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 alice is rich or tall then alice is not kind. Everyone who is both curious and kind is either creative or quiet and vice versa. If someone is both not kind and rich then someone is quiet and vice versa. If someone is patient then someone is kind. Everyone who is rich is patient and vice versa. Everyone who is both humble and not rich is not quiet and vice versa. Everyone who is not patient or funny is not curious or not generous. Everyone who is both funny and not old is not happy or not strong. If someone is old then mary is not creative and vice versa. Everyone who is not old is calm or old and vice versa. Everyone who is both not funny and brave is strong or not strong. Everyone who is not funny or patient is not curious or patient and vice versa. If lucy is not kind or happy then susan is both not calm and creative. If paul is both creative and rich then mary is either not brave or not rich and vice versa. Everyone who is both curious and not humble is wise and vice versa. If john is not quiet then susan is either not humble or funny. Someone is not kind or kind. Lucy is either not calm or not tall. John is patient. Someone is both not brave and not generous. Fred is curious or not tall. Someone is not quiet. Someone is rich. | Mary is not brave. | neutral | (((rich(alice)|tall(alice)))=>(~kind(alice)))&
(![X]:((curious(X)&kind(X))<=>(creative(X)<~>quiet(X))))&
((?[X]:((~kind(X)&rich(X))))<=>(?[X]:(quiet(X))))&
((?[X]:(patient(X)))=>(?[X]:(kind(X))))&
(![X]:(rich(X)<=>patient(X)))&
(![X]:((humble(X)&~rich(X))<=>~quiet(X)))&
(![X]:((~patient(X)|funny(X))=>(~curious(X)|~generous(X))))&
(![X]:((funny(X)&~old(X))=>(~happy(X)|~strong(X))))&
((?[X]:(old(X)))<=>(~creative(mary)))&
(![X]:(~old(X)<=>(calm(X)|old(X))))&
(![X]:((~funny(X)&brave(X))=>(strong(X)|~strong(X))))&
(![X]:((~funny(X)|patient(X))<=>(~curious(X)|patient(X))))&
(((~kind(lucy)|happy(lucy)))=>((~calm(susan)&creative(susan))))&
(((creative(paul)&rich(paul)))<=>((~brave(mary)<~>~rich(mary))))&
(![X]:((curious(X)&~humble(X))<=>wise(X)))&
((~quiet(john))=>((~humble(susan)<~>funny(susan))))&
(?[X]:((~kind(X)|kind(X))))&
((~calm(lucy)<~>~tall(lucy)))&
(patient(john))&
(?[X]:((~brave(X)&~generous(X))))&
((curious(fred)|~tall(fred)))&
(?[X]:(~quiet(X)))&
(?[X]:(rich(X))) | ~brave(mary) | []
| null | 0 |
Everyone who is old is either not humble or not strong. Everyone who is creative or wise is both not generous and not curious and vice versa. Everyone who is both not rich and funny is wise or curious. If someone is either funny or creative then someone is either not kind or rich and vice versa. If mary is either brave or not creative then alice is both not tall and tall. If someone is both not strong and not humble then alice is tall. If someone is both old and not kind then someone is either not creative or not rich. Everyone who is both not calm and not wise is both funny and not quiet. If mary is both not calm and happy then someone is creative or not old. Everyone who is not rich or not quiet is not curious. Everyone who is calm is funny and vice versa. If someone is either not generous or not brave then mary is patient or not generous. Everyone who is either curious or patient is both not rich and not humble. If lucy is not generous or generous then someone is either quiet or not rich and vice versa. If someone is either not tall or old then fred is not funny or strong. If alice is both not funny and not quiet then someone is both old and quiet and vice versa. Paul is not funny. Lucy is not funny. Someone is not creative. Someone is both not rich and strong. Someone is old or not strong. Lucy is either tall or curious. Someone is happy. Alice is not funny or not old. | Lucy is generous. | contradiction | (![X]:(old(X)=>(~humble(X)<~>~strong(X))))&
(![X]:((creative(X)|wise(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~rich(X)&funny(X))=>(wise(X)|curious(X))))&
((?[X]:((funny(X)<~>creative(X))))<=>(?[X]:((~kind(X)<~>rich(X)))))&
(((brave(mary)<~>~creative(mary)))=>((~tall(alice)&tall(alice))))&
((?[X]:((~strong(X)&~humble(X))))=>(tall(alice)))&
((?[X]:((old(X)&~kind(X))))=>(?[X]:((~creative(X)<~>~rich(X)))))&
(![X]:((~calm(X)&~wise(X))=>(funny(X)&~quiet(X))))&
(((~calm(mary)&happy(mary)))=>(?[X]:((creative(X)|~old(X)))))&
(![X]:((~rich(X)|~quiet(X))=>~curious(X)))&
(![X]:(calm(X)<=>funny(X)))&
((?[X]:((~generous(X)<~>~brave(X))))=>((patient(mary)|~generous(mary))))&
(![X]:((curious(X)<~>patient(X))=>(~rich(X)&~humble(X))))&
(((~generous(lucy)|generous(lucy)))<=>(?[X]:((quiet(X)<~>~rich(X)))))&
((?[X]:((~tall(X)<~>old(X))))=>((~funny(fred)|strong(fred))))&
(((~funny(alice)&~quiet(alice)))<=>(?[X]:((old(X)&quiet(X)))))&
(~funny(paul))&
(~funny(lucy))&
(?[X]:(~creative(X)))&
(?[X]:((~rich(X)&strong(X))))&
(?[X]:((old(X)|~strong(X))))&
((tall(lucy)<~>curious(lucy)))&
(?[X]:(happy(X)))&
((~funny(alice)|~old(alice))) | generous(lucy) | [
"p1",
"p7",
"p10",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 2087179740974864318742577
% SZS output start Proof for 2087179740974864318742577
2. ! [X0] : ((wise(X0) | creative(X0)) <=> (~curious(X0) & ~generous(X0))) [input p1]
8. ! [X0] : ((~wise(X0) & ~calm(X0)) => (~quiet(X0) & funny(X0))) [input p7]
11. ! [X0] : (calm(X0) <=> funny(X0)) [input p10]
18. ~funny(lucy) [input p17]
25. generous(lucy) [input hypothesis]
28. ! [X0] : (calm(X0) => funny(X0)) [unused predicate definition removal 11]
35. ! [X0] : ((~quiet(X0) & funny(X0)) | (wise(X0) | calm(X0))) [ennf transformation 8]
36. ! [X0] : ((~quiet(X0) & funny(X0)) | wise(X0) | calm(X0)) [flattening 35]
40. ! [X0] : (funny(X0) | ~calm(X0)) [ennf transformation 28]
47. ! [X0] : (((wise(X0) | creative(X0)) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [nnf transformation 2]
48. ! [X0] : ((wise(X0) | creative(X0) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | (~wise(X0) & ~creative(X0)))) [flattening 47]
86. ~generous(X0) | ~wise(X0) [cnf transformation 48]
106. calm(X0) | wise(X0) | funny(X0) [cnf transformation 36]
111. ~calm(X0) | funny(X0) [cnf transformation 40]
131. ~funny(lucy) [cnf transformation 18]
140. generous(lucy) [cnf transformation 25]
245. 24 <=> generous(lucy) [avatar definition]
246. generous(lucy) <- (24) [avatar component clause 245]
323. 24 [avatar split clause 140,245]
325. ~wise(lucy) <- (24) [resolution 86,246]
338. wise(X0) | funny(X0) | funny(X0) [resolution 106,111]
339. funny(X0) | wise(X0) [duplicate literal removal 338]
350. wise(lucy) [resolution 339,131]
353. $false <- (24) [subsumption resolution 350,325]
354. ~24 [avatar contradiction clause 353]
355. $false [avatar sat refutation 323,354]
% SZS output end Proof for 2087179740974864318742577
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or quiet is both brave and not curious.
Everyone who is either not patient or not brave is both not kind and humble and vice versa.
If someone is tall or not quiet then fred is happy.
If alice is either not calm or not old then lucy is not funny.
If lucy is curious or not kind then alice is both strong and old.
If susan is both not wise and kind then someone is either generous or not humble and vice versa.
Everyone who is both not brave and quiet is both not rich and rich and vice versa.
Everyone who is humble or not rich is not happy.
Everyone who is either kind or not quiet is either not patient or not old and vice versa.
Everyone who is both creative and not funny is both not calm and not curious.
Everyone who is calm or not calm is either not patient or not curious and vice versa.
Everyone who is both not happy and not patient is either creative or not old and vice versa.
Everyone who is either not curious or not funny is both patient and funny and vice versa.
Everyone who is either creative or kind is both happy and not tall.
If susan is both rich and not humble then someone is both not creative and not old.
Everyone who is both happy and funny is brave or not humble.
Fred is either not curious or not quiet.
Someone is rich.
Lucy is both not old and not kind.
Someone is wise or rich.
Someone is wise or brave.
Susan is not funny.
Fred is quiet or curious. | Alice is not brave. | contradiction | (![X]:((funny(X)<~>quiet(X))=>(brave(X)&~curious(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~kind(X)&humble(X))))&
((?[X]:((tall(X)|~quiet(X))))=>(happy(fred)))&
(((~calm(alice)<~>~old(alice)))=>(~funny(lucy)))&
(((curious(lucy)|~kind(lucy)))=>((strong(alice)&old(alice))))&
(((~wise(susan)&kind(susan)))<=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~brave(X)&quiet(X))<=>(~rich(X)&rich(X))))&
(![X]:((humble(X)|~rich(X))=>~happy(X)))&
(![X]:((kind(X)<~>~quiet(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((creative(X)&~funny(X))=>(~calm(X)&~curious(X))))&
(![X]:((calm(X)|~calm(X))<=>(~patient(X)<~>~curious(X))))&
(![X]:((~happy(X)&~patient(X))<=>(creative(X)<~>~old(X))))&
(![X]:((~curious(X)<~>~funny(X))<=>(patient(X)&funny(X))))&
(![X]:((creative(X)<~>kind(X))=>(happy(X)&~tall(X))))&
(((rich(susan)&~humble(susan)))=>(?[X]:((~creative(X)&~old(X)))))&
(![X]:((happy(X)&funny(X))=>(brave(X)|~humble(X))))&
((~curious(fred)<~>~quiet(fred)))&
(?[X]:(rich(X)))&
((~old(lucy)&~kind(lucy)))&
(?[X]:((wise(X)|rich(X))))&
(?[X]:((wise(X)|brave(X))))&
(~funny(susan))&
((quiet(fred)|curious(fred))) | ~brave(alice) | [
"p0",
"p1",
"p4",
"p6",
"p8",
"p10",
"p12",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 2852929651999924731144476
% SZS output start Proof for 2852929651999924731144476
1. ! [X0] : ((funny(X0) <~> quiet(X0)) => (~curious(X0) & brave(X0))) [input p0]
2. ! [X0] : ((~patient(X0) <~> ~brave(X0)) <=> (humble(X0) & ~kind(X0))) [input p1]
5. (~kind(lucy) | curious(lucy)) => (old(alice) & strong(alice)) [input p4]
7. ! [X0] : ((quiet(X0) & ~brave(X0)) <=> (rich(X0) & ~rich(X0))) [input p6]
9. ! [X0] : ((kind(X0) <~> ~quiet(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((~calm(X0) | calm(X0)) <=> (~patient(X0) <~> ~curious(X0))) [input p10]
13. ! [X0] : ((~curious(X0) <~> ~funny(X0)) <=> (funny(X0) & patient(X0))) [input p12]
19. ~kind(lucy) & ~old(lucy) [input p18]
24. ~brave(alice) [input hypothesis]
25. (~kind(lucy) | curious(lucy)) => old(alice) [pure predicate removal 5]
28. ! [X0] : ((~curious(X0) & brave(X0)) | (funny(X0) <=> quiet(X0))) [ennf transformation 1]
31. old(alice) | (kind(lucy) & ~curious(lucy)) [ennf transformation 25]
40. ! [X0] : ((~curious(X0) & brave(X0)) | ((funny(X0) | ~quiet(X0)) & (quiet(X0) | ~funny(X0)))) [nnf transformation 28]
41. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [nnf transformation 2]
42. ! [X0] : ((((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0))))) [flattening 41]
49. ! [X0] : (((quiet(X0) & ~brave(X0)) | (~rich(X0) | rich(X0))) & ((rich(X0) & ~rich(X0)) | (~quiet(X0) | brave(X0)))) [nnf transformation 7]
50. ! [X0] : (((quiet(X0) & ~brave(X0)) | ~rich(X0) | rich(X0)) & ((rich(X0) & ~rich(X0)) | ~quiet(X0) | brave(X0))) [flattening 49]
51. ! [X0] : ((((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0))))) [nnf transformation 9]
52. ! [X0] : (((~calm(X0) | calm(X0)) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (calm(X0) & ~calm(X0)))) [nnf transformation 11]
53. ! [X0] : ((~calm(X0) | calm(X0) | ((~patient(X0) | curious(X0)) & (~curious(X0) | patient(X0)))) & (((curious(X0) | patient(X0)) & (~curious(X0) | ~patient(X0))) | (calm(X0) & ~calm(X0)))) [flattening 52]
56. ! [X0] : ((((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | (~funny(X0) | ~patient(X0))) & ((funny(X0) & patient(X0)) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0))))) [nnf transformation 13]
57. ! [X0] : ((((funny(X0) | curious(X0)) & (~funny(X0) | ~curious(X0))) | ~funny(X0) | ~patient(X0)) & ((funny(X0) & patient(X0)) | ((~curious(X0) | funny(X0)) & (~funny(X0) | curious(X0))))) [flattening 56]
70. ~curious(X0) | quiet(X0) | ~funny(X0) [cnf transformation 40]
73. ~kind(X0) | ~patient(X0) | brave(X0) [cnf transformation 42]
82. old(alice) | kind(lucy) [cnf transformation 31]
89. ~rich(X0) | ~quiet(X0) | brave(X0) [cnf transformation 50]
90. ~quiet(X0) | rich(X0) | brave(X0) [cnf transformation 50]
96. ~old(X0) | ~patient(X0) | kind(X0) | quiet(X0) [cnf transformation 51]
107. curious(X0) | patient(X0) | ~calm(X0) [cnf transformation 53]
108. calm(X0) | patient(X0) | curious(X0) [cnf transformation 53]
120. funny(X0) | ~curious(X0) | funny(X0) [cnf transformation 57]
132. ~kind(lucy) [cnf transformation 19]
137. ~brave(alice) [cnf transformation 24]
138. ~curious(X0) | funny(X0) [duplicate literal removal 120]
149. 3 <=> old(alice) [avatar definition]
151. old(alice) <- (3) [avatar component clause 149]
163. 6 <=> kind(lucy) [avatar definition]
166. 6 | 3 [avatar split clause 82,149,163]
200. ~quiet(X0) | brave(X0) [subsumption resolution 89,90]
201. patient(X0) | curious(X0) [subsumption resolution 107,108]
231. ~6 [avatar split clause 132,163]
409. 40 <=> kind(alice) [avatar definition]
410. kind(alice) <- (40) [avatar component clause 409]
413. 41 <=> quiet(alice) [avatar definition]
414. quiet(alice) <- (41) [avatar component clause 413]
415. ~quiet(alice) <- (~41) [avatar component clause 413]
417. 42 <=> patient(alice) [avatar definition]
419. ~patient(alice) <- (~42) [avatar component clause 417]
423. ~patient(alice) | kind(alice) | quiet(alice) <- (3) [resolution 96,151]
430. curious(alice) <- (~42) [resolution 419,201]
541. quiet(alice) | ~funny(alice) <- (~42) [resolution 430,70]
542. funny(alice) <- (~42) [resolution 430,138]
543. ~funny(alice) <- (~41, ~42) [subsumption resolution 541,415]
544. $false <- (~41, ~42) [subsumption resolution 542,543]
545. 41 | 42 [avatar contradiction clause 544]
548. ~patient(alice) | kind(alice) <- (3, ~41) [subsumption resolution 423,415]
549. 40 | ~42 | ~3 | 41 [avatar split clause 548,413,149,417,409]
553. ~patient(alice) | brave(alice) <- (40) [resolution 410,73]
560. ~patient(alice) <- (40) [subsumption resolution 553,137]
561. ~42 | ~40 [avatar split clause 560,409,417]
565. brave(alice) <- (41) [resolution 414,200]
567. $false <- (41) [subsumption resolution 565,137]
568. ~41 [avatar contradiction clause 567]
569. $false [avatar sat refutation 166,231,545,549,561,568]
% SZS output end Proof for 2852929651999924731144476
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both brave and not wise then alice is either not creative or not humble and vice versa.
If mary is not kind then someone is either funny or brave and vice versa.
Everyone who is both not patient and rich is both patient and not quiet.
If someone is strong then someone is both not strong and humble and vice versa.
If someone is either not happy or not calm then lucy is not humble.
Everyone who is both not brave and humble is either tall or kind and vice versa.
Everyone who is either kind or not funny is curious or tall and vice versa.
Everyone who is both not tall and old is not kind or curious.
If someone is either funny or not wise then someone is rich.
Everyone who is either not brave or patient is both generous and kind.
Everyone who is both not patient and not generous is not kind or not patient.
If someone is either funny or not rich then someone is old and vice versa.
Everyone who is both not wise and curious is not funny or not humble and vice versa.
Everyone who is not humble is not humble or not wise and vice versa.
Everyone who is patient is creative and vice versa.
If mary is not tall or not funny then someone is quiet or tall and vice versa.
Someone is not happy.
Paul is both not wise and not happy.
Fred is calm.
Mary is rich or happy.
Fred is not old.
Someone is both happy and rich.
Someone is both not happy and old.
Paul is either rich or not patient. | Paul is humble. | contradiction | (((brave(mary)&~wise(mary)))<=>((~creative(alice)<~>~humble(alice))))&
((~kind(mary))<=>(?[X]:((funny(X)<~>brave(X)))))&
(![X]:((~patient(X)&rich(X))=>(patient(X)&~quiet(X))))&
((?[X]:(strong(X)))<=>(?[X]:((~strong(X)&humble(X)))))&
((?[X]:((~happy(X)<~>~calm(X))))=>(~humble(lucy)))&
(![X]:((~brave(X)&humble(X))<=>(tall(X)<~>kind(X))))&
(![X]:((kind(X)<~>~funny(X))<=>(curious(X)|tall(X))))&
(![X]:((~tall(X)&old(X))=>(~kind(X)|curious(X))))&
((?[X]:((funny(X)<~>~wise(X))))=>(?[X]:(rich(X))))&
(![X]:((~brave(X)<~>patient(X))=>(generous(X)&kind(X))))&
(![X]:((~patient(X)&~generous(X))=>(~kind(X)|~patient(X))))&
((?[X]:((funny(X)<~>~rich(X))))<=>(?[X]:(old(X))))&
(![X]:((~wise(X)&curious(X))<=>(~funny(X)|~humble(X))))&
(![X]:(~humble(X)<=>(~humble(X)|~wise(X))))&
(![X]:(patient(X)<=>creative(X)))&
(((~tall(mary)|~funny(mary)))<=>(?[X]:((quiet(X)|tall(X)))))&
(?[X]:(~happy(X)))&
((~wise(paul)&~happy(paul)))&
(calm(fred))&
((rich(mary)|happy(mary)))&
(~old(fred))&
(?[X]:((happy(X)&rich(X))))&
(?[X]:((~happy(X)&old(X))))&
((rich(paul)<~>~patient(paul))) | humble(paul) | [
"p13",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4203267502069227361452508
% SZS output start Proof for 4203267502069227361452508
14. ! [X0] : (~humble(X0) <=> (~wise(X0) | ~humble(X0))) [input p13]
18. ~happy(paul) & ~wise(paul) [input p17]
25. humble(paul) [input hypothesis]
66. ! [X0] : ((~humble(X0) | (wise(X0) & humble(X0))) & ((~wise(X0) | ~humble(X0)) | humble(X0))) [nnf transformation 14]
67. ! [X0] : ((~humble(X0) | (wise(X0) & humble(X0))) & (~wise(X0) | ~humble(X0) | humble(X0))) [flattening 66]
126. ~humble(X0) | wise(X0) [cnf transformation 67]
134. ~wise(paul) [cnf transformation 18]
145. humble(paul) [cnf transformation 25]
312. wise(paul) [resolution 126,145]
314. $false [subsumption resolution 312,134]
% SZS output end Proof for 4203267502069227361452508
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not old then someone is not quiet and vice versa.
If susan is calm then someone is not patient and vice versa.
If paul is either not brave or not humble then john is both not generous and not happy.
Everyone who is both not rich and humble is both not creative and not wise and vice versa.
If someone is not rich or rich then someone is not strong.
If someone is both not wise and tall then someone is both not funny and happy and vice versa.
Everyone who is both not brave and not rich is patient.
Everyone who is not brave is patient or not strong and vice versa.
Everyone who is either not brave or curious is not strong.
If paul is either rich or not quiet then someone is both not strong and calm and vice versa.
Everyone who is either happy or not creative is either not brave or not curious and vice versa.
Everyone who is patient is either funny or not wise and vice versa.
Everyone who is either not old or not calm is either kind or rich.
Everyone who is either rich or not happy is both not funny and not humble.
If someone is both not humble and not funny then someone is either not creative or not humble.
Everyone who is curious or wise is both calm and strong.
Alice is either not old or happy.
Susan is patient.
Susan is both not funny and curious.
Mary is happy or not quiet.
Mary is both not funny and not calm.
Paul is both rich and not humble.
Someone is not happy or not calm.
Someone is either not brave or wise. | Susan is wise. | contradiction | ((~old(paul))<=>(?[X]:(~quiet(X))))&
((calm(susan))<=>(?[X]:(~patient(X))))&
(((~brave(paul)<~>~humble(paul)))=>((~generous(john)&~happy(john))))&
(![X]:((~rich(X)&humble(X))<=>(~creative(X)&~wise(X))))&
((?[X]:((~rich(X)|rich(X))))=>(?[X]:(~strong(X))))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:((~funny(X)&happy(X)))))&
(![X]:((~brave(X)&~rich(X))=>patient(X)))&
(![X]:(~brave(X)<=>(patient(X)|~strong(X))))&
(![X]:((~brave(X)<~>curious(X))=>~strong(X)))&
(((rich(paul)<~>~quiet(paul)))<=>(?[X]:((~strong(X)&calm(X)))))&
(![X]:((happy(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:(patient(X)<=>(funny(X)<~>~wise(X))))&
(![X]:((~old(X)<~>~calm(X))=>(kind(X)<~>rich(X))))&
(![X]:((rich(X)<~>~happy(X))=>(~funny(X)&~humble(X))))&
((?[X]:((~humble(X)&~funny(X))))=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:((curious(X)|wise(X))=>(calm(X)&strong(X))))&
((~old(alice)<~>happy(alice)))&
(patient(susan))&
((~funny(susan)&curious(susan)))&
((happy(mary)|~quiet(mary)))&
((~funny(mary)&~calm(mary)))&
((rich(paul)&~humble(paul)))&
(?[X]:((~happy(X)|~calm(X))))&
(?[X]:((~brave(X)<~>wise(X)))) | wise(susan) | [
"p11",
"p17",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 5283015755085084878360885
% SZS output start Proof for 5283015755085084878360885
12. ! [X0] : (patient(X0) <=> (funny(X0) <~> ~wise(X0))) [input p11]
18. patient(susan) [input p17]
19. curious(susan) & ~funny(susan) [input p18]
25. wise(susan) [input hypothesis]
66. ! [X0] : ((patient(X0) | ((funny(X0) | wise(X0)) & (~wise(X0) | ~funny(X0)))) & (((wise(X0) | ~funny(X0)) & (~wise(X0) | funny(X0))) | ~patient(X0))) [nnf transformation 12]
115. ~wise(X0) | funny(X0) | ~patient(X0) [cnf transformation 66]
135. patient(susan) [cnf transformation 18]
136. ~funny(susan) [cnf transformation 19]
146. wise(susan) [cnf transformation 25]
364. funny(susan) | ~patient(susan) [resolution 115,146]
367. ~patient(susan) [subsumption resolution 364,136]
368. $false [subsumption resolution 367,135]
% SZS output end Proof for 5283015755085084878360885
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is brave or not curious.
Everyone who is calm or not tall is curious.
If someone is not tall then fred is rich.
If john is both not funny and not generous then alice is either not strong or happy.
If someone is strong or old then someone is creative or not rich.
If someone is not brave or not old then alice is kind or brave and vice versa.
Everyone who is both rich and not quiet is both not patient and not happy.
Everyone who is funny is not calm or not patient and vice versa.
Everyone who is tall is both happy and not strong.
If someone is brave then someone is not rich.
If someone is happy then lucy is both rich and not old and vice versa.
If alice is either not patient or quiet then alice is not happy and vice versa.
If alice is not curious then someone is not brave or not generous.
Everyone who is not humble is tall.
Everyone who is not humble or patient is either not patient or kind and vice versa.
If someone is either not tall or curious then fred is both not calm and creative.
John is either not calm or old.
Someone is not wise.
Someone is either not quiet or not tall.
Someone is both not quiet and strong.
Alice is funny or humble.
John is either humble or calm.
Lucy is strong.
Someone is both not brave and not patient. | Alice is kind. | neutral | (![X]:((~creative(X)<~>old(X))=>(brave(X)|~curious(X))))&
(![X]:((calm(X)|~tall(X))=>curious(X)))&
((?[X]:(~tall(X)))=>(rich(fred)))&
(((~funny(john)&~generous(john)))=>((~strong(alice)<~>happy(alice))))&
((?[X]:((strong(X)|old(X))))=>(?[X]:((creative(X)|~rich(X)))))&
((?[X]:((~brave(X)|~old(X))))<=>((kind(alice)|brave(alice))))&
(![X]:((rich(X)&~quiet(X))=>(~patient(X)&~happy(X))))&
(![X]:(funny(X)<=>(~calm(X)|~patient(X))))&
(![X]:(tall(X)=>(happy(X)&~strong(X))))&
((?[X]:(brave(X)))=>(?[X]:(~rich(X))))&
((?[X]:(happy(X)))<=>((rich(lucy)&~old(lucy))))&
(((~patient(alice)<~>quiet(alice)))<=>(~happy(alice)))&
((~curious(alice))=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:(~humble(X)=>tall(X)))&
(![X]:((~humble(X)|patient(X))<=>(~patient(X)<~>kind(X))))&
((?[X]:((~tall(X)<~>curious(X))))=>((~calm(fred)&creative(fred))))&
((~calm(john)<~>old(john)))&
(?[X]:(~wise(X)))&
(?[X]:((~quiet(X)<~>~tall(X))))&
(?[X]:((~quiet(X)&strong(X))))&
((funny(alice)|humble(alice)))&
((humble(john)<~>calm(john)))&
(strong(lucy))&
(?[X]:((~brave(X)&~patient(X)))) | kind(alice) | []
| null | 0 |
Everyone who is either not rich or old is either not creative or not wise. If someone is patient or not kind then lucy is not patient and vice versa. If someone is either old or quiet then susan is not brave or not kind and vice versa. Everyone who is both patient and not funny is either not funny or not calm and vice versa. If paul is not calm then paul is curious or patient and vice versa. Everyone who is 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. John is both kind and happy. Someone is both wise and curious. Someone is either strong or patient. Someone is either not wise or patient. Someone is happy or creative. Someone is both not generous and not tall. Susan is not generous or not old. | Susan is humble. | neutral | (![X]:((~rich(X)<~>old(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(~patient(lucy)))&
((?[X]:((old(X)<~>quiet(X))))<=>((~brave(susan)|~kind(susan))))&
(![X]:((patient(X)&~funny(X))<=>(~funny(X)<~>~calm(X))))&
((~calm(paul))<=>((curious(paul)|patient(paul))))&
(![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))))&
((kind(john)&happy(john)))&
(?[X]:((wise(X)&curious(X))))&
(?[X]:((strong(X)<~>patient(X))))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:((~generous(X)&~tall(X))))&
((~generous(susan)|~old(susan))) | humble(susan) | []
| null | 0 |
If lucy is not kind then someone is either old or patient and vice versa. Everyone who is tall is both funny and not tall and vice versa. Everyone who is not tall or not generous is not generous and vice versa. Everyone who is either calm or rich is both not funny and curious. If lucy is strong then someone is funny or not kind. If someone is not kind or old then someone is not strong or not old. If fred is either not tall or strong then someone is either not wise or generous and vice versa. If alice is both not creative and rich then someone is both tall and humble and vice versa. Everyone who is not strong is not generous and vice versa. If fred is creative or not kind then someone is not creative or creative and vice versa. Everyone who is patient is not calm or not strong and vice versa. If someone is strong then john is either generous or happy. If someone is either generous or not brave then mary is either calm or not quiet. Everyone who is either kind or wise is both not curious and calm and vice versa. Everyone who is either not strong or quiet is both wise and not patient. Everyone who is not happy or patient is not wise and vice versa. Someone is wise or not wise. Paul is not rich. Alice is both not funny and rich. Someone is not funny. Someone is either not curious or generous. Paul is humble or creative. Someone is generous or creative. Paul is both not old and humble. | Paul is quiet. | entailment | ((~kind(lucy))<=>(?[X]:((old(X)<~>patient(X)))))&
(![X]:(tall(X)<=>(funny(X)&~tall(X))))&
(![X]:((~tall(X)|~generous(X))<=>~generous(X)))&
(![X]:((calm(X)<~>rich(X))=>(~funny(X)&curious(X))))&
((strong(lucy))=>(?[X]:((funny(X)|~kind(X)))))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:((~strong(X)|~old(X)))))&
(((~tall(fred)<~>strong(fred)))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(((~creative(alice)&rich(alice)))<=>(?[X]:((tall(X)&humble(X)))))&
(![X]:(~strong(X)<=>~generous(X)))&
(((creative(fred)|~kind(fred)))<=>(?[X]:((~creative(X)|creative(X)))))&
(![X]:(patient(X)<=>(~calm(X)|~strong(X))))&
((?[X]:(strong(X)))=>((generous(john)<~>happy(john))))&
((?[X]:((generous(X)<~>~brave(X))))=>((calm(mary)<~>~quiet(mary))))&
(![X]:((kind(X)<~>wise(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>quiet(X))=>(wise(X)&~patient(X))))&
(![X]:((~happy(X)|patient(X))<=>~wise(X)))&
(?[X]:((wise(X)|~wise(X))))&
(~rich(paul))&
((~funny(alice)&rich(alice)))&
(?[X]:(~funny(X)))&
(?[X]:((~curious(X)<~>generous(X))))&
((humble(paul)|creative(paul)))&
(?[X]:((generous(X)|creative(X))))&
((~old(paul)&humble(paul))) | quiet(paul) | [
"p1",
"p2",
"p8",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 6036942926435118210668183
% SZS output start Proof for 6036942926435118210668183
2. ! [X0] : (tall(X0) <=> (~tall(X0) & funny(X0))) [input p1]
3. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> ~generous(X0)) [input p2]
9. ! [X0] : (~strong(X0) <=> ~generous(X0)) [input p8]
11. ! [X0] : (patient(X0) <=> (~strong(X0) | ~calm(X0))) [input p10]
15. ! [X0] : ((~strong(X0) <~> quiet(X0)) => (~patient(X0) & wise(X0))) [input p14]
25. ~quiet(paul) [input hypothesis]
32. ! [X0] : ((~patient(X0) & wise(X0)) | (~strong(X0) <=> quiet(X0))) [ennf transformation 15]
37. ! [X0] : ((tall(X0) | (tall(X0) | ~funny(X0))) & ((~tall(X0) & funny(X0)) | ~tall(X0))) [nnf transformation 2]
38. ! [X0] : ((tall(X0) | tall(X0) | ~funny(X0)) & ((~tall(X0) & funny(X0)) | ~tall(X0))) [flattening 37]
39. ! [X0] : (((~generous(X0) | ~tall(X0)) | generous(X0)) & (~generous(X0) | (generous(X0) & tall(X0)))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | ~tall(X0) | generous(X0)) & (~generous(X0) | (generous(X0) & tall(X0)))) [flattening 39]
56. ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 9]
62. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & ((~strong(X0) | ~calm(X0)) | ~patient(X0))) [nnf transformation 11]
63. ! [X0] : ((patient(X0) | (strong(X0) & calm(X0))) & (~strong(X0) | ~calm(X0) | ~patient(X0))) [flattening 62]
68. ! [X0] : ((~patient(X0) & wise(X0)) | ((~strong(X0) | ~quiet(X0)) & (quiet(X0) | strong(X0)))) [nnf transformation 32]
85. ~tall(X0) | ~tall(X0) [cnf transformation 38]
87. ~generous(X0) | tall(X0) [cnf transformation 40]
110. ~strong(X0) | generous(X0) [cnf transformation 56]
117. patient(X0) | strong(X0) [cnf transformation 63]
132. ~patient(X0) | quiet(X0) | strong(X0) [cnf transformation 68]
148. ~quiet(paul) [cnf transformation 25]
149. ~tall(X0) [duplicate literal removal 85]
173. ~generous(X0) [subsumption resolution 87,149]
235. ~strong(X0) [subsumption resolution 110,173]
252. patient(X0) [subsumption resolution 117,235]
268. quiet(X0) | strong(X0) [subsumption resolution 132,252]
269. quiet(X0) [subsumption resolution 268,235]
284. $false [subsumption resolution 148,269]
% SZS output end Proof for 6036942926435118210668183
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and kind is both not generous and humble.
If someone is both quiet and not generous then someone is not rich.
If paul is not happy then someone is quiet and vice versa.
Everyone who is not rich is both generous and rich and vice versa.
Everyone who is not rich is both creative and not old and vice versa.
Everyone who is strong or kind is either not curious or patient and vice versa.
If lucy is both not quiet and wise then someone is either not tall or not calm and vice versa.
Everyone who is patient or not calm is not kind.
If mary is not rich then mary is not happy or not patient and vice versa.
Everyone who is both quiet and not rich is both not funny and rich.
Everyone who is either not strong or patient is both not funny and not strong.
If fred is patient or happy then lucy is rich or not tall and vice versa.
If paul is quiet then alice is creative and vice versa.
If someone is not funny then paul is both not humble and not wise.
If alice is not patient then someone is both not generous and not humble.
Everyone who is not creative is not kind or not funny and vice versa.
Someone is both not brave and happy.
Someone is not curious or calm.
Lucy is not curious or calm.
Lucy is not tall or not quiet.
Alice is not strong or not rich.
Alice is both patient and not generous.
Someone is not tall or kind.
Someone is funny or not calm. | Paul is rich. | entailment | (![X]:((~calm(X)&kind(X))=>(~generous(X)&humble(X))))&
((?[X]:((quiet(X)&~generous(X))))=>(?[X]:(~rich(X))))&
((~happy(paul))<=>(?[X]:(quiet(X))))&
(![X]:(~rich(X)<=>(generous(X)&rich(X))))&
(![X]:(~rich(X)<=>(creative(X)&~old(X))))&
(![X]:((strong(X)|kind(X))<=>(~curious(X)<~>patient(X))))&
(((~quiet(lucy)&wise(lucy)))<=>(?[X]:((~tall(X)<~>~calm(X)))))&
(![X]:((patient(X)|~calm(X))=>~kind(X)))&
((~rich(mary))<=>((~happy(mary)|~patient(mary))))&
(![X]:((quiet(X)&~rich(X))=>(~funny(X)&rich(X))))&
(![X]:((~strong(X)<~>patient(X))=>(~funny(X)&~strong(X))))&
(((patient(fred)|happy(fred)))<=>((rich(lucy)|~tall(lucy))))&
((quiet(paul))<=>(creative(alice)))&
((?[X]:(~funny(X)))=>((~humble(paul)&~wise(paul))))&
((~patient(alice))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:(~creative(X)<=>(~kind(X)|~funny(X))))&
(?[X]:((~brave(X)&happy(X))))&
(?[X]:((~curious(X)|calm(X))))&
((~curious(lucy)|calm(lucy)))&
((~tall(lucy)|~quiet(lucy)))&
((~strong(alice)|~rich(alice)))&
((patient(alice)&~generous(alice)))&
(?[X]:((~tall(X)|kind(X))))&
(?[X]:((funny(X)|~calm(X)))) | rich(paul) | [
"p3",
"hypothesis"
]
| % SZS status Unsatisfiable for 1754180185012032284124504
% SZS output start Proof for 1754180185012032284124504
4. ! [X0] : (~rich(X0) <=> (rich(X0) & generous(X0))) [input p3]
25. ~rich(paul) [input hypothesis]
44. ! [X0] : ((~rich(X0) | (~rich(X0) | ~generous(X0))) & ((rich(X0) & generous(X0)) | rich(X0))) [nnf transformation 4]
45. ! [X0] : ((~rich(X0) | ~rich(X0) | ~generous(X0)) & ((rich(X0) & generous(X0)) | rich(X0))) [flattening 44]
79. rich(X0) | rich(X0) [cnf transformation 45]
129. ~rich(paul) [cnf transformation 25]
132. rich(X0) [duplicate literal removal 79]
277. $false [subsumption resolution 129,132]
% SZS output end Proof for 1754180185012032284124504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or strong is rich and vice versa. Everyone who is curious is both not quiet and wise and vice versa. Everyone who is not calm or not strong is both not wise and funny. Everyone who is not brave is either brave or not happy. Everyone who is not happy or not creative is not strong and vice versa. If paul is either happy or not old then fred is either tall or creative and vice versa. Everyone who is not curious is either rich or not strong. Everyone who is not calm or not happy is both not funny and not rich and vice versa. If fred is funny then someone is funny or calm. Everyone who is tall or rich is either humble or not rich. If alice is either patient or not rich then lucy is not old and vice versa. If paul is not kind then someone is both quiet and not happy and vice versa. Everyone who is not happy is both not creative and not tall and vice versa. Everyone who is wise or not quiet is tall. If someone is rich then fred is not happy or happy. Someone is not creative or curious. John is not curious or not creative. John is both not curious and quiet. | Alice is happy. | entailment | (![X]:((curious(X)<~>strong(X))<=>rich(X)))&
(![X]:(curious(X)<=>(~quiet(X)&wise(X))))&
(![X]:((~calm(X)|~strong(X))=>(~wise(X)&funny(X))))&
(![X]:(~brave(X)=>(brave(X)<~>~happy(X))))&
(![X]:((~happy(X)|~creative(X))<=>~strong(X)))&
(((happy(paul)<~>~old(paul)))<=>((tall(fred)<~>creative(fred))))&
(![X]:(~curious(X)=>(rich(X)<~>~strong(X))))&
(![X]:((~calm(X)|~happy(X))<=>(~funny(X)&~rich(X))))&
((funny(fred))=>(?[X]:((funny(X)|calm(X)))))&
(![X]:((tall(X)|rich(X))=>(humble(X)<~>~rich(X))))&
(((patient(alice)<~>~rich(alice)))<=>(~old(lucy)))&
((~kind(paul))<=>(?[X]:((quiet(X)&~happy(X)))))&
(![X]:(~happy(X)<=>(~creative(X)&~tall(X))))&
(![X]:((wise(X)|~quiet(X))=>tall(X)))&
((?[X]:(rich(X)))=>((~happy(fred)|happy(fred))))&
(?[X]:((~creative(X)|curious(X))))&
((~curious(john)|~creative(john)))&
((~curious(john)&quiet(john))) | happy(alice) | [
"p2",
"p4",
"p7",
"hypothesis"
]
| % SZS status Unsatisfiable for 4549381556604638696513526
% SZS output start Proof for 4549381556604638696513526
3. ! [X0] : ((~strong(X0) | ~calm(X0)) => (funny(X0) & ~wise(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | ~happy(X0)) <=> ~strong(X0)) [input p4]
8. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (~rich(X0) & ~funny(X0))) [input p7]
19. ~happy(alice) [input hypothesis]
20. ! [X0] : ((funny(X0) & ~wise(X0)) | (strong(X0) & calm(X0))) [ennf transformation 3]
32. ! [X0] : (((~creative(X0) | ~happy(X0)) | strong(X0)) & (~strong(X0) | (creative(X0) & happy(X0)))) [nnf transformation 5]
33. ! [X0] : ((~creative(X0) | ~happy(X0) | strong(X0)) & (~strong(X0) | (creative(X0) & happy(X0)))) [flattening 32]
36. ! [X0] : (((~happy(X0) | ~calm(X0)) | (rich(X0) | funny(X0))) & ((~rich(X0) & ~funny(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 8]
37. ! [X0] : ((~happy(X0) | ~calm(X0) | rich(X0) | funny(X0)) & ((~rich(X0) & ~funny(X0)) | (happy(X0) & calm(X0)))) [flattening 36]
60. funny(X0) | strong(X0) [cnf transformation 20]
63. ~strong(X0) | happy(X0) [cnf transformation 33]
77. ~funny(X0) | happy(X0) [cnf transformation 37]
103. ~happy(alice) [cnf transformation 19]
186. happy(X0) | strong(X0) [resolution 77,60]
188. happy(X0) [subsumption resolution 186,63]
189. $false [resolution 188,103]
% SZS output end Proof for 4549381556604638696513526
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not curious is both not kind and curious and vice versa.
Everyone who is both tall and not rich is both creative and curious.
Everyone who is kind is brave and vice versa.
If someone is funny or generous then mary is tall or not patient.
If someone is either humble or tall then alice is quiet and vice versa.
If alice is both not old and rich then someone is both patient and not quiet.
Everyone who is either rich or not humble is not calm and vice versa.
Everyone who is both humble and not curious is either humble or not calm.
If alice is either not funny or patient then someone is both brave and wise.
If mary is not patient then someone is tall and vice versa.
If fred is both kind and not curious then alice is both not quiet and creative and vice versa.
Everyone who is either not wise or not strong is not humble or tall.
Everyone who is curious or not humble is both not funny and old.
Everyone who is both not patient and not quiet is both strong and brave.
Everyone who is either rich or quiet is brave or kind and vice versa.
Everyone who is quiet or happy is both not old and rich and vice versa.
Paul is both calm and kind.
John is both not kind and curious.
Someone is calm.
Mary is either not humble or not brave.
Someone is either happy or wise.
Someone is not rich. | Fred is funny. | contradiction | (![X]:((tall(X)<~>~curious(X))<=>(~kind(X)&curious(X))))&
(![X]:((tall(X)&~rich(X))=>(creative(X)&curious(X))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((funny(X)|generous(X))))=>((tall(mary)|~patient(mary))))&
((?[X]:((humble(X)<~>tall(X))))<=>(quiet(alice)))&
(((~old(alice)&rich(alice)))=>(?[X]:((patient(X)&~quiet(X)))))&
(![X]:((rich(X)<~>~humble(X))<=>~calm(X)))&
(![X]:((humble(X)&~curious(X))=>(humble(X)<~>~calm(X))))&
(((~funny(alice)<~>patient(alice)))=>(?[X]:((brave(X)&wise(X)))))&
((~patient(mary))<=>(?[X]:(tall(X))))&
(((kind(fred)&~curious(fred)))<=>((~quiet(alice)&creative(alice))))&
(![X]:((~wise(X)<~>~strong(X))=>(~humble(X)|tall(X))))&
(![X]:((curious(X)|~humble(X))=>(~funny(X)&old(X))))&
(![X]:((~patient(X)&~quiet(X))=>(strong(X)&brave(X))))&
(![X]:((rich(X)<~>quiet(X))<=>(brave(X)|kind(X))))&
(![X]:((quiet(X)|happy(X))<=>(~old(X)&rich(X))))&
((calm(paul)&kind(paul)))&
((~kind(john)&curious(john)))&
(?[X]:(calm(X)))&
((~humble(mary)<~>~brave(mary)))&
(?[X]:((happy(X)<~>wise(X))))&
(?[X]:(~rich(X))) | funny(fred) | [
"p0",
"p1",
"p6",
"p7",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 1471372772988698989165038
% SZS output start Proof for 1471372772988698989165038
1. ! [X0] : ((tall(X0) <~> ~curious(X0)) <=> (curious(X0) & ~kind(X0))) [input p0]
2. ! [X0] : ((~rich(X0) & tall(X0)) => (curious(X0) & creative(X0))) [input p1]
7. ! [X0] : ((rich(X0) <~> ~humble(X0)) <=> ~calm(X0)) [input p6]
8. ! [X0] : ((~curious(X0) & humble(X0)) => (humble(X0) <~> ~calm(X0))) [input p7]
13. ! [X0] : ((~humble(X0) | curious(X0)) => (old(X0) & ~funny(X0))) [input p12]
23. funny(fred) [input hypothesis]
25. ! [X0] : ((curious(X0) & creative(X0)) | (rich(X0) | ~tall(X0))) [ennf transformation 2]
26. ! [X0] : ((curious(X0) & creative(X0)) | rich(X0) | ~tall(X0)) [flattening 25]
31. ! [X0] : ((humble(X0) <~> ~calm(X0)) | (curious(X0) | ~humble(X0))) [ennf transformation 8]
32. ! [X0] : ((humble(X0) <~> ~calm(X0)) | curious(X0) | ~humble(X0)) [flattening 31]
36. ! [X0] : ((old(X0) & ~funny(X0)) | (humble(X0) & ~curious(X0))) [ennf transformation 13]
39. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (~curious(X0) | kind(X0))) & ((curious(X0) & ~kind(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [nnf transformation 1]
40. ! [X0] : ((((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | ~curious(X0) | kind(X0)) & ((curious(X0) & ~kind(X0)) | ((tall(X0) | curious(X0)) & (~curious(X0) | ~tall(X0))))) [flattening 39]
48. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | calm(X0)) & (~calm(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [nnf transformation 7]
49. ! [X0] : (((calm(X0) | ~humble(X0)) & (~calm(X0) | humble(X0))) | curious(X0) | ~humble(X0)) [nnf transformation 32]
75. curious(X0) | tall(X0) | curious(X0) [cnf transformation 40]
79. curious(X0) | rich(X0) | ~tall(X0) [cnf transformation 26]
89. ~calm(X0) | ~humble(X0) | ~rich(X0) [cnf transformation 48]
92. ~rich(X0) | humble(X0) | calm(X0) [cnf transformation 48]
94. calm(X0) | ~humble(X0) | curious(X0) | ~humble(X0) [cnf transformation 49]
107. ~funny(X0) | ~curious(X0) [cnf transformation 36]
108. ~funny(X0) | humble(X0) [cnf transformation 36]
134. funny(fred) [cnf transformation 23]
135. ~humble(X0) | calm(X0) | curious(X0) [duplicate literal removal 94]
136. curious(X0) | tall(X0) [duplicate literal removal 75]
138. rich(X0) | curious(X0) [subsumption resolution 79,136]
225. 20 <=> curious(fred) [avatar definition]
227. ~curious(fred) <- (~20) [avatar component clause 225]
262. ~curious(fred) [resolution 107,134]
263. ~20 [avatar split clause 262,225]
264. humble(fred) [resolution 108,134]
366. humble(X0) | calm(X0) | curious(X0) [resolution 92,138]
370. calm(X0) | curious(X0) [subsumption resolution 366,135]
501. curious(X1) | ~humble(X1) | ~rich(X1) [resolution 370,89]
502. ~humble(X1) | curious(X1) [subsumption resolution 501,138]
624. curious(fred) [resolution 502,264]
629. $false <- (~20) [subsumption resolution 624,227]
630. 20 [avatar contradiction clause 629]
631. $false [avatar sat refutation 263,630]
% SZS output end Proof for 1471372772988698989165038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not brave then someone is both old and happy. Everyone who is not rich or not calm is either tall or generous and vice versa. Everyone who is either not tall or not humble is humble. Everyone who is both curious and not generous is both not tall and happy. Everyone who is either patient or funny is not humble or not patient. If john is not humble or not funny then lucy is not creative. If lucy is either not brave or rich then alice is not brave and vice versa. If mary is both rich and tall then lucy is either not quiet or brave. If someone is not old or not calm then someone is both patient and funny. Everyone who is not kind is either not curious or rich. If alice is both creative and tall then lucy is not brave. Everyone who is generous or not generous is not patient or generous. Everyone who is both not old and not patient is old. If someone is not humble then someone is both brave and generous. Everyone who is not happy is not rich. If someone is happy then someone is both not quiet and strong. Someone is tall or rich. Fred is not quiet or not strong. Paul is both not quiet and rich. Someone is not brave or curious. Alice is not wise or not brave. Someone is both curious and brave. Someone is not rich. Someone is both patient and creative. | Lucy is not creative. | neutral | ((?[X]:((creative(X)<~>~brave(X))))=>(?[X]:((old(X)&happy(X)))))&
(![X]:((~rich(X)|~calm(X))<=>(tall(X)<~>generous(X))))&
(![X]:((~tall(X)<~>~humble(X))=>humble(X)))&
(![X]:((curious(X)&~generous(X))=>(~tall(X)&happy(X))))&
(![X]:((patient(X)<~>funny(X))=>(~humble(X)|~patient(X))))&
(((~humble(john)|~funny(john)))=>(~creative(lucy)))&
(((~brave(lucy)<~>rich(lucy)))<=>(~brave(alice)))&
(((rich(mary)&tall(mary)))=>((~quiet(lucy)<~>brave(lucy))))&
((?[X]:((~old(X)|~calm(X))))=>(?[X]:((patient(X)&funny(X)))))&
(![X]:(~kind(X)=>(~curious(X)<~>rich(X))))&
(((creative(alice)&tall(alice)))=>(~brave(lucy)))&
(![X]:((generous(X)|~generous(X))=>(~patient(X)|generous(X))))&
(![X]:((~old(X)&~patient(X))=>old(X)))&
((?[X]:(~humble(X)))=>(?[X]:((brave(X)&generous(X)))))&
(![X]:(~happy(X)=>~rich(X)))&
((?[X]:(happy(X)))=>(?[X]:((~quiet(X)&strong(X)))))&
(?[X]:((tall(X)|rich(X))))&
((~quiet(fred)|~strong(fred)))&
((~quiet(paul)&rich(paul)))&
(?[X]:((~brave(X)|curious(X))))&
((~wise(alice)|~brave(alice)))&
(?[X]:((curious(X)&brave(X))))&
(?[X]:(~rich(X)))&
(?[X]:((patient(X)&creative(X)))) | ~creative(lucy) | []
| null | 0 |
Everyone who is both kind and humble is generous and vice versa.
Everyone who is kind is both not brave and not rich.
If lucy is either not wise or brave then john is brave and vice versa.
Everyone who is generous or quiet is old or not generous and vice versa.
Everyone who is not brave or not happy is both not quiet and generous.
Everyone who is either not wise or not humble is happy.
Everyone who is calm is quiet or not calm.
If alice is quiet or creative then someone is not quiet or funny and vice versa.
Everyone who is creative or not rich is both not brave and old.
Everyone who is not generous is either not happy or not tall.
Everyone who is not funny is either brave or curious and vice versa.
If mary is both not creative and brave then someone is calm and vice versa.
Everyone who is calm or not creative is strong or not kind.
Everyone who is either not curious or not quiet is either quiet or not generous.
Everyone who is not brave is not old.
Someone is either humble or calm.
Someone is strong.
Alice is patient or calm. | Alice is not curious. | contradiction | (![X]:((kind(X)&humble(X))<=>generous(X)))&
(![X]:(kind(X)=>(~brave(X)&~rich(X))))&
(((~wise(lucy)<~>brave(lucy)))<=>(brave(john)))&
(![X]:((generous(X)|quiet(X))<=>(old(X)|~generous(X))))&
(![X]:((~brave(X)|~happy(X))=>(~quiet(X)&generous(X))))&
(![X]:((~wise(X)<~>~humble(X))=>happy(X)))&
(![X]:(calm(X)=>(quiet(X)|~calm(X))))&
(((quiet(alice)|creative(alice)))<=>(?[X]:((~quiet(X)|funny(X)))))&
(![X]:((creative(X)|~rich(X))=>(~brave(X)&old(X))))&
(![X]:(~generous(X)=>(~happy(X)<~>~tall(X))))&
(![X]:(~funny(X)<=>(brave(X)<~>curious(X))))&
(((~creative(mary)&brave(mary)))<=>(?[X]:(calm(X))))&
(![X]:((calm(X)|~creative(X))=>(strong(X)|~kind(X))))&
(![X]:((~curious(X)<~>~quiet(X))=>(quiet(X)<~>~generous(X))))&
(![X]:(~brave(X)=>~old(X)))&
(?[X]:((humble(X)<~>calm(X))))&
(?[X]:(strong(X)))&
((patient(alice)|calm(alice))) | ~curious(alice) | [
"p0",
"p1",
"p3",
"p8",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5101596942292411690320937
% SZS output start Proof for 5101596942292411690320937
1. ! [X0] : ((humble(X0) & kind(X0)) <=> generous(X0)) [input p0]
2. ! [X0] : (kind(X0) => (~rich(X0) & ~brave(X0))) [input p1]
4. ! [X0] : ((quiet(X0) | generous(X0)) <=> (~generous(X0) | old(X0))) [input p3]
9. ! [X0] : ((~rich(X0) | creative(X0)) => (old(X0) & ~brave(X0))) [input p8]
14. ! [X0] : ((~curious(X0) <~> ~quiet(X0)) => (quiet(X0) <~> ~generous(X0))) [input p13]
15. ! [X0] : (~brave(X0) => ~old(X0)) [input p14]
19. ~curious(alice) [input hypothesis]
23. ! [X0] : ((~rich(X0) & ~brave(X0)) | ~kind(X0)) [ennf transformation 2]
28. ! [X0] : ((old(X0) & ~brave(X0)) | (rich(X0) & ~creative(X0))) [ennf transformation 9]
30. ! [X0] : ((quiet(X0) <~> ~generous(X0)) | (~curious(X0) <=> ~quiet(X0))) [ennf transformation 14]
31. ! [X0] : (~old(X0) | brave(X0)) [ennf transformation 15]
32. ! [X0] : (((humble(X0) & kind(X0)) | ~generous(X0)) & (generous(X0) | (~humble(X0) | ~kind(X0)))) [nnf transformation 1]
33. ! [X0] : (((humble(X0) & kind(X0)) | ~generous(X0)) & (generous(X0) | ~humble(X0) | ~kind(X0))) [flattening 32]
35. ! [X0] : (((quiet(X0) | generous(X0)) | (generous(X0) & ~old(X0))) & ((~generous(X0) | old(X0)) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 4]
36. ! [X0] : ((quiet(X0) | generous(X0) | (generous(X0) & ~old(X0))) & (~generous(X0) | old(X0) | (~quiet(X0) & ~generous(X0)))) [flattening 35]
50. ! [X0] : (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0)))) [nnf transformation 30]
55. ~generous(X0) | kind(X0) [cnf transformation 33]
58. ~rich(X0) | ~kind(X0) [cnf transformation 23]
66. quiet(X0) | generous(X0) | generous(X0) [cnf transformation 36]
79. ~brave(X0) | rich(X0) [cnf transformation 28]
81. old(X0) | rich(X0) [cnf transformation 28]
93. generous(X0) | ~quiet(X0) | ~quiet(X0) | curious(X0) [cnf transformation 50]
95. ~old(X0) | brave(X0) [cnf transformation 31]
98. ~curious(alice) [cnf transformation 19]
100. generous(X0) | ~quiet(X0) | curious(X0) [duplicate literal removal 93]
103. quiet(X0) | generous(X0) [duplicate literal removal 66]
166. curious(X0) | generous(X0) [subsumption resolution 100,103]
193. brave(X0) | rich(X0) [resolution 95,81]
194. rich(X0) [subsumption resolution 193,79]
195. ~kind(X0) [resolution 194,58]
215. generous(alice) [resolution 166,98]
234. kind(alice) [resolution 215,55]
235. $false [subsumption resolution 234,195]
% SZS output end Proof for 5101596942292411690320937
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is either funny or old then fred is quiet and vice versa.
If someone is calm then susan is funny.
If someone is both not patient and humble then someone is calm or not old and vice versa.
Everyone who is not wise is rich.
Everyone who is either not kind or kind is both happy and wise and vice versa.
If someone is not wise then someone is not patient.
Everyone who is happy or not brave is both not quiet and not old and vice versa.
If fred is either not tall or funny then alice is calm or not curious and vice versa.
If someone is not humble or strong then john is not humble or not patient and vice versa.
If susan is patient then mary is either brave or not wise and vice versa.
If someone is either not humble or strong then someone is either curious or kind and vice versa.
Everyone who is not generous is either not tall or not humble.
If someone is funny then someone is not wise or humble and vice versa.
Everyone who is not creative is not patient.
If susan is either kind or patient then john is both calm and not patient and vice versa.
John is tall.
Someone is wise or kind.
Fred is wise.
Someone is both brave and not strong.
Paul is either creative or kind.
Alice is quiet or not funny. | John is not old. | entailment | (((funny(mary)<~>old(mary)))<=>(quiet(fred)))&
((?[X]:(calm(X)))=>(funny(susan)))&
((?[X]:((~patient(X)&humble(X))))<=>(?[X]:((calm(X)|~old(X)))))&
(![X]:(~wise(X)=>rich(X)))&
(![X]:((~kind(X)<~>kind(X))<=>(happy(X)&wise(X))))&
((?[X]:(~wise(X)))=>(?[X]:(~patient(X))))&
(![X]:((happy(X)|~brave(X))<=>(~quiet(X)&~old(X))))&
(((~tall(fred)<~>funny(fred)))<=>((calm(alice)|~curious(alice))))&
((?[X]:((~humble(X)|strong(X))))<=>((~humble(john)|~patient(john))))&
((patient(susan))<=>((brave(mary)<~>~wise(mary))))&
((?[X]:((~humble(X)<~>strong(X))))<=>(?[X]:((curious(X)<~>kind(X)))))&
(![X]:(~generous(X)=>(~tall(X)<~>~humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~wise(X)|humble(X)))))&
(![X]:(~creative(X)=>~patient(X)))&
(((kind(susan)<~>patient(susan)))<=>((calm(john)&~patient(john))))&
(tall(john))&
(?[X]:((wise(X)|kind(X))))&
(wise(fred))&
(?[X]:((brave(X)&~strong(X))))&
((creative(paul)<~>kind(paul)))&
((quiet(alice)|~funny(alice))) | ~old(john) | [
"p4",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 7965194040445580117911542
% SZS output start Proof for 7965194040445580117911542
5. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> (wise(X0) & happy(X0))) [input p4]
7. ! [X0] : ((~brave(X0) | happy(X0)) <=> (~old(X0) & ~quiet(X0))) [input p6]
22. old(john) [input hypothesis]
38. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | (~wise(X0) | ~happy(X0))) & ((wise(X0) & happy(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 5]
39. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~wise(X0) | ~happy(X0)) & ((wise(X0) & happy(X0)) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [flattening 38]
43. ! [X0] : (((~brave(X0) | happy(X0)) | (old(X0) | quiet(X0))) & ((~old(X0) & ~quiet(X0)) | (brave(X0) & ~happy(X0)))) [nnf transformation 7]
44. ! [X0] : ((~brave(X0) | happy(X0) | old(X0) | quiet(X0)) & ((~old(X0) & ~quiet(X0)) | (brave(X0) & ~happy(X0)))) [flattening 43]
80. happy(X0) | kind(X0) | kind(X0) [cnf transformation 39]
81. happy(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 39]
89. ~old(X0) | ~happy(X0) [cnf transformation 44]
132. old(john) [cnf transformation 22]
133. happy(X0) | kind(X0) [duplicate literal removal 80]
134. happy(X0) | ~kind(X0) [duplicate literal removal 81]
189. happy(X0) [subsumption resolution 133,134]
190. ~old(X0) [subsumption resolution 89,189]
330. $false [subsumption resolution 132,190]
% SZS output end Proof for 7965194040445580117911542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and happy is not calm or strong. Everyone who is both not rich and not funny is calm. If john is not wise or calm then someone is either not wise or generous. If mary is tall or not strong then lucy is both not tall and not generous and vice versa. If someone is both not rich and not brave then lucy is either happy or curious and vice versa. Everyone who is both generous and not old is creative. If lucy is both kind and not quiet then john is either not kind or generous. Everyone who is not calm is either not kind or not rich and vice versa. Everyone who is humble is either humble or not humble and vice versa. Everyone who is either brave or not generous is not tall or funny. If alice is tall then paul is kind or old and vice versa. If paul is both not generous and old then susan is calm. If alice is either kind or generous then someone is both tall and not brave and vice versa. Everyone who is tall is not creative and vice versa. Everyone who is not brave is generous and vice versa. If someone is either wise or not brave then alice is not quiet or funny and vice versa. Someone is both not generous and not wise. Someone is both not creative and happy. Susan is either tall or not calm. Someone is happy or not old. Alice is not tall. Someone is both wise and calm. Someone is both not tall and brave. Someone is not tall. | Mary is humble. | entailment | (![X]:((~humble(X)&happy(X))=>(~calm(X)|strong(X))))&
(![X]:((~rich(X)&~funny(X))=>calm(X)))&
(((~wise(john)|calm(john)))=>(?[X]:((~wise(X)<~>generous(X)))))&
(((tall(mary)|~strong(mary)))<=>((~tall(lucy)&~generous(lucy))))&
((?[X]:((~rich(X)&~brave(X))))<=>((happy(lucy)<~>curious(lucy))))&
(![X]:((generous(X)&~old(X))=>creative(X)))&
(((kind(lucy)&~quiet(lucy)))=>((~kind(john)<~>generous(john))))&
(![X]:(~calm(X)<=>(~kind(X)<~>~rich(X))))&
(![X]:(humble(X)<=>(humble(X)<~>~humble(X))))&
(![X]:((brave(X)<~>~generous(X))=>(~tall(X)|funny(X))))&
((tall(alice))<=>((kind(paul)|old(paul))))&
(((~generous(paul)&old(paul)))=>(calm(susan)))&
(((kind(alice)<~>generous(alice)))<=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:(tall(X)<=>~creative(X)))&
(![X]:(~brave(X)<=>generous(X)))&
((?[X]:((wise(X)<~>~brave(X))))<=>((~quiet(alice)|funny(alice))))&
(?[X]:((~generous(X)&~wise(X))))&
(?[X]:((~creative(X)&happy(X))))&
((tall(susan)<~>~calm(susan)))&
(?[X]:((happy(X)|~old(X))))&
(~tall(alice))&
(?[X]:((wise(X)&calm(X))))&
(?[X]:((~tall(X)&brave(X))))&
(?[X]:(~tall(X))) | humble(mary) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 838057273057261749699534
% SZS output start Proof for 838057273057261749699534
9. ! [X0] : (humble(X0) <=> (humble(X0) <~> ~humble(X0))) [input p8]
25. ~humble(mary) [input hypothesis]
50. ! [X0] : ((humble(X0) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) & (((humble(X0) | ~humble(X0)) & (~humble(X0) | humble(X0))) | ~humble(X0))) [nnf transformation 9]
105. humble(X0) | humble(X0) | humble(X0) [cnf transformation 50]
141. ~humble(mary) [cnf transformation 25]
145. humble(X0) [duplicate literal removal 105]
323. $false [subsumption resolution 141,145]
% SZS output end Proof for 838057273057261749699534
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not kind and patient is both not kind and funny and vice versa.
Everyone who is either not patient or generous is both not patient and generous and vice versa.
If someone is either rich or brave then paul is quiet or not patient.
If someone is either not humble or not generous then someone is either not humble or not patient and vice versa.
Everyone who is not funny is either not generous or not creative and vice versa.
Everyone who is not kind or rich is either quiet or not funny and vice versa.
If someone is not happy then someone is either not old or not calm and vice versa.
Everyone who is humble is both not brave and rich and vice versa.
Everyone who is tall is both not strong and not quiet.
If john is either not wise or not funny then someone is old or funny.
Everyone who is either not funny or rich is funny.
Everyone who is not humble is not humble or generous and vice versa.
If someone is not rich then paul is both not humble and brave and vice versa.
If susan is both not happy and not strong then mary is both not humble and curious.
Everyone who is either not patient or not generous is rich or generous.
Someone is funny.
Someone is kind.
Fred is both not happy and not strong.
Lucy is both not wise and not generous.
Someone is either rich or not creative.
John is both wise and not calm.
Someone is both not curious and happy.
Someone is both rich and not curious. | Fred is generous. | contradiction | (![X]:((~kind(X)&patient(X))<=>(~kind(X)&funny(X))))&
(![X]:((~patient(X)<~>generous(X))<=>(~patient(X)&generous(X))))&
((?[X]:((rich(X)<~>brave(X))))=>((quiet(paul)|~patient(paul))))&
((?[X]:((~humble(X)<~>~generous(X))))<=>(?[X]:((~humble(X)<~>~patient(X)))))&
(![X]:(~funny(X)<=>(~generous(X)<~>~creative(X))))&
(![X]:((~kind(X)|rich(X))<=>(quiet(X)<~>~funny(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((~old(X)<~>~calm(X)))))&
(![X]:(humble(X)<=>(~brave(X)&rich(X))))&
(![X]:(tall(X)=>(~strong(X)&~quiet(X))))&
(((~wise(john)<~>~funny(john)))=>(?[X]:((old(X)|funny(X)))))&
(![X]:((~funny(X)<~>rich(X))=>funny(X)))&
(![X]:(~humble(X)<=>(~humble(X)|generous(X))))&
((?[X]:(~rich(X)))<=>((~humble(paul)&brave(paul))))&
(((~happy(susan)&~strong(susan)))=>((~humble(mary)&curious(mary))))&
(![X]:((~patient(X)<~>~generous(X))=>(rich(X)|generous(X))))&
(?[X]:(funny(X)))&
(?[X]:(kind(X)))&
((~happy(fred)&~strong(fred)))&
((~wise(lucy)&~generous(lucy)))&
(?[X]:((rich(X)<~>~creative(X))))&
((wise(john)&~calm(john)))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:((rich(X)&~curious(X)))) | generous(fred) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 5125671450932377466917233
% SZS output start Proof for 5125671450932377466917233
2. ! [X0] : ((~patient(X0) <~> generous(X0)) <=> (generous(X0) & ~patient(X0))) [input p1]
24. generous(fred) [input hypothesis]
38. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | (~generous(X0) | patient(X0))) & ((generous(X0) & ~patient(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~generous(X0) | patient(X0)) & (generous(X0) | ~patient(X0))) | ~generous(X0) | patient(X0)) & ((generous(X0) & ~patient(X0)) | ((~patient(X0) | ~generous(X0)) & (generous(X0) | patient(X0))))) [flattening 38]
84. ~patient(X0) | ~patient(X0) | ~generous(X0) [cnf transformation 39]
85. generous(X0) | generous(X0) | patient(X0) [cnf transformation 39]
88. ~generous(X0) | patient(X0) | ~generous(X0) | patient(X0) [cnf transformation 39]
144. generous(fred) [cnf transformation 24]
147. ~patient(X0) | ~generous(X0) [duplicate literal removal 84]
148. generous(X0) | patient(X0) [duplicate literal removal 85]
149. ~generous(X0) | patient(X0) [duplicate literal removal 88]
150. patient(X0) [subsumption resolution 148,149]
151. ~generous(X0) [subsumption resolution 147,150]
282. $false [subsumption resolution 144,151]
% SZS output end Proof for 5125671450932377466917233
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not rich is either rich or not generous and vice versa.
If someone is either curious or not calm then lucy is both not generous and calm and vice versa.
If someone is curious or not wise then someone is both not quiet and old.
Everyone who is both happy and not wise is generous or funny.
If someone is both happy and not quiet then someone is not happy or not tall.
Everyone who is either not patient or not kind is patient and vice versa.
If paul is not strong then someone is either wise or not happy.
Everyone who is both tall and not happy is generous or kind and vice versa.
Everyone who is either rich or not rich is both not happy and not old.
If someone is quiet then someone is old or not calm and vice versa.
If someone is both funny and not patient then someone is quiet.
If alice is both happy and tall then paul is both curious and not calm and vice versa.
If someone is not happy then fred is brave or not kind and vice versa.
Everyone who is brave or wise is rich or strong.
If susan is creative then someone is strong and vice versa.
If someone is strong then someone is not funny.
Someone is not quiet.
Someone is either happy or strong.
Alice is both funny and not quiet.
Someone is patient or quiet.
Someone is either not patient or not creative. | Susan is not happy. | entailment | (![X]:((patient(X)|~rich(X))<=>(rich(X)<~>~generous(X))))&
((?[X]:((curious(X)<~>~calm(X))))<=>((~generous(lucy)&calm(lucy))))&
((?[X]:((curious(X)|~wise(X))))=>(?[X]:((~quiet(X)&old(X)))))&
(![X]:((happy(X)&~wise(X))=>(generous(X)|funny(X))))&
((?[X]:((happy(X)&~quiet(X))))=>(?[X]:((~happy(X)|~tall(X)))))&
(![X]:((~patient(X)<~>~kind(X))<=>patient(X)))&
((~strong(paul))=>(?[X]:((wise(X)<~>~happy(X)))))&
(![X]:((tall(X)&~happy(X))<=>(generous(X)|kind(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~happy(X)&~old(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~calm(X)))))&
((?[X]:((funny(X)&~patient(X))))=>(?[X]:(quiet(X))))&
(((happy(alice)&tall(alice)))<=>((curious(paul)&~calm(paul))))&
((?[X]:(~happy(X)))<=>((brave(fred)|~kind(fred))))&
(![X]:((brave(X)|wise(X))=>(rich(X)|strong(X))))&
((creative(susan))<=>(?[X]:(strong(X))))&
((?[X]:(strong(X)))=>(?[X]:(~funny(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((happy(X)<~>strong(X))))&
((funny(alice)&~quiet(alice)))&
(?[X]:((patient(X)|quiet(X))))&
(?[X]:((~patient(X)<~>~creative(X)))) | ~happy(susan) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 3389685406894812739577336
% SZS output start Proof for 3389685406894812739577336
9. ! [X0] : ((rich(X0) <~> ~rich(X0)) => (~old(X0) & ~happy(X0))) [input p8]
22. happy(susan) [input hypothesis]
33. ! [X0] : ((~old(X0) & ~happy(X0)) | (rich(X0) <=> ~rich(X0))) [ennf transformation 9]
57. ! [X0] : ((~old(X0) & ~happy(X0)) | ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0)))) [nnf transformation 33]
119. ~happy(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 57]
120. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 57]
147. happy(susan) [cnf transformation 22]
148. ~happy(X0) | ~rich(X0) [duplicate literal removal 119]
149. ~happy(X0) | rich(X0) [duplicate literal removal 120]
231. ~happy(X0) [subsumption resolution 148,149]
310. $false [subsumption resolution 147,231]
% SZS output end Proof for 3389685406894812739577336
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and creative is generous or not strong.
If someone is both not patient and funny then fred is either not happy or calm.
Everyone who is not generous is both kind and not curious and vice versa.
If someone is not humble or strong then paul is both not patient and not wise.
If someone is quiet or not wise then someone is both not rich and generous.
If john is happy then someone is both happy and curious.
Everyone who is both not tall and not humble is both not old and creative.
Everyone who is either not funny or not patient is both kind and wise.
Everyone who is both not humble and wise is not curious.
Everyone who is both not happy and not funny is generous or not rich and vice versa.
Everyone who is either not rich or generous is either not kind or kind and vice versa.
If mary is happy then someone is either not creative or old and vice versa.
If someone is funny or not calm then john is either not tall or not strong.
Everyone who is creative or not brave is either not happy or not generous and vice versa.
If fred is brave or funny then someone is not tall or not strong and vice versa.
If susan is kind then fred is both not brave and not strong.
Lucy is both brave and rich.
John is either not happy or not tall.
Paul is not rich or not generous.
Someone is not kind.
Someone is happy or patient.
Lucy is not funny.
Someone is wise. | Mary is quiet. | contradiction | (![X]:((quiet(X)&creative(X))=>(generous(X)|~strong(X))))&
((?[X]:((~patient(X)&funny(X))))=>((~happy(fred)<~>calm(fred))))&
(![X]:(~generous(X)<=>(kind(X)&~curious(X))))&
((?[X]:((~humble(X)|strong(X))))=>((~patient(paul)&~wise(paul))))&
((?[X]:((quiet(X)|~wise(X))))=>(?[X]:((~rich(X)&generous(X)))))&
((happy(john))=>(?[X]:((happy(X)&curious(X)))))&
(![X]:((~tall(X)&~humble(X))=>(~old(X)&creative(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(kind(X)&wise(X))))&
(![X]:((~humble(X)&wise(X))=>~curious(X)))&
(![X]:((~happy(X)&~funny(X))<=>(generous(X)|~rich(X))))&
(![X]:((~rich(X)<~>generous(X))<=>(~kind(X)<~>kind(X))))&
((happy(mary))<=>(?[X]:((~creative(X)<~>old(X)))))&
((?[X]:((funny(X)|~calm(X))))=>((~tall(john)<~>~strong(john))))&
(![X]:((creative(X)|~brave(X))<=>(~happy(X)<~>~generous(X))))&
(((brave(fred)|funny(fred)))<=>(?[X]:((~tall(X)|~strong(X)))))&
((kind(susan))=>((~brave(fred)&~strong(fred))))&
((brave(lucy)&rich(lucy)))&
((~happy(john)<~>~tall(john)))&
((~rich(paul)|~generous(paul)))&
(?[X]:(~kind(X)))&
(?[X]:((happy(X)|patient(X))))&
(~funny(lucy))&
(?[X]:(wise(X))) | quiet(mary) | [
"p2",
"p4",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 2854484648916320851427244
% SZS output start Proof for 2854484648916320851427244
3. ! [X0] : (~generous(X0) <=> (~curious(X0) & kind(X0))) [input p2]
5. ? [X0] : (~wise(X0) | quiet(X0)) => ? [X0] : (generous(X0) & ~rich(X0)) [input p4]
11. ! [X0] : ((~rich(X0) <~> generous(X0)) <=> (~kind(X0) <~> kind(X0))) [input p10]
24. quiet(mary) [input hypothesis]
25. ? [X0] : (~wise(X0) | quiet(X0)) => ? [X1] : (generous(X1) & ~rich(X1)) [rectify 5]
33. ? [X1] : (generous(X1) & ~rich(X1)) | ! [X0] : (wise(X0) & ~quiet(X0)) [ennf transformation 25]
39. ! [X0] : ((~generous(X0) | (curious(X0) | ~kind(X0))) & ((~curious(X0) & kind(X0)) | generous(X0))) [nnf transformation 3]
40. ! [X0] : ((~generous(X0) | curious(X0) | ~kind(X0)) & ((~curious(X0) & kind(X0)) | generous(X0))) [flattening 39]
41. ? [X0] : (generous(X0) & ~rich(X0)) | ! [X1] : (wise(X1) & ~quiet(X1)) [rectify 33]
42. ? [X0] : (generous(X0) & ~rich(X0)) => (generous(sK0) & ~rich(sK0)) [choice axiom]
43. (generous(sK0) & ~rich(sK0)) | ! [X1] : (wise(X1) & ~quiet(X1)) [skolemisation 41,42]
49. ! [X0] : ((((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))))) [nnf transformation 11]
72. kind(X0) | generous(X0) [cnf transformation 40]
77. ~rich(sK0) | ~quiet(X1) [cnf transformation 43]
79. generous(sK0) | ~quiet(X1) [cnf transformation 43]
98. ~generous(X0) | rich(X0) | kind(X0) | kind(X0) [cnf transformation 49]
99. ~generous(X0) | rich(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 49]
129. quiet(mary) [cnf transformation 24]
132. ~generous(X0) | rich(X0) | kind(X0) [duplicate literal removal 98]
133. ~kind(X0) | rich(X0) | ~generous(X0) [duplicate literal removal 99]
164. 8 <=> generous(sK0) [avatar definition]
169. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
170. ~quiet(X1) <- (9) [avatar component clause 169]
171. 9 | 8 [avatar split clause 79,164,169]
173. 10 <=> rich(sK0) [avatar definition]
175. ~rich(sK0) <- (~10) [avatar component clause 173]
177. 9 | ~10 [avatar split clause 77,173,169]
192. rich(X0) | kind(X0) [subsumption resolution 132,72]
290. kind(sK0) <- (~10) [resolution 192,175]
365. rich(sK0) | ~generous(sK0) <- (~10) [resolution 133,290]
367. ~generous(sK0) <- (~10) [subsumption resolution 365,175]
370. ~8 | 10 [avatar split clause 367,173,164]
378. $false <- (9) [resolution 170,129]
379. ~9 [avatar contradiction clause 378]
380. $false [avatar sat refutation 171,177,370,379]
% SZS output end Proof for 2854484648916320851427244
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not calm then susan is both not patient and not creative. Everyone who is both patient and happy is generous. Everyone who is not wise is either not tall or not old. Everyone who is rich is not generous or brave. Everyone who is funny is happy or not tall and vice versa. Everyone who is not quiet is not humble or generous and vice versa. Everyone who is not old is both not happy and calm. Everyone who is either not happy or not kind is either humble or old. If someone is either humble or patient then someone is not humble or rich and vice versa. If susan is either patient or not happy then fred is not kind. Everyone who is not happy or quiet is either rich or wise and vice versa. If alice is either quiet or rich then someone is both not old and calm. Everyone who is both not tall and brave is not calm. Everyone who is not generous or funny is not wise or not humble and vice versa. Everyone who is either strong or not funny is both calm and not generous. Everyone who is either not tall or not wise is either humble or not patient and vice versa. Alice is funny. Someone is not wise. Susan is calm. Someone is either not calm or not patient. Alice is both not generous and kind. Susan is either not curious or not old. Someone is either not happy or tall. Someone is either not funny or patient. | Alice is not old. | contradiction | ((~calm(lucy))=>((~patient(susan)&~creative(susan))))&
(![X]:((patient(X)&happy(X))=>generous(X)))&
(![X]:(~wise(X)=>(~tall(X)<~>~old(X))))&
(![X]:(rich(X)=>(~generous(X)|brave(X))))&
(![X]:(funny(X)<=>(happy(X)|~tall(X))))&
(![X]:(~quiet(X)<=>(~humble(X)|generous(X))))&
(![X]:(~old(X)=>(~happy(X)&calm(X))))&
(![X]:((~happy(X)<~>~kind(X))=>(humble(X)<~>old(X))))&
((?[X]:((humble(X)<~>patient(X))))<=>(?[X]:((~humble(X)|rich(X)))))&
(((patient(susan)<~>~happy(susan)))=>(~kind(fred)))&
(![X]:((~happy(X)|quiet(X))<=>(rich(X)<~>wise(X))))&
(((quiet(alice)<~>rich(alice)))=>(?[X]:((~old(X)&calm(X)))))&
(![X]:((~tall(X)&brave(X))=>~calm(X)))&
(![X]:((~generous(X)|funny(X))<=>(~wise(X)|~humble(X))))&
(![X]:((strong(X)<~>~funny(X))=>(calm(X)&~generous(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(humble(X)<~>~patient(X))))&
(funny(alice))&
(?[X]:(~wise(X)))&
(calm(susan))&
(?[X]:((~calm(X)<~>~patient(X))))&
((~generous(alice)&kind(alice)))&
((~curious(susan)<~>~old(susan)))&
(?[X]:((~happy(X)<~>tall(X))))&
(?[X]:((~funny(X)<~>patient(X)))) | ~old(alice) | [
"p2",
"p4",
"p6",
"p7",
"p13",
"p16",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3503576030287096504730528
% SZS output start Proof for 3503576030287096504730528
3. ! [X0] : (~wise(X0) => (~tall(X0) <~> ~old(X0))) [input p2]
5. ! [X0] : (funny(X0) <=> (~tall(X0) | happy(X0))) [input p4]
7. ! [X0] : (~old(X0) => (calm(X0) & ~happy(X0))) [input p6]
8. ! [X0] : ((~happy(X0) <~> ~kind(X0)) => (humble(X0) <~> old(X0))) [input p7]
14. ! [X0] : ((funny(X0) | ~generous(X0)) <=> (~humble(X0) | ~wise(X0))) [input p13]
17. funny(alice) [input p16]
21. kind(alice) & ~generous(alice) [input p20]
25. ~old(alice) [input hypothesis]
31. ! [X0] : ((~tall(X0) <~> ~old(X0)) | wise(X0)) [ennf transformation 3]
34. ! [X0] : ((calm(X0) & ~happy(X0)) | old(X0)) [ennf transformation 7]
35. ! [X0] : ((humble(X0) <~> old(X0)) | (~happy(X0) <=> ~kind(X0))) [ennf transformation 8]
41. ! [X0] : (((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | wise(X0)) [nnf transformation 31]
42. ! [X0] : ((funny(X0) | (tall(X0) & ~happy(X0))) & ((~tall(X0) | happy(X0)) | ~funny(X0))) [nnf transformation 5]
43. ! [X0] : ((funny(X0) | (tall(X0) & ~happy(X0))) & (~tall(X0) | happy(X0) | ~funny(X0))) [flattening 42]
46. ! [X0] : (((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ((~happy(X0) | kind(X0)) & (~kind(X0) | happy(X0)))) [nnf transformation 35]
58. ! [X0] : (((funny(X0) | ~generous(X0)) | (humble(X0) & wise(X0))) & ((~humble(X0) | ~wise(X0)) | (~funny(X0) & generous(X0)))) [nnf transformation 14]
59. ! [X0] : ((funny(X0) | ~generous(X0) | (humble(X0) & wise(X0))) & (~humble(X0) | ~wise(X0) | (~funny(X0) & generous(X0)))) [flattening 58]
77. old(X0) | tall(X0) | wise(X0) [cnf transformation 41]
79. ~funny(X0) | happy(X0) | ~tall(X0) [cnf transformation 43]
85. ~happy(X0) | old(X0) [cnf transformation 34]
87. old(X0) | humble(X0) | ~kind(X0) | happy(X0) [cnf transformation 46]
111. ~humble(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 59]
126. funny(alice) [cnf transformation 17]
132. kind(alice) [cnf transformation 21]
139. ~old(alice) [cnf transformation 25]
150. ~kind(X0) | humble(X0) | old(X0) [subsumption resolution 87,85]
259. tall(alice) | wise(alice) [resolution 77,139]
264. 25 <=> wise(alice) [avatar definition]
268. 26 <=> tall(alice) [avatar definition]
271. 25 | 26 [avatar split clause 259,268,264]
283. happy(alice) | ~tall(alice) [resolution 79,126]
286. 29 <=> happy(alice) [avatar definition]
288. happy(alice) <- (29) [avatar component clause 286]
289. ~26 | 29 [avatar split clause 283,286,268]
307. humble(alice) | old(alice) [resolution 150,132]
308. humble(alice) [subsumption resolution 307,139]
311. ~wise(alice) | ~funny(alice) [resolution 308,111]
326. ~wise(alice) [subsumption resolution 311,126]
327. ~25 [avatar split clause 326,264]
338. old(alice) <- (29) [resolution 288,85]
341. $false <- (29) [subsumption resolution 338,139]
342. ~29 [avatar contradiction clause 341]
343. $false [avatar sat refutation 271,289,327,342]
% SZS output end Proof for 3503576030287096504730528
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not brave or rich and vice versa.
Everyone who is not quiet is creative or old and vice versa.
Everyone who is either curious or not humble is either generous or wise.
If mary is not calm then someone is both not rich and patient.
If john is patient then paul is not rich.
If alice is either calm or not rich then alice is kind or not kind and vice versa.
If someone is calm then someone is both not curious and tall.
If susan is not quiet or not calm then paul is either not old or not generous.
If someone is both brave and not kind then someone is both not kind and old.
Everyone who is either strong or old is both not patient and not happy.
Everyone who is either generous or not curious is both kind and not humble and vice versa.
If someone is either funny or not brave then someone is curious and vice versa.
Everyone who is both not creative and not patient is either curious or not curious and vice versa.
Everyone who is not wise or brave is kind and vice versa.
Everyone who is not patient is either calm or not quiet.
Someone is not funny or humble.
Someone is both not happy and not calm.
Lucy is both generous and not brave.
Alice is both humble and funny.
John is both tall and not brave.
Alice is kind or tall.
Alice is funny. | Alice is not creative. | entailment | (![X]:(happy(X)<=>(~brave(X)|rich(X))))&
(![X]:(~quiet(X)<=>(creative(X)|old(X))))&
(![X]:((curious(X)<~>~humble(X))=>(generous(X)<~>wise(X))))&
((~calm(mary))=>(?[X]:((~rich(X)&patient(X)))))&
((patient(john))=>(~rich(paul)))&
(((calm(alice)<~>~rich(alice)))<=>((kind(alice)|~kind(alice))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&tall(X)))))&
(((~quiet(susan)|~calm(susan)))=>((~old(paul)<~>~generous(paul))))&
((?[X]:((brave(X)&~kind(X))))=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((strong(X)<~>old(X))=>(~patient(X)&~happy(X))))&
(![X]:((generous(X)<~>~curious(X))<=>(kind(X)&~humble(X))))&
((?[X]:((funny(X)<~>~brave(X))))<=>(?[X]:(curious(X))))&
(![X]:((~creative(X)&~patient(X))<=>(curious(X)<~>~curious(X))))&
(![X]:((~wise(X)|brave(X))<=>kind(X)))&
(![X]:(~patient(X)=>(calm(X)<~>~quiet(X))))&
(?[X]:((~funny(X)|humble(X))))&
(?[X]:((~happy(X)&~calm(X))))&
((generous(lucy)&~brave(lucy)))&
((humble(alice)&funny(alice)))&
((tall(john)&~brave(john)))&
((kind(alice)|tall(alice)))&
(funny(alice)) | ~creative(alice) | [
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 672096713801343578293133
% SZS output start Proof for 672096713801343578293133
13. ! [X0] : ((~patient(X0) & ~creative(X0)) <=> (curious(X0) <~> ~curious(X0))) [input p12]
23. creative(alice) [input hypothesis]
62. ! [X0] : (((~patient(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (patient(X0) | creative(X0)))) [nnf transformation 13]
63. ! [X0] : (((~patient(X0) & ~creative(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) & (((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | patient(X0) | creative(X0))) [flattening 62]
112. ~creative(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 63]
113. ~creative(X0) | curious(X0) | curious(X0) [cnf transformation 63]
130. creative(alice) [cnf transformation 23]
131. ~creative(X0) | ~curious(X0) [duplicate literal removal 112]
132. ~creative(X0) | curious(X0) [duplicate literal removal 113]
241. ~creative(X0) [subsumption resolution 131,132]
254. $false [subsumption resolution 130,241]
% SZS output end Proof for 672096713801343578293133
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not tall is brave.
Everyone who is not tall or not kind is either not strong or not calm.
Everyone who is strong or brave is both not strong and creative.
If john is not kind or tall then john is both not brave and generous.
Everyone who is both not generous and wise is not calm and vice versa.
If someone is both humble and rich then john is not old and vice versa.
If mary is either funny or not curious then someone is not creative and vice versa.
Everyone who is both not strong and rich is strong.
Everyone who is calm or creative is old or brave and vice versa.
Everyone who is not funny is not curious.
Everyone who is not calm or not patient is either not old or not curious and vice versa.
Everyone who is not quiet or not rich is either not tall or rich.
Everyone who is either happy or not funny is both not patient and old and vice versa.
If someone is not brave or generous then john is not calm and vice versa.
Everyone who is quiet or old is not curious.
Everyone who is both not happy and humble is either not brave or not generous and vice versa.
Paul is not generous.
Someone is not quiet or not patient.
Lucy is both not rich and kind.
Someone is either patient or not strong.
Someone is either curious or not happy. | John is patient. | contradiction | (![X]:((patient(X)|~tall(X))=>brave(X)))&
(![X]:((~tall(X)|~kind(X))=>(~strong(X)<~>~calm(X))))&
(![X]:((strong(X)|brave(X))=>(~strong(X)&creative(X))))&
(((~kind(john)|tall(john)))=>((~brave(john)&generous(john))))&
(![X]:((~generous(X)&wise(X))<=>~calm(X)))&
((?[X]:((humble(X)&rich(X))))<=>(~old(john)))&
(((funny(mary)<~>~curious(mary)))<=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)&rich(X))=>strong(X)))&
(![X]:((calm(X)|creative(X))<=>(old(X)|brave(X))))&
(![X]:(~funny(X)=>~curious(X)))&
(![X]:((~calm(X)|~patient(X))<=>(~old(X)<~>~curious(X))))&
(![X]:((~quiet(X)|~rich(X))=>(~tall(X)<~>rich(X))))&
(![X]:((happy(X)<~>~funny(X))<=>(~patient(X)&old(X))))&
((?[X]:((~brave(X)|generous(X))))<=>(~calm(john)))&
(![X]:((quiet(X)|old(X))=>~curious(X)))&
(![X]:((~happy(X)&humble(X))<=>(~brave(X)<~>~generous(X))))&
(~generous(paul))&
(?[X]:((~quiet(X)|~patient(X))))&
((~rich(lucy)&kind(lucy)))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:((curious(X)<~>~happy(X)))) | patient(john) | [
"p1",
"p2",
"p5",
"p7",
"p10",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3142933464577175674746626
% SZS output start Proof for 3142933464577175674746626
2. ! [X0] : ((~kind(X0) | ~tall(X0)) => (~strong(X0) <~> ~calm(X0))) [input p1]
3. ! [X0] : ((brave(X0) | strong(X0)) => (creative(X0) & ~strong(X0))) [input p2]
6. ? [X0] : (rich(X0) & humble(X0)) <=> ~old(john) [input p5]
8. ! [X0] : ((rich(X0) & ~strong(X0)) => strong(X0)) [input p7]
11. ! [X0] : ((~patient(X0) | ~calm(X0)) <=> (~old(X0) <~> ~curious(X0))) [input p10]
12. ! [X0] : ((~rich(X0) | ~quiet(X0)) => (~tall(X0) <~> rich(X0))) [input p11]
15. ! [X0] : ((old(X0) | quiet(X0)) => ~curious(X0)) [input p14]
22. patient(john) [input hypothesis]
23. ! [X0] : (~tall(X0) => (~strong(X0) <~> ~calm(X0))) [pure predicate removal 2]
27. ! [X0] : ((~strong(X0) <~> ~calm(X0)) | tall(X0)) [ennf transformation 23]
28. ! [X0] : ((creative(X0) & ~strong(X0)) | (~brave(X0) & ~strong(X0))) [ennf transformation 3]
30. ! [X0] : (strong(X0) | (~rich(X0) | strong(X0))) [ennf transformation 8]
31. ! [X0] : (strong(X0) | ~rich(X0) | strong(X0)) [flattening 30]
33. ! [X0] : ((~tall(X0) <~> rich(X0)) | (rich(X0) & quiet(X0))) [ennf transformation 12]
34. ! [X0] : (~curious(X0) | (~old(X0) & ~quiet(X0))) [ennf transformation 15]
35. ! [X0] : (((calm(X0) | strong(X0)) & (~calm(X0) | ~strong(X0))) | tall(X0)) [nnf transformation 27]
38. (? [X0] : (rich(X0) & humble(X0)) | old(john)) & (~old(john) | ! [X0] : (~rich(X0) | ~humble(X0))) [nnf transformation 6]
39. (? [X0] : (rich(X0) & humble(X0)) | old(john)) & (~old(john) | ! [X1] : (~rich(X1) | ~humble(X1))) [rectify 38]
40. ? [X0] : (rich(X0) & humble(X0)) => (rich(sK0) & humble(sK0)) [choice axiom]
41. ((rich(sK0) & humble(sK0)) | old(john)) & (~old(john) | ! [X1] : (~rich(X1) | ~humble(X1))) [skolemisation 39,40]
48. ! [X0] : (((~patient(X0) | ~calm(X0)) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (patient(X0) & calm(X0)))) [nnf transformation 11]
49. ! [X0] : ((~patient(X0) | ~calm(X0) | ((~old(X0) | curious(X0)) & (~curious(X0) | old(X0)))) & (((curious(X0) | old(X0)) & (~curious(X0) | ~old(X0))) | (patient(X0) & calm(X0)))) [flattening 48]
50. ! [X0] : (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (rich(X0) & quiet(X0))) [nnf transformation 33]
70. calm(X0) | strong(X0) | tall(X0) [cnf transformation 35]
71. ~strong(X0) | ~strong(X0) [cnf transformation 28]
82. rich(sK0) | old(john) [cnf transformation 41]
87. strong(X0) | ~rich(X0) | strong(X0) [cnf transformation 31]
98. ~old(X0) | ~calm(X0) | ~patient(X0) | curious(X0) [cnf transformation 49]
100. rich(X0) | ~tall(X0) | rich(X0) [cnf transformation 50]
113. ~curious(X0) | ~old(X0) [cnf transformation 34]
127. patient(john) [cnf transformation 22]
128. rich(X0) | ~tall(X0) [duplicate literal removal 100]
129. strong(X0) | ~rich(X0) [duplicate literal removal 87]
130. ~strong(X0) [duplicate literal removal 71]
146. 4 <=> old(john) [avatar definition]
148. old(john) <- (4) [avatar component clause 146]
150. 5 <=> rich(sK0) [avatar definition]
152. rich(sK0) <- (5) [avatar component clause 150]
153. 4 | 5 [avatar split clause 82,150,146]
182. ~rich(X0) [subsumption resolution 129,130]
183. ~tall(X0) [subsumption resolution 128,182]
185. 12 <=> calm(john) [avatar definition]
186. ~calm(john) <- (~12) [avatar component clause 185]
187. calm(john) <- (12) [avatar component clause 185]
225. $false <- (5) [subsumption resolution 152,182]
226. ~5 [avatar contradiction clause 225]
241. strong(john) | tall(john) <- (~12) [resolution 70,186]
244. tall(john) <- (~12) [subsumption resolution 241,130]
245. $false <- (~12) [subsumption resolution 244,183]
246. 12 [avatar contradiction clause 245]
363. ~calm(john) | ~patient(john) | curious(john) <- (4) [resolution 98,148]
366. ~patient(john) | curious(john) <- (4, 12) [subsumption resolution 363,187]
367. curious(john) <- (4, 12) [subsumption resolution 366,127]
379. ~old(john) <- (4, 12) [resolution 367,113]
381. $false <- (4, 12) [subsumption resolution 379,148]
382. ~4 | ~12 [avatar contradiction clause 381]
383. $false [avatar sat refutation 153,226,246,382]
% SZS output end Proof for 3142933464577175674746626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is not rich.
Everyone who is not funny or funny is either not tall or humble.
If someone is both patient and not wise then someone is both generous and happy.
If fred is both not happy and kind then someone is both not quiet and quiet.
If someone is both not creative and not wise then someone is not humble or not creative.
If susan is either brave or not calm then someone is not patient and vice versa.
If alice is both not calm and creative then mary is both not funny and rich and vice versa.
Everyone who is both rich and humble is not quiet or old and vice versa.
Everyone who is not generous is either not funny or not curious and vice versa.
Everyone who is either generous or not strong is both brave and not wise and vice versa.
If someone is both wise and tall then someone is both happy and wise and vice versa.
If someone is either not generous or wise then john is either patient or kind.
If mary is tall or not generous then someone is both brave and strong and vice versa.
If someone is strong then someone is kind or not curious and vice versa.
If fred is quiet then someone is not wise.
If someone is both not creative and funny then lucy is both old and not patient.
Someone is either strong or tall.
Someone is creative or strong.
Susan is not generous.
Someone is old or not patient.
Susan is old or rich.
Someone is either not funny or not wise.
Someone is either kind or patient.
Someone is calm. | Susan is not happy. | contradiction | (![X]:(~happy(X)=>~rich(X)))&
(![X]:((~funny(X)|funny(X))=>(~tall(X)<~>humble(X))))&
((?[X]:((patient(X)&~wise(X))))=>(?[X]:((generous(X)&happy(X)))))&
(((~happy(fred)&kind(fred)))=>(?[X]:((~quiet(X)&quiet(X)))))&
((?[X]:((~creative(X)&~wise(X))))=>(?[X]:((~humble(X)|~creative(X)))))&
(((brave(susan)<~>~calm(susan)))<=>(?[X]:(~patient(X))))&
(((~calm(alice)&creative(alice)))<=>((~funny(mary)&rich(mary))))&
(![X]:((rich(X)&humble(X))<=>(~quiet(X)|old(X))))&
(![X]:(~generous(X)<=>(~funny(X)<~>~curious(X))))&
(![X]:((generous(X)<~>~strong(X))<=>(brave(X)&~wise(X))))&
((?[X]:((wise(X)&tall(X))))<=>(?[X]:((happy(X)&wise(X)))))&
((?[X]:((~generous(X)<~>wise(X))))=>((patient(john)<~>kind(john))))&
(((tall(mary)|~generous(mary)))<=>(?[X]:((brave(X)&strong(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((kind(X)|~curious(X)))))&
((quiet(fred))=>(?[X]:(~wise(X))))&
((?[X]:((~creative(X)&funny(X))))=>((old(lucy)&~patient(lucy))))&
(?[X]:((strong(X)<~>tall(X))))&
(?[X]:((creative(X)|strong(X))))&
(~generous(susan))&
(?[X]:((old(X)|~patient(X))))&
((old(susan)|rich(susan)))&
(?[X]:((~funny(X)<~>~wise(X))))&
(?[X]:((kind(X)<~>patient(X))))&
(?[X]:(calm(X))) | ~happy(susan) | [
"p0",
"p7",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 375501729977566448469458
% SZS output start Proof for 375501729977566448469458
1. ! [X0] : (~happy(X0) => ~rich(X0)) [input p0]
8. ! [X0] : ((humble(X0) & rich(X0)) <=> (old(X0) | ~quiet(X0))) [input p7]
21. rich(susan) | old(susan) [input p20]
25. ~happy(susan) [input hypothesis]
30. ! [X0] : (~rich(X0) | happy(X0)) [ennf transformation 1]
54. ! [X0] : (((humble(X0) & rich(X0)) | (~old(X0) & quiet(X0))) & ((old(X0) | ~quiet(X0)) | (~humble(X0) | ~rich(X0)))) [nnf transformation 8]
55. ! [X0] : (((humble(X0) & rich(X0)) | (~old(X0) & quiet(X0))) & (old(X0) | ~quiet(X0) | ~humble(X0) | ~rich(X0))) [flattening 54]
92. ~rich(X0) | happy(X0) [cnf transformation 30]
112. rich(X0) | ~old(X0) [cnf transformation 55]
149. rich(susan) | old(susan) [cnf transformation 21]
155. ~happy(susan) [cnf transformation 25]
378. rich(susan) [subsumption resolution 149,112]
399. happy(susan) [resolution 92,378]
400. $false [subsumption resolution 399,155]
% SZS output end Proof for 375501729977566448469458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or old is both not quiet and not old and vice versa.
Everyone who is generous is not curious and vice versa.
If mary is not rich then someone is not strong or not quiet and vice versa.
If john is not generous or not rich then susan is strong and vice versa.
If lucy is both not happy and rich then paul is not humble and vice versa.
Everyone who is happy is not brave or creative and vice versa.
Everyone who is calm is not old or not tall.
Everyone who is not wise is either curious or not wise and vice versa.
Everyone who is not tall or brave is both not kind and curious and vice versa.
Everyone who is not happy or generous is funny.
Everyone who is quiet is happy and vice versa.
If mary is both humble and generous then someone is both tall and kind and vice versa.
Everyone who is strong or not patient is not brave or generous and vice versa.
Everyone who is both calm and not wise is not brave or calm.
Mary is funny.
Someone is kind or funny.
Someone is not calm or not quiet.
Paul is generous or not curious.
Paul is either not brave or not rich.
Alice is generous or strong. | Mary is rich. | entailment | (![X]:((~strong(X)|old(X))<=>(~quiet(X)&~old(X))))&
(![X]:(generous(X)<=>~curious(X)))&
((~rich(mary))<=>(?[X]:((~strong(X)|~quiet(X)))))&
(((~generous(john)|~rich(john)))<=>(strong(susan)))&
(((~happy(lucy)&rich(lucy)))<=>(~humble(paul)))&
(![X]:(happy(X)<=>(~brave(X)|creative(X))))&
(![X]:(calm(X)=>(~old(X)|~tall(X))))&
(![X]:(~wise(X)<=>(curious(X)<~>~wise(X))))&
(![X]:((~tall(X)|brave(X))<=>(~kind(X)&curious(X))))&
(![X]:((~happy(X)|generous(X))=>funny(X)))&
(![X]:(quiet(X)<=>happy(X)))&
(((humble(mary)&generous(mary)))<=>(?[X]:((tall(X)&kind(X)))))&
(![X]:((strong(X)|~patient(X))<=>(~brave(X)|generous(X))))&
(![X]:((calm(X)&~wise(X))=>(~brave(X)|calm(X))))&
(funny(mary))&
(?[X]:((kind(X)|funny(X))))&
(?[X]:((~calm(X)|~quiet(X))))&
((generous(paul)|~curious(paul)))&
((~brave(paul)<~>~rich(paul)))&
((generous(alice)|strong(alice))) | rich(mary) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 8239091023952937223850458
% SZS output start Proof for 8239091023952937223850458
1. ! [X0] : ((old(X0) | ~strong(X0)) <=> (~old(X0) & ~quiet(X0))) [input p0]
3. ~rich(mary) <=> ? [X0] : (~quiet(X0) | ~strong(X0)) [input p2]
6. ! [X0] : (happy(X0) <=> (creative(X0) | ~brave(X0))) [input p5]
8. ! [X0] : (~wise(X0) <=> (curious(X0) <~> ~wise(X0))) [input p7]
9. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (curious(X0) & ~kind(X0))) [input p8]
11. ! [X0] : (quiet(X0) <=> happy(X0)) [input p10]
21. ~rich(mary) [input hypothesis]
29. ! [X0] : (((old(X0) | ~strong(X0)) | (old(X0) | quiet(X0))) & ((~old(X0) & ~quiet(X0)) | (~old(X0) & strong(X0)))) [nnf transformation 1]
30. ! [X0] : ((old(X0) | ~strong(X0) | old(X0) | quiet(X0)) & ((~old(X0) & ~quiet(X0)) | (~old(X0) & strong(X0)))) [flattening 29]
32. (~rich(mary) | ! [X0] : (quiet(X0) & strong(X0))) & (? [X0] : (~quiet(X0) | ~strong(X0)) | rich(mary)) [nnf transformation 3]
33. (~rich(mary) | ! [X0] : (quiet(X0) & strong(X0))) & (? [X1] : (~quiet(X1) | ~strong(X1)) | rich(mary)) [rectify 32]
34. ? [X1] : (~quiet(X1) | ~strong(X1)) => (~quiet(sK0) | ~strong(sK0)) [choice axiom]
35. (~rich(mary) | ! [X0] : (quiet(X0) & strong(X0))) & ((~quiet(sK0) | ~strong(sK0)) | rich(mary)) [skolemisation 33,34]
40. ! [X0] : ((happy(X0) | (~creative(X0) & brave(X0))) & ((creative(X0) | ~brave(X0)) | ~happy(X0))) [nnf transformation 6]
41. ! [X0] : ((happy(X0) | (~creative(X0) & brave(X0))) & (creative(X0) | ~brave(X0) | ~happy(X0))) [flattening 40]
42. ! [X0] : ((~wise(X0) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | wise(X0))) [nnf transformation 8]
43. ! [X0] : (((brave(X0) | ~tall(X0)) | (~curious(X0) | kind(X0))) & ((curious(X0) & ~kind(X0)) | (~brave(X0) & tall(X0)))) [nnf transformation 9]
44. ! [X0] : ((brave(X0) | ~tall(X0) | ~curious(X0) | kind(X0)) & ((curious(X0) & ~kind(X0)) | (~brave(X0) & tall(X0)))) [flattening 43]
45. ! [X0] : ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))) [nnf transformation 11]
56. ~quiet(X0) | strong(X0) [cnf transformation 30]
63. ~quiet(sK0) | ~strong(sK0) | rich(mary) [cnf transformation 35]
73. brave(X0) | happy(X0) [cnf transformation 41]
77. wise(X0) | ~curious(X0) | wise(X0) [cnf transformation 42]
78. ~wise(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 42]
83. curious(X0) | ~brave(X0) [cnf transformation 44]
86. ~happy(X0) | quiet(X0) [cnf transformation 45]
101. ~rich(mary) [cnf transformation 21]
102. wise(X0) | ~curious(X0) [duplicate literal removal 77]
103. ~wise(X0) | ~curious(X0) [duplicate literal removal 78]
107. 1 <=> ! [X0] : quiet(X0) [avatar definition]
108. quiet(X0) <- (1) [avatar component clause 107]
110. 2 <=> rich(mary) [avatar definition]
118. ~quiet(sK0) | rich(mary) [subsumption resolution 63,56]
120. 4 <=> quiet(sK0) [avatar definition]
122. ~quiet(sK0) <- (~4) [avatar component clause 120]
123. 2 | ~4 [avatar split clause 118,120,110]
154. ~curious(X0) [subsumption resolution 102,103]
155. ~brave(X0) [subsumption resolution 83,154]
197. ~2 [avatar split clause 101,110]
202. happy(X0) [resolution 73,155]
203. quiet(X0) [resolution 86,202]
204. 1 [avatar split clause 203,107]
205. $false <- (1, ~4) [resolution 108,122]
208. ~1 | 4 [avatar contradiction clause 205]
210. $false [avatar sat refutation 123,197,204,208]
% SZS output end Proof for 8239091023952937223850458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not kind and not strong is calm or not calm.
If susan is not humble or not patient then someone is old or not calm and vice versa.
If lucy is either creative or calm then lucy is both not wise and not funny and vice versa.
If someone is both strong and not brave then john is either strong or old and vice versa.
Everyone who is either not calm or not curious is either quiet or curious.
If lucy is not brave or not wise then fred is both quiet and not kind.
If someone is both not calm and not brave then fred is either not funny or funny and vice versa.
If susan is both not curious and not funny then paul is both calm and not happy and vice versa.
Everyone who is curious or not tall is either not strong or not happy.
Everyone who is both not happy and not patient is both not quiet and generous and vice versa.
Everyone who is not creative or not calm is both happy and quiet and vice versa.
Everyone who is not curious is either not brave or not strong and vice versa.
Everyone who is quiet or old is humble.
Everyone who is rich is both not quiet and not old and vice versa.
If paul is not old or quiet then someone is brave or quiet.
Everyone who is either creative or not creative is not brave or not humble.
Paul is either curious or not brave.
Alice is both strong and not old.
Alice is both creative and not humble.
Someone is either curious or not rich.
Alice is funny.
Someone is either happy or not brave. | John is not patient. | neutral | (![X]:((~kind(X)&~strong(X))=>(calm(X)|~calm(X))))&
(((~humble(susan)|~patient(susan)))<=>(?[X]:((old(X)|~calm(X)))))&
(((creative(lucy)<~>calm(lucy)))<=>((~wise(lucy)&~funny(lucy))))&
((?[X]:((strong(X)&~brave(X))))<=>((strong(john)<~>old(john))))&
(![X]:((~calm(X)<~>~curious(X))=>(quiet(X)<~>curious(X))))&
(((~brave(lucy)|~wise(lucy)))=>((quiet(fred)&~kind(fred))))&
((?[X]:((~calm(X)&~brave(X))))<=>((~funny(fred)<~>funny(fred))))&
(((~curious(susan)&~funny(susan)))<=>((calm(paul)&~happy(paul))))&
(![X]:((curious(X)|~tall(X))=>(~strong(X)<~>~happy(X))))&
(![X]:((~happy(X)&~patient(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~creative(X)|~calm(X))<=>(happy(X)&quiet(X))))&
(![X]:(~curious(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((quiet(X)|old(X))=>humble(X)))&
(![X]:(rich(X)<=>(~quiet(X)&~old(X))))&
(((~old(paul)|quiet(paul)))=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((creative(X)<~>~creative(X))=>(~brave(X)|~humble(X))))&
((curious(paul)<~>~brave(paul)))&
((strong(alice)&~old(alice)))&
((creative(alice)&~humble(alice)))&
(?[X]:((curious(X)<~>~rich(X))))&
(funny(alice))&
(?[X]:((happy(X)<~>~brave(X)))) | ~patient(john) | []
| null | 0 |
If someone is both generous and curious then someone is both tall and not quiet and vice versa.
If alice is not humble or not quiet then fred is both not kind and not rich and vice versa.
If someone is either not humble or tall then fred is both not strong and not humble.
If someone is both not curious and old then mary is curious.
If paul is both patient and not brave then fred is wise.
If alice is tall then paul is both not brave and not tall.
Everyone who is rich or kind is both not patient and happy.
If someone is both old and calm then someone is either old or not generous.
If someone is creative or not happy then john is either not happy or rich.
If someone is not generous or not old then someone is not curious or generous and vice versa.
If lucy is creative then someone is both quiet and generous.
Everyone who is curious or wise is tall or strong and vice versa.
Everyone who is funny or not wise is either patient or humble.
If alice is rich then susan is not patient.
Everyone who is creative or strong is both not creative and brave and vice versa.
Everyone who is not kind is calm.
Paul is kind.
Paul is either not humble or quiet.
Someone is either not calm or not funny.
Someone is either quiet or generous.
Fred is kind or patient.
Alice is generous or not strong.
Fred is old.
Someone is either not happy or not old. | Lucy is not creative. | entailment | ((?[X]:((generous(X)&curious(X))))<=>(?[X]:((tall(X)&~quiet(X)))))&
(((~humble(alice)|~quiet(alice)))<=>((~kind(fred)&~rich(fred))))&
((?[X]:((~humble(X)<~>tall(X))))=>((~strong(fred)&~humble(fred))))&
((?[X]:((~curious(X)&old(X))))=>(curious(mary)))&
(((patient(paul)&~brave(paul)))=>(wise(fred)))&
((tall(alice))=>((~brave(paul)&~tall(paul))))&
(![X]:((rich(X)|kind(X))=>(~patient(X)&happy(X))))&
((?[X]:((old(X)&calm(X))))=>(?[X]:((old(X)<~>~generous(X)))))&
((?[X]:((creative(X)|~happy(X))))=>((~happy(john)<~>rich(john))))&
((?[X]:((~generous(X)|~old(X))))<=>(?[X]:((~curious(X)|generous(X)))))&
((creative(lucy))=>(?[X]:((quiet(X)&generous(X)))))&
(![X]:((curious(X)|wise(X))<=>(tall(X)|strong(X))))&
(![X]:((funny(X)|~wise(X))=>(patient(X)<~>humble(X))))&
((rich(alice))=>(~patient(susan)))&
(![X]:((creative(X)|strong(X))<=>(~creative(X)&brave(X))))&
(![X]:(~kind(X)=>calm(X)))&
(kind(paul))&
((~humble(paul)<~>quiet(paul)))&
(?[X]:((~calm(X)<~>~funny(X))))&
(?[X]:((quiet(X)<~>generous(X))))&
((kind(fred)|patient(fred)))&
((generous(alice)|~strong(alice)))&
(old(fred))&
(?[X]:((~happy(X)<~>~old(X)))) | ~creative(lucy) | [
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 70949182342130560221670
% SZS output start Proof for 70949182342130560221670
15. ! [X0] : ((strong(X0) | creative(X0)) <=> (brave(X0) & ~creative(X0))) [input p14]
25. creative(lucy) [input hypothesis]
64. ! [X0] : (((strong(X0) | creative(X0)) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | (~strong(X0) & ~creative(X0)))) [nnf transformation 15]
65. ! [X0] : ((strong(X0) | creative(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | (~strong(X0) & ~creative(X0)))) [flattening 64]
118. ~creative(X0) | ~creative(X0) [cnf transformation 65]
136. creative(lucy) [cnf transformation 25]
137. ~creative(X0) [duplicate literal removal 118]
261. 28 <=> ! [X0] : ~creative(X0) [avatar definition]
262. ~creative(X0) <- (28) [avatar component clause 261]
297. 37 <=> creative(lucy) [avatar definition]
298. creative(lucy) <- (37) [avatar component clause 297]
319. 28 [avatar split clause 137,261]
374. 37 [avatar split clause 136,297]
375. $false <- (28, 37) [resolution 298,262]
376. ~28 | ~37 [avatar contradiction clause 375]
377. $false [avatar sat refutation 319,374,376]
% SZS output end Proof for 70949182342130560221670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not curious is both not creative and tall and vice versa.
Everyone who is both not humble and generous is both humble and not creative and vice versa.
Everyone who is either happy or not old is both not tall and not old.
Everyone who is either creative or patient is either not funny or funny and vice versa.
If someone is both brave and generous then alice is either brave or kind.
Everyone who is both not funny and strong is creative or not tall.
If john is not wise then someone is both rich and strong.
If paul is wise or kind then someone is not wise or rich.
Everyone who is not rich is either not brave or not tall and vice versa.
Everyone who is not happy or not brave is not old and vice versa.
If fred is not old then alice is both not happy and not calm and vice versa.
Everyone who is strong is both not funny and not humble.
If someone is both not funny and not kind then someone is either old or not calm and vice versa.
Everyone who is either not old or not rich is either not creative or not old and vice versa.
If someone is either humble or not patient then someone is either tall or not kind.
If paul is both not humble and creative then someone is happy or not curious.
Someone is not kind.
Someone is both not wise and patient.
Alice is both wise and not rich.
Paul is old or not rich.
Someone is either tall or not funny.
Alice is quiet.
Someone is not generous.
Fred is not humble or quiet. | Alice is not brave. | contradiction | (![X]:((strong(X)|~curious(X))<=>(~creative(X)&tall(X))))&
(![X]:((~humble(X)&generous(X))<=>(humble(X)&~creative(X))))&
(![X]:((happy(X)<~>~old(X))=>(~tall(X)&~old(X))))&
(![X]:((creative(X)<~>patient(X))<=>(~funny(X)<~>funny(X))))&
((?[X]:((brave(X)&generous(X))))=>((brave(alice)<~>kind(alice))))&
(![X]:((~funny(X)&strong(X))=>(creative(X)|~tall(X))))&
((~wise(john))=>(?[X]:((rich(X)&strong(X)))))&
(((wise(paul)|kind(paul)))=>(?[X]:((~wise(X)|rich(X)))))&
(![X]:(~rich(X)<=>(~brave(X)<~>~tall(X))))&
(![X]:((~happy(X)|~brave(X))<=>~old(X)))&
((~old(fred))<=>((~happy(alice)&~calm(alice))))&
(![X]:(strong(X)=>(~funny(X)&~humble(X))))&
((?[X]:((~funny(X)&~kind(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((~old(X)<~>~rich(X))<=>(~creative(X)<~>~old(X))))&
((?[X]:((humble(X)<~>~patient(X))))=>(?[X]:((tall(X)<~>~kind(X)))))&
(((~humble(paul)&creative(paul)))=>(?[X]:((happy(X)|~curious(X)))))&
(?[X]:(~kind(X)))&
(?[X]:((~wise(X)&patient(X))))&
((wise(alice)&~rich(alice)))&
((old(paul)|~rich(paul)))&
(?[X]:((tall(X)<~>~funny(X))))&
(quiet(alice))&
(?[X]:(~generous(X)))&
((~humble(fred)|quiet(fred))) | ~brave(alice) | [
"p2",
"p8",
"p9",
"p10",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 2574473985259903462783897
% SZS output start Proof for 2574473985259903462783897
3. ! [X0] : ((happy(X0) <~> ~old(X0)) => (~old(X0) & ~tall(X0))) [input p2]
9. ! [X0] : (~rich(X0) <=> (~brave(X0) <~> ~tall(X0))) [input p8]
10. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> ~old(X0)) [input p9]
11. ~old(fred) <=> (~calm(alice) & ~happy(alice)) [input p10]
19. ~rich(alice) & wise(alice) [input p18]
25. ~brave(alice) [input hypothesis]
30. ! [X0] : ((~old(X0) & ~tall(X0)) | (happy(X0) <=> ~old(X0))) [ennf transformation 3]
44. ! [X0] : ((~old(X0) & ~tall(X0)) | ((happy(X0) | old(X0)) & (~old(X0) | ~happy(X0)))) [nnf transformation 30]
51. ! [X0] : ((~rich(X0) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0)))) & (((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | rich(X0))) [nnf transformation 9]
52. ! [X0] : (((~brave(X0) | ~happy(X0)) | old(X0)) & (~old(X0) | (brave(X0) & happy(X0)))) [nnf transformation 10]
53. ! [X0] : ((~brave(X0) | ~happy(X0) | old(X0)) & (~old(X0) | (brave(X0) & happy(X0)))) [flattening 52]
54. (~old(fred) | (calm(alice) | happy(alice))) & ((~calm(alice) & ~happy(alice)) | old(fred)) [nnf transformation 11]
55. (~old(fred) | calm(alice) | happy(alice)) & ((~calm(alice) & ~happy(alice)) | old(fred)) [flattening 54]
87. ~tall(X0) | happy(X0) | old(X0) [cnf transformation 44]
88. ~old(X0) | ~old(X0) | ~happy(X0) [cnf transformation 44]
106. rich(X0) | brave(X0) | tall(X0) [cnf transformation 51]
109. ~old(X0) | happy(X0) [cnf transformation 53]
112. ~happy(alice) | old(fred) [cnf transformation 55]
140. ~rich(alice) [cnf transformation 19]
145. ~brave(alice) [cnf transformation 25]
154. ~old(X0) | ~happy(X0) [duplicate literal removal 88]
163. 2 <=> brave(alice) [avatar definition]
165. ~brave(alice) <- (~2) [avatar component clause 163]
207. ~old(X0) [subsumption resolution 109,154]
209. ~happy(alice) [subsumption resolution 112,207]
283. ~2 [avatar split clause 145,163]
291. brave(alice) | tall(alice) [resolution 106,140]
294. tall(alice) <- (~2) [subsumption resolution 291,165]
304. happy(alice) | old(alice) <- (~2) [resolution 294,87]
305. old(alice) <- (~2) [subsumption resolution 304,209]
306. $false <- (~2) [subsumption resolution 305,207]
307. 2 [avatar contradiction clause 306]
308. $false [avatar sat refutation 283,307]
% SZS output end Proof for 2574473985259903462783897
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either calm or generous then someone is not wise and vice versa.
If someone is either old or not strong then someone is tall and vice versa.
Everyone who is humble or quiet is both not humble and not brave and vice versa.
Everyone who is old is either not tall or not strong.
If fred is not wise or old then someone is not brave and vice versa.
Everyone who is wise or not funny is generous or not calm and vice versa.
If lucy is not rich or generous then lucy is kind and vice versa.
Everyone who is both not rich and not calm is not strong or tall.
If john is not wise or not brave then someone is creative or not happy and vice versa.
Everyone who is not brave is quiet or not wise.
Everyone who is quiet is either not brave or brave and vice versa.
Everyone who is either generous or not humble is either not tall or kind.
Everyone who is both tall and not kind is both not rich and calm.
Everyone who is either not calm or not brave is either quiet or not generous and vice versa.
Everyone who is rich is either not tall or not old and vice versa.
Everyone who is not old is funny or curious and vice versa.
Paul is curious or not tall.
Alice is wise or not patient.
Someone is not humble or rich.
Someone is not kind.
Someone is quiet.
Someone is both generous and not strong.
Someone is either humble or not patient. | Paul is not generous. | neutral | (((calm(john)<~>generous(john)))<=>(?[X]:(~wise(X))))&
((?[X]:((old(X)<~>~strong(X))))<=>(?[X]:(tall(X))))&
(![X]:((humble(X)|quiet(X))<=>(~humble(X)&~brave(X))))&
(![X]:(old(X)=>(~tall(X)<~>~strong(X))))&
(((~wise(fred)|old(fred)))<=>(?[X]:(~brave(X))))&
(![X]:((wise(X)|~funny(X))<=>(generous(X)|~calm(X))))&
(((~rich(lucy)|generous(lucy)))<=>(kind(lucy)))&
(![X]:((~rich(X)&~calm(X))=>(~strong(X)|tall(X))))&
(((~wise(john)|~brave(john)))<=>(?[X]:((creative(X)|~happy(X)))))&
(![X]:(~brave(X)=>(quiet(X)|~wise(X))))&
(![X]:(quiet(X)<=>(~brave(X)<~>brave(X))))&
(![X]:((generous(X)<~>~humble(X))=>(~tall(X)<~>kind(X))))&
(![X]:((tall(X)&~kind(X))=>(~rich(X)&calm(X))))&
(![X]:((~calm(X)<~>~brave(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:(rich(X)<=>(~tall(X)<~>~old(X))))&
(![X]:(~old(X)<=>(funny(X)|curious(X))))&
((curious(paul)|~tall(paul)))&
((wise(alice)|~patient(alice)))&
(?[X]:((~humble(X)|rich(X))))&
(?[X]:(~kind(X)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)&~strong(X))))&
(?[X]:((humble(X)<~>~patient(X)))) | ~generous(paul) | []
| null | 0 |
Everyone who is either not humble or not happy is either not happy or curious and vice versa.
If lucy is both not curious and not strong then someone is either not brave or not patient and vice versa.
Everyone who is either not tall or quiet is brave or not calm.
Everyone who is either not kind or not rich is either not quiet or generous.
Everyone who is tall or not funny is not wise or wise and vice versa.
Everyone who is either funny or rich is both not wise and not rich and vice versa.
Everyone who is both not generous and not creative is either humble or not generous.
Everyone who is either creative or calm is strong or not old and vice versa.
If susan is patient or not brave then susan is both not patient and not old and vice versa.
If someone is happy or tall then john is either not calm or tall.
Everyone who is not calm is generous and vice versa.
Everyone who is not tall or not funny is either rich or not calm and vice versa.
Everyone who is either not kind or not wise is brave and vice versa.
If someone is either not brave or not patient then someone is not funny or not curious.
Everyone who is not humble or not calm is not patient or not creative and vice versa.
If someone is generous then alice is either happy or funny and vice versa.
Fred is not calm or funny.
Mary is both not creative and not kind.
Someone is wise or not rich.
Fred is both creative and not generous.
John is creative or not wise.
Alice is both funny and not brave.
John is either tall or not happy. | Fred is calm. | entailment | (![X]:((~humble(X)<~>~happy(X))<=>(~happy(X)<~>curious(X))))&
(((~curious(lucy)&~strong(lucy)))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
(![X]:((~tall(X)<~>quiet(X))=>(brave(X)|~calm(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((tall(X)|~funny(X))<=>(~wise(X)|wise(X))))&
(![X]:((funny(X)<~>rich(X))<=>(~wise(X)&~rich(X))))&
(![X]:((~generous(X)&~creative(X))=>(humble(X)<~>~generous(X))))&
(![X]:((creative(X)<~>calm(X))<=>(strong(X)|~old(X))))&
(((patient(susan)|~brave(susan)))<=>((~patient(susan)&~old(susan))))&
((?[X]:((happy(X)|tall(X))))=>((~calm(john)<~>tall(john))))&
(![X]:(~calm(X)<=>generous(X)))&
(![X]:((~tall(X)|~funny(X))<=>(rich(X)<~>~calm(X))))&
(![X]:((~kind(X)<~>~wise(X))<=>brave(X)))&
((?[X]:((~brave(X)<~>~patient(X))))=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~humble(X)|~calm(X))<=>(~patient(X)|~creative(X))))&
((?[X]:(generous(X)))<=>((happy(alice)<~>funny(alice))))&
((~calm(fred)|funny(fred)))&
((~creative(mary)&~kind(mary)))&
(?[X]:((wise(X)|~rich(X))))&
((creative(fred)&~generous(fred)))&
((creative(john)|~wise(john)))&
((funny(alice)&~brave(alice)))&
((tall(john)<~>~happy(john))) | calm(fred) | [
"p10",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 12336116058334607284719
% SZS output start Proof for 12336116058334607284719
11. ! [X0] : (~calm(X0) <=> generous(X0)) [input p10]
20. ~generous(fred) & creative(fred) [input p19]
24. ~calm(fred) [input hypothesis]
51. ! [X0] : ((~calm(X0) | ~generous(X0)) & (generous(X0) | calm(X0))) [nnf transformation 11]
115. generous(X0) | calm(X0) [cnf transformation 51]
142. ~generous(fred) [cnf transformation 20]
148. ~calm(fred) [cnf transformation 24]
284. calm(fred) [resolution 115,142]
285. $false [subsumption resolution 284,148]
% SZS output end Proof for 12336116058334607284719
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave then fred is wise or tall and vice versa. Everyone who is funny is humble. Everyone who is both rich and happy is either not strong or not creative. Everyone who is not rich is either not strong or not patient and vice versa. Everyone who is both not curious and quiet is not generous and vice versa. If someone is both not funny and not humble then mary is not strong or not brave. Everyone who is generous or kind is not tall and vice versa. Everyone who is both not patient and not strong is kind or not brave and vice versa. Everyone who is either tall or not wise is tall and vice versa. Everyone who is both not funny and not tall is both not calm and old and vice versa. Everyone who is both rich and not generous is either not tall or not funny. Everyone who is not strong is both not generous and not patient. Everyone who is either not humble or not generous is quiet or not brave. If someone is either kind or happy then alice is both funny and generous and vice versa. If john is either old or not funny then someone is not old. Fred is either calm or not tall. Lucy is either humble or creative. Mary is both not old and calm. Mary is not kind or not quiet. Lucy is not funny or happy. Someone is not old. John is funny. Someone is either not quiet or not kind. | Fred is not rich. | contradiction | ((~brave(fred))<=>((wise(fred)|tall(fred))))&
(![X]:(funny(X)=>humble(X)))&
(![X]:((rich(X)&happy(X))=>(~strong(X)<~>~creative(X))))&
(![X]:(~rich(X)<=>(~strong(X)<~>~patient(X))))&
(![X]:((~curious(X)&quiet(X))<=>~generous(X)))&
((?[X]:((~funny(X)&~humble(X))))=>((~strong(mary)|~brave(mary))))&
(![X]:((generous(X)|kind(X))<=>~tall(X)))&
(![X]:((~patient(X)&~strong(X))<=>(kind(X)|~brave(X))))&
(![X]:((tall(X)<~>~wise(X))<=>tall(X)))&
(![X]:((~funny(X)&~tall(X))<=>(~calm(X)&old(X))))&
(![X]:((rich(X)&~generous(X))=>(~tall(X)<~>~funny(X))))&
(![X]:(~strong(X)=>(~generous(X)&~patient(X))))&
(![X]:((~humble(X)<~>~generous(X))=>(quiet(X)|~brave(X))))&
((?[X]:((kind(X)<~>happy(X))))<=>((funny(alice)&generous(alice))))&
(((old(john)<~>~funny(john)))=>(?[X]:(~old(X))))&
((calm(fred)<~>~tall(fred)))&
((humble(lucy)<~>creative(lucy)))&
((~old(mary)&calm(mary)))&
((~kind(mary)|~quiet(mary)))&
((~funny(lucy)|happy(lucy)))&
(?[X]:(~old(X)))&
(funny(john))&
(?[X]:((~quiet(X)<~>~kind(X)))) | ~rich(fred) | [
"p0",
"p3",
"p7",
"p8",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 6455480757131813962813310
% SZS output start Proof for 6455480757131813962813310
1. ~brave(fred) <=> (tall(fred) | wise(fred)) [input p0]
4. ! [X0] : (~rich(X0) <=> (~strong(X0) <~> ~patient(X0))) [input p3]
8. ! [X0] : ((~strong(X0) & ~patient(X0)) <=> (~brave(X0) | kind(X0))) [input p7]
9. ! [X0] : ((tall(X0) <~> ~wise(X0)) <=> tall(X0)) [input p8]
12. ! [X0] : (~strong(X0) => (~patient(X0) & ~generous(X0))) [input p11]
24. ~rich(fred) [input hypothesis]
25. ! [X0] : (~rich(X0) => (~strong(X0) <~> ~patient(X0))) [unused predicate definition removal 4]
29. ! [X0] : ((~strong(X0) <~> ~patient(X0)) | rich(X0)) [ennf transformation 25]
34. ! [X0] : ((~patient(X0) & ~generous(X0)) | strong(X0)) [ennf transformation 12]
38. (~brave(fred) | (~tall(fred) & ~wise(fred))) & ((tall(fred) | wise(fred)) | brave(fred)) [nnf transformation 1]
39. (~brave(fred) | (~tall(fred) & ~wise(fred))) & (tall(fred) | wise(fred) | brave(fred)) [flattening 38]
41. ! [X0] : (((patient(X0) | strong(X0)) & (~patient(X0) | ~strong(X0))) | rich(X0)) [nnf transformation 29]
46. ! [X0] : (((~strong(X0) & ~patient(X0)) | (brave(X0) & ~kind(X0))) & ((~brave(X0) | kind(X0)) | (strong(X0) | patient(X0)))) [nnf transformation 8]
47. ! [X0] : (((~strong(X0) & ~patient(X0)) | (brave(X0) & ~kind(X0))) & (~brave(X0) | kind(X0) | strong(X0) | patient(X0))) [flattening 46]
48. ! [X0] : ((((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | ~tall(X0)) & (tall(X0) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0))))) [nnf transformation 9]
69. ~brave(fred) | ~wise(fred) [cnf transformation 39]
75. patient(X0) | strong(X0) | rich(X0) [cnf transformation 41]
87. ~strong(X0) | brave(X0) [cnf transformation 47]
89. tall(X0) | tall(X0) | wise(X0) [cnf transformation 48]
91. wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 48]
99. ~patient(X0) | strong(X0) [cnf transformation 34]
122. ~rich(fred) [cnf transformation 24]
123. tall(X0) | wise(X0) [duplicate literal removal 89]
124. ~tall(X0) | wise(X0) [duplicate literal removal 91]
130. 2 <=> brave(fred) [avatar definition]
132. ~brave(fred) <- (~2) [avatar component clause 130]
135. 3 <=> wise(fred) [avatar definition]
137. ~wise(fred) <- (~3) [avatar component clause 135]
138. ~3 | ~2 [avatar split clause 69,130,135]
153. wise(X0) [subsumption resolution 123,124]
243. $false <- (~3) [subsumption resolution 137,153]
244. 3 [avatar contradiction clause 243]
256. strong(X1) | rich(X1) | strong(X1) [resolution 75,99]
259. strong(X1) | rich(X1) [duplicate literal removal 256]
268. rich(X0) | brave(X0) [resolution 259,87]
349. brave(fred) [resolution 268,122]
351. $false <- (~2) [subsumption resolution 349,132]
352. 2 [avatar contradiction clause 351]
353. $false [avatar sat refutation 138,244,352]
% SZS output end Proof for 6455480757131813962813310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and kind is happy and vice versa.
If alice is either patient or not happy then someone is not strong.
Everyone who is both humble and happy is both rich and not old.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Everyone who is both rich and strong is tall or not tall and vice versa.
Fred is both quiet and funny.
Lucy is both not brave and creative.
Someone is not kind or not tall.
Mary is both not humble and brave.
Someone is not patient.
Lucy is either not humble or funny. | Mary is curious. | entailment | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((patient(alice)<~>~happy(alice)))=>(?[X]:(~strong(X))))&
(![X]:((humble(X)&happy(X))=>(rich(X)&~old(X))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(![X]:((rich(X)&strong(X))<=>(tall(X)|~tall(X))))&
((quiet(fred)&funny(fred)))&
((~brave(lucy)&creative(lucy)))&
(?[X]:((~kind(X)|~tall(X))))&
((~humble(mary)&brave(mary)))&
(?[X]:(~patient(X)))&
((~humble(lucy)<~>funny(lucy))) | curious(mary) | [
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 1587881388148256754505675
% SZS output start Proof for 1587881388148256754505675
12. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p11]
22. ~curious(mary) [input hypothesis]
51. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 12]
52. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 51]
91. curious(X0) | curious(X0) [cnf transformation 52]
121. ~curious(mary) [cnf transformation 22]
122. curious(X0) [duplicate literal removal 91]
218. $false [subsumption resolution 121,122]
% SZS output end Proof for 1587881388148256754505675
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or funny then alice is not kind or not generous and vice versa.
Everyone who is wise or tall is not happy and vice versa.
Everyone who is not patient is not quiet.
Everyone who is not kind is both generous and wise and vice versa.
If john is both not old and curious then someone is not patient or wise and vice versa.
Everyone who is both calm and not calm is not happy or funny and vice versa.
If someone is either not rich or not humble then someone is both tall and not strong and vice versa.
If someone is both not curious and strong then someone is both generous and not wise.
Everyone who is either not curious or funny is both happy and not rich.
If mary is either not funny or curious then someone is either funny or brave.
If paul is not wise then someone is rich or tall.
Everyone who is both not funny and funny is not creative.
Everyone who is not funny is both patient and rich.
Everyone who is not wise is not generous or not kind and vice versa.
Everyone who is either not quiet or quiet is both not brave and quiet and vice versa.
If paul is both old and not creative then someone is both brave and not generous.
Paul is calm.
Paul is both not generous and quiet.
Susan is generous or not creative.
Someone is patient or not humble.
Someone is both humble and not tall. | Paul is curious. | entailment | ((?[X]:((~wise(X)<~>funny(X))))<=>((~kind(alice)|~generous(alice))))&
(![X]:((wise(X)|tall(X))<=>~happy(X)))&
(![X]:(~patient(X)=>~quiet(X)))&
(![X]:(~kind(X)<=>(generous(X)&wise(X))))&
(((~old(john)&curious(john)))<=>(?[X]:((~patient(X)|wise(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~happy(X)|funny(X))))&
((?[X]:((~rich(X)<~>~humble(X))))<=>(?[X]:((tall(X)&~strong(X)))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:((generous(X)&~wise(X)))))&
(![X]:((~curious(X)<~>funny(X))=>(happy(X)&~rich(X))))&
(((~funny(mary)<~>curious(mary)))=>(?[X]:((funny(X)<~>brave(X)))))&
((~wise(paul))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~funny(X)&funny(X))=>~creative(X)))&
(![X]:(~funny(X)=>(patient(X)&rich(X))))&
(![X]:(~wise(X)<=>(~generous(X)|~kind(X))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(~brave(X)&quiet(X))))&
(((old(paul)&~creative(paul)))=>(?[X]:((brave(X)&~generous(X)))))&
(calm(paul))&
((~generous(paul)&quiet(paul)))&
((generous(susan)|~creative(susan)))&
(?[X]:((patient(X)|~humble(X))))&
(?[X]:((humble(X)&~tall(X)))) | curious(paul) | [
"p5",
"p8",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 8090721220292933859662822
% SZS output start Proof for 8090721220292933859662822
6. ! [X0] : ((~calm(X0) & calm(X0)) <=> (funny(X0) | ~happy(X0))) [input p5]
9. ! [X0] : ((~curious(X0) <~> funny(X0)) => (~rich(X0) & happy(X0))) [input p8]
13. ! [X0] : (~funny(X0) => (rich(X0) & patient(X0))) [input p12]
22. ~curious(paul) [input hypothesis]
27. ! [X0] : ((~rich(X0) & happy(X0)) | (~curious(X0) <=> funny(X0))) [ennf transformation 9]
32. ! [X0] : ((rich(X0) & patient(X0)) | funny(X0)) [ennf transformation 13]
49. ! [X0] : (((~calm(X0) & calm(X0)) | (~funny(X0) & happy(X0))) & ((funny(X0) | ~happy(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 6]
50. ! [X0] : (((~calm(X0) & calm(X0)) | (~funny(X0) & happy(X0))) & (funny(X0) | ~happy(X0) | calm(X0) | ~calm(X0))) [flattening 49]
59. ! [X0] : ((~rich(X0) & happy(X0)) | ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) [nnf transformation 27]
95. calm(X0) | ~funny(X0) [cnf transformation 50]
97. ~calm(X0) | ~funny(X0) [cnf transformation 50]
108. ~rich(X0) | funny(X0) | curious(X0) [cnf transformation 59]
117. rich(X0) | funny(X0) [cnf transformation 32]
136. ~curious(paul) [cnf transformation 22]
198. ~funny(X0) [subsumption resolution 95,97]
244. ~rich(X0) | curious(X0) [subsumption resolution 108,198]
269. rich(X0) [subsumption resolution 117,198]
328. curious(X0) [resolution 244,269]
330. $false [resolution 328,136]
% SZS output end Proof for 8090721220292933859662822
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and generous is both humble and kind and vice versa.
Everyone who is not creative or not patient is either quiet or not humble and vice versa.
Everyone who is either old or humble is either brave or curious.
If alice is not funny then someone is both generous and tall and vice versa.
Everyone who is both rich and kind is both calm and creative.
Everyone who is either kind or tall is not rich or not kind.
If someone is either calm or not patient then someone is either brave or not funny and vice versa.
Everyone who is creative is both not calm and not kind and vice versa.
If someone is not creative or patient then fred is rich or not funny and vice versa.
Everyone who is not wise is either not creative or not humble.
If someone is either creative or not happy then fred is either not creative or not tall and vice versa.
Everyone who is either not calm or strong is tall and vice versa.
If someone is brave or happy then susan is both quiet and not rich.
Everyone who is creative or not calm is not tall or old.
Everyone who is not calm or not rich is both generous and not humble and vice versa.
If fred is either strong or not quiet then paul is either humble or not humble.
Paul is quiet or patient.
Someone is not creative.
Alice is not strong or tall.
Mary is curious.
Mary is both calm and kind.
Someone is not happy or happy.
Susan is not quiet or not generous. | Mary is brave. | contradiction | (![X]:((~generous(X)&generous(X))<=>(humble(X)&kind(X))))&
(![X]:((~creative(X)|~patient(X))<=>(quiet(X)<~>~humble(X))))&
(![X]:((old(X)<~>humble(X))=>(brave(X)<~>curious(X))))&
((~funny(alice))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((rich(X)&kind(X))=>(calm(X)&creative(X))))&
(![X]:((kind(X)<~>tall(X))=>(~rich(X)|~kind(X))))&
((?[X]:((calm(X)<~>~patient(X))))<=>(?[X]:((brave(X)<~>~funny(X)))))&
(![X]:(creative(X)<=>(~calm(X)&~kind(X))))&
((?[X]:((~creative(X)|patient(X))))<=>((rich(fred)|~funny(fred))))&
(![X]:(~wise(X)=>(~creative(X)<~>~humble(X))))&
((?[X]:((creative(X)<~>~happy(X))))<=>((~creative(fred)<~>~tall(fred))))&
(![X]:((~calm(X)<~>strong(X))<=>tall(X)))&
((?[X]:((brave(X)|happy(X))))=>((quiet(susan)&~rich(susan))))&
(![X]:((creative(X)|~calm(X))=>(~tall(X)|old(X))))&
(![X]:((~calm(X)|~rich(X))<=>(generous(X)&~humble(X))))&
(((strong(fred)<~>~quiet(fred)))=>((humble(paul)<~>~humble(paul))))&
((quiet(paul)|patient(paul)))&
(?[X]:(~creative(X)))&
((~strong(alice)|tall(alice)))&
(curious(mary))&
((calm(mary)&kind(mary)))&
(?[X]:((~happy(X)|happy(X))))&
((~quiet(susan)|~generous(susan))) | brave(mary) | [
"p12",
"p14",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 1169865225381377289800184
% SZS output start Proof for 1169865225381377289800184
13. ? [X0] : (happy(X0) | brave(X0)) => (~rich(susan) & quiet(susan)) [input p12]
15. ! [X0] : ((~rich(X0) | ~calm(X0)) <=> (~humble(X0) & generous(X0))) [input p14]
23. ~generous(susan) | ~quiet(susan) [input p22]
24. brave(mary) [input hypothesis]
32. (~rich(susan) & quiet(susan)) | ! [X0] : (~happy(X0) & ~brave(X0)) [ennf transformation 13]
63. ! [X0] : (((~rich(X0) | ~calm(X0)) | (humble(X0) | ~generous(X0))) & ((~humble(X0) & generous(X0)) | (rich(X0) & calm(X0)))) [nnf transformation 15]
64. ! [X0] : ((~rich(X0) | ~calm(X0) | humble(X0) | ~generous(X0)) & ((~humble(X0) & generous(X0)) | (rich(X0) & calm(X0)))) [flattening 63]
118. quiet(susan) | ~brave(X0) [cnf transformation 32]
120. ~rich(susan) | ~brave(X0) [cnf transformation 32]
125. rich(X0) | generous(X0) [cnf transformation 64]
140. ~generous(susan) | ~quiet(susan) [cnf transformation 23]
141. brave(mary) [cnf transformation 24]
258. 26 <=> rich(susan) [avatar definition]
260. ~rich(susan) <- (~26) [avatar component clause 258]
263. 27 <=> ! [X0] : ~brave(X0) [avatar definition]
264. ~brave(X0) <- (27) [avatar component clause 263]
265. 27 | ~26 [avatar split clause 120,258,263]
267. 28 <=> quiet(susan) [avatar definition]
271. 27 | 28 [avatar split clause 118,267,263]
291. 33 <=> generous(susan) [avatar definition]
293. ~generous(susan) <- (~33) [avatar component clause 291]
294. ~28 | ~33 [avatar split clause 140,291,267]
295. $false <- (27) [resolution 264,141]
296. ~27 [avatar contradiction clause 295]
300. generous(susan) <- (~26) [resolution 125,260]
301. $false <- (~26, ~33) [subsumption resolution 300,293]
302. 26 | 33 [avatar contradiction clause 301]
303. $false [avatar sat refutation 265,271,294,296,302]
% SZS output end Proof for 1169865225381377289800184
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or not kind is both not wise and brave.
Everyone who is not curious or not quiet is either not patient or humble.
If paul is not wise or generous then fred is either not strong or not tall.
Everyone who is both brave and generous is either rich or kind and vice versa.
If fred is both not calm and not rich then someone is not strong or quiet and vice versa.
Everyone who is not calm or not creative is not tall.
Everyone who is wise is either not strong or calm.
Everyone who is not brave or creative is either humble or not creative.
If someone is not funny then john is humble or tall and vice versa.
Everyone who is both rich and not creative is funny or not tall.
If someone is quiet then lucy is tall.
Everyone who is not calm is not quiet or happy.
Everyone who is tall is curious and vice versa.
Everyone who is either tall or humble is curious and vice versa.
If paul is not happy or wise then paul is either humble or not strong and vice versa.
If lucy is either not kind or not funny then fred is both wise and not rich and vice versa.
Alice is not funny or calm.
Someone is brave.
Someone is both brave and not kind.
Susan is not generous or not funny.
Susan is rich or not generous.
Someone is not humble or not tall. | Alice is humble. | contradiction | (![X]:((funny(X)|~kind(X))=>(~wise(X)&brave(X))))&
(![X]:((~curious(X)|~quiet(X))=>(~patient(X)<~>humble(X))))&
(((~wise(paul)|generous(paul)))=>((~strong(fred)<~>~tall(fred))))&
(![X]:((brave(X)&generous(X))<=>(rich(X)<~>kind(X))))&
(((~calm(fred)&~rich(fred)))<=>(?[X]:((~strong(X)|quiet(X)))))&
(![X]:((~calm(X)|~creative(X))=>~tall(X)))&
(![X]:(wise(X)=>(~strong(X)<~>calm(X))))&
(![X]:((~brave(X)|creative(X))=>(humble(X)<~>~creative(X))))&
((?[X]:(~funny(X)))<=>((humble(john)|tall(john))))&
(![X]:((rich(X)&~creative(X))=>(funny(X)|~tall(X))))&
((?[X]:(quiet(X)))=>(tall(lucy)))&
(![X]:(~calm(X)=>(~quiet(X)|happy(X))))&
(![X]:(tall(X)<=>curious(X)))&
(![X]:((tall(X)<~>humble(X))<=>curious(X)))&
(((~happy(paul)|wise(paul)))<=>((humble(paul)<~>~strong(paul))))&
(((~kind(lucy)<~>~funny(lucy)))<=>((wise(fred)&~rich(fred))))&
((~funny(alice)|calm(alice)))&
(?[X]:(brave(X)))&
(?[X]:((brave(X)&~kind(X))))&
((~generous(susan)|~funny(susan)))&
((rich(susan)|~generous(susan)))&
(?[X]:((~humble(X)|~tall(X)))) | humble(alice) | [
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8431065962888121039865263
% SZS output start Proof for 8431065962888121039865263
13. ! [X0] : (tall(X0) <=> curious(X0)) [input p12]
14. ! [X0] : ((tall(X0) <~> humble(X0)) <=> curious(X0)) [input p13]
23. humble(alice) [input hypothesis]
51. ! [X0] : ((tall(X0) | ~curious(X0)) & (curious(X0) | ~tall(X0))) [nnf transformation 13]
52. ! [X0] : ((((~humble(X0) | ~tall(X0)) & (humble(X0) | tall(X0))) | ~curious(X0)) & (curious(X0) | ((tall(X0) | ~humble(X0)) & (humble(X0) | ~tall(X0))))) [nnf transformation 14]
100. ~tall(X0) | curious(X0) [cnf transformation 51]
101. ~curious(X0) | tall(X0) [cnf transformation 51]
103. curious(X0) | tall(X0) | ~humble(X0) [cnf transformation 52]
105. ~humble(X0) | ~tall(X0) | ~curious(X0) [cnf transformation 52]
125. humble(alice) [cnf transformation 23]
199. ~tall(X0) | ~humble(X0) [subsumption resolution 105,100]
200. ~humble(X0) | curious(X0) [subsumption resolution 103,199]
270. curious(alice) [resolution 200,125]
272. tall(alice) [resolution 270,101]
288. ~humble(alice) [resolution 272,199]
292. $false [subsumption resolution 288,125]
% SZS output end Proof for 8431065962888121039865263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not old or not kind then someone is not old or funny.
Everyone who is not strong is old or generous and vice versa.
Everyone who is not funny is curious.
If someone is either calm or patient then someone is not funny.
Everyone who is not tall or old is not curious and vice versa.
If someone is wise or not creative then someone is either not quiet or kind.
If alice is both tall and generous then someone is either not happy or strong and vice versa.
Everyone who is not happy is both not curious and not old.
Everyone who is both not kind and rich is either not kind or patient and vice versa.
If alice is either generous or not curious then someone is patient and vice versa.
Everyone who is not old or not happy is wise.
Everyone who is not creative is creative.
Everyone who is both strong and not brave is not patient.
Everyone who is either patient or not brave is rich and vice versa.
Everyone who is both not quiet and not happy is not happy and vice versa.
If alice is not generous or humble then alice is calm or generous and vice versa.
John is calm.
Someone is not humble or humble.
Someone is either not strong or calm.
Lucy is curious or not wise.
Someone is calm.
Someone is generous.
Someone is not calm or quiet.
Susan is both curious and kind. | Lucy is not strong. | neutral | ((?[X]:((~old(X)<~>~kind(X))))=>(?[X]:((~old(X)|funny(X)))))&
(![X]:(~strong(X)<=>(old(X)|generous(X))))&
(![X]:(~funny(X)=>curious(X)))&
((?[X]:((calm(X)<~>patient(X))))=>(?[X]:(~funny(X))))&
(![X]:((~tall(X)|old(X))<=>~curious(X)))&
((?[X]:((wise(X)|~creative(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((tall(alice)&generous(alice)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
(![X]:(~happy(X)=>(~curious(X)&~old(X))))&
(![X]:((~kind(X)&rich(X))<=>(~kind(X)<~>patient(X))))&
(((generous(alice)<~>~curious(alice)))<=>(?[X]:(patient(X))))&
(![X]:((~old(X)|~happy(X))=>wise(X)))&
(![X]:(~creative(X)=>creative(X)))&
(![X]:((strong(X)&~brave(X))=>~patient(X)))&
(![X]:((patient(X)<~>~brave(X))<=>rich(X)))&
(![X]:((~quiet(X)&~happy(X))<=>~happy(X)))&
(((~generous(alice)|humble(alice)))<=>((calm(alice)|generous(alice))))&
(calm(john))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((~strong(X)<~>calm(X))))&
((curious(lucy)|~wise(lucy)))&
(?[X]:(calm(X)))&
(?[X]:(generous(X)))&
(?[X]:((~calm(X)|quiet(X))))&
((curious(susan)&kind(susan))) | ~strong(lucy) | []
| null | 0 |
Everyone who is both not funny and not old is strong and vice versa. Everyone who is either not rich or not generous is not old and vice versa. If fred is both not humble and quiet then fred is not funny or generous and vice versa. Everyone who is strong or wise is not tall or humble. If someone is either quiet or kind then someone is either curious or not curious and vice versa. Everyone who is not brave is quiet. Everyone who is happy is tall. If someone is calm then someone is creative. If someone is not rich or not calm then someone is not tall. Everyone who is both not tall and rich is humble or patient and vice versa. Everyone who is both not curious and not wise is old or not calm and vice versa. Everyone who is both not kind and not calm is old and vice versa. Everyone who is either not strong or rich is both rich and not patient. Everyone who is either curious or not generous is wise or not funny and vice versa. Everyone who is both not rich and not creative is either not humble or not kind and vice versa. Everyone who is either rich or humble is both kind and strong and vice versa. Mary is brave or rich. Someone is not wise or not kind. Lucy is quiet. Someone is not tall or funny. Susan is quiet. Someone is not happy or not wise. Alice is either not calm or quiet. | Lucy is not happy. | entailment | (![X]:((~funny(X)&~old(X))<=>strong(X)))&
(![X]:((~rich(X)<~>~generous(X))<=>~old(X)))&
(((~humble(fred)&quiet(fred)))<=>((~funny(fred)|generous(fred))))&
(![X]:((strong(X)|wise(X))=>(~tall(X)|humble(X))))&
((?[X]:((quiet(X)<~>kind(X))))<=>(?[X]:((curious(X)<~>~curious(X)))))&
(![X]:(~brave(X)=>quiet(X)))&
(![X]:(happy(X)=>tall(X)))&
((?[X]:(calm(X)))=>(?[X]:(creative(X))))&
((?[X]:((~rich(X)|~calm(X))))=>(?[X]:(~tall(X))))&
(![X]:((~tall(X)&rich(X))<=>(humble(X)|patient(X))))&
(![X]:((~curious(X)&~wise(X))<=>(old(X)|~calm(X))))&
(![X]:((~kind(X)&~calm(X))<=>old(X)))&
(![X]:((~strong(X)<~>rich(X))=>(rich(X)&~patient(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(wise(X)|~funny(X))))&
(![X]:((~rich(X)&~creative(X))<=>(~humble(X)<~>~kind(X))))&
(![X]:((rich(X)<~>humble(X))<=>(kind(X)&strong(X))))&
((brave(mary)|rich(mary)))&
(?[X]:((~wise(X)|~kind(X))))&
(quiet(lucy))&
(?[X]:((~tall(X)|funny(X))))&
(quiet(susan))&
(?[X]:((~happy(X)|~wise(X))))&
((~calm(alice)<~>quiet(alice))) | ~happy(lucy) | [
"p3",
"p6",
"p9",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 9094277834352091985135191
% SZS output start Proof for 9094277834352091985135191
4. ! [X0] : ((wise(X0) | strong(X0)) => (humble(X0) | ~tall(X0))) [input p3]
7. ! [X0] : (happy(X0) => tall(X0)) [input p6]
10. ! [X0] : ((rich(X0) & ~tall(X0)) <=> (patient(X0) | humble(X0))) [input p9]
13. ! [X0] : ((~strong(X0) <~> rich(X0)) => (~patient(X0) & rich(X0))) [input p12]
16. ! [X0] : ((rich(X0) <~> humble(X0)) <=> (strong(X0) & kind(X0))) [input p15]
24. happy(lucy) [input hypothesis]
30. ! [X0] : ((humble(X0) | ~tall(X0)) | (~wise(X0) & ~strong(X0))) [ennf transformation 4]
31. ! [X0] : (humble(X0) | ~tall(X0) | (~wise(X0) & ~strong(X0))) [flattening 30]
32. ! [X0] : (tall(X0) | ~happy(X0)) [ennf transformation 7]
35. ! [X0] : ((~patient(X0) & rich(X0)) | (~strong(X0) <=> rich(X0))) [ennf transformation 13]
52. ! [X0] : (((rich(X0) & ~tall(X0)) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | (~rich(X0) | tall(X0)))) [nnf transformation 10]
53. ! [X0] : (((rich(X0) & ~tall(X0)) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | ~rich(X0) | tall(X0))) [flattening 52]
58. ! [X0] : ((~patient(X0) & rich(X0)) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0)))) [nnf transformation 35]
63. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | (~strong(X0) | ~kind(X0))) & ((strong(X0) & kind(X0)) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [nnf transformation 16]
64. ! [X0] : ((((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | ~strong(X0) | ~kind(X0)) & ((strong(X0) & kind(X0)) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0))))) [flattening 63]
84. ~tall(X0) | humble(X0) | ~strong(X0) [cnf transformation 31]
94. ~happy(X0) | tall(X0) [cnf transformation 32]
99. ~tall(X0) | ~humble(X0) [cnf transformation 53]
111. rich(X0) | rich(X0) | strong(X0) [cnf transformation 58]
129. strong(X0) | humble(X0) | ~rich(X0) [cnf transformation 64]
140. happy(lucy) [cnf transformation 24]
141. rich(X0) | strong(X0) [duplicate literal removal 111]
210. humble(X0) | strong(X0) [subsumption resolution 129,141]
249. tall(lucy) [resolution 94,140]
250. ~humble(lucy) [resolution 249,99]
252. strong(lucy) [resolution 210,250]
288. humble(lucy) | ~strong(lucy) [resolution 84,249]
289. ~strong(lucy) [subsumption resolution 288,250]
290. $false [subsumption resolution 289,252]
% SZS output end Proof for 9094277834352091985135191
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and generous is either not quiet or funny and vice versa.
Everyone who is both not happy and not curious is tall or rich and vice versa.
If someone is both happy and not rich then someone is funny or not rich and vice versa.
Everyone who is not patient or calm is both tall and funny and vice versa.
Everyone who is not curious or patient is not curious or generous and vice versa.
Everyone who is both not curious and not strong is either happy or funny.
If someone is not calm then fred is not rich or not calm.
If lucy is happy then susan is old and vice versa.
Everyone who is both not calm and not rich is either kind or not tall and vice versa.
Everyone who is both not quiet and not brave is old and vice versa.
Everyone who is not patient is both old and generous and vice versa.
Everyone who is not quiet is not patient and vice versa.
If mary is either humble or wise then john is either not curious or wise.
Everyone who is either quiet or not patient is creative or rich and vice versa.
Everyone who is not patient or rich is creative or strong and vice versa.
If alice is either generous or wise then lucy is not old and vice versa.
Someone is either not happy or calm.
Mary is not rich or rich.
Someone is not old or not tall.
Paul is generous or not curious.
Someone is patient or not creative.
Paul is either curious or not happy. | Susan is not generous. | neutral | (![X]:((humble(X)&generous(X))<=>(~quiet(X)<~>funny(X))))&
(![X]:((~happy(X)&~curious(X))<=>(tall(X)|rich(X))))&
((?[X]:((happy(X)&~rich(X))))<=>(?[X]:((funny(X)|~rich(X)))))&
(![X]:((~patient(X)|calm(X))<=>(tall(X)&funny(X))))&
(![X]:((~curious(X)|patient(X))<=>(~curious(X)|generous(X))))&
(![X]:((~curious(X)&~strong(X))=>(happy(X)<~>funny(X))))&
((?[X]:(~calm(X)))=>((~rich(fred)|~calm(fred))))&
((happy(lucy))<=>(old(susan)))&
(![X]:((~calm(X)&~rich(X))<=>(kind(X)<~>~tall(X))))&
(![X]:((~quiet(X)&~brave(X))<=>old(X)))&
(![X]:(~patient(X)<=>(old(X)&generous(X))))&
(![X]:(~quiet(X)<=>~patient(X)))&
(((humble(mary)<~>wise(mary)))=>((~curious(john)<~>wise(john))))&
(![X]:((quiet(X)<~>~patient(X))<=>(creative(X)|rich(X))))&
(![X]:((~patient(X)|rich(X))<=>(creative(X)|strong(X))))&
(((generous(alice)<~>wise(alice)))<=>(~old(lucy)))&
(?[X]:((~happy(X)<~>calm(X))))&
((~rich(mary)|rich(mary)))&
(?[X]:((~old(X)|~tall(X))))&
((generous(paul)|~curious(paul)))&
(?[X]:((patient(X)|~creative(X))))&
((curious(paul)<~>~happy(paul))) | ~generous(susan) | []
| null | 0 |
Everyone who is not curious or not kind is both not funny and curious.
Everyone who is not patient is either not curious or brave.
Everyone who is both curious and not old is not humble.
Everyone who is either not creative or creative is both generous and curious and vice versa.
If someone is both generous and not funny then john is not generous and vice versa.
If someone is both strong and not strong then paul is not wise and vice versa.
Everyone who is either rich or not brave is patient or not tall and vice versa.
Everyone who is both not creative and not patient is not humble or not curious.
If mary is not kind then someone is tall or not curious.
If someone is not funny then alice is not old or not patient and vice versa.
If someone is not brave or generous then susan is either not calm or strong and vice versa.
Everyone who is strong is old or patient and vice versa.
Everyone who is either not creative or calm is humble and vice versa.
If mary is not generous then lucy is either brave or creative.
Everyone who is old is wise or quiet and vice versa.
Susan is both not tall and not creative.
Someone is either not strong or not old.
Someone is either not brave or not tall.
John is not brave or patient.
Someone is either wise or strong.
Susan is old or not rich.
Someone is creative. | Mary is not humble. | neutral | (![X]:((~curious(X)|~kind(X))=>(~funny(X)&curious(X))))&
(![X]:(~patient(X)=>(~curious(X)<~>brave(X))))&
(![X]:((curious(X)&~old(X))=>~humble(X)))&
(![X]:((~creative(X)<~>creative(X))<=>(generous(X)&curious(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(~generous(john)))&
((?[X]:((strong(X)&~strong(X))))<=>(~wise(paul)))&
(![X]:((rich(X)<~>~brave(X))<=>(patient(X)|~tall(X))))&
(![X]:((~creative(X)&~patient(X))=>(~humble(X)|~curious(X))))&
((~kind(mary))=>(?[X]:((tall(X)|~curious(X)))))&
((?[X]:(~funny(X)))<=>((~old(alice)|~patient(alice))))&
((?[X]:((~brave(X)|generous(X))))<=>((~calm(susan)<~>strong(susan))))&
(![X]:(strong(X)<=>(old(X)|patient(X))))&
(![X]:((~creative(X)<~>calm(X))<=>humble(X)))&
((~generous(mary))=>((brave(lucy)<~>creative(lucy))))&
(![X]:(old(X)<=>(wise(X)|quiet(X))))&
((~tall(susan)&~creative(susan)))&
(?[X]:((~strong(X)<~>~old(X))))&
(?[X]:((~brave(X)<~>~tall(X))))&
((~brave(john)|patient(john)))&
(?[X]:((wise(X)<~>strong(X))))&
((old(susan)|~rich(susan)))&
(?[X]:(creative(X))) | ~humble(mary) | []
| null | 0 |
If someone is not old then fred is not generous or old.
Everyone who is both creative and funny is either not rich or happy and vice versa.
If susan is generous then someone is not patient and vice versa.
If paul is both not patient and kind then someone is quiet or not humble.
Everyone who is not old or not generous is both not humble and not rich.
If someone is strong or kind then someone is not creative or not curious.
If fred is either wise or happy then lucy is both humble and not calm.
Everyone who is quiet is either funny or not brave and vice versa.
If paul is not kind then paul is either not tall or not wise and vice versa.
Everyone who is either not funny or creative is happy or humble and vice versa.
Everyone who is either not old or not quiet is strong or not humble and vice versa.
Everyone who is either wise or not kind is kind or not strong and vice versa.
Everyone who is both old and quiet is kind.
If someone is quiet or strong then alice is both not generous and not happy.
If someone is both rich and not quiet then john is both not strong and humble and vice versa.
If someone is either quiet or not old then someone is calm and vice versa.
Mary is kind.
Lucy is not calm.
Paul is either not funny or calm.
Someone is both not quiet and generous.
Mary is both not tall and not quiet. | Susan is old. | entailment | ((?[X]:(~old(X)))=>((~generous(fred)|old(fred))))&
(![X]:((creative(X)&funny(X))<=>(~rich(X)<~>happy(X))))&
((generous(susan))<=>(?[X]:(~patient(X))))&
(((~patient(paul)&kind(paul)))=>(?[X]:((quiet(X)|~humble(X)))))&
(![X]:((~old(X)|~generous(X))=>(~humble(X)&~rich(X))))&
((?[X]:((strong(X)|kind(X))))=>(?[X]:((~creative(X)|~curious(X)))))&
(((wise(fred)<~>happy(fred)))=>((humble(lucy)&~calm(lucy))))&
(![X]:(quiet(X)<=>(funny(X)<~>~brave(X))))&
((~kind(paul))<=>((~tall(paul)<~>~wise(paul))))&
(![X]:((~funny(X)<~>creative(X))<=>(happy(X)|humble(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(strong(X)|~humble(X))))&
(![X]:((wise(X)<~>~kind(X))<=>(kind(X)|~strong(X))))&
(![X]:((old(X)&quiet(X))=>kind(X)))&
((?[X]:((quiet(X)|strong(X))))=>((~generous(alice)&~happy(alice))))&
((?[X]:((rich(X)&~quiet(X))))<=>((~strong(john)&humble(john))))&
((?[X]:((quiet(X)<~>~old(X))))<=>(?[X]:(calm(X))))&
(kind(mary))&
(~calm(lucy))&
((~funny(paul)<~>calm(paul)))&
(?[X]:((~quiet(X)&generous(X))))&
((~tall(mary)&~quiet(mary))) | old(susan) | [
"p1",
"p4",
"p9",
"p10",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5111725589480510845385392
% SZS output start Proof for 5111725589480510845385392
2. ! [X0] : ((funny(X0) & creative(X0)) <=> (~rich(X0) <~> happy(X0))) [input p1]
5. ! [X0] : ((~generous(X0) | ~old(X0)) => (~rich(X0) & ~humble(X0))) [input p4]
10. ! [X0] : ((~funny(X0) <~> creative(X0)) <=> (humble(X0) | happy(X0))) [input p9]
11. ! [X0] : ((~old(X0) <~> ~quiet(X0)) <=> (~humble(X0) | strong(X0))) [input p10]
14. ? [X0] : (strong(X0) | quiet(X0)) => (~happy(alice) & ~generous(alice)) [input p13]
22. ~old(susan) [input hypothesis]
30. ! [X0] : ((~rich(X0) & ~humble(X0)) | (generous(X0) & old(X0))) [ennf transformation 5]
34. (~happy(alice) & ~generous(alice)) | ! [X0] : (~strong(X0) & ~quiet(X0)) [ennf transformation 14]
35. ! [X0] : (((funny(X0) & creative(X0)) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) & (((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | (~funny(X0) | ~creative(X0)))) [nnf transformation 2]
36. ! [X0] : (((funny(X0) & creative(X0)) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) & (((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | ~funny(X0) | ~creative(X0))) [flattening 35]
46. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [nnf transformation 10]
47. ! [X0] : ((((~creative(X0) | funny(X0)) & (creative(X0) | ~funny(X0))) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | ((~funny(X0) | ~creative(X0)) & (creative(X0) | funny(X0))))) [flattening 46]
48. ! [X0] : ((((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (humble(X0) & ~strong(X0))) & ((~humble(X0) | strong(X0)) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))))) [nnf transformation 11]
49. ! [X0] : ((((quiet(X0) | old(X0)) & (~quiet(X0) | ~old(X0))) | (humble(X0) & ~strong(X0))) & (~humble(X0) | strong(X0) | ((~old(X0) | quiet(X0)) & (~quiet(X0) | old(X0))))) [flattening 48]
68. happy(X0) | creative(X0) | rich(X0) [cnf transformation 36]
70. happy(X0) | funny(X0) | rich(X0) [cnf transformation 36]
75. ~humble(X0) | old(X0) [cnf transformation 30]
76. ~humble(X0) | generous(X0) [cnf transformation 30]
78. ~rich(X0) | generous(X0) [cnf transformation 30]
92. ~funny(X0) | happy(X0) | humble(X0) | ~creative(X0) [cnf transformation 47]
102. quiet(X0) | old(X0) | humble(X0) [cnf transformation 49]
110. ~generous(alice) | ~quiet(X0) [cnf transformation 34]
112. ~happy(alice) | ~quiet(X0) [cnf transformation 34]
130. ~old(susan) [cnf transformation 22]
134. 1 <=> ! [X0] : old(X0) [avatar definition]
135. old(X0) <- (1) [avatar component clause 134]
207. quiet(X0) | old(X0) [subsumption resolution 102,75]
214. 18 <=> happy(alice) [avatar definition]
216. ~happy(alice) <- (~18) [avatar component clause 214]
219. 19 <=> ! [X0] : ~quiet(X0) [avatar definition]
220. ~quiet(X0) <- (19) [avatar component clause 219]
221. 19 | ~18 [avatar split clause 112,214,219]
223. 20 <=> generous(alice) [avatar definition]
225. ~generous(alice) <- (~20) [avatar component clause 223]
227. 19 | ~20 [avatar split clause 110,223,219]
300. creative(alice) | rich(alice) <- (~18) [resolution 68,216]
311. 35 <=> rich(alice) [avatar definition]
313. rich(alice) <- (35) [avatar component clause 311]
315. 36 <=> creative(alice) [avatar definition]
317. creative(alice) <- (36) [avatar component clause 315]
318. 35 | 36 | 18 [avatar split clause 300,214,315,311]
323. funny(alice) | rich(alice) <- (~18) [resolution 70,216]
326. 37 <=> funny(alice) [avatar definition]
328. funny(alice) <- (37) [avatar component clause 326]
329. 35 | 37 | 18 [avatar split clause 323,214,326,311]
475. happy(alice) | humble(alice) | ~creative(alice) <- (37) [resolution 92,328]
476. humble(alice) | ~creative(alice) <- (~18, 37) [subsumption resolution 475,216]
477. humble(alice) <- (~18, 36, 37) [subsumption resolution 476,317]
523. generous(alice) <- (~18, 36, 37) [resolution 477,76]
534. $false <- (~18, ~20, 36, 37) [subsumption resolution 523,225]
535. 18 | 20 | ~36 | ~37 [avatar contradiction clause 534]
538. generous(alice) <- (35) [resolution 313,78]
540. $false <- (~20, 35) [subsumption resolution 538,225]
541. 20 | ~35 [avatar contradiction clause 540]
546. old(X0) <- (19) [resolution 220,207]
551. 1 | ~19 [avatar split clause 546,219,134]
553. $false <- (1) [resolution 135,130]
558. ~1 [avatar contradiction clause 553]
559. $false [avatar sat refutation 221,227,318,329,535,541,551,558]
% SZS output end Proof for 5111725589480510845385392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both not calm and not patient then someone is either not calm or tall.
If mary is not brave then mary is either patient or rich.
Everyone who is both not wise and not brave is calm and vice versa.
Everyone who is both not humble and funny is either not rich or tall.
Everyone who is not creative is either not patient or wise.
Everyone who is both not curious and old is both kind and not calm.
Everyone who is not wise or generous is old or calm.
Everyone who is brave is kind and vice versa.
Everyone who is creative is not humble and vice versa.
If mary is either funny or not tall then someone is both funny and old.
If someone is both not calm and not wise then someone is either not patient or not calm and vice versa.
Everyone who is either strong or wise is either funny or old.
If john is both generous and funny then someone is not brave or not tall and vice versa.
If someone is both funny and patient then alice is not calm or not strong and vice versa.
Everyone who is curious is both kind and curious.
If someone is wise then someone is not wise or old.
Someone is rich or not strong.
John is not happy or curious.
Someone is both kind and not strong.
Someone is either creative or not rich.
Someone is creative.
Fred is both old and not patient.
Alice is happy or strong. | John is funny. | entailment | (((~calm(fred)&~patient(fred)))=>(?[X]:((~calm(X)<~>tall(X)))))&
((~brave(mary))=>((patient(mary)<~>rich(mary))))&
(![X]:((~wise(X)&~brave(X))<=>calm(X)))&
(![X]:((~humble(X)&funny(X))=>(~rich(X)<~>tall(X))))&
(![X]:(~creative(X)=>(~patient(X)<~>wise(X))))&
(![X]:((~curious(X)&old(X))=>(kind(X)&~calm(X))))&
(![X]:((~wise(X)|generous(X))=>(old(X)|calm(X))))&
(![X]:(brave(X)<=>kind(X)))&
(![X]:(creative(X)<=>~humble(X)))&
(((funny(mary)<~>~tall(mary)))=>(?[X]:((funny(X)&old(X)))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
(![X]:((strong(X)<~>wise(X))=>(funny(X)<~>old(X))))&
(((generous(john)&funny(john)))<=>(?[X]:((~brave(X)|~tall(X)))))&
((?[X]:((funny(X)&patient(X))))<=>((~calm(alice)|~strong(alice))))&
(![X]:(curious(X)=>(kind(X)&curious(X))))&
((?[X]:(wise(X)))=>(?[X]:((~wise(X)|old(X)))))&
(?[X]:((rich(X)|~strong(X))))&
((~happy(john)|curious(john)))&
(?[X]:((kind(X)&~strong(X))))&
(?[X]:((creative(X)<~>~rich(X))))&
(?[X]:(creative(X)))&
((old(fred)&~patient(fred)))&
((happy(alice)|strong(alice))) | funny(john) | [
"p0",
"p2",
"p12",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5516149582458327907928777
% SZS output start Proof for 5516149582458327907928777
1. (~patient(fred) & ~calm(fred)) => ? [X0] : (~calm(X0) <~> tall(X0)) [input p0]
3. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> calm(X0)) [input p2]
13. (funny(john) & generous(john)) <=> ? [X0] : (~tall(X0) | ~brave(X0)) [input p12]
22. ~patient(fred) & old(fred) [input p21]
24. ~funny(john) [input hypothesis]
27. ? [X0] : (~calm(X0) <~> tall(X0)) | (patient(fred) | calm(fred)) [ennf transformation 1]
28. ? [X0] : (~calm(X0) <~> tall(X0)) | patient(fred) | calm(fred) [flattening 27]
41. ? [X0] : ((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) | patient(fred) | calm(fred) [nnf transformation 28]
42. ? [X0] : ((~tall(X0) | calm(X0)) & (tall(X0) | ~calm(X0))) => ((~tall(sK0) | calm(sK0)) & (tall(sK0) | ~calm(sK0))) [choice axiom]
43. ((~tall(sK0) | calm(sK0)) & (tall(sK0) | ~calm(sK0))) | patient(fred) | calm(fred) [skolemisation 41,42]
45. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~calm(X0)) & (calm(X0) | (brave(X0) | wise(X0)))) [nnf transformation 3]
46. ! [X0] : (((~brave(X0) & ~wise(X0)) | ~calm(X0)) & (calm(X0) | brave(X0) | wise(X0))) [flattening 45]
60. ((funny(john) & generous(john)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | (~funny(john) | ~generous(john))) [nnf transformation 13]
61. ((funny(john) & generous(john)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X0] : (~tall(X0) | ~brave(X0)) | ~funny(john) | ~generous(john)) [flattening 60]
62. ((funny(john) & generous(john)) | ! [X0] : (tall(X0) & brave(X0))) & (? [X1] : (~tall(X1) | ~brave(X1)) | ~funny(john) | ~generous(john)) [rectify 61]
63. ? [X1] : (~tall(X1) | ~brave(X1)) => (~tall(sK4) | ~brave(sK4)) [choice axiom]
64. ((funny(john) & generous(john)) | ! [X0] : (tall(X0) & brave(X0))) & ((~tall(sK4) | ~brave(sK4)) | ~funny(john) | ~generous(john)) [skolemisation 62,63]
83. ~tall(sK0) | calm(sK0) | patient(fred) | calm(fred) [cnf transformation 43]
88. ~brave(X0) | ~calm(X0) [cnf transformation 46]
118. funny(john) | brave(X0) [cnf transformation 64]
119. funny(john) | tall(X0) [cnf transformation 64]
136. ~patient(fred) [cnf transformation 22]
138. ~funny(john) [cnf transformation 24]
140. 1 <=> calm(fred) [avatar definition]
142. calm(fred) <- (1) [avatar component clause 140]
144. 2 <=> patient(fred) [avatar definition]
148. 3 <=> calm(sK0) [avatar definition]
150. calm(sK0) <- (3) [avatar component clause 148]
152. 4 <=> tall(sK0) [avatar definition]
154. ~tall(sK0) <- (~4) [avatar component clause 152]
155. 1 | 2 | 3 | ~4 [avatar split clause 83,152,148,144,140]
223. 19 <=> ! [X0] : tall(X0) [avatar definition]
224. tall(X0) <- (19) [avatar component clause 223]
226. 20 <=> funny(john) [avatar definition]
229. 19 | 20 [avatar split clause 119,226,223]
231. 21 <=> ! [X0] : brave(X0) [avatar definition]
232. brave(X0) <- (21) [avatar component clause 231]
233. 21 | 20 [avatar split clause 118,226,231]
313. ~2 [avatar split clause 136,144]
319. ~20 [avatar split clause 138,226]
320. $false <- (~4, 19) [subsumption resolution 154,224]
321. 4 | ~19 [avatar contradiction clause 320]
322. ~calm(X0) <- (21) [resolution 88,232]
323. $false <- (1, 21) [resolution 322,142]
324. ~1 | ~21 [avatar contradiction clause 323]
325. $false <- (3, 21) [subsumption resolution 150,322]
326. ~3 | ~21 [avatar contradiction clause 325]
327. $false [avatar sat refutation 155,229,233,313,319,321,324,326]
% SZS output end Proof for 5516149582458327907928777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not strong then someone is not old and vice versa. If john is both not rich and not quiet then fred is rich or not quiet and vice versa. Everyone who is quiet is wise and vice versa. Everyone who is quiet is either not tall or curious and vice versa. If alice is either curious or kind then someone is both not funny and not quiet. If mary is both wise and patient then someone is not brave or not calm and vice versa. Everyone who is not wise or creative is both tall and happy. If someone is either not kind or not funny then someone is both brave and not old and vice versa. Everyone who is both patient and tall is quiet or not patient and vice versa. Everyone who is either funny or rich is not calm and vice versa. If fred is either not wise or not happy then mary is happy or not funny. Everyone who is not patient or not funny is not creative or old and vice versa. If someone is not old then someone is not old or not rich. If paul is either old or not old then paul is creative. Everyone who is either not humble or wise is patient or funny. If someone is patient or strong then mary is either not wise or calm. Fred is both funny and not humble. Someone is either rich or not wise. Someone is kind. Paul is either kind or not brave. Someone is wise. | Paul is not patient. | contradiction | ((?[X]:(~strong(X)))<=>(?[X]:(~old(X))))&
(((~rich(john)&~quiet(john)))<=>((rich(fred)|~quiet(fred))))&
(![X]:(quiet(X)<=>wise(X)))&
(![X]:(quiet(X)<=>(~tall(X)<~>curious(X))))&
(((curious(alice)<~>kind(alice)))=>(?[X]:((~funny(X)&~quiet(X)))))&
(((wise(mary)&patient(mary)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(![X]:((~wise(X)|creative(X))=>(tall(X)&happy(X))))&
((?[X]:((~kind(X)<~>~funny(X))))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((patient(X)&tall(X))<=>(quiet(X)|~patient(X))))&
(![X]:((funny(X)<~>rich(X))<=>~calm(X)))&
(((~wise(fred)<~>~happy(fred)))=>((happy(mary)|~funny(mary))))&
(![X]:((~patient(X)|~funny(X))<=>(~creative(X)|old(X))))&
((?[X]:(~old(X)))=>(?[X]:((~old(X)|~rich(X)))))&
(((old(paul)<~>~old(paul)))=>(creative(paul)))&
(![X]:((~humble(X)<~>wise(X))=>(patient(X)|funny(X))))&
((?[X]:((patient(X)|strong(X))))=>((~wise(mary)<~>calm(mary))))&
((funny(fred)&~humble(fred)))&
(?[X]:((rich(X)<~>~wise(X))))&
(?[X]:(kind(X)))&
((kind(paul)<~>~brave(paul)))&
(?[X]:(wise(X))) | ~patient(paul) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 7258692801327634326338828
% SZS output start Proof for 7258692801327634326338828
9. ! [X0] : ((tall(X0) & patient(X0)) <=> (~patient(X0) | quiet(X0))) [input p8]
22. ~patient(paul) [input hypothesis]
57. ! [X0] : (((tall(X0) & patient(X0)) | (patient(X0) & ~quiet(X0))) & ((~patient(X0) | quiet(X0)) | (~tall(X0) | ~patient(X0)))) [nnf transformation 9]
58. ! [X0] : (((tall(X0) & patient(X0)) | (patient(X0) & ~quiet(X0))) & (~patient(X0) | quiet(X0) | ~tall(X0) | ~patient(X0))) [flattening 57]
111. patient(X0) | patient(X0) [cnf transformation 58]
141. ~patient(paul) [cnf transformation 22]
145. patient(X0) [duplicate literal removal 111]
336. $false [subsumption resolution 141,145]
% SZS output end Proof for 7258692801327634326338828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or curious is either not rich or funny.
Everyone who is both not brave and not happy is both kind and not creative and vice versa.
If someone is not generous or not quiet then someone is not brave and vice versa.
Everyone who is not old or old is not happy.
Everyone who is both tall and calm is generous and vice versa.
Everyone who is not strong is not brave or not tall and vice versa.
If someone is either not old or patient then someone is humble and vice versa.
If someone is strong then alice is curious.
Everyone who is both not funny and old is kind or rich.
Everyone who is either not rich or patient is either not brave or not patient and vice versa.
Everyone who is both not funny and funny is both not brave and not strong and vice versa.
If lucy is not wise then someone is either not patient or not funny.
If someone is either humble or wise then someone is either not brave or kind.
Everyone who is either not old or not creative is curious.
Everyone who is either tall or not old is not creative or curious.
Alice is both wise and not creative.
Someone is either not old or old.
Someone is either not wise or strong.
Someone is not kind or calm.
Paul is either not wise or funny.
John is not happy. | Paul is tall. | entailment | (![X]:((~strong(X)<~>curious(X))=>(~rich(X)<~>funny(X))))&
(![X]:((~brave(X)&~happy(X))<=>(kind(X)&~creative(X))))&
((?[X]:((~generous(X)|~quiet(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|old(X))=>~happy(X)))&
(![X]:((tall(X)&calm(X))<=>generous(X)))&
(![X]:(~strong(X)<=>(~brave(X)|~tall(X))))&
((?[X]:((~old(X)<~>patient(X))))<=>(?[X]:(humble(X))))&
((?[X]:(strong(X)))=>(curious(alice)))&
(![X]:((~funny(X)&old(X))=>(kind(X)|rich(X))))&
(![X]:((~rich(X)<~>patient(X))<=>(~brave(X)<~>~patient(X))))&
(![X]:((~funny(X)&funny(X))<=>(~brave(X)&~strong(X))))&
((~wise(lucy))=>(?[X]:((~patient(X)<~>~funny(X)))))&
((?[X]:((humble(X)<~>wise(X))))=>(?[X]:((~brave(X)<~>kind(X)))))&
(![X]:((~old(X)<~>~creative(X))=>curious(X)))&
(![X]:((tall(X)<~>~old(X))=>(~creative(X)|curious(X))))&
((wise(alice)&~creative(alice)))&
(?[X]:((~old(X)<~>old(X))))&
(?[X]:((~wise(X)<~>strong(X))))&
(?[X]:((~kind(X)|calm(X))))&
((~wise(paul)<~>funny(paul)))&
(~happy(john)) | tall(paul) | [
"p2",
"p4",
"p5",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 5133328773326761964540980
% SZS output start Proof for 5133328773326761964540980
3. ? [X0] : (~quiet(X0) | ~generous(X0)) <=> ? [X0] : ~brave(X0) [input p2]
5. ! [X0] : ((calm(X0) & tall(X0)) <=> generous(X0)) [input p4]
6. ! [X0] : (~strong(X0) <=> (~tall(X0) | ~brave(X0))) [input p5]
11. ! [X0] : ((funny(X0) & ~funny(X0)) <=> (~strong(X0) & ~brave(X0))) [input p10]
22. ~tall(paul) [input hypothesis]
23. ? [X0] : (~quiet(X0) | ~generous(X0)) <=> ? [X1] : ~brave(X1) [rectify 3]
39. (? [X0] : (~quiet(X0) | ~generous(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (quiet(X0) & generous(X0))) [nnf transformation 23]
40. (? [X0] : (~quiet(X0) | ~generous(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (quiet(X3) & generous(X3))) [rectify 39]
41. ? [X0] : (~quiet(X0) | ~generous(X0)) => (~quiet(sK0) | ~generous(sK0)) [choice axiom]
42. ? [X2] : ~brave(X2) => ~brave(sK1) [choice axiom]
43. ((~quiet(sK0) | ~generous(sK0)) | ! [X1] : brave(X1)) & (~brave(sK1) | ! [X3] : (quiet(X3) & generous(X3))) [skolemisation 40,42,41]
44. ! [X0] : (((calm(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | (~calm(X0) | ~tall(X0)))) [nnf transformation 5]
45. ! [X0] : (((calm(X0) & tall(X0)) | ~generous(X0)) & (generous(X0) | ~calm(X0) | ~tall(X0))) [flattening 44]
46. ! [X0] : ((~strong(X0) | (tall(X0) & brave(X0))) & ((~tall(X0) | ~brave(X0)) | strong(X0))) [nnf transformation 6]
47. ! [X0] : ((~strong(X0) | (tall(X0) & brave(X0))) & (~tall(X0) | ~brave(X0) | strong(X0))) [flattening 46]
54. ! [X0] : (((funny(X0) & ~funny(X0)) | (strong(X0) | brave(X0))) & ((~strong(X0) & ~brave(X0)) | (~funny(X0) | funny(X0)))) [nnf transformation 11]
55. ! [X0] : (((funny(X0) & ~funny(X0)) | strong(X0) | brave(X0)) & ((~strong(X0) & ~brave(X0)) | ~funny(X0) | funny(X0))) [flattening 54]
82. ~brave(sK1) | generous(X3) [cnf transformation 43]
88. ~generous(X0) | tall(X0) [cnf transformation 45]
91. ~strong(X0) | brave(X0) [cnf transformation 47]
109. ~funny(X0) | strong(X0) | brave(X0) [cnf transformation 55]
110. funny(X0) | strong(X0) | brave(X0) [cnf transformation 55]
131. ~tall(paul) [cnf transformation 22]
137. 1 <=> ! [X1] : brave(X1) [avatar definition]
138. brave(X1) <- (1) [avatar component clause 137]
152. 5 <=> brave(sK1) [avatar definition]
154. ~brave(sK1) <- (~5) [avatar component clause 152]
157. 6 <=> ! [X3] : generous(X3) [avatar definition]
158. generous(X3) <- (6) [avatar component clause 157]
159. 6 | ~5 [avatar split clause 82,152,157]
196. funny(X0) | brave(X0) [subsumption resolution 110,91]
197. ~funny(X0) | brave(X0) [subsumption resolution 109,91]
198. brave(X0) [subsumption resolution 197,196]
199. 1 [avatar split clause 198,137]
262. $false <- (1, ~5) [resolution 154,138]
263. ~1 | 5 [avatar contradiction clause 262]
266. tall(X0) <- (6) [resolution 88,158]
267. $false <- (6) [resolution 266,131]
268. ~6 [avatar contradiction clause 267]
269. $false [avatar sat refutation 159,199,263,268]
% SZS output end Proof for 5133328773326761964540980
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not brave then someone is tall or not rich.
Everyone who is both not curious and patient is both patient and curious and vice versa.
If paul is not happy or not curious then someone is either not funny or strong.
Everyone who is either not creative or not generous is not strong or generous.
Everyone who is either brave or not wise is not kind or funny.
Everyone who is strong or funny is either not curious or not happy and vice versa.
If someone is wise then susan is funny or generous and vice versa.
Everyone who is either not creative or humble is not strong or curious.
If paul is both not calm and not patient then someone is not rich and vice versa.
If someone is either brave or not happy then fred is not funny or not happy and vice versa.
Everyone who is not generous or not strong is either not calm or curious.
If alice is not generous or quiet then susan is either not rich or not brave and vice versa.
If alice is both not patient and kind then someone is both not happy and not quiet and vice versa.
Everyone who is both not generous and funny is either not quiet or not humble.
If john is both not wise and curious then someone is both not quiet and not happy and vice versa.
Everyone who is not generous is either not generous or patient.
Fred is not creative.
Someone is either not quiet or patient.
John is creative.
Mary is both not curious and quiet.
Alice is either tall or not rich.
Alice is both calm and humble.
Someone is not humble or curious. | Alice is funny. | neutral | ((?[X]:(~brave(X)))=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~curious(X)&patient(X))<=>(patient(X)&curious(X))))&
(((~happy(paul)|~curious(paul)))=>(?[X]:((~funny(X)<~>strong(X)))))&
(![X]:((~creative(X)<~>~generous(X))=>(~strong(X)|generous(X))))&
(![X]:((brave(X)<~>~wise(X))=>(~kind(X)|funny(X))))&
(![X]:((strong(X)|funny(X))<=>(~curious(X)<~>~happy(X))))&
((?[X]:(wise(X)))<=>((funny(susan)|generous(susan))))&
(![X]:((~creative(X)<~>humble(X))=>(~strong(X)|curious(X))))&
(((~calm(paul)&~patient(paul)))<=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)<~>~happy(X))))<=>((~funny(fred)|~happy(fred))))&
(![X]:((~generous(X)|~strong(X))=>(~calm(X)<~>curious(X))))&
(((~generous(alice)|quiet(alice)))<=>((~rich(susan)<~>~brave(susan))))&
(((~patient(alice)&kind(alice)))<=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:((~generous(X)&funny(X))=>(~quiet(X)<~>~humble(X))))&
(((~wise(john)&curious(john)))<=>(?[X]:((~quiet(X)&~happy(X)))))&
(![X]:(~generous(X)=>(~generous(X)<~>patient(X))))&
(~creative(fred))&
(?[X]:((~quiet(X)<~>patient(X))))&
(creative(john))&
((~curious(mary)&quiet(mary)))&
((tall(alice)<~>~rich(alice)))&
((calm(alice)&humble(alice)))&
(?[X]:((~humble(X)|curious(X)))) | funny(alice) | []
| null | 0 |
Everyone who is both kind and tall is calm.
If john is both patient and rich then someone is not tall or humble.
If someone is both curious and quiet then someone is both patient and brave.
If someone is calm or humble then someone is either curious or not funny and vice versa.
Everyone who is not creative is both not creative and not quiet and vice versa.
Everyone who is either rich or not rich is both rich and generous and vice versa.
If someone is strong then fred is both not old and patient.
Everyone who is calm or not funny is old and vice versa.
Everyone who is old or humble is both brave and not rich.
Everyone who is either funny or not humble is generous or not funny.
If fred is not humble or not old then john is either not curious or not wise.
Everyone who is either not wise or generous is both not tall and not creative and vice versa.
Everyone who is patient or not funny is both funny and not calm.
Everyone who is not brave or not curious is either not strong or not humble and vice versa.
Everyone who is funny or not happy is rich or not old and vice versa.
Someone is either not tall or calm.
Someone is funny or not quiet.
Paul is both not curious and not wise.
Someone is not creative.
John is generous or funny.
Alice is either quiet or not wise. | Paul is wise. | contradiction | (![X]:((kind(X)&tall(X))=>calm(X)))&
(((patient(john)&rich(john)))=>(?[X]:((~tall(X)|humble(X)))))&
((?[X]:((curious(X)&quiet(X))))=>(?[X]:((patient(X)&brave(X)))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:((curious(X)<~>~funny(X)))))&
(![X]:(~creative(X)<=>(~creative(X)&~quiet(X))))&
(![X]:((rich(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
((?[X]:(strong(X)))=>((~old(fred)&patient(fred))))&
(![X]:((calm(X)|~funny(X))<=>old(X)))&
(![X]:((old(X)|humble(X))=>(brave(X)&~rich(X))))&
(![X]:((funny(X)<~>~humble(X))=>(generous(X)|~funny(X))))&
(((~humble(fred)|~old(fred)))=>((~curious(john)<~>~wise(john))))&
(![X]:((~wise(X)<~>generous(X))<=>(~tall(X)&~creative(X))))&
(![X]:((patient(X)|~funny(X))=>(funny(X)&~calm(X))))&
(![X]:((~brave(X)|~curious(X))<=>(~strong(X)<~>~humble(X))))&
(![X]:((funny(X)|~happy(X))<=>(rich(X)|~old(X))))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:((funny(X)|~quiet(X))))&
((~curious(paul)&~wise(paul)))&
(?[X]:(~creative(X)))&
((generous(john)|funny(john)))&
((quiet(alice)<~>~wise(alice))) | wise(paul) | [
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 6271389759383753434423760
% SZS output start Proof for 6271389759383753434423760
18. ~wise(paul) & ~curious(paul) [input p17]
22. wise(paul) [input hypothesis]
124. ~wise(paul) [cnf transformation 18]
129. wise(paul) [cnf transformation 22]
262. $false [subsumption resolution 129,124]
% SZS output end Proof for 6271389759383753434423760
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or generous is not funny. If someone is either calm or not humble then someone is both wise and not tall and vice versa. Everyone who is either funny or old is not brave or not happy and vice versa. Everyone who is either not kind or not creative is both generous and not old and vice versa. Everyone who is rich or not funny is humble or curious and vice versa. If lucy is either not wise or brave then john is both humble and old and vice versa. If someone is tall or humble then mary is quiet or not rich. If someone is either not quiet or tall then lucy is both not generous and creative and vice versa. Everyone who is not old or calm is both not kind and creative and vice versa. Everyone who is both not patient and not funny is not humble or tall and vice versa. Everyone who is happy or creative is either not patient or not rich. If someone is not patient or brave then paul is patient. If someone is both not quiet and not humble then someone is not tall. Everyone who is not rich or not creative is kind or funny. If someone is not curious or not quiet then someone is old and vice versa. Someone is both not strong and rich. John is either wise or not wise. Someone is either not strong or not brave. Someone is either funny or not curious. Someone is humble. Fred is either kind or calm. | Paul is tall. | contradiction | (![X]:((~humble(X)<~>generous(X))=>~funny(X)))&
((?[X]:((calm(X)<~>~humble(X))))<=>(?[X]:((wise(X)&~tall(X)))))&
(![X]:((funny(X)<~>old(X))<=>(~brave(X)|~happy(X))))&
(![X]:((~kind(X)<~>~creative(X))<=>(generous(X)&~old(X))))&
(![X]:((rich(X)|~funny(X))<=>(humble(X)|curious(X))))&
(((~wise(lucy)<~>brave(lucy)))<=>((humble(john)&old(john))))&
((?[X]:((tall(X)|humble(X))))=>((quiet(mary)|~rich(mary))))&
((?[X]:((~quiet(X)<~>tall(X))))<=>((~generous(lucy)&creative(lucy))))&
(![X]:((~old(X)|calm(X))<=>(~kind(X)&creative(X))))&
(![X]:((~patient(X)&~funny(X))<=>(~humble(X)|tall(X))))&
(![X]:((happy(X)|creative(X))=>(~patient(X)<~>~rich(X))))&
((?[X]:((~patient(X)|brave(X))))=>(patient(paul)))&
((?[X]:((~quiet(X)&~humble(X))))=>(?[X]:(~tall(X))))&
(![X]:((~rich(X)|~creative(X))=>(kind(X)|funny(X))))&
((?[X]:((~curious(X)|~quiet(X))))<=>(?[X]:(old(X))))&
(?[X]:((~strong(X)&rich(X))))&
((wise(john)<~>~wise(john)))&
(?[X]:((~strong(X)<~>~brave(X))))&
(?[X]:((funny(X)<~>~curious(X))))&
(?[X]:(humble(X)))&
((kind(fred)<~>calm(fred))) | tall(paul) | [
"p9",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 248233226465279808743451
% SZS output start Proof for 248233226465279808743451
10. ! [X0] : ((~funny(X0) & ~patient(X0)) <=> (tall(X0) | ~humble(X0))) [input p9]
12. ? [X0] : (brave(X0) | ~patient(X0)) => patient(paul) [input p11]
22. tall(paul) [input hypothesis]
30. patient(paul) | ! [X0] : (~brave(X0) & patient(X0)) [ennf transformation 12]
55. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | (funny(X0) | patient(X0)))) [nnf transformation 10]
56. ! [X0] : (((~funny(X0) & ~patient(X0)) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | funny(X0) | patient(X0))) [flattening 55]
123. ~patient(X0) | ~tall(X0) [cnf transformation 56]
130. patient(paul) | patient(X0) [cnf transformation 30]
149. tall(paul) [cnf transformation 22]
251. 23 <=> patient(paul) [avatar definition]
252. ~patient(paul) <- (~23) [avatar component clause 251]
253. patient(paul) <- (23) [avatar component clause 251]
256. 24 <=> ! [X0] : patient(X0) [avatar definition]
257. patient(X0) <- (24) [avatar component clause 256]
258. 24 | 23 [avatar split clause 130,251,256]
324. ~tall(paul) <- (23) [resolution 123,253]
325. $false <- (23) [subsumption resolution 324,149]
326. ~23 [avatar contradiction clause 325]
327. $false <- (~23, 24) [subsumption resolution 252,257]
328. 23 | ~24 [avatar contradiction clause 327]
329. $false [avatar sat refutation 258,326,328]
% SZS output end Proof for 248233226465279808743451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not kind is not rich or not funny and vice versa. Everyone who is either not creative or not happy is both not humble and not kind and vice versa. Everyone who is curious is both not funny and patient. If someone is strong then mary is not happy and vice versa. Everyone who is calm or not old is brave or not wise and vice versa. Everyone who is not funny is either not funny or curious. Everyone who is both not happy and not calm is either not kind or not humble. Everyone who is not strong or not quiet is either brave or not tall. If someone is both generous and strong then paul is not funny or happy and vice versa. If john is rich or not humble then lucy is either old or not calm. If someone is not wise or not brave then john is not tall. If paul is either not rich or not generous then lucy is generous or not strong. If someone is both not happy and patient then someone is both curious and not creative. If someone is both happy and patient then someone is generous or humble. If paul is both tall and not funny then john is not strong. If someone is either calm or not brave then susan is tall or not tall. Someone is either not tall or humble. John is not kind or not creative. Someone is both not creative and not curious. Someone is either not strong or not curious. Lucy is patient or wise. Alice is both not happy and not old. Someone is quiet or not strong. Susan is either not old or calm. | John is not tall. | neutral | (![X]:((~happy(X)|~kind(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~creative(X)<~>~happy(X))<=>(~humble(X)&~kind(X))))&
(![X]:(curious(X)=>(~funny(X)&patient(X))))&
((?[X]:(strong(X)))<=>(~happy(mary)))&
(![X]:((calm(X)|~old(X))<=>(brave(X)|~wise(X))))&
(![X]:(~funny(X)=>(~funny(X)<~>curious(X))))&
(![X]:((~happy(X)&~calm(X))=>(~kind(X)<~>~humble(X))))&
(![X]:((~strong(X)|~quiet(X))=>(brave(X)<~>~tall(X))))&
((?[X]:((generous(X)&strong(X))))<=>((~funny(paul)|happy(paul))))&
(((rich(john)|~humble(john)))=>((old(lucy)<~>~calm(lucy))))&
((?[X]:((~wise(X)|~brave(X))))=>(~tall(john)))&
(((~rich(paul)<~>~generous(paul)))=>((generous(lucy)|~strong(lucy))))&
((?[X]:((~happy(X)&patient(X))))=>(?[X]:((curious(X)&~creative(X)))))&
((?[X]:((happy(X)&patient(X))))=>(?[X]:((generous(X)|humble(X)))))&
(((tall(paul)&~funny(paul)))=>(~strong(john)))&
((?[X]:((calm(X)<~>~brave(X))))=>((tall(susan)|~tall(susan))))&
(?[X]:((~tall(X)<~>humble(X))))&
((~kind(john)|~creative(john)))&
(?[X]:((~creative(X)&~curious(X))))&
(?[X]:((~strong(X)<~>~curious(X))))&
((patient(lucy)|wise(lucy)))&
((~happy(alice)&~old(alice)))&
(?[X]:((quiet(X)|~strong(X))))&
((~old(susan)<~>calm(susan))) | ~tall(john) | []
| null | 0 |
Everyone who is both creative and brave is both not strong and calm.
If paul is quiet or not old then someone is both tall and calm and vice versa.
If someone is not creative then someone is either generous or tall and vice versa.
Everyone who is creative or not wise is both not kind and not brave and vice versa.
If someone is not calm or quiet then someone is either curious or brave.
Everyone who is generous is old and vice versa.
Everyone who is not creative is either not creative or not funny.
Everyone who is not brave is either not brave or not old and vice versa.
Everyone who is both quiet and creative is both humble and kind.
Everyone who is not creative or funny is both calm and not kind.
Everyone who is either not creative or tall is kind and vice versa.
If someone is both not rich and not generous then someone is not strong and vice versa.
Everyone who is funny or not brave is either brave or strong.
Everyone who is either not generous or funny is either kind or not happy.
Everyone who is funny or not brave is not quiet or curious.
Someone is either not patient or not old.
Someone is not funny.
Someone is either kind or not happy.
Lucy is brave or funny. | Lucy is not calm. | contradiction | (![X]:((creative(X)&brave(X))=>(~strong(X)&calm(X))))&
(((quiet(paul)|~old(paul)))<=>(?[X]:((tall(X)&calm(X)))))&
((?[X]:(~creative(X)))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((creative(X)|~wise(X))<=>(~kind(X)&~brave(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:(generous(X)<=>old(X)))&
(![X]:(~creative(X)=>(~creative(X)<~>~funny(X))))&
(![X]:(~brave(X)<=>(~brave(X)<~>~old(X))))&
(![X]:((quiet(X)&creative(X))=>(humble(X)&kind(X))))&
(![X]:((~creative(X)|funny(X))=>(calm(X)&~kind(X))))&
(![X]:((~creative(X)<~>tall(X))<=>kind(X)))&
((?[X]:((~rich(X)&~generous(X))))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|~brave(X))=>(brave(X)<~>strong(X))))&
(![X]:((~generous(X)<~>funny(X))=>(kind(X)<~>~happy(X))))&
(![X]:((funny(X)|~brave(X))=>(~quiet(X)|curious(X))))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
((brave(lucy)|funny(lucy))) | ~calm(lucy) | [
"p3",
"p9",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 3573533292456731637466659
% SZS output start Proof for 3573533292456731637466659
4. ! [X0] : ((~wise(X0) | creative(X0)) <=> (~brave(X0) & ~kind(X0))) [input p3]
10. ! [X0] : ((funny(X0) | ~creative(X0)) => (~kind(X0) & calm(X0))) [input p9]
19. funny(lucy) | brave(lucy) [input p18]
20. ~calm(lucy) [input hypothesis]
31. ! [X0] : ((~kind(X0) & calm(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 10]
46. ! [X0] : (((~wise(X0) | creative(X0)) | (brave(X0) | kind(X0))) & ((~brave(X0) & ~kind(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 4]
47. ! [X0] : ((~wise(X0) | creative(X0) | brave(X0) | kind(X0)) & ((~brave(X0) & ~kind(X0)) | (wise(X0) & ~creative(X0)))) [flattening 46]
84. ~brave(X0) | ~creative(X0) [cnf transformation 47]
100. calm(X0) | creative(X0) [cnf transformation 31]
101. ~funny(X0) | calm(X0) [cnf transformation 31]
126. funny(lucy) | brave(lucy) [cnf transformation 19]
127. ~calm(lucy) [cnf transformation 20]
230. 21 <=> brave(lucy) [avatar definition]
232. brave(lucy) <- (21) [avatar component clause 230]
234. 22 <=> funny(lucy) [avatar definition]
236. funny(lucy) <- (22) [avatar component clause 234]
237. 21 | 22 [avatar split clause 126,234,230]
242. ~creative(lucy) <- (21) [resolution 84,232]
248. creative(lucy) [resolution 100,127]
249. $false <- (21) [subsumption resolution 248,242]
250. ~21 [avatar contradiction clause 249]
256. calm(lucy) <- (22) [resolution 101,236]
257. $false <- (22) [subsumption resolution 256,127]
258. ~22 [avatar contradiction clause 257]
259. $false [avatar sat refutation 237,250,258]
% SZS output end Proof for 3573533292456731637466659
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both old and not quiet then someone is both not wise and happy and vice versa. Everyone who is happy or not curious is not kind or generous. If john is both not curious and patient then paul is both kind and not brave. If fred is both not curious and creative then susan is both tall and not strong. If someone is either not funny or old then someone is generous. If someone is either not tall or not funny then someone is not happy or not calm. Everyone who is patient or not brave is not quiet or quiet. If fred is not kind or not tall then mary is not rich and vice versa. Everyone who is not kind is creative and vice versa. Everyone who is not wise or not curious is both not kind and patient. Everyone who is wise or not old is both not tall and not old. If someone is both funny and generous then someone is either old or creative and vice versa. If someone is quiet then someone is not patient or patient. Everyone who is both not calm and quiet is both not creative and not tall. Everyone who is creative or not brave is either not funny or not brave. Everyone who is not old is either not brave or funny. Someone is calm. Mary is both not creative and not tall. Someone is not quiet or not curious. John is strong or not humble. Lucy is not creative or generous. Mary is both not rich and not creative. Mary is either creative or brave. Someone is both not quiet and not brave. | Mary is happy. | contradiction | (((old(mary)&~quiet(mary)))<=>(?[X]:((~wise(X)&happy(X)))))&
(![X]:((happy(X)|~curious(X))=>(~kind(X)|generous(X))))&
(((~curious(john)&patient(john)))=>((kind(paul)&~brave(paul))))&
(((~curious(fred)&creative(fred)))=>((tall(susan)&~strong(susan))))&
((?[X]:((~funny(X)<~>old(X))))=>(?[X]:(generous(X))))&
((?[X]:((~tall(X)<~>~funny(X))))=>(?[X]:((~happy(X)|~calm(X)))))&
(![X]:((patient(X)|~brave(X))=>(~quiet(X)|quiet(X))))&
(((~kind(fred)|~tall(fred)))<=>(~rich(mary)))&
(![X]:(~kind(X)<=>creative(X)))&
(![X]:((~wise(X)|~curious(X))=>(~kind(X)&patient(X))))&
(![X]:((wise(X)|~old(X))=>(~tall(X)&~old(X))))&
((?[X]:((funny(X)&generous(X))))<=>(?[X]:((old(X)<~>creative(X)))))&
((?[X]:(quiet(X)))=>(?[X]:((~patient(X)|patient(X)))))&
(![X]:((~calm(X)&quiet(X))=>(~creative(X)&~tall(X))))&
(![X]:((creative(X)|~brave(X))=>(~funny(X)<~>~brave(X))))&
(![X]:(~old(X)=>(~brave(X)<~>funny(X))))&
(?[X]:(calm(X)))&
((~creative(mary)&~tall(mary)))&
(?[X]:((~quiet(X)|~curious(X))))&
((strong(john)|~humble(john)))&
((~creative(lucy)|generous(lucy)))&
((~rich(mary)&~creative(mary)))&
((creative(mary)<~>brave(mary)))&
(?[X]:((~quiet(X)&~brave(X)))) | happy(mary) | [
"p1",
"p8",
"p9",
"p10",
"p11",
"p14",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 146057638566436078448002
% SZS output start Proof for 146057638566436078448002
2. ! [X0] : ((~curious(X0) | happy(X0)) => (generous(X0) | ~kind(X0))) [input p1]
9. ! [X0] : (~kind(X0) <=> creative(X0)) [input p8]
10. ! [X0] : ((~curious(X0) | ~wise(X0)) => (patient(X0) & ~kind(X0))) [input p9]
11. ! [X0] : ((~old(X0) | wise(X0)) => (~old(X0) & ~tall(X0))) [input p10]
12. ? [X0] : (generous(X0) & funny(X0)) <=> ? [X0] : (old(X0) <~> creative(X0)) [input p11]
15. ! [X0] : ((~brave(X0) | creative(X0)) => (~funny(X0) <~> ~brave(X0))) [input p14]
16. ! [X0] : (~old(X0) => (~brave(X0) <~> funny(X0))) [input p15]
18. ~tall(mary) & ~creative(mary) [input p17]
25. happy(mary) [input hypothesis]
28. ? [X0] : (generous(X0) & funny(X0)) <=> ? [X1] : (old(X1) <~> creative(X1)) [rectify 12]
32. ! [X0] : ((generous(X0) | ~kind(X0)) | (curious(X0) & ~happy(X0))) [ennf transformation 2]
33. ! [X0] : (generous(X0) | ~kind(X0) | (curious(X0) & ~happy(X0))) [flattening 32]
42. ! [X0] : ((patient(X0) & ~kind(X0)) | (curious(X0) & wise(X0))) [ennf transformation 10]
43. ! [X0] : ((~old(X0) & ~tall(X0)) | (old(X0) & ~wise(X0))) [ennf transformation 11]
47. ! [X0] : ((~funny(X0) <~> ~brave(X0)) | (brave(X0) & ~creative(X0))) [ennf transformation 15]
48. ! [X0] : ((~brave(X0) <~> funny(X0)) | old(X0)) [ennf transformation 16]
64. ! [X0] : ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0))) [nnf transformation 9]
65. (? [X0] : (generous(X0) & funny(X0)) | ! [X1] : ((old(X1) | ~creative(X1)) & (creative(X1) | ~old(X1)))) & (? [X1] : ((~creative(X1) | ~old(X1)) & (creative(X1) | old(X1))) | ! [X0] : (~generous(X0) | ~funny(X0))) [nnf transformation 28]
66. (? [X0] : (generous(X0) & funny(X0)) | ! [X1] : ((old(X1) | ~creative(X1)) & (creative(X1) | ~old(X1)))) & (? [X2] : ((~creative(X2) | ~old(X2)) & (creative(X2) | old(X2))) | ! [X3] : (~generous(X3) | ~funny(X3))) [rectify 65]
67. ? [X0] : (generous(X0) & funny(X0)) => (generous(sK3) & funny(sK3)) [choice axiom]
68. ? [X2] : ((~creative(X2) | ~old(X2)) & (creative(X2) | old(X2))) => ((~creative(sK4) | ~old(sK4)) & (creative(sK4) | old(sK4))) [choice axiom]
69. ((generous(sK3) & funny(sK3)) | ! [X1] : ((old(X1) | ~creative(X1)) & (creative(X1) | ~old(X1)))) & (((~creative(sK4) | ~old(sK4)) & (creative(sK4) | old(sK4))) | ! [X3] : (~generous(X3) | ~funny(X3))) [skolemisation 66,68,67]
73. ! [X0] : (((brave(X0) | funny(X0)) & (~brave(X0) | ~funny(X0))) | (brave(X0) & ~creative(X0))) [nnf transformation 47]
74. ! [X0] : (((~funny(X0) | brave(X0)) & (funny(X0) | ~brave(X0))) | old(X0)) [nnf transformation 48]
86. ~kind(X0) | generous(X0) | ~happy(X0) [cnf transformation 33]
100. creative(X0) | kind(X0) [cnf transformation 64]
102. ~kind(X0) | wise(X0) [cnf transformation 42]
108. ~wise(X0) | ~old(X0) [cnf transformation 43]
110. creative(sK4) | old(sK4) | ~generous(X3) | ~funny(X3) [cnf transformation 69]
111. ~creative(sK4) | ~old(sK4) | ~generous(X3) | ~funny(X3) [cnf transformation 69]
119. ~funny(X0) | ~brave(X0) | ~creative(X0) [cnf transformation 73]
122. brave(X0) | funny(X0) | brave(X0) [cnf transformation 73]
123. funny(X0) | ~brave(X0) | old(X0) [cnf transformation 74]
124. ~funny(X0) | brave(X0) | old(X0) [cnf transformation 74]
126. ~creative(mary) [cnf transformation 18]
136. happy(mary) [cnf transformation 25]
137. funny(X0) | brave(X0) [duplicate literal removal 122]
147. 3 <=> old(mary) [avatar definition]
148. ~old(mary) <- (~3) [avatar component clause 147]
201. 15 <=> ! [X1] : (old(X1) | funny(X1)) [avatar definition]
202. funny(X1) | old(X1) <- (15) [avatar component clause 201]
236. 23 <=> ! [X1] : (old(X1) | ~creative(X1)) [avatar definition]
237. ~creative(X1) | old(X1) <- (23) [avatar component clause 236]
254. 27 <=> ! [X3] : (~generous(X3) | ~funny(X3)) [avatar definition]
255. ~funny(X3) | ~generous(X3) <- (27) [avatar component clause 254]
257. 28 <=> old(sK4) [avatar definition]
258. old(sK4) <- (28) [avatar component clause 257]
259. ~old(sK4) <- (~28) [avatar component clause 257]
261. 29 <=> creative(sK4) [avatar definition]
262. creative(sK4) <- (29) [avatar component clause 261]
263. ~creative(sK4) <- (~29) [avatar component clause 261]
264. 27 | ~28 | ~29 [avatar split clause 111,261,257,254]
265. 27 | 28 | 29 [avatar split clause 110,261,257,254]
266. brave(X0) | old(X0) [subsumption resolution 124,137]
267. funny(X0) | old(X0) [subsumption resolution 123,266]
268. 15 [avatar split clause 267,201]
289. kind(mary) [resolution 100,126]
296. wise(mary) [resolution 102,289]
305. ~old(mary) [resolution 108,296]
309. ~3 [avatar split clause 305,147]
324. ~generous(X0) | old(X0) <- (15, 27) [resolution 255,202]
331. generous(mary) | ~happy(mary) [resolution 86,289]
334. generous(mary) [subsumption resolution 331,136]
366. ~brave(X0) | ~creative(X0) | old(X0) <- (15) [resolution 119,202]
377. old(mary) <- (15, 27) [resolution 324,334]
378. $false <- (~3, 15, 27) [subsumption resolution 377,148]
379. 3 | ~15 | ~27 [avatar contradiction clause 378]
415. old(sK4) <- (23, 29) [resolution 262,237]
426. $false <- (23, ~28, 29) [subsumption resolution 415,259]
427. ~23 | 28 | ~29 [avatar contradiction clause 426]
428. ~creative(X0) | old(X0) <- (15) [subsumption resolution 366,266]
429. 23 | ~15 [avatar split clause 428,201,236]
430. kind(sK4) <- (~29) [resolution 263,100]
436. wise(sK4) <- (~29) [resolution 430,102]
446. ~old(sK4) <- (~29) [resolution 436,108]
447. $false <- (28, ~29) [subsumption resolution 446,258]
448. ~28 | 29 [avatar contradiction clause 447]
449. $false [avatar sat refutation 264,265,268,309,379,427,429,448]
% SZS output end Proof for 146057638566436078448002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not old and humble is patient and vice versa.
If john is not humble then mary is wise or not wise.
Everyone who is old or not old is wise and vice versa.
Everyone who is both funny and not rich is both not brave and calm.
Everyone who is wise or not happy is both not calm and creative.
Everyone who is not rich or not happy is both brave and kind.
If someone is either not wise or brave then someone is not happy and vice versa.
Everyone who is either not generous or not creative is calm or generous.
If someone is quiet then someone is both happy and generous.
Everyone who is both not happy and not curious is either calm or creative.
Everyone who is not generous is both not quiet and not calm.
If susan is both not quiet and funny then john is not happy or not quiet and vice versa.
Everyone who is either not curious or funny is both strong and not rich and vice versa.
Everyone who is both creative and patient is not kind and vice versa.
If someone is not old then paul is patient and vice versa.
Everyone who is either wise or brave is either not quiet or not calm and vice versa.
Alice is patient.
John is both rich and wise.
Someone is not strong.
Someone is not calm.
Someone is either not funny or not patient.
Someone is kind. | Alice is not patient. | contradiction | (![X]:((~old(X)&humble(X))<=>patient(X)))&
((~humble(john))=>((wise(mary)|~wise(mary))))&
(![X]:((old(X)|~old(X))<=>wise(X)))&
(![X]:((funny(X)&~rich(X))=>(~brave(X)&calm(X))))&
(![X]:((wise(X)|~happy(X))=>(~calm(X)&creative(X))))&
(![X]:((~rich(X)|~happy(X))=>(brave(X)&kind(X))))&
((?[X]:((~wise(X)<~>brave(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~generous(X)<~>~creative(X))=>(calm(X)|generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((happy(X)&generous(X)))))&
(![X]:((~happy(X)&~curious(X))=>(calm(X)<~>creative(X))))&
(![X]:(~generous(X)=>(~quiet(X)&~calm(X))))&
(((~quiet(susan)&funny(susan)))<=>((~happy(john)|~quiet(john))))&
(![X]:((~curious(X)<~>funny(X))<=>(strong(X)&~rich(X))))&
(![X]:((creative(X)&patient(X))<=>~kind(X)))&
((?[X]:(~old(X)))<=>(patient(paul)))&
(![X]:((wise(X)<~>brave(X))<=>(~quiet(X)<~>~calm(X))))&
(patient(alice))&
((rich(john)&wise(john)))&
(?[X]:(~strong(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~funny(X)<~>~patient(X))))&
(?[X]:(kind(X))) | ~patient(alice) | [
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8612056089319340754553804
% SZS output start Proof for 8612056089319340754553804
17. patient(alice) [input p16]
23. ~patient(alice) [input hypothesis]
124. patient(alice) [cnf transformation 17]
132. ~patient(alice) [cnf transformation 23]
214. $false [subsumption resolution 132,124]
% SZS output end Proof for 8612056089319340754553804
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and kind is generous. If someone is both happy and humble then someone is both rich and not funny and vice versa. If someone is curious or not calm then mary is both not quiet and patient. If someone is not humble or not brave then someone is both wise and humble. Everyone who is not curious is generous or creative and vice versa. If mary is either funny or not creative then someone is both happy and not generous. Everyone who is both brave and humble is not rich or not generous and vice versa. If someone is quiet or wise then someone is generous or strong. Everyone who is either wise or happy is both not humble and not patient and vice versa. Everyone who is either not kind or not happy is not curious. If lucy is either calm or not patient then someone is strong or not kind and vice versa. Everyone who is either not brave or strong is both not strong and strong and vice versa. If mary is not quiet then alice is both patient and creative. If susan is either generous or calm then someone is both not calm and strong. Everyone who is both curious and not brave is both rich and funny. If alice is strong then someone is both not calm and patient. Someone is either not tall or not patient. Someone is old. Alice is both tall and not kind. Alice is kind or not quiet. John is not kind. Someone is either tall or not humble. Someone is quiet or funny. | Mary is funny. | neutral | (![X]:((rich(X)&kind(X))=>generous(X)))&
((?[X]:((happy(X)&humble(X))))<=>(?[X]:((rich(X)&~funny(X)))))&
((?[X]:((curious(X)|~calm(X))))=>((~quiet(mary)&patient(mary))))&
((?[X]:((~humble(X)|~brave(X))))=>(?[X]:((wise(X)&humble(X)))))&
(![X]:(~curious(X)<=>(generous(X)|creative(X))))&
(((funny(mary)<~>~creative(mary)))=>(?[X]:((happy(X)&~generous(X)))))&
(![X]:((brave(X)&humble(X))<=>(~rich(X)|~generous(X))))&
((?[X]:((quiet(X)|wise(X))))=>(?[X]:((generous(X)|strong(X)))))&
(![X]:((wise(X)<~>happy(X))<=>(~humble(X)&~patient(X))))&
(![X]:((~kind(X)<~>~happy(X))=>~curious(X)))&
(((calm(lucy)<~>~patient(lucy)))<=>(?[X]:((strong(X)|~kind(X)))))&
(![X]:((~brave(X)<~>strong(X))<=>(~strong(X)&strong(X))))&
((~quiet(mary))=>((patient(alice)&creative(alice))))&
(((generous(susan)<~>calm(susan)))=>(?[X]:((~calm(X)&strong(X)))))&
(![X]:((curious(X)&~brave(X))=>(rich(X)&funny(X))))&
((strong(alice))=>(?[X]:((~calm(X)&patient(X)))))&
(?[X]:((~tall(X)<~>~patient(X))))&
(?[X]:(old(X)))&
((tall(alice)&~kind(alice)))&
((kind(alice)|~quiet(alice)))&
(~kind(john))&
(?[X]:((tall(X)<~>~humble(X))))&
(?[X]:((quiet(X)|funny(X)))) | funny(mary) | []
| null | 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. | John is rich. | neutral | (![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)))) | rich(john) | []
| null | 0 |
If someone is both old and not creative then someone is both not tall and not happy.
Everyone who is not calm or not humble is both not strong and not brave.
If fred is both kind and not humble then someone is not curious.
Everyone who is either calm or generous is not brave.
If someone is not patient or not calm then mary is either humble or rich and vice versa.
Everyone who is creative or not wise is both not curious and not wise and vice versa.
Everyone who is both not quiet and not creative is either not happy or rich.
Everyone who is not generous is generous.
Everyone who is not wise or funny is not happy.
Everyone who is either not patient or wise is either not brave or not strong.
If someone is either rich or not curious then lucy is both happy and tall and vice versa.
Everyone who is tall is both happy and not calm.
Everyone who is either not patient or not humble is either strong or happy and vice versa.
Everyone who is both curious and generous is either not happy or brave.
Everyone who is either not generous or not strong is funny or not generous.
If someone is both not creative and calm then susan is both brave and not quiet.
Susan is both patient and kind.
John is either not tall or old.
Paul is not happy.
Someone is calm or not curious.
Fred is brave or curious.
Someone is both kind and not brave. | Susan is rich. | entailment | ((?[X]:((old(X)&~creative(X))))=>(?[X]:((~tall(X)&~happy(X)))))&
(![X]:((~calm(X)|~humble(X))=>(~strong(X)&~brave(X))))&
(((kind(fred)&~humble(fred)))=>(?[X]:(~curious(X))))&
(![X]:((calm(X)<~>generous(X))=>~brave(X)))&
((?[X]:((~patient(X)|~calm(X))))<=>((humble(mary)<~>rich(mary))))&
(![X]:((creative(X)|~wise(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~quiet(X)&~creative(X))=>(~happy(X)<~>rich(X))))&
(![X]:(~generous(X)=>generous(X)))&
(![X]:((~wise(X)|funny(X))=>~happy(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~brave(X)<~>~strong(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((happy(lucy)&tall(lucy))))&
(![X]:(tall(X)=>(happy(X)&~calm(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(strong(X)<~>happy(X))))&
(![X]:((curious(X)&generous(X))=>(~happy(X)<~>brave(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(funny(X)|~generous(X))))&
((?[X]:((~creative(X)&calm(X))))=>((brave(susan)&~quiet(susan))))&
((patient(susan)&kind(susan)))&
((~tall(john)<~>old(john)))&
(~happy(paul))&
(?[X]:((calm(X)|~curious(X))))&
((brave(fred)|curious(fred)))&
(?[X]:((kind(X)&~brave(X)))) | rich(susan) | [
"p1",
"p5",
"p7",
"p8",
"p9",
"p10",
"p11",
"p12",
"p13",
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 4062431635458897216261288
% SZS output start Proof for 4062431635458897216261288
2. ! [X0] : ((~humble(X0) | ~calm(X0)) => (~brave(X0) & ~strong(X0))) [input p1]
6. ! [X0] : ((~wise(X0) | creative(X0)) <=> (~wise(X0) & ~curious(X0))) [input p5]
8. ! [X0] : (~generous(X0) => generous(X0)) [input p7]
9. ! [X0] : ((funny(X0) | ~wise(X0)) => ~happy(X0)) [input p8]
10. ! [X0] : ((~patient(X0) <~> wise(X0)) => (~brave(X0) <~> ~strong(X0))) [input p9]
11. ? [X0] : (rich(X0) <~> ~curious(X0)) <=> (tall(lucy) & happy(lucy)) [input p10]
12. ! [X0] : (tall(X0) => (~calm(X0) & happy(X0))) [input p11]
13. ! [X0] : ((~patient(X0) <~> ~humble(X0)) <=> (strong(X0) <~> happy(X0))) [input p12]
14. ! [X0] : ((generous(X0) & curious(X0)) => (~happy(X0) <~> brave(X0))) [input p13]
15. ! [X0] : ((~generous(X0) <~> ~strong(X0)) => (~generous(X0) | funny(X0))) [input p14]
17. kind(susan) & patient(susan) [input p16]
23. ~rich(susan) [input hypothesis]
26. ! [X0] : ((~brave(X0) & ~strong(X0)) | (humble(X0) & calm(X0))) [ennf transformation 2]
32. ! [X0] : (generous(X0) | generous(X0)) [ennf transformation 8]
33. ! [X0] : (~happy(X0) | (~funny(X0) & wise(X0))) [ennf transformation 9]
34. ! [X0] : ((~brave(X0) <~> ~strong(X0)) | (~patient(X0) <=> wise(X0))) [ennf transformation 10]
35. ! [X0] : ((~calm(X0) & happy(X0)) | ~tall(X0)) [ennf transformation 12]
36. ! [X0] : ((~happy(X0) <~> brave(X0)) | (~generous(X0) | ~curious(X0))) [ennf transformation 14]
37. ! [X0] : ((~happy(X0) <~> brave(X0)) | ~generous(X0) | ~curious(X0)) [flattening 36]
38. ! [X0] : ((~generous(X0) | funny(X0)) | (~generous(X0) <=> ~strong(X0))) [ennf transformation 15]
39. ! [X0] : (~generous(X0) | funny(X0) | (~generous(X0) <=> ~strong(X0))) [flattening 38]
51. ! [X0] : (((~wise(X0) | creative(X0)) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~creative(X0)))) [nnf transformation 6]
52. ! [X0] : ((~wise(X0) | creative(X0) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~creative(X0)))) [flattening 51]
54. ! [X0] : (((strong(X0) | brave(X0)) & (~strong(X0) | ~brave(X0))) | ((~patient(X0) | ~wise(X0)) & (wise(X0) | patient(X0)))) [nnf transformation 34]
55. (? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~tall(lucy) | ~happy(lucy))) & ((tall(lucy) & happy(lucy)) | ! [X0] : ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) [nnf transformation 11]
56. (? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~tall(lucy) | ~happy(lucy)) & ((tall(lucy) & happy(lucy)) | ! [X0] : ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) [flattening 55]
57. (? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~tall(lucy) | ~happy(lucy)) & ((tall(lucy) & happy(lucy)) | ! [X1] : ((rich(X1) | curious(X1)) & (~curious(X1) | ~rich(X1)))) [rectify 56]
58. ? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) => ((curious(sK3) | ~rich(sK3)) & (~curious(sK3) | rich(sK3))) [choice axiom]
59. (((curious(sK3) | ~rich(sK3)) & (~curious(sK3) | rich(sK3))) | ~tall(lucy) | ~happy(lucy)) & ((tall(lucy) & happy(lucy)) | ! [X1] : ((rich(X1) | curious(X1)) & (~curious(X1) | ~rich(X1)))) [skolemisation 57,58]
60. ! [X0] : ((((humble(X0) | patient(X0)) & (~humble(X0) | ~patient(X0))) | ((strong(X0) | ~happy(X0)) & (happy(X0) | ~strong(X0)))) & (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | ((~patient(X0) | humble(X0)) & (~humble(X0) | patient(X0))))) [nnf transformation 13]
61. ! [X0] : (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~generous(X0) | ~curious(X0)) [nnf transformation 37]
62. ! [X0] : (~generous(X0) | funny(X0) | ((~generous(X0) | strong(X0)) & (~strong(X0) | generous(X0)))) [nnf transformation 39]
70. ~strong(X0) | calm(X0) [cnf transformation 26]
71. ~strong(X0) | humble(X0) [cnf transformation 26]
84. ~curious(X0) | wise(X0) [cnf transformation 52]
90. generous(X0) | generous(X0) [cnf transformation 32]
92. ~funny(X0) | ~happy(X0) [cnf transformation 33]
94. ~wise(X0) | ~brave(X0) | ~patient(X0) | ~strong(X0) [cnf transformation 54]
96. ~wise(X0) | brave(X0) | ~patient(X0) | strong(X0) [cnf transformation 54]
98. happy(lucy) | rich(X1) | curious(X1) [cnf transformation 59]
100. tall(lucy) | rich(X1) | curious(X1) [cnf transformation 59]
104. ~calm(X0) | ~tall(X0) [cnf transformation 35]
109. ~humble(X0) | ~patient(X0) | happy(X0) | ~strong(X0) [cnf transformation 60]
113. brave(X0) | ~happy(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 61]
114. ~brave(X0) | happy(X0) | ~generous(X0) | ~curious(X0) [cnf transformation 61]
116. ~generous(X0) | funny(X0) | ~generous(X0) | strong(X0) [cnf transformation 62]
119. patient(susan) [cnf transformation 17]
128. ~rich(susan) [cnf transformation 23]
129. ~generous(X0) | funny(X0) | strong(X0) [duplicate literal removal 116]
130. generous(X0) [duplicate literal removal 90]
187. 13 <=> happy(lucy) [avatar definition]
188. happy(lucy) <- (13) [avatar component clause 187]
191. 14 <=> tall(lucy) [avatar definition]
192. tall(lucy) <- (14) [avatar component clause 191]
205. 17 <=> ! [X1] : (rich(X1) | curious(X1)) [avatar definition]
206. rich(X1) | curious(X1) <- (17) [avatar component clause 205]
207. 17 | 14 [avatar split clause 100,191,205]
212. 17 | 13 [avatar split clause 98,187,205]
215. ~patient(X0) | happy(X0) | ~strong(X0) [subsumption resolution 109,71]
218. ~curious(X0) | happy(X0) | ~brave(X0) [subsumption resolution 114,130]
219. ~curious(X0) | ~happy(X0) | brave(X0) [subsumption resolution 113,130]
220. funny(X0) | strong(X0) [subsumption resolution 129,130]
230. 21 <=> brave(susan) [avatar definition]
270. ~happy(X0) | strong(X0) [resolution 220,92]
292. happy(susan) | ~strong(susan) [resolution 215,119]
294. 30 <=> strong(susan) [avatar definition]
296. ~strong(susan) <- (~30) [avatar component clause 294]
298. 31 <=> happy(susan) [avatar definition]
300. happy(susan) <- (31) [avatar component clause 298]
301. ~30 | 31 [avatar split clause 292,298,294]
440. 50 <=> strong(lucy) [avatar definition]
442. strong(lucy) <- (50) [avatar component clause 440]
507. strong(lucy) <- (13) [resolution 270,188]
513. 50 | ~13 [avatar split clause 507,187,440]
517. calm(lucy) <- (50) [resolution 442,70]
518. ~tall(lucy) <- (50) [resolution 517,104]
519. $false <- (14, 50) [subsumption resolution 518,192]
520. ~14 | ~50 [avatar contradiction clause 519]
531. curious(susan) <- (17) [resolution 206,128]
552. ~happy(susan) | brave(susan) <- (17) [resolution 531,219]
553. happy(susan) | ~brave(susan) <- (17) [resolution 531,218]
554. wise(susan) <- (17) [resolution 531,84]
599. brave(susan) | ~patient(susan) | strong(susan) <- (17) [resolution 554,96]
600. ~brave(susan) | ~patient(susan) | ~strong(susan) <- (17) [resolution 554,94]
606. ~brave(susan) | ~strong(susan) <- (17) [subsumption resolution 600,119]
607. ~30 | ~21 | ~17 [avatar split clause 606,205,230,294]
608. brave(susan) | strong(susan) <- (17) [subsumption resolution 599,119]
609. 30 | 21 | ~17 [avatar split clause 608,205,230,294]
610. ~21 | 31 | ~17 [avatar split clause 553,205,298,230]
611. 21 | ~31 | ~17 [avatar split clause 552,205,298,230]
616. strong(susan) <- (31) [resolution 300,270]
620. $false <- (~30, 31) [subsumption resolution 616,296]
621. 30 | ~31 [avatar contradiction clause 620]
622. $false [avatar sat refutation 207,212,301,513,520,607,609,610,611,621]
% SZS output end Proof for 4062431635458897216261288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or not creative is calm or funny and vice versa.
If someone is not kind or not wise then mary is both not patient and rich and vice versa.
Everyone who is not curious or calm is both not humble and kind and vice versa.
If john is humble then alice is either not rich or not quiet.
If john is both creative and funny then susan is either not quiet or brave and vice versa.
If mary is kind then paul is creative or curious and vice versa.
Everyone who is both not generous and not kind is both not happy and not creative.
If fred is both old and not humble then someone is either old or not tall and vice versa.
Everyone who is quiet is both humble and not creative and vice versa.
If paul is not creative or not strong then someone is strong and vice versa.
Everyone who is quiet is kind.
Everyone who is both not brave and not tall is both not humble and not tall and vice versa.
If alice is both wise and kind then lucy is not old or funny.
Everyone who is both brave and wise is not brave and vice versa.
Everyone who is both not wise and wise is not quiet or not strong.
Everyone who is not happy is rich and vice versa.
Someone is both patient and not funny.
Fred is either not calm or not creative.
Someone is either not strong or not happy.
Fred is both not quiet and strong.
Lucy is not strong or not generous.
Someone is curious or generous.
Someone is brave or not rich.
Someone is both humble and tall. | Susan is generous. | neutral | (![X]:((~happy(X)<~>~creative(X))<=>(calm(X)|funny(X))))&
((?[X]:((~kind(X)|~wise(X))))<=>((~patient(mary)&rich(mary))))&
(![X]:((~curious(X)|calm(X))<=>(~humble(X)&kind(X))))&
((humble(john))=>((~rich(alice)<~>~quiet(alice))))&
(((creative(john)&funny(john)))<=>((~quiet(susan)<~>brave(susan))))&
((kind(mary))<=>((creative(paul)|curious(paul))))&
(![X]:((~generous(X)&~kind(X))=>(~happy(X)&~creative(X))))&
(((old(fred)&~humble(fred)))<=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:(quiet(X)<=>(humble(X)&~creative(X))))&
(((~creative(paul)|~strong(paul)))<=>(?[X]:(strong(X))))&
(![X]:(quiet(X)=>kind(X)))&
(![X]:((~brave(X)&~tall(X))<=>(~humble(X)&~tall(X))))&
(((wise(alice)&kind(alice)))=>((~old(lucy)|funny(lucy))))&
(![X]:((brave(X)&wise(X))<=>~brave(X)))&
(![X]:((~wise(X)&wise(X))=>(~quiet(X)|~strong(X))))&
(![X]:(~happy(X)<=>rich(X)))&
(?[X]:((patient(X)&~funny(X))))&
((~calm(fred)<~>~creative(fred)))&
(?[X]:((~strong(X)<~>~happy(X))))&
((~quiet(fred)&strong(fred)))&
((~strong(lucy)|~generous(lucy)))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((brave(X)|~rich(X))))&
(?[X]:((humble(X)&tall(X)))) | generous(susan) | []
| null | 0 |
If fred is either quiet or wise then alice is both humble and not humble.
If paul is either quiet or not happy then someone is not brave or patient.
If john is either generous or calm then someone is either not calm or not tall.
Everyone who is humble or calm is not strong.
If paul is both humble and not creative then someone is not strong or creative.
Everyone who is either not curious or not rich is both funny and not happy.
Everyone who is either not old or not kind is either wise or generous and vice versa.
Everyone who is wise or not brave is not brave or not old and vice versa.
If someone is creative or generous then someone is not humble and vice versa.
Everyone who is both happy and not happy is either not old or not creative and vice versa.
If someone is both not quiet and not patient then fred is quiet or strong and vice versa.
If someone is not curious or not old then lucy is either creative or old and vice versa.
Everyone who is not calm or calm is not creative or not happy and vice versa.
Everyone who is calm or curious is not funny.
If someone is not calm then alice is both quiet and not curious.
Someone is either wise or brave.
Someone is tall or not rich.
Someone is funny or quiet.
Someone is either curious or kind.
Susan is either not quiet or happy.
Someone is either rich or strong.
Someone is humble or not rich.
Lucy is not happy. | Lucy is not rich. | contradiction | (((quiet(fred)<~>wise(fred)))=>((humble(alice)&~humble(alice))))&
(((quiet(paul)<~>~happy(paul)))=>(?[X]:((~brave(X)|patient(X)))))&
(((generous(john)<~>calm(john)))=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:((humble(X)|calm(X))=>~strong(X)))&
(((humble(paul)&~creative(paul)))=>(?[X]:((~strong(X)|creative(X)))))&
(![X]:((~curious(X)<~>~rich(X))=>(funny(X)&~happy(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(wise(X)<~>generous(X))))&
(![X]:((wise(X)|~brave(X))<=>(~brave(X)|~old(X))))&
((?[X]:((creative(X)|generous(X))))<=>(?[X]:(~humble(X))))&
(![X]:((happy(X)&~happy(X))<=>(~old(X)<~>~creative(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>((quiet(fred)|strong(fred))))&
((?[X]:((~curious(X)|~old(X))))<=>((creative(lucy)<~>old(lucy))))&
(![X]:((~calm(X)|calm(X))<=>(~creative(X)|~happy(X))))&
(![X]:((calm(X)|curious(X))=>~funny(X)))&
((?[X]:(~calm(X)))=>((quiet(alice)&~curious(alice))))&
(?[X]:((wise(X)<~>brave(X))))&
(?[X]:((tall(X)|~rich(X))))&
(?[X]:((funny(X)|quiet(X))))&
(?[X]:((curious(X)<~>kind(X))))&
((~quiet(susan)<~>happy(susan)))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((humble(X)|~rich(X))))&
(~happy(lucy)) | ~rich(lucy) | [
"p5",
"p9",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 211422259350621541625803
% SZS output start Proof for 211422259350621541625803
6. ! [X0] : ((~curious(X0) <~> ~rich(X0)) => (~happy(X0) & funny(X0))) [input p5]
10. ! [X0] : ((~happy(X0) & happy(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p9]
12. ? [X0] : (~old(X0) | ~curious(X0)) <=> (creative(lucy) <~> old(lucy)) [input p11]
14. ! [X0] : ((curious(X0) | calm(X0)) => ~funny(X0)) [input p13]
24. ~rich(lucy) [input hypothesis]
32. ! [X0] : ((~happy(X0) & funny(X0)) | (~curious(X0) <=> ~rich(X0))) [ennf transformation 6]
33. ! [X0] : (~funny(X0) | (~curious(X0) & ~calm(X0))) [ennf transformation 14]
44. ! [X0] : ((~happy(X0) & funny(X0)) | ((~curious(X0) | rich(X0)) & (~rich(X0) | curious(X0)))) [nnf transformation 32]
53. ! [X0] : (((~happy(X0) & happy(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (happy(X0) | ~happy(X0)))) [nnf transformation 10]
54. ! [X0] : (((~happy(X0) & happy(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | happy(X0) | ~happy(X0))) [flattening 53]
60. (? [X0] : (~old(X0) | ~curious(X0)) | ((creative(lucy) | ~old(lucy)) & (old(lucy) | ~creative(lucy)))) & (((~old(lucy) | ~creative(lucy)) & (old(lucy) | creative(lucy))) | ! [X0] : (old(X0) & curious(X0))) [nnf transformation 12]
61. (? [X0] : (~old(X0) | ~curious(X0)) | ((creative(lucy) | ~old(lucy)) & (old(lucy) | ~creative(lucy)))) & (((~old(lucy) | ~creative(lucy)) & (old(lucy) | creative(lucy))) | ! [X1] : (old(X1) & curious(X1))) [rectify 60]
62. ? [X0] : (~old(X0) | ~curious(X0)) => (~old(sK6) | ~curious(sK6)) [choice axiom]
63. ((~old(sK6) | ~curious(sK6)) | ((creative(lucy) | ~old(lucy)) & (old(lucy) | ~creative(lucy)))) & (((~old(lucy) | ~creative(lucy)) & (old(lucy) | creative(lucy))) | ! [X1] : (old(X1) & curious(X1))) [skolemisation 61,62]
96. ~curious(X0) | funny(X0) | rich(X0) [cnf transformation 44]
116. happy(X0) | ~creative(X0) | old(X0) [cnf transformation 54]
117. happy(X0) | ~old(X0) | creative(X0) [cnf transformation 54]
118. ~happy(X0) | ~creative(X0) | old(X0) [cnf transformation 54]
119. ~happy(X0) | ~old(X0) | creative(X0) [cnf transformation 54]
125. old(lucy) | creative(lucy) | curious(X1) [cnf transformation 63]
127. ~old(lucy) | ~creative(lucy) | curious(X1) [cnf transformation 63]
136. ~funny(X0) | ~curious(X0) [cnf transformation 33]
151. ~rich(lucy) [cnf transformation 24]
247. ~old(X0) | creative(X0) [subsumption resolution 117,119]
248. ~creative(X0) | old(X0) [subsumption resolution 116,118]
274. 27 <=> creative(lucy) [avatar definition]
278. ~creative(lucy) | curious(X1) [subsumption resolution 127,248]
280. 28 <=> ! [X1] : curious(X1) [avatar definition]
281. curious(X1) <- (28) [avatar component clause 280]
282. 28 | ~27 [avatar split clause 278,274,280]
285. creative(lucy) | curious(X1) [subsumption resolution 125,247]
286. 28 | 27 [avatar split clause 285,274,280]
385. funny(X0) | rich(X0) <- (28) [resolution 96,281]
387. rich(X0) | ~curious(X0) <- (28) [resolution 385,136]
390. rich(X0) <- (28) [subsumption resolution 387,281]
394. $false <- (28) [resolution 390,151]
399. ~28 [avatar contradiction clause 394]
400. $false [avatar sat refutation 282,286,399]
% SZS output end Proof for 211422259350621541625803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall and generous then paul is not tall.
Everyone who is tall or wise is both old and not creative.
Everyone who is both not curious and not rich is not calm or not creative.
Everyone who is either tall or patient is both not quiet and old and vice versa.
Everyone who is either happy or not generous is not kind and vice versa.
Everyone who is not old is wise and vice versa.
Everyone who is quiet or funny is calm or kind and vice versa.
Everyone who is brave or not brave is either rich or wise.
If fred is calm or tall then john is both not brave and not tall and vice versa.
Everyone who is brave or strong is not creative and vice versa.
If alice is rich then someone is both not brave and not humble and vice versa.
Everyone who is not kind or not quiet is both tall and not wise and vice versa.
Everyone who is patient or not kind is not happy.
If someone is either wise or not kind then john is not kind.
Everyone who is either not rich or creative is not patient or old and vice versa.
If fred is both quiet and funny then someone is either creative or not generous.
Fred is both calm and kind.
Alice is either not old or not generous.
John is funny.
Susan is either not brave or humble.
Someone is either not creative or happy.
Someone is calm or not brave. | Alice is not brave. | entailment | ((?[X]:((~tall(X)&generous(X))))=>(~tall(paul)))&
(![X]:((tall(X)|wise(X))=>(old(X)&~creative(X))))&
(![X]:((~curious(X)&~rich(X))=>(~calm(X)|~creative(X))))&
(![X]:((tall(X)<~>patient(X))<=>(~quiet(X)&old(X))))&
(![X]:((happy(X)<~>~generous(X))<=>~kind(X)))&
(![X]:(~old(X)<=>wise(X)))&
(![X]:((quiet(X)|funny(X))<=>(calm(X)|kind(X))))&
(![X]:((brave(X)|~brave(X))=>(rich(X)<~>wise(X))))&
(((calm(fred)|tall(fred)))<=>((~brave(john)&~tall(john))))&
(![X]:((brave(X)|strong(X))<=>~creative(X)))&
((rich(alice))<=>(?[X]:((~brave(X)&~humble(X)))))&
(![X]:((~kind(X)|~quiet(X))<=>(tall(X)&~wise(X))))&
(![X]:((patient(X)|~kind(X))=>~happy(X)))&
((?[X]:((wise(X)<~>~kind(X))))=>(~kind(john)))&
(![X]:((~rich(X)<~>creative(X))<=>(~patient(X)|old(X))))&
(((quiet(fred)&funny(fred)))=>(?[X]:((creative(X)<~>~generous(X)))))&
((calm(fred)&kind(fred)))&
((~old(alice)<~>~generous(alice)))&
(funny(john))&
((~brave(susan)<~>humble(susan)))&
(?[X]:((~creative(X)<~>happy(X))))&
(?[X]:((calm(X)|~brave(X)))) | ~brave(alice) | [
"p1",
"p5",
"p7",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1349376742010868301571143
% SZS output start Proof for 1349376742010868301571143
2. ! [X0] : ((wise(X0) | tall(X0)) => (~creative(X0) & old(X0))) [input p1]
6. ! [X0] : (~old(X0) <=> wise(X0)) [input p5]
8. ! [X0] : ((~brave(X0) | brave(X0)) => (rich(X0) <~> wise(X0))) [input p7]
10. ! [X0] : ((strong(X0) | brave(X0)) <=> ~creative(X0)) [input p9]
15. ! [X0] : ((~rich(X0) <~> creative(X0)) <=> (old(X0) | ~patient(X0))) [input p14]
23. brave(alice) [input hypothesis]
26. ! [X0] : ((~creative(X0) & old(X0)) | (~wise(X0) & ~tall(X0))) [ennf transformation 2]
27. ! [X0] : ((rich(X0) <~> wise(X0)) | (brave(X0) & ~brave(X0))) [ennf transformation 8]
35. ! [X0] : ((~old(X0) | ~wise(X0)) & (wise(X0) | old(X0))) [nnf transformation 6]
38. ! [X0] : (((~wise(X0) | ~rich(X0)) & (wise(X0) | rich(X0))) | (brave(X0) & ~brave(X0))) [nnf transformation 27]
41. ! [X0] : (((strong(X0) | brave(X0)) | creative(X0)) & (~creative(X0) | (~strong(X0) & ~brave(X0)))) [nnf transformation 10]
42. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & (~creative(X0) | (~strong(X0) & ~brave(X0)))) [flattening 41]
50. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [nnf transformation 15]
51. ! [X0] : ((((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0))))) [flattening 50]
64. ~wise(X0) | old(X0) [cnf transformation 26]
77. wise(X0) | old(X0) [cnf transformation 35]
78. ~old(X0) | ~wise(X0) [cnf transformation 35]
83. wise(X0) | rich(X0) | ~brave(X0) [cnf transformation 38]
84. wise(X0) | rich(X0) | brave(X0) [cnf transformation 38]
92. ~brave(X0) | ~creative(X0) [cnf transformation 42]
110. creative(X0) | ~rich(X0) | ~old(X0) [cnf transformation 51]
125. brave(alice) [cnf transformation 23]
136. ~wise(X0) [subsumption resolution 78,64]
137. old(X0) [subsumption resolution 77,136]
138. rich(X0) | brave(X0) [subsumption resolution 84,136]
139. rich(X0) | ~brave(X0) [subsumption resolution 83,136]
140. rich(X0) [subsumption resolution 139,138]
174. creative(X0) | ~old(X0) [subsumption resolution 110,140]
175. creative(X0) [subsumption resolution 174,137]
214. ~creative(alice) [resolution 92,125]
215. $false [subsumption resolution 214,175]
% SZS output end Proof for 1349376742010868301571143
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is rich then lucy is either not quiet or not calm.
If susan is happy then alice is not generous or rich and vice versa.
If someone is not curious or quiet then susan is both not creative and brave and vice versa.
Everyone who is either not happy or not old is either not patient or not calm and vice versa.
Everyone who is strong is happy.
Everyone who is both not generous and calm is either not kind or not old and vice versa.
Everyone who is either tall or happy is humble.
If someone is both tall and brave then someone is generous and vice versa.
Everyone who is both funny and curious is both not tall and not calm and vice versa.
If someone is both kind and not kind then someone is both wise and not patient.
If someone is both brave and old then susan is both happy and not kind and vice versa.
Everyone who is both curious and tall is old and vice versa.
If someone is not calm or quiet then someone is either not creative or not old.
Everyone who is either not calm or not patient is either not generous or not funny and vice versa.
Everyone who is both not humble and humble is patient.
Everyone who is either happy or not kind is either calm or kind.
John is humble or not humble.
John is humble or not wise.
Fred is both rich and tall.
Someone is either not funny or not strong.
Lucy is not creative.
Mary is not patient.
Fred is not quiet or kind.
Someone is both curious and not creative. | Fred is strong. | neutral | ((rich(john))=>((~quiet(lucy)<~>~calm(lucy))))&
((happy(susan))<=>((~generous(alice)|rich(alice))))&
((?[X]:((~curious(X)|quiet(X))))<=>((~creative(susan)&brave(susan))))&
(![X]:((~happy(X)<~>~old(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:(strong(X)=>happy(X)))&
(![X]:((~generous(X)&calm(X))<=>(~kind(X)<~>~old(X))))&
(![X]:((tall(X)<~>happy(X))=>humble(X)))&
((?[X]:((tall(X)&brave(X))))<=>(?[X]:(generous(X))))&
(![X]:((funny(X)&curious(X))<=>(~tall(X)&~calm(X))))&
((?[X]:((kind(X)&~kind(X))))=>(?[X]:((wise(X)&~patient(X)))))&
((?[X]:((brave(X)&old(X))))<=>((happy(susan)&~kind(susan))))&
(![X]:((curious(X)&tall(X))<=>old(X)))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((~creative(X)<~>~old(X)))))&
(![X]:((~calm(X)<~>~patient(X))<=>(~generous(X)<~>~funny(X))))&
(![X]:((~humble(X)&humble(X))=>patient(X)))&
(![X]:((happy(X)<~>~kind(X))=>(calm(X)<~>kind(X))))&
((humble(john)|~humble(john)))&
((humble(john)|~wise(john)))&
((rich(fred)&tall(fred)))&
(?[X]:((~funny(X)<~>~strong(X))))&
(~creative(lucy))&
(~patient(mary))&
((~quiet(fred)|kind(fred)))&
(?[X]:((curious(X)&~creative(X)))) | strong(fred) | []
| null | 0 |
If someone is not tall or rich then john is both not generous and not kind.
If paul is not funny then someone is both brave and quiet.
Everyone who is both not strong and patient is happy or humble and vice versa.
Everyone who is not old is either curious or quiet and vice versa.
If someone is not happy then fred is both not funny and not patient.
If fred is not rich then someone is strong or not brave.
Everyone who is either curious or not generous is not kind or generous.
Everyone who is either generous or rich is either rich or not strong and vice versa.
If someone is both not quiet and happy then mary is calm or tall and vice versa.
Everyone who is funny or not strong is funny or not quiet and vice versa.
Everyone who is not humble is not patient.
Everyone who is not happy or not humble is either not creative or not tall.
Everyone who is kind is both happy and not old and vice versa.
Everyone who is both not quiet and not happy is both not happy and patient and vice versa.
Everyone who is not wise or brave is both not patient and funny and vice versa.
Someone is both not generous and not curious.
Someone is either tall or kind.
Mary is humble.
Lucy is either not calm or not funny.
Alice is calm or tall.
Fred is rich or generous.
Lucy is either calm or humble. | Lucy is brave. | contradiction | ((?[X]:((~tall(X)|rich(X))))=>((~generous(john)&~kind(john))))&
((~funny(paul))=>(?[X]:((brave(X)&quiet(X)))))&
(![X]:((~strong(X)&patient(X))<=>(happy(X)|humble(X))))&
(![X]:(~old(X)<=>(curious(X)<~>quiet(X))))&
((?[X]:(~happy(X)))=>((~funny(fred)&~patient(fred))))&
((~rich(fred))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:((curious(X)<~>~generous(X))=>(~kind(X)|generous(X))))&
(![X]:((generous(X)<~>rich(X))<=>(rich(X)<~>~strong(X))))&
((?[X]:((~quiet(X)&happy(X))))<=>((calm(mary)|tall(mary))))&
(![X]:((funny(X)|~strong(X))<=>(funny(X)|~quiet(X))))&
(![X]:(~humble(X)=>~patient(X)))&
(![X]:((~happy(X)|~humble(X))=>(~creative(X)<~>~tall(X))))&
(![X]:(kind(X)<=>(happy(X)&~old(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(~happy(X)&patient(X))))&
(![X]:((~wise(X)|brave(X))<=>(~patient(X)&funny(X))))&
(?[X]:((~generous(X)&~curious(X))))&
(?[X]:((tall(X)<~>kind(X))))&
(humble(mary))&
((~calm(lucy)<~>~funny(lucy)))&
((calm(alice)|tall(alice)))&
((rich(fred)|generous(fred)))&
((calm(lucy)<~>humble(lucy))) | brave(lucy) | [
"p2",
"p14",
"p18",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 4207495321013308581784926
% SZS output start Proof for 4207495321013308581784926
3. ! [X0] : ((patient(X0) & ~strong(X0)) <=> (humble(X0) | happy(X0))) [input p2]
15. ! [X0] : ((brave(X0) | ~wise(X0)) <=> (funny(X0) & ~patient(X0))) [input p14]
19. ~calm(lucy) <~> ~funny(lucy) [input p18]
22. calm(lucy) <~> humble(lucy) [input p21]
23. brave(lucy) [input hypothesis]
34. ! [X0] : (((patient(X0) & ~strong(X0)) | (~humble(X0) & ~happy(X0))) & ((humble(X0) | happy(X0)) | (~patient(X0) | strong(X0)))) [nnf transformation 3]
35. ! [X0] : (((patient(X0) & ~strong(X0)) | (~humble(X0) & ~happy(X0))) & (humble(X0) | happy(X0) | ~patient(X0) | strong(X0))) [flattening 34]
53. ! [X0] : (((brave(X0) | ~wise(X0)) | (~funny(X0) | patient(X0))) & ((funny(X0) & ~patient(X0)) | (~brave(X0) & wise(X0)))) [nnf transformation 15]
54. ! [X0] : ((brave(X0) | ~wise(X0) | ~funny(X0) | patient(X0)) & ((funny(X0) & ~patient(X0)) | (~brave(X0) & wise(X0)))) [flattening 53]
60. (funny(lucy) | calm(lucy)) & (~funny(lucy) | ~calm(lucy)) [nnf transformation 19]
61. (~humble(lucy) | ~calm(lucy)) & (humble(lucy) | calm(lucy)) [nnf transformation 22]
72. ~humble(X0) | patient(X0) [cnf transformation 35]
112. ~patient(X0) | ~brave(X0) [cnf transformation 54]
114. ~brave(X0) | funny(X0) [cnf transformation 54]
121. ~funny(lucy) | ~calm(lucy) [cnf transformation 60]
125. humble(lucy) | calm(lucy) [cnf transformation 61]
127. brave(lucy) [cnf transformation 23]
229. 21 <=> calm(lucy) [avatar definition]
233. 22 <=> funny(lucy) [avatar definition]
237. ~21 | ~22 [avatar split clause 121,233,229]
253. 26 <=> humble(lucy) [avatar definition]
254. humble(lucy) <- (26) [avatar component clause 253]
257. 21 | 26 [avatar split clause 125,253,229]
270. funny(lucy) [resolution 114,127]
273. 22 [avatar split clause 270,233]
274. patient(lucy) <- (26) [resolution 254,72]
278. ~brave(lucy) <- (26) [resolution 274,112]
281. $false <- (26) [subsumption resolution 278,127]
282. ~26 [avatar contradiction clause 281]
283. $false [avatar sat refutation 237,257,273,282]
% SZS output end Proof for 4207495321013308581784926
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both humble and not happy then fred is curious or rich.
If someone is either not strong or not old then john is either not funny or not kind and vice versa.
Everyone who is happy is both not calm and patient and vice versa.
If someone is not generous then someone is patient or not brave and vice versa.
If paul is both strong and not wise then someone is both creative and not generous and vice versa.
If fred is not calm then someone is both not rich and not tall and vice versa.
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.
Everyone who is kind is generous or brave and vice versa.
If mary is not calm or not wise then someone is creative or rich.
If susan is funny or not quiet then lucy is not patient or not tall and vice versa.
If john is not wise then someone is either not wise or quiet.
Someone is either patient or calm.
Fred is curious.
Someone is not humble or not curious.
Paul is both not humble and not creative.
Someone is either not generous or quiet.
Someone is not strong or funny. | Fred is not happy. | entailment | (((humble(fred)&~happy(fred)))=>((curious(fred)|rich(fred))))&
((?[X]:((~strong(X)<~>~old(X))))<=>((~funny(john)<~>~kind(john))))&
(![X]:(happy(X)<=>(~calm(X)&patient(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((patient(X)|~brave(X)))))&
(((strong(paul)&~wise(paul)))<=>(?[X]:((creative(X)&~generous(X)))))&
((~calm(fred))<=>(?[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]:(kind(X)<=>(generous(X)|brave(X))))&
(((~calm(mary)|~wise(mary)))=>(?[X]:((creative(X)|rich(X)))))&
(((funny(susan)|~quiet(susan)))<=>((~patient(lucy)|~tall(lucy))))&
((~wise(john))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(?[X]:((patient(X)<~>calm(X))))&
(curious(fred))&
(?[X]:((~humble(X)|~curious(X))))&
((~humble(paul)&~creative(paul)))&
(?[X]:((~generous(X)<~>quiet(X))))&
(?[X]:((~strong(X)|funny(X)))) | ~happy(fred) | [
"p2",
"p3",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 8658626353206678683520410
% SZS output start Proof for 8658626353206678683520410
3. ! [X0] : (happy(X0) <=> (patient(X0) & ~calm(X0))) [input p2]
4. ? [X0] : ~generous(X0) <=> ? [X0] : (~brave(X0) | patient(X0)) [input p3]
11. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (tall(X0) & generous(X0))) [input p10]
23. happy(fred) [input hypothesis]
24. ? [X0] : ~generous(X0) <=> ? [X1] : (~brave(X1) | patient(X1)) [rectify 4]
35. ! [X0] : ((happy(X0) | (~patient(X0) | calm(X0))) & ((patient(X0) & ~calm(X0)) | ~happy(X0))) [nnf transformation 3]
36. ! [X0] : ((happy(X0) | ~patient(X0) | calm(X0)) & ((patient(X0) & ~calm(X0)) | ~happy(X0))) [flattening 35]
37. (? [X0] : ~generous(X0) | ! [X1] : (brave(X1) & ~patient(X1))) & (? [X1] : (~brave(X1) | patient(X1)) | ! [X0] : generous(X0)) [nnf transformation 24]
38. (? [X0] : ~generous(X0) | ! [X1] : (brave(X1) & ~patient(X1))) & (? [X2] : (~brave(X2) | patient(X2)) | ! [X3] : generous(X3)) [rectify 37]
39. ? [X0] : ~generous(X0) => ~generous(sK1) [choice axiom]
40. ? [X2] : (~brave(X2) | patient(X2)) => (~brave(sK2) | patient(sK2)) [choice axiom]
41. (~generous(sK1) | ! [X1] : (brave(X1) & ~patient(X1))) & ((~brave(sK2) | patient(sK2)) | ! [X3] : generous(X3)) [skolemisation 38,40,39]
63. ! [X0] : (((~happy(X0) | ~calm(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 11]
64. ! [X0] : ((~happy(X0) | ~calm(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (happy(X0) & calm(X0)))) [flattening 63]
94. ~calm(X0) | ~happy(X0) [cnf transformation 36]
95. ~happy(X0) | patient(X0) [cnf transformation 36]
98. ~generous(sK1) | ~patient(X1) [cnf transformation 41]
120. generous(X0) | calm(X0) [cnf transformation 64]
121. generous(X0) | happy(X0) [cnf transformation 64]
149. happy(fred) [cnf transformation 23]
159. 2 <=> happy(fred) [avatar definition]
161. happy(fred) <- (2) [avatar component clause 159]
205. 12 <=> generous(sK1) [avatar definition]
207. ~generous(sK1) <- (~12) [avatar component clause 205]
210. 13 <=> ! [X1] : ~patient(X1) [avatar definition]
211. ~patient(X1) <- (13) [avatar component clause 210]
212. 13 | ~12 [avatar split clause 98,205,210]
391. 2 [avatar split clause 149,159]
394. patient(fred) <- (2) [resolution 95,161]
397. calm(sK1) <- (~12) [resolution 120,207]
399. ~happy(sK1) <- (~12) [resolution 397,94]
400. happy(sK1) <- (~12) [resolution 121,207]
402. $false <- (~12) [subsumption resolution 400,399]
403. 12 [avatar contradiction clause 402]
408. $false <- (2, 13) [resolution 211,394]
409. ~2 | ~13 [avatar contradiction clause 408]
412. $false [avatar sat refutation 212,391,403,409]
% SZS output end Proof for 8658626353206678683520410
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or not wise is happy and vice versa. Everyone who is curious is calm. Everyone who is either curious or not brave is strong and vice versa. Everyone who is either not wise or not kind is both quiet and brave and vice versa. Everyone who is both curious and not creative is not funny or calm and vice versa. If fred is rich then someone is both not strong and kind. Everyone who is not brave or quiet is quiet and vice versa. If mary is not wise then someone is either not old or brave. Everyone who is not calm or not old is either not generous or calm and vice versa. If fred is calm or not kind then alice is old and vice versa. If someone is either generous or curious then someone is brave. Everyone who is not quiet or not funny is both strong and wise and vice versa. Everyone who is strong is brave and vice versa. If someone is both not happy and kind then someone is either not old or patient and vice versa. If alice is not funny or creative then someone is strong. Lucy is both brave and not kind. Susan is either not old or not happy. Someone is either humble or wise. Someone is not creative. Paul is not curious or not strong. John is both quiet and kind. | Susan is not calm. | contradiction | (![X]:((patient(X)|~wise(X))<=>happy(X)))&
(![X]:(curious(X)=>calm(X)))&
(![X]:((curious(X)<~>~brave(X))<=>strong(X)))&
(![X]:((~wise(X)<~>~kind(X))<=>(quiet(X)&brave(X))))&
(![X]:((curious(X)&~creative(X))<=>(~funny(X)|calm(X))))&
((rich(fred))=>(?[X]:((~strong(X)&kind(X)))))&
(![X]:((~brave(X)|quiet(X))<=>quiet(X)))&
((~wise(mary))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((~calm(X)|~old(X))<=>(~generous(X)<~>calm(X))))&
(((calm(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((generous(X)<~>curious(X))))=>(?[X]:(brave(X))))&
(![X]:((~quiet(X)|~funny(X))<=>(strong(X)&wise(X))))&
(![X]:(strong(X)<=>brave(X)))&
((?[X]:((~happy(X)&kind(X))))<=>(?[X]:((~old(X)<~>patient(X)))))&
(((~funny(alice)|creative(alice)))=>(?[X]:(strong(X))))&
((brave(lucy)&~kind(lucy)))&
((~old(susan)<~>~happy(susan)))&
(?[X]:((humble(X)<~>wise(X))))&
(?[X]:(~creative(X)))&
((~curious(paul)|~strong(paul)))&
((quiet(john)&kind(john))) | ~calm(susan) | [
"p1",
"p2",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3942517644860231692330144
% SZS output start Proof for 3942517644860231692330144
2. ! [X0] : (curious(X0) => calm(X0)) [input p1]
3. ! [X0] : ((curious(X0) <~> ~brave(X0)) <=> strong(X0)) [input p2]
13. ! [X0] : (strong(X0) <=> brave(X0)) [input p12]
22. ~calm(susan) [input hypothesis]
26. ! [X0] : (calm(X0) | ~curious(X0)) [ennf transformation 2]
32. ! [X0] : ((((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~strong(X0)) & (strong(X0) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0))))) [nnf transformation 3]
52. ! [X0] : ((strong(X0) | ~brave(X0)) & (brave(X0) | ~strong(X0))) [nnf transformation 13]
69. ~curious(X0) | calm(X0) [cnf transformation 26]
71. strong(X0) | curious(X0) | brave(X0) [cnf transformation 32]
72. ~strong(X0) | curious(X0) | ~brave(X0) [cnf transformation 32]
106. ~strong(X0) | brave(X0) [cnf transformation 52]
107. ~brave(X0) | strong(X0) [cnf transformation 52]
126. ~calm(susan) [cnf transformation 22]
257. curious(X0) | brave(X0) | brave(X0) [resolution 71,106]
258. brave(X0) | curious(X0) [duplicate literal removal 257]
386. strong(X1) | curious(X1) [resolution 258,107]
426. curious(X1) | curious(X1) | ~brave(X1) [resolution 386,72]
431. curious(X1) | ~brave(X1) [duplicate literal removal 426]
432. curious(X1) [subsumption resolution 431,258]
467. calm(X0) [resolution 432,69]
471. $false [resolution 467,126]
% SZS output end Proof for 3942517644860231692330144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not happy is humble or not rich.
If someone is not brave or strong then someone is not happy or funny and vice versa.
If someone is both not old and patient then someone is not old.
Everyone who is both not kind and not brave is humble and vice versa.
If lucy is not strong then someone is both not wise and kind.
Everyone who is not quiet is not strong or not humble and vice versa.
If someone is old then alice is old.
If lucy is both old and not creative then fred is generous or not tall.
If susan is either brave or not creative then susan is not curious or not generous and vice versa.
Everyone who is quiet is both not strong and calm and vice versa.
If someone is not curious then paul is both not calm and wise.
Everyone who is both generous and not quiet is either not calm or curious and vice versa.
If someone is either happy or not old then paul is happy and vice versa.
If lucy is both not strong and not quiet then john is either tall or happy and vice versa.
Everyone who is both tall and not generous is not quiet or not happy and vice versa.
If lucy is both curious and generous then susan is either not calm or quiet.
Someone is either not happy or patient.
Someone is both not kind and calm.
Susan is both tall and not strong.
Lucy is not quiet or not calm.
Someone is not kind.
Someone is not calm.
Someone is either not wise or kind. | Fred is generous. | contradiction | (![X]:((patient(X)&~happy(X))=>(humble(X)|~rich(X))))&
((?[X]:((~brave(X)|strong(X))))<=>(?[X]:((~happy(X)|funny(X)))))&
((?[X]:((~old(X)&patient(X))))=>(?[X]:(~old(X))))&
(![X]:((~kind(X)&~brave(X))<=>humble(X)))&
((~strong(lucy))=>(?[X]:((~wise(X)&kind(X)))))&
(![X]:(~quiet(X)<=>(~strong(X)|~humble(X))))&
((?[X]:(old(X)))=>(old(alice)))&
(((old(lucy)&~creative(lucy)))=>((generous(fred)|~tall(fred))))&
(((brave(susan)<~>~creative(susan)))<=>((~curious(susan)|~generous(susan))))&
(![X]:(quiet(X)<=>(~strong(X)&calm(X))))&
((?[X]:(~curious(X)))=>((~calm(paul)&wise(paul))))&
(![X]:((generous(X)&~quiet(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((happy(X)<~>~old(X))))<=>(happy(paul)))&
(((~strong(lucy)&~quiet(lucy)))<=>((tall(john)<~>happy(john))))&
(![X]:((tall(X)&~generous(X))<=>(~quiet(X)|~happy(X))))&
(((curious(lucy)&generous(lucy)))=>((~calm(susan)<~>quiet(susan))))&
(?[X]:((~happy(X)<~>patient(X))))&
(?[X]:((~kind(X)&calm(X))))&
((tall(susan)&~strong(susan)))&
((~quiet(lucy)|~calm(lucy)))&
(?[X]:(~kind(X)))&
(?[X]:(~calm(X)))&
(?[X]:((~wise(X)<~>kind(X)))) | generous(fred) | [
"p5",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1712606090149192809119254
% SZS output start Proof for 1712606090149192809119254
6. ! [X0] : (~quiet(X0) <=> (~humble(X0) | ~strong(X0))) [input p5]
10. ! [X0] : (quiet(X0) <=> (calm(X0) & ~strong(X0))) [input p9]
15. ! [X0] : ((~generous(X0) & tall(X0)) <=> (~happy(X0) | ~quiet(X0))) [input p14]
24. generous(fred) [input hypothesis]
48. ! [X0] : ((~quiet(X0) | (humble(X0) & strong(X0))) & ((~humble(X0) | ~strong(X0)) | quiet(X0))) [nnf transformation 6]
49. ! [X0] : ((~quiet(X0) | (humble(X0) & strong(X0))) & (~humble(X0) | ~strong(X0) | quiet(X0))) [flattening 48]
52. ! [X0] : ((quiet(X0) | (~calm(X0) | strong(X0))) & ((calm(X0) & ~strong(X0)) | ~quiet(X0))) [nnf transformation 10]
53. ! [X0] : ((quiet(X0) | ~calm(X0) | strong(X0)) & ((calm(X0) & ~strong(X0)) | ~quiet(X0))) [flattening 52]
62. ! [X0] : (((~generous(X0) & tall(X0)) | (happy(X0) & quiet(X0))) & ((~happy(X0) | ~quiet(X0)) | (generous(X0) | ~tall(X0)))) [nnf transformation 15]
63. ! [X0] : (((~generous(X0) & tall(X0)) | (happy(X0) & quiet(X0))) & (~happy(X0) | ~quiet(X0) | generous(X0) | ~tall(X0))) [flattening 62]
88. ~quiet(X0) | strong(X0) [cnf transformation 49]
98. ~strong(X0) | ~quiet(X0) [cnf transformation 53]
122. ~generous(X0) | quiet(X0) [cnf transformation 63]
137. generous(fred) [cnf transformation 24]
240. ~quiet(X0) [subsumption resolution 98,88]
292. ~generous(X0) [subsumption resolution 122,240]
314. $false [subsumption resolution 137,292]
% SZS output end Proof for 1712606090149192809119254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then john is happy.
Everyone who is not rich or strong is not curious or not calm.
If susan is strong then alice is both kind and not humble.
If someone is either calm or creative then someone is quiet and vice versa.
Everyone who is not creative is either not creative or not tall and vice versa.
Everyone who is either not rich or not humble is tall.
Everyone who is both not patient and not creative is curious.
If someone is quiet then someone is not curious.
If paul is both not humble and calm then john is old.
If someone is old then alice is not strong.
Everyone who is both calm and not happy is either not funny or calm.
Everyone who is either not tall or patient is not humble and vice versa.
If someone is not tall then someone is either not tall or old and vice versa.
Everyone who is either not strong or brave is not old.
If someone is both quiet and not quiet then someone is both strong and not humble.
Everyone who is both not curious and wise is happy or not old.
Someone is either tall or not tall.
John is both strong and not old.
Someone is tall.
Someone is either calm or happy.
Lucy is not rich or brave.
Someone is both strong and happy.
John is not rich. | Lucy is kind. | neutral | ((?[X]:(happy(X)))=>(happy(john)))&
(![X]:((~rich(X)|strong(X))=>(~curious(X)|~calm(X))))&
((strong(susan))=>((kind(alice)&~humble(alice))))&
((?[X]:((calm(X)<~>creative(X))))<=>(?[X]:(quiet(X))))&
(![X]:(~creative(X)<=>(~creative(X)<~>~tall(X))))&
(![X]:((~rich(X)<~>~humble(X))=>tall(X)))&
(![X]:((~patient(X)&~creative(X))=>curious(X)))&
((?[X]:(quiet(X)))=>(?[X]:(~curious(X))))&
(((~humble(paul)&calm(paul)))=>(old(john)))&
((?[X]:(old(X)))=>(~strong(alice)))&
(![X]:((calm(X)&~happy(X))=>(~funny(X)<~>calm(X))))&
(![X]:((~tall(X)<~>patient(X))<=>~humble(X)))&
((?[X]:(~tall(X)))<=>(?[X]:((~tall(X)<~>old(X)))))&
(![X]:((~strong(X)<~>brave(X))=>~old(X)))&
((?[X]:((quiet(X)&~quiet(X))))=>(?[X]:((strong(X)&~humble(X)))))&
(![X]:((~curious(X)&wise(X))=>(happy(X)|~old(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((strong(john)&~old(john)))&
(?[X]:(tall(X)))&
(?[X]:((calm(X)<~>happy(X))))&
((~rich(lucy)|brave(lucy)))&
(?[X]:((strong(X)&happy(X))))&
(~rich(john)) | kind(lucy) | []
| null | 0 |
If someone is generous then mary is not tall or not quiet and vice versa.
Everyone who is either curious or not funny is both strong and not patient and vice versa.
If someone is not rich or not quiet then alice is both calm and not old.
If someone is rich or strong then mary is not strong or not tall.
Everyone who is either not funny or humble is both not old and curious.
Everyone who is funny or kind is both tall and quiet.
If someone is both funny and strong then paul is not funny.
If someone is either calm or not strong then mary is either not patient or humble.
Everyone who is generous or happy is both not quiet and funny and vice versa.
If someone is either not tall or not happy then someone is either not humble or humble and vice versa.
If alice is not humble or calm then someone is tall and vice versa.
Everyone who is either not funny or happy is rich and vice versa.
If someone is both not patient and humble then alice is not rich or not calm.
Everyone who is curious is curious or not wise.
Everyone who is either not humble or curious is both generous and happy and vice versa.
If alice is not quiet or kind then john is either tall or happy and vice versa.
Someone is not kind or tall.
Fred is tall or old.
Someone is brave.
Someone is both not rich and not generous.
Someone is humble.
Paul is both creative and tall.
Someone is not old or kind. | Mary is not curious. | contradiction | ((?[X]:(generous(X)))<=>((~tall(mary)|~quiet(mary))))&
(![X]:((curious(X)<~>~funny(X))<=>(strong(X)&~patient(X))))&
((?[X]:((~rich(X)|~quiet(X))))=>((calm(alice)&~old(alice))))&
((?[X]:((rich(X)|strong(X))))=>((~strong(mary)|~tall(mary))))&
(![X]:((~funny(X)<~>humble(X))=>(~old(X)&curious(X))))&
(![X]:((funny(X)|kind(X))=>(tall(X)&quiet(X))))&
((?[X]:((funny(X)&strong(X))))=>(~funny(paul)))&
((?[X]:((calm(X)<~>~strong(X))))=>((~patient(mary)<~>humble(mary))))&
(![X]:((generous(X)|happy(X))<=>(~quiet(X)&funny(X))))&
((?[X]:((~tall(X)<~>~happy(X))))<=>(?[X]:((~humble(X)<~>humble(X)))))&
(((~humble(alice)|calm(alice)))<=>(?[X]:(tall(X))))&
(![X]:((~funny(X)<~>happy(X))<=>rich(X)))&
((?[X]:((~patient(X)&humble(X))))=>((~rich(alice)|~calm(alice))))&
(![X]:(curious(X)=>(curious(X)|~wise(X))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)&happy(X))))&
(((~quiet(alice)|kind(alice)))<=>((tall(john)<~>happy(john))))&
(?[X]:((~kind(X)|tall(X))))&
((tall(fred)|old(fred)))&
(?[X]:(brave(X)))&
(?[X]:((~rich(X)&~generous(X))))&
(?[X]:(humble(X)))&
((creative(paul)&tall(paul)))&
(?[X]:((~old(X)|kind(X)))) | ~curious(mary) | [
"p0",
"p1",
"p3",
"p4",
"p5",
"p8",
"p14",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 7288471224765571366483235
% SZS output start Proof for 7288471224765571366483235
1. ? [X0] : generous(X0) <=> (~quiet(mary) | ~tall(mary)) [input p0]
2. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (~patient(X0) & strong(X0))) [input p1]
4. ? [X0] : (strong(X0) | rich(X0)) => (~tall(mary) | ~strong(mary)) [input p3]
5. ! [X0] : ((~funny(X0) <~> humble(X0)) => (curious(X0) & ~old(X0))) [input p4]
6. ! [X0] : ((kind(X0) | funny(X0)) => (quiet(X0) & tall(X0))) [input p5]
9. ! [X0] : ((happy(X0) | generous(X0)) <=> (funny(X0) & ~quiet(X0))) [input p8]
15. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (happy(X0) & generous(X0))) [input p14]
21. ? [X0] : humble(X0) [input p20]
24. ~curious(mary) [input hypothesis]
30. (~tall(mary) | ~strong(mary)) | ! [X0] : (~strong(X0) & ~rich(X0)) [ennf transformation 4]
31. ~tall(mary) | ~strong(mary) | ! [X0] : (~strong(X0) & ~rich(X0)) [flattening 30]
32. ! [X0] : ((curious(X0) & ~old(X0)) | (~funny(X0) <=> humble(X0))) [ennf transformation 5]
33. ! [X0] : ((quiet(X0) & tall(X0)) | (~kind(X0) & ~funny(X0))) [ennf transformation 6]
38. (? [X0] : generous(X0) | (quiet(mary) & tall(mary))) & ((~quiet(mary) | ~tall(mary)) | ! [X0] : ~generous(X0)) [nnf transformation 1]
39. (? [X0] : generous(X0) | (quiet(mary) & tall(mary))) & (~quiet(mary) | ~tall(mary) | ! [X0] : ~generous(X0)) [flattening 38]
40. (? [X0] : generous(X0) | (quiet(mary) & tall(mary))) & (~quiet(mary) | ~tall(mary) | ! [X1] : ~generous(X1)) [rectify 39]
41. ? [X0] : generous(X0) => generous(sK0) [choice axiom]
42. (generous(sK0) | (quiet(mary) & tall(mary))) & (~quiet(mary) | ~tall(mary) | ! [X1] : ~generous(X1)) [skolemisation 40,41]
43. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (patient(X0) | ~strong(X0))) & ((~patient(X0) & strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 2]
44. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | patient(X0) | ~strong(X0)) & ((~patient(X0) & strong(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 43]
45. ! [X0] : ((curious(X0) & ~old(X0)) | ((~funny(X0) | ~humble(X0)) & (humble(X0) | funny(X0)))) [nnf transformation 32]
47. ! [X0] : (((happy(X0) | generous(X0)) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~generous(X0)))) [nnf transformation 9]
48. ! [X0] : ((happy(X0) | generous(X0) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | (~happy(X0) & ~generous(X0)))) [flattening 47]
60. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | (~happy(X0) | ~generous(X0))) & ((happy(X0) & generous(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | ~happy(X0) | ~generous(X0)) & ((happy(X0) & generous(X0)) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [flattening 60]
68. ? [X0] : humble(X0) => humble(sK6) [choice axiom]
69. humble(sK6) [skolemisation 21,68]
72. ~quiet(mary) | ~tall(mary) | ~generous(X1) [cnf transformation 42]
73. generous(sK0) | tall(mary) [cnf transformation 42]
74. generous(sK0) | quiet(mary) [cnf transformation 42]
76. strong(X0) | curious(X0) | funny(X0) [cnf transformation 44]
86. ~tall(mary) | ~strong(mary) | ~strong(X0) [cnf transformation 31]
90. ~humble(X0) | ~funny(X0) | curious(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 33]
100. ~quiet(X0) | ~generous(X0) [cnf transformation 48]
102. ~generous(X0) | funny(X0) [cnf transformation 48]
121. humble(X0) | curious(X0) | generous(X0) [cnf transformation 61]
122. ~humble(X0) | generous(X0) | ~curious(X0) [cnf transformation 61]
137. humble(sK6) [cnf transformation 69]
140. ~curious(mary) [cnf transformation 24]
146. 1 <=> quiet(mary) [avatar definition]
150. 2 <=> generous(sK0) [avatar definition]
152. generous(sK0) <- (2) [avatar component clause 150]
153. 1 | 2 [avatar split clause 74,150,146]
155. 3 <=> tall(mary) [avatar definition]
158. 3 | 2 [avatar split clause 73,150,155]
160. 4 <=> ! [X1] : ~generous(X1) [avatar definition]
161. ~generous(X1) <- (4) [avatar component clause 160]
162. 4 | ~3 | ~1 [avatar split clause 72,146,155,160]
182. 9 <=> ! [X0] : ~strong(X0) [avatar definition]
183. ~strong(X0) <- (9) [avatar component clause 182]
185. 10 <=> strong(mary) [avatar definition]
187. ~strong(mary) <- (~10) [avatar component clause 185]
188. 9 | ~10 | ~3 [avatar split clause 86,155,185,182]
311. funny(sK0) <- (2) [resolution 102,152]
314. quiet(sK0) <- (2) [resolution 311,93]
368. ~generous(sK0) <- (2) [resolution 314,100]
369. $false <- (2) [subsumption resolution 368,152]
370. ~2 [avatar contradiction clause 369]
372. curious(mary) | funny(mary) <- (~10) [resolution 187,76]
373. funny(mary) <- (~10) [subsumption resolution 372,140]
417. curious(X0) | generous(X0) | ~funny(X0) | curious(X0) [resolution 121,90]
420. curious(X0) | generous(X0) | ~funny(X0) [duplicate literal removal 417]
424. ~funny(X0) | curious(X0) <- (4) [subsumption resolution 420,161]
436. generous(sK6) | ~curious(sK6) [resolution 122,137]
511. curious(mary) <- (4, ~10) [resolution 424,373]
515. $false <- (4, ~10) [subsumption resolution 511,140]
516. ~4 | 10 [avatar contradiction clause 515]
529. curious(X0) | funny(X0) <- (9) [resolution 183,76]
532. curious(X0) <- (4, 9) [subsumption resolution 529,424]
534. ~curious(sK6) <- (4) [subsumption resolution 436,161]
535. $false <- (4, 9) [subsumption resolution 534,532]
536. ~4 | ~9 [avatar contradiction clause 535]
539. $false [avatar sat refutation 153,158,162,188,370,516,536]
% SZS output end Proof for 7288471224765571366483235
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious is either not wise or strong and vice versa.
Everyone who is both brave and not brave is either not quiet or happy and vice versa.
If someone is not patient then fred is humble.
Everyone who is funny is either not curious or curious and vice versa.
If mary is either tall or rich then someone is not rich or wise.
If someone is either curious or creative then paul is not kind or not quiet.
Everyone who is not kind or not curious is not patient or curious and vice versa.
Everyone who is either generous or not calm is both not wise and quiet and vice versa.
Everyone who is brave or funny is both old and not rich.
If mary is old then someone is either generous or tall and vice versa.
Everyone who is not creative or not kind is creative or quiet.
Everyone who is happy is either not rich or not happy.
If someone is both humble and generous then someone is not curious or patient and vice versa.
Everyone who is either brave or strong is not creative or not happy and vice versa.
Everyone who is either generous or rich is not rich or not kind.
Everyone who is either old or not tall is both not patient and not creative and vice versa.
Someone is not wise.
Someone is either rich or happy.
Susan is tall.
Someone is either generous or not humble.
Paul is not calm or not curious.
Mary is kind or not humble.
Someone is not rich or rich. | Fred is calm. | neutral | (![X]:(~curious(X)<=>(~wise(X)<~>strong(X))))&
(![X]:((brave(X)&~brave(X))<=>(~quiet(X)<~>happy(X))))&
((?[X]:(~patient(X)))=>(humble(fred)))&
(![X]:(funny(X)<=>(~curious(X)<~>curious(X))))&
(((tall(mary)<~>rich(mary)))=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((curious(X)<~>creative(X))))=>((~kind(paul)|~quiet(paul))))&
(![X]:((~kind(X)|~curious(X))<=>(~patient(X)|curious(X))))&
(![X]:((generous(X)<~>~calm(X))<=>(~wise(X)&quiet(X))))&
(![X]:((brave(X)|funny(X))=>(old(X)&~rich(X))))&
((old(mary))<=>(?[X]:((generous(X)<~>tall(X)))))&
(![X]:((~creative(X)|~kind(X))=>(creative(X)|quiet(X))))&
(![X]:(happy(X)=>(~rich(X)<~>~happy(X))))&
((?[X]:((humble(X)&generous(X))))<=>(?[X]:((~curious(X)|patient(X)))))&
(![X]:((brave(X)<~>strong(X))<=>(~creative(X)|~happy(X))))&
(![X]:((generous(X)<~>rich(X))=>(~rich(X)|~kind(X))))&
(![X]:((old(X)<~>~tall(X))<=>(~patient(X)&~creative(X))))&
(?[X]:(~wise(X)))&
(?[X]:((rich(X)<~>happy(X))))&
(tall(susan))&
(?[X]:((generous(X)<~>~humble(X))))&
((~calm(paul)|~curious(paul)))&
((kind(mary)|~humble(mary)))&
(?[X]:((~rich(X)|rich(X)))) | calm(fred) | []
| null | 0 |
Everyone who is both not generous and creative is either not patient or not generous and vice versa.
If paul is both not wise and creative then lucy is either kind or not old.
If someone is either not old or not funny then lucy is either calm or not funny and vice versa.
If fred is both funny and not humble then paul is both not rich and quiet and vice versa.
If alice is both humble and funny then mary is generous or creative.
Everyone who is either generous or not generous is either creative or not rich.
If paul is both rich and generous then someone is either not humble or not tall and vice versa.
Everyone who is not kind is either not tall or not happy.
If lucy is either funny or not brave then susan is either wise or not curious and vice versa.
Everyone who is either wise or not wise is not strong or not tall.
Everyone who is tall is not humble and vice versa.
If lucy is not funny then someone is calm and vice versa.
If susan is either creative or calm then fred is both curious and not calm.
Everyone who is both wise and patient is both tall and rich and vice versa.
If someone is both not curious and not wise then paul is not wise or not brave.
If someone is either not generous or not funny then someone is either not curious or not generous and vice versa.
John is either tall or generous.
Someone is old or not old.
Someone is both not tall and not quiet.
Susan is both not humble and not happy.
Susan is both not rich and old.
Susan is either not tall or kind.
Someone is either rich or patient. | Paul is creative. | entailment | (![X]:((~generous(X)&creative(X))<=>(~patient(X)<~>~generous(X))))&
(((~wise(paul)&creative(paul)))=>((kind(lucy)<~>~old(lucy))))&
((?[X]:((~old(X)<~>~funny(X))))<=>((calm(lucy)<~>~funny(lucy))))&
(((funny(fred)&~humble(fred)))<=>((~rich(paul)&quiet(paul))))&
(((humble(alice)&funny(alice)))=>((generous(mary)|creative(mary))))&
(![X]:((generous(X)<~>~generous(X))=>(creative(X)<~>~rich(X))))&
(((rich(paul)&generous(paul)))<=>(?[X]:((~humble(X)<~>~tall(X)))))&
(![X]:(~kind(X)=>(~tall(X)<~>~happy(X))))&
(((funny(lucy)<~>~brave(lucy)))<=>((wise(susan)<~>~curious(susan))))&
(![X]:((wise(X)<~>~wise(X))=>(~strong(X)|~tall(X))))&
(![X]:(tall(X)<=>~humble(X)))&
((~funny(lucy))<=>(?[X]:(calm(X))))&
(((creative(susan)<~>calm(susan)))=>((curious(fred)&~calm(fred))))&
(![X]:((wise(X)&patient(X))<=>(tall(X)&rich(X))))&
((?[X]:((~curious(X)&~wise(X))))=>((~wise(paul)|~brave(paul))))&
((?[X]:((~generous(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~generous(X)))))&
((tall(john)<~>generous(john)))&
(?[X]:((old(X)|~old(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
((~humble(susan)&~happy(susan)))&
((~rich(susan)&old(susan)))&
((~tall(susan)<~>kind(susan)))&
(?[X]:((rich(X)<~>patient(X)))) | creative(paul) | [
"p5",
"p6",
"p10",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 5790358822630570536251169
% SZS output start Proof for 5790358822630570536251169
6. ! [X0] : ((generous(X0) <~> ~generous(X0)) => (creative(X0) <~> ~rich(X0))) [input p5]
7. (generous(paul) & rich(paul)) <=> ? [X0] : (~humble(X0) <~> ~tall(X0)) [input p6]
11. ! [X0] : (tall(X0) <=> ~humble(X0)) [input p10]
20. ~happy(susan) & ~humble(susan) [input p19]
24. ~creative(paul) [input hypothesis]
31. ! [X0] : ((creative(X0) <~> ~rich(X0)) | (generous(X0) <=> ~generous(X0))) [ennf transformation 6]
45. ! [X0] : (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) [nnf transformation 31]
46. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | (~generous(paul) | ~rich(paul))) [nnf transformation 7]
47. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X0] : ((tall(X0) | humble(X0)) & (~tall(X0) | ~humble(X0))) | ~generous(paul) | ~rich(paul)) [flattening 46]
48. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) | ~generous(paul) | ~rich(paul)) [rectify 47]
49. ? [X1] : ((tall(X1) | humble(X1)) & (~tall(X1) | ~humble(X1))) => ((tall(sK1) | humble(sK1)) & (~tall(sK1) | ~humble(sK1))) [choice axiom]
50. ((generous(paul) & rich(paul)) | ! [X0] : ((~humble(X0) | tall(X0)) & (~tall(X0) | humble(X0)))) & (((tall(sK1) | humble(sK1)) & (~tall(sK1) | ~humble(sK1))) | ~generous(paul) | ~rich(paul)) [skolemisation 48,49]
53. ! [X0] : ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))) [nnf transformation 11]
96. ~rich(X0) | creative(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 45]
97. ~rich(X0) | creative(X0) | generous(X0) | generous(X0) [cnf transformation 45]
102. rich(paul) | ~tall(X0) | humble(X0) [cnf transformation 50]
116. ~tall(X0) | ~humble(X0) [cnf transformation 53]
117. tall(X0) | humble(X0) [cnf transformation 53]
142. ~humble(susan) [cnf transformation 20]
150. ~creative(paul) [cnf transformation 24]
151. ~rich(X0) | creative(X0) | ~generous(X0) [duplicate literal removal 96]
152. ~rich(X0) | creative(X0) | generous(X0) [duplicate literal removal 97]
163. 2 <=> creative(paul) [avatar definition]
165. ~creative(paul) <- (~2) [avatar component clause 163]
207. 11 <=> rich(paul) [avatar definition]
209. rich(paul) <- (11) [avatar component clause 207]
244. ~rich(X0) | creative(X0) [subsumption resolution 151,152]
254. 21 <=> ! [X0] : (~tall(X0) | humble(X0)) [avatar definition]
255. ~tall(X0) | humble(X0) <- (21) [avatar component clause 254]
258. 21 | 11 [avatar split clause 102,207,254]
373. 45 <=> tall(susan) [avatar definition]
374. ~tall(susan) <- (~45) [avatar component clause 373]
375. tall(susan) <- (45) [avatar component clause 373]
392. ~2 [avatar split clause 150,163]
393. ~tall(X0) <- (21) [subsumption resolution 255,116]
398. humble(susan) <- (~45) [resolution 117,374]
403. $false <- (~45) [subsumption resolution 398,142]
404. 45 [avatar contradiction clause 403]
409. $false <- (21, 45) [subsumption resolution 375,393]
410. ~21 | ~45 [avatar contradiction clause 409]
421. creative(paul) <- (11) [resolution 244,209]
423. $false <- (~2, 11) [subsumption resolution 421,165]
424. 2 | ~11 [avatar contradiction clause 423]
425. $false [avatar sat refutation 258,392,404,410,424]
% SZS output end Proof for 5790358822630570536251169
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm and patient is not rich or not tall and vice versa.
Everyone who is either not calm or not wise is either not strong or wise and vice versa.
Everyone who is both not curious and rich is not creative.
Everyone who is humble or creative is both not tall and not old and vice versa.
Everyone who is not generous is funny.
Everyone who is not patient or calm is not tall and vice versa.
If mary is either quiet or not curious then someone is both not kind and not strong.
If someone is either not patient or not strong then someone is creative or humble.
Everyone who is both quiet and not kind is both calm and happy and vice versa.
Everyone who is not happy or happy is both not wise and not brave and vice versa.
Everyone who is both not strong and kind is both not kind and rich.
Everyone who is either happy or not old is both quiet and not humble and vice versa.
Everyone who is either rich or quiet is both not rich and curious.
Everyone who is both not curious and kind is both not wise and not creative.
Everyone who is happy or curious is either kind or not brave.
Mary is strong.
Susan is not brave.
John is either creative or patient.
Fred is not wise or not curious.
Lucy is curious or not generous.
Susan is not old. | Fred is not tall. | contradiction | (![X]:((~calm(X)&patient(X))<=>(~rich(X)|~tall(X))))&
(![X]:((~calm(X)<~>~wise(X))<=>(~strong(X)<~>wise(X))))&
(![X]:((~curious(X)&rich(X))=>~creative(X)))&
(![X]:((humble(X)|creative(X))<=>(~tall(X)&~old(X))))&
(![X]:(~generous(X)=>funny(X)))&
(![X]:((~patient(X)|calm(X))<=>~tall(X)))&
(((quiet(mary)<~>~curious(mary)))=>(?[X]:((~kind(X)&~strong(X)))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:((creative(X)|humble(X)))))&
(![X]:((quiet(X)&~kind(X))<=>(calm(X)&happy(X))))&
(![X]:((~happy(X)|happy(X))<=>(~wise(X)&~brave(X))))&
(![X]:((~strong(X)&kind(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)<~>~old(X))<=>(quiet(X)&~humble(X))))&
(![X]:((rich(X)<~>quiet(X))=>(~rich(X)&curious(X))))&
(![X]:((~curious(X)&kind(X))=>(~wise(X)&~creative(X))))&
(![X]:((happy(X)|curious(X))=>(kind(X)<~>~brave(X))))&
(strong(mary))&
(~brave(susan))&
((creative(john)<~>patient(john)))&
((~wise(fred)|~curious(fred)))&
((curious(lucy)|~generous(lucy)))&
(~old(susan)) | ~tall(fred) | [
"p0",
"p5",
"hypothesis"
]
| % SZS status Unsatisfiable for 7543442715589981184279252
% SZS output start Proof for 7543442715589981184279252
1. ! [X0] : ((patient(X0) & ~calm(X0)) <=> (~tall(X0) | ~rich(X0))) [input p0]
6. ! [X0] : ((calm(X0) | ~patient(X0)) <=> ~tall(X0)) [input p5]
22. ~tall(fred) [input hypothesis]
36. ! [X0] : (((patient(X0) & ~calm(X0)) | (tall(X0) & rich(X0))) & ((~tall(X0) | ~rich(X0)) | (~patient(X0) | calm(X0)))) [nnf transformation 1]
37. ! [X0] : (((patient(X0) & ~calm(X0)) | (tall(X0) & rich(X0))) & (~tall(X0) | ~rich(X0) | ~patient(X0) | calm(X0))) [flattening 36]
41. ! [X0] : (((calm(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [nnf transformation 6]
42. ! [X0] : ((calm(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~calm(X0) & patient(X0)))) [flattening 41]
61. ~calm(X0) | tall(X0) [cnf transformation 37]
63. patient(X0) | tall(X0) [cnf transformation 37]
80. calm(X0) | ~patient(X0) | tall(X0) [cnf transformation 42]
120. ~tall(fred) [cnf transformation 22]
129. calm(X0) | tall(X0) [subsumption resolution 80,63]
130. tall(X0) [subsumption resolution 129,61]
174. $false [subsumption resolution 120,130]
% SZS output end Proof for 7543442715589981184279252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and creative is both not patient and rich and vice versa.
Everyone who is generous or not happy is rich or not generous and vice versa.
If someone is both tall and funny then paul is not old.
If someone is either strong or not kind then someone is creative and vice versa.
If someone is patient then someone is not curious and vice versa.
Everyone who is not funny is brave.
Everyone who is either not brave or not rich is both not patient and not generous.
Everyone who is both tall and not brave is not tall and vice versa.
Everyone who is not creative or wise is calm or rich and vice versa.
Everyone who is brave or strong is both happy and kind.
If someone is both generous and creative then someone is quiet and vice versa.
If susan is wise then susan is not happy and vice versa.
If john is not calm or happy then someone is both funny and tall and vice versa.
If someone is both happy and kind then alice is both calm and wise.
If lucy is either kind or wise then someone is creative and vice versa.
Mary is either not curious or not calm.
John is either not old or quiet.
Someone is creative or tall.
Someone is either old or not rich.
Someone is generous.
Someone is either not brave or not calm. | John is rich. | entailment | (![X]:((~wise(X)&creative(X))<=>(~patient(X)&rich(X))))&
(![X]:((generous(X)|~happy(X))<=>(rich(X)|~generous(X))))&
((?[X]:((tall(X)&funny(X))))=>(~old(paul)))&
((?[X]:((strong(X)<~>~kind(X))))<=>(?[X]:(creative(X))))&
((?[X]:(patient(X)))<=>(?[X]:(~curious(X))))&
(![X]:(~funny(X)=>brave(X)))&
(![X]:((~brave(X)<~>~rich(X))=>(~patient(X)&~generous(X))))&
(![X]:((tall(X)&~brave(X))<=>~tall(X)))&
(![X]:((~creative(X)|wise(X))<=>(calm(X)|rich(X))))&
(![X]:((brave(X)|strong(X))=>(happy(X)&kind(X))))&
((?[X]:((generous(X)&creative(X))))<=>(?[X]:(quiet(X))))&
((wise(susan))<=>(~happy(susan)))&
(((~calm(john)|happy(john)))<=>(?[X]:((funny(X)&tall(X)))))&
((?[X]:((happy(X)&kind(X))))=>((calm(alice)&wise(alice))))&
(((kind(lucy)<~>wise(lucy)))<=>(?[X]:(creative(X))))&
((~curious(mary)<~>~calm(mary)))&
((~old(john)<~>quiet(john)))&
(?[X]:((creative(X)|tall(X))))&
(?[X]:((old(X)<~>~rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((~brave(X)<~>~calm(X)))) | rich(john) | [
"p1",
"p7",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 3569893575395951839279795
% SZS output start Proof for 3569893575395951839279795
2. ! [X0] : ((~happy(X0) | generous(X0)) <=> (~generous(X0) | rich(X0))) [input p1]
8. ! [X0] : ((~brave(X0) & tall(X0)) <=> ~tall(X0)) [input p7]
10. ! [X0] : ((strong(X0) | brave(X0)) => (kind(X0) & happy(X0))) [input p9]
22. ~rich(john) [input hypothesis]
29. ! [X0] : ((kind(X0) & happy(X0)) | (~strong(X0) & ~brave(X0))) [ennf transformation 10]
33. ! [X0] : (((~happy(X0) | generous(X0)) | (generous(X0) & ~rich(X0))) & ((~generous(X0) | rich(X0)) | (happy(X0) & ~generous(X0)))) [nnf transformation 2]
34. ! [X0] : ((~happy(X0) | generous(X0) | (generous(X0) & ~rich(X0))) & (~generous(X0) | rich(X0) | (happy(X0) & ~generous(X0)))) [flattening 33]
46. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (brave(X0) | ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((~brave(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | brave(X0) | ~tall(X0))) [flattening 46]
81. ~generous(X0) | rich(X0) | ~generous(X0) [cnf transformation 34]
84. ~happy(X0) | generous(X0) | generous(X0) [cnf transformation 34]
97. ~tall(X0) | brave(X0) | ~tall(X0) [cnf transformation 47]
98. tall(X0) | tall(X0) [cnf transformation 47]
104. happy(X0) | ~brave(X0) [cnf transformation 29]
134. ~rich(john) [cnf transformation 22]
135. ~tall(X0) | brave(X0) [duplicate literal removal 97]
136. tall(X0) [duplicate literal removal 98]
137. ~generous(X0) | rich(X0) [duplicate literal removal 81]
138. ~happy(X0) | generous(X0) [duplicate literal removal 84]
189. brave(X0) [subsumption resolution 135,136]
192. happy(X0) [subsumption resolution 104,189]
271. generous(X0) [resolution 138,192]
274. rich(X1) [resolution 271,137]
275. $false [resolution 274,134]
% SZS output end Proof for 3569893575395951839279795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not humble is either not curious or old and vice versa.
Everyone who is brave is both quiet and humble and vice versa.
If someone is calm or funny then someone is either funny or generous and vice versa.
Everyone who is not wise or creative is wise or not happy and vice versa.
Everyone who is not brave or not tall is both happy and calm and vice versa.
If someone is not strong or humble then susan is not curious or not quiet and vice versa.
If alice is either not kind or quiet then fred is both not old and not tall and vice versa.
Everyone who is tall or not funny is either not rich or not old and vice versa.
If someone is not old then someone is patient and vice versa.
Everyone who is generous or old is rich or creative and vice versa.
Everyone who is both not generous and not quiet is both quiet and not humble and vice versa.
Everyone who is not happy or tall is either not quiet or not humble.
Everyone who is not wise or not curious is not humble and vice versa.
Everyone who is not strong or not generous is either generous or funny and vice versa.
If someone is either curious or old then someone is both not kind and funny.
If someone is curious then mary is either creative or not brave and vice versa.
Someone is either not wise or patient.
Someone is strong or not creative.
Someone is not kind or brave.
Someone is both rich and creative.
Someone is old or tall. | Fred is wise. | entailment | (![X]:((~quiet(X)<~>~humble(X))<=>(~curious(X)<~>old(X))))&
(![X]:(brave(X)<=>(quiet(X)&humble(X))))&
((?[X]:((calm(X)|funny(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((~wise(X)|creative(X))<=>(wise(X)|~happy(X))))&
(![X]:((~brave(X)|~tall(X))<=>(happy(X)&calm(X))))&
((?[X]:((~strong(X)|humble(X))))<=>((~curious(susan)|~quiet(susan))))&
(((~kind(alice)<~>quiet(alice)))<=>((~old(fred)&~tall(fred))))&
(![X]:((tall(X)|~funny(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|old(X))<=>(rich(X)|creative(X))))&
(![X]:((~generous(X)&~quiet(X))<=>(quiet(X)&~humble(X))))&
(![X]:((~happy(X)|tall(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:((~wise(X)|~curious(X))<=>~humble(X)))&
(![X]:((~strong(X)|~generous(X))<=>(generous(X)<~>funny(X))))&
((?[X]:((curious(X)<~>old(X))))=>(?[X]:((~kind(X)&funny(X)))))&
((?[X]:(curious(X)))<=>((creative(mary)<~>~brave(mary))))&
(?[X]:((~wise(X)<~>patient(X))))&
(?[X]:((strong(X)|~creative(X))))&
(?[X]:((~kind(X)|brave(X))))&
(?[X]:((rich(X)&creative(X))))&
(?[X]:((old(X)|tall(X)))) | wise(fred) | [
"p3",
"p4",
"p10",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3222746495332297034238210
% SZS output start Proof for 3222746495332297034238210
4. ! [X0] : ((creative(X0) | ~wise(X0)) <=> (~happy(X0) | wise(X0))) [input p3]
5. ! [X0] : ((~tall(X0) | ~brave(X0)) <=> (calm(X0) & happy(X0))) [input p4]
11. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (~humble(X0) & quiet(X0))) [input p10]
12. ! [X0] : ((tall(X0) | ~happy(X0)) => (~quiet(X0) <~> ~humble(X0))) [input p11]
13. ! [X0] : ((~curious(X0) | ~wise(X0)) <=> ~humble(X0)) [input p12]
22. ~wise(fred) [input hypothesis]
26. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) | (~tall(X0) & happy(X0))) [ennf transformation 12]
36. ! [X0] : (((creative(X0) | ~wise(X0)) | (happy(X0) & ~wise(X0))) & ((~happy(X0) | wise(X0)) | (~creative(X0) & wise(X0)))) [nnf transformation 4]
37. ! [X0] : ((creative(X0) | ~wise(X0) | (happy(X0) & ~wise(X0))) & (~happy(X0) | wise(X0) | (~creative(X0) & wise(X0)))) [flattening 36]
38. ! [X0] : (((~tall(X0) | ~brave(X0)) | (~calm(X0) | ~happy(X0))) & ((calm(X0) & happy(X0)) | (tall(X0) & brave(X0)))) [nnf transformation 5]
39. ! [X0] : ((~tall(X0) | ~brave(X0) | ~calm(X0) | ~happy(X0)) & ((calm(X0) & happy(X0)) | (tall(X0) & brave(X0)))) [flattening 38]
56. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 11]
57. ! [X0] : (((~quiet(X0) & ~generous(X0)) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | quiet(X0) | generous(X0))) [flattening 56]
58. ! [X0] : (((humble(X0) | quiet(X0)) & (~humble(X0) | ~quiet(X0))) | (~tall(X0) & happy(X0))) [nnf transformation 26]
59. ! [X0] : (((~curious(X0) | ~wise(X0)) | humble(X0)) & (~humble(X0) | (curious(X0) & wise(X0)))) [nnf transformation 13]
60. ! [X0] : ((~curious(X0) | ~wise(X0) | humble(X0)) & (~humble(X0) | (curious(X0) & wise(X0)))) [flattening 59]
99. ~happy(X0) | wise(X0) | wise(X0) [cnf transformation 37]
104. tall(X0) | happy(X0) [cnf transformation 39]
133. ~quiet(X0) | humble(X0) | ~quiet(X0) [cnf transformation 57]
137. humble(X0) | quiet(X0) | ~tall(X0) [cnf transformation 58]
138. ~humble(X0) | wise(X0) [cnf transformation 60]
162. ~wise(fred) [cnf transformation 22]
166. ~quiet(X0) | humble(X0) [duplicate literal removal 133]
167. ~happy(X0) | wise(X0) [duplicate literal removal 99]
234. 16 <=> tall(fred) [avatar definition]
235. ~tall(fred) <- (~16) [avatar component clause 234]
236. tall(fred) <- (16) [avatar component clause 234]
267. ~tall(X0) | humble(X0) [subsumption resolution 137,166]
353. happy(fred) <- (~16) [resolution 104,235]
361. wise(fred) <- (~16) [resolution 167,353]
362. $false <- (~16) [subsumption resolution 361,162]
363. 16 [avatar contradiction clause 362]
367. humble(fred) <- (16) [resolution 267,236]
369. wise(fred) <- (16) [resolution 367,138]
370. $false <- (16) [subsumption resolution 369,162]
371. ~16 [avatar contradiction clause 370]
372. $false [avatar sat refutation 363,371]
% SZS output end Proof for 3222746495332297034238210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and funny is not wise or tall.
Everyone who is both not wise and not quiet is both calm and not kind.
Everyone who is humble is either not funny or not curious.
If susan is either funny or wise then paul is calm or not creative and vice versa.
If someone is either brave or funny then someone is not humble.
Everyone who is either humble or curious is not calm or not old.
Everyone who is both old and kind is both not rich and calm and vice versa.
If someone is both not generous and tall then fred is not calm or not generous.
Everyone who is generous is not curious.
If john is not rich or not old then john is curious or not funny and vice versa.
If someone is not humble or creative then lucy is not generous or curious and vice versa.
Everyone who is either not brave or wise is both kind and curious.
If alice is generous then someone is both creative and not old and vice versa.
If someone is either patient or generous then alice is either calm or not calm.
Everyone who is both not generous and brave is not rich or not old and vice versa.
Everyone who is either not rich or generous is both not old and funny.
Alice is both not happy and not brave.
Someone is both not generous and not calm.
John is not creative.
Someone is either kind or not calm.
Someone is not humble or happy.
Fred is both not kind and not strong. | Paul is calm. | neutral | (![X]:((happy(X)&funny(X))=>(~wise(X)|tall(X))))&
(![X]:((~wise(X)&~quiet(X))=>(calm(X)&~kind(X))))&
(![X]:(humble(X)=>(~funny(X)<~>~curious(X))))&
(((funny(susan)<~>wise(susan)))<=>((calm(paul)|~creative(paul))))&
((?[X]:((brave(X)<~>funny(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)<~>curious(X))=>(~calm(X)|~old(X))))&
(![X]:((old(X)&kind(X))<=>(~rich(X)&calm(X))))&
((?[X]:((~generous(X)&tall(X))))=>((~calm(fred)|~generous(fred))))&
(![X]:(generous(X)=>~curious(X)))&
(((~rich(john)|~old(john)))<=>((curious(john)|~funny(john))))&
((?[X]:((~humble(X)|creative(X))))<=>((~generous(lucy)|curious(lucy))))&
(![X]:((~brave(X)<~>wise(X))=>(kind(X)&curious(X))))&
((generous(alice))<=>(?[X]:((creative(X)&~old(X)))))&
((?[X]:((patient(X)<~>generous(X))))=>((calm(alice)<~>~calm(alice))))&
(![X]:((~generous(X)&brave(X))<=>(~rich(X)|~old(X))))&
(![X]:((~rich(X)<~>generous(X))=>(~old(X)&funny(X))))&
((~happy(alice)&~brave(alice)))&
(?[X]:((~generous(X)&~calm(X))))&
(~creative(john))&
(?[X]:((kind(X)<~>~calm(X))))&
(?[X]:((~humble(X)|happy(X))))&
((~kind(fred)&~strong(fred))) | calm(paul) | []
| null | 0 |
If someone is kind then fred is either not old or funny.
If someone is both humble and generous then mary is both brave and not quiet and vice versa.
Everyone who is not strong is not wise and vice versa.
Everyone who is not quiet or not happy is both creative and not funny.
If someone is both quiet and not patient then fred is not humble.
Everyone who is both creative and tall is not kind or not happy and vice versa.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Mary is either not patient or not wise.
Someone is not funny or kind. | Mary is rich. | contradiction | ((?[X]:(kind(X)))=>((~old(fred)<~>funny(fred))))&
((?[X]:((humble(X)&generous(X))))<=>((brave(mary)&~quiet(mary))))&
(![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~quiet(X)|~happy(X))=>(creative(X)&~funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(~humble(fred)))&
(![X]:((creative(X)&tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X)))) | rich(mary) | [
"p1",
"p2",
"p3",
"p5",
"p6",
"p8",
"p9",
"p10",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 1583093802018593425767059
% SZS output start Proof for 1583093802018593425767059
2. ? [X0] : (generous(X0) & humble(X0)) <=> (~quiet(mary) & brave(mary)) [input p1]
3. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p2]
4. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (~funny(X0) & creative(X0))) [input p3]
6. ! [X0] : ((tall(X0) & creative(X0)) <=> (~happy(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p6]
9. ! [X0] : ((creative(X0) <~> rich(X0)) <=> (old(X0) | ~funny(X0))) [input p8]
10. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~strong(X0))) [input p9]
11. (generous(susan) & curious(susan)) <=> ? [X0] : curious(X0) [input p10]
12. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p11]
14. ! [X0] : ((strong(X0) <~> creative(X0)) => (curious(X0) & generous(X0))) [input p13]
21. rich(mary) [input hypothesis]
23. ! [X0] : ((~funny(X0) & creative(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 4]
25. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 7]
26. ! [X0] : ((curious(X0) & generous(X0)) | (strong(X0) <=> creative(X0))) [ennf transformation 14]
28. (? [X0] : (generous(X0) & humble(X0)) | (quiet(mary) | ~brave(mary))) & ((~quiet(mary) & brave(mary)) | ! [X0] : (~generous(X0) | ~humble(X0))) [nnf transformation 2]
29. (? [X0] : (generous(X0) & humble(X0)) | quiet(mary) | ~brave(mary)) & ((~quiet(mary) & brave(mary)) | ! [X0] : (~generous(X0) | ~humble(X0))) [flattening 28]
30. (? [X0] : (generous(X0) & humble(X0)) | quiet(mary) | ~brave(mary)) & ((~quiet(mary) & brave(mary)) | ! [X1] : (~generous(X1) | ~humble(X1))) [rectify 29]
31. ? [X0] : (generous(X0) & humble(X0)) => (generous(sK0) & humble(sK0)) [choice axiom]
32. ((generous(sK0) & humble(sK0)) | quiet(mary) | ~brave(mary)) & ((~quiet(mary) & brave(mary)) | ! [X1] : (~generous(X1) | ~humble(X1))) [skolemisation 30,31]
33. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 3]
34. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 6]
35. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | ~creative(X0))) [flattening 34]
41. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & ((old(X0) | ~funny(X0)) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [nnf transformation 9]
42. ! [X0] : ((((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | (~old(X0) & funny(X0))) & (old(X0) | ~funny(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0))))) [flattening 41]
43. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 10]
44. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 43]
45. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | (~generous(susan) | ~curious(susan))) [nnf transformation 11]
46. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X0] : curious(X0) | ~generous(susan) | ~curious(susan)) [flattening 45]
47. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (? [X1] : curious(X1) | ~generous(susan) | ~curious(susan)) [rectify 46]
48. ? [X1] : curious(X1) => curious(sK2) [choice axiom]
49. ((generous(susan) & curious(susan)) | ! [X0] : ~curious(X0)) & (curious(sK2) | ~generous(susan) | ~curious(susan)) [skolemisation 47,48]
50. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 12]
51. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 50]
54. ! [X0] : ((curious(X0) & generous(X0)) | ((strong(X0) | ~creative(X0)) & (creative(X0) | ~strong(X0)))) [nnf transformation 26]
68. ~quiet(mary) | ~generous(X1) | ~humble(X1) [cnf transformation 32]
71. ~wise(X0) | strong(X0) [cnf transformation 33]
72. ~strong(X0) | wise(X0) [cnf transformation 33]
73. creative(X0) | quiet(X0) [cnf transformation 23]
75. ~funny(X0) | quiet(X0) [cnf transformation 23]
76. ~funny(X0) | happy(X0) [cnf transformation 23]
78. ~tall(X0) | ~kind(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 35]
81. tall(X0) | kind(X0) [cnf transformation 35]
85. ~generous(X0) | wise(X0) [cnf transformation 25]
97. ~rich(X0) | ~creative(X0) | funny(X0) [cnf transformation 42]
99. ~strong(X0) | ~kind(X0) | tall(X0) [cnf transformation 44]
100. ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 44]
107. generous(susan) | ~curious(X0) [cnf transformation 49]
108. ~strong(X0) | humble(X0) | ~generous(X0) [cnf transformation 51]
109. strong(X0) | generous(X0) [cnf transformation 51]
117. generous(X0) | creative(X0) | ~strong(X0) [cnf transformation 54]
119. ~strong(X0) | creative(X0) | curious(X0) [cnf transformation 54]
131. rich(mary) [cnf transformation 21]
150. 5 <=> quiet(mary) [avatar definition]
164. 8 <=> ! [X1] : (~generous(X1) | ~humble(X1)) [avatar definition]
165. ~generous(X1) | ~humble(X1) <- (8) [avatar component clause 164]
166. 8 | ~5 [avatar split clause 68,150,164]
206. ~strong(X0) | kind(X0) [subsumption resolution 100,81]
207. ~strong(X0) | tall(X0) [subsumption resolution 99,81]
209. 17 <=> ! [X0] : ~curious(X0) [avatar definition]
210. ~curious(X0) <- (17) [avatar component clause 209]
212. 18 <=> generous(susan) [avatar definition]
214. generous(susan) <- (18) [avatar component clause 212]
215. 17 | 18 [avatar split clause 107,212,209]
226. creative(X0) | generous(X0) [subsumption resolution 117,109]
238. 23 <=> generous(mary) [avatar definition]
239. ~generous(mary) <- (~23) [avatar component clause 238]
240. generous(mary) <- (23) [avatar component clause 238]
283. wise(susan) <- (18) [resolution 85,214]
284. strong(susan) <- (18) [resolution 283,71]
288. generous(X0) | wise(X0) [resolution 109,72]
289. wise(X0) [subsumption resolution 288,85]
291. strong(X0) [resolution 289,71]
294. ~humble(susan) <- (8, 18) [resolution 165,214]
301. kind(X0) [resolution 206,291]
304. tall(X0) [resolution 207,291]
311. ~creative(mary) | funny(mary) [resolution 97,131]
315. 30 <=> funny(mary) [avatar definition]
317. funny(mary) <- (30) [avatar component clause 315]
319. 31 <=> creative(mary) [avatar definition]
321. ~creative(mary) <- (~31) [avatar component clause 319]
322. 30 | ~31 [avatar split clause 311,319,315]
323. generous(mary) <- (~31) [resolution 321,226]
327. $false <- (~23, ~31) [subsumption resolution 323,239]
328. 23 | 31 [avatar contradiction clause 327]
333. quiet(mary) <- (30) [resolution 317,75]
334. humble(susan) | ~generous(susan) <- (18) [resolution 108,284]
335. humble(X0) | ~generous(X0) [resolution 108,291]
337. ~generous(susan) <- (8, 18) [subsumption resolution 334,294]
338. $false <- (8, 18) [subsumption resolution 337,214]
339. ~8 | ~18 [avatar contradiction clause 338]
341. 5 | ~30 [avatar split clause 333,315,150]
357. quiet(mary) <- (~31) [resolution 321,73]
360. 5 | 31 [avatar split clause 357,319,150]
361. ~generous(X1) <- (8) [subsumption resolution 165,335]
366. $false <- (8, 23) [resolution 361,240]
371. ~8 | ~23 [avatar contradiction clause 366]
376. happy(mary) <- (30) [resolution 317,76]
386. creative(X0) | curious(X0) [resolution 119,291]
388. creative(X0) <- (17) [subsumption resolution 386,210]
398. ~kind(X0) | ~happy(X0) | ~creative(X0) [resolution 78,304]
401. ~happy(X0) | ~creative(X0) [subsumption resolution 398,301]
402. ~happy(X0) <- (17) [subsumption resolution 401,388]
403. $false <- (17, 30) [resolution 402,376]
404. ~17 | ~30 [avatar contradiction clause 403]
405. $false [avatar sat refutation 166,215,322,328,339,341,360,371,404]
% SZS output end Proof for 1583093802018593425767059
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not curious or wise is not quiet or happy and vice versa. If mary is both wise and brave then someone is either not wise or not patient. Everyone who is kind is either not humble or creative and vice versa. Everyone who is strong or not creative is not rich and vice versa. If paul is rich or kind then paul is not brave or not kind. Everyone who is either not wise or not generous is either not humble or quiet. Everyone who is quiet is kind. If mary is not wise then susan is happy or not happy and vice versa. If john is funny then paul is not creative and vice versa. Everyone who is not happy is not patient or happy and vice versa. Everyone who is either not strong or not tall is humble and vice versa. If fred is not strong then someone is either tall or creative and vice versa. If lucy is both not tall and not kind then john is not strong or curious and vice versa. Everyone who is either old or not quiet is humble and vice versa. Everyone who is both not wise and not quiet is not rich or not curious and vice versa. Everyone who is not funny or not tall is both not kind and rich. Someone is happy or rich. Fred is not patient or old. Mary is both strong and brave. Lucy is both not kind and tall. Paul is either generous or not tall. Mary is both generous and not calm. Someone is not old. | Mary is not curious. | entailment | (![X]:((~curious(X)|wise(X))<=>(~quiet(X)|happy(X))))&
(((wise(mary)&brave(mary)))=>(?[X]:((~wise(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((strong(X)|~creative(X))<=>~rich(X)))&
(((rich(paul)|kind(paul)))=>((~brave(paul)|~kind(paul))))&
(![X]:((~wise(X)<~>~generous(X))=>(~humble(X)<~>quiet(X))))&
(![X]:(quiet(X)=>kind(X)))&
((~wise(mary))<=>((happy(susan)|~happy(susan))))&
((funny(john))<=>(~creative(paul)))&
(![X]:(~happy(X)<=>(~patient(X)|happy(X))))&
(![X]:((~strong(X)<~>~tall(X))<=>humble(X)))&
((~strong(fred))<=>(?[X]:((tall(X)<~>creative(X)))))&
(((~tall(lucy)&~kind(lucy)))<=>((~strong(john)|curious(john))))&
(![X]:((old(X)<~>~quiet(X))<=>humble(X)))&
(![X]:((~wise(X)&~quiet(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~funny(X)|~tall(X))=>(~kind(X)&rich(X))))&
(?[X]:((happy(X)|rich(X))))&
((~patient(fred)|old(fred)))&
((strong(mary)&brave(mary)))&
((~kind(lucy)&tall(lucy)))&
((generous(paul)<~>~tall(paul)))&
((generous(mary)&~calm(mary)))&
(?[X]:(~old(X))) | ~curious(mary) | [
"p0",
"p3",
"p7",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 3209307587212999227212310
% SZS output start Proof for 3209307587212999227212310
1. ! [X0] : ((wise(X0) | ~curious(X0)) <=> (happy(X0) | ~quiet(X0))) [input p0]
4. ! [X0] : ((~creative(X0) | strong(X0)) <=> ~rich(X0)) [input p3]
8. ~wise(mary) <=> (~happy(susan) | happy(susan)) [input p7]
15. ! [X0] : ((~quiet(X0) & ~wise(X0)) <=> (~curious(X0) | ~rich(X0))) [input p14]
19. brave(mary) & strong(mary) [input p18]
24. curious(mary) [input hypothesis]
33. ! [X0] : (((wise(X0) | ~curious(X0)) | (~happy(X0) & quiet(X0))) & ((happy(X0) | ~quiet(X0)) | (~wise(X0) & curious(X0)))) [nnf transformation 1]
34. ! [X0] : ((wise(X0) | ~curious(X0) | (~happy(X0) & quiet(X0))) & (happy(X0) | ~quiet(X0) | (~wise(X0) & curious(X0)))) [flattening 33]
39. ! [X0] : (((~creative(X0) | strong(X0)) | rich(X0)) & (~rich(X0) | (creative(X0) & ~strong(X0)))) [nnf transformation 4]
40. ! [X0] : ((~creative(X0) | strong(X0) | rich(X0)) & (~rich(X0) | (creative(X0) & ~strong(X0)))) [flattening 39]
42. (~wise(mary) | (happy(susan) & ~happy(susan))) & ((~happy(susan) | happy(susan)) | wise(mary)) [nnf transformation 8]
43. (~wise(mary) | (happy(susan) & ~happy(susan))) & (~happy(susan) | happy(susan) | wise(mary)) [flattening 42]
55. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (curious(X0) & rich(X0))) & ((~curious(X0) | ~rich(X0)) | (quiet(X0) | wise(X0)))) [nnf transformation 15]
56. ! [X0] : (((~quiet(X0) & ~wise(X0)) | (curious(X0) & rich(X0))) & (~curious(X0) | ~rich(X0) | quiet(X0) | wise(X0))) [flattening 55]
64. ~curious(X0) | wise(X0) | quiet(X0) [cnf transformation 34]
72. ~rich(X0) | ~strong(X0) [cnf transformation 40]
83. ~wise(mary) | ~happy(susan) [cnf transformation 43]
84. ~wise(mary) | happy(susan) [cnf transformation 43]
110. ~quiet(X0) | rich(X0) [cnf transformation 56]
118. strong(mary) [cnf transformation 19]
126. curious(mary) [cnf transformation 24]
131. 1 <=> wise(mary) [avatar definition]
133. ~wise(mary) <- (~1) [avatar component clause 131]
163. 8 <=> happy(susan) [avatar definition]
166. 8 | ~1 [avatar split clause 84,131,163]
167. ~8 | ~1 [avatar split clause 83,131,163]
259. wise(mary) | quiet(mary) [resolution 64,126]
260. quiet(mary) <- (~1) [subsumption resolution 259,133]
264. rich(mary) <- (~1) [resolution 260,110]
267. ~strong(mary) <- (~1) [resolution 264,72]
268. $false <- (~1) [subsumption resolution 267,118]
269. 1 [avatar contradiction clause 268]
270. $false [avatar sat refutation 166,167,269]
% SZS output end Proof for 3209307587212999227212310
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not calm is both not wise and not brave and vice versa.
Everyone who is both quiet and not patient is either happy or not generous.
Everyone who is creative or funny is not tall.
Everyone who is not kind or calm is either not patient or not creative.
If fred is not quiet or generous then someone is old or not curious.
If someone is both strong and not patient then someone is rich or patient and vice versa.
Everyone who is both humble and old is both brave and not generous and vice versa.
If paul is both not generous and brave then someone is tall or happy and vice versa.
If alice is both patient and not brave then lucy is not rich or quiet and vice versa.
If someone is either not funny or strong then someone is both wise and not curious and vice versa.
Everyone who is not tall is both old and not patient.
Everyone who is humble or not humble is not calm and vice versa.
Everyone who is both not wise and not calm is not kind or not calm.
If paul is generous then someone is not curious.
If someone is not kind or funny then someone is both patient and happy and vice versa.
Fred is old or curious.
John is either not rich or brave.
Mary is old or not creative.
Susan is not strong or generous. | John is not funny. | entailment | (![X]:((~humble(X)|~calm(X))<=>(~wise(X)&~brave(X))))&
(![X]:((quiet(X)&~patient(X))=>(happy(X)<~>~generous(X))))&
(![X]:((creative(X)|funny(X))=>~tall(X)))&
(![X]:((~kind(X)|calm(X))=>(~patient(X)<~>~creative(X))))&
(((~quiet(fred)|generous(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:((strong(X)&~patient(X))))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:((humble(X)&old(X))<=>(brave(X)&~generous(X))))&
(((~generous(paul)&brave(paul)))<=>(?[X]:((tall(X)|happy(X)))))&
(((patient(alice)&~brave(alice)))<=>((~rich(lucy)|quiet(lucy))))&
((?[X]:((~funny(X)<~>strong(X))))<=>(?[X]:((wise(X)&~curious(X)))))&
(![X]:(~tall(X)=>(old(X)&~patient(X))))&
(![X]:((humble(X)|~humble(X))<=>~calm(X)))&
(![X]:((~wise(X)&~calm(X))=>(~kind(X)|~calm(X))))&
((generous(paul))=>(?[X]:(~curious(X))))&
((?[X]:((~kind(X)|funny(X))))<=>(?[X]:((patient(X)&happy(X)))))&
((old(fred)|curious(fred)))&
((~rich(john)<~>brave(john)))&
((old(mary)|~creative(mary)))&
((~strong(susan)|generous(susan))) | ~funny(john) | [
"p0",
"p7",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3806340325644268876210312
% SZS output start Proof for 3806340325644268876210312
1. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (~brave(X0) & ~wise(X0))) [input p0]
8. (brave(paul) & ~generous(paul)) <=> ? [X0] : (happy(X0) | tall(X0)) [input p7]
12. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~calm(X0)) [input p11]
15. ? [X0] : (funny(X0) | ~kind(X0)) <=> ? [X0] : (happy(X0) & patient(X0)) [input p14]
20. funny(john) [input hypothesis]
23. ? [X0] : (funny(X0) | ~kind(X0)) <=> ? [X1] : (happy(X1) & patient(X1)) [rectify 15]
33. ! [X0] : (((~calm(X0) | ~humble(X0)) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 1]
34. ! [X0] : ((~calm(X0) | ~humble(X0) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [flattening 33]
46. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | (~brave(paul) | generous(paul))) [nnf transformation 8]
47. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X0] : (happy(X0) | tall(X0)) | ~brave(paul) | generous(paul)) [flattening 46]
48. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & (? [X1] : (happy(X1) | tall(X1)) | ~brave(paul) | generous(paul)) [rectify 47]
49. ? [X1] : (happy(X1) | tall(X1)) => (happy(sK3) | tall(sK3)) [choice axiom]
50. ((brave(paul) & ~generous(paul)) | ! [X0] : (~happy(X0) & ~tall(X0))) & ((happy(sK3) | tall(sK3)) | ~brave(paul) | generous(paul)) [skolemisation 48,49]
58. ! [X0] : (((~humble(X0) | humble(X0)) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 12]
59. ! [X0] : ((~humble(X0) | humble(X0) | calm(X0)) & (~calm(X0) | (humble(X0) & ~humble(X0)))) [flattening 58]
62. (? [X0] : (funny(X0) | ~kind(X0)) | ! [X1] : (~happy(X1) | ~patient(X1))) & (? [X1] : (happy(X1) & patient(X1)) | ! [X0] : (~funny(X0) & kind(X0))) [nnf transformation 23]
63. (? [X0] : (funny(X0) | ~kind(X0)) | ! [X1] : (~happy(X1) | ~patient(X1))) & (? [X2] : (happy(X2) & patient(X2)) | ! [X3] : (~funny(X3) & kind(X3))) [rectify 62]
64. ? [X0] : (funny(X0) | ~kind(X0)) => (funny(sK7) | ~kind(sK7)) [choice axiom]
65. ? [X2] : (happy(X2) & patient(X2)) => (happy(sK8) & patient(sK8)) [choice axiom]
66. ((funny(sK7) | ~kind(sK7)) | ! [X1] : (~happy(X1) | ~patient(X1))) & ((happy(sK8) & patient(sK8)) | ! [X3] : (~funny(X3) & kind(X3))) [skolemisation 63,65,64]
71. ~brave(X0) | calm(X0) [cnf transformation 34]
96. brave(paul) | ~happy(X0) [cnf transformation 50]
110. ~calm(X0) | ~humble(X0) [cnf transformation 59]
111. ~calm(X0) | humble(X0) [cnf transformation 59]
118. happy(sK8) | ~funny(X3) [cnf transformation 66]
125. funny(john) [cnf transformation 20]
175. 12 <=> ! [X0] : ~happy(X0) [avatar definition]
176. ~happy(X0) <- (12) [avatar component clause 175]
178. 13 <=> brave(paul) [avatar definition]
180. brave(paul) <- (13) [avatar component clause 178]
181. 12 | 13 [avatar split clause 96,178,175]
253. ~calm(X0) [subsumption resolution 110,111]
272. 33 <=> ! [X3] : ~funny(X3) [avatar definition]
273. ~funny(X3) <- (33) [avatar component clause 272]
275. 34 <=> happy(sK8) [avatar definition]
277. happy(sK8) <- (34) [avatar component clause 275]
278. 33 | 34 [avatar split clause 118,275,272]
338. $false <- (33) [resolution 273,125]
339. ~33 [avatar contradiction clause 338]
340. $false <- (12, 34) [subsumption resolution 277,176]
341. ~12 | ~34 [avatar contradiction clause 340]
345. calm(paul) <- (13) [resolution 71,180]
346. $false <- (13) [subsumption resolution 345,253]
347. ~13 [avatar contradiction clause 346]
348. $false [avatar sat refutation 181,278,339,341,347]
% SZS output end Proof for 3806340325644268876210312
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich or not happy is curious or not wise and vice versa.
Everyone who is quiet or rich is both not rich and patient.
If mary is either not brave or kind then someone is both kind and not old.
If someone is not brave or not generous then paul is wise.
Everyone who is brave is not generous or old.
Everyone who is both quiet and strong is not calm.
If someone is either tall or patient then susan is not happy or happy and vice versa.
If someone is both funny and not generous then paul is not happy.
If someone is not kind or not brave then someone is not calm.
If mary is both not kind and happy then someone is not strong or not curious.
Everyone who is old is not funny or not rich.
If someone is generous or not curious then paul is both not rich and wise and vice versa.
If john is both strong and generous then someone is happy and vice versa.
Everyone who is both rich and not kind is quiet or not calm.
Everyone who is both not rich and calm is not rich and vice versa.
If mary is both happy and not strong then someone is both not strong and not generous and vice versa.
Someone is happy or not humble.
Alice is not rich.
Someone is not wise.
John is not happy.
Mary is brave.
John is either old or not humble.
Paul is either kind or not strong.
Someone is either not brave or not tall. | Paul is curious. | entailment | (![X]:((~rich(X)|~happy(X))<=>(curious(X)|~wise(X))))&
(![X]:((quiet(X)|rich(X))=>(~rich(X)&patient(X))))&
(((~brave(mary)<~>kind(mary)))=>(?[X]:((kind(X)&~old(X)))))&
((?[X]:((~brave(X)|~generous(X))))=>(wise(paul)))&
(![X]:(brave(X)=>(~generous(X)|old(X))))&
(![X]:((quiet(X)&strong(X))=>~calm(X)))&
((?[X]:((tall(X)<~>patient(X))))<=>((~happy(susan)|happy(susan))))&
((?[X]:((funny(X)&~generous(X))))=>(~happy(paul)))&
((?[X]:((~kind(X)|~brave(X))))=>(?[X]:(~calm(X))))&
(((~kind(mary)&happy(mary)))=>(?[X]:((~strong(X)|~curious(X)))))&
(![X]:(old(X)=>(~funny(X)|~rich(X))))&
((?[X]:((generous(X)|~curious(X))))<=>((~rich(paul)&wise(paul))))&
(((strong(john)&generous(john)))<=>(?[X]:(happy(X))))&
(![X]:((rich(X)&~kind(X))=>(quiet(X)|~calm(X))))&
(![X]:((~rich(X)&calm(X))<=>~rich(X)))&
(((happy(mary)&~strong(mary)))<=>(?[X]:((~strong(X)&~generous(X)))))&
(?[X]:((happy(X)|~humble(X))))&
(~rich(alice))&
(?[X]:(~wise(X)))&
(~happy(john))&
(brave(mary))&
((old(john)<~>~humble(john)))&
((kind(paul)<~>~strong(paul)))&
(?[X]:((~brave(X)<~>~tall(X)))) | curious(paul) | [
"p0",
"p1",
"p3",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 7200529633142964364414020
% SZS output start Proof for 7200529633142964364414020
1. ! [X0] : ((~happy(X0) | ~rich(X0)) <=> (~wise(X0) | curious(X0))) [input p0]
2. ! [X0] : ((rich(X0) | quiet(X0)) => (patient(X0) & ~rich(X0))) [input p1]
4. ? [X0] : (~generous(X0) | ~brave(X0)) => wise(paul) [input p3]
12. ? [X0] : (~curious(X0) | generous(X0)) <=> (wise(paul) & ~rich(paul)) [input p11]
25. ~curious(paul) [input hypothesis]
29. ! [X0] : ((patient(X0) & ~rich(X0)) | (~rich(X0) & ~quiet(X0))) [ennf transformation 2]
31. wise(paul) | ! [X0] : (generous(X0) & brave(X0)) [ennf transformation 4]
41. ! [X0] : (((~happy(X0) | ~rich(X0)) | (wise(X0) & ~curious(X0))) & ((~wise(X0) | curious(X0)) | (happy(X0) & rich(X0)))) [nnf transformation 1]
42. ! [X0] : ((~happy(X0) | ~rich(X0) | (wise(X0) & ~curious(X0))) & (~wise(X0) | curious(X0) | (happy(X0) & rich(X0)))) [flattening 41]
56. (? [X0] : (~curious(X0) | generous(X0)) | (~wise(paul) | rich(paul))) & ((wise(paul) & ~rich(paul)) | ! [X0] : (curious(X0) & ~generous(X0))) [nnf transformation 12]
57. (? [X0] : (~curious(X0) | generous(X0)) | ~wise(paul) | rich(paul)) & ((wise(paul) & ~rich(paul)) | ! [X0] : (curious(X0) & ~generous(X0))) [flattening 56]
58. (? [X0] : (~curious(X0) | generous(X0)) | ~wise(paul) | rich(paul)) & ((wise(paul) & ~rich(paul)) | ! [X1] : (curious(X1) & ~generous(X1))) [rectify 57]
59. ? [X0] : (~curious(X0) | generous(X0)) => (~curious(sK4) | generous(sK4)) [choice axiom]
60. ((~curious(sK4) | generous(sK4)) | ~wise(paul) | rich(paul)) & ((wise(paul) & ~rich(paul)) | ! [X1] : (curious(X1) & ~generous(X1))) [skolemisation 58,59]
82. ~wise(X0) | curious(X0) | rich(X0) [cnf transformation 42]
87. ~rich(X0) | ~rich(X0) [cnf transformation 29]
95. wise(paul) | generous(X0) [cnf transformation 31]
109. wise(paul) | ~generous(X1) [cnf transformation 60]
134. ~curious(paul) [cnf transformation 25]
135. ~rich(X0) [duplicate literal removal 87]
157. 5 <=> ! [X0] : generous(X0) [avatar definition]
158. generous(X0) <- (5) [avatar component clause 157]
160. 6 <=> wise(paul) [avatar definition]
162. wise(paul) <- (6) [avatar component clause 160]
163. 5 | 6 [avatar split clause 95,160,157]
221. 19 <=> ! [X1] : ~generous(X1) [avatar definition]
222. ~generous(X1) <- (19) [avatar component clause 221]
223. 19 | 6 [avatar split clause 109,160,221]
310. curious(paul) | rich(paul) <- (6) [resolution 82,162]
311. rich(paul) <- (6) [subsumption resolution 310,134]
312. $false <- (6) [subsumption resolution 311,135]
313. ~6 [avatar contradiction clause 312]
314. $false <- (5, 19) [subsumption resolution 158,222]
315. ~5 | ~19 [avatar contradiction clause 314]
316. $false [avatar sat refutation 163,223,313,315]
% SZS output end Proof for 7200529633142964364414020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not quiet is both happy and wise.
If paul is either calm or humble then fred is not funny or strong and vice versa.
Everyone who is happy or not creative is not tall or not old and vice versa.
If lucy is either quiet or not brave then someone is either strong or not creative and vice versa.
Everyone who is either creative or kind is either humble or not rich.
Everyone who is either wise or humble is either not quiet or humble.
Everyone who is patient or not wise is strong or brave.
If someone is quiet then fred is either kind or tall and vice versa.
If someone is happy then mary is happy or generous and vice versa.
Everyone who is either not funny or not humble is both not tall and tall.
If someone is creative then susan is rich or not generous and vice versa.
Everyone who is happy is not kind or kind and vice versa.
If someone is not happy then someone is patient or funny and vice versa.
If fred is both not old and not rich then paul is both not strong and old and vice versa.
Everyone who is patient is both creative and not creative and vice versa.
Susan is not funny.
Someone is either kind or humble.
Someone is both happy and kind.
Someone is creative or funny.
Someone is not patient or not kind.
Someone is either tall or not patient.
Lucy is not humble. | Susan is humble. | contradiction | (![X]:((~kind(X)|~quiet(X))=>(happy(X)&wise(X))))&
(((calm(paul)<~>humble(paul)))<=>((~funny(fred)|strong(fred))))&
(![X]:((happy(X)|~creative(X))<=>(~tall(X)|~old(X))))&
(((quiet(lucy)<~>~brave(lucy)))<=>(?[X]:((strong(X)<~>~creative(X)))))&
(![X]:((creative(X)<~>kind(X))=>(humble(X)<~>~rich(X))))&
(![X]:((wise(X)<~>humble(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((patient(X)|~wise(X))=>(strong(X)|brave(X))))&
((?[X]:(quiet(X)))<=>((kind(fred)<~>tall(fred))))&
((?[X]:(happy(X)))<=>((happy(mary)|generous(mary))))&
(![X]:((~funny(X)<~>~humble(X))=>(~tall(X)&tall(X))))&
((?[X]:(creative(X)))<=>((rich(susan)|~generous(susan))))&
(![X]:(happy(X)<=>(~kind(X)|kind(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((patient(X)|funny(X)))))&
(((~old(fred)&~rich(fred)))<=>((~strong(paul)&old(paul))))&
(![X]:(patient(X)<=>(creative(X)&~creative(X))))&
(~funny(susan))&
(?[X]:((kind(X)<~>humble(X))))&
(?[X]:((happy(X)&kind(X))))&
(?[X]:((creative(X)|funny(X))))&
(?[X]:((~patient(X)|~kind(X))))&
(?[X]:((tall(X)<~>~patient(X))))&
(~humble(lucy)) | humble(susan) | [
"p0",
"p9",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 4689425978796877750245351
% SZS output start Proof for 4689425978796877750245351
1. ! [X0] : ((~quiet(X0) | ~kind(X0)) => (wise(X0) & happy(X0))) [input p0]
10. ! [X0] : ((~funny(X0) <~> ~humble(X0)) => (tall(X0) & ~tall(X0))) [input p9]
12. ! [X0] : (happy(X0) <=> (kind(X0) | ~kind(X0))) [input p11]
13. ? [X0] : ~happy(X0) <=> ? [X0] : (funny(X0) | patient(X0)) [input p12]
23. humble(susan) [input hypothesis]
24. ? [X0] : ~happy(X0) <=> ? [X1] : (funny(X1) | patient(X1)) [rectify 13]
25. ! [X0] : ((wise(X0) & happy(X0)) | (quiet(X0) & kind(X0))) [ennf transformation 1]
30. ! [X0] : ((tall(X0) & ~tall(X0)) | (~funny(X0) <=> ~humble(X0))) [ennf transformation 10]
50. ! [X0] : ((tall(X0) & ~tall(X0)) | ((~funny(X0) | humble(X0)) & (~humble(X0) | funny(X0)))) [nnf transformation 30]
56. ! [X0] : ((happy(X0) | (~kind(X0) & kind(X0))) & ((kind(X0) | ~kind(X0)) | ~happy(X0))) [nnf transformation 12]
57. ! [X0] : ((happy(X0) | (~kind(X0) & kind(X0))) & (kind(X0) | ~kind(X0) | ~happy(X0))) [flattening 56]
58. (? [X0] : ~happy(X0) | ! [X1] : (~funny(X1) & ~patient(X1))) & (? [X1] : (funny(X1) | patient(X1)) | ! [X0] : happy(X0)) [nnf transformation 24]
59. (? [X0] : ~happy(X0) | ! [X1] : (~funny(X1) & ~patient(X1))) & (? [X2] : (funny(X2) | patient(X2)) | ! [X3] : happy(X3)) [rectify 58]
60. ? [X0] : ~happy(X0) => ~happy(sK4) [choice axiom]
61. ? [X2] : (funny(X2) | patient(X2)) => (funny(sK5) | patient(sK5)) [choice axiom]
62. (~happy(sK4) | ! [X1] : (~funny(X1) & ~patient(X1))) & ((funny(sK5) | patient(sK5)) | ! [X3] : happy(X3)) [skolemisation 59,61,60]
79. happy(X0) | kind(X0) [cnf transformation 25]
118. ~tall(X0) | ~humble(X0) | funny(X0) [cnf transformation 50]
120. tall(X0) | ~humble(X0) | funny(X0) [cnf transformation 50]
127. happy(X0) | ~kind(X0) [cnf transformation 57]
130. ~happy(sK4) | ~funny(X1) [cnf transformation 62]
148. humble(susan) [cnf transformation 23]
241. ~humble(X0) | funny(X0) [subsumption resolution 118,120]
260. happy(X0) [subsumption resolution 127,79]
261. ~funny(X1) [subsumption resolution 130,260]
297. funny(susan) [resolution 241,148]
299. $false [subsumption resolution 297,261]
% SZS output end Proof for 4689425978796877750245351
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or not strong is wise or not calm.
Everyone who is either not strong or happy is not quiet and vice versa.
Everyone who is humble is wise and vice versa.
If john is both not calm and not strong then susan is not curious.
Everyone who is both rich and creative is not wise.
Everyone who is not generous or not kind is either wise or not strong and vice versa.
Everyone who is tall or not strong is not kind or not strong.
Everyone who is either not tall or strong is not creative or not brave and vice versa.
Everyone who is not humble is both tall and calm and vice versa.
If someone is brave or not old then someone is either wise or not brave and vice versa.
Everyone who is either not patient or not brave is both not kind and not rich and vice versa.
Everyone who is not wise or creative is both not calm and strong.
If someone is either patient or funny then john is quiet or not generous.
Everyone who is both not kind and generous is not strong or not old and vice versa.
Everyone who is both curious and not kind is either not wise or not happy and vice versa.
Everyone who is both generous and not curious is either brave or patient and vice versa.
Mary is not tall.
Fred is not rich or old.
Someone is quiet.
Someone is either not old or not patient.
Lucy is both old and not kind.
Susan is either not generous or not tall.
Someone is kind. | John is not funny. | neutral | (![X]:((old(X)|~strong(X))=>(wise(X)|~calm(X))))&
(![X]:((~strong(X)<~>happy(X))<=>~quiet(X)))&
(![X]:(humble(X)<=>wise(X)))&
(((~calm(john)&~strong(john)))=>(~curious(susan)))&
(![X]:((rich(X)&creative(X))=>~wise(X)))&
(![X]:((~generous(X)|~kind(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((tall(X)|~strong(X))=>(~kind(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))<=>(~creative(X)|~brave(X))))&
(![X]:(~humble(X)<=>(tall(X)&calm(X))))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~kind(X)&~rich(X))))&
(![X]:((~wise(X)|creative(X))=>(~calm(X)&strong(X))))&
((?[X]:((patient(X)<~>funny(X))))=>((quiet(john)|~generous(john))))&
(![X]:((~kind(X)&generous(X))<=>(~strong(X)|~old(X))))&
(![X]:((curious(X)&~kind(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((generous(X)&~curious(X))<=>(brave(X)<~>patient(X))))&
(~tall(mary))&
((~rich(fred)|old(fred)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)<~>~patient(X))))&
((old(lucy)&~kind(lucy)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(kind(X))) | ~funny(john) | []
| null | 0 |
If fred is both not tall and not wise then lucy is both humble and patient and vice versa. Everyone who is either strong or not rich is both not quiet and happy and vice versa. If someone is either not patient or not tall then fred is humble or not tall and vice versa. Everyone who is both kind and curious is both not wise and not kind and vice versa. If someone is both not brave and not humble then paul is not humble. If lucy is generous then someone is either not creative or old. Everyone who is calm is either curious or old and vice versa. Everyone who is both not brave and patient is either not patient or not calm. If fred is not patient then john is both funny and old. If someone is either quiet or happy then alice is not strong and vice versa. If lucy is both not strong and old then someone is both not generous and not kind. If john is either not calm or creative then someone is either not curious or strong and vice versa. Everyone who is either funny or not strong is either brave or funny. If fred is either not brave or creative then someone is generous and vice versa. Everyone who is either not patient or not kind is not creative or strong and vice versa. If someone is either curious or happy then alice is strong or not wise and vice versa. Someone is either not old or brave. Mary is not curious. Alice is not patient or not creative. Someone is not brave. Someone is either calm or old. Lucy is both creative and not wise. John is either brave or quiet. | John is curious. | neutral | (((~tall(fred)&~wise(fred)))<=>((humble(lucy)&patient(lucy))))&
(![X]:((strong(X)<~>~rich(X))<=>(~quiet(X)&happy(X))))&
((?[X]:((~patient(X)<~>~tall(X))))<=>((humble(fred)|~tall(fred))))&
(![X]:((kind(X)&curious(X))<=>(~wise(X)&~kind(X))))&
((?[X]:((~brave(X)&~humble(X))))=>(~humble(paul)))&
((generous(lucy))=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:(calm(X)<=>(curious(X)<~>old(X))))&
(![X]:((~brave(X)&patient(X))=>(~patient(X)<~>~calm(X))))&
((~patient(fred))=>((funny(john)&old(john))))&
((?[X]:((quiet(X)<~>happy(X))))<=>(~strong(alice)))&
(((~strong(lucy)&old(lucy)))=>(?[X]:((~generous(X)&~kind(X)))))&
(((~calm(john)<~>creative(john)))<=>(?[X]:((~curious(X)<~>strong(X)))))&
(![X]:((funny(X)<~>~strong(X))=>(brave(X)<~>funny(X))))&
(((~brave(fred)<~>creative(fred)))<=>(?[X]:(generous(X))))&
(![X]:((~patient(X)<~>~kind(X))<=>(~creative(X)|strong(X))))&
((?[X]:((curious(X)<~>happy(X))))<=>((strong(alice)|~wise(alice))))&
(?[X]:((~old(X)<~>brave(X))))&
(~curious(mary))&
((~patient(alice)|~creative(alice)))&
(?[X]:(~brave(X)))&
(?[X]:((calm(X)<~>old(X))))&
((creative(lucy)&~wise(lucy)))&
((brave(john)<~>quiet(john))) | curious(john) | []
| null | 0 |
Everyone who is not funny is brave and vice versa. If someone is not kind or old then someone is creative. Everyone who is not creative is kind or not brave. If john is either quiet or funny then someone is both not generous and not patient. Everyone who is not kind or funny is both patient and not old and vice versa. If alice is either calm or not strong then paul is either not funny or not quiet and vice versa. Everyone who is either not wise or not generous is either brave or not quiet. Everyone who is not wise or not happy is both quiet and humble and vice versa. If someone is not happy then susan is either not old or quiet. If paul is either quiet or not strong then paul is either happy or not quiet and vice versa. Everyone who is either quiet or curious is either not strong or happy and vice versa. Everyone who is both humble and curious is not humble or not patient and vice versa. If someone is both not curious and not old then john is not patient and vice versa. If someone is both not wise and tall then someone is tall and vice versa. If lucy is creative or not creative then someone is either calm or not kind and vice versa. If susan is either not brave or quiet then alice is quiet or not old and vice versa. Alice is not curious. Mary is either old or rich. Alice is both calm and strong. Someone is both not generous and curious. Someone is either old or not rich. | Paul is funny. | contradiction | (![X]:(~funny(X)<=>brave(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(kind(X)|~brave(X))))&
(((quiet(john)<~>funny(john)))=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~kind(X)|funny(X))<=>(patient(X)&~old(X))))&
(((calm(alice)<~>~strong(alice)))<=>((~funny(paul)<~>~quiet(paul))))&
(![X]:((~wise(X)<~>~generous(X))=>(brave(X)<~>~quiet(X))))&
(![X]:((~wise(X)|~happy(X))<=>(quiet(X)&humble(X))))&
((?[X]:(~happy(X)))=>((~old(susan)<~>quiet(susan))))&
(((quiet(paul)<~>~strong(paul)))<=>((happy(paul)<~>~quiet(paul))))&
(![X]:((quiet(X)<~>curious(X))<=>(~strong(X)<~>happy(X))))&
(![X]:((humble(X)&curious(X))<=>(~humble(X)|~patient(X))))&
((?[X]:((~curious(X)&~old(X))))<=>(~patient(john)))&
((?[X]:((~wise(X)&tall(X))))<=>(?[X]:(tall(X))))&
(((creative(lucy)|~creative(lucy)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
(((~brave(susan)<~>quiet(susan)))<=>((quiet(alice)|~old(alice))))&
(~curious(alice))&
((old(mary)<~>rich(mary)))&
((calm(alice)&strong(alice)))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((old(X)<~>~rich(X)))) | funny(paul) | [
"p4",
"p5",
"p7",
"p9",
"p10",
"p11",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 8511054314664319345504919
% SZS output start Proof for 8511054314664319345504919
5. ! [X0] : ((funny(X0) | ~kind(X0)) <=> (~old(X0) & patient(X0))) [input p4]
6. (calm(alice) <~> ~strong(alice)) <=> (~funny(paul) <~> ~quiet(paul)) [input p5]
8. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (humble(X0) & quiet(X0))) [input p7]
10. (quiet(paul) <~> ~strong(paul)) <=> (happy(paul) <~> ~quiet(paul)) [input p9]
11. ! [X0] : ((quiet(X0) <~> curious(X0)) <=> (~strong(X0) <~> happy(X0))) [input p10]
12. ! [X0] : ((curious(X0) & humble(X0)) <=> (~patient(X0) | ~humble(X0))) [input p11]
19. strong(alice) & calm(alice) [input p18]
22. funny(paul) [input hypothesis]
38. ! [X0] : (((funny(X0) | ~kind(X0)) | (old(X0) | ~patient(X0))) & ((~old(X0) & patient(X0)) | (~funny(X0) & kind(X0)))) [nnf transformation 5]
39. ! [X0] : ((funny(X0) | ~kind(X0) | old(X0) | ~patient(X0)) & ((~old(X0) & patient(X0)) | (~funny(X0) & kind(X0)))) [flattening 38]
40. (((strong(alice) | ~calm(alice)) & (~strong(alice) | calm(alice))) | ((~funny(paul) | quiet(paul)) & (~quiet(paul) | funny(paul)))) & (((quiet(paul) | funny(paul)) & (~quiet(paul) | ~funny(paul))) | ((calm(alice) | strong(alice)) & (~strong(alice) | ~calm(alice)))) [nnf transformation 6]
42. ! [X0] : (((~happy(X0) | ~wise(X0)) | (~humble(X0) | ~quiet(X0))) & ((humble(X0) & quiet(X0)) | (happy(X0) & wise(X0)))) [nnf transformation 8]
43. ! [X0] : ((~happy(X0) | ~wise(X0) | ~humble(X0) | ~quiet(X0)) & ((humble(X0) & quiet(X0)) | (happy(X0) & wise(X0)))) [flattening 42]
45. (((strong(paul) | ~quiet(paul)) & (~strong(paul) | quiet(paul))) | ((happy(paul) | quiet(paul)) & (~quiet(paul) | ~happy(paul)))) & (((quiet(paul) | ~happy(paul)) & (~quiet(paul) | happy(paul))) | ((quiet(paul) | strong(paul)) & (~strong(paul) | ~quiet(paul)))) [nnf transformation 10]
46. ! [X0] : ((((~curious(X0) | ~quiet(X0)) & (curious(X0) | quiet(X0))) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0)))) & (((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | ((quiet(X0) | ~curious(X0)) & (curious(X0) | ~quiet(X0))))) [nnf transformation 11]
47. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (~curious(X0) | ~humble(X0)))) [nnf transformation 12]
48. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 47]
81. ~funny(X0) | patient(X0) [cnf transformation 39]
85. ~quiet(paul) | ~funny(paul) | ~strong(alice) | ~calm(alice) [cnf transformation 40]
98. happy(X0) | quiet(X0) [cnf transformation 43]
107. quiet(paul) | ~happy(paul) | quiet(paul) | strong(paul) [cnf transformation 45]
117. curious(X0) | quiet(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 46]
120. ~patient(X0) | ~humble(X0) | ~curious(X0) | ~humble(X0) [cnf transformation 48]
121. humble(X0) | humble(X0) [cnf transformation 48]
146. calm(alice) [cnf transformation 19]
147. strong(alice) [cnf transformation 19]
152. funny(paul) [cnf transformation 22]
153. ~patient(X0) | ~humble(X0) | ~curious(X0) [duplicate literal removal 120]
154. humble(X0) [duplicate literal removal 121]
156. quiet(paul) | ~happy(paul) | strong(paul) [duplicate literal removal 107]
192. 8 <=> quiet(paul) [avatar definition]
193. ~quiet(paul) <- (~8) [avatar component clause 192]
196. 9 <=> funny(paul) [avatar definition]
197. funny(paul) <- (9) [avatar component clause 196]
200. 10 <=> calm(alice) [avatar definition]
204. 11 <=> strong(alice) [avatar definition]
214. ~10 | ~11 | ~9 | ~8 [avatar split clause 85,192,196,204,200]
233. 16 <=> strong(paul) [avatar definition]
235. strong(paul) <- (16) [avatar component clause 233]
237. quiet(paul) | strong(paul) [subsumption resolution 156,98]
238. 16 | 8 [avatar split clause 237,192,233]
242. ~strong(X0) | quiet(X0) | curious(X0) [subsumption resolution 117,98]
245. ~curious(X0) | ~patient(X0) [subsumption resolution 153,154]
329. 11 [avatar split clause 147,204]
330. 10 [avatar split clause 146,200]
341. 9 [avatar split clause 152,196]
345. patient(paul) <- (9) [resolution 81,197]
371. quiet(paul) | curious(paul) <- (16) [resolution 242,235]
375. curious(paul) <- (~8, 16) [subsumption resolution 371,193]
381. ~patient(paul) <- (~8, 16) [resolution 375,245]
382. $false <- (~8, 9, 16) [subsumption resolution 381,345]
383. 8 | ~9 | ~16 [avatar contradiction clause 382]
384. $false [avatar sat refutation 214,238,329,330,341,383]
% SZS output end Proof for 8511054314664319345504919
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or generous is not happy or not curious and vice versa.
If someone is both not patient and wise then someone is both tall and curious and vice versa.
If someone is both not kind and humble then someone is humble.
If alice is both not brave and not wise then paul is funny or quiet.
Everyone who is not creative is both not patient and kind and vice versa.
If fred is calm or not strong then someone is either not kind or generous.
If someone is not rich or not kind then john is kind and vice versa.
Everyone who is happy is strong or not kind and vice versa.
If john is generous or not quiet then mary is both not kind and quiet.
Everyone who is both not brave and generous is funny or not generous and vice versa.
Everyone who is both not wise and not tall is tall or not wise and vice versa.
Everyone who is both strong and not calm is not quiet.
If susan is not strong then mary is both not humble and creative and vice versa.
Everyone who is both not old and not wise is both old and not rich.
Everyone who is either curious or old is both not brave and humble.
If paul is either old or not kind then someone is not generous and vice versa.
Paul is calm.
Someone is either not creative or not strong.
Someone is both old and kind.
John is either quiet or curious.
Someone is strong or not kind.
Someone is either not tall or not kind.
Mary is both rich and funny. | Mary is quiet. | entailment | (![X]:((old(X)|generous(X))<=>(~happy(X)|~curious(X))))&
((?[X]:((~patient(X)&wise(X))))<=>(?[X]:((tall(X)&curious(X)))))&
((?[X]:((~kind(X)&humble(X))))=>(?[X]:(humble(X))))&
(((~brave(alice)&~wise(alice)))=>((funny(paul)|quiet(paul))))&
(![X]:(~creative(X)<=>(~patient(X)&kind(X))))&
(((calm(fred)|~strong(fred)))=>(?[X]:((~kind(X)<~>generous(X)))))&
((?[X]:((~rich(X)|~kind(X))))<=>(kind(john)))&
(![X]:(happy(X)<=>(strong(X)|~kind(X))))&
(((generous(john)|~quiet(john)))=>((~kind(mary)&quiet(mary))))&
(![X]:((~brave(X)&generous(X))<=>(funny(X)|~generous(X))))&
(![X]:((~wise(X)&~tall(X))<=>(tall(X)|~wise(X))))&
(![X]:((strong(X)&~calm(X))=>~quiet(X)))&
((~strong(susan))<=>((~humble(mary)&creative(mary))))&
(![X]:((~old(X)&~wise(X))=>(old(X)&~rich(X))))&
(![X]:((curious(X)<~>old(X))=>(~brave(X)&humble(X))))&
(((old(paul)<~>~kind(paul)))<=>(?[X]:(~generous(X))))&
(calm(paul))&
(?[X]:((~creative(X)<~>~strong(X))))&
(?[X]:((old(X)&kind(X))))&
((quiet(john)<~>curious(john)))&
(?[X]:((strong(X)|~kind(X))))&
(?[X]:((~tall(X)<~>~kind(X))))&
((rich(mary)&funny(mary))) | quiet(mary) | [
"p8",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 3303049299525993781409862
% SZS output start Proof for 3303049299525993781409862
9. (~quiet(john) | generous(john)) => (quiet(mary) & ~kind(mary)) [input p8]
10. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (~generous(X0) | funny(X0))) [input p9]
24. ~quiet(mary) [input hypothesis]
31. (quiet(mary) & ~kind(mary)) | (quiet(john) & ~generous(john)) [ennf transformation 9]
58. ! [X0] : (((generous(X0) & ~brave(X0)) | (generous(X0) & ~funny(X0))) & ((~generous(X0) | funny(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 10]
59. ! [X0] : (((generous(X0) & ~brave(X0)) | (generous(X0) & ~funny(X0))) & (~generous(X0) | funny(X0) | ~generous(X0) | brave(X0))) [flattening 58]
105. quiet(mary) | ~generous(john) [cnf transformation 31]
111. generous(X0) | generous(X0) [cnf transformation 59]
143. ~quiet(mary) [cnf transformation 24]
148. generous(X0) [duplicate literal removal 111]
246. 23 <=> quiet(mary) [avatar definition]
251. 24 <=> generous(john) [avatar definition]
253. ~generous(john) <- (~24) [avatar component clause 251]
254. ~24 | 23 [avatar split clause 105,246,251]
315. ~23 [avatar split clause 143,246]
316. $false <- (~24) [subsumption resolution 253,148]
317. 24 [avatar contradiction clause 316]
320. $false [avatar sat refutation 254,315,317]
% SZS output end Proof for 3303049299525993781409862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then fred is either old or brave and vice versa.
Everyone who is kind or not tall is either not strong or not brave and vice versa.
If paul is either not curious or patient then someone is both quiet and not rich and vice versa.
Everyone who is curious or not calm is calm.
Everyone who is not tall is both not creative and not strong and vice versa.
If mary is either quiet or not quiet then lucy is either not humble or not rich.
Everyone who is kind is not calm and vice versa.
If someone is either wise or curious then alice is not curious or tall and vice versa.
Everyone who is not strong is funny and vice versa.
Everyone who is either not wise or not generous is either humble or strong and vice versa.
Everyone who is patient or humble is not funny or not humble.
Everyone who is either kind or wise is rich or wise and vice versa.
If someone is brave then someone is either not rich or creative and vice versa.
Everyone who is either creative or not brave is both rich and not patient.
If paul is both not brave and humble then susan is humble.
Everyone who is brave or wise is not tall or not strong.
Alice is both not strong and not generous.
Someone is quiet or brave.
John is calm or not calm.
Someone is either not old or creative.
Lucy is quiet or wise.
Mary is either not humble or not old. | Mary is not curious. | neutral | ((?[X]:(~old(X)))<=>((old(fred)<~>brave(fred))))&
(![X]:((kind(X)|~tall(X))<=>(~strong(X)<~>~brave(X))))&
(((~curious(paul)<~>patient(paul)))<=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:((curious(X)|~calm(X))=>calm(X)))&
(![X]:(~tall(X)<=>(~creative(X)&~strong(X))))&
(((quiet(mary)<~>~quiet(mary)))=>((~humble(lucy)<~>~rich(lucy))))&
(![X]:(kind(X)<=>~calm(X)))&
((?[X]:((wise(X)<~>curious(X))))<=>((~curious(alice)|tall(alice))))&
(![X]:(~strong(X)<=>funny(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>(humble(X)<~>strong(X))))&
(![X]:((patient(X)|humble(X))=>(~funny(X)|~humble(X))))&
(![X]:((kind(X)<~>wise(X))<=>(rich(X)|wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((creative(X)<~>~brave(X))=>(rich(X)&~patient(X))))&
(((~brave(paul)&humble(paul)))=>(humble(susan)))&
(![X]:((brave(X)|wise(X))=>(~tall(X)|~strong(X))))&
((~strong(alice)&~generous(alice)))&
(?[X]:((quiet(X)|brave(X))))&
((calm(john)|~calm(john)))&
(?[X]:((~old(X)<~>creative(X))))&
((quiet(lucy)|wise(lucy)))&
((~humble(mary)<~>~old(mary))) | ~curious(mary) | []
| null | 0 |
If lucy is not patient or kind then someone is both kind and not wise. Everyone who is wise or not happy is not old or patient. If lucy is both calm and rich then someone is old or quiet and vice versa. If paul is kind or rich then lucy is both not strong and happy and vice versa. Everyone who is patient is both not brave and not curious. Everyone who is both calm and tall is either not wise or wise. If lucy is both not strong and strong then paul is funny or not rich and vice versa. If someone is brave then alice is either old or not quiet. If susan is wise then susan is funny or not curious and vice versa. Everyone who is either rich or humble is not brave and vice versa. If someone is either wise or not brave then susan is not funny. Everyone who is not calm or wise is not quiet or not old. If mary is either not funny or humble then paul is tall and vice versa. If fred is both funny and not calm then someone is both not kind and not happy. Everyone who is calm is both kind and patient. Everyone who is calm or not happy is rich or patient and vice versa. John is not calm. Someone is either not strong or calm. John is either kind or creative. Lucy is not curious or wise. Susan is both not calm and not quiet. Someone is either not happy or not rich. | Fred is not rich. | neutral | (((~patient(lucy)|kind(lucy)))=>(?[X]:((kind(X)&~wise(X)))))&
(![X]:((wise(X)|~happy(X))=>(~old(X)|patient(X))))&
(((calm(lucy)&rich(lucy)))<=>(?[X]:((old(X)|quiet(X)))))&
(((kind(paul)|rich(paul)))<=>((~strong(lucy)&happy(lucy))))&
(![X]:(patient(X)=>(~brave(X)&~curious(X))))&
(![X]:((calm(X)&tall(X))=>(~wise(X)<~>wise(X))))&
(((~strong(lucy)&strong(lucy)))<=>((funny(paul)|~rich(paul))))&
((?[X]:(brave(X)))=>((old(alice)<~>~quiet(alice))))&
((wise(susan))<=>((funny(susan)|~curious(susan))))&
(![X]:((rich(X)<~>humble(X))<=>~brave(X)))&
((?[X]:((wise(X)<~>~brave(X))))=>(~funny(susan)))&
(![X]:((~calm(X)|wise(X))=>(~quiet(X)|~old(X))))&
(((~funny(mary)<~>humble(mary)))<=>(tall(paul)))&
(((funny(fred)&~calm(fred)))=>(?[X]:((~kind(X)&~happy(X)))))&
(![X]:(calm(X)=>(kind(X)&patient(X))))&
(![X]:((calm(X)|~happy(X))<=>(rich(X)|patient(X))))&
(~calm(john))&
(?[X]:((~strong(X)<~>calm(X))))&
((kind(john)<~>creative(john)))&
((~curious(lucy)|wise(lucy)))&
((~calm(susan)&~quiet(susan)))&
(?[X]:((~happy(X)<~>~rich(X)))) | ~rich(fred) | []
| null | 0 |
Everyone who is wise is both not kind and not quiet.
Everyone who is not strong is either not patient or not quiet and vice versa.
If someone is both brave and humble then mary is wise or creative and vice versa.
Everyone who is quiet is either creative or tall and vice versa.
Everyone who is old is both kind and calm.
If someone is not creative then susan is either not curious or generous.
Everyone who is both strong and old is patient or not funny.
Everyone who is curious or not curious is either rich or not creative and vice versa.
If fred is not happy then alice is either happy or humble and vice versa.
Everyone who is kind or tall is either rich or not kind and vice versa.
If susan is patient or funny then someone is not strong and vice versa.
Everyone who is both not calm and funny is calm.
Everyone who is not kind or curious is both strong and not rich.
If someone is not old then someone is either rich or brave and vice versa.
If alice is both not humble and humble then john is not funny or not creative and vice versa.
Everyone who is either not happy or not kind is not old or quiet.
Mary is not rich.
Someone is either not humble or not rich.
Mary is either tall or not calm.
Someone is tall or generous.
Susan is either not patient or brave.
Paul is both happy and tall.
Alice is funny.
Someone is kind or curious. | Mary is not patient. | contradiction | (![X]:(wise(X)=>(~kind(X)&~quiet(X))))&
(![X]:(~strong(X)<=>(~patient(X)<~>~quiet(X))))&
((?[X]:((brave(X)&humble(X))))<=>((wise(mary)|creative(mary))))&
(![X]:(quiet(X)<=>(creative(X)<~>tall(X))))&
(![X]:(old(X)=>(kind(X)&calm(X))))&
((?[X]:(~creative(X)))=>((~curious(susan)<~>generous(susan))))&
(![X]:((strong(X)&old(X))=>(patient(X)|~funny(X))))&
(![X]:((curious(X)|~curious(X))<=>(rich(X)<~>~creative(X))))&
((~happy(fred))<=>((happy(alice)<~>humble(alice))))&
(![X]:((kind(X)|tall(X))<=>(rich(X)<~>~kind(X))))&
(((patient(susan)|funny(susan)))<=>(?[X]:(~strong(X))))&
(![X]:((~calm(X)&funny(X))=>calm(X)))&
(![X]:((~kind(X)|curious(X))=>(strong(X)&~rich(X))))&
((?[X]:(~old(X)))<=>(?[X]:((rich(X)<~>brave(X)))))&
(((~humble(alice)&humble(alice)))<=>((~funny(john)|~creative(john))))&
(![X]:((~happy(X)<~>~kind(X))=>(~old(X)|quiet(X))))&
(~rich(mary))&
(?[X]:((~humble(X)<~>~rich(X))))&
((tall(mary)<~>~calm(mary)))&
(?[X]:((tall(X)|generous(X))))&
((~patient(susan)<~>brave(susan)))&
((happy(paul)&tall(paul)))&
(funny(alice))&
(?[X]:((kind(X)|curious(X)))) | ~patient(mary) | [
"p1",
"p3",
"p7",
"p9",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 4298185027381370686473254
% SZS output start Proof for 4298185027381370686473254
2. ! [X0] : (~strong(X0) <=> (~patient(X0) <~> ~quiet(X0))) [input p1]
4. ! [X0] : (quiet(X0) <=> (creative(X0) <~> tall(X0))) [input p3]
8. ! [X0] : ((~curious(X0) | curious(X0)) <=> (rich(X0) <~> ~creative(X0))) [input p7]
10. ! [X0] : ((tall(X0) | kind(X0)) <=> (rich(X0) <~> ~kind(X0))) [input p9]
13. ! [X0] : ((curious(X0) | ~kind(X0)) => (~rich(X0) & strong(X0))) [input p12]
17. ~rich(mary) [input p16]
25. ~patient(mary) [input hypothesis]
34. ! [X0] : ((~rich(X0) & strong(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 13]
37. ! [X0] : ((~strong(X0) | ((~patient(X0) | quiet(X0)) & (~quiet(X0) | patient(X0)))) & (((quiet(X0) | patient(X0)) & (~quiet(X0) | ~patient(X0))) | strong(X0))) [nnf transformation 2]
43. ! [X0] : ((quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | ~quiet(X0))) [nnf transformation 4]
45. ! [X0] : (((~curious(X0) | curious(X0)) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (curious(X0) & ~curious(X0)))) [nnf transformation 8]
46. ! [X0] : ((~curious(X0) | curious(X0) | ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0)))) & (((creative(X0) | ~rich(X0)) & (~creative(X0) | rich(X0))) | (curious(X0) & ~curious(X0)))) [flattening 45]
48. ! [X0] : (((tall(X0) | kind(X0)) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (~tall(X0) & ~kind(X0)))) [nnf transformation 10]
49. ! [X0] : ((tall(X0) | kind(X0) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) & (((kind(X0) | ~rich(X0)) & (~kind(X0) | rich(X0))) | (~tall(X0) & ~kind(X0)))) [flattening 48]
76. ~strong(X0) | ~quiet(X0) | patient(X0) [cnf transformation 37]
86. ~tall(X0) | creative(X0) | quiet(X0) [cnf transformation 43]
92. ~creative(X0) | rich(X0) | ~curious(X0) [cnf transformation 46]
93. ~creative(X0) | rich(X0) | curious(X0) [cnf transformation 46]
102. ~kind(X0) | rich(X0) | ~kind(X0) [cnf transformation 49]
107. tall(X0) | kind(X0) | rich(X0) | kind(X0) [cnf transformation 49]
112. strong(X0) | kind(X0) [cnf transformation 34]
127. ~rich(mary) [cnf transformation 17]
139. ~patient(mary) [cnf transformation 25]
141. ~kind(X0) | rich(X0) [duplicate literal removal 102]
142. rich(X0) | kind(X0) | tall(X0) [duplicate literal removal 107]
144. 1 <=> creative(mary) [avatar definition]
145. creative(mary) <- (1) [avatar component clause 144]
146. ~creative(mary) <- (~1) [avatar component clause 144]
181. ~creative(X0) | rich(X0) [subsumption resolution 92,93]
265. 26 <=> tall(mary) [avatar definition]
266. tall(mary) <- (26) [avatar component clause 265]
267. ~tall(mary) <- (~26) [avatar component clause 265]
322. rich(mary) <- (1) [resolution 181,145]
325. $false <- (1) [subsumption resolution 322,127]
326. ~1 [avatar contradiction clause 325]
345. ~quiet(X0) | patient(X0) | kind(X0) [resolution 76,112]
441. kind(mary) | tall(mary) [resolution 142,127]
450. kind(mary) <- (~26) [subsumption resolution 441,267]
460. rich(mary) <- (~26) [resolution 450,141]
462. $false <- (~26) [subsumption resolution 460,127]
463. 26 [avatar contradiction clause 462]
467. creative(mary) | quiet(mary) <- (26) [resolution 266,86]
469. quiet(mary) <- (~1, 26) [subsumption resolution 467,146]
557. patient(mary) | kind(mary) <- (~1, 26) [resolution 345,469]
562. kind(mary) <- (~1, 26) [subsumption resolution 557,139]
634. rich(mary) <- (~1, 26) [resolution 562,141]
636. $false <- (~1, 26) [subsumption resolution 634,127]
637. 1 | ~26 [avatar contradiction clause 636]
638. $false [avatar sat refutation 326,463,637]
% SZS output end Proof for 4298185027381370686473254
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and not creative is either patient or not tall and vice versa. If someone is either not rich or creative then fred is either wise or calm and vice versa. Everyone who is both not rich and not curious is old or funny and vice versa. Everyone who is not wise is kind and vice versa. If fred is happy or creative then someone is not strong or not quiet. If susan is not funny then someone is either funny or not calm. If alice is either not kind or rich then someone is either not funny or not generous and vice versa. If lucy is not strong then someone is calm and vice versa. Everyone who is not strong or not humble is both not generous and generous. Everyone who is not calm is not happy or wise. Everyone who is both brave and not wise is either humble or not creative and vice versa. Everyone who is either wise or not rich is either not tall or not humble and vice versa. Everyone who is either not creative or not curious is not patient or old. If alice is funny then susan is either not strong or not quiet. If alice is brave then mary is both not humble and not quiet and vice versa. If lucy is both old and patient then someone is generous or not strong. Susan is either not kind or not quiet. Alice is either quiet or calm. Someone is either curious or not tall. Someone is both generous and wise. Mary is both not rich and happy. Someone is not curious or not happy. Someone is not curious or not kind. | Mary is not tall. | contradiction | (![X]:((rich(X)&~creative(X))<=>(patient(X)<~>~tall(X))))&
((?[X]:((~rich(X)<~>creative(X))))<=>((wise(fred)<~>calm(fred))))&
(![X]:((~rich(X)&~curious(X))<=>(old(X)|funny(X))))&
(![X]:(~wise(X)<=>kind(X)))&
(((happy(fred)|creative(fred)))=>(?[X]:((~strong(X)|~quiet(X)))))&
((~funny(susan))=>(?[X]:((funny(X)<~>~calm(X)))))&
(((~kind(alice)<~>rich(alice)))<=>(?[X]:((~funny(X)<~>~generous(X)))))&
((~strong(lucy))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)|~humble(X))=>(~generous(X)&generous(X))))&
(![X]:(~calm(X)=>(~happy(X)|wise(X))))&
(![X]:((brave(X)&~wise(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((wise(X)<~>~rich(X))<=>(~tall(X)<~>~humble(X))))&
(![X]:((~creative(X)<~>~curious(X))=>(~patient(X)|old(X))))&
((funny(alice))=>((~strong(susan)<~>~quiet(susan))))&
((brave(alice))<=>((~humble(mary)&~quiet(mary))))&
(((old(lucy)&patient(lucy)))=>(?[X]:((generous(X)|~strong(X)))))&
((~kind(susan)<~>~quiet(susan)))&
((quiet(alice)<~>calm(alice)))&
(?[X]:((curious(X)<~>~tall(X))))&
(?[X]:((generous(X)&wise(X))))&
((~rich(mary)&happy(mary)))&
(?[X]:((~curious(X)|~happy(X))))&
(?[X]:((~curious(X)|~kind(X)))) | ~tall(mary) | [
"p7",
"p8",
"p9",
"p11",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 1146556031147818250139983
% SZS output start Proof for 1146556031147818250139983
8. ~strong(lucy) <=> ? [X0] : calm(X0) [input p7]
9. ! [X0] : ((~humble(X0) | ~strong(X0)) => (generous(X0) & ~generous(X0))) [input p8]
10. ! [X0] : (~calm(X0) => (wise(X0) | ~happy(X0))) [input p9]
12. ! [X0] : ((wise(X0) <~> ~rich(X0)) <=> (~tall(X0) <~> ~humble(X0))) [input p11]
21. happy(mary) & ~rich(mary) [input p20]
24. ~tall(mary) [input hypothesis]
27. ! [X0] : ((generous(X0) & ~generous(X0)) | (humble(X0) & strong(X0))) [ennf transformation 9]
28. ! [X0] : ((wise(X0) | ~happy(X0)) | calm(X0)) [ennf transformation 10]
29. ! [X0] : (wise(X0) | ~happy(X0) | calm(X0)) [flattening 28]
53. (~strong(lucy) | ! [X0] : ~calm(X0)) & (? [X0] : calm(X0) | strong(lucy)) [nnf transformation 8]
54. (~strong(lucy) | ! [X0] : ~calm(X0)) & (? [X1] : calm(X1) | strong(lucy)) [rectify 53]
55. ? [X1] : calm(X1) => calm(sK4) [choice axiom]
56. (~strong(lucy) | ! [X0] : ~calm(X0)) & (calm(sK4) | strong(lucy)) [skolemisation 54,55]
59. ! [X0] : ((((rich(X0) | ~wise(X0)) & (~rich(X0) | wise(X0))) | ((~tall(X0) | humble(X0)) & (~humble(X0) | tall(X0)))) & (((humble(X0) | tall(X0)) & (~humble(X0) | ~tall(X0))) | ((wise(X0) | rich(X0)) & (~rich(X0) | ~wise(X0))))) [nnf transformation 12]
111. ~strong(lucy) | ~calm(X0) [cnf transformation 56]
112. ~generous(X0) | strong(X0) [cnf transformation 27]
113. ~generous(X0) | humble(X0) [cnf transformation 27]
114. generous(X0) | strong(X0) [cnf transformation 27]
115. humble(X0) | generous(X0) [cnf transformation 27]
116. ~happy(X0) | wise(X0) | calm(X0) [cnf transformation 29]
129. rich(X0) | ~wise(X0) | ~humble(X0) | tall(X0) [cnf transformation 59]
147. ~rich(mary) [cnf transformation 21]
148. happy(mary) [cnf transformation 21]
151. ~tall(mary) [cnf transformation 24]
245. 20 <=> ! [X0] : ~calm(X0) [avatar definition]
246. ~calm(X0) <- (20) [avatar component clause 245]
248. 21 <=> strong(lucy) [avatar definition]
250. ~strong(lucy) <- (~21) [avatar component clause 248]
251. 20 | ~21 [avatar split clause 111,248,245]
257. humble(X0) [subsumption resolution 113,115]
258. strong(X0) [subsumption resolution 112,114]
262. ~wise(X0) | rich(X0) | tall(X0) [subsumption resolution 129,257]
377. wise(mary) | calm(mary) [resolution 116,148]
378. wise(mary) <- (20) [subsumption resolution 377,246]
382. rich(mary) | tall(mary) <- (20) [resolution 262,378]
403. tall(mary) <- (20) [subsumption resolution 382,147]
404. $false <- (20) [subsumption resolution 403,151]
405. ~20 [avatar contradiction clause 404]
425. $false <- (~21) [subsumption resolution 250,258]
426. 21 [avatar contradiction clause 425]
427. $false [avatar sat refutation 251,405,426]
% SZS output end Proof for 1146556031147818250139983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is both curious and not funny.
If mary is not humble then someone is either not tall or brave.
If paul is brave then john is patient or not strong.
If paul is generous or tall then john is both not creative and not humble.
Everyone who is either not kind or not patient is not humble.
If someone is not patient or kind then susan is either not calm or not wise and vice versa.
Everyone who is either creative or not calm is either not brave or not tall.
If someone is funny then john is not patient or not quiet and vice versa.
Everyone who is not quiet is strong or not calm and vice versa.
Everyone who is calm is not humble and vice versa.
Everyone who is curious is not calm and vice versa.
Everyone who is both not calm and humble is either calm or not old and vice versa.
Everyone who is either calm or tall is either not patient or not kind and vice versa.
Everyone who is funny or quiet is not kind and vice versa.
If someone is not humble or not quiet then paul is either not calm or not strong and vice versa.
Everyone who is tall or not curious is both not patient and not quiet.
Someone is curious or creative.
Someone is rich or not brave.
Someone is tall.
Someone is creative or not generous.
Paul is either not creative or patient.
Susan is either not brave or not rich.
Someone is not curious. | Paul is not strong. | contradiction | ((?[X]:(~curious(X)))=>(?[X]:((curious(X)&~funny(X)))))&
((~humble(mary))=>(?[X]:((~tall(X)<~>brave(X)))))&
((brave(paul))=>((patient(john)|~strong(john))))&
(((generous(paul)|tall(paul)))=>((~creative(john)&~humble(john))))&
(![X]:((~kind(X)<~>~patient(X))=>~humble(X)))&
((?[X]:((~patient(X)|kind(X))))<=>((~calm(susan)<~>~wise(susan))))&
(![X]:((creative(X)<~>~calm(X))=>(~brave(X)<~>~tall(X))))&
((?[X]:(funny(X)))<=>((~patient(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(strong(X)|~calm(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
(![X]:((funny(X)|quiet(X))<=>~kind(X)))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~calm(paul)<~>~strong(paul))))&
(![X]:((tall(X)|~curious(X))=>(~patient(X)&~quiet(X))))&
(?[X]:((curious(X)|creative(X))))&
(?[X]:((rich(X)|~brave(X))))&
(?[X]:(tall(X)))&
(?[X]:((creative(X)|~generous(X))))&
((~creative(paul)<~>patient(paul)))&
((~brave(susan)<~>~rich(susan)))&
(?[X]:(~curious(X))) | ~strong(paul) | [
"p8",
"p10",
"p14",
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4890651319747771174136447
% SZS output start Proof for 4890651319747771174136447
9. ! [X0] : (~quiet(X0) <=> (~calm(X0) | strong(X0))) [input p8]
11. ! [X0] : (curious(X0) <=> ~calm(X0)) [input p10]
15. ? [X0] : (~quiet(X0) | ~humble(X0)) <=> (~calm(paul) <~> ~strong(paul)) [input p14]
16. ! [X0] : ((~curious(X0) | tall(X0)) => (~quiet(X0) & ~patient(X0))) [input p15]
23. ? [X0] : ~curious(X0) [input p22]
24. ~strong(paul) [input hypothesis]
35. ! [X0] : ((~quiet(X0) & ~patient(X0)) | (curious(X0) & ~tall(X0))) [ennf transformation 16]
53. ! [X0] : ((~quiet(X0) | (calm(X0) & ~strong(X0))) & ((~calm(X0) | strong(X0)) | quiet(X0))) [nnf transformation 9]
54. ! [X0] : ((~quiet(X0) | (calm(X0) & ~strong(X0))) & (~calm(X0) | strong(X0) | quiet(X0))) [flattening 53]
56. ! [X0] : ((curious(X0) | calm(X0)) & (~calm(X0) | ~curious(X0))) [nnf transformation 11]
62. (? [X0] : (~quiet(X0) | ~humble(X0)) | ((~calm(paul) | strong(paul)) & (~strong(paul) | calm(paul)))) & (((strong(paul) | calm(paul)) & (~strong(paul) | ~calm(paul))) | ! [X0] : (quiet(X0) & humble(X0))) [nnf transformation 15]
63. (? [X0] : (~quiet(X0) | ~humble(X0)) | ((~calm(paul) | strong(paul)) & (~strong(paul) | calm(paul)))) & (((strong(paul) | calm(paul)) & (~strong(paul) | ~calm(paul))) | ! [X1] : (quiet(X1) & humble(X1))) [rectify 62]
64. ? [X0] : (~quiet(X0) | ~humble(X0)) => (~quiet(sK4) | ~humble(sK4)) [choice axiom]
65. ((~quiet(sK4) | ~humble(sK4)) | ((~calm(paul) | strong(paul)) & (~strong(paul) | calm(paul)))) & (((strong(paul) | calm(paul)) & (~strong(paul) | ~calm(paul))) | ! [X1] : (quiet(X1) & humble(X1))) [skolemisation 63,64]
74. ? [X0] : ~curious(X0) => ~curious(sK8) [choice axiom]
75. ~curious(sK8) [skolemisation 23,74]
98. ~calm(X0) | strong(X0) | quiet(X0) [cnf transformation 54]
103. ~calm(X0) | ~curious(X0) [cnf transformation 56]
125. strong(paul) | calm(paul) | quiet(X1) [cnf transformation 65]
131. ~quiet(X0) | curious(X0) [cnf transformation 35]
139. ~curious(sK8) [cnf transformation 75]
140. ~strong(paul) [cnf transformation 24]
144. 1 <=> ! [X1] : curious(X1) [avatar definition]
145. curious(X1) <- (1) [avatar component clause 144]
243. 22 <=> strong(paul) [avatar definition]
244. ~strong(paul) <- (~22) [avatar component clause 243]
247. 23 <=> calm(paul) [avatar definition]
248. calm(paul) <- (23) [avatar component clause 247]
261. 26 <=> ! [X1] : quiet(X1) [avatar definition]
262. quiet(X1) <- (26) [avatar component clause 261]
263. 26 | 23 | 22 [avatar split clause 125,243,247,261]
308. ~22 [avatar split clause 140,243]
312. ~curious(paul) <- (23) [resolution 103,248]
328. strong(paul) | quiet(paul) <- (23) [resolution 98,248]
331. quiet(paul) <- (~22, 23) [subsumption resolution 328,244]
333. curious(paul) <- (~22, 23) [resolution 331,131]
338. $false <- (~22, 23) [subsumption resolution 333,312]
339. 22 | ~23 [avatar contradiction clause 338]
343. curious(X0) <- (26) [resolution 262,131]
349. 1 | ~26 [avatar split clause 343,261,144]
351. $false <- (1) [resolution 145,139]
353. ~1 [avatar contradiction clause 351]
354. $false [avatar sat refutation 263,308,339,349,353]
% SZS output end Proof for 4890651319747771174136447
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not tall or not humble then john is both not kind and wise.
If someone is not generous then someone is not kind or strong.
If someone is both not quiet and not rich then susan is not funny.
Everyone who is not humble or old is either old or not happy and vice versa.
Everyone who is not curious is both creative and not generous.
Everyone who is both humble and not humble is not quiet and vice versa.
If fred is both not humble and not funny then paul is either creative or brave.
Everyone who is not rich is not calm or happy and vice versa.
Everyone who is calm is not patient or not tall.
Everyone who is both not funny and quiet is wise or generous.
If someone is not tall then someone is either funny or not generous.
If someone is both not curious and not patient then someone is both happy and not curious and vice versa.
If someone is either not brave or brave then john is calm or rich.
Everyone who is both calm and patient is either not kind or patient and vice versa.
If someone is happy then someone is generous or tall.
If susan is not kind then john is not rich or not humble.
Someone is both creative and quiet.
Someone is both calm and creative.
Someone is both curious and not wise.
Someone is not kind.
Paul is patient.
Mary is both patient and not rich.
Someone is quiet. | John is happy. | entailment | ((?[X]:((~tall(X)|~humble(X))))=>((~kind(john)&wise(john))))&
((?[X]:(~generous(X)))=>(?[X]:((~kind(X)|strong(X)))))&
((?[X]:((~quiet(X)&~rich(X))))=>(~funny(susan)))&
(![X]:((~humble(X)|old(X))<=>(old(X)<~>~happy(X))))&
(![X]:(~curious(X)=>(creative(X)&~generous(X))))&
(![X]:((humble(X)&~humble(X))<=>~quiet(X)))&
(((~humble(fred)&~funny(fred)))=>((creative(paul)<~>brave(paul))))&
(![X]:(~rich(X)<=>(~calm(X)|happy(X))))&
(![X]:(calm(X)=>(~patient(X)|~tall(X))))&
(![X]:((~funny(X)&quiet(X))=>(wise(X)|generous(X))))&
((?[X]:(~tall(X)))=>(?[X]:((funny(X)<~>~generous(X)))))&
((?[X]:((~curious(X)&~patient(X))))<=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:((~brave(X)<~>brave(X))))=>((calm(john)|rich(john))))&
(![X]:((calm(X)&patient(X))<=>(~kind(X)<~>patient(X))))&
((?[X]:(happy(X)))=>(?[X]:((generous(X)|tall(X)))))&
((~kind(susan))=>((~rich(john)|~humble(john))))&
(?[X]:((creative(X)&quiet(X))))&
(?[X]:((calm(X)&creative(X))))&
(?[X]:((curious(X)&~wise(X))))&
(?[X]:(~kind(X)))&
(patient(paul))&
((patient(mary)&~rich(mary)))&
(?[X]:(quiet(X))) | happy(john) | [
"p0",
"p3",
"p7",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 2445770193513925840257627
% SZS output start Proof for 2445770193513925840257627
1. ? [X0] : (~humble(X0) | ~tall(X0)) => (wise(john) & ~kind(john)) [input p0]
4. ! [X0] : ((old(X0) | ~humble(X0)) <=> (old(X0) <~> ~happy(X0))) [input p3]
8. ! [X0] : (~rich(X0) <=> (happy(X0) | ~calm(X0))) [input p7]
13. ? [X0] : (~brave(X0) <~> brave(X0)) => (rich(john) | calm(john)) [input p12]
14. ! [X0] : ((patient(X0) & calm(X0)) <=> (~kind(X0) <~> patient(X0))) [input p13]
24. ~happy(john) [input hypothesis]
30. (wise(john) & ~kind(john)) | ! [X0] : (humble(X0) & tall(X0)) [ennf transformation 1]
40. (rich(john) | calm(john)) | ! [X0] : (~brave(X0) <=> brave(X0)) [ennf transformation 13]
41. rich(john) | calm(john) | ! [X0] : (~brave(X0) <=> brave(X0)) [flattening 40]
45. ! [X0] : (((old(X0) | ~humble(X0)) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (~old(X0) & humble(X0)))) [nnf transformation 4]
46. ! [X0] : ((old(X0) | ~humble(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) & (((happy(X0) | ~old(X0)) & (~happy(X0) | old(X0))) | (~old(X0) & humble(X0)))) [flattening 45]
50. ! [X0] : ((~rich(X0) | (~happy(X0) & calm(X0))) & ((happy(X0) | ~calm(X0)) | rich(X0))) [nnf transformation 8]
51. ! [X0] : ((~rich(X0) | (~happy(X0) & calm(X0))) & (happy(X0) | ~calm(X0) | rich(X0))) [flattening 50]
61. rich(john) | calm(john) | ! [X0] : ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))) [nnf transformation 41]
62. ! [X0] : (((patient(X0) & calm(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | (~patient(X0) | ~calm(X0)))) [nnf transformation 14]
63. ! [X0] : (((patient(X0) & calm(X0)) | ((~kind(X0) | ~patient(X0)) & (patient(X0) | kind(X0)))) & (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | ~patient(X0) | ~calm(X0))) [flattening 62]
78. ~kind(john) | humble(X0) [cnf transformation 30]
85. happy(X0) | ~old(X0) | ~old(X0) [cnf transformation 46]
87. old(X0) | ~humble(X0) | old(X0) | happy(X0) [cnf transformation 46]
96. ~rich(X0) | calm(X0) [cnf transformation 51]
106. rich(john) | calm(john) | brave(X0) | brave(X0) [cnf transformation 61]
107. rich(john) | calm(john) | ~brave(X0) | ~brave(X0) [cnf transformation 61]
109. ~patient(X0) | kind(X0) | ~patient(X0) | ~calm(X0) [cnf transformation 63]
112. patient(X0) | patient(X0) | kind(X0) [cnf transformation 63]
127. ~happy(john) [cnf transformation 24]
128. ~patient(X0) | kind(X0) | ~calm(X0) [duplicate literal removal 109]
129. patient(X0) | kind(X0) [duplicate literal removal 112]
130. rich(john) | calm(john) | brave(X0) [duplicate literal removal 106]
131. rich(john) | calm(john) | ~brave(X0) [duplicate literal removal 107]
132. ~old(X0) | happy(X0) [duplicate literal removal 85]
133. ~humble(X0) | old(X0) | happy(X0) [duplicate literal removal 87]
135. 1 <=> ! [X0] : humble(X0) [avatar definition]
136. humble(X0) <- (1) [avatar component clause 135]
147. 4 <=> kind(john) [avatar definition]
149. ~kind(john) <- (~4) [avatar component clause 147]
150. 1 | ~4 [avatar split clause 78,147,135]
216. calm(john) | ~brave(X0) [subsumption resolution 131,96]
218. 19 <=> ! [X0] : ~brave(X0) [avatar definition]
219. ~brave(X0) <- (19) [avatar component clause 218]
221. 20 <=> calm(john) [avatar definition]
223. calm(john) <- (20) [avatar component clause 221]
224. 19 | 20 [avatar split clause 216,221,218]
225. calm(john) | brave(X0) [subsumption resolution 130,96]
227. 21 <=> ! [X0] : brave(X0) [avatar definition]
228. brave(X0) <- (21) [avatar component clause 227]
229. 21 | 20 [avatar split clause 225,221,227]
230. ~calm(X0) | kind(X0) [subsumption resolution 128,129]
262. kind(john) <- (20) [resolution 230,223]
263. $false <- (~4, 20) [subsumption resolution 262,149]
264. 4 | ~20 [avatar contradiction clause 263]
265. $false <- (19, 21) [subsumption resolution 219,228]
266. ~19 | ~21 [avatar contradiction clause 265]
299. old(X0) | happy(X0) <- (1) [resolution 133,136]
319. happy(X0) <- (1) [subsumption resolution 299,132]
324. $false <- (1) [resolution 319,127]
327. ~1 [avatar contradiction clause 324]
328. $false [avatar sat refutation 150,224,229,264,266,327]
% SZS output end Proof for 2445770193513925840257627
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not funny or wise.
If lucy is either happy or humble then alice is not strong or not creative.
If someone is tall or creative then susan is both tall and not calm.
Everyone who is either not patient or not generous is not funny.
Everyone who is either kind or not old is not wise or humble.
Everyone who is either not funny or not brave is not tall and vice versa.
If someone is funny then john is not patient or not quiet and vice versa.
Everyone who is not quiet is strong or not calm and vice versa.
Everyone who is calm is not humble and vice versa.
Everyone who is curious is not calm and vice versa.
Everyone who is both not calm and humble is either calm or not old and vice versa.
Everyone who is either calm or tall is either not patient or not kind and vice versa.
Everyone who is funny or quiet is not kind and vice versa.
If someone is not humble or not quiet then paul is either not calm or not strong and vice versa.
Everyone who is tall or not curious is both not patient and not quiet.
Everyone who is both humble and creative is rich or not brave and vice versa.
Someone is tall.
Someone is creative or not generous.
Paul is either not creative or patient.
Susan is either not brave or not rich.
Someone is not curious.
Someone is not humble. | Alice is not kind. | neutral | (![X]:(~funny(X)=>(~funny(X)<~>wise(X))))&
(((happy(lucy)<~>humble(lucy)))=>((~strong(alice)|~creative(alice))))&
((?[X]:((tall(X)|creative(X))))=>((tall(susan)&~calm(susan))))&
(![X]:((~patient(X)<~>~generous(X))=>~funny(X)))&
(![X]:((kind(X)<~>~old(X))=>(~wise(X)|humble(X))))&
(![X]:((~funny(X)<~>~brave(X))<=>~tall(X)))&
((?[X]:(funny(X)))<=>((~patient(john)|~quiet(john))))&
(![X]:(~quiet(X)<=>(strong(X)|~calm(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(![X]:(curious(X)<=>~calm(X)))&
(![X]:((~calm(X)&humble(X))<=>(calm(X)<~>~old(X))))&
(![X]:((calm(X)<~>tall(X))<=>(~patient(X)<~>~kind(X))))&
(![X]:((funny(X)|quiet(X))<=>~kind(X)))&
((?[X]:((~humble(X)|~quiet(X))))<=>((~calm(paul)<~>~strong(paul))))&
(![X]:((tall(X)|~curious(X))=>(~patient(X)&~quiet(X))))&
(![X]:((humble(X)&creative(X))<=>(rich(X)|~brave(X))))&
(?[X]:(tall(X)))&
(?[X]:((creative(X)|~generous(X))))&
((~creative(paul)<~>patient(paul)))&
((~brave(susan)<~>~rich(susan)))&
(?[X]:(~curious(X)))&
(?[X]:(~humble(X))) | ~kind(alice) | []
| null | 0 |
If someone is both calm and old then lucy is either not tall or calm. If john is either humble or not old then someone is both not curious and not generous. Everyone who is rich is either strong or not strong. Everyone who is either not calm or quiet is either not calm or humble and vice versa. Everyone who is not tall or not generous is both not patient and tall. Everyone who is curious or not tall is either not tall or kind and vice versa. Everyone who is both not strong and not calm is not funny or funny and vice versa. Everyone who is calm or not funny is not creative or not tall. Everyone who is not old is either brave or curious. Everyone who is happy is not patient. Everyone who is not tall is either not creative or curious and vice versa. If john is either not creative or not brave then paul is either tall or funny. Everyone who is curious is not old. If someone is either not happy or brave then alice is funny or tall. Everyone who is not old or calm is both strong and not funny. Everyone who is either happy or not curious is both generous and not old. Someone is brave or not humble. Someone is funny or not brave. Someone is happy. Someone is both quiet and funny. Someone is funny. Lucy is rich or old. | Paul is creative. | entailment | ((?[X]:((calm(X)&old(X))))=>((~tall(lucy)<~>calm(lucy))))&
(((humble(john)<~>~old(john)))=>(?[X]:((~curious(X)&~generous(X)))))&
(![X]:(rich(X)=>(strong(X)<~>~strong(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~calm(X)<~>humble(X))))&
(![X]:((~tall(X)|~generous(X))=>(~patient(X)&tall(X))))&
(![X]:((curious(X)|~tall(X))<=>(~tall(X)<~>kind(X))))&
(![X]:((~strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
(![X]:((calm(X)|~funny(X))=>(~creative(X)|~tall(X))))&
(![X]:(~old(X)=>(brave(X)<~>curious(X))))&
(![X]:(happy(X)=>~patient(X)))&
(![X]:(~tall(X)<=>(~creative(X)<~>curious(X))))&
(((~creative(john)<~>~brave(john)))=>((tall(paul)<~>funny(paul))))&
(![X]:(curious(X)=>~old(X)))&
((?[X]:((~happy(X)<~>brave(X))))=>((funny(alice)|tall(alice))))&
(![X]:((~old(X)|calm(X))=>(strong(X)&~funny(X))))&
(![X]:((happy(X)<~>~curious(X))=>(generous(X)&~old(X))))&
(?[X]:((brave(X)|~humble(X))))&
(?[X]:((funny(X)|~brave(X))))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:(funny(X)))&
((rich(lucy)|old(lucy))) | creative(paul) | [
"p4",
"p6",
"p10",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3995234610891280160747959
% SZS output start Proof for 3995234610891280160747959
5. ! [X0] : ((~generous(X0) | ~tall(X0)) => (tall(X0) & ~patient(X0))) [input p4]
7. ! [X0] : ((~calm(X0) & ~strong(X0)) <=> (funny(X0) | ~funny(X0))) [input p6]
11. ! [X0] : (~tall(X0) <=> (~creative(X0) <~> curious(X0))) [input p10]
13. ! [X0] : (curious(X0) => ~old(X0)) [input p12]
15. ! [X0] : ((calm(X0) | ~old(X0)) => (~funny(X0) & strong(X0))) [input p14]
23. ~creative(paul) [input hypothesis]
25. ! [X0] : ((~generous(X0) | ~tall(X0)) => tall(X0)) [pure predicate removal 5]
29. ! [X0] : (tall(X0) | (generous(X0) & tall(X0))) [ennf transformation 25]
34. ! [X0] : (~old(X0) | ~curious(X0)) [ennf transformation 13]
37. ! [X0] : ((~funny(X0) & strong(X0)) | (~calm(X0) & old(X0))) [ennf transformation 15]
47. ! [X0] : (((~calm(X0) & ~strong(X0)) | (~funny(X0) & funny(X0))) & ((funny(X0) | ~funny(X0)) | (calm(X0) | strong(X0)))) [nnf transformation 7]
48. ! [X0] : (((~calm(X0) & ~strong(X0)) | (~funny(X0) & funny(X0))) & (funny(X0) | ~funny(X0) | calm(X0) | strong(X0))) [flattening 47]
50. ! [X0] : ((~tall(X0) | ((~creative(X0) | ~curious(X0)) & (curious(X0) | creative(X0)))) & (((~curious(X0) | creative(X0)) & (curious(X0) | ~creative(X0))) | tall(X0))) [nnf transformation 11]
80. tall(X0) | tall(X0) [cnf transformation 29]
89. ~strong(X0) | funny(X0) [cnf transformation 48]
90. ~funny(X0) | ~strong(X0) [cnf transformation 48]
99. ~tall(X0) | curious(X0) | creative(X0) [cnf transformation 50]
105. ~curious(X0) | ~old(X0) [cnf transformation 34]
108. strong(X0) | old(X0) [cnf transformation 37]
123. ~creative(paul) [cnf transformation 23]
126. tall(X0) [duplicate literal removal 80]
169. ~strong(X0) [subsumption resolution 89,90]
172. creative(X0) | curious(X0) [subsumption resolution 99,126]
189. old(X0) [subsumption resolution 108,169]
222. curious(paul) [resolution 172,123]
226. ~old(paul) [resolution 222,105]
227. $false [subsumption resolution 226,189]
% SZS output end Proof for 3995234610891280160747959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not brave is strong and vice versa.
Everyone who is strong or not old is either wise or curious.
Everyone who is not tall or kind is old or not generous and vice versa.
If fred is both humble and not happy then lucy is not wise.
If someone is patient then alice is wise or not brave.
If someone is either tall or not brave then someone is both not quiet and not generous and vice versa.
If someone is creative or not strong then someone is rich.
If someone is not wise or quiet then someone is not brave or old and vice versa.
If someone is funny or tall then paul is not wise.
If someone is both kind and happy then mary is generous.
If someone is quiet then someone is not strong or not kind.
Everyone who is kind is both not brave and not curious and vice versa.
Everyone who is generous is calm or funny.
Everyone who is calm is not humble and vice versa.
If fred is both not old and creative then john is both humble and tall and vice versa.
If someone is not old or not curious then susan is both strong and not creative and vice versa.
John is either kind or rich.
Lucy is both happy and quiet.
Someone is both patient and calm.
Someone is both creative and happy.
Someone is creative or kind.
Susan is not wise.
Susan is both patient and creative. | Alice is old. | entailment | (![X]:((~kind(X)|~brave(X))<=>strong(X)))&
(![X]:((strong(X)|~old(X))=>(wise(X)<~>curious(X))))&
(![X]:((~tall(X)|kind(X))<=>(old(X)|~generous(X))))&
(((humble(fred)&~happy(fred)))=>(~wise(lucy)))&
((?[X]:(patient(X)))=>((wise(alice)|~brave(alice))))&
((?[X]:((tall(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)&~generous(X)))))&
((?[X]:((creative(X)|~strong(X))))=>(?[X]:(rich(X))))&
((?[X]:((~wise(X)|quiet(X))))<=>(?[X]:((~brave(X)|old(X)))))&
((?[X]:((funny(X)|tall(X))))=>(~wise(paul)))&
((?[X]:((kind(X)&happy(X))))=>(generous(mary)))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|~kind(X)))))&
(![X]:(kind(X)<=>(~brave(X)&~curious(X))))&
(![X]:(generous(X)=>(calm(X)|funny(X))))&
(![X]:(calm(X)<=>~humble(X)))&
(((~old(fred)&creative(fred)))<=>((humble(john)&tall(john))))&
((?[X]:((~old(X)|~curious(X))))<=>((strong(susan)&~creative(susan))))&
((kind(john)<~>rich(john)))&
((happy(lucy)&quiet(lucy)))&
(?[X]:((patient(X)&calm(X))))&
(?[X]:((creative(X)&happy(X))))&
(?[X]:((creative(X)|kind(X))))&
(~wise(susan))&
((patient(susan)&creative(susan))) | old(alice) | [
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4436566181789410369967576
% SZS output start Proof for 4436566181789410369967576
16. ? [X0] : (~curious(X0) | ~old(X0)) <=> (~creative(susan) & strong(susan)) [input p15]
23. creative(susan) & patient(susan) [input p22]
24. ~old(alice) [input hypothesis]
67. (? [X0] : (~curious(X0) | ~old(X0)) | (creative(susan) | ~strong(susan))) & ((~creative(susan) & strong(susan)) | ! [X0] : (curious(X0) & old(X0))) [nnf transformation 16]
68. (? [X0] : (~curious(X0) | ~old(X0)) | creative(susan) | ~strong(susan)) & ((~creative(susan) & strong(susan)) | ! [X0] : (curious(X0) & old(X0))) [flattening 67]
69. (? [X0] : (~curious(X0) | ~old(X0)) | creative(susan) | ~strong(susan)) & ((~creative(susan) & strong(susan)) | ! [X1] : (curious(X1) & old(X1))) [rectify 68]
70. ? [X0] : (~curious(X0) | ~old(X0)) => (~curious(sK6) | ~old(sK6)) [choice axiom]
71. ((~curious(sK6) | ~old(sK6)) | creative(susan) | ~strong(susan)) & ((~creative(susan) & strong(susan)) | ! [X1] : (curious(X1) & old(X1))) [skolemisation 69,70]
119. ~creative(susan) | old(X1) [cnf transformation 71]
133. creative(susan) [cnf transformation 23]
134. ~old(alice) [cnf transformation 24]
289. 37 <=> creative(susan) [avatar definition]
306. 41 <=> ! [X1] : old(X1) [avatar definition]
307. old(X1) <- (41) [avatar component clause 306]
308. 41 | ~37 [avatar split clause 119,289,306]
330. 37 [avatar split clause 133,289]
331. $false <- (41) [resolution 307,134]
332. ~41 [avatar contradiction clause 331]
333. $false [avatar sat refutation 308,330,332]
% SZS output end Proof for 4436566181789410369967576
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then someone is either not strong or creative. If lucy is both not curious and not calm then someone is both generous and not old. If john is not curious or not calm then someone is both not quiet and strong and vice versa. If alice is tall then lucy is not tall. Everyone who is either happy or generous is generous. If someone is not humble then lucy is curious and vice versa. Everyone who is kind or not rich is not happy. If someone is either not patient or not strong then alice is both patient and generous and vice versa. Everyone who is curious is funny. Everyone who is both wise and not generous is either happy or rich and vice versa. If someone is not strong then someone is either old or not quiet. If someone is generous then paul is either wise or kind and vice versa. Everyone who is not brave is both not creative and funny and vice versa. Everyone who is either not strong or generous is both kind and brave. If mary is both not calm and kind then someone is either curious or tall and vice versa. If someone is both not funny and not curious then someone is either kind or not old and vice versa. Lucy is not creative. Paul is wise or not curious. Lucy is not funny. Someone is rich. Someone is both old and not generous. Mary is both not quiet and happy. Someone is not tall. John is not kind or quiet. | Mary is not strong. | entailment | ((?[X]:(happy(X)))=>(?[X]:((~strong(X)<~>creative(X)))))&
(((~curious(lucy)&~calm(lucy)))=>(?[X]:((generous(X)&~old(X)))))&
(((~curious(john)|~calm(john)))<=>(?[X]:((~quiet(X)&strong(X)))))&
((tall(alice))=>(~tall(lucy)))&
(![X]:((happy(X)<~>generous(X))=>generous(X)))&
((?[X]:(~humble(X)))<=>(curious(lucy)))&
(![X]:((kind(X)|~rich(X))=>~happy(X)))&
((?[X]:((~patient(X)<~>~strong(X))))<=>((patient(alice)&generous(alice))))&
(![X]:(curious(X)=>funny(X)))&
(![X]:((wise(X)&~generous(X))<=>(happy(X)<~>rich(X))))&
((?[X]:(~strong(X)))=>(?[X]:((old(X)<~>~quiet(X)))))&
((?[X]:(generous(X)))<=>((wise(paul)<~>kind(paul))))&
(![X]:(~brave(X)<=>(~creative(X)&funny(X))))&
(![X]:((~strong(X)<~>generous(X))=>(kind(X)&brave(X))))&
(((~calm(mary)&kind(mary)))<=>(?[X]:((curious(X)<~>tall(X)))))&
((?[X]:((~funny(X)&~curious(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
(~creative(lucy))&
((wise(paul)|~curious(paul)))&
(~funny(lucy))&
(?[X]:(rich(X)))&
(?[X]:((old(X)&~generous(X))))&
((~quiet(mary)&happy(mary)))&
(?[X]:(~tall(X)))&
((~kind(john)|quiet(john))) | ~strong(mary) | [
"p4",
"p6",
"p13",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 4800913914375609617933368
% SZS output start Proof for 4800913914375609617933368
5. ! [X0] : ((happy(X0) <~> generous(X0)) => generous(X0)) [input p4]
7. ! [X0] : ((~rich(X0) | kind(X0)) => ~happy(X0)) [input p6]
14. ! [X0] : ((~strong(X0) <~> generous(X0)) => (brave(X0) & kind(X0))) [input p13]
22. happy(mary) & ~quiet(mary) [input p21]
25. strong(mary) [input hypothesis]
34. ! [X0] : (generous(X0) | (happy(X0) <=> generous(X0))) [ennf transformation 5]
35. ! [X0] : (~happy(X0) | (rich(X0) & ~kind(X0))) [ennf transformation 7]
40. ! [X0] : ((brave(X0) & kind(X0)) | (~strong(X0) <=> generous(X0))) [ennf transformation 14]
52. ! [X0] : (generous(X0) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0)))) [nnf transformation 34]
72. ! [X0] : ((brave(X0) & kind(X0)) | ((~strong(X0) | ~generous(X0)) & (generous(X0) | strong(X0)))) [nnf transformation 40]
99. generous(X0) | generous(X0) | ~happy(X0) [cnf transformation 52]
103. ~kind(X0) | ~happy(X0) [cnf transformation 35]
126. ~generous(X0) | ~strong(X0) | kind(X0) [cnf transformation 72]
148. happy(mary) [cnf transformation 22]
151. strong(mary) [cnf transformation 25]
152. ~happy(X0) | generous(X0) [duplicate literal removal 99]
291. 31 <=> kind(mary) [avatar definition]
293. kind(mary) <- (31) [avatar component clause 291]
370. generous(mary) [resolution 152,148]
418. ~strong(mary) | kind(mary) [resolution 126,370]
431. kind(mary) [subsumption resolution 418,151]
443. 31 [avatar split clause 431,291]
444. ~happy(mary) <- (31) [resolution 293,103]
445. $false <- (31) [subsumption resolution 444,148]
446. ~31 [avatar contradiction clause 445]
447. $false [avatar sat refutation 443,446]
% SZS output end Proof for 4800913914375609617933368
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both generous and not happy is not calm and vice versa.
If someone is not curious then mary is either not happy or not rich and vice versa.
If someone is either quiet or not calm then someone is both not old and funny.
Everyone who is creative or patient is either not old or happy and vice versa.
Everyone who is both strong and quiet is either not quiet or funny and vice versa.
If alice is not happy or not humble then fred is either wise or generous.
If someone is either not rich or not generous then someone is both curious and not calm and vice versa.
Everyone who is both patient and not wise is either creative or not happy.
Everyone who is both humble and old is not strong.
Everyone who is kind or rich is either not calm or curious.
Everyone who is both humble and generous is not humble.
Everyone who is both not patient and not quiet is not patient or wise and vice versa.
Everyone who is happy or not strong is either not wise or curious and vice versa.
Everyone who is not quiet is either not patient or kind and vice versa.
Everyone who is either happy or generous is not kind or kind.
Everyone who is patient or humble is both not kind and tall.
Someone is wise or brave.
Mary is either funny or not patient.
Alice is either rich or not brave.
Alice is both not patient and not wise.
Someone is happy or not patient.
Fred is humble or funny.
Someone is either not old or not wise. | Mary is not strong. | contradiction | (![X]:((generous(X)&~happy(X))<=>~calm(X)))&
((?[X]:(~curious(X)))<=>((~happy(mary)<~>~rich(mary))))&
((?[X]:((quiet(X)<~>~calm(X))))=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((creative(X)|patient(X))<=>(~old(X)<~>happy(X))))&
(![X]:((strong(X)&quiet(X))<=>(~quiet(X)<~>funny(X))))&
(((~happy(alice)|~humble(alice)))=>((wise(fred)<~>generous(fred))))&
((?[X]:((~rich(X)<~>~generous(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((patient(X)&~wise(X))=>(creative(X)<~>~happy(X))))&
(![X]:((humble(X)&old(X))=>~strong(X)))&
(![X]:((kind(X)|rich(X))=>(~calm(X)<~>curious(X))))&
(![X]:((humble(X)&generous(X))=>~humble(X)))&
(![X]:((~patient(X)&~quiet(X))<=>(~patient(X)|wise(X))))&
(![X]:((happy(X)|~strong(X))<=>(~wise(X)<~>curious(X))))&
(![X]:(~quiet(X)<=>(~patient(X)<~>kind(X))))&
(![X]:((happy(X)<~>generous(X))=>(~kind(X)|kind(X))))&
(![X]:((patient(X)|humble(X))=>(~kind(X)&tall(X))))&
(?[X]:((wise(X)|brave(X))))&
((funny(mary)<~>~patient(mary)))&
((rich(alice)<~>~brave(alice)))&
((~patient(alice)&~wise(alice)))&
(?[X]:((happy(X)|~patient(X))))&
((humble(fred)|funny(fred)))&
(?[X]:((~old(X)<~>~wise(X)))) | ~strong(mary) | [
"p4",
"p11",
"p13",
"p15",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 2532861524056279053678592
% SZS output start Proof for 2532861524056279053678592
5. ! [X0] : ((quiet(X0) & strong(X0)) <=> (~quiet(X0) <~> funny(X0))) [input p4]
12. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (wise(X0) | ~patient(X0))) [input p11]
14. ! [X0] : (~quiet(X0) <=> (~patient(X0) <~> kind(X0))) [input p13]
16. ! [X0] : ((humble(X0) | patient(X0)) => (tall(X0) & ~kind(X0))) [input p15]
18. funny(mary) <~> ~patient(mary) [input p17]
24. ~strong(mary) [input hypothesis]
27. ! [X0] : ((humble(X0) | patient(X0)) => ~kind(X0)) [pure predicate removal 16]
39. ! [X0] : (~kind(X0) | (~humble(X0) & ~patient(X0))) [ennf transformation 27]
52. ! [X0] : (((quiet(X0) & strong(X0)) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | (~quiet(X0) | ~strong(X0)))) [nnf transformation 5]
53. ! [X0] : (((quiet(X0) & strong(X0)) | ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0)))) & (((~funny(X0) | quiet(X0)) & (funny(X0) | ~quiet(X0))) | ~quiet(X0) | ~strong(X0))) [flattening 52]
62. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (quiet(X0) | patient(X0)))) [nnf transformation 12]
63. ! [X0] : (((~quiet(X0) & ~patient(X0)) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | quiet(X0) | patient(X0))) [flattening 62]
66. ! [X0] : ((~quiet(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0)))) & (((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | quiet(X0))) [nnf transformation 14]
70. (patient(mary) | ~funny(mary)) & (~patient(mary) | funny(mary)) [nnf transformation 18]
97. ~funny(X0) | ~quiet(X0) | strong(X0) [cnf transformation 53]
98. quiet(X0) | funny(X0) | quiet(X0) [cnf transformation 53]
121. ~quiet(X0) | patient(X0) [cnf transformation 63]
129. ~patient(X0) | kind(X0) | quiet(X0) [cnf transformation 66]
130. ~kind(X0) | patient(X0) | quiet(X0) [cnf transformation 66]
132. ~quiet(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 66]
135. ~kind(X0) | ~patient(X0) [cnf transformation 39]
138. ~patient(mary) | funny(mary) [cnf transformation 70]
139. patient(mary) | ~funny(mary) [cnf transformation 70]
148. ~strong(mary) [cnf transformation 24]
151. funny(X0) | quiet(X0) [duplicate literal removal 98]
241. ~kind(X0) | ~quiet(X0) [subsumption resolution 132,121]
242. ~kind(X0) | patient(X0) [subsumption resolution 130,241]
243. ~kind(X0) [subsumption resolution 135,242]
254. 22 <=> funny(mary) [avatar definition]
255. funny(mary) <- (22) [avatar component clause 254]
256. ~funny(mary) <- (~22) [avatar component clause 254]
258. 23 <=> patient(mary) [avatar definition]
259. ~patient(mary) <- (~23) [avatar component clause 258]
260. patient(mary) <- (23) [avatar component clause 258]
261. ~22 | 23 [avatar split clause 139,258,254]
262. 22 | ~23 [avatar split clause 138,258,254]
307. quiet(mary) <- (~22) [resolution 151,256]
308. patient(mary) <- (~22) [resolution 307,121]
309. $false <- (~22, ~23) [subsumption resolution 308,259]
310. 22 | 23 [avatar contradiction clause 309]
318. ~quiet(mary) | strong(mary) <- (22) [resolution 97,255]
328. ~quiet(mary) <- (22) [subsumption resolution 318,148]
381. kind(mary) | quiet(mary) <- (23) [resolution 129,260]
382. quiet(mary) <- (23) [subsumption resolution 381,243]
383. $false <- (22, 23) [subsumption resolution 382,328]
384. ~22 | ~23 [avatar contradiction clause 383]
385. $false [avatar sat refutation 261,262,310,384]
% SZS output end Proof for 2532861524056279053678592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is strong then paul is either not happy or not curious and vice versa. Everyone who is old is not tall or not creative and vice versa. Everyone who is not funny or not happy is not funny and vice versa. If alice is either not funny or not curious then someone is happy or not happy. Everyone who is generous or happy is not quiet and vice versa. If susan is either not rich or rich then someone is not quiet and vice versa. Everyone who is not curious or not quiet is either generous or curious. Everyone who is not strong or not old is brave. If someone is both kind and not kind then alice is either generous or not patient and vice versa. If someone is not quiet then someone is either not strong or quiet and vice versa. Everyone who is either not creative or not brave is both patient and not generous. If john is either patient or kind then someone is either tall or not quiet. If someone is generous then someone is both kind and not funny. Everyone who is generous or not brave is either not creative or old. Everyone who is either not quiet or humble is creative. Everyone who is rich is both not old and not wise. Someone is brave. Someone is not curious. Someone is not quiet or rich. John is both not kind and patient. Lucy is not creative or tall. Someone is either kind or not happy. Someone is either old or not brave. Paul is either happy or not humble. | Lucy is not curious. | contradiction | ((strong(paul))<=>((~happy(paul)<~>~curious(paul))))&
(![X]:(old(X)<=>(~tall(X)|~creative(X))))&
(![X]:((~funny(X)|~happy(X))<=>~funny(X)))&
(((~funny(alice)<~>~curious(alice)))=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((generous(X)|happy(X))<=>~quiet(X)))&
(((~rich(susan)<~>rich(susan)))<=>(?[X]:(~quiet(X))))&
(![X]:((~curious(X)|~quiet(X))=>(generous(X)<~>curious(X))))&
(![X]:((~strong(X)|~old(X))=>brave(X)))&
((?[X]:((kind(X)&~kind(X))))<=>((generous(alice)<~>~patient(alice))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~strong(X)<~>quiet(X)))))&
(![X]:((~creative(X)<~>~brave(X))=>(patient(X)&~generous(X))))&
(((patient(john)<~>kind(john)))=>(?[X]:((tall(X)<~>~quiet(X)))))&
((?[X]:(generous(X)))=>(?[X]:((kind(X)&~funny(X)))))&
(![X]:((generous(X)|~brave(X))=>(~creative(X)<~>old(X))))&
(![X]:((~quiet(X)<~>humble(X))=>creative(X)))&
(![X]:(rich(X)=>(~old(X)&~wise(X))))&
(?[X]:(brave(X)))&
(?[X]:(~curious(X)))&
(?[X]:((~quiet(X)|rich(X))))&
((~kind(john)&patient(john)))&
((~creative(lucy)|tall(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((happy(paul)<~>~humble(paul))) | ~curious(lucy) | [
"p1",
"p6",
"p13",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 6734902720750172208720382
% SZS output start Proof for 6734902720750172208720382
2. ! [X0] : (old(X0) <=> (~creative(X0) | ~tall(X0))) [input p1]
7. ! [X0] : ((~quiet(X0) | ~curious(X0)) => (generous(X0) <~> curious(X0))) [input p6]
14. ! [X0] : ((~brave(X0) | generous(X0)) => (~creative(X0) <~> old(X0))) [input p13]
21. tall(lucy) | ~creative(lucy) [input p20]
25. ~curious(lucy) [input hypothesis]
30. ! [X0] : ((generous(X0) <~> curious(X0)) | (quiet(X0) & curious(X0))) [ennf transformation 7]
35. ! [X0] : ((~creative(X0) <~> old(X0)) | (brave(X0) & ~generous(X0))) [ennf transformation 14]
39. ! [X0] : ((old(X0) | (creative(X0) & tall(X0))) & ((~creative(X0) | ~tall(X0)) | ~old(X0))) [nnf transformation 2]
40. ! [X0] : ((old(X0) | (creative(X0) & tall(X0))) & (~creative(X0) | ~tall(X0) | ~old(X0))) [flattening 39]
52. ! [X0] : (((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | (quiet(X0) & curious(X0))) [nnf transformation 30]
69. ! [X0] : (((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | (brave(X0) & ~generous(X0))) [nnf transformation 35]
88. ~creative(X0) | ~tall(X0) | ~old(X0) [cnf transformation 40]
90. creative(X0) | old(X0) [cnf transformation 40]
103. curious(X0) | generous(X0) | curious(X0) [cnf transformation 52]
129. old(X0) | ~creative(X0) | ~generous(X0) [cnf transformation 69]
131. ~old(X0) | creative(X0) | ~generous(X0) [cnf transformation 69]
141. tall(lucy) | ~creative(lucy) [cnf transformation 21]
148. ~curious(lucy) [cnf transformation 25]
149. generous(X0) | curious(X0) [duplicate literal removal 103]
254. ~generous(X0) | creative(X0) [subsumption resolution 131,90]
255. ~generous(X0) | old(X0) [subsumption resolution 129,254]
268. 24 <=> creative(lucy) [avatar definition]
269. creative(lucy) <- (24) [avatar component clause 268]
270. ~creative(lucy) <- (~24) [avatar component clause 268]
272. 25 <=> tall(lucy) [avatar definition]
274. tall(lucy) <- (25) [avatar component clause 272]
275. ~24 | 25 [avatar split clause 141,272,268]
305. creative(X0) | curious(X0) [resolution 254,149]
306. old(X0) | curious(X0) [resolution 255,149]
307. curious(lucy) <- (~24) [resolution 305,270]
308. $false <- (~24) [subsumption resolution 307,148]
309. 24 [avatar contradiction clause 308]
312. ~tall(lucy) | ~old(lucy) <- (24) [resolution 88,269]
314. ~old(lucy) <- (24, 25) [subsumption resolution 312,274]
494. curious(lucy) <- (24, 25) [resolution 306,314]
496. $false <- (24, 25) [subsumption resolution 494,148]
497. ~24 | ~25 [avatar contradiction clause 496]
498. $false [avatar sat refutation 275,309,497]
% SZS output end Proof for 6734902720750172208720382
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and not brave is either humble or funny. Everyone who is not rich or not wise is both kind and not generous. Everyone who is either not funny or funny is wise and vice versa. If someone is both not tall and happy then someone is both not kind and not funny and vice versa. If someone is not humble then someone is both creative and not rich. Everyone who is both generous and kind is not rich and vice versa. If mary is either not funny or patient then someone is old or not calm. Everyone who is both not kind and tall is either funny or not brave. Everyone who is wise or patient is kind. Everyone who is tall is either not brave or generous. If mary is creative then someone is either not tall or creative. If susan is not humble or happy then mary is both not rich and not old and vice versa. If someone is both not curious and wise then mary is not curious or old and vice versa. If someone is generous or not funny then someone is both not quiet and not curious and vice versa. Everyone who is either creative or brave is kind. Lucy is brave or tall. Someone is both calm and not creative. Someone is either not rich or not tall. Fred is tall. Someone is rich or patient. Susan is not humble or humble. | Mary is tall. | neutral | (![X]:((old(X)&~brave(X))=>(humble(X)<~>funny(X))))&
(![X]:((~rich(X)|~wise(X))=>(kind(X)&~generous(X))))&
(![X]:((~funny(X)<~>funny(X))<=>wise(X)))&
((?[X]:((~tall(X)&happy(X))))<=>(?[X]:((~kind(X)&~funny(X)))))&
((?[X]:(~humble(X)))=>(?[X]:((creative(X)&~rich(X)))))&
(![X]:((generous(X)&kind(X))<=>~rich(X)))&
(((~funny(mary)<~>patient(mary)))=>(?[X]:((old(X)|~calm(X)))))&
(![X]:((~kind(X)&tall(X))=>(funny(X)<~>~brave(X))))&
(![X]:((wise(X)|patient(X))=>kind(X)))&
(![X]:(tall(X)=>(~brave(X)<~>generous(X))))&
((creative(mary))=>(?[X]:((~tall(X)<~>creative(X)))))&
(((~humble(susan)|happy(susan)))<=>((~rich(mary)&~old(mary))))&
((?[X]:((~curious(X)&wise(X))))<=>((~curious(mary)|old(mary))))&
((?[X]:((generous(X)|~funny(X))))<=>(?[X]:((~quiet(X)&~curious(X)))))&
(![X]:((creative(X)<~>brave(X))=>kind(X)))&
((brave(lucy)|tall(lucy)))&
(?[X]:((calm(X)&~creative(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
(tall(fred))&
(?[X]:((rich(X)|patient(X))))&
((~humble(susan)|humble(susan))) | tall(mary) | []
| null | 0 |
Everyone who is curious or not creative is old and vice versa. Everyone who is both not generous and rich is both old and calm. If someone is either not wise or kind then paul is either wise or calm. Everyone who is not generous is not old and vice versa. If someone is both not wise and not rich then susan is either brave or tall. If someone is either not kind or not old then someone is not kind and vice versa. If someone is humble then lucy is both old and not generous. Everyone who is brave is happy. Everyone who is quiet is both not curious and not old and vice versa. If someone is brave then someone is not humble or not brave and vice versa. If someone is not happy or not calm then paul is either rich or tall and vice versa. Everyone who is kind is both calm and happy and vice versa. If someone is not creative then john is either tall or curious. If someone is kind then someone is either generous or not wise and vice versa. Everyone who is humble is both rich and not humble. If fred is both rich and not wise then alice is not happy and vice versa. Someone is brave. Someone is calm or not curious. Alice is both not old and patient. Someone is creative. Someone is creative or not generous. John is either rich or not brave. Someone is not kind. | Alice is not happy. | neutral | (![X]:((curious(X)|~creative(X))<=>old(X)))&
(![X]:((~generous(X)&rich(X))=>(old(X)&calm(X))))&
((?[X]:((~wise(X)<~>kind(X))))=>((wise(paul)<~>calm(paul))))&
(![X]:(~generous(X)<=>~old(X)))&
((?[X]:((~wise(X)&~rich(X))))=>((brave(susan)<~>tall(susan))))&
((?[X]:((~kind(X)<~>~old(X))))<=>(?[X]:(~kind(X))))&
((?[X]:(humble(X)))=>((old(lucy)&~generous(lucy))))&
(![X]:(brave(X)=>happy(X)))&
(![X]:(quiet(X)<=>(~curious(X)&~old(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~humble(X)|~brave(X)))))&
((?[X]:((~happy(X)|~calm(X))))<=>((rich(paul)<~>tall(paul))))&
(![X]:(kind(X)<=>(calm(X)&happy(X))))&
((?[X]:(~creative(X)))=>((tall(john)<~>curious(john))))&
((?[X]:(kind(X)))<=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:(humble(X)=>(rich(X)&~humble(X))))&
(((rich(fred)&~wise(fred)))<=>(~happy(alice)))&
(?[X]:(brave(X)))&
(?[X]:((calm(X)|~curious(X))))&
((~old(alice)&patient(alice)))&
(?[X]:(creative(X)))&
(?[X]:((creative(X)|~generous(X))))&
((rich(john)<~>~brave(john)))&
(?[X]:(~kind(X))) | ~happy(alice) | []
| null | 0 |
If someone is both not wise and humble then someone is not tall. If mary is both not quiet and rich then paul is either curious or not patient. Everyone who is both quiet and not strong is either not curious or not happy and vice versa. Everyone who is both not tall and humble is both not curious and not calm and vice versa. Everyone who is not brave is not rich. Everyone who is happy is either patient or old and vice versa. Everyone who is generous or not generous is strong and vice versa. If john is not funny then susan is both not tall and kind and vice versa. Everyone who is not brave is either creative or curious. If someone is curious or humble then someone is either not humble or strong. If mary is both patient and calm then someone is creative and vice versa. If susan is both not strong and patient then someone is either not wise or not tall and vice versa. If someone is both not wise and brave then alice is not tall. Everyone who is either wise or not brave is both patient and not creative. If someone is both generous and not creative then john is either not quiet or happy. If fred is kind then lucy is both generous and quiet. Fred is both not tall and kind. Someone is not generous or not kind. Someone is both not brave and not funny. Someone is either not curious or calm. Someone is old or patient. Susan is either not happy or not brave. John is both not rich and not quiet. Paul is not calm. | Fred is not wise. | entailment | ((?[X]:((~wise(X)&humble(X))))=>(?[X]:(~tall(X))))&
(((~quiet(mary)&rich(mary)))=>((curious(paul)<~>~patient(paul))))&
(![X]:((quiet(X)&~strong(X))<=>(~curious(X)<~>~happy(X))))&
(![X]:((~tall(X)&humble(X))<=>(~curious(X)&~calm(X))))&
(![X]:(~brave(X)=>~rich(X)))&
(![X]:(happy(X)<=>(patient(X)<~>old(X))))&
(![X]:((generous(X)|~generous(X))<=>strong(X)))&
((~funny(john))<=>((~tall(susan)&kind(susan))))&
(![X]:(~brave(X)=>(creative(X)<~>curious(X))))&
((?[X]:((curious(X)|humble(X))))=>(?[X]:((~humble(X)<~>strong(X)))))&
(((patient(mary)&calm(mary)))<=>(?[X]:(creative(X))))&
(((~strong(susan)&patient(susan)))<=>(?[X]:((~wise(X)<~>~tall(X)))))&
((?[X]:((~wise(X)&brave(X))))=>(~tall(alice)))&
(![X]:((wise(X)<~>~brave(X))=>(patient(X)&~creative(X))))&
((?[X]:((generous(X)&~creative(X))))=>((~quiet(john)<~>happy(john))))&
((kind(fred))=>((generous(lucy)&quiet(lucy))))&
((~tall(fred)&kind(fred)))&
(?[X]:((~generous(X)|~kind(X))))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:((~curious(X)<~>calm(X))))&
(?[X]:((old(X)|patient(X))))&
((~happy(susan)<~>~brave(susan)))&
((~rich(john)&~quiet(john)))&
(~calm(paul)) | ~wise(fred) | [
"p6",
"p11",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8787741668639232892782651
% SZS output start Proof for 8787741668639232892782651
7. ! [X0] : ((~generous(X0) | generous(X0)) <=> strong(X0)) [input p6]
12. (patient(susan) & ~strong(susan)) <=> ? [X0] : (~wise(X0) <~> ~tall(X0)) [input p11]
17. kind(fred) & ~tall(fred) [input p16]
25. wise(fred) [input hypothesis]
46. ! [X0] : (((~generous(X0) | generous(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & ~generous(X0)))) [nnf transformation 7]
47. ! [X0] : ((~generous(X0) | generous(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & ~generous(X0)))) [flattening 46]
60. ((patient(susan) & ~strong(susan)) | ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (? [X0] : ((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | (~patient(susan) | strong(susan))) [nnf transformation 12]
61. ((patient(susan) & ~strong(susan)) | ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (? [X0] : ((tall(X0) | wise(X0)) & (~tall(X0) | ~wise(X0))) | ~patient(susan) | strong(susan)) [flattening 60]
62. ((patient(susan) & ~strong(susan)) | ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (? [X1] : ((tall(X1) | wise(X1)) & (~tall(X1) | ~wise(X1))) | ~patient(susan) | strong(susan)) [rectify 61]
63. ? [X1] : ((tall(X1) | wise(X1)) & (~tall(X1) | ~wise(X1))) => ((tall(sK3) | wise(sK3)) & (~tall(sK3) | ~wise(sK3))) [choice axiom]
64. ((patient(susan) & ~strong(susan)) | ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0)))) & (((tall(sK3) | wise(sK3)) & (~tall(sK3) | ~wise(sK3))) | ~patient(susan) | strong(susan)) [skolemisation 62,63]
92. strong(X0) | ~generous(X0) [cnf transformation 47]
93. generous(X0) | strong(X0) [cnf transformation 47]
110. ~strong(susan) | ~wise(X0) | tall(X0) [cnf transformation 64]
122. ~tall(fred) [cnf transformation 17]
134. wise(fred) [cnf transformation 25]
143. strong(X0) [subsumption resolution 92,93]
192. 13 <=> ! [X0] : (~wise(X0) | tall(X0)) [avatar definition]
193. ~wise(X0) | tall(X0) <- (13) [avatar component clause 192]
203. ~wise(X0) | tall(X0) [subsumption resolution 110,143]
204. 13 [avatar split clause 203,192]
282. tall(fred) <- (13) [resolution 193,134]
283. $false <- (13) [subsumption resolution 282,122]
284. ~13 [avatar contradiction clause 283]
285. $false [avatar sat refutation 204,284]
% SZS output end Proof for 8787741668639232892782651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or old is both wise and not quiet and vice versa. Everyone who is quiet or not brave is not happy or wise and vice versa. If paul is tall or old then susan is both generous and not old and vice versa. If susan is rich or not funny then alice is happy or not generous and vice versa. Everyone who is not humble or not calm is both not wise and brave and vice versa. Everyone who is either brave or not patient is not calm. Everyone who is not rich or kind is either not tall or kind and vice versa. Everyone who is not quiet is either not humble or happy and vice versa. If lucy is either creative or not wise then alice is not funny or strong and vice versa. If john is both patient and tall then someone is both not patient and tall. Everyone who is strong or kind is happy and vice versa. Everyone who is funny is both tall and brave. Everyone who is either not calm or strong is not strong. Everyone who is happy or not creative is both brave and not generous. If john is both not strong and strong then someone is brave or generous. Everyone who is not funny is both not kind and patient and vice versa. Someone is creative. Someone is tall. Someone is quiet. Someone is not calm or rich. | John is not calm. | entailment | (![X]:((calm(X)|old(X))<=>(wise(X)&~quiet(X))))&
(![X]:((quiet(X)|~brave(X))<=>(~happy(X)|wise(X))))&
(((tall(paul)|old(paul)))<=>((generous(susan)&~old(susan))))&
(((rich(susan)|~funny(susan)))<=>((happy(alice)|~generous(alice))))&
(![X]:((~humble(X)|~calm(X))<=>(~wise(X)&brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>~calm(X)))&
(![X]:((~rich(X)|kind(X))<=>(~tall(X)<~>kind(X))))&
(![X]:(~quiet(X)<=>(~humble(X)<~>happy(X))))&
(((creative(lucy)<~>~wise(lucy)))<=>((~funny(alice)|strong(alice))))&
(((patient(john)&tall(john)))=>(?[X]:((~patient(X)&tall(X)))))&
(![X]:((strong(X)|kind(X))<=>happy(X)))&
(![X]:(funny(X)=>(tall(X)&brave(X))))&
(![X]:((~calm(X)<~>strong(X))=>~strong(X)))&
(![X]:((happy(X)|~creative(X))=>(brave(X)&~generous(X))))&
(((~strong(john)&strong(john)))=>(?[X]:((brave(X)|generous(X)))))&
(![X]:(~funny(X)<=>(~kind(X)&patient(X))))&
(?[X]:(creative(X)))&
(?[X]:(tall(X)))&
(?[X]:(quiet(X)))&
(?[X]:((~calm(X)|rich(X)))) | ~calm(john) | [
"p0",
"p1",
"p4",
"p7",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 3016586381247742479551179
% SZS output start Proof for 3016586381247742479551179
1. ! [X0] : ((old(X0) | calm(X0)) <=> (~quiet(X0) & wise(X0))) [input p0]
2. ! [X0] : ((~brave(X0) | quiet(X0)) <=> (wise(X0) | ~happy(X0))) [input p1]
5. ! [X0] : ((~calm(X0) | ~humble(X0)) <=> (brave(X0) & ~wise(X0))) [input p4]
8. ! [X0] : (~quiet(X0) <=> (~humble(X0) <~> happy(X0))) [input p7]
14. ! [X0] : ((~creative(X0) | happy(X0)) => (~generous(X0) & brave(X0))) [input p13]
21. calm(john) [input hypothesis]
27. ! [X0] : ((~generous(X0) & brave(X0)) | (creative(X0) & ~happy(X0))) [ennf transformation 14]
30. ! [X0] : (((old(X0) | calm(X0)) | (quiet(X0) | ~wise(X0))) & ((~quiet(X0) & wise(X0)) | (~old(X0) & ~calm(X0)))) [nnf transformation 1]
31. ! [X0] : ((old(X0) | calm(X0) | quiet(X0) | ~wise(X0)) & ((~quiet(X0) & wise(X0)) | (~old(X0) & ~calm(X0)))) [flattening 30]
32. ! [X0] : (((~brave(X0) | quiet(X0)) | (~wise(X0) & happy(X0))) & ((wise(X0) | ~happy(X0)) | (brave(X0) & ~quiet(X0)))) [nnf transformation 2]
33. ! [X0] : ((~brave(X0) | quiet(X0) | (~wise(X0) & happy(X0))) & (wise(X0) | ~happy(X0) | (brave(X0) & ~quiet(X0)))) [flattening 32]
38. ! [X0] : (((~calm(X0) | ~humble(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [nnf transformation 5]
39. ! [X0] : ((~calm(X0) | ~humble(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | (calm(X0) & humble(X0)))) [flattening 38]
43. ! [X0] : ((~quiet(X0) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0)))) & (((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | quiet(X0))) [nnf transformation 8]
63. ~calm(X0) | wise(X0) [cnf transformation 31]
65. ~quiet(X0) | ~calm(X0) [cnf transformation 31]
71. ~brave(X0) | quiet(X0) | ~wise(X0) [cnf transformation 33]
81. ~wise(X0) | humble(X0) [cnf transformation 39]
94. ~humble(X0) | happy(X0) | quiet(X0) [cnf transformation 43]
113. ~happy(X0) | brave(X0) [cnf transformation 27]
125. calm(john) [cnf transformation 21]
220. wise(john) [resolution 63,125]
223. humble(john) [resolution 81,220]
253. happy(john) | quiet(john) [resolution 94,223]
257. 23 <=> quiet(john) [avatar definition]
258. ~quiet(john) <- (~23) [avatar component clause 257]
259. quiet(john) <- (23) [avatar component clause 257]
261. 24 <=> happy(john) [avatar definition]
263. happy(john) <- (24) [avatar component clause 261]
264. 23 | 24 [avatar split clause 253,261,257]
267. ~calm(john) <- (23) [resolution 259,65]
268. $false <- (23) [subsumption resolution 267,125]
269. ~23 [avatar contradiction clause 268]
294. brave(john) <- (24) [resolution 263,113]
305. quiet(john) | ~wise(john) <- (24) [resolution 294,71]
307. ~wise(john) <- (~23, 24) [subsumption resolution 305,258]
308. $false <- (~23, 24) [subsumption resolution 307,220]
309. 23 | ~24 [avatar contradiction clause 308]
310. $false [avatar sat refutation 264,269,309]
% SZS output end Proof for 3016586381247742479551179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not patient or not creative then mary is happy.
If mary is either not strong or kind then someone is both calm and not generous.
Everyone who is either not brave or creative is strong or patient.
Everyone who is not strong is not funny and vice versa.
If someone is wise then fred is either not calm or creative and vice versa.
If paul is not wise then lucy is both rich and not happy.
If paul is both generous and calm then fred is brave or quiet and vice versa.
If someone is both quiet and not happy then john is both not creative and curious and vice versa.
Everyone who is either not curious or tall is both strong and not rich.
If someone is not calm or not kind then fred is humble.
Everyone who is both not rich and not kind is both humble and not happy.
If someone is not creative or not humble then susan is either not funny or not strong.
Everyone who is either curious or not calm is both not brave and not creative.
Everyone who is not calm is not brave and vice versa.
If someone is strong then john is both strong and old.
Everyone who is both not funny and not kind is both humble and creative and vice versa.
Lucy is both calm and not curious.
Alice is tall or old.
Fred is not humble or humble.
Someone is not creative or not funny.
Paul is old.
Someone is not curious or not patient.
Someone is not curious.
Someone is either happy or not patient. | Fred is not kind. | entailment | (((~patient(fred)<~>~creative(fred)))=>(happy(mary)))&
(((~strong(mary)<~>kind(mary)))=>(?[X]:((calm(X)&~generous(X)))))&
(![X]:((~brave(X)<~>creative(X))=>(strong(X)|patient(X))))&
(![X]:(~strong(X)<=>~funny(X)))&
((?[X]:(wise(X)))<=>((~calm(fred)<~>creative(fred))))&
((~wise(paul))=>((rich(lucy)&~happy(lucy))))&
(((generous(paul)&calm(paul)))<=>((brave(fred)|quiet(fred))))&
((?[X]:((quiet(X)&~happy(X))))<=>((~creative(john)&curious(john))))&
(![X]:((~curious(X)<~>tall(X))=>(strong(X)&~rich(X))))&
((?[X]:((~calm(X)|~kind(X))))=>(humble(fred)))&
(![X]:((~rich(X)&~kind(X))=>(humble(X)&~happy(X))))&
((?[X]:((~creative(X)|~humble(X))))=>((~funny(susan)<~>~strong(susan))))&
(![X]:((curious(X)<~>~calm(X))=>(~brave(X)&~creative(X))))&
(![X]:(~calm(X)<=>~brave(X)))&
((?[X]:(strong(X)))=>((strong(john)&old(john))))&
(![X]:((~funny(X)&~kind(X))<=>(humble(X)&creative(X))))&
((calm(lucy)&~curious(lucy)))&
((tall(alice)|old(alice)))&
((~humble(fred)|humble(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(old(paul))&
(?[X]:((~curious(X)|~patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((happy(X)<~>~patient(X)))) | ~kind(fred) | [
"p3",
"p11",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 26098516208773751742228
% SZS output start Proof for 26098516208773751742228
4. ! [X0] : (~strong(X0) <=> ~funny(X0)) [input p3]
12. ? [X0] : (~humble(X0) | ~creative(X0)) => (~funny(susan) <~> ~strong(susan)) [input p11]
16. ! [X0] : ((~kind(X0) & ~funny(X0)) <=> (creative(X0) & humble(X0))) [input p15]
25. kind(fred) [input hypothesis]
38. (~funny(susan) <~> ~strong(susan)) | ! [X0] : (humble(X0) & creative(X0)) [ennf transformation 12]
46. ! [X0] : ((~strong(X0) | funny(X0)) & (~funny(X0) | strong(X0))) [nnf transformation 4]
59. ((strong(susan) | funny(susan)) & (~strong(susan) | ~funny(susan))) | ! [X0] : (humble(X0) & creative(X0)) [nnf transformation 38]
62. ! [X0] : (((~kind(X0) & ~funny(X0)) | (~creative(X0) | ~humble(X0))) & ((creative(X0) & humble(X0)) | (kind(X0) | funny(X0)))) [nnf transformation 16]
63. ! [X0] : (((~kind(X0) & ~funny(X0)) | ~creative(X0) | ~humble(X0)) & ((creative(X0) & humble(X0)) | kind(X0) | funny(X0))) [flattening 62]
81. ~funny(X0) | strong(X0) [cnf transformation 46]
82. ~strong(X0) | funny(X0) [cnf transformation 46]
106. ~strong(susan) | ~funny(susan) | creative(X0) [cnf transformation 59]
107. ~strong(susan) | ~funny(susan) | humble(X0) [cnf transformation 59]
108. strong(susan) | funny(susan) | creative(X0) [cnf transformation 59]
109. strong(susan) | funny(susan) | humble(X0) [cnf transformation 59]
120. ~humble(X0) | ~creative(X0) | ~kind(X0) [cnf transformation 63]
129. kind(fred) [cnf transformation 25]
249. funny(susan) | humble(X0) [subsumption resolution 109,82]
251. 26 <=> ! [X0] : humble(X0) [avatar definition]
252. humble(X0) <- (26) [avatar component clause 251]
254. 27 <=> funny(susan) [avatar definition]
257. 26 | 27 [avatar split clause 249,254,251]
258. funny(susan) | creative(X0) [subsumption resolution 108,82]
260. 28 <=> ! [X0] : creative(X0) [avatar definition]
261. creative(X0) <- (28) [avatar component clause 260]
262. 28 | 27 [avatar split clause 258,254,260]
263. ~funny(susan) | humble(X0) [subsumption resolution 107,81]
264. 26 | ~27 [avatar split clause 263,254,251]
265. ~funny(susan) | creative(X0) [subsumption resolution 106,81]
266. 28 | ~27 [avatar split clause 265,254,260]
359. ~creative(X2) | ~kind(X2) <- (26) [resolution 120,252]
360. ~kind(X2) <- (26, 28) [subsumption resolution 359,261]
361. $false <- (26, 28) [resolution 360,129]
366. ~26 | ~28 [avatar contradiction clause 361]
367. $false [avatar sat refutation 257,262,264,266,366]
% SZS output end Proof for 26098516208773751742228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then someone is either not old or not rich and vice versa.
Everyone who is either tall or brave is both not humble and humble and vice versa.
If mary is either humble or kind then someone is both humble and generous.
If someone is not funny then paul is either not calm or not tall.
If fred is either brave or happy then someone is not funny or not generous and vice versa.
Everyone who is funny is both not funny and not generous and vice versa.
Everyone who is either curious or not strong is either not calm or old and vice versa.
Everyone who is not funny is either not curious or not happy.
If someone is happy or quiet then someone is both funny and calm and vice versa.
If mary is either funny or humble then susan is either not tall or not generous and vice versa.
If fred is not funny or patient then someone is not old and vice versa.
If paul is quiet or humble then someone is either not rich or not patient and vice versa.
Everyone who is not kind or rich is creative.
Everyone who is both calm and not creative is either generous or not calm.
Everyone who is either tall or wise is tall.
Everyone who is old or not rich is either wise or strong.
Alice is not old or not strong.
John is not funny.
Someone is either not rich or humble.
Someone is not humble.
Alice is wise.
Mary is calm. | Paul is not patient. | neutral | ((?[X]:(~old(X)))<=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~humble(X)&humble(X))))&
(((humble(mary)<~>kind(mary)))=>(?[X]:((humble(X)&generous(X)))))&
((?[X]:(~funny(X)))=>((~calm(paul)<~>~tall(paul))))&
(((brave(fred)<~>happy(fred)))<=>(?[X]:((~funny(X)|~generous(X)))))&
(![X]:(funny(X)<=>(~funny(X)&~generous(X))))&
(![X]:((curious(X)<~>~strong(X))<=>(~calm(X)<~>old(X))))&
(![X]:(~funny(X)=>(~curious(X)<~>~happy(X))))&
((?[X]:((happy(X)|quiet(X))))<=>(?[X]:((funny(X)&calm(X)))))&
(((funny(mary)<~>humble(mary)))<=>((~tall(susan)<~>~generous(susan))))&
(((~funny(fred)|patient(fred)))<=>(?[X]:(~old(X))))&
(((quiet(paul)|humble(paul)))<=>(?[X]:((~rich(X)<~>~patient(X)))))&
(![X]:((~kind(X)|rich(X))=>creative(X)))&
(![X]:((calm(X)&~creative(X))=>(generous(X)<~>~calm(X))))&
(![X]:((tall(X)<~>wise(X))=>tall(X)))&
(![X]:((old(X)|~rich(X))=>(wise(X)<~>strong(X))))&
((~old(alice)|~strong(alice)))&
(~funny(john))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:(~humble(X)))&
(wise(alice))&
(calm(mary)) | ~patient(paul) | []
| null | 0 |
Everyone who is either not wise or humble is not generous and vice versa. If john is both tall and strong then mary is not quiet or not humble and vice versa. If someone is funny or happy then alice is kind or rich. If someone is either tall or not quiet then mary is either old or not humble and vice versa. Everyone who is either happy or brave is either not creative or kind. Everyone who is not strong or brave is not humble or not happy and vice versa. If paul is either quiet or not old then susan is tall or not generous and vice versa. Everyone who is not curious is not kind or rich and vice versa. Everyone who is calm is both not humble and rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Someone is not kind or creative. Lucy is not kind or not patient. John is either generous or wise. | Alice is happy. | entailment | (![X]:((~wise(X)<~>humble(X))<=>~generous(X)))&
(((tall(john)&strong(john)))<=>((~quiet(mary)|~humble(mary))))&
((?[X]:((funny(X)|happy(X))))=>((kind(alice)|rich(alice))))&
((?[X]:((tall(X)<~>~quiet(X))))<=>((old(mary)<~>~humble(mary))))&
(![X]:((happy(X)<~>brave(X))=>(~creative(X)<~>kind(X))))&
(![X]:((~strong(X)|brave(X))<=>(~humble(X)|~happy(X))))&
(((quiet(paul)<~>~old(paul)))<=>((tall(susan)|~generous(susan))))&
(![X]:(~curious(X)<=>(~kind(X)|rich(X))))&
(![X]:(calm(X)<=>(~humble(X)&rich(X))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(?[X]:((~kind(X)|creative(X))))&
((~kind(lucy)|~patient(lucy)))&
((generous(john)<~>wise(john))) | happy(alice) | [
"p5",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 41359928698282825721632
% SZS output start Proof for 41359928698282825721632
6. ! [X0] : ((brave(X0) | ~strong(X0)) <=> (~happy(X0) | ~humble(X0))) [input p5]
11. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p10]
12. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p11]
20. ~happy(alice) [input hypothesis]
25. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 11]
38. ! [X0] : (((brave(X0) | ~strong(X0)) | (happy(X0) & humble(X0))) & ((~happy(X0) | ~humble(X0)) | (~brave(X0) & strong(X0)))) [nnf transformation 6]
39. ! [X0] : ((brave(X0) | ~strong(X0) | (happy(X0) & humble(X0))) & (~happy(X0) | ~humble(X0) | (~brave(X0) & strong(X0)))) [flattening 38]
48. ! [X0] : ((strong(X0) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [nnf transformation 12]
49. ! [X0] : ((strong(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | ~strong(X0))) [flattening 48]
81. ~strong(X0) | brave(X0) | happy(X0) [cnf transformation 39]
100. strong(X0) | brave(X0) [cnf transformation 25]
101. ~brave(X0) | strong(X0) [cnf transformation 25]
103. ~brave(X0) | ~strong(X0) [cnf transformation 49]
123. ~happy(alice) [cnf transformation 20]
205. strong(X0) [subsumption resolution 100,101]
207. ~brave(X0) [subsumption resolution 103,205]
237. brave(X0) | happy(X0) [resolution 81,205]
238. happy(X0) [subsumption resolution 237,207]
253. $false [resolution 238,123]
% SZS output end Proof for 41359928698282825721632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is old then someone is either rich or not old.
Everyone who is either not old or kind is not generous or calm and vice versa.
Everyone who is both old and not humble is both not tall and patient and vice versa.
If someone is both not wise and not happy then someone is either not strong or tall.
Everyone who is calm or humble is both brave and happy.
If lucy is not humble or strong then susan is wise.
If someone is both not old and old then someone is both brave and humble.
Everyone who is either not tall or not calm is both not kind and not calm and vice versa.
Everyone who is either not calm or quiet is both happy and not funny.
Everyone who is both rich and kind is either not patient or happy.
Everyone who is either brave or not quiet is both brave and patient.
If alice is creative then paul is either not calm or strong.
Everyone who is not patient is both rich and not happy and vice versa.
If someone is both kind and not generous then alice is both wise and funny.
If someone is both not old and quiet then someone is both funny and happy.
Everyone who is brave is either not strong or not old and vice versa.
Lucy is both not wise and not quiet.
Susan is humble.
Fred is strong.
Susan is either not calm or calm.
Someone is not humble or not rich.
John is both not brave and not strong.
Someone is not patient.
Fred is either funny or not quiet. | John is strong. | contradiction | ((old(susan))=>(?[X]:((rich(X)<~>~old(X)))))&
(![X]:((~old(X)<~>kind(X))<=>(~generous(X)|calm(X))))&
(![X]:((old(X)&~humble(X))<=>(~tall(X)&patient(X))))&
((?[X]:((~wise(X)&~happy(X))))=>(?[X]:((~strong(X)<~>tall(X)))))&
(![X]:((calm(X)|humble(X))=>(brave(X)&happy(X))))&
(((~humble(lucy)|strong(lucy)))=>(wise(susan)))&
((?[X]:((~old(X)&old(X))))=>(?[X]:((brave(X)&humble(X)))))&
(![X]:((~tall(X)<~>~calm(X))<=>(~kind(X)&~calm(X))))&
(![X]:((~calm(X)<~>quiet(X))=>(happy(X)&~funny(X))))&
(![X]:((rich(X)&kind(X))=>(~patient(X)<~>happy(X))))&
(![X]:((brave(X)<~>~quiet(X))=>(brave(X)&patient(X))))&
((creative(alice))=>((~calm(paul)<~>strong(paul))))&
(![X]:(~patient(X)<=>(rich(X)&~happy(X))))&
((?[X]:((kind(X)&~generous(X))))=>((wise(alice)&funny(alice))))&
((?[X]:((~old(X)&quiet(X))))=>(?[X]:((funny(X)&happy(X)))))&
(![X]:(brave(X)<=>(~strong(X)<~>~old(X))))&
((~wise(lucy)&~quiet(lucy)))&
(humble(susan))&
(strong(fred))&
((~calm(susan)<~>calm(susan)))&
(?[X]:((~humble(X)|~rich(X))))&
((~brave(john)&~strong(john)))&
(?[X]:(~patient(X)))&
((funny(fred)<~>~quiet(fred))) | strong(john) | [
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5887508090966967664219381
% SZS output start Proof for 5887508090966967664219381
22. ~strong(john) & ~brave(john) [input p21]
25. strong(john) [input hypothesis]
129. ~strong(john) [cnf transformation 22]
133. strong(john) [cnf transformation 25]
224. $false [subsumption resolution 133,129]
% SZS output end Proof for 5887508090966967664219381
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and not creative is kind or not patient. If mary is rich then someone is both not rich and not wise and vice versa. Everyone who is either old or not brave is both not humble and humble. Everyone who is not generous is either rich or happy and vice versa. Everyone who is either not calm or not curious is kind and vice versa. Everyone who is rich is both happy and not wise and vice versa. If someone is both quiet and not wise then alice is happy or not strong. Everyone who is either brave or calm is both strong and not strong and vice versa. If someone is both kind and not generous then john is either not humble or wise and vice versa. Everyone who is not curious is strong or calm. Everyone who is not generous or curious is either humble or not calm. Everyone who is not curious or brave is either not tall or strong. If someone is creative then someone is both not quiet and not humble and vice versa. Everyone who is either brave or old is quiet or calm. If someone is both not calm and tall then someone is both creative and not strong and vice versa. Everyone who is both wise and not quiet is rich and vice versa. Someone is either not brave or not creative. Alice is funny or not creative. Alice is creative or strong. Fred is either wise or generous. Someone is not kind or old. Mary is calm or not generous. Fred is both calm and curious. Mary is humble. | John is not old. | neutral | (![X]:((creative(X)&~creative(X))=>(kind(X)|~patient(X))))&
((rich(mary))<=>(?[X]:((~rich(X)&~wise(X)))))&
(![X]:((old(X)<~>~brave(X))=>(~humble(X)&humble(X))))&
(![X]:(~generous(X)<=>(rich(X)<~>happy(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>kind(X)))&
(![X]:(rich(X)<=>(happy(X)&~wise(X))))&
((?[X]:((quiet(X)&~wise(X))))=>((happy(alice)|~strong(alice))))&
(![X]:((brave(X)<~>calm(X))<=>(strong(X)&~strong(X))))&
((?[X]:((kind(X)&~generous(X))))<=>((~humble(john)<~>wise(john))))&
(![X]:(~curious(X)=>(strong(X)|calm(X))))&
(![X]:((~generous(X)|curious(X))=>(humble(X)<~>~calm(X))))&
(![X]:((~curious(X)|brave(X))=>(~tall(X)<~>strong(X))))&
((?[X]:(creative(X)))<=>(?[X]:((~quiet(X)&~humble(X)))))&
(![X]:((brave(X)<~>old(X))=>(quiet(X)|calm(X))))&
((?[X]:((~calm(X)&tall(X))))<=>(?[X]:((creative(X)&~strong(X)))))&
(![X]:((wise(X)&~quiet(X))<=>rich(X)))&
(?[X]:((~brave(X)<~>~creative(X))))&
((funny(alice)|~creative(alice)))&
((creative(alice)|strong(alice)))&
((wise(fred)<~>generous(fred)))&
(?[X]:((~kind(X)|old(X))))&
((calm(mary)|~generous(mary)))&
((calm(fred)&curious(fred)))&
(humble(mary)) | ~old(john) | []
| null | 0 |
Everyone who is either old or not old is either humble or kind and vice versa.
Everyone who is not kind is both brave and creative and vice versa.
Everyone who is both strong and not strong is both not kind and not strong and vice versa.
Everyone who is either not funny or not curious is either strong or quiet and vice versa.
If someone is not old then lucy is humble.
If someone is funny then someone is either patient or kind and vice versa.
Everyone who is both brave and creative is not quiet or generous and vice versa.
Everyone who is both quiet and not brave is not creative and vice versa.
Everyone who is both happy and strong is patient.
Everyone who is calm or not rich is not humble and vice versa.
Everyone who is both not quiet and old is both not creative and not wise and vice versa.
If susan is either quiet or creative then susan is either not patient or rich and vice versa.
Everyone who is not happy is either not patient or patient.
Everyone who is old is either not strong or not old and vice versa.
Everyone who is not curious is either not generous or not creative.
Someone is not generous or humble.
Someone is not tall.
Someone is both not humble and not happy.
Lucy is not rich or not patient.
Alice is wise or not kind.
Lucy is not wise or wise. | Susan is not calm. | contradiction | (![X]:((old(X)<~>~old(X))<=>(humble(X)<~>kind(X))))&
(![X]:(~kind(X)<=>(brave(X)&creative(X))))&
(![X]:((strong(X)&~strong(X))<=>(~kind(X)&~strong(X))))&
(![X]:((~funny(X)<~>~curious(X))<=>(strong(X)<~>quiet(X))))&
((?[X]:(~old(X)))=>(humble(lucy)))&
((?[X]:(funny(X)))<=>(?[X]:((patient(X)<~>kind(X)))))&
(![X]:((brave(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((quiet(X)&~brave(X))<=>~creative(X)))&
(![X]:((happy(X)&strong(X))=>patient(X)))&
(![X]:((calm(X)|~rich(X))<=>~humble(X)))&
(![X]:((~quiet(X)&old(X))<=>(~creative(X)&~wise(X))))&
(((quiet(susan)<~>creative(susan)))<=>((~patient(susan)<~>rich(susan))))&
(![X]:(~happy(X)=>(~patient(X)<~>patient(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~old(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~creative(X))))&
(?[X]:((~generous(X)|humble(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~humble(X)&~happy(X))))&
((~rich(lucy)|~patient(lucy)))&
((wise(alice)|~kind(alice)))&
((~wise(lucy)|wise(lucy))) | ~calm(susan) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p6",
"p7",
"p9",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3092555933738909705280795
% SZS output start Proof for 3092555933738909705280795
1. ! [X0] : ((old(X0) <~> ~old(X0)) <=> (humble(X0) <~> kind(X0))) [input p0]
2. ! [X0] : (~kind(X0) <=> (creative(X0) & brave(X0))) [input p1]
3. ! [X0] : ((~strong(X0) & strong(X0)) <=> (~strong(X0) & ~kind(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> ~curious(X0)) <=> (strong(X0) <~> quiet(X0))) [input p3]
5. ? [X0] : ~old(X0) => humble(lucy) [input p4]
6. ? [X0] : funny(X0) <=> ? [X0] : (patient(X0) <~> kind(X0)) [input p5]
7. ! [X0] : ((creative(X0) & brave(X0)) <=> (generous(X0) | ~quiet(X0))) [input p6]
8. ! [X0] : ((~brave(X0) & quiet(X0)) <=> ~creative(X0)) [input p7]
10. ! [X0] : ((~rich(X0) | calm(X0)) <=> ~humble(X0)) [input p9]
11. ! [X0] : ((old(X0) & ~quiet(X0)) <=> (~wise(X0) & ~creative(X0))) [input p10]
12. (quiet(susan) <~> creative(susan)) <=> (~patient(susan) <~> rich(susan)) [input p11]
14. ! [X0] : (old(X0) <=> (~strong(X0) <~> ~old(X0))) [input p13]
15. ! [X0] : (~curious(X0) => (~generous(X0) <~> ~creative(X0))) [input p14]
22. ~calm(susan) [input hypothesis]
23. ? [X0] : funny(X0) <=> ? [X1] : (patient(X1) <~> kind(X1)) [rectify 6]
25. humble(lucy) | ! [X0] : old(X0) [ennf transformation 5]
29. ! [X0] : ((~generous(X0) <~> ~creative(X0)) | curious(X0)) [ennf transformation 15]
30. ! [X0] : ((((old(X0) | ~old(X0)) & (~old(X0) | old(X0))) | ((humble(X0) | ~kind(X0)) & (kind(X0) | ~humble(X0)))) & (((~kind(X0) | ~humble(X0)) & (kind(X0) | humble(X0))) | ((old(X0) | old(X0)) & (~old(X0) | ~old(X0))))) [nnf transformation 1]
31. ! [X0] : ((~kind(X0) | (~creative(X0) | ~brave(X0))) & ((creative(X0) & brave(X0)) | kind(X0))) [nnf transformation 2]
32. ! [X0] : ((~kind(X0) | ~creative(X0) | ~brave(X0)) & ((creative(X0) & brave(X0)) | kind(X0))) [flattening 31]
33. ! [X0] : (((~strong(X0) & strong(X0)) | (strong(X0) | kind(X0))) & ((~strong(X0) & ~kind(X0)) | (strong(X0) | ~strong(X0)))) [nnf transformation 3]
34. ! [X0] : (((~strong(X0) & strong(X0)) | strong(X0) | kind(X0)) & ((~strong(X0) & ~kind(X0)) | strong(X0) | ~strong(X0))) [flattening 33]
35. ! [X0] : ((((curious(X0) | funny(X0)) & (~curious(X0) | ~funny(X0))) | ((strong(X0) | ~quiet(X0)) & (quiet(X0) | ~strong(X0)))) & (((~quiet(X0) | ~strong(X0)) & (quiet(X0) | strong(X0))) | ((~funny(X0) | curious(X0)) & (~curious(X0) | funny(X0))))) [nnf transformation 4]
36. (? [X0] : funny(X0) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1)))) & (? [X1] : ((~kind(X1) | ~patient(X1)) & (kind(X1) | patient(X1))) | ! [X0] : ~funny(X0)) [nnf transformation 23]
37. (? [X0] : funny(X0) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1)))) & (? [X2] : ((~kind(X2) | ~patient(X2)) & (kind(X2) | patient(X2))) | ! [X3] : ~funny(X3)) [rectify 36]
38. ? [X0] : funny(X0) => funny(sK0) [choice axiom]
39. ? [X2] : ((~kind(X2) | ~patient(X2)) & (kind(X2) | patient(X2))) => ((~kind(sK1) | ~patient(sK1)) & (kind(sK1) | patient(sK1))) [choice axiom]
40. (funny(sK0) | ! [X1] : ((patient(X1) | ~kind(X1)) & (kind(X1) | ~patient(X1)))) & (((~kind(sK1) | ~patient(sK1)) & (kind(sK1) | patient(sK1))) | ! [X3] : ~funny(X3)) [skolemisation 37,39,38]
41. ! [X0] : (((creative(X0) & brave(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~creative(X0) | ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : (((creative(X0) & brave(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0) | ~brave(X0))) [flattening 41]
43. ! [X0] : (((~brave(X0) & quiet(X0)) | creative(X0)) & (~creative(X0) | (brave(X0) | ~quiet(X0)))) [nnf transformation 8]
44. ! [X0] : (((~brave(X0) & quiet(X0)) | creative(X0)) & (~creative(X0) | brave(X0) | ~quiet(X0))) [flattening 43]
45. ! [X0] : (((~rich(X0) | calm(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) & ~calm(X0)))) [nnf transformation 10]
46. ! [X0] : ((~rich(X0) | calm(X0) | humble(X0)) & (~humble(X0) | (rich(X0) & ~calm(X0)))) [flattening 45]
47. ! [X0] : (((old(X0) & ~quiet(X0)) | (wise(X0) | creative(X0))) & ((~wise(X0) & ~creative(X0)) | (~old(X0) | quiet(X0)))) [nnf transformation 11]
48. ! [X0] : (((old(X0) & ~quiet(X0)) | wise(X0) | creative(X0)) & ((~wise(X0) & ~creative(X0)) | ~old(X0) | quiet(X0))) [flattening 47]
49. (((~creative(susan) | ~quiet(susan)) & (creative(susan) | quiet(susan))) | ((~patient(susan) | ~rich(susan)) & (rich(susan) | patient(susan)))) & (((~rich(susan) | patient(susan)) & (rich(susan) | ~patient(susan))) | ((quiet(susan) | ~creative(susan)) & (creative(susan) | ~quiet(susan)))) [nnf transformation 12]
51. ! [X0] : ((old(X0) | ((~strong(X0) | old(X0)) & (~old(X0) | strong(X0)))) & (((old(X0) | strong(X0)) & (~old(X0) | ~strong(X0))) | ~old(X0))) [nnf transformation 14]
52. ! [X0] : (((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | curious(X0)) [nnf transformation 29]
59. ~kind(X0) | ~humble(X0) | ~old(X0) | ~old(X0) [cnf transformation 30]
60. ~kind(X0) | ~humble(X0) | old(X0) | old(X0) [cnf transformation 30]
67. ~creative(X0) | ~kind(X0) | ~brave(X0) [cnf transformation 32]
70. strong(X0) | strong(X0) | kind(X0) [cnf transformation 34]
77. ~quiet(X0) | ~funny(X0) | strong(X0) | ~curious(X0) [cnf transformation 35]
80. humble(lucy) | old(X0) [cnf transformation 25]
84. funny(sK0) | patient(X1) | ~kind(X1) [cnf transformation 40]
86. quiet(X0) | brave(X0) [cnf transformation 42]
88. quiet(X0) | creative(X0) [cnf transformation 42]
89. ~generous(X0) | creative(X0) [cnf transformation 42]
90. ~creative(X0) | brave(X0) | ~quiet(X0) [cnf transformation 44]
96. ~rich(X0) | calm(X0) | humble(X0) [cnf transformation 46]
97. ~creative(X0) | ~old(X0) | quiet(X0) [cnf transformation 48]
101. rich(susan) | ~patient(susan) | creative(susan) | ~quiet(susan) [cnf transformation 49]
111. ~old(X0) | ~strong(X0) | ~old(X0) [cnf transformation 51]
114. old(X0) | ~strong(X0) | old(X0) [cnf transformation 51]
116. creative(X0) | generous(X0) | curious(X0) [cnf transformation 52]
123. ~calm(susan) [cnf transformation 22]
124. ~old(X0) | ~strong(X0) [duplicate literal removal 111]
125. ~strong(X0) | old(X0) [duplicate literal removal 114]
127. strong(X0) | kind(X0) [duplicate literal removal 70]
130. ~kind(X0) | ~humble(X0) | ~old(X0) [duplicate literal removal 59]
131. ~kind(X0) | ~humble(X0) | old(X0) [duplicate literal removal 60]
132. ~kind(X0) | ~humble(X0) [subsumption resolution 130,131]
135. 1 <=> ! [X0] : old(X0) [avatar definition]
136. old(X0) <- (1) [avatar component clause 135]
138. 2 <=> humble(lucy) [avatar definition]
140. humble(lucy) <- (2) [avatar component clause 138]
141. 1 | 2 [avatar split clause 80,138,135]
143. 3 <=> ! [X1] : (patient(X1) | ~kind(X1)) [avatar definition]
144. patient(X1) | ~kind(X1) <- (3) [avatar component clause 143]
146. 4 <=> funny(sK0) [avatar definition]
148. funny(sK0) <- (4) [avatar component clause 146]
149. 3 | 4 [avatar split clause 84,146,143]
167. ~creative(X0) | brave(X0) [subsumption resolution 90,86]
169. ~old(X0) | quiet(X0) [subsumption resolution 97,88]
171. 9 <=> rich(susan) [avatar definition]
172. rich(susan) <- (9) [avatar component clause 171]
175. 10 <=> patient(susan) [avatar definition]
177. ~patient(susan) <- (~10) [avatar component clause 175]
183. 12 <=> creative(susan) [avatar definition]
184. creative(susan) <- (12) [avatar component clause 183]
194. rich(susan) | ~patient(susan) | creative(susan) [subsumption resolution 101,88]
195. 12 | ~10 | 9 [avatar split clause 194,171,175,183]
196. ~strong(X0) [subsumption resolution 124,125]
197. curious(X0) | creative(X0) [subsumption resolution 116,89]
233. kind(X1) [resolution 127,196]
237. ~humble(X0) [resolution 233,132]
240. patient(X1) <- (3) [subsumption resolution 144,233]
241. $false <- (3, ~10) [resolution 240,177]
244. ~3 | 10 [avatar contradiction clause 241]
246. $false <- (2) [resolution 237,140]
247. ~2 [avatar contradiction clause 246]
249. quiet(X0) <- (1) [resolution 169,136]
275. ~funny(X0) | strong(X0) | ~curious(X0) <- (1) [resolution 77,249]
278. ~curious(X0) | ~funny(X0) <- (1) [subsumption resolution 275,196]
280. ~funny(X0) | creative(X0) <- (1) [resolution 278,197]
294. creative(sK0) <- (1, 4) [resolution 280,148]
295. ~kind(sK0) | ~brave(sK0) <- (1, 4) [resolution 294,67]
296. brave(sK0) <- (1, 4) [resolution 294,167]
297. ~brave(sK0) <- (1, 4) [subsumption resolution 295,233]
298. $false <- (1, 4) [subsumption resolution 296,297]
299. ~1 | ~4 [avatar contradiction clause 298]
301. calm(susan) | humble(susan) <- (9) [resolution 172,96]
302. humble(susan) <- (9) [subsumption resolution 301,123]
305. $false <- (9) [subsumption resolution 302,237]
306. ~9 [avatar contradiction clause 305]
309. ~kind(susan) | ~brave(susan) <- (12) [resolution 184,67]
310. brave(susan) <- (12) [resolution 184,167]
311. ~brave(susan) <- (12) [subsumption resolution 309,233]
312. $false <- (12) [subsumption resolution 310,311]
313. ~12 [avatar contradiction clause 312]
314. $false [avatar sat refutation 141,149,195,244,247,299,306,313]
% SZS output end Proof for 3092555933738909705280795
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not creative then someone is creative.
Everyone who is not tall or not calm is both rich and not humble and vice versa.
Everyone who is both generous and not wise is calm or not brave and vice versa.
If john is not wise or rich then someone is kind or not strong and vice versa.
If someone is either tall or calm then someone is humble or not rich.
Everyone who is humble is both curious and quiet and vice versa.
Everyone who is either not generous or not old is generous and vice versa.
Everyone who is both humble and not old is not curious.
Everyone who is both patient and generous is both not generous and not curious.
If someone is both rich and old then someone is not calm or patient.
If mary is rich then someone is funny or not calm.
If fred is brave then fred is both not patient and humble.
Everyone who is either not strong or quiet is both generous and not strong and vice versa.
If fred is both not generous and tall then someone is wise and vice versa.
If fred is either wise or not happy then alice is not wise or not patient and vice versa.
If someone is either generous or not quiet then someone is both curious and not curious.
Alice is not tall or generous.
John is either patient or creative.
Someone is both not quiet and generous.
Alice is either humble or quiet.
Someone is both strong and not curious.
Someone is either not kind or generous.
Someone is both not old and not wise.
Someone is not rich. | Alice is not curious. | entailment | ((?[X]:((~brave(X)|~creative(X))))=>(?[X]:(creative(X))))&
(![X]:((~tall(X)|~calm(X))<=>(rich(X)&~humble(X))))&
(![X]:((generous(X)&~wise(X))<=>(calm(X)|~brave(X))))&
(((~wise(john)|rich(john)))<=>(?[X]:((kind(X)|~strong(X)))))&
((?[X]:((tall(X)<~>calm(X))))=>(?[X]:((humble(X)|~rich(X)))))&
(![X]:(humble(X)<=>(curious(X)&quiet(X))))&
(![X]:((~generous(X)<~>~old(X))<=>generous(X)))&
(![X]:((humble(X)&~old(X))=>~curious(X)))&
(![X]:((patient(X)&generous(X))=>(~generous(X)&~curious(X))))&
((?[X]:((rich(X)&old(X))))=>(?[X]:((~calm(X)|patient(X)))))&
((rich(mary))=>(?[X]:((funny(X)|~calm(X)))))&
((brave(fred))=>((~patient(fred)&humble(fred))))&
(![X]:((~strong(X)<~>quiet(X))<=>(generous(X)&~strong(X))))&
(((~generous(fred)&tall(fred)))<=>(?[X]:(wise(X))))&
(((wise(fred)<~>~happy(fred)))<=>((~wise(alice)|~patient(alice))))&
((?[X]:((generous(X)<~>~quiet(X))))=>(?[X]:((curious(X)&~curious(X)))))&
((~tall(alice)|generous(alice)))&
((patient(john)<~>creative(john)))&
(?[X]:((~quiet(X)&generous(X))))&
((humble(alice)<~>quiet(alice)))&
(?[X]:((strong(X)&~curious(X))))&
(?[X]:((~kind(X)<~>generous(X))))&
(?[X]:((~old(X)&~wise(X))))&
(?[X]:(~rich(X))) | ~curious(alice) | [
"p5",
"p6",
"p7",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 7722075429161404060881905
% SZS output start Proof for 7722075429161404060881905
6. ! [X0] : (humble(X0) <=> (quiet(X0) & curious(X0))) [input p5]
7. ! [X0] : ((~generous(X0) <~> ~old(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : ((~old(X0) & humble(X0)) => ~curious(X0)) [input p7]
20. humble(alice) <~> quiet(alice) [input p19]
25. curious(alice) [input hypothesis]
33. ! [X0] : (~curious(X0) | (old(X0) | ~humble(X0))) [ennf transformation 8]
34. ! [X0] : (~curious(X0) | old(X0) | ~humble(X0)) [flattening 33]
56. ! [X0] : ((humble(X0) | (~quiet(X0) | ~curious(X0))) & ((quiet(X0) & curious(X0)) | ~humble(X0))) [nnf transformation 6]
57. ! [X0] : ((humble(X0) | ~quiet(X0) | ~curious(X0)) & ((quiet(X0) & curious(X0)) | ~humble(X0))) [flattening 56]
58. ! [X0] : ((((old(X0) | generous(X0)) & (~old(X0) | ~generous(X0))) | ~generous(X0)) & (generous(X0) | ((~generous(X0) | old(X0)) & (~old(X0) | generous(X0))))) [nnf transformation 7]
78. (~quiet(alice) | ~humble(alice)) & (quiet(alice) | humble(alice)) [nnf transformation 20]
106. ~humble(X0) | curious(X0) [cnf transformation 57]
108. ~quiet(X0) | humble(X0) | ~curious(X0) [cnf transformation 57]
109. generous(X0) | ~old(X0) | generous(X0) [cnf transformation 58]
111. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 58]
113. ~curious(X0) | old(X0) | ~humble(X0) [cnf transformation 34]
143. quiet(alice) | humble(alice) [cnf transformation 78]
152. curious(alice) [cnf transformation 25]
156. generous(X0) | ~old(X0) [duplicate literal removal 109]
157. ~old(X0) | ~generous(X0) [duplicate literal removal 111]
212. ~old(X0) [subsumption resolution 156,157]
213. ~curious(X0) | ~humble(X0) [subsumption resolution 113,212]
214. ~humble(X0) [subsumption resolution 213,106]
289. quiet(alice) [subsumption resolution 143,214]
316. humble(alice) | ~curious(alice) [resolution 108,289]
318. ~curious(alice) [subsumption resolution 316,214]
319. $false [subsumption resolution 318,152]
% SZS output end Proof for 7722075429161404060881905
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both curious and rich then john is not happy or not humble and vice versa.
Everyone who is calm or not creative is both patient and not kind.
Everyone who is happy or not generous is tall or not generous and vice versa.
If someone is humble or tall then john is not funny and vice versa.
If john is not rich or not tall then someone is either generous or not strong.
Everyone who is either not patient or brave is both not generous and not humble.
Everyone who is both not calm and old is either happy or calm and vice versa.
If someone is not humble or tall then someone is both strong and not patient and vice versa.
If someone is both not strong and brave then someone is either not quiet or not old.
If susan is both not generous and not patient then john is both quiet and curious.
If someone is both happy and funny then someone is calm.
If fred is both creative and curious then lucy is not strong or not funny and vice versa.
If someone is both happy and not old then mary is not kind or brave and vice versa.
Everyone who is brave is both not quiet and not old and vice versa.
Everyone who is funny or curious is brave or not creative and vice versa.
Everyone who is both curious and creative is not rich and vice versa.
Someone is both kind and not curious.
Alice is patient.
Lucy is not funny.
Someone is not calm.
John is not happy.
Someone is both not strong and happy.
Someone is either not patient or humble. | Paul is not creative. | entailment | (((curious(paul)&rich(paul)))<=>((~happy(john)|~humble(john))))&
(![X]:((calm(X)|~creative(X))=>(patient(X)&~kind(X))))&
(![X]:((happy(X)|~generous(X))<=>(tall(X)|~generous(X))))&
((?[X]:((humble(X)|tall(X))))<=>(~funny(john)))&
(((~rich(john)|~tall(john)))=>(?[X]:((generous(X)<~>~strong(X)))))&
(![X]:((~patient(X)<~>brave(X))=>(~generous(X)&~humble(X))))&
(![X]:((~calm(X)&old(X))<=>(happy(X)<~>calm(X))))&
((?[X]:((~humble(X)|tall(X))))<=>(?[X]:((strong(X)&~patient(X)))))&
((?[X]:((~strong(X)&brave(X))))=>(?[X]:((~quiet(X)<~>~old(X)))))&
(((~generous(susan)&~patient(susan)))=>((quiet(john)&curious(john))))&
((?[X]:((happy(X)&funny(X))))=>(?[X]:(calm(X))))&
(((creative(fred)&curious(fred)))<=>((~strong(lucy)|~funny(lucy))))&
((?[X]:((happy(X)&~old(X))))<=>((~kind(mary)|brave(mary))))&
(![X]:(brave(X)<=>(~quiet(X)&~old(X))))&
(![X]:((funny(X)|curious(X))<=>(brave(X)|~creative(X))))&
(![X]:((curious(X)&creative(X))<=>~rich(X)))&
(?[X]:((kind(X)&~curious(X))))&
(patient(alice))&
(~funny(lucy))&
(?[X]:(~calm(X)))&
(~happy(john))&
(?[X]:((~strong(X)&happy(X))))&
(?[X]:((~patient(X)<~>humble(X)))) | ~creative(paul) | [
"p0",
"p15",
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3410905900813892646334844
% SZS output start Proof for 3410905900813892646334844
1. (rich(paul) & curious(paul)) <=> (~humble(john) | ~happy(john)) [input p0]
16. ! [X0] : ((creative(X0) & curious(X0)) <=> ~rich(X0)) [input p15]
21. ~happy(john) [input p20]
24. creative(paul) [input hypothesis]
35. ((rich(paul) & curious(paul)) | (humble(john) & happy(john))) & ((~humble(john) | ~happy(john)) | (~rich(paul) | ~curious(paul))) [nnf transformation 1]
36. ((rich(paul) & curious(paul)) | (humble(john) & happy(john))) & (~humble(john) | ~happy(john) | ~rich(paul) | ~curious(paul)) [flattening 35]
72. ! [X0] : (((creative(X0) & curious(X0)) | rich(X0)) & (~rich(X0) | (~creative(X0) | ~curious(X0)))) [nnf transformation 16]
73. ! [X0] : (((creative(X0) & curious(X0)) | rich(X0)) & (~rich(X0) | ~creative(X0) | ~curious(X0))) [flattening 72]
84. curious(paul) | happy(john) [cnf transformation 36]
86. rich(paul) | happy(john) [cnf transformation 36]
140. ~creative(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 73]
148. ~happy(john) [cnf transformation 21]
153. creative(paul) [cnf transformation 24]
161. 2 <=> rich(paul) [avatar definition]
163. rich(paul) <- (2) [avatar component clause 161]
166. 3 <=> happy(john) [avatar definition]
169. 3 | 2 [avatar split clause 86,161,166]
171. 4 <=> curious(paul) [avatar definition]
173. curious(paul) <- (4) [avatar component clause 171]
175. 3 | 4 [avatar split clause 84,171,166]
331. ~3 [avatar split clause 148,166]
487. ~rich(paul) | ~curious(paul) [resolution 140,153]
493. ~curious(paul) <- (2) [subsumption resolution 487,163]
494. $false <- (2, 4) [subsumption resolution 493,173]
495. ~2 | ~4 [avatar contradiction clause 494]
503. $false [avatar sat refutation 169,175,331,495]
% SZS output end Proof for 3410905900813892646334844
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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