Everyone who is both not patient and generous is either not patient or generous.
If someone is either tall or old then alice is strong.
Everyone who is generous or kind is not humble or not quiet and vice versa.
Everyone who is both kind and not brave is both rich and not funny and vice versa.
Everyone who is either not rich or curious is calm.
Paul is not creative or not patient.
Someone is not creative or funny.
Someone is either rich or old.
Someone is funny or not generous.
Alice is not rich or not wise.
Someone is old.
Someone is not quiet or creative. | Paul is not old. | neutral | (![X]:((wise(X)<~>calm(X))<=>wise(X)))&
(((~rich(alice)|~generous(alice)))<=>((old(susan)<~>~creative(susan))))&
(![X]:((funny(X)&humble(X))<=>(creative(X)|funny(X))))&
(![X]:((strong(X)|~humble(X))=>(rich(X)<~>~strong(X))))&
(![X]:((calm(X)&quiet(X))<=>~brave(X)))&
(((happy(alice)&strong(alice)))=>((~quiet(fred)&quiet(fred))))&
(![X]:((~kind(X)|~creative(X))=>~rich(X)))&
(![X]:((curious(X)&~generous(X))<=>(strong(X)<~>~quiet(X))))&
(((~happy(fred)<~>~kind(fred)))<=>(?[X]:((humble(X)&~generous(X)))))&
(![X]:(curious(X)=>wise(X)))&
(![X]:((~quiet(X)&~kind(X))<=>(~tall(X)|~strong(X))))&
(![X]:((~patient(X)&generous(X))=>(~patient(X)<~>generous(X))))&
((?[X]:((tall(X)<~>old(X))))=>(strong(alice)))&
(![X]:((generous(X)|kind(X))<=>(~humble(X)|~quiet(X))))&
(![X]:((kind(X)&~brave(X))<=>(rich(X)&~funny(X))))&
(![X]:((~rich(X)<~>curious(X))=>calm(X)))&
((~creative(paul)|~patient(paul)))&
(?[X]:((~creative(X)|funny(X))))&
(?[X]:((rich(X)<~>old(X))))&
(?[X]:((funny(X)|~generous(X))))&
((~rich(alice)|~wise(alice)))&
(?[X]:(old(X)))&
(?[X]:((~quiet(X)|creative(X)))) | ~old(paul) | [] | null | 0 |
If someone is both not strong and not patient then someone is either not humble or tall and vice versa.
Everyone who is both not brave and not patient is both not strong and happy.
If lucy is both calm and generous then someone is both quiet and not generous.
If someone is both not brave and not creative then someone is either not kind or calm and vice versa.
Everyone who is wise is both not brave and rich and vice versa.
Everyone who is not humble is either patient or not creative.
Everyone who is not tall or funny is either not happy or tall.
If lucy is rich then someone is either brave or not tall.
Everyone who is both creative and not curious is happy or rich and vice versa.
If someone is both not kind and tall then someone is not kind and vice versa.
Everyone who is either quiet or not old is either rich or generous and vice versa.
If someone is either not rich or generous then mary is patient and vice versa.
If john is calm then john is either not rich or kind.
If someone is not happy then john is both not happy and not generous and vice versa.
Everyone who is either not old or not happy is either tall or happy and vice versa.
Everyone who is either calm or generous is both not calm and rich and vice versa.
Someone is curious or patient.
Someone is both not calm and not generous.
Fred is not happy.
Someone is calm or not patient.
Someone is both rich and not kind.
Lucy is either calm or not generous.
Someone is both not wise and not curious.
Someone is not wise. | John is happy. | contradiction | ((?[X]:((~strong(X)&~patient(X))))<=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:((~brave(X)&~patient(X))=>(~strong(X)&happy(X))))&
(((calm(lucy)&generous(lucy)))=>(?[X]:((quiet(X)&~generous(X)))))&
((?[X]:((~brave(X)&~creative(X))))<=>(?[X]:((~kind(X)<~>calm(X)))))&
(![X]:(wise(X)<=>(~brave(X)&rich(X))))&
(![X]:(~humble(X)=>(patient(X)<~>~creative(X))))&
(![X]:((~tall(X)|funny(X))=>(~happy(X)<~>tall(X))))&
((rich(lucy))=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((creative(X)&~curious(X))<=>(happy(X)|rich(X))))&
((?[X]:((~kind(X)&tall(X))))<=>(?[X]:(~kind(X))))&
(![X]:((quiet(X)<~>~old(X))<=>(rich(X)<~>generous(X))))&
((?[X]:((~rich(X)<~>generous(X))))<=>(patient(mary)))&
((calm(john))=>((~rich(john)<~>kind(john))))&
((?[X]:(~happy(X)))<=>((~happy(john)&~generous(john))))&
(![X]:((~old(X)<~>~happy(X))<=>(tall(X)<~>happy(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~calm(X)&rich(X))))&
(?[X]:((curious(X)|patient(X))))&
(?[X]:((~calm(X)&~generous(X))))&
(~happy(fred))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((rich(X)&~kind(X))))&
((calm(lucy)<~>~generous(lucy)))&
(?[X]:((~wise(X)&~curious(X))))&
(?[X]:(~wise(X))) | happy(john) | [
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1063736105657562366314155
% SZS output start Proof for 1063736105657562366314155
14. ? [X0] : ~happy(X0) <=> (~generous(john) & ~happy(john)) [input p13]
19. ~happy(fred) [input p18]
25. happy(john) [input hypothesis]
71. (? [X0] : ~happy(X0) | (generous(john) | happy(john))) & ((~generous(john) & ~happy(john)) | ! [X0] : happy(X0)) [nnf transformation 14]
72. (? [X0] : ~happy(X0) | generous(john) | happy(john)) & ((~generous(john) & ~happy(john)) | ! [X0] : happy(X0)) [flattening 71]
73. (? [X0] : ~happy(X0) | generous(john) | happy(john)) & ((~generous(john) & ~happy(john)) | ! [X1] : happy(X1)) [rectify 72]
74. ? [X0] : ~happy(X0) => ~happy(sK9) [choice axiom]
75. (~happy(sK9) | generous(john) | happy(john)) & ((~generous(john) & ~happy(john)) | ! [X1] : happy(X1)) [skolemisation 73,74]
137. ~happy(john) | happy(X1) [cnf transformation 75]
157. ~happy(fred) [cnf transformation 19]
166. happy(john) [cnf transformation 25]
326. 35 <=> happy(john) [avatar definition]
339. 38 <=> ! [X1] : happy(X1) [avatar definition]
340. happy(X1) <- (38) [avatar component clause 339]
342. 38 | ~35 [avatar split clause 137,326,339]
364. 35 [avatar split clause 166,326]
369. $false <- (38) [resolution 340,157]
370. ~38 [avatar contradiction clause 369]
371. $false [avatar sat refutation 342,364,370]
% SZS output end Proof for 1063736105657562366314155
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is both tall and not wise and vice versa.
If john is humble then fred is not rich or not happy.
If susan is either not quiet or not old then john is either not brave or patient.
Everyone who is not old or not tall is both generous and not old.
Everyone who is both old and not rich is kind or not generous and vice versa.
If lucy is either not humble or not brave then john is both not tall and not patient and vice versa.
If someone is not calm then mary is both not humble and kind and vice versa.
Everyone who is both not patient and not curious is both not generous and not tall.
If someone is either kind or not quiet then someone is both curious and not patient.
If someone is either not tall or creative then susan is creative or quiet and vice versa.
If someone is not humble or not generous then someone is not quiet or strong and vice versa.
Everyone who is both funny and not rich is kind or not old.
Everyone who is funny is either humble or not curious.
Everyone who is both not curious and funny is either not humble or old.
If someone is either not kind or not calm then susan is both old and brave.
Everyone who is not happy is wise.
Someone is either not brave or not tall.
Someone is not old.
Fred is humble.
John is either quiet or not creative.
John is both not humble and calm.
Alice is both not curious and not tall.
Someone is not old or not rich.
Someone is not strong. | Susan is not brave. | contradiction | (![X]:(~calm(X)<=>(tall(X)&~wise(X))))&
((humble(john))=>((~rich(fred)|~happy(fred))))&
(((~quiet(susan)<~>~old(susan)))=>((~brave(john)<~>patient(john))))&
(![X]:((~old(X)|~tall(X))=>(generous(X)&~old(X))))&
(![X]:((old(X)&~rich(X))<=>(kind(X)|~generous(X))))&
(((~humble(lucy)<~>~brave(lucy)))<=>((~tall(john)&~patient(john))))&
((?[X]:(~calm(X)))<=>((~humble(mary)&kind(mary))))&
(![X]:((~patient(X)&~curious(X))=>(~generous(X)&~tall(X))))&
((?[X]:((kind(X)<~>~quiet(X))))=>(?[X]:((curious(X)&~patient(X)))))&
((?[X]:((~tall(X)<~>creative(X))))<=>((creative(susan)|quiet(susan))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:((~quiet(X)|strong(X)))))&
(![X]:((funny(X)&~rich(X))=>(kind(X)|~old(X))))&
(![X]:(funny(X)=>(humble(X)<~>~curious(X))))&
(![X]:((~curious(X)&funny(X))=>(~humble(X)<~>old(X))))&
((?[X]:((~kind(X)<~>~calm(X))))=>((old(susan)&brave(susan))))&
(![X]:(~happy(X)=>wise(X)))&
(?[X]:((~brave(X)<~>~tall(X))))&
(?[X]:(~old(X)))&
(humble(fred))&
((quiet(john)<~>~creative(john)))&
((~humble(john)&calm(john)))&
((~curious(alice)&~tall(alice)))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:(~strong(X))) | ~brave(susan) | [
"p0",
"p3",
"p4",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5983686920410159710725423
% SZS output start Proof for 5983686920410159710725423
1. ! [X0] : (~calm(X0) <=> (~wise(X0) & tall(X0))) [input p0]
4. ! [X0] : ((~tall(X0) | ~old(X0)) => (~old(X0) & generous(X0))) [input p3]
5. ! [X0] : ((~rich(X0) & old(X0)) <=> (~generous(X0) | kind(X0))) [input p4]
15. ? [X0] : (~kind(X0) <~> ~calm(X0)) => (brave(susan) & old(susan)) [input p14]
22. ~tall(alice) & ~curious(alice) [input p21]
25. ~brave(susan) [input hypothesis]
34. ! [X0] : ((~old(X0) & generous(X0)) | (tall(X0) & old(X0))) [ennf transformation 4]
38. (brave(susan) & old(susan)) | ! [X0] : (~kind(X0) <=> ~calm(X0)) [ennf transformation 15]
40. ! [X0] : ((~calm(X0) | (wise(X0) | ~tall(X0))) & ((~wise(X0) & tall(X0)) | calm(X0))) [nnf transformation 1]
41. ! [X0] : ((~calm(X0) | wise(X0) | ~tall(X0)) & ((~wise(X0) & tall(X0)) | calm(X0))) [flattening 40]
43. ! [X0] : (((~rich(X0) & old(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (rich(X0) | ~old(X0)))) [nnf transformation 5]
44. ! [X0] : (((~rich(X0) & old(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | rich(X0) | ~old(X0))) [flattening 43]
66. (brave(susan) & old(susan)) | ! [X0] : ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))) [nnf transformation 38]
77. tall(X0) | calm(X0) [cnf transformation 41]
88. ~old(X0) | tall(X0) [cnf transformation 34]
90. ~kind(X0) | old(X0) [cnf transformation 44]
121. brave(susan) | ~calm(X0) | kind(X0) [cnf transformation 66]
133. ~tall(alice) [cnf transformation 22]
136. ~brave(susan) [cnf transformation 25]
284. 33 <=> brave(susan) [avatar definition]
289. 34 <=> ! [X0] : (~calm(X0) | kind(X0)) [avatar definition]
290. ~calm(X0) | kind(X0) <- (34) [avatar component clause 289]
291. 34 | 33 [avatar split clause 121,284,289]
324. ~33 [avatar split clause 136,284]
325. calm(alice) [resolution 77,133]
340. kind(alice) <- (34) [resolution 290,325]
363. old(alice) <- (34) [resolution 340,90]
401. tall(alice) <- (34) [resolution 363,88]
402. $false <- (34) [subsumption resolution 401,133]
403. ~34 [avatar contradiction clause 402]
404. $false [avatar sat refutation 291,324,403]
% SZS output end Proof for 5983686920410159710725423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not tall then john is either not kind or rich and vice versa.
If someone is both not funny and not old then paul is both not curious and not funny and vice versa.
Everyone who is not brave is either not creative or not patient and vice versa.
If lucy is calm or not curious then alice is not funny and vice versa.
If mary is either not strong or rich then fred is brave or kind.
If john is both brave and not tall then someone is either not humble or rich and vice versa.
If paul is both tall and funny then someone is not happy or not tall and vice versa.
Everyone who is either brave or strong is patient.
If someone is calm then john is both quiet and not creative.
Everyone who is either not generous or kind is generous or strong.
If paul is quiet then someone is either not rich or wise.
Everyone who is both brave and not humble is either not generous or tall and vice versa.
Everyone who is both not patient and curious is strong or not quiet and vice versa.
If someone is both funny and patient then someone is generous.
Everyone who is either patient or not patient is either not humble or funny and vice versa.
Everyone who is not humble is either not humble or not rich and vice versa.
Fred is creative or tall.
Someone is not funny.
Someone is both funny and not creative.
Mary is not calm.
Mary is not generous or not rich.
Someone is strong.
John is humble or old.
Someone is not happy or not calm. | John is tall. | contradiction | ((?[X]:((~rich(X)|~tall(X))))<=>((~kind(john)<~>rich(john))))&
((?[X]:((~funny(X)&~old(X))))<=>((~curious(paul)&~funny(paul))))&
(![X]:(~brave(X)<=>(~creative(X)<~>~patient(X))))&
(((calm(lucy)|~curious(lucy)))<=>(~funny(alice)))&
(((~strong(mary)<~>rich(mary)))=>((brave(fred)|kind(fred))))&
(((brave(john)&~tall(john)))<=>(?[X]:((~humble(X)<~>rich(X)))))&
(((tall(paul)&funny(paul)))<=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((brave(X)<~>strong(X))=>patient(X)))&
((?[X]:(calm(X)))=>((quiet(john)&~creative(john))))&
(![X]:((~generous(X)<~>kind(X))=>(generous(X)|strong(X))))&
((quiet(paul))=>(?[X]:((~rich(X)<~>wise(X)))))&
(![X]:((brave(X)&~humble(X))<=>(~generous(X)<~>tall(X))))&
(![X]:((~patient(X)&curious(X))<=>(strong(X)|~quiet(X))))&
((?[X]:((funny(X)&patient(X))))=>(?[X]:(generous(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~humble(X)<~>funny(X))))&
(![X]:(~humble(X)<=>(~humble(X)<~>~rich(X))))&
((creative(fred)|tall(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((funny(X)&~creative(X))))&
(~calm(mary))&
((~generous(mary)|~rich(mary)))&
(?[X]:(strong(X)))&
((humble(john)|old(john)))&
(?[X]:((~happy(X)|~calm(X)))) | tall(john) | [
"p5",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1686064229209720113653382
% SZS output start Proof for 1686064229209720113653382
6. (~tall(john) & brave(john)) <=> ? [X0] : (~humble(X0) <~> rich(X0)) [input p5]
15. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (~humble(X0) <~> funny(X0))) [input p14]
16. ! [X0] : (~humble(X0) <=> (~humble(X0) <~> ~rich(X0))) [input p15]
19. ? [X0] : (~creative(X0) & funny(X0)) [input p18]
25. tall(john) [input hypothesis]
48. ((~tall(john) & brave(john)) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (? [X0] : ((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | (tall(john) | ~brave(john))) [nnf transformation 6]
49. ((~tall(john) & brave(john)) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (? [X0] : ((~rich(X0) | humble(X0)) & (rich(X0) | ~humble(X0))) | tall(john) | ~brave(john)) [flattening 48]
50. ((~tall(john) & brave(john)) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (? [X1] : ((~rich(X1) | humble(X1)) & (rich(X1) | ~humble(X1))) | tall(john) | ~brave(john)) [rectify 49]
51. ? [X1] : ((~rich(X1) | humble(X1)) & (rich(X1) | ~humble(X1))) => ((~rich(sK2) | humble(sK2)) & (rich(sK2) | ~humble(sK2))) [choice axiom]
52. ((~tall(john) & brave(john)) | ! [X0] : ((~humble(X0) | ~rich(X0)) & (rich(X0) | humble(X0)))) & (((~rich(sK2) | humble(sK2)) & (rich(sK2) | ~humble(sK2))) | tall(john) | ~brave(john)) [skolemisation 50,51]
70. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) & (((~funny(X0) | humble(X0)) & (funny(X0) | ~humble(X0))) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 15]
71. ! [X0] : ((~humble(X0) | ((~humble(X0) | rich(X0)) & (~rich(X0) | humble(X0)))) & (((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | humble(X0))) [nnf transformation 16]
74. ? [X0] : (~creative(X0) & funny(X0)) => (~creative(sK7) & funny(sK7)) [choice axiom]
75. ~creative(sK7) & funny(sK7) [skolemisation 19,74]
104. ~tall(john) | ~humble(X0) | ~rich(X0) [cnf transformation 52]
132. ~funny(X0) | humble(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 70]
133. ~funny(X0) | humble(X0) | patient(X0) | patient(X0) [cnf transformation 70]
141. ~humble(X0) | ~humble(X0) | rich(X0) [cnf transformation 71]
144. funny(sK7) [cnf transformation 75]
151. tall(john) [cnf transformation 25]
153. ~humble(X0) | rich(X0) [duplicate literal removal 141]
156. ~funny(X0) | humble(X0) | ~patient(X0) [duplicate literal removal 132]
157. ~funny(X0) | humble(X0) | patient(X0) [duplicate literal removal 133]
244. 19 <=> ! [X0] : (~humble(X0) | ~rich(X0)) [avatar definition]
245. ~humble(X0) | ~rich(X0) <- (19) [avatar component clause 244]
247. 20 <=> tall(john) [avatar definition]
250. 19 | ~20 [avatar split clause 104,247,244]
326. ~funny(X0) | humble(X0) [subsumption resolution 156,157]
362. 20 [avatar split clause 151,247]
365. ~humble(X0) <- (19) [subsumption resolution 245,153]
386. humble(sK7) [resolution 326,144]
387. $false <- (19) [subsumption resolution 386,365]
388. ~19 [avatar contradiction clause 387]
389. $false [avatar sat refutation 250,362,388]
% SZS output end Proof for 1686064229209720113653382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and brave is both not rich and not brave and vice versa.
If lucy is not quiet or rich then alice is not rich or not funny.
Everyone who is either not kind or not humble is not brave or creative and vice versa.
If susan is both not wise and calm then someone is either generous or humble and vice versa.
Everyone who is not calm is creative.
Everyone who is brave is either not brave or funny.
Everyone who is either creative or curious is not humble and vice versa.
If someone is not rich or not creative then someone is both kind and happy.
Everyone who is not quiet or not kind is not strong and vice versa.
Everyone who is generous or not curious is both not quiet and creative and vice versa.
Everyone who is either not happy or wise is generous and vice versa.
If lucy is either not rich or not tall then someone is either generous or not funny and vice versa.
Everyone who is either not generous or not creative is both kind and not brave and vice versa.
Everyone who is both not rich and calm is both not wise and happy and vice versa.
If someone is both curious and creative then fred is not patient or not old.
If paul is both strong and not old then someone is patient and vice versa.
Alice is not kind or not wise.
Mary is either not kind or not happy.
Someone is not rich or not patient.
Susan is not calm or rich.
Lucy is brave.
Lucy is either not kind or patient.
John is both not tall and curious. | John is strong. | contradiction | (![X]:((~calm(X)&brave(X))<=>(~rich(X)&~brave(X))))&
(((~quiet(lucy)|rich(lucy)))=>((~rich(alice)|~funny(alice))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~brave(X)|creative(X))))&
(((~wise(susan)&calm(susan)))<=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:(~calm(X)=>creative(X)))&
(![X]:(brave(X)=>(~brave(X)<~>funny(X))))&
(![X]:((creative(X)<~>curious(X))<=>~humble(X)))&
((?[X]:((~rich(X)|~creative(X))))=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((~quiet(X)|~kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~curious(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~happy(X)<~>wise(X))<=>generous(X)))&
(((~rich(lucy)<~>~tall(lucy)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))<=>(kind(X)&~brave(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&happy(X))))&
((?[X]:((curious(X)&creative(X))))=>((~patient(fred)|~old(fred))))&
(((strong(paul)&~old(paul)))<=>(?[X]:(patient(X))))&
((~kind(alice)|~wise(alice)))&
((~kind(mary)<~>~happy(mary)))&
(?[X]:((~rich(X)|~patient(X))))&
((~calm(susan)|rich(susan)))&
(brave(lucy))&
((~kind(lucy)<~>patient(lucy)))&
((~tall(john)&curious(john))) | strong(john) | [
"p2",
"p6",
"p8",
"p9",
"p12",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3959351556014601936169888
% SZS output start Proof for 3959351556014601936169888
3. ! [X0] : ((~kind(X0) <~> ~humble(X0)) <=> (creative(X0) | ~brave(X0))) [input p2]
7. ! [X0] : ((creative(X0) <~> curious(X0)) <=> ~humble(X0)) [input p6]
9. ! [X0] : ((~kind(X0) | ~quiet(X0)) <=> ~strong(X0)) [input p8]
10. ! [X0] : ((~curious(X0) | generous(X0)) <=> (creative(X0) & ~quiet(X0))) [input p9]
13. ! [X0] : ((~generous(X0) <~> ~creative(X0)) <=> (~brave(X0) & kind(X0))) [input p12]
23. curious(john) & ~tall(john) [input p22]
24. strong(john) [input hypothesis]
35. ! [X0] : ((((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))))) [nnf transformation 3]
36. ! [X0] : ((((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))))) [flattening 35]
43. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | humble(X0)) & (~humble(X0) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 7]
47. ! [X0] : (((~kind(X0) | ~quiet(X0)) | strong(X0)) & (~strong(X0) | (kind(X0) & quiet(X0)))) [nnf transformation 9]
48. ! [X0] : ((~kind(X0) | ~quiet(X0) | strong(X0)) & (~strong(X0) | (kind(X0) & quiet(X0)))) [flattening 47]
49. ! [X0] : (((~curious(X0) | generous(X0)) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | (curious(X0) & ~generous(X0)))) [nnf transformation 10]
50. ! [X0] : ((~curious(X0) | generous(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | (curious(X0) & ~generous(X0)))) [flattening 49]
56. ! [X0] : ((((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))))) [nnf transformation 13]
57. ! [X0] : ((((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))))) [flattening 56]
76. ~kind(X0) | ~brave(X0) | creative(X0) | humble(X0) [cnf transformation 36]
78. ~creative(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 36]
79. humble(X0) | kind(X0) | brave(X0) [cnf transformation 36]
91. ~curious(X0) | creative(X0) | ~humble(X0) [cnf transformation 43]
93. ~curious(X0) | ~creative(X0) | humble(X0) [cnf transformation 43]
99. ~strong(X0) | kind(X0) [cnf transformation 48]
103. ~generous(X0) | creative(X0) [cnf transformation 50]
104. curious(X0) | creative(X0) [cnf transformation 50]
123. creative(X0) | generous(X0) | brave(X0) | ~kind(X0) [cnf transformation 57]
141. curious(john) [cnf transformation 23]
142. strong(john) [cnf transformation 24]
236. ~kind(X0) | brave(X0) | creative(X0) [subsumption resolution 123,103]
314. kind(john) [resolution 99,142]
333. creative(X0) | ~humble(X0) | creative(X0) [resolution 91,104]
334. ~humble(X0) | creative(X0) [duplicate literal removal 333]
343. ~creative(john) | humble(john) [resolution 93,141]
356. 36 <=> humble(john) [avatar definition]
358. humble(john) <- (36) [avatar component clause 356]
360. 37 <=> creative(john) [avatar definition]
361. creative(john) <- (37) [avatar component clause 360]
362. ~creative(john) <- (~37) [avatar component clause 360]
363. 36 | ~37 [avatar split clause 343,360,356]
445. ~kind(john) | ~humble(john) <- (37) [resolution 361,78]
446. ~humble(john) <- (37) [subsumption resolution 445,314]
447. $false <- (36, 37) [subsumption resolution 446,358]
448. ~36 | ~37 [avatar contradiction clause 447]
493. ~brave(john) | creative(john) | humble(john) [resolution 76,314]
555. creative(X0) | kind(X0) | brave(X0) [resolution 334,79]
556. creative(john) <- (36) [resolution 334,358]
559. creative(X0) | brave(X0) [subsumption resolution 555,236]
560. $false <- (36, ~37) [subsumption resolution 556,362]
561. ~36 | 37 [avatar contradiction clause 560]
565. ~brave(john) | humble(john) <- (~37) [subsumption resolution 493,362]
567. 57 <=> brave(john) [avatar definition]
569. ~brave(john) <- (~57) [avatar component clause 567]
570. 36 | ~57 | 37 [avatar split clause 565,360,567,356]
799. brave(john) <- (~37) [resolution 559,362]
800. $false <- (~37, ~57) [subsumption resolution 799,569]
801. 37 | 57 [avatar contradiction clause 800]
802. $false [avatar sat refutation 363,448,561,570,801]
% SZS output end Proof for 3959351556014601936169888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and kind is curious or not old.
If someone is either kind or curious then john is both not tall and calm.
Everyone who is not rich or not quiet is creative or not wise.
Everyone who is either curious or not humble is both generous and happy and vice versa.
Everyone who is not patient or patient is both calm and not generous.
If someone is strong or not kind then someone is not humble or strong and vice versa.
Everyone who is both not old and funny is both not creative and humble and vice versa.
Everyone who is both not curious and wise is either not humble or not brave.
Everyone who is either not humble or not curious is wise.
Everyone who is old or happy is not old.
Everyone who is not humble is old or not old.
If someone is humble then mary is both rich and kind and vice versa.
If someone is either not happy or not brave then someone is both not quiet and happy and vice versa.
If someone is either kind or tall then alice is not funny.
Everyone who is not strong is generous.
Alice is both calm and not patient.
Someone is patient or tall.
Someone is not brave.
Someone is both strong and not curious.
Someone is creative or generous.
Fred is not brave.
Someone is either not kind or creative. | Mary is not creative. | neutral | (![X]:((~wise(X)&kind(X))=>(curious(X)|~old(X))))&
((?[X]:((kind(X)<~>curious(X))))=>((~tall(john)&calm(john))))&
(![X]:((~rich(X)|~quiet(X))=>(creative(X)|~wise(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(generous(X)&happy(X))))&
(![X]:((~patient(X)|patient(X))=>(calm(X)&~generous(X))))&
((?[X]:((strong(X)|~kind(X))))<=>(?[X]:((~humble(X)|strong(X)))))&
(![X]:((~old(X)&funny(X))<=>(~creative(X)&humble(X))))&
(![X]:((~curious(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((~humble(X)<~>~curious(X))=>wise(X)))&
(![X]:((old(X)|happy(X))=>~old(X)))&
(![X]:(~humble(X)=>(old(X)|~old(X))))&
((?[X]:(humble(X)))<=>((rich(mary)&kind(mary))))&
((?[X]:((~happy(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&happy(X)))))&
((?[X]:((kind(X)<~>tall(X))))=>(~funny(alice)))&
(![X]:(~strong(X)=>generous(X)))&
((calm(alice)&~patient(alice)))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:(~brave(X)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((creative(X)|generous(X))))&
(~brave(fred))&
(?[X]:((~kind(X)<~>creative(X)))) | ~creative(mary) | [] | null | 0 |
Everyone who is not creative is either strong or not quiet. Everyone who is not humble or patient is not patient. If lucy is both curious and rich then mary is not kind and vice versa. If fred is not happy or not rich then someone is both not old and not calm. If someone is both patient and happy then someone is either funny or rich and vice versa. If someone is not old or tall then fred is strong. If someone is either creative or not old then paul is both not generous and not quiet and vice versa. If fred is either not creative or creative then alice is curious and vice versa. If mary is wise then someone is generous or curious. Everyone who is curious or creative is either strong or not patient. Everyone who is not generous or creative is either not rich or not funny and vice versa. Everyone who is not rich is either not tall or brave and vice versa. If someone is both not tall and not generous then someone is either wise or patient and vice versa. Everyone who is both not rich and not happy is both wise and creative. Everyone who is patient is kind. If paul is not generous or curious then fred is strong or not tall. Someone is kind. Someone is humble or happy. Paul is either rich or not creative. Paul is calm or rich. | Mary is calm. | neutral | (![X]:(~creative(X)=>(strong(X)<~>~quiet(X))))&
(![X]:((~humble(X)|patient(X))=>~patient(X)))&
(((curious(lucy)&rich(lucy)))<=>(~kind(mary)))&
(((~happy(fred)|~rich(fred)))=>(?[X]:((~old(X)&~calm(X)))))&
((?[X]:((patient(X)&happy(X))))<=>(?[X]:((funny(X)<~>rich(X)))))&
((?[X]:((~old(X)|tall(X))))=>(strong(fred)))&
((?[X]:((creative(X)<~>~old(X))))<=>((~generous(paul)&~quiet(paul))))&
(((~creative(fred)<~>creative(fred)))<=>(curious(alice)))&
((wise(mary))=>(?[X]:((generous(X)|curious(X)))))&
(![X]:((curious(X)|creative(X))=>(strong(X)<~>~patient(X))))&
(![X]:((~generous(X)|creative(X))<=>(~rich(X)<~>~funny(X))))&
(![X]:(~rich(X)<=>(~tall(X)<~>brave(X))))&
((?[X]:((~tall(X)&~generous(X))))<=>(?[X]:((wise(X)<~>patient(X)))))&
(![X]:((~rich(X)&~happy(X))=>(wise(X)&creative(X))))&
(![X]:(patient(X)=>kind(X)))&
(((~generous(paul)|curious(paul)))=>((strong(fred)|~tall(fred))))&
(?[X]:(kind(X)))&
(?[X]:((humble(X)|happy(X))))&
((rich(paul)<~>~creative(paul)))&
((calm(paul)|rich(paul))) | calm(mary) | [] | null | 0 |
Everyone who is brave is both not patient and not curious. If lucy is not happy then john is either not patient or not rich and vice versa. Everyone who is either curious or not rich is either funny or not quiet and vice versa. Everyone who is not calm or not quiet is strong or not calm. If lucy is not wise then someone is not brave or not curious. Everyone who is either funny or not happy is wise and vice versa. If someone is not wise then alice is happy. Everyone who is either not creative or wise is brave. If susan is both not strong and not rich then john is both not happy and not rich and vice versa. If someone is rich or wise then someone is not kind and vice versa. If someone is creative or not patient then someone is either brave or funny and vice versa. Everyone who is both not brave and not wise is not patient. Everyone who is calm is either not wise or tall and vice versa. Everyone who is both patient and not brave is both brave and not wise and vice versa. Everyone who is either not old or not wise is either not humble or creative and vice versa. Everyone who is both not strong and brave is both not kind and quiet and vice versa. Someone is humble or happy. Someone is curious or not tall. John is not strong. Someone is not old or not kind. Alice is not creative. Someone is both not curious and quiet. Lucy is kind or creative. Lucy is curious or not rich. | John is quiet. | neutral | (![X]:(brave(X)=>(~patient(X)&~curious(X))))&
((~happy(lucy))<=>((~patient(john)<~>~rich(john))))&
(![X]:((curious(X)<~>~rich(X))<=>(funny(X)<~>~quiet(X))))&
(![X]:((~calm(X)|~quiet(X))=>(strong(X)|~calm(X))))&
((~wise(lucy))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:((funny(X)<~>~happy(X))<=>wise(X)))&
((?[X]:(~wise(X)))=>(happy(alice)))&
(![X]:((~creative(X)<~>wise(X))=>brave(X)))&
(((~strong(susan)&~rich(susan)))<=>((~happy(john)&~rich(john))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((brave(X)<~>funny(X)))))&
(![X]:((~brave(X)&~wise(X))=>~patient(X)))&
(![X]:(calm(X)<=>(~wise(X)<~>tall(X))))&
(![X]:((patient(X)&~brave(X))<=>(brave(X)&~wise(X))))&
(![X]:((~old(X)<~>~wise(X))<=>(~humble(X)<~>creative(X))))&
(![X]:((~strong(X)&brave(X))<=>(~kind(X)&quiet(X))))&
(?[X]:((humble(X)|happy(X))))&
(?[X]:((curious(X)|~tall(X))))&
(~strong(john))&
(?[X]:((~old(X)|~kind(X))))&
(~creative(alice))&
(?[X]:((~curious(X)&quiet(X))))&
((kind(lucy)|creative(lucy)))&
((curious(lucy)|~rich(lucy))) | quiet(john) | [] | null | 0 |
If someone is not funny then someone is both not patient and wise and vice versa. Everyone who is generous is calm or tall and vice versa. Everyone who is kind is either not old or wise. Everyone who is creative is not wise and vice versa. Everyone who is not curious or curious is not creative or not old. If susan is either not humble or funny then paul is not quiet or not strong and vice versa. Everyone who is not wise is both not tall and tall. Everyone who is both strong and not generous is funny or not calm and vice versa. Everyone who is not creative is not old. Everyone who is either tall or not generous is both not generous and not quiet and vice versa. If someone is not brave or brave then someone is not rich. Everyone who is both old and not creative is both funny and patient and vice versa. Everyone who is both creative and old is both not kind and wise. Everyone who is either not tall or humble is both not strong and not curious. If john is either not rich or not old then lucy is both not old and not tall and vice versa. Everyone who is not rich or strong is either not strong or creative. Someone is either not patient or brave. Alice is not quiet or wise. Someone is funny or wise. | John is old. | contradiction | ((?[X]:(~funny(X)))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:(generous(X)<=>(calm(X)|tall(X))))&
(![X]:(kind(X)=>(~old(X)<~>wise(X))))&
(![X]:(creative(X)<=>~wise(X)))&
(![X]:((~curious(X)|curious(X))=>(~creative(X)|~old(X))))&
(((~humble(susan)<~>funny(susan)))<=>((~quiet(paul)|~strong(paul))))&
(![X]:(~wise(X)=>(~tall(X)&tall(X))))&
(![X]:((strong(X)&~generous(X))<=>(funny(X)|~calm(X))))&
(![X]:(~creative(X)=>~old(X)))&
(![X]:((tall(X)<~>~generous(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:(~rich(X))))&
(![X]:((old(X)&~creative(X))<=>(funny(X)&patient(X))))&
(![X]:((creative(X)&old(X))=>(~kind(X)&wise(X))))&
(![X]:((~tall(X)<~>humble(X))=>(~strong(X)&~curious(X))))&
(((~rich(john)<~>~old(john)))<=>((~old(lucy)&~tall(lucy))))&
(![X]:((~rich(X)|strong(X))=>(~strong(X)<~>creative(X))))&
(?[X]:((~patient(X)<~>brave(X))))&
((~quiet(alice)|wise(alice)))&
(?[X]:((funny(X)|wise(X)))) | old(john) | [
"p4",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5234096529043759993539257
% SZS output start Proof for 5234096529043759993539257
5. ! [X0] : ((curious(X0) | ~curious(X0)) => (~old(X0) | ~creative(X0))) [input p4]
9. ! [X0] : (~creative(X0) => ~old(X0)) [input p8]
20. old(john) [input hypothesis]
25. ! [X0] : ((~old(X0) | ~creative(X0)) | (~curious(X0) & curious(X0))) [ennf transformation 5]
26. ! [X0] : (~old(X0) | ~creative(X0) | (~curious(X0) & curious(X0))) [flattening 25]
28. ! [X0] : (~old(X0) | creative(X0)) [ennf transformation 9]
70. ~old(X0) | ~creative(X0) | curious(X0) [cnf transformation 26]
71. ~old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 26]
85. ~old(X0) | creative(X0) [cnf transformation 28]
117. old(john) [cnf transformation 20]
142. ~old(X0) | ~creative(X0) [subsumption resolution 70,71]
166. ~old(X0) [subsumption resolution 85,142]
198. $false [subsumption resolution 117,166]
% SZS output end Proof for 5234096529043759993539257
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not funny or not curious then someone is not creative and vice versa. Everyone who is rich or strong is both happy and not creative. If someone is both not happy and patient then mary is not generous or calm and vice versa. Everyone who is either creative or calm is both old and wise. Everyone who is both curious and quiet is both not curious and strong. Everyone who is not old is wise and vice versa. Everyone who is not patient or brave is either not humble or kind and vice versa. If someone is either not kind or not brave then someone is not rich or not kind. If someone is not rich then someone is curious or not creative and vice versa. Everyone who is curious is not rich. If someone is curious then someone is tall or not funny and vice versa. If fred is both not generous and not brave then john is either not curious or humble and vice versa. Everyone who is either old or strong is funny. If alice is funny then someone is not calm or not old. If someone is both not generous and not old then someone is both happy and generous. Everyone who is rich or brave is not rich. Fred is both curious and not happy. John is both brave and wise. Someone is not tall or not calm. Someone is both happy and calm. Someone is both funny and old. Mary is both creative and not wise. Lucy is not happy. Someone is generous or not creative. | Fred is generous. | neutral | (((~funny(fred)|~curious(fred)))<=>(?[X]:(~creative(X))))&
(![X]:((rich(X)|strong(X))=>(happy(X)&~creative(X))))&
((?[X]:((~happy(X)&patient(X))))<=>((~generous(mary)|calm(mary))))&
(![X]:((creative(X)<~>calm(X))=>(old(X)&wise(X))))&
(![X]:((curious(X)&quiet(X))=>(~curious(X)&strong(X))))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((~patient(X)|brave(X))<=>(~humble(X)<~>kind(X))))&
((?[X]:((~kind(X)<~>~brave(X))))=>(?[X]:((~rich(X)|~kind(X)))))&
((?[X]:(~rich(X)))<=>(?[X]:((curious(X)|~creative(X)))))&
(![X]:(curious(X)=>~rich(X)))&
((?[X]:(curious(X)))<=>(?[X]:((tall(X)|~funny(X)))))&
(((~generous(fred)&~brave(fred)))<=>((~curious(john)<~>humble(john))))&
(![X]:((old(X)<~>strong(X))=>funny(X)))&
((funny(alice))=>(?[X]:((~calm(X)|~old(X)))))&
((?[X]:((~generous(X)&~old(X))))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((rich(X)|brave(X))=>~rich(X)))&
((curious(fred)&~happy(fred)))&
((brave(john)&wise(john)))&
(?[X]:((~tall(X)|~calm(X))))&
(?[X]:((happy(X)&calm(X))))&
(?[X]:((funny(X)&old(X))))&
((creative(mary)&~wise(mary)))&
(~happy(lucy))&
(?[X]:((generous(X)|~creative(X)))) | generous(fred) | [] | null | 0 |
Everyone who is both brave and kind is either not creative or calm and vice versa.
Everyone who is both not strong and not quiet is brave and vice versa.
Everyone who is rich is curious or not happy and vice versa.
Everyone who is either tall or humble is either not happy or tall.
Everyone who is not happy is either quiet or humble and vice versa.
If someone is generous or old then someone is kind or not old and vice versa.
Everyone who is strong or humble is rich or strong and vice versa.
Everyone who is both quiet and strong is not wise.
If alice is both happy and generous then john is not calm or calm.
If someone is both not strong and not curious then fred is both not kind and not brave.
Everyone who is either happy or not wise is not brave or quiet and vice versa.
If someone is not brave or kind then lucy is both tall and wise and vice versa.
If someone is both calm and not brave then susan is humble and vice versa.
If someone is tall then alice is creative or not curious and vice versa.
If someone is not curious or not creative then someone is not humble and vice versa.
If lucy is either not creative or not happy then susan is both happy and not patient and vice versa.
Fred is not patient.
Someone is not curious or humble.
Lucy is either not kind or creative.
Someone is both not patient and brave.
Alice is not creative.
Someone is not brave or tall.
Someone is either not rich or not humble.
Someone is both not patient and not happy. | Lucy is quiet. | neutral | (![X]:((brave(X)&kind(X))<=>(~creative(X)<~>calm(X))))&
(![X]:((~strong(X)&~quiet(X))<=>brave(X)))&
(![X]:(rich(X)<=>(curious(X)|~happy(X))))&
(![X]:((tall(X)<~>humble(X))=>(~happy(X)<~>tall(X))))&
(![X]:(~happy(X)<=>(quiet(X)<~>humble(X))))&
((?[X]:((generous(X)|old(X))))<=>(?[X]:((kind(X)|~old(X)))))&
(![X]:((strong(X)|humble(X))<=>(rich(X)|strong(X))))&
(![X]:((quiet(X)&strong(X))=>~wise(X)))&
(((happy(alice)&generous(alice)))=>((~calm(john)|calm(john))))&
((?[X]:((~strong(X)&~curious(X))))=>((~kind(fred)&~brave(fred))))&
(![X]:((happy(X)<~>~wise(X))<=>(~brave(X)|quiet(X))))&
((?[X]:((~brave(X)|kind(X))))<=>((tall(lucy)&wise(lucy))))&
((?[X]:((calm(X)&~brave(X))))<=>(humble(susan)))&
((?[X]:(tall(X)))<=>((creative(alice)|~curious(alice))))&
((?[X]:((~curious(X)|~creative(X))))<=>(?[X]:(~humble(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>((happy(susan)&~patient(susan))))&
(~patient(fred))&
(?[X]:((~curious(X)|humble(X))))&
((~kind(lucy)<~>creative(lucy)))&
(?[X]:((~patient(X)&brave(X))))&
(~creative(alice))&
(?[X]:((~brave(X)|tall(X))))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((~patient(X)&~happy(X)))) | quiet(lucy) | [] | null | 0 |
If susan is both not calm and curious then someone is not brave or not creative and vice versa.
Everyone who is either curious or brave is quiet and vice versa.
If someone is quiet then john is not brave and vice versa.
If alice is either patient or strong then mary is both not creative and not tall.
Everyone who is not strong is both tall and not creative.
If someone is kind then someone is not patient.
If someone is generous or not patient then someone is not creative or not funny.
Everyone who is happy or not strong is either not tall or calm.
Everyone who is not generous is both not kind and creative and vice versa.
Everyone who is tall is both not old and funny.
Everyone who is quiet is both tall and calm.
Everyone who is both generous and not happy is funny or not tall.
If someone is either curious or generous then susan is either patient or not brave and vice versa.
Everyone who is either brave or not tall is either strong or not curious and vice versa.
If lucy is not patient then lucy is brave or patient.
John is either funny or not brave.
Someone is either old or curious.
Someone is not humble.
Someone is not old.
Mary is kind or quiet.
Mary is strong.
Alice is happy. | Lucy is not strong. | contradiction | (((~calm(susan)&curious(susan)))<=>(?[X]:((~brave(X)|~creative(X)))))&
(![X]:((curious(X)<~>brave(X))<=>quiet(X)))&
((?[X]:(quiet(X)))<=>(~brave(john)))&
(((patient(alice)<~>strong(alice)))=>((~creative(mary)&~tall(mary))))&
(![X]:(~strong(X)=>(tall(X)&~creative(X))))&
((?[X]:(kind(X)))=>(?[X]:(~patient(X))))&
((?[X]:((generous(X)|~patient(X))))=>(?[X]:((~creative(X)|~funny(X)))))&
(![X]:((happy(X)|~strong(X))=>(~tall(X)<~>calm(X))))&
(![X]:(~generous(X)<=>(~kind(X)&creative(X))))&
(![X]:(tall(X)=>(~old(X)&funny(X))))&
(![X]:(quiet(X)=>(tall(X)&calm(X))))&
(![X]:((generous(X)&~happy(X))=>(funny(X)|~tall(X))))&
((?[X]:((curious(X)<~>generous(X))))<=>((patient(susan)<~>~brave(susan))))&
(![X]:((brave(X)<~>~tall(X))<=>(strong(X)<~>~curious(X))))&
((~patient(lucy))=>((brave(lucy)|patient(lucy))))&
((funny(john)<~>~brave(john)))&
(?[X]:((old(X)<~>curious(X))))&
(?[X]:(~humble(X)))&
(?[X]:(~old(X)))&
((kind(mary)|quiet(mary)))&
(strong(mary))&
(happy(alice)) | ~strong(lucy) | [
"p1",
"p2",
"p4",
"p9",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 704418718528224572169253
% SZS output start Proof for 704418718528224572169253
2. ! [X0] : ((curious(X0) <~> brave(X0)) <=> quiet(X0)) [input p1]
3. ? [X0] : quiet(X0) <=> ~brave(john) [input p2]
5. ! [X0] : (~strong(X0) => (~creative(X0) & tall(X0))) [input p4]
10. ! [X0] : (tall(X0) => (funny(X0) & ~old(X0))) [input p9]
11. ! [X0] : (quiet(X0) => (calm(X0) & tall(X0))) [input p10]
14. ! [X0] : ((brave(X0) <~> ~tall(X0)) <=> (strong(X0) <~> ~curious(X0))) [input p13]
16. funny(john) <~> ~brave(john) [input p15]
23. ~strong(lucy) [input hypothesis]
28. ! [X0] : ((~creative(X0) & tall(X0)) | strong(X0)) [ennf transformation 5]
32. ! [X0] : ((funny(X0) & ~old(X0)) | ~tall(X0)) [ennf transformation 10]
33. ! [X0] : ((calm(X0) & tall(X0)) | ~quiet(X0)) [ennf transformation 11]
43. ! [X0] : ((((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | ~quiet(X0)) & (quiet(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0))))) [nnf transformation 2]
44. (? [X0] : quiet(X0) | brave(john)) & (~brave(john) | ! [X0] : ~quiet(X0)) [nnf transformation 3]
45. (? [X0] : quiet(X0) | brave(john)) & (~brave(john) | ! [X1] : ~quiet(X1)) [rectify 44]
46. ? [X0] : quiet(X0) => quiet(sK1) [choice axiom]
47. (quiet(sK1) | brave(john)) & (~brave(john) | ! [X1] : ~quiet(X1)) [skolemisation 45,46]
62. ! [X0] : ((((tall(X0) | ~brave(X0)) & (~tall(X0) | brave(X0))) | ((strong(X0) | curious(X0)) & (~curious(X0) | ~strong(X0)))) & (((curious(X0) | ~strong(X0)) & (~curious(X0) | strong(X0))) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0))))) [nnf transformation 14]
63. (brave(john) | ~funny(john)) & (~brave(john) | funny(john)) [nnf transformation 16]
74. ~curious(X0) | brave(X0) | quiet(X0) [cnf transformation 43]
75. ~brave(X0) | curious(X0) | quiet(X0) [cnf transformation 43]
78. ~brave(john) | ~quiet(X1) [cnf transformation 47]
84. tall(X0) | strong(X0) [cnf transformation 28]
97. ~tall(X0) | funny(X0) [cnf transformation 32]
98. ~quiet(X0) | tall(X0) [cnf transformation 33]
109. ~curious(X0) | strong(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 62]
112. curious(X0) | ~strong(X0) | brave(X0) | tall(X0) [cnf transformation 62]
114. ~tall(X0) | brave(X0) | strong(X0) | curious(X0) [cnf transformation 62]
115. tall(X0) | ~brave(X0) | ~curious(X0) | ~strong(X0) [cnf transformation 62]
119. brave(john) | ~funny(john) [cnf transformation 63]
126. ~strong(lucy) [cnf transformation 23]
156. 7 <=> brave(john) [avatar definition]
157. ~brave(john) <- (~7) [avatar component clause 156]
165. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
166. ~quiet(X1) <- (9) [avatar component clause 165]
167. 9 | ~7 [avatar split clause 78,156,165]
243. ~brave(X0) | tall(X0) | ~curious(X0) [subsumption resolution 115,84]
244. strong(X0) | brave(X0) | curious(X0) [subsumption resolution 114,84]
245. tall(X0) | brave(X0) | curious(X0) [subsumption resolution 112,84]
246. ~brave(X0) | strong(X0) | ~curious(X0) [subsumption resolution 109,243]
248. 26 <=> brave(lucy) [avatar definition]
249. ~brave(lucy) <- (~26) [avatar component clause 248]
250. brave(lucy) <- (26) [avatar component clause 248]
257. 28 <=> funny(john) [avatar definition]
259. ~funny(john) <- (~28) [avatar component clause 257]
260. ~28 | 7 [avatar split clause 119,156,257]
304. curious(lucy) | quiet(lucy) <- (26) [resolution 75,250]
306. 35 <=> quiet(lucy) [avatar definition]
308. quiet(lucy) <- (35) [avatar component clause 306]
310. 36 <=> curious(lucy) [avatar definition]
312. curious(lucy) <- (36) [avatar component clause 310]
313. 35 | 36 | ~26 [avatar split clause 304,248,310,306]
340. $false <- (9, 35) [resolution 308,166]
343. ~9 | ~35 [avatar contradiction clause 340]
361. brave(lucy) | curious(lucy) [resolution 244,126]
363. funny(X0) | curious(X0) | brave(X0) [resolution 245,97]
366. strong(lucy) | ~curious(lucy) <- (26) [resolution 246,250]
368. ~curious(lucy) <- (26) [subsumption resolution 366,126]
369. $false <- (26, 36) [subsumption resolution 368,312]
370. ~26 | ~36 [avatar contradiction clause 369]
411. 42 <=> curious(john) [avatar definition]
412. curious(john) <- (42) [avatar component clause 411]
420. 44 <=> tall(john) [avatar definition]
421. ~tall(john) <- (~44) [avatar component clause 420]
422. tall(john) <- (44) [avatar component clause 420]
443. brave(lucy) | quiet(lucy) <- (36) [resolution 312,74]
444. quiet(lucy) <- (~26, 36) [subsumption resolution 443,249]
445. $false <- (9, ~26, 36) [subsumption resolution 444,166]
446. ~9 | 26 | ~36 [avatar contradiction clause 445]
452. 36 | 26 [avatar split clause 361,248,310]
484. brave(john) | quiet(john) <- (42) [resolution 412,74]
485. quiet(john) <- (~7, 42) [subsumption resolution 484,157]
488. funny(john) <- (44) [resolution 422,97]
493. $false <- (~28, 44) [subsumption resolution 488,259]
494. 28 | ~44 [avatar contradiction clause 493]
520. curious(john) | brave(john) <- (~28) [resolution 363,259]
542. tall(john) <- (~7, 42) [resolution 485,98]
543. $false <- (~7, 42, ~44) [subsumption resolution 542,421]
544. 7 | ~42 | 44 [avatar contradiction clause 543]
545. curious(john) <- (~7, ~28) [subsumption resolution 520,157]
546. 42 | 7 | 28 [avatar split clause 545,257,156,411]
549. $false [avatar sat refutation 167,260,313,343,370,446,452,494,544,546]
% SZS output end Proof for 704418718528224572169253
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not kind or quiet then someone is rich or kind and vice versa.
If alice is both patient and strong then someone is not happy and vice versa.
Everyone who is not calm is not curious and vice versa.
Everyone who is rich is not tall and vice versa.
Everyone who is either not humble or funny is either kind or wise.
Everyone who is both calm and not tall is not wise or tall and vice versa.
Everyone who is both not patient and not calm is quiet or not wise.
If paul is not tall or not strong then fred is not funny or creative and vice versa.
Everyone who is not humble or old is not funny or funny and vice versa.
Everyone who is either not funny or not happy is either curious or not patient and vice versa.
Everyone who is wise or generous is curious.
Everyone who is both not humble and old is not happy or not patient.
Everyone who is funny or creative is humble.
If john is both old and wise then paul is both funny and patient and vice versa.
If paul is both not quiet and brave then someone is not generous or not tall.
Everyone who is kind is either quiet or rich.
Lucy is both happy and not kind.
Fred is patient or not old.
Someone is not funny or not brave.
Someone is either strong or patient.
Someone is happy.
Someone is not patient or creative.
Someone is strong or wise. | Fred is not patient. | contradiction | (((~kind(fred)<~>quiet(fred)))<=>(?[X]:((rich(X)|kind(X)))))&
(((patient(alice)&strong(alice)))<=>(?[X]:(~happy(X))))&
(![X]:(~calm(X)<=>~curious(X)))&
(![X]:(rich(X)<=>~tall(X)))&
(![X]:((~humble(X)<~>funny(X))=>(kind(X)<~>wise(X))))&
(![X]:((calm(X)&~tall(X))<=>(~wise(X)|tall(X))))&
(![X]:((~patient(X)&~calm(X))=>(quiet(X)|~wise(X))))&
(((~tall(paul)|~strong(paul)))<=>((~funny(fred)|creative(fred))))&
(![X]:((~humble(X)|old(X))<=>(~funny(X)|funny(X))))&
(![X]:((~funny(X)<~>~happy(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((wise(X)|generous(X))=>curious(X)))&
(![X]:((~humble(X)&old(X))=>(~happy(X)|~patient(X))))&
(![X]:((funny(X)|creative(X))=>humble(X)))&
(((old(john)&wise(john)))<=>((funny(paul)&patient(paul))))&
(((~quiet(paul)&brave(paul)))=>(?[X]:((~generous(X)|~tall(X)))))&
(![X]:(kind(X)=>(quiet(X)<~>rich(X))))&
((happy(lucy)&~kind(lucy)))&
((patient(fred)|~old(fred)))&
(?[X]:((~funny(X)|~brave(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:(happy(X)))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:((strong(X)|wise(X)))) | ~patient(fred) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p12",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 4339276956715264937627760
% SZS output start Proof for 4339276956715264937627760
1. (~kind(fred) <~> quiet(fred)) <=> ? [X0] : (kind(X0) | rich(X0)) [input p0]
3. ! [X0] : (~calm(X0) <=> ~curious(X0)) [input p2]
4. ! [X0] : (rich(X0) <=> ~tall(X0)) [input p3]
5. ! [X0] : ((~humble(X0) <~> funny(X0)) => (kind(X0) <~> wise(X0))) [input p4]
6. ! [X0] : ((~tall(X0) & calm(X0)) <=> (tall(X0) | ~wise(X0))) [input p5]
9. ! [X0] : ((old(X0) | ~humble(X0)) <=> (funny(X0) | ~funny(X0))) [input p8]
11. ! [X0] : ((generous(X0) | wise(X0)) => curious(X0)) [input p10]
13. ! [X0] : ((creative(X0) | funny(X0)) => humble(X0)) [input p12]
16. ! [X0] : (kind(X0) => (quiet(X0) <~> rich(X0))) [input p15]
18. ~old(fred) | patient(fred) [input p17]
24. ~patient(fred) [input hypothesis]
27. ! [X0] : (wise(X0) => curious(X0)) [pure predicate removal 11]
28. ! [X0] : ((kind(X0) <~> wise(X0)) | (~humble(X0) <=> funny(X0))) [ennf transformation 5]
31. ! [X0] : (curious(X0) | ~wise(X0)) [ennf transformation 27]
34. ! [X0] : (humble(X0) | (~creative(X0) & ~funny(X0))) [ennf transformation 13]
35. ! [X0] : ((quiet(X0) <~> rich(X0)) | ~kind(X0)) [ennf transformation 16]
36. (((~quiet(fred) | kind(fred)) & (quiet(fred) | ~kind(fred))) | ! [X0] : (~kind(X0) & ~rich(X0))) & (? [X0] : (kind(X0) | rich(X0)) | ((~kind(fred) | ~quiet(fred)) & (quiet(fred) | kind(fred)))) [nnf transformation 1]
37. (((~quiet(fred) | kind(fred)) & (quiet(fred) | ~kind(fred))) | ! [X0] : (~kind(X0) & ~rich(X0))) & (? [X1] : (kind(X1) | rich(X1)) | ((~kind(fred) | ~quiet(fred)) & (quiet(fred) | kind(fred)))) [rectify 36]
38. ? [X1] : (kind(X1) | rich(X1)) => (kind(sK0) | rich(sK0)) [choice axiom]
39. (((~quiet(fred) | kind(fred)) & (quiet(fred) | ~kind(fred))) | ! [X0] : (~kind(X0) & ~rich(X0))) & ((kind(sK0) | rich(sK0)) | ((~kind(fred) | ~quiet(fred)) & (quiet(fred) | kind(fred)))) [skolemisation 37,38]
45. ! [X0] : ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))) [nnf transformation 3]
46. ! [X0] : ((rich(X0) | tall(X0)) & (~tall(X0) | ~rich(X0))) [nnf transformation 4]
47. ! [X0] : (((~wise(X0) | ~kind(X0)) & (wise(X0) | kind(X0))) | ((~humble(X0) | ~funny(X0)) & (funny(X0) | humble(X0)))) [nnf transformation 28]
48. ! [X0] : (((~tall(X0) & calm(X0)) | (~tall(X0) & wise(X0))) & ((tall(X0) | ~wise(X0)) | (tall(X0) | ~calm(X0)))) [nnf transformation 6]
49. ! [X0] : (((~tall(X0) & calm(X0)) | (~tall(X0) & wise(X0))) & (tall(X0) | ~wise(X0) | tall(X0) | ~calm(X0))) [flattening 48]
52. ! [X0] : (((old(X0) | ~humble(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (~old(X0) & humble(X0)))) [nnf transformation 9]
53. ! [X0] : ((old(X0) | ~humble(X0) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | (~old(X0) & humble(X0)))) [flattening 52]
57. ! [X0] : (((~rich(X0) | ~quiet(X0)) & (rich(X0) | quiet(X0))) | ~kind(X0)) [nnf transformation 35]
69. quiet(fred) | ~kind(fred) | ~rich(X0) [cnf transformation 39]
76. ~curious(X0) | calm(X0) [cnf transformation 45]
77. ~calm(X0) | curious(X0) [cnf transformation 45]
79. tall(X0) | rich(X0) [cnf transformation 46]
80. wise(X0) | kind(X0) | funny(X0) | humble(X0) [cnf transformation 47]
84. tall(X0) | ~wise(X0) | tall(X0) | ~calm(X0) [cnf transformation 49]
85. wise(X0) | calm(X0) [cnf transformation 49]
88. ~tall(X0) | ~tall(X0) [cnf transformation 49]
96. old(X0) | ~humble(X0) | funny(X0) [cnf transformation 53]
97. ~funny(X0) | ~humble(X0) | old(X0) [cnf transformation 53]
106. ~wise(X0) | curious(X0) [cnf transformation 31]
108. ~funny(X0) | humble(X0) [cnf transformation 34]
115. ~rich(X0) | ~quiet(X0) | ~kind(X0) [cnf transformation 57]
118. ~old(fred) | patient(fred) [cnf transformation 18]
124. ~patient(fred) [cnf transformation 24]
125. tall(X0) | ~wise(X0) | ~calm(X0) [duplicate literal removal 84]
126. ~tall(X0) [duplicate literal removal 88]
131. 2 <=> kind(fred) [avatar definition]
133. kind(fred) <- (2) [avatar component clause 131]
135. 3 <=> quiet(fred) [avatar definition]
136. quiet(fred) <- (3) [avatar component clause 135]
140. 4 <=> ! [X0] : ~rich(X0) [avatar definition]
141. ~rich(X0) <- (4) [avatar component clause 140]
144. 4 | ~2 | 3 [avatar split clause 69,135,131,140]
173. ~wise(X0) | ~calm(X0) [subsumption resolution 125,126]
190. ~humble(X0) | old(X0) [subsumption resolution 96,97]
212. 18 <=> patient(fred) [avatar definition]
216. 19 <=> old(fred) [avatar definition]
218. ~old(fred) <- (~19) [avatar component clause 216]
219. 18 | ~19 [avatar split clause 118,216,212]
248. ~18 [avatar split clause 124,212]
252. rich(X1) [resolution 79,126]
255. curious(X0) | calm(X0) [resolution 106,85]
256. curious(X0) [subsumption resolution 255,77]
257. calm(X0) [resolution 256,76]
262. ~quiet(X0) | ~kind(X0) [resolution 115,252]
271. kind(X1) | funny(X1) | humble(X1) | ~calm(X1) [resolution 80,173]
284. kind(X1) | funny(X1) | humble(X1) [subsumption resolution 271,257]
285. humble(X1) | kind(X1) [subsumption resolution 284,108]
306. old(X0) | kind(X0) [resolution 285,190]
309. kind(fred) <- (~19) [resolution 306,218]
313. 2 | 19 [avatar split clause 309,216,131]
314. $false <- (4) [subsumption resolution 141,252]
315. ~4 [avatar contradiction clause 314]
323. ~kind(fred) <- (3) [resolution 136,262]
324. $false <- (2, 3) [subsumption resolution 323,133]
325. ~2 | ~3 [avatar contradiction clause 324]
326. $false [avatar sat refutation 144,219,248,313,315,325]
% SZS output end Proof for 4339276956715264937627760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is either not strong or not humble is not generous or generous.
Everyone who is curious or not generous is either not funny or not wise and vice versa.
Everyone who is not rich is both not funny and calm and vice versa.
If someone is either not old or not funny then someone is both not rich and not calm.
Everyone who is either not tall or strong is either not brave or not strong and vice versa.
If someone is patient or calm then someone is either wise or brave and vice versa.
Everyone who is both rich and brave is not curious and vice versa.
If fred is not creative then someone is either not creative or generous and vice versa.
If someone is brave then susan is both old and kind.
If someone is both not old and not kind then mary is both not generous and not strong and vice versa.
Everyone who is patient or not calm is not brave and vice versa.
If someone is not generous or not quiet then someone is not calm or not old and vice versa.
If john is rich then mary is not generous or generous.
Everyone who is either strong or not tall is not tall.
Everyone who is creative or not generous is rich or funny.
Everyone who is both calm and tall is not happy or brave.
Someone is not generous.
Fred is kind or generous.
Mary is either not tall or not old.
Paul is both not brave and not happy.
Lucy is either humble or not old.
Paul is both not patient and old.
Someone is generous.
John is kind. | Paul is not patient. | entailment | (![X]:((~strong(X)<~>~humble(X))=>(~generous(X)|generous(X))))&
(![X]:((curious(X)|~generous(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:(~rich(X)<=>(~funny(X)&calm(X))))&
((?[X]:((~old(X)<~>~funny(X))))=>(?[X]:((~rich(X)&~calm(X)))))&
(![X]:((~tall(X)<~>strong(X))<=>(~brave(X)<~>~strong(X))))&
((?[X]:((patient(X)|calm(X))))<=>(?[X]:((wise(X)<~>brave(X)))))&
(![X]:((rich(X)&brave(X))<=>~curious(X)))&
((~creative(fred))<=>(?[X]:((~creative(X)<~>generous(X)))))&
((?[X]:(brave(X)))=>((old(susan)&kind(susan))))&
((?[X]:((~old(X)&~kind(X))))<=>((~generous(mary)&~strong(mary))))&
(![X]:((patient(X)|~calm(X))<=>~brave(X)))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:((~calm(X)|~old(X)))))&
((rich(john))=>((~generous(mary)|generous(mary))))&
(![X]:((strong(X)<~>~tall(X))=>~tall(X)))&
(![X]:((creative(X)|~generous(X))=>(rich(X)|funny(X))))&
(![X]:((calm(X)&tall(X))=>(~happy(X)|brave(X))))&
(?[X]:(~generous(X)))&
((kind(fred)|generous(fred)))&
((~tall(mary)<~>~old(mary)))&
((~brave(paul)&~happy(paul)))&
((humble(lucy)<~>~old(lucy)))&
((~patient(paul)&old(paul)))&
(?[X]:(generous(X)))&
(kind(john)) | ~patient(paul) | [
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8433353047458629233967198
% SZS output start Proof for 8433353047458629233967198
22. old(paul) & ~patient(paul) [input p21]
25. patient(paul) [input hypothesis]
141. ~patient(paul) [cnf transformation 22]
145. patient(paul) [cnf transformation 25]
326. $false [subsumption resolution 145,141]
% SZS output end Proof for 8433353047458629233967198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both happy and calm is both quiet and kind.
Everyone who is either not curious or kind is either kind or tall and vice versa.
Everyone who is either not strong or not wise is rich or wise.
Everyone who is patient or rich is either brave or not funny and vice versa.
If susan is rich then someone is either not quiet or not funny and vice versa.
If someone is either humble or not funny then susan is both not patient and not funny and vice versa.
Everyone who is both not brave and not funny is either strong or not kind and vice versa.
If someone is either humble or not patient then someone is strong or not generous and vice versa.
If paul is patient then mary is not generous.
Everyone who is both not curious and not tall is either generous or not wise.
Everyone who is not calm is both strong and wise and vice versa.
Everyone who is both patient and not patient is not curious and vice versa.
Everyone who is both not tall and brave is not calm and vice versa.
Everyone who is both rich and patient is not patient.
Everyone who is kind is either not generous or kind.
Everyone who is humble is quiet and vice versa.
Someone is either patient or generous.
Someone is both not wise and not kind.
Mary is not brave.
Someone is either creative or happy.
Paul is not creative.
Lucy is either not humble or happy.
Mary is creative.
Someone is happy. | Paul is brave. | neutral | (![X]:((happy(X)&calm(X))=>(quiet(X)&kind(X))))&
(![X]:((~curious(X)<~>kind(X))<=>(kind(X)<~>tall(X))))&
(![X]:((~strong(X)<~>~wise(X))=>(rich(X)|wise(X))))&
(![X]:((patient(X)|rich(X))<=>(brave(X)<~>~funny(X))))&
((rich(susan))<=>(?[X]:((~quiet(X)<~>~funny(X)))))&
((?[X]:((humble(X)<~>~funny(X))))<=>((~patient(susan)&~funny(susan))))&
(![X]:((~brave(X)&~funny(X))<=>(strong(X)<~>~kind(X))))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((strong(X)|~generous(X)))))&
((patient(paul))=>(~generous(mary)))&
(![X]:((~curious(X)&~tall(X))=>(generous(X)<~>~wise(X))))&
(![X]:(~calm(X)<=>(strong(X)&wise(X))))&
(![X]:((patient(X)&~patient(X))<=>~curious(X)))&
(![X]:((~tall(X)&brave(X))<=>~calm(X)))&
(![X]:((rich(X)&patient(X))=>~patient(X)))&
(![X]:(kind(X)=>(~generous(X)<~>kind(X))))&
(![X]:(humble(X)<=>quiet(X)))&
(?[X]:((patient(X)<~>generous(X))))&
(?[X]:((~wise(X)&~kind(X))))&
(~brave(mary))&
(?[X]:((creative(X)<~>happy(X))))&
(~creative(paul))&
((~humble(lucy)<~>happy(lucy)))&
(creative(mary))&
(?[X]:(happy(X))) | brave(paul) | [] | null | 0 |
If susan is not rich then lucy is both wise and generous. Everyone who is not humble is not quiet and vice versa. Everyone who is either not strong or wise is either not humble or not calm. Everyone who is quiet is not kind or humble and vice versa. Everyone who is quiet or not rich is old or not humble. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Someone is both not kind and not creative. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Alice is rich. | entailment | ((~rich(susan))=>((wise(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:((~strong(X)<~>wise(X))=>(~humble(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~kind(X)|humble(X))))&
(![X]:((quiet(X)|~rich(X))=>(old(X)|~humble(X))))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~kind(X)&~creative(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | rich(alice) | [
"p1",
"p3",
"p4",
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5066406710625267207136943
% SZS output start Proof for 5066406710625267207136943
2. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (quiet(X0) <=> (humble(X0) | ~kind(X0))) [input p3]
5. ! [X0] : ((~rich(X0) | quiet(X0)) => (~humble(X0) | old(X0))) [input p4]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
10. ! [X0] : ((~generous(X0) & ~humble(X0)) <=> (~rich(X0) <~> ~old(X0))) [input p9]
23. ~rich(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) | old(X0)) | (rich(X0) & ~quiet(X0))) [ennf transformation 5]
33. ! [X0] : (~humble(X0) | old(X0) | (rich(X0) & ~quiet(X0))) [flattening 32]
34. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
38. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 2]
40. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~quiet(X0))) [flattening 40]
44. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (generous(X0) | humble(X0)))) [nnf transformation 10]
45. ! [X0] : (((~generous(X0) & ~humble(X0)) | ((~rich(X0) | old(X0)) & (~old(X0) | rich(X0)))) & (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | generous(X0) | humble(X0))) [flattening 44]
63. ~quiet(X0) | humble(X0) [cnf transformation 38]
70. kind(X0) | quiet(X0) [cnf transformation 41]
73. ~humble(X0) | old(X0) | rich(X0) [cnf transformation 33]
75. quiet(X0) | ~kind(X0) [cnf transformation 34]
84. ~humble(X0) | ~old(X0) | rich(X0) [cnf transformation 45]
85. ~humble(X0) | ~rich(X0) | old(X0) [cnf transformation 45]
104. ~rich(alice) [cnf transformation 23]
120. quiet(X0) [subsumption resolution 75,70]
121. ~humble(X0) | old(X0) [subsumption resolution 85,73]
122. ~humble(X0) | rich(X0) [subsumption resolution 84,121]
164. humble(X0) [resolution 63,120]
174. rich(X0) [resolution 122,164]
176. $false [resolution 174,104]
% SZS output end Proof for 5066406710625267207136943
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or calm is either quiet or not humble.
If someone is brave or not calm then lucy is both not curious and not funny.
Everyone who is both curious and patient is strong or not creative and vice versa.
Everyone who is not strong is not kind or rich and vice versa.
If someone is not rich then someone is both not kind and not creative and vice versa.
If alice is old or not humble then susan is either not tall or not brave and vice versa.
If someone is not generous then someone is both kind and not old and vice versa.
Everyone who is either not rich or patient is both not happy and not calm and vice versa.
If fred is strong or quiet then someone is not kind or tall.
If someone is both tall and not generous then susan is either not calm or tall and vice versa.
If fred is not old then someone is both old and not brave and vice versa.
Everyone who is both patient and not tall is both creative and not funny and vice versa.
If lucy is humble then mary is both humble and brave.
If someone is not rich then someone is calm or not wise and vice versa.
Everyone who is not curious or not rich is either wise or brave.
Everyone who is not humble is not kind or strong.
Fred is creative.
Fred is wise or generous.
John is humble or brave.
Someone is not strong or not patient.
Susan is both not kind and rich.
Someone is either strong or not patient.
Fred is either curious or kind.
Susan is strong or not kind. | Lucy is not old. | neutral | (![X]:((~quiet(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((brave(X)|~calm(X))))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|~creative(X))))&
(![X]:(~strong(X)<=>(~kind(X)|rich(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)&~creative(X)))))&
(((old(alice)|~humble(alice)))<=>((~tall(susan)<~>~brave(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~happy(X)&~calm(X))))&
(((strong(fred)|quiet(fred)))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((tall(X)&~generous(X))))<=>((~calm(susan)<~>tall(susan))))&
((~old(fred))<=>(?[X]:((old(X)&~brave(X)))))&
(![X]:((patient(X)&~tall(X))<=>(creative(X)&~funny(X))))&
((humble(lucy))=>((humble(mary)&brave(mary))))&
((?[X]:(~rich(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((~curious(X)|~rich(X))=>(wise(X)<~>brave(X))))&
(![X]:(~humble(X)=>(~kind(X)|strong(X))))&
(creative(fred))&
((wise(fred)|generous(fred)))&
((humble(john)|brave(john)))&
(?[X]:((~strong(X)|~patient(X))))&
((~kind(susan)&rich(susan)))&
(?[X]:((strong(X)<~>~patient(X))))&
((curious(fred)<~>kind(fred)))&
((strong(susan)|~kind(susan))) | ~old(lucy) | [] | null | 0 |
Everyone who is calm is quiet or not creative and vice versa.
Everyone who is not humble is both funny and rich.
If someone is either humble or not curious then alice is both not humble and not curious and vice versa.
If someone is both not humble and not kind then john is not old or rich and vice versa.
Everyone who is rich is wise or not patient.
Everyone who is either patient or not patient is not generous or not wise and vice versa.
If susan is both not generous and not calm then fred is both rich and not wise.
Everyone who is not wise is rich or old and vice versa.
If lucy is not humble or not rich then someone is not quiet and vice versa.
Everyone who is both not rich and not kind is happy or rich and vice versa.
If someone is either not patient or old then lucy is not strong or humble.
If paul is not calm or brave then someone is both not old and not rich and vice versa.
Everyone who is brave or not wise is humble and vice versa.
Everyone who is not quiet or humble is both creative and not tall.
Everyone who is either not creative or generous is humble or not generous and vice versa.
Everyone who is either not funny or not quiet is either not old or curious.
Someone is not wise or calm.
Someone is either funny or not humble.
Mary is kind.
Someone is both happy and not patient.
Someone is creative or funny. | John is generous. | entailment | (![X]:(calm(X)<=>(quiet(X)|~creative(X))))&
(![X]:(~humble(X)=>(funny(X)&rich(X))))&
((?[X]:((humble(X)<~>~curious(X))))<=>((~humble(alice)&~curious(alice))))&
((?[X]:((~humble(X)&~kind(X))))<=>((~old(john)|rich(john))))&
(![X]:(rich(X)=>(wise(X)|~patient(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~generous(X)|~wise(X))))&
(((~generous(susan)&~calm(susan)))=>((rich(fred)&~wise(fred))))&
(![X]:(~wise(X)<=>(rich(X)|old(X))))&
(((~humble(lucy)|~rich(lucy)))<=>(?[X]:(~quiet(X))))&
(![X]:((~rich(X)&~kind(X))<=>(happy(X)|rich(X))))&
((?[X]:((~patient(X)<~>old(X))))=>((~strong(lucy)|humble(lucy))))&
(((~calm(paul)|brave(paul)))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((brave(X)|~wise(X))<=>humble(X)))&
(![X]:((~quiet(X)|humble(X))=>(creative(X)&~tall(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(humble(X)|~generous(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>(~old(X)<~>curious(X))))&
(?[X]:((~wise(X)|calm(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(kind(mary))&
(?[X]:((happy(X)&~patient(X))))&
(?[X]:((creative(X)|funny(X)))) | generous(john) | [
"p1",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5436637538859863622563890
% SZS output start Proof for 5436637538859863622563890
2. ! [X0] : (~humble(X0) => (rich(X0) & funny(X0))) [input p1]
10. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (rich(X0) | happy(X0))) [input p9]
14. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~tall(X0) & creative(X0))) [input p13]
15. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (~generous(X0) | humble(X0))) [input p14]
22. ~generous(john) [input hypothesis]
23. ! [X0] : ((humble(X0) | ~quiet(X0)) => creative(X0)) [pure predicate removal 14]
25. ! [X0] : ((rich(X0) & funny(X0)) | humble(X0)) [ennf transformation 2]
30. ! [X0] : (creative(X0) | (~humble(X0) & quiet(X0))) [ennf transformation 23]
53. ! [X0] : (((~kind(X0) & ~rich(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 10]
54. ! [X0] : (((~kind(X0) & ~rich(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | kind(X0) | rich(X0))) [flattening 53]
62. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (generous(X0) & ~humble(X0))) & ((~generous(X0) | humble(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 15]
63. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (generous(X0) & ~humble(X0))) & (~generous(X0) | humble(X0) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [flattening 62]
78. rich(X0) | humble(X0) [cnf transformation 25]
107. ~rich(X0) | ~rich(X0) [cnf transformation 54]
119. ~humble(X0) | creative(X0) [cnf transformation 30]
123. generous(X0) | ~creative(X0) | generous(X0) [cnf transformation 63]
137. ~generous(john) [cnf transformation 22]
139. ~creative(X0) | generous(X0) [duplicate literal removal 123]
141. ~rich(X0) [duplicate literal removal 107]
274. humble(X0) [resolution 78,141]
288. creative(X0) [resolution 119,274]
297. generous(X0) [resolution 288,139]
335. $false [resolution 297,137]
% SZS output end Proof for 5436637538859863622563890
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or tall is brave and vice versa.
If lucy is both not calm and calm then someone is humble and vice versa.
Everyone who is calm is not tall or not wise and vice versa.
Everyone who is both happy and not creative is either not patient or old and vice versa.
Everyone who is quiet is calm.
Everyone who is both calm and not quiet is both not generous and patient and vice versa.
Everyone who is generous is either rich or humble.
If someone is either curious or calm then lucy is strong or not brave and vice versa.
Everyone who is both quiet and not happy is happy or old.
Everyone who is not patient is either humble or not curious and vice versa.
Everyone who is both not quiet and old is both not strong and not rich.
If susan is both brave and rich then fred is both rich and not wise and vice versa.
Everyone who is either tall or not generous is both not old and patient.
If someone is calm or not generous then susan is old or humble.
Everyone who is both wise and not old is either strong or not curious.
Everyone who is not creative or patient is not calm.
John is not tall or strong.
Susan is funny or not brave.
Mary is old.
Mary is either patient or not wise.
Mary is not calm or not rich.
Someone is either calm or not calm.
Susan is not brave or creative. | Susan is humble. | contradiction | (![X]:((creative(X)|tall(X))<=>brave(X)))&
(((~calm(lucy)&calm(lucy)))<=>(?[X]:(humble(X))))&
(![X]:(calm(X)<=>(~tall(X)|~wise(X))))&
(![X]:((happy(X)&~creative(X))<=>(~patient(X)<~>old(X))))&
(![X]:(quiet(X)=>calm(X)))&
(![X]:((calm(X)&~quiet(X))<=>(~generous(X)&patient(X))))&
(![X]:(generous(X)=>(rich(X)<~>humble(X))))&
((?[X]:((curious(X)<~>calm(X))))<=>((strong(lucy)|~brave(lucy))))&
(![X]:((quiet(X)&~happy(X))=>(happy(X)|old(X))))&
(![X]:(~patient(X)<=>(humble(X)<~>~curious(X))))&
(![X]:((~quiet(X)&old(X))=>(~strong(X)&~rich(X))))&
(((brave(susan)&rich(susan)))<=>((rich(fred)&~wise(fred))))&
(![X]:((tall(X)<~>~generous(X))=>(~old(X)&patient(X))))&
((?[X]:((calm(X)|~generous(X))))=>((old(susan)|humble(susan))))&
(![X]:((wise(X)&~old(X))=>(strong(X)<~>~curious(X))))&
(![X]:((~creative(X)|patient(X))=>~calm(X)))&
((~tall(john)|strong(john)))&
((funny(susan)|~brave(susan)))&
(old(mary))&
((patient(mary)<~>~wise(mary)))&
((~calm(mary)|~rich(mary)))&
(?[X]:((calm(X)<~>~calm(X))))&
((~brave(susan)|creative(susan))) | humble(susan) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 471362092190658588171419
% SZS output start Proof for 471362092190658588171419
2. (calm(lucy) & ~calm(lucy)) <=> ? [X0] : humble(X0) [input p1]
24. humble(susan) [input hypothesis]
40. ((calm(lucy) & ~calm(lucy)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | (~calm(lucy) | calm(lucy))) [nnf transformation 2]
41. ((calm(lucy) & ~calm(lucy)) | ! [X0] : ~humble(X0)) & (? [X0] : humble(X0) | ~calm(lucy) | calm(lucy)) [flattening 40]
42. ((calm(lucy) & ~calm(lucy)) | ! [X0] : ~humble(X0)) & (? [X1] : humble(X1) | ~calm(lucy) | calm(lucy)) [rectify 41]
43. ? [X1] : humble(X1) => humble(sK0) [choice axiom]
44. ((calm(lucy) & ~calm(lucy)) | ! [X0] : ~humble(X0)) & (humble(sK0) | ~calm(lucy) | calm(lucy)) [skolemisation 42,43]
70. ~calm(lucy) | ~humble(X0) [cnf transformation 44]
71. calm(lucy) | ~humble(X0) [cnf transformation 44]
123. humble(susan) [cnf transformation 24]
126. 1 <=> ! [X0] : ~humble(X0) [avatar definition]
127. ~humble(X0) <- (1) [avatar component clause 126]
129. 2 <=> calm(lucy) [avatar definition]
132. 1 | 2 [avatar split clause 71,129,126]
133. 1 | ~2 [avatar split clause 70,129,126]
190. 15 <=> humble(susan) [avatar definition]
192. humble(susan) <- (15) [avatar component clause 190]
231. 15 [avatar split clause 123,190]
232. $false <- (1, 15) [resolution 192,127]
233. ~1 | ~15 [avatar contradiction clause 232]
234. $false [avatar sat refutation 132,133,231,233]
% SZS output end Proof for 471362092190658588171419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm then mary is not humble or rich.
Everyone who is humble or not funny is both funny and not strong.
If paul is either calm or rich then lucy is both wise and not tall and vice versa.
If someone is generous then someone is not humble and vice versa.
If mary is either not wise or humble then susan is both not old and not brave and vice versa.
If lucy is not strong or not calm then fred is old or generous.
Everyone who is either wise or not old is creative or brave and vice versa.
Everyone who is quiet is both not strong and not tall.
If mary is either humble or not calm then mary is quiet and vice versa.
Everyone who is curious is both strong and not patient.
Everyone who is either not old or not wise is either curious or creative.
Everyone who is tall or brave is not tall and vice versa.
If someone is humble then someone is either creative or quiet.
Everyone who is both funny and patient is both not generous and not tall and vice versa.
If mary is either not tall or brave then someone is both not quiet and funny and vice versa.
Everyone who is either old or not old is either not patient or wise.
Someone is not old.
Fred is both not rich and patient.
John is wise or happy.
Someone is not calm or not happy.
Paul is either humble or not quiet.
Someone is either tall or patient.
Someone is both not happy and not tall.
Someone is generous or not rich. | Lucy is not quiet. | contradiction | ((?[X]:(~calm(X)))=>((~humble(mary)|rich(mary))))&
(![X]:((humble(X)|~funny(X))=>(funny(X)&~strong(X))))&
(((calm(paul)<~>rich(paul)))<=>((wise(lucy)&~tall(lucy))))&
((?[X]:(generous(X)))<=>(?[X]:(~humble(X))))&
(((~wise(mary)<~>humble(mary)))<=>((~old(susan)&~brave(susan))))&
(((~strong(lucy)|~calm(lucy)))=>((old(fred)|generous(fred))))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)|brave(X))))&
(![X]:(quiet(X)=>(~strong(X)&~tall(X))))&
(((humble(mary)<~>~calm(mary)))<=>(quiet(mary)))&
(![X]:(curious(X)=>(strong(X)&~patient(X))))&
(![X]:((~old(X)<~>~wise(X))=>(curious(X)<~>creative(X))))&
(![X]:((tall(X)|brave(X))<=>~tall(X)))&
((?[X]:(humble(X)))=>(?[X]:((creative(X)<~>quiet(X)))))&
(![X]:((funny(X)&patient(X))<=>(~generous(X)&~tall(X))))&
(((~tall(mary)<~>brave(mary)))<=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:((old(X)<~>~old(X))=>(~patient(X)<~>wise(X))))&
(?[X]:(~old(X)))&
((~rich(fred)&patient(fred)))&
((wise(john)|happy(john)))&
(?[X]:((~calm(X)|~happy(X))))&
((humble(paul)<~>~quiet(paul)))&
(?[X]:((tall(X)<~>patient(X))))&
(?[X]:((~happy(X)&~tall(X))))&
(?[X]:((generous(X)|~rich(X)))) | ~quiet(lucy) | [
"p1",
"p11",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 784454436260272888728386
% SZS output start Proof for 784454436260272888728386
2. ! [X0] : ((~funny(X0) | humble(X0)) => (~strong(X0) & funny(X0))) [input p1]
12. ! [X0] : ((brave(X0) | tall(X0)) <=> ~tall(X0)) [input p11]
15. (~tall(mary) <~> brave(mary)) <=> ? [X0] : (funny(X0) & ~quiet(X0)) [input p14]
25. ~quiet(lucy) [input hypothesis]
30. ! [X0] : ((~strong(X0) & funny(X0)) | (funny(X0) & ~humble(X0))) [ennf transformation 2]
51. ! [X0] : (((brave(X0) | tall(X0)) | tall(X0)) & (~tall(X0) | (~brave(X0) & ~tall(X0)))) [nnf transformation 12]
52. ! [X0] : ((brave(X0) | tall(X0) | tall(X0)) & (~tall(X0) | (~brave(X0) & ~tall(X0)))) [flattening 51]
59. (((~brave(mary) | tall(mary)) & (brave(mary) | ~tall(mary))) | ! [X0] : (~funny(X0) | quiet(X0))) & (? [X0] : (funny(X0) & ~quiet(X0)) | ((~tall(mary) | ~brave(mary)) & (brave(mary) | tall(mary)))) [nnf transformation 15]
60. (((~brave(mary) | tall(mary)) & (brave(mary) | ~tall(mary))) | ! [X0] : (~funny(X0) | quiet(X0))) & (? [X1] : (funny(X1) & ~quiet(X1)) | ((~tall(mary) | ~brave(mary)) & (brave(mary) | tall(mary)))) [rectify 59]
61. ? [X1] : (funny(X1) & ~quiet(X1)) => (funny(sK3) & ~quiet(sK3)) [choice axiom]
62. (((~brave(mary) | tall(mary)) & (brave(mary) | ~tall(mary))) | ! [X0] : (~funny(X0) | quiet(X0))) & ((funny(sK3) & ~quiet(sK3)) | ((~tall(mary) | ~brave(mary)) & (brave(mary) | tall(mary)))) [skolemisation 60,61]
78. funny(X0) | funny(X0) [cnf transformation 30]
115. ~tall(X0) | ~tall(X0) [cnf transformation 52]
117. brave(X0) | tall(X0) | tall(X0) [cnf transformation 52]
129. ~brave(mary) | tall(mary) | ~funny(X0) | quiet(X0) [cnf transformation 62]
146. ~quiet(lucy) [cnf transformation 25]
151. ~tall(X0) [duplicate literal removal 115]
152. brave(X0) | tall(X0) [duplicate literal removal 117]
153. funny(X0) [duplicate literal removal 78]
269. ~brave(mary) | ~funny(X0) | quiet(X0) [subsumption resolution 129,151]
270. ~brave(mary) | quiet(X0) [subsumption resolution 269,153]
272. 24 <=> ! [X0] : quiet(X0) [avatar definition]
273. quiet(X0) <- (24) [avatar component clause 272]
275. 25 <=> brave(mary) [avatar definition]
277. ~brave(mary) <- (~25) [avatar component clause 275]
278. 24 | ~25 [avatar split clause 270,275,272]
328. tall(mary) <- (~25) [resolution 152,277]
332. $false <- (~25) [subsumption resolution 328,151]
333. 25 [avatar contradiction clause 332]
335. $false <- (24) [resolution 273,146]
340. ~24 [avatar contradiction clause 335]
341. $false [avatar sat refutation 278,333,340]
% SZS output end Proof for 784454436260272888728386
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or humble is both rich and not kind and vice versa. Everyone who is either not calm or wise is not generous or humble and vice versa. If someone is not old then fred is not funny or rich and vice versa. Everyone who is not strong or brave is both not kind and humble. Everyone who is both brave and not brave is tall or brave and vice versa. Everyone who is tall is not happy and vice versa. If someone is either creative or not creative then someone is not humble and vice versa. Everyone who is not curious or happy is either quiet or kind and vice versa. If fred is either generous or not tall then john is either wise or funny. Everyone who is either humble or creative is not quiet. Everyone who is quiet is not creative or not generous. Everyone who is happy is not patient and vice versa. Everyone who is either old or generous is not wise. Everyone who is either humble or not patient is either calm or humble and vice versa. Everyone who is either not funny or tall is not brave and vice versa. If john is not creative then john is not strong and vice versa. Someone is happy or not wise. Mary is either not rich or not kind. Alice is either creative or not curious. Someone is either humble or old. Someone is either not happy or curious. Someone is either not brave or patient. Someone is happy. Someone is either not creative or patient. | John is not wise. | contradiction | (![X]:((calm(X)<~>humble(X))<=>(rich(X)&~kind(X))))&
(![X]:((~calm(X)<~>wise(X))<=>(~generous(X)|humble(X))))&
((?[X]:(~old(X)))<=>((~funny(fred)|rich(fred))))&
(![X]:((~strong(X)|brave(X))=>(~kind(X)&humble(X))))&
(![X]:((brave(X)&~brave(X))<=>(tall(X)|brave(X))))&
(![X]:(tall(X)<=>~happy(X)))&
((?[X]:((creative(X)<~>~creative(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~curious(X)|happy(X))<=>(quiet(X)<~>kind(X))))&
(((generous(fred)<~>~tall(fred)))=>((wise(john)<~>funny(john))))&
(![X]:((humble(X)<~>creative(X))=>~quiet(X)))&
(![X]:(quiet(X)=>(~creative(X)|~generous(X))))&
(![X]:(happy(X)<=>~patient(X)))&
(![X]:((old(X)<~>generous(X))=>~wise(X)))&
(![X]:((humble(X)<~>~patient(X))<=>(calm(X)<~>humble(X))))&
(![X]:((~funny(X)<~>tall(X))<=>~brave(X)))&
((~creative(john))<=>(~strong(john)))&
(?[X]:((happy(X)|~wise(X))))&
((~rich(mary)<~>~kind(mary)))&
((creative(alice)<~>~curious(alice)))&
(?[X]:((humble(X)<~>old(X))))&
(?[X]:((~happy(X)<~>curious(X))))&
(?[X]:((~brave(X)<~>patient(X))))&
(?[X]:(happy(X)))&
(?[X]:((~creative(X)<~>patient(X)))) | ~wise(john) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p7",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2016829277903362975449306
% SZS output start Proof for 2016829277903362975449306
1. ! [X0] : ((calm(X0) <~> humble(X0)) <=> (~kind(X0) & rich(X0))) [input p0]
2. ! [X0] : ((~calm(X0) <~> wise(X0)) <=> (humble(X0) | ~generous(X0))) [input p1]
4. ! [X0] : ((brave(X0) | ~strong(X0)) => (humble(X0) & ~kind(X0))) [input p3]
5. ! [X0] : ((~brave(X0) & brave(X0)) <=> (brave(X0) | tall(X0))) [input p4]
6. ! [X0] : (tall(X0) <=> ~happy(X0)) [input p5]
8. ! [X0] : ((happy(X0) | ~curious(X0)) <=> (quiet(X0) <~> kind(X0))) [input p7]
10. ! [X0] : ((humble(X0) <~> creative(X0)) => ~quiet(X0)) [input p9]
12. ! [X0] : (happy(X0) <=> ~patient(X0)) [input p11]
14. ! [X0] : ((humble(X0) <~> ~patient(X0)) <=> (calm(X0) <~> humble(X0))) [input p13]
16. ~creative(john) <=> ~strong(john) [input p15]
25. ~wise(john) [input hypothesis]
27. ! [X0] : ((humble(X0) & ~kind(X0)) | (~brave(X0) & strong(X0))) [ennf transformation 4]
29. ! [X0] : (~quiet(X0) | (humble(X0) <=> creative(X0))) [ennf transformation 10]
33. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | (kind(X0) | ~rich(X0))) & ((~kind(X0) & rich(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [nnf transformation 1]
34. ! [X0] : ((((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | kind(X0) | ~rich(X0)) & ((~kind(X0) & rich(X0)) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0))))) [flattening 33]
35. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [nnf transformation 2]
36. ! [X0] : ((((~wise(X0) | calm(X0)) & (wise(X0) | ~calm(X0))) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | ((~calm(X0) | ~wise(X0)) & (wise(X0) | calm(X0))))) [flattening 35]
42. ! [X0] : (((~brave(X0) & brave(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (brave(X0) | ~brave(X0)))) [nnf transformation 5]
43. ! [X0] : (((~brave(X0) & brave(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | brave(X0) | ~brave(X0))) [flattening 42]
44. ! [X0] : ((tall(X0) | happy(X0)) & (~happy(X0) | ~tall(X0))) [nnf transformation 6]
50. ! [X0] : (((happy(X0) | ~curious(X0)) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (~happy(X0) & curious(X0)))) [nnf transformation 8]
51. ! [X0] : ((happy(X0) | ~curious(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0)))) & (((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | (~happy(X0) & curious(X0)))) [flattening 50]
53. ! [X0] : (~quiet(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) [nnf transformation 29]
54. ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))) [nnf transformation 12]
56. ! [X0] : ((((patient(X0) | ~humble(X0)) & (~patient(X0) | humble(X0))) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ((humble(X0) | patient(X0)) & (~patient(X0) | ~humble(X0))))) [nnf transformation 14]
58. (~creative(john) | strong(john)) & (~strong(john) | creative(john)) [nnf transformation 16]
79. ~kind(X0) | humble(X0) | ~calm(X0) [cnf transformation 34]
86. ~humble(X0) | ~calm(X0) | wise(X0) [cnf transformation 36]
94. strong(X0) | humble(X0) [cnf transformation 27]
97. brave(X0) | ~tall(X0) [cnf transformation 43]
100. ~brave(X0) | ~brave(X0) [cnf transformation 43]
102. tall(X0) | happy(X0) [cnf transformation 44]
108. kind(X0) | quiet(X0) | ~happy(X0) [cnf transformation 51]
118. ~quiet(X0) | humble(X0) | ~creative(X0) [cnf transformation 53]
120. ~patient(X0) | ~happy(X0) [cnf transformation 54]
125. humble(X0) | calm(X0) | humble(X0) | patient(X0) [cnf transformation 56]
131. patient(X0) | ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 56]
136. ~strong(john) | creative(john) [cnf transformation 58]
152. ~wise(john) [cnf transformation 25]
153. humble(X0) | calm(X0) | patient(X0) [duplicate literal removal 125]
156. patient(X0) | ~humble(X0) | calm(X0) [duplicate literal removal 131]
160. ~brave(X0) [duplicate literal removal 100]
179. ~tall(X0) [subsumption resolution 97,160]
180. happy(X0) [subsumption resolution 102,179]
194. quiet(X0) | kind(X0) [subsumption resolution 108,180]
201. 9 <=> wise(john) [avatar definition]
203. ~wise(john) <- (~9) [avatar component clause 201]
211. ~patient(X0) [subsumption resolution 120,180]
212. ~humble(X0) | calm(X0) [subsumption resolution 156,211]
213. humble(X0) | calm(X0) [subsumption resolution 153,211]
214. calm(X0) [subsumption resolution 213,212]
218. 11 <=> strong(john) [avatar definition]
219. ~strong(john) <- (~11) [avatar component clause 218]
222. 12 <=> creative(john) [avatar definition]
223. creative(john) <- (12) [avatar component clause 222]
226. 12 | ~11 [avatar split clause 136,218,222]
259. ~9 [avatar split clause 152,201]
260. humble(john) <- (~11) [resolution 94,219]
269. ~calm(john) | wise(john) <- (~11) [resolution 86,260]
271. wise(john) <- (~11) [subsumption resolution 269,214]
272. $false <- (~9, ~11) [subsumption resolution 271,203]
273. 9 | 11 [avatar contradiction clause 272]
277. ~creative(X0) | humble(X0) | kind(X0) [resolution 118,194]
319. humble(john) | kind(john) <- (12) [resolution 277,223]
321. 23 <=> kind(john) [avatar definition]
323. kind(john) <- (23) [avatar component clause 321]
325. 24 <=> humble(john) [avatar definition]
327. humble(john) <- (24) [avatar component clause 325]
328. 23 | 24 | ~12 [avatar split clause 319,222,325,321]
330. humble(john) | ~calm(john) <- (23) [resolution 323,79]
332. humble(john) <- (23) [subsumption resolution 330,214]
333. 24 | ~23 [avatar split clause 332,321,325]
336. ~calm(john) | wise(john) <- (24) [resolution 327,86]
339. wise(john) <- (24) [subsumption resolution 336,214]
340. $false <- (~9, 24) [subsumption resolution 339,203]
341. 9 | ~24 [avatar contradiction clause 340]
342. $false [avatar sat refutation 226,259,273,328,333,341]
% SZS output end Proof for 2016829277903362975449306
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or funny is not wise and vice versa.
Everyone who is not old or curious is either strong or not happy and vice versa.
Everyone who is either not calm or not patient is creative or wise and vice versa.
Everyone who is not calm is both not old and generous.
Everyone who is not old is both kind and old.
Everyone who is both not strong and not kind is not brave.
If someone is both brave and calm then someone is curious and vice versa.
Everyone who is not creative is either not funny or humble.
Everyone who is patient or quiet is either happy or humble.
If someone is not old or not patient then someone is either not curious or not strong and vice versa.
If john is calm then someone is curious or not wise.
Everyone who is quiet is either rich or not happy and vice versa.
Everyone who is both not generous and rich is both not rich and kind.
If someone is both calm and not generous then someone is not funny and vice versa.
Everyone who is both not old and old is funny or rich and vice versa.
If someone is not calm or tall then someone is either not rich or tall.
Someone is both wise and not creative.
Someone is kind or not kind.
Someone is either humble or creative.
John is both not creative and patient.
John is either funny or patient.
Someone is strong or funny. | John is not creative. | entailment | (![X]:((~kind(X)|funny(X))<=>~wise(X)))&
(![X]:((~old(X)|curious(X))<=>(strong(X)<~>~happy(X))))&
(![X]:((~calm(X)<~>~patient(X))<=>(creative(X)|wise(X))))&
(![X]:(~calm(X)=>(~old(X)&generous(X))))&
(![X]:(~old(X)=>(kind(X)&old(X))))&
(![X]:((~strong(X)&~kind(X))=>~brave(X)))&
((?[X]:((brave(X)&calm(X))))<=>(?[X]:(curious(X))))&
(![X]:(~creative(X)=>(~funny(X)<~>humble(X))))&
(![X]:((patient(X)|quiet(X))=>(happy(X)<~>humble(X))))&
((?[X]:((~old(X)|~patient(X))))<=>(?[X]:((~curious(X)<~>~strong(X)))))&
((calm(john))=>(?[X]:((curious(X)|~wise(X)))))&
(![X]:(quiet(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((~generous(X)&rich(X))=>(~rich(X)&kind(X))))&
((?[X]:((calm(X)&~generous(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)&old(X))<=>(funny(X)|rich(X))))&
((?[X]:((~calm(X)|tall(X))))=>(?[X]:((~rich(X)<~>tall(X)))))&
(?[X]:((wise(X)&~creative(X))))&
(?[X]:((kind(X)|~kind(X))))&
(?[X]:((humble(X)<~>creative(X))))&
((~creative(john)&patient(john)))&
((funny(john)<~>patient(john)))&
(?[X]:((strong(X)|funny(X)))) | ~creative(john) | [
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3732079089593591760636785
% SZS output start Proof for 3732079089593591760636785
20. patient(john) & ~creative(john) [input p19]
23. creative(john) [input hypothesis]
139. ~creative(john) [cnf transformation 20]
144. creative(john) [cnf transformation 23]
257. $false [subsumption resolution 144,139]
% SZS output end Proof for 3732079089593591760636785
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is not calm or not humble then someone is not happy or not old.
Everyone who is not funny or curious is not strong and vice versa.
Everyone who is not funny is both not tall and not patient.
Everyone who is both not tall and generous is not humble or brave and vice versa.
If someone is both not old and kind then someone is old or not brave.
Everyone who is happy or not strong is not calm and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is both wise and not curious is either patient or not happy and vice versa.
If someone is not tall or not wise then someone is both patient and not wise.
Everyone who is either humble or not old is both brave and funny and vice versa.
Everyone who is funny is both not kind and humble.
If someone is either not wise or not brave then paul is not humble and vice versa.
Everyone who is not quiet is either not tall or not quiet and vice versa.
If susan is either old or strong then susan is happy.
Everyone who is either creative or not generous is not generous or not wise.
If someone is not old then someone is both not strong and quiet.
Alice is quiet or funny.
Alice is funny or not kind.
Someone is both not calm and creative.
Someone is either brave or not happy.
Lucy is patient or not rich.
Someone is tall. | Alice is curious. | neutral | (((~calm(lucy)|~humble(lucy)))=>(?[X]:((~happy(X)|~old(X)))))&
(![X]:((~funny(X)|curious(X))<=>~strong(X)))&
(![X]:(~funny(X)=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&generous(X))<=>(~humble(X)|brave(X))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>~calm(X)))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)&~curious(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((humble(X)<~>~old(X))<=>(brave(X)&funny(X))))&
(![X]:(funny(X)=>(~kind(X)&humble(X))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(~humble(paul)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~quiet(X))))&
(((old(susan)<~>strong(susan)))=>(happy(susan)))&
(![X]:((creative(X)<~>~generous(X))=>(~generous(X)|~wise(X))))&
((?[X]:(~old(X)))=>(?[X]:((~strong(X)&quiet(X)))))&
((quiet(alice)|funny(alice)))&
((funny(alice)|~kind(alice)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((brave(X)<~>~happy(X))))&
((patient(lucy)|~rich(lucy)))&
(?[X]:(tall(X))) | curious(alice) | [] | null | 0 |
Everyone who is not humble or kind is either not wise or curious and vice versa. If someone is not calm or old then someone is generous and vice versa. If john is both curious and not wise then paul is both curious and not rich and vice versa. Everyone who is both creative and funny is not brave or strong. If fred is either not patient or wise then john is not humble or not kind. Everyone who is both not kind and strong is not happy or creative and vice versa. Everyone who is both curious and not generous is both not patient and not strong. Everyone who is either creative or rich is both not old and not calm. If someone is not patient or tall then someone is not funny or not kind. If fred is either not brave or happy then john is either brave or not brave and vice versa. Everyone who is both not kind and brave is humble or not curious. If john is either kind or generous then fred is quiet and vice versa. Everyone who is either not humble or not quiet is either quiet or funny and vice versa. If lucy is not funny or not kind then someone is either not generous or generous. Everyone who is old is either strong or creative and vice versa. Lucy is both tall and not wise. John is calm or not calm. Fred is rich. Paul is both funny and old. Someone is either not brave or not generous. Someone is either not kind or patient. Fred is either calm or not calm. | Fred is curious. | neutral | (![X]:((~humble(X)|kind(X))<=>(~wise(X)<~>curious(X))))&
((?[X]:((~calm(X)|old(X))))<=>(?[X]:(generous(X))))&
(((curious(john)&~wise(john)))<=>((curious(paul)&~rich(paul))))&
(![X]:((creative(X)&funny(X))=>(~brave(X)|strong(X))))&
(((~patient(fred)<~>wise(fred)))=>((~humble(john)|~kind(john))))&
(![X]:((~kind(X)&strong(X))<=>(~happy(X)|creative(X))))&
(![X]:((curious(X)&~generous(X))=>(~patient(X)&~strong(X))))&
(![X]:((creative(X)<~>rich(X))=>(~old(X)&~calm(X))))&
((?[X]:((~patient(X)|tall(X))))=>(?[X]:((~funny(X)|~kind(X)))))&
(((~brave(fred)<~>happy(fred)))<=>((brave(john)<~>~brave(john))))&
(![X]:((~kind(X)&brave(X))=>(humble(X)|~curious(X))))&
(((kind(john)<~>generous(john)))<=>(quiet(fred)))&
(![X]:((~humble(X)<~>~quiet(X))<=>(quiet(X)<~>funny(X))))&
(((~funny(lucy)|~kind(lucy)))=>(?[X]:((~generous(X)<~>generous(X)))))&
(![X]:(old(X)<=>(strong(X)<~>creative(X))))&
((tall(lucy)&~wise(lucy)))&
((calm(john)|~calm(john)))&
(rich(fred))&
((funny(paul)&old(paul)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(?[X]:((~kind(X)<~>patient(X))))&
((calm(fred)<~>~calm(fred))) | curious(fred) | [] | null | 0 |
If someone is not funny or not humble then someone is kind and vice versa. Everyone who is either not quiet or funny is both kind and not funny and vice versa. Everyone who is either funny or curious is brave or curious and vice versa. Everyone who is kind or generous is generous or wise. If alice is happy then fred is both kind and old and vice versa. If john is not brave then fred is either wise or not humble. Everyone who is calm or not creative is either not curious or humble. If fred is not tall or calm then paul is either not tall or generous and vice versa. If someone is calm or not creative then john is either not creative or not old. Everyone who is both tall and not brave is brave or funny and vice versa. If someone is patient then fred is both not wise and not calm. Everyone who is not creative or old is both old and wise. If someone is not wise then alice is either curious or not brave and vice versa. Everyone who is either kind or not old is brave. Everyone who is creative or not curious is either not kind or humble. Mary is either not calm or tall. Lucy is not happy or not quiet. Someone is generous. Someone is not humble. Someone is both not rich and not wise. Someone is both not happy and not kind. | Lucy is brave. | contradiction | ((?[X]:((~funny(X)|~humble(X))))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>funny(X))<=>(kind(X)&~funny(X))))&
(![X]:((funny(X)<~>curious(X))<=>(brave(X)|curious(X))))&
(![X]:((kind(X)|generous(X))=>(generous(X)|wise(X))))&
((happy(alice))<=>((kind(fred)&old(fred))))&
((~brave(john))=>((wise(fred)<~>~humble(fred))))&
(![X]:((calm(X)|~creative(X))=>(~curious(X)<~>humble(X))))&
(((~tall(fred)|calm(fred)))<=>((~tall(paul)<~>generous(paul))))&
((?[X]:((calm(X)|~creative(X))))=>((~creative(john)<~>~old(john))))&
(![X]:((tall(X)&~brave(X))<=>(brave(X)|funny(X))))&
((?[X]:(patient(X)))=>((~wise(fred)&~calm(fred))))&
(![X]:((~creative(X)|old(X))=>(old(X)&wise(X))))&
((?[X]:(~wise(X)))<=>((curious(alice)<~>~brave(alice))))&
(![X]:((kind(X)<~>~old(X))=>brave(X)))&
(![X]:((creative(X)|~curious(X))=>(~kind(X)<~>humble(X))))&
((~calm(mary)<~>tall(mary)))&
((~happy(lucy)|~quiet(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~rich(X)&~wise(X))))&
(?[X]:((~happy(X)&~kind(X)))) | brave(lucy) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 550620261781817302930516
% SZS output start Proof for 550620261781817302930516
10. ! [X0] : ((~brave(X0) & tall(X0)) <=> (funny(X0) | brave(X0))) [input p9]
22. brave(lucy) [input hypothesis]
50. ! [X0] : (((~brave(X0) & tall(X0)) | (~funny(X0) & ~brave(X0))) & ((funny(X0) | brave(X0)) | (brave(X0) | ~tall(X0)))) [nnf transformation 10]
51. ! [X0] : (((~brave(X0) & tall(X0)) | (~funny(X0) & ~brave(X0))) & (funny(X0) | brave(X0) | brave(X0) | ~tall(X0))) [flattening 50]
106. ~brave(X0) | ~brave(X0) [cnf transformation 51]
130. brave(lucy) [cnf transformation 22]
132. ~brave(X0) [duplicate literal removal 106]
261. $false [subsumption resolution 130,132]
% SZS output end Proof for 550620261781817302930516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both creative and generous then susan is funny or creative and vice versa.
If paul is not funny then someone is both brave and not old and vice versa.
Everyone who is not strong or patient is either not generous or old.
If someone is humble or generous then someone is either not happy or calm and vice versa.
Everyone who is either not kind or rich is not strong or not rich.
Everyone who is curious or not curious is both not rich and humble.
Everyone who is not humble or creative is patient or creative.
If someone is either not creative or not wise then mary is either not rich or wise and vice versa.
Everyone who is either kind or not generous is both not brave and wise and vice versa.
Everyone who is either not rich or kind is either creative or not patient.
Everyone who is not humble or humble is generous or not strong and vice versa.
If alice is not creative or calm then someone is either strong or humble and vice versa.
Everyone who is both funny and calm is quiet.
Everyone who is patient is not tall or not wise.
If someone is not quiet or curious then mary is tall and vice versa.
If john is both not curious and not humble then paul is both patient and old and vice versa.
Someone is not tall.
Susan is not old.
John is not wise.
Someone is patient or brave.
Fred is not generous.
Someone is both not calm and curious.
Mary is either old or not curious. | Alice is happy. | neutral | (((creative(paul)&generous(paul)))<=>((funny(susan)|creative(susan))))&
((~funny(paul))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((~strong(X)|patient(X))=>(~generous(X)<~>old(X))))&
((?[X]:((humble(X)|generous(X))))<=>(?[X]:((~happy(X)<~>calm(X)))))&
(![X]:((~kind(X)<~>rich(X))=>(~strong(X)|~rich(X))))&
(![X]:((curious(X)|~curious(X))=>(~rich(X)&humble(X))))&
(![X]:((~humble(X)|creative(X))=>(patient(X)|creative(X))))&
((?[X]:((~creative(X)<~>~wise(X))))<=>((~rich(mary)<~>wise(mary))))&
(![X]:((kind(X)<~>~generous(X))<=>(~brave(X)&wise(X))))&
(![X]:((~rich(X)<~>kind(X))=>(creative(X)<~>~patient(X))))&
(![X]:((~humble(X)|humble(X))<=>(generous(X)|~strong(X))))&
(((~creative(alice)|calm(alice)))<=>(?[X]:((strong(X)<~>humble(X)))))&
(![X]:((funny(X)&calm(X))=>quiet(X)))&
(![X]:(patient(X)=>(~tall(X)|~wise(X))))&
((?[X]:((~quiet(X)|curious(X))))<=>(tall(mary)))&
(((~curious(john)&~humble(john)))<=>((patient(paul)&old(paul))))&
(?[X]:(~tall(X)))&
(~old(susan))&
(~wise(john))&
(?[X]:((patient(X)|brave(X))))&
(~generous(fred))&
(?[X]:((~calm(X)&curious(X))))&
((old(mary)<~>~curious(mary))) | happy(alice) | [] | null | 0 |
Everyone who is not curious or strong is strong and vice versa. Everyone who is not kind is generous. Everyone who is happy is not curious or calm and vice versa. Everyone who is not generous or not rich is either rich or not tall and vice versa. If someone is either not humble or not rich then someone is not calm or rich. Everyone who is both curious and not tall is not tall or curious and vice versa. If susan is not funny then lucy is either not creative or not quiet and vice versa. If someone is curious or not humble then paul is not calm. If paul is curious then susan is not tall or not patient and vice versa. If someone is not strong then susan is both strong and wise and vice versa. If john is not rich then someone is both tall and humble and vice versa. Everyone who is not rich or not funny is happy or patient and vice versa. If john is not calm or rich then lucy is strong. Everyone who is not calm is not funny. Everyone who is both wise and brave is strong or not curious. Everyone who is wise or not calm is not patient and vice versa. Fred is either funny or rich. Someone is either not calm or not humble. Someone is either not curious or humble. Someone is either patient or not strong. Mary is both not kind and not brave. Paul is both happy and tall. Alice is both generous and old. | Fred is not happy. | contradiction | (![X]:((~curious(X)|strong(X))<=>strong(X)))&
(![X]:(~kind(X)=>generous(X)))&
(![X]:(happy(X)<=>(~curious(X)|calm(X))))&
(![X]:((~generous(X)|~rich(X))<=>(rich(X)<~>~tall(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~calm(X)|rich(X)))))&
(![X]:((curious(X)&~tall(X))<=>(~tall(X)|curious(X))))&
((~funny(susan))<=>((~creative(lucy)<~>~quiet(lucy))))&
((?[X]:((curious(X)|~humble(X))))=>(~calm(paul)))&
((curious(paul))<=>((~tall(susan)|~patient(susan))))&
((?[X]:(~strong(X)))<=>((strong(susan)&wise(susan))))&
((~rich(john))<=>(?[X]:((tall(X)&humble(X)))))&
(![X]:((~rich(X)|~funny(X))<=>(happy(X)|patient(X))))&
(((~calm(john)|rich(john)))=>(strong(lucy)))&
(![X]:(~calm(X)=>~funny(X)))&
(![X]:((wise(X)&brave(X))=>(strong(X)|~curious(X))))&
(![X]:((wise(X)|~calm(X))<=>~patient(X)))&
((funny(fred)<~>rich(fred)))&
(?[X]:((~calm(X)<~>~humble(X))))&
(?[X]:((~curious(X)<~>humble(X))))&
(?[X]:((patient(X)<~>~strong(X))))&
((~kind(mary)&~brave(mary)))&
((happy(paul)&tall(paul)))&
((generous(alice)&old(alice))) | ~happy(fred) | [
"p2",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3680940304420978335695060
% SZS output start Proof for 3680940304420978335695060
3. ! [X0] : (happy(X0) <=> (calm(X0) | ~curious(X0))) [input p2]
12. ! [X0] : ((~funny(X0) | ~rich(X0)) <=> (patient(X0) | happy(X0))) [input p11]
14. ! [X0] : (~calm(X0) => ~funny(X0)) [input p13]
16. ! [X0] : ((~calm(X0) | wise(X0)) <=> ~patient(X0)) [input p15]
24. ~happy(fred) [input hypothesis]
33. ! [X0] : (~funny(X0) | calm(X0)) [ennf transformation 14]
36. ! [X0] : ((happy(X0) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | ~happy(X0))) [nnf transformation 3]
37. ! [X0] : ((happy(X0) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ~happy(X0))) [flattening 36]
58. ! [X0] : (((~funny(X0) | ~rich(X0)) | (~patient(X0) & ~happy(X0))) & ((patient(X0) | happy(X0)) | (funny(X0) & rich(X0)))) [nnf transformation 12]
59. ! [X0] : ((~funny(X0) | ~rich(X0) | (~patient(X0) & ~happy(X0))) & (patient(X0) | happy(X0) | (funny(X0) & rich(X0)))) [flattening 58]
60. ! [X0] : (((~calm(X0) | wise(X0)) | patient(X0)) & (~patient(X0) | (calm(X0) & ~wise(X0)))) [nnf transformation 16]
61. ! [X0] : ((~calm(X0) | wise(X0) | patient(X0)) & (~patient(X0) | (calm(X0) & ~wise(X0)))) [flattening 60]
78. ~calm(X0) | happy(X0) [cnf transformation 37]
108. patient(X0) | happy(X0) | funny(X0) [cnf transformation 59]
113. ~funny(X0) | calm(X0) [cnf transformation 33]
115. ~patient(X0) | calm(X0) [cnf transformation 61]
129. ~happy(fred) [cnf transformation 24]
337. happy(X0) | funny(X0) | calm(X0) [resolution 108,115]
338. happy(X0) | calm(X0) [subsumption resolution 337,113]
339. happy(X0) [subsumption resolution 338,78]
354. $false [resolution 339,129]
% SZS output end Proof for 3680940304420978335695060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is both old and not happy is generous or not rich and vice versa.
If someone is wise then lucy is both creative and happy and vice versa.
Everyone who is either strong or happy is both quiet and not quiet.
If someone is happy then someone is both not strong and not happy.
Everyone who is both funny and not curious is both not rich and funny.
Everyone who is strong is both not wise and creative.
Everyone who is not rich or not quiet is not tall or not old and vice versa.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Someone is calm.
John is both calm and brave.
Alice is funny.
Mary is either not brave or tall.
Someone is both not kind and humble.
Someone is not tall or not wise.
Paul is not kind or curious.
John is quiet or not strong. | Fred is not brave. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((old(X)&~happy(X))<=>(generous(X)|~rich(X))))&
((?[X]:(wise(X)))<=>((creative(lucy)&happy(lucy))))&
(![X]:((strong(X)<~>happy(X))=>(quiet(X)&~quiet(X))))&
((?[X]:(happy(X)))=>(?[X]:((~strong(X)&~happy(X)))))&
(![X]:((funny(X)&~curious(X))=>(~rich(X)&funny(X))))&
(![X]:(strong(X)=>(~wise(X)&creative(X))))&
(![X]:((~rich(X)|~quiet(X))<=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(?[X]:(calm(X)))&
((calm(john)&brave(john)))&
(funny(alice))&
((~brave(mary)<~>tall(mary)))&
(?[X]:((~kind(X)&humble(X))))&
(?[X]:((~tall(X)|~wise(X))))&
((~kind(paul)|curious(paul)))&
((quiet(john)|~strong(john))) | ~brave(fred) | [
"p1",
"p2",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6010434421701118998111990
% SZS output start Proof for 6010434421701118998111990
2. ! [X0] : (old(X0) => (happy(X0) <~> ~creative(X0))) [input p1]
3. ! [X0] : ((~happy(X0) & old(X0)) <=> (~rich(X0) | generous(X0))) [input p2]
11. (~creative(alice) | rich(alice)) <=> (brave(fred) & ~patient(fred)) [input p10]
24. ~brave(fred) [input hypothesis]
29. ! [X0] : ((happy(X0) <~> ~creative(X0)) | ~old(X0)) [ennf transformation 2]
39. ! [X0] : (((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ~old(X0)) [nnf transformation 29]
40. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & ((~rich(X0) | generous(X0)) | (happy(X0) | ~old(X0)))) [nnf transformation 3]
41. ! [X0] : (((~happy(X0) & old(X0)) | (rich(X0) & ~generous(X0))) & (~rich(X0) | generous(X0) | happy(X0) | ~old(X0))) [flattening 40]
58. ((~creative(alice) | rich(alice)) | (~brave(fred) | patient(fred))) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [nnf transformation 11]
59. (~creative(alice) | rich(alice) | ~brave(fred) | patient(fred)) & ((brave(fred) & ~patient(fred)) | (creative(alice) & ~rich(alice))) [flattening 58]
85. ~creative(X0) | happy(X0) | ~old(X0) [cnf transformation 39]
89. rich(X0) | old(X0) [cnf transformation 41]
91. ~happy(X0) | rich(X0) [cnf transformation 41]
114. brave(fred) | ~rich(alice) [cnf transformation 59]
115. brave(fred) | creative(alice) [cnf transformation 59]
143. ~brave(fred) [cnf transformation 24]
202. 13 <=> brave(fred) [avatar definition]
206. 14 <=> rich(alice) [avatar definition]
207. ~rich(alice) <- (~14) [avatar component clause 206]
210. 15 <=> creative(alice) [avatar definition]
211. creative(alice) <- (15) [avatar component clause 210]
214. 15 | 13 [avatar split clause 115,202,210]
215. ~14 | 13 [avatar split clause 114,202,206]
323. ~13 [avatar split clause 143,202]
330. old(alice) <- (~14) [resolution 89,207]
359. happy(alice) | ~old(alice) <- (15) [resolution 85,211]
361. happy(alice) <- (~14, 15) [subsumption resolution 359,330]
372. rich(alice) <- (~14, 15) [resolution 361,91]
374. $false <- (~14, 15) [subsumption resolution 372,207]
375. 14 | ~15 [avatar contradiction clause 374]
376. $false [avatar sat refutation 214,215,323,375]
% SZS output end Proof for 6010434421701118998111990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not rich is both happy and brave and vice versa. Everyone who is not funny or not calm is either patient or kind and vice versa. Everyone who is not brave is either brave or not happy. Everyone who is both not rich and not happy is wise. If someone is either not happy or brave then someone is happy or not wise and vice versa. If fred is calm or not kind then someone is patient and vice versa. Everyone who is either calm or generous is both old and tall and vice versa. Everyone who is rich or kind is both not old and curious and vice versa. Everyone who is either strong or not quiet is either rich or not brave and vice versa. Everyone who is not calm is humble. If someone is not old then someone is not funny. Everyone who is either old or not curious is patient or kind and vice versa. If paul is not tall or not brave then fred is curious and vice versa. Everyone who is both not patient and not brave is either not funny or not wise and vice versa. Everyone who is either not curious or wise is either not funny or patient. Everyone who is not strong is both patient and not curious. John is both not kind and not rich. John is both not patient and calm. Someone is not calm or old. Paul is not brave or curious. John is either quiet or not creative. Susan is both not quiet and not curious. Paul is not quiet or not generous. Susan is not kind or old. | Susan is not wise. | contradiction | (![X]:((old(X)<~>~rich(X))<=>(happy(X)&brave(X))))&
(![X]:((~funny(X)|~calm(X))<=>(patient(X)<~>kind(X))))&
(![X]:(~brave(X)=>(brave(X)<~>~happy(X))))&
(![X]:((~rich(X)&~happy(X))=>wise(X)))&
((?[X]:((~happy(X)<~>brave(X))))<=>(?[X]:((happy(X)|~wise(X)))))&
(((calm(fred)|~kind(fred)))<=>(?[X]:(patient(X))))&
(![X]:((calm(X)<~>generous(X))<=>(old(X)&tall(X))))&
(![X]:((rich(X)|kind(X))<=>(~old(X)&curious(X))))&
(![X]:((strong(X)<~>~quiet(X))<=>(rich(X)<~>~brave(X))))&
(![X]:(~calm(X)=>humble(X)))&
((?[X]:(~old(X)))=>(?[X]:(~funny(X))))&
(![X]:((old(X)<~>~curious(X))<=>(patient(X)|kind(X))))&
(((~tall(paul)|~brave(paul)))<=>(curious(fred)))&
(![X]:((~patient(X)&~brave(X))<=>(~funny(X)<~>~wise(X))))&
(![X]:((~curious(X)<~>wise(X))=>(~funny(X)<~>patient(X))))&
(![X]:(~strong(X)=>(patient(X)&~curious(X))))&
((~kind(john)&~rich(john)))&
((~patient(john)&calm(john)))&
(?[X]:((~calm(X)|old(X))))&
((~brave(paul)|curious(paul)))&
((quiet(john)<~>~creative(john)))&
((~quiet(susan)&~curious(susan)))&
((~quiet(paul)|~generous(paul)))&
((~kind(susan)|old(susan))) | ~wise(susan) | [
"p0",
"p2",
"p3",
"p7",
"p11",
"p13",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 308777971386265011122047
% SZS output start Proof for 308777971386265011122047
1. ! [X0] : ((old(X0) <~> ~rich(X0)) <=> (brave(X0) & happy(X0))) [input p0]
3. ! [X0] : (~brave(X0) => (brave(X0) <~> ~happy(X0))) [input p2]
4. ! [X0] : ((~happy(X0) & ~rich(X0)) => wise(X0)) [input p3]
8. ! [X0] : ((kind(X0) | rich(X0)) <=> (curious(X0) & ~old(X0))) [input p7]
12. ! [X0] : ((old(X0) <~> ~curious(X0)) <=> (kind(X0) | patient(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & ~patient(X0)) <=> (~funny(X0) <~> ~wise(X0))) [input p13]
15. ! [X0] : ((~curious(X0) <~> wise(X0)) => (~funny(X0) <~> patient(X0))) [input p14]
22. ~curious(susan) & ~quiet(susan) [input p21]
25. ~wise(susan) [input hypothesis]
29. ! [X0] : ((brave(X0) <~> ~happy(X0)) | brave(X0)) [ennf transformation 3]
30. ! [X0] : (wise(X0) | (happy(X0) | rich(X0))) [ennf transformation 4]
31. ! [X0] : (wise(X0) | happy(X0) | rich(X0)) [flattening 30]
33. ! [X0] : ((~funny(X0) <~> patient(X0)) | (~curious(X0) <=> wise(X0))) [ennf transformation 15]
35. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | (~brave(X0) | ~happy(X0))) & ((brave(X0) & happy(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [nnf transformation 1]
36. ! [X0] : ((((rich(X0) | ~old(X0)) & (~rich(X0) | old(X0))) | ~brave(X0) | ~happy(X0)) & ((brave(X0) & happy(X0)) | ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))))) [flattening 35]
39. ! [X0] : (((happy(X0) | ~brave(X0)) & (~happy(X0) | brave(X0))) | brave(X0)) [nnf transformation 29]
52. ! [X0] : (((kind(X0) | rich(X0)) | (~curious(X0) | old(X0))) & ((curious(X0) & ~old(X0)) | (~kind(X0) & ~rich(X0)))) [nnf transformation 8]
53. ! [X0] : ((kind(X0) | rich(X0) | ~curious(X0) | old(X0)) & ((curious(X0) & ~old(X0)) | (~kind(X0) & ~rich(X0)))) [flattening 52]
58. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~kind(X0) & ~patient(X0))) & ((kind(X0) | patient(X0)) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [nnf transformation 12]
59. ! [X0] : ((((curious(X0) | ~old(X0)) & (~curious(X0) | old(X0))) | (~kind(X0) & ~patient(X0))) & (kind(X0) | patient(X0) | ((old(X0) | curious(X0)) & (~curious(X0) | ~old(X0))))) [flattening 58]
62. ! [X0] : (((~brave(X0) & ~patient(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | (brave(X0) | patient(X0)))) [nnf transformation 14]
63. ! [X0] : (((~brave(X0) & ~patient(X0)) | ((~funny(X0) | wise(X0)) & (~wise(X0) | funny(X0)))) & (((wise(X0) | funny(X0)) & (~wise(X0) | ~funny(X0))) | brave(X0) | patient(X0))) [flattening 62]
64. ! [X0] : (((~patient(X0) | funny(X0)) & (patient(X0) | ~funny(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0)))) [nnf transformation 33]
73. ~brave(X0) | ~old(X0) | rich(X0) | ~happy(X0) [cnf transformation 36]
80. ~happy(X0) | brave(X0) | brave(X0) [cnf transformation 39]
82. wise(X0) | happy(X0) | rich(X0) [cnf transformation 31]
98. ~rich(X0) | ~old(X0) [cnf transformation 53]
99. ~kind(X0) | ~old(X0) [cnf transformation 53]
101. ~kind(X0) | curious(X0) [cnf transformation 53]
113. kind(X0) | patient(X0) | old(X0) | curious(X0) [cnf transformation 59]
115. ~curious(X0) | old(X0) | ~kind(X0) [cnf transformation 59]
124. ~patient(X0) | ~funny(X0) | wise(X0) [cnf transformation 63]
129. ~patient(X0) | funny(X0) | wise(X0) | curious(X0) [cnf transformation 64]
142. ~curious(susan) [cnf transformation 22]
145. ~wise(susan) [cnf transformation 25]
146. ~happy(X0) | brave(X0) [duplicate literal removal 80]
204. old(X0) | ~kind(X0) [subsumption resolution 115,101]
205. ~kind(X0) [subsumption resolution 204,99]
206. curious(X0) | old(X0) | patient(X0) [subsumption resolution 113,205]
223. ~patient(X0) | wise(X0) | curious(X0) [subsumption resolution 129,124]
313. happy(susan) | rich(susan) [resolution 82,145]
322. 28 <=> old(susan) [avatar definition]
326. 29 <=> brave(susan) [avatar definition]
328. brave(susan) <- (29) [avatar component clause 326]
341. 31 <=> rich(susan) [avatar definition]
342. ~rich(susan) <- (~31) [avatar component clause 341]
343. rich(susan) <- (31) [avatar component clause 341]
345. 32 <=> happy(susan) [avatar definition]
347. happy(susan) <- (32) [avatar component clause 345]
348. 31 | 32 [avatar split clause 313,345,341]
377. ~old(susan) <- (31) [resolution 343,98]
382. ~28 | ~31 [avatar split clause 377,341,322]
389. brave(susan) <- (32) [resolution 347,146]
390. 29 | ~32 [avatar split clause 389,345,326]
434. old(susan) | patient(susan) [resolution 206,142]
439. 45 <=> patient(susan) [avatar definition]
441. patient(susan) <- (45) [avatar component clause 439]
442. 45 | 28 [avatar split clause 434,322,439]
475. ~old(susan) | rich(susan) | ~happy(susan) <- (29) [resolution 328,73]
481. ~old(susan) | ~happy(susan) <- (29, ~31) [subsumption resolution 475,342]
482. ~old(susan) <- (29, ~31, 32) [subsumption resolution 481,347]
483. ~28 | ~29 | 31 | ~32 [avatar split clause 482,345,341,326,322]
489. wise(susan) | curious(susan) <- (45) [resolution 441,223]
502. curious(susan) <- (45) [subsumption resolution 489,145]
503. $false <- (45) [subsumption resolution 502,142]
504. ~45 [avatar contradiction clause 503]
507. $false [avatar sat refutation 348,382,390,442,483,504]
% SZS output end Proof for 308777971386265011122047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or calm is calm or not creative. Everyone who is rich is quiet and vice versa. If someone is both old and tall then susan is either not humble or not calm and vice versa. Everyone who is creative or not creative is not rich. Everyone who is not humble or tall is either old or not generous and vice versa. Everyone who is either not rich or humble is happy or not creative and vice versa. If someone is both not kind and humble then mary is both not strong and not curious and vice versa. Everyone who is both not humble and not tall is wise or not old. If mary is not calm then someone is both curious and not humble and vice versa. Everyone who is not tall or rich is either creative or not curious. If someone is either not brave or not kind then alice is generous or not brave and vice versa. If someone is either not curious or rich then someone is either not curious or kind and vice versa. If someone is both not calm and not curious then lucy is not tall. Everyone who is not strong or strong is tall and vice versa. If someone is strong then someone is not kind and vice versa. If someone is either wise or not humble then someone is kind or tall and vice versa. Mary is either creative or not creative. Someone is patient or not tall. Someone is not wise or kind. Someone is patient or wise. Lucy is either not brave or humble. Someone is either not humble or not rich. Someone is generous. | Susan is rich. | contradiction | (![X]:((kind(X)<~>calm(X))=>(calm(X)|~creative(X))))&
(![X]:(rich(X)<=>quiet(X)))&
((?[X]:((old(X)&tall(X))))<=>((~humble(susan)<~>~calm(susan))))&
(![X]:((creative(X)|~creative(X))=>~rich(X)))&
(![X]:((~humble(X)|tall(X))<=>(old(X)<~>~generous(X))))&
(![X]:((~rich(X)<~>humble(X))<=>(happy(X)|~creative(X))))&
((?[X]:((~kind(X)&humble(X))))<=>((~strong(mary)&~curious(mary))))&
(![X]:((~humble(X)&~tall(X))=>(wise(X)|~old(X))))&
((~calm(mary))<=>(?[X]:((curious(X)&~humble(X)))))&
(![X]:((~tall(X)|rich(X))=>(creative(X)<~>~curious(X))))&
((?[X]:((~brave(X)<~>~kind(X))))<=>((generous(alice)|~brave(alice))))&
((?[X]:((~curious(X)<~>rich(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:((~calm(X)&~curious(X))))=>(~tall(lucy)))&
(![X]:((~strong(X)|strong(X))<=>tall(X)))&
((?[X]:(strong(X)))<=>(?[X]:(~kind(X))))&
((?[X]:((wise(X)<~>~humble(X))))<=>(?[X]:((kind(X)|tall(X)))))&
((creative(mary)<~>~creative(mary)))&
(?[X]:((patient(X)|~tall(X))))&
(?[X]:((~wise(X)|kind(X))))&
(?[X]:((patient(X)|wise(X))))&
((~brave(lucy)<~>humble(lucy)))&
(?[X]:((~humble(X)<~>~rich(X))))&
(?[X]:(generous(X))) | rich(susan) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 3892498427505670784650901
% SZS output start Proof for 3892498427505670784650901
4. ! [X0] : ((~creative(X0) | creative(X0)) => ~rich(X0)) [input p3]
24. rich(susan) [input hypothesis]
32. ! [X0] : (~rich(X0) | (creative(X0) & ~creative(X0))) [ennf transformation 4]
98. ~rich(X0) | ~creative(X0) [cnf transformation 32]
99. ~rich(X0) | creative(X0) [cnf transformation 32]
158. rich(susan) [cnf transformation 24]
185. ~rich(X0) [subsumption resolution 98,99]
349. $false [subsumption resolution 158,185]
% SZS output end Proof for 3892498427505670784650901
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not happy or curious then mary is both not creative and creative. Everyone who is not humble or not tall is both generous and strong and vice versa. Everyone who is either not calm or not generous is either not kind or brave. Everyone who is either happy or not rich is both not brave and not strong. Everyone who is both not rich and not quiet is curious and vice versa. Everyone who is either happy or humble is brave. If fred is both not rich and tall then someone is quiet or not patient and vice versa. If someone is both not curious and not strong then someone is happy or not quiet. Everyone who is not funny or generous is not kind and vice versa. Everyone who is both not brave and wise is happy and vice versa. If lucy is curious then john is patient or not old. Everyone who is creative is either strong or not happy. If lucy is creative or not funny then fred is either creative or not generous and vice versa. Everyone who is not creative is rich and vice versa. Everyone who is not rich is both not strong and not patient and vice versa. If paul is quiet then someone is both not generous and quiet. Paul is rich. John is kind. Someone is not funny or funny. | Mary is kind. | neutral | ((?[X]:((~happy(X)<~>curious(X))))=>((~creative(mary)&creative(mary))))&
(![X]:((~humble(X)|~tall(X))<=>(generous(X)&strong(X))))&
(![X]:((~calm(X)<~>~generous(X))=>(~kind(X)<~>brave(X))))&
(![X]:((happy(X)<~>~rich(X))=>(~brave(X)&~strong(X))))&
(![X]:((~rich(X)&~quiet(X))<=>curious(X)))&
(![X]:((happy(X)<~>humble(X))=>brave(X)))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)|~patient(X)))))&
((?[X]:((~curious(X)&~strong(X))))=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:((~funny(X)|generous(X))<=>~kind(X)))&
(![X]:((~brave(X)&wise(X))<=>happy(X)))&
((curious(lucy))=>((patient(john)|~old(john))))&
(![X]:(creative(X)=>(strong(X)<~>~happy(X))))&
(((creative(lucy)|~funny(lucy)))<=>((creative(fred)<~>~generous(fred))))&
(![X]:(~creative(X)<=>rich(X)))&
(![X]:(~rich(X)<=>(~strong(X)&~patient(X))))&
((quiet(paul))=>(?[X]:((~generous(X)&quiet(X)))))&
(rich(paul))&
(kind(john))&
(?[X]:((~funny(X)|funny(X)))) | kind(mary) | [] | null | 0 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.