premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is not strong or old then someone is both calm and not quiet. If someone is either not patient or not rich then mary is either strong or not calm. Everyone who is both not old and not quiet is not creative or not calm and vice versa. Everyone who is both not generous and not curious is both not humble and creative and vice versa. If mary is brave or not quiet then mary is not wise and vice versa. Everyone who is both curious and quiet is both brave and tall. Everyone who is creative is either not quiet or not calm. Everyone who is not happy is either old or not kind and vice versa. If someone is not humble then someone is kind. Everyone who is both not kind and not humble is brave or not wise and vice versa. If paul is both humble and patient then someone is both not happy and old. If someone is both rich and not funny then paul is wise or not curious and vice versa. If fred is both quiet and rich then paul is quiet and vice versa. If someone is tall then someone is both not strong and tall. If someone is quiet then someone is old or not strong and vice versa. Everyone who is not creative or quiet is either not curious or not old and vice versa. Someone is either not old or kind. Paul is both not tall and happy. Someone is either not curious or not generous. Someone is both patient and not old. Alice is either not creative or generous. Someone is not patient. | Fred is not tall. | entailment | ((?[X]:((~strong(X)|old(X))))=>(?[X]:((calm(X)&~quiet(X)))))&
((?[X]:((~patient(X)<~>~rich(X))))=>((strong(mary)<~>~calm(mary))))&
(![X]:((~old(X)&~quiet(X))<=>(~creative(X)|~calm(X))))&
(![X]:((~generous(X)&~curious(X))<=>(~humble(X)&creative(X))))&
(((brave(mary)|~quiet(mary)))<=>(~wise(mary)))&
(![X]:((curious(X)&quiet(X))=>(brave(X)&tall(X))))&
(![X]:(creative(X)=>(~quiet(X)<~>~calm(X))))&
(![X]:(~happy(X)<=>(old(X)<~>~kind(X))))&
((?[X]:(~humble(X)))=>(?[X]:(kind(X))))&
(![X]:((~kind(X)&~humble(X))<=>(brave(X)|~wise(X))))&
(((humble(paul)&patient(paul)))=>(?[X]:((~happy(X)&old(X)))))&
((?[X]:((rich(X)&~funny(X))))<=>((wise(paul)|~curious(paul))))&
(((quiet(fred)&rich(fred)))<=>(quiet(paul)))&
((?[X]:(tall(X)))=>(?[X]:((~strong(X)&tall(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~curious(X)<~>~old(X))))&
(?[X]:((~old(X)<~>kind(X))))&
((~tall(paul)&happy(paul)))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((patient(X)&~old(X))))&
((~creative(alice)<~>generous(alice)))&
(?[X]:(~patient(X))) | ~tall(fred) | [
"p2",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 640294669769840896251283
% SZS output start Proof for 640294669769840896251283
3. ! [X0] : ((~quiet(X0) & ~old(X0)) <=> (~calm(X0) | ~creative(X0))) [input p2]
7. ! [X0] : (creative(X0) => (~quiet(X0) <~> ~calm(X0))) [input p6]
14. ? [X0] : tall(X0) => ? [X0] : (tall(X0) & ~strong(X0)) [input p13]
15. ? [X0] : quiet(X0) <=> ? [X0] : (~strong(X0) | old(X0)) [input p14]
23. tall(fred) [input hypothesis]
26. ? [X0] : tall(X0) => ? [X1] : (tall(X1) & ~strong(X1)) [rectify 14]
27. ? [X0] : quiet(X0) <=> ? [X1] : (~strong(X1) | old(X1)) [rectify 15]
32. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | ~creative(X0)) [ennf transformation 7]
36. ? [X1] : (tall(X1) & ~strong(X1)) | ! [X0] : ~tall(X0) [ennf transformation 26]
41. ! [X0] : (((~quiet(X0) & ~old(X0)) | (calm(X0) & creative(X0))) & ((~calm(X0) | ~creative(X0)) | (quiet(X0) | old(X0)))) [nnf transformation 3]
42. ! [X0] : (((~quiet(X0) & ~old(X0)) | (calm(X0) & creative(X0))) & (~calm(X0) | ~creative(X0) | quiet(X0) | old(X0))) [flattening 41]
47. ! [X0] : (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~creative(X0)) [nnf transformation 32]
63. ? [X0] : (tall(X0) & ~strong(X0)) | ! [X1] : ~tall(X1) [rectify 36]
64. ? [X0] : (tall(X0) & ~strong(X0)) => (tall(sK4) & ~strong(sK4)) [choice axiom]
65. (tall(sK4) & ~strong(sK4)) | ! [X1] : ~tall(X1) [skolemisation 63,64]
66. (? [X0] : quiet(X0) | ! [X1] : (strong(X1) & ~old(X1))) & (? [X1] : (~strong(X1) | old(X1)) | ! [X0] : ~quiet(X0)) [nnf transformation 27]
67. (? [X0] : quiet(X0) | ! [X1] : (strong(X1) & ~old(X1))) & (? [X2] : (~strong(X2) | old(X2)) | ! [X3] : ~quiet(X3)) [rectify 66]
68. ? [X0] : quiet(X0) => quiet(sK5) [choice axiom]
69. ? [X2] : (~strong(X2) | old(X2)) => (~strong(sK6) | old(sK6)) [choice axiom]
70. (quiet(sK5) | ! [X1] : (strong(X1) & ~old(X1))) & ((~strong(sK6) | old(sK6)) | ! [X3] : ~quiet(X3)) [skolemisation 67,69,68]
95. ~quiet(X0) | creative(X0) [cnf transformation 42]
96. ~quiet(X0) | calm(X0) [cnf transformation 42]
106. ~calm(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 47]
107. calm(X0) | quiet(X0) | ~creative(X0) [cnf transformation 47]
128. ~strong(sK4) | ~tall(X1) [cnf transformation 65]
132. quiet(sK5) | strong(X1) [cnf transformation 70]
150. tall(fred) [cnf transformation 23]
160. 3 <=> ! [X1] : strong(X1) [avatar definition]
161. strong(X1) <- (3) [avatar component clause 160]
202. calm(X0) | ~creative(X0) [subsumption resolution 107,96]
203. ~quiet(X0) | ~creative(X0) [subsumption resolution 106,202]
204. ~quiet(X0) [subsumption resolution 203,95]
256. 23 <=> ! [X1] : ~tall(X1) [avatar definition]
257. ~tall(X1) <- (23) [avatar component clause 256]
264. 25 <=> strong(sK4) [avatar definition]
266. ~strong(sK4) <- (~25) [avatar component clause 264]
267. 23 | ~25 [avatar split clause 128,264,256]
268. strong(X1) [subsumption resolution 132,204]
269. 3 [avatar split clause 268,160]
308. $false <- (23) [resolution 257,150]
309. ~23 [avatar contradiction clause 308]
310. $false <- (3, ~25) [subsumption resolution 266,161]
311. ~3 | 25 [avatar contradiction clause 310]
312. $false [avatar sat refutation 267,269,309,311]
% SZS output end Proof for 640294669769840896251283
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not old or quiet then someone is either not happy or generous. Everyone who is old is both not tall and not funny and vice versa. If fred is both not rich and tall then fred is not wise or patient and vice versa. Everyone who is not funny is brave and vice versa. If someone is either funny or kind then alice is either quiet or not funny. Everyone who is humble or not curious is not curious. Everyone who is kind or old is wise or quiet and vice versa. If lucy is either curious or not patient then someone is not old. If someone is calm or happy then someone is patient or not happy and vice versa. If john is not happy or old then lucy is either kind or not patient. Everyone who is funny or not rich is both humble and rich and vice versa. Everyone who is not tall or brave is not tall or humble and vice versa. If alice is either patient or not kind then someone is not quiet or patient. If someone is not tall or generous then someone is not funny or not calm. Everyone who is generous is not quiet. Everyone who is both kind and not creative is patient or not tall and vice versa. Someone is not rich or not wise. Someone is both curious and generous. Lucy is either not brave or creative. Someone is kind. Lucy is brave or calm. | Fred is not tall. | entailment | (((~old(fred)|quiet(fred)))=>(?[X]:((~happy(X)<~>generous(X)))))&
(![X]:(old(X)<=>(~tall(X)&~funny(X))))&
(((~rich(fred)&tall(fred)))<=>((~wise(fred)|patient(fred))))&
(![X]:(~funny(X)<=>brave(X)))&
((?[X]:((funny(X)<~>kind(X))))=>((quiet(alice)<~>~funny(alice))))&
(![X]:((humble(X)|~curious(X))=>~curious(X)))&
(![X]:((kind(X)|old(X))<=>(wise(X)|quiet(X))))&
(((curious(lucy)<~>~patient(lucy)))=>(?[X]:(~old(X))))&
((?[X]:((calm(X)|happy(X))))<=>(?[X]:((patient(X)|~happy(X)))))&
(((~happy(john)|old(john)))=>((kind(lucy)<~>~patient(lucy))))&
(![X]:((funny(X)|~rich(X))<=>(humble(X)&rich(X))))&
(![X]:((~tall(X)|brave(X))<=>(~tall(X)|humble(X))))&
(((patient(alice)<~>~kind(alice)))=>(?[X]:((~quiet(X)|patient(X)))))&
((?[X]:((~tall(X)|generous(X))))=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:(generous(X)=>~quiet(X)))&
(![X]:((kind(X)&~creative(X))<=>(patient(X)|~tall(X))))&
(?[X]:((~rich(X)|~wise(X))))&
(?[X]:((curious(X)&generous(X))))&
((~brave(lucy)<~>creative(lucy)))&
(?[X]:(kind(X)))&
((brave(lucy)|calm(lucy))) | ~tall(fred) | [
"p3",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5559898241835660119942904
% SZS output start Proof for 5559898241835660119942904
4. ! [X0] : (~funny(X0) <=> brave(X0)) [input p3]
11. ! [X0] : ((~rich(X0) | funny(X0)) <=> (rich(X0) & humble(X0))) [input p10]
12. ! [X0] : ((brave(X0) | ~tall(X0)) <=> (humble(X0) | ~tall(X0))) [input p11]
22. tall(fred) [input hypothesis]
40. ! [X0] : ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))) [nnf transformation 4]
53. ! [X0] : (((~rich(X0) | funny(X0)) | (~rich(X0) | ~humble(X0))) & ((rich(X0) & humble(X0)) | (rich(X0) & ~funny(X0)))) [nnf transformation 11]
54. ! [X0] : ((~rich(X0) | funny(X0) | ~rich(X0) | ~humble(X0)) & ((rich(X0) & humble(X0)) | (rich(X0) & ~funny(X0)))) [flattening 53]
55. ! [X0] : (((brave(X0) | ~tall(X0)) | (~humble(X0) & tall(X0))) & ((humble(X0) | ~tall(X0)) | (~brave(X0) & tall(X0)))) [nnf transformation 12]
56. ! [X0] : ((brave(X0) | ~tall(X0) | (~humble(X0) & tall(X0))) & (humble(X0) | ~tall(X0) | (~brave(X0) & tall(X0)))) [flattening 55]
84. brave(X0) | funny(X0) [cnf transformation 40]
85. ~brave(X0) | ~funny(X0) [cnf transformation 40]
106. ~funny(X0) | humble(X0) [cnf transformation 54]
109. rich(X0) | rich(X0) [cnf transformation 54]
110. ~rich(X0) | funny(X0) | ~rich(X0) | ~humble(X0) [cnf transformation 54]
112. ~brave(X0) | ~tall(X0) | humble(X0) [cnf transformation 56]
114. ~humble(X0) | ~tall(X0) | brave(X0) [cnf transformation 56]
132. tall(fred) [cnf transformation 22]
133. rich(X0) [duplicate literal removal 109]
134. ~humble(X0) | funny(X0) | ~rich(X0) [duplicate literal removal 110]
160. 6 <=> tall(fred) [avatar definition]
162. tall(fred) <- (6) [avatar component clause 160]
306. 6 [avatar split clause 132,160]
366. ~tall(X0) | humble(X0) | funny(X0) [resolution 112,84]
368. ~tall(X0) | humble(X0) [subsumption resolution 366,106]
438. humble(fred) <- (6) [resolution 368,162]
479. funny(fred) | ~rich(fred) <- (6) [resolution 438,134]
480. ~tall(fred) | brave(fred) <- (6) [resolution 438,114]
481. funny(fred) <- (6) [subsumption resolution 479,133]
482. brave(fred) <- (6) [subsumption resolution 480,162]
502. ~funny(fred) <- (6) [resolution 482,85]
503. $false <- (6) [subsumption resolution 502,481]
504. ~6 [avatar contradiction clause 503]
505. $false [avatar sat refutation 306,504]
% SZS output end Proof for 5559898241835660119942904
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both not generous and humble then john is happy or tall and vice versa.
Everyone who is kind or not happy is either not quiet or kind.
Everyone who is either funny or humble is not humble or not wise and vice versa.
Everyone who is not quiet is not generous or funny.
If mary is either generous or strong then someone is both not brave and not patient and vice versa.
Everyone who is either not brave or calm is either humble or not generous and vice versa.
Everyone who is both not happy and not humble is patient and vice versa.
If someone is either old or patient then paul is not generous and vice versa.
Everyone who is both not funny and brave is not curious or old and vice versa.
Everyone who is not humble is creative and vice versa.
Everyone who is creative is curious or humble.
If someone is happy or old then john is not creative.
Everyone who is either not happy or curious is either happy or not kind.
If someone is both not curious and not old then fred is either strong or not generous.
Everyone who is either not happy or not generous is happy or not rich.
Everyone who is both brave and not kind is not wise.
Someone is both funny and rich.
Fred is creative or happy.
Paul is not brave.
Lucy is old.
Someone is humble.
Someone is both not patient and strong.
Someone is not brave or not quiet.
Fred is either creative or strong. | John is not patient. | entailment | (((~generous(fred)&humble(fred)))<=>((happy(john)|tall(john))))&
(![X]:((kind(X)|~happy(X))=>(~quiet(X)<~>kind(X))))&
(![X]:((funny(X)<~>humble(X))<=>(~humble(X)|~wise(X))))&
(![X]:(~quiet(X)=>(~generous(X)|funny(X))))&
(((generous(mary)<~>strong(mary)))<=>(?[X]:((~brave(X)&~patient(X)))))&
(![X]:((~brave(X)<~>calm(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((~happy(X)&~humble(X))<=>patient(X)))&
((?[X]:((old(X)<~>patient(X))))<=>(~generous(paul)))&
(![X]:((~funny(X)&brave(X))<=>(~curious(X)|old(X))))&
(![X]:(~humble(X)<=>creative(X)))&
(![X]:(creative(X)=>(curious(X)|humble(X))))&
((?[X]:((happy(X)|old(X))))=>(~creative(john)))&
(![X]:((~happy(X)<~>curious(X))=>(happy(X)<~>~kind(X))))&
((?[X]:((~curious(X)&~old(X))))=>((strong(fred)<~>~generous(fred))))&
(![X]:((~happy(X)<~>~generous(X))=>(happy(X)|~rich(X))))&
(![X]:((brave(X)&~kind(X))=>~wise(X)))&
(?[X]:((funny(X)&rich(X))))&
((creative(fred)|happy(fred)))&
(~brave(paul))&
(old(lucy))&
(?[X]:(humble(X)))&
(?[X]:((~patient(X)&strong(X))))&
(?[X]:((~brave(X)|~quiet(X))))&
((creative(fred)<~>strong(fred))) | ~patient(john) | [
"p6",
"p9",
"p11",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 311967997609441746390114
% SZS output start Proof for 311967997609441746390114
7. ! [X0] : ((~humble(X0) & ~happy(X0)) <=> patient(X0)) [input p6]
10. ! [X0] : (~humble(X0) <=> creative(X0)) [input p9]
12. ? [X0] : (old(X0) | happy(X0)) => ~creative(john) [input p11]
20. old(lucy) [input p19]
25. patient(john) [input hypothesis]
31. ~creative(john) | ! [X0] : (~old(X0) & ~happy(X0)) [ennf transformation 12]
48. ! [X0] : (((~humble(X0) & ~happy(X0)) | ~patient(X0)) & (patient(X0) | (humble(X0) | happy(X0)))) [nnf transformation 7]
49. ! [X0] : (((~humble(X0) & ~happy(X0)) | ~patient(X0)) & (patient(X0) | humble(X0) | happy(X0))) [flattening 48]
56. ! [X0] : ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0))) [nnf transformation 10]
101. ~patient(X0) | ~humble(X0) [cnf transformation 49]
111. creative(X0) | humble(X0) [cnf transformation 56]
115. ~creative(john) | ~old(X0) [cnf transformation 31]
129. old(lucy) [cnf transformation 20]
136. patient(john) [cnf transformation 25]
214. 15 <=> ! [X0] : ~old(X0) [avatar definition]
215. ~old(X0) <- (15) [avatar component clause 214]
217. 16 <=> creative(john) [avatar definition]
219. ~creative(john) <- (~16) [avatar component clause 217]
220. 15 | ~16 [avatar split clause 115,217,214]
255. ~humble(john) [resolution 101,136]
261. humble(john) <- (~16) [resolution 111,219]
262. $false <- (~16) [subsumption resolution 261,255]
263. 16 [avatar contradiction clause 262]
264. $false <- (15) [resolution 215,129]
267. ~15 [avatar contradiction clause 264]
268. $false [avatar sat refutation 220,263,267]
% SZS output end Proof for 311967997609441746390114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not quiet or not creative then someone is not rich. Everyone who is both strong and creative is not quiet and vice versa. If someone is both not strong and funny then paul is either humble or not tall and vice versa. Everyone who is kind is not funny and vice versa. Everyone who is old is either calm or strong. If someone is not wise then someone is humble. Everyone who is not quiet or not creative is both calm and happy. Everyone who is rich is either tall or strong and vice versa. Everyone who is either old or strong is calm or not wise. Everyone who is both not happy and humble is either strong or curious and vice versa. If alice is either strong or not quiet then someone is either not tall or happy. Everyone who is both generous and not wise is not kind or not rich and vice versa. Everyone who is strong or kind is funny. Everyone who is both rich and not generous is either old or wise and vice versa. Everyone who is either not quiet or not wise is not old or tall and vice versa. Fred is both strong and happy. Someone is kind or not curious. Someone is either strong or humble. Someone is funny. | Alice is calm. | neutral | ((?[X]:((~quiet(X)|~creative(X))))=>(?[X]:(~rich(X))))&
(![X]:((strong(X)&creative(X))<=>~quiet(X)))&
((?[X]:((~strong(X)&funny(X))))<=>((humble(paul)<~>~tall(paul))))&
(![X]:(kind(X)<=>~funny(X)))&
(![X]:(old(X)=>(calm(X)<~>strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:(humble(X))))&
(![X]:((~quiet(X)|~creative(X))=>(calm(X)&happy(X))))&
(![X]:(rich(X)<=>(tall(X)<~>strong(X))))&
(![X]:((old(X)<~>strong(X))=>(calm(X)|~wise(X))))&
(![X]:((~happy(X)&humble(X))<=>(strong(X)<~>curious(X))))&
(((strong(alice)<~>~quiet(alice)))=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((generous(X)&~wise(X))<=>(~kind(X)|~rich(X))))&
(![X]:((strong(X)|kind(X))=>funny(X)))&
(![X]:((rich(X)&~generous(X))<=>(old(X)<~>wise(X))))&
(![X]:((~quiet(X)<~>~wise(X))<=>(~old(X)|tall(X))))&
((strong(fred)&happy(fred)))&
(?[X]:((kind(X)|~curious(X))))&
(?[X]:((strong(X)<~>humble(X))))&
(?[X]:(funny(X))) | calm(alice) | [] | null | 0 |
Everyone who is brave is both not patient and not curious. If lucy is not happy then john is either not patient or not rich and vice versa. Everyone who is either curious or not rich is either funny or not quiet and vice versa. Everyone who is not calm or not quiet is strong or not calm. If lucy is not wise then someone is not brave or not curious. Everyone who is either funny or not happy is wise and vice versa. If someone is not wise then alice is happy. Everyone who is either not creative or wise is brave. If susan is both not strong and not rich then john is both not happy and not rich and vice versa. If someone is rich or wise then someone is not kind and vice versa. If someone is creative or not patient then someone is either brave or funny and vice versa. Everyone who is both not brave and not wise is not patient. Everyone who is calm is either not wise or tall and vice versa. Everyone who is both patient and not brave is both brave and not wise and vice versa. Everyone who is either not old or not wise is either not humble or creative and vice versa. Everyone who is both not strong and brave is both not kind and quiet and vice versa. Someone is humble or happy. Someone is curious or not tall. John is not strong. Someone is not old or not kind. Alice is not creative. Someone is both not curious and quiet. Lucy is kind or creative. Lucy is curious or not rich. | Alice is not strong. | neutral | (![X]:(brave(X)=>(~patient(X)&~curious(X))))&
((~happy(lucy))<=>((~patient(john)<~>~rich(john))))&
(![X]:((curious(X)<~>~rich(X))<=>(funny(X)<~>~quiet(X))))&
(![X]:((~calm(X)|~quiet(X))=>(strong(X)|~calm(X))))&
((~wise(lucy))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:((funny(X)<~>~happy(X))<=>wise(X)))&
((?[X]:(~wise(X)))=>(happy(alice)))&
(![X]:((~creative(X)<~>wise(X))=>brave(X)))&
(((~strong(susan)&~rich(susan)))<=>((~happy(john)&~rich(john))))&
((?[X]:((rich(X)|wise(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((creative(X)|~patient(X))))<=>(?[X]:((brave(X)<~>funny(X)))))&
(![X]:((~brave(X)&~wise(X))=>~patient(X)))&
(![X]:(calm(X)<=>(~wise(X)<~>tall(X))))&
(![X]:((patient(X)&~brave(X))<=>(brave(X)&~wise(X))))&
(![X]:((~old(X)<~>~wise(X))<=>(~humble(X)<~>creative(X))))&
(![X]:((~strong(X)&brave(X))<=>(~kind(X)&quiet(X))))&
(?[X]:((humble(X)|happy(X))))&
(?[X]:((curious(X)|~tall(X))))&
(~strong(john))&
(?[X]:((~old(X)|~kind(X))))&
(~creative(alice))&
(?[X]:((~curious(X)&quiet(X))))&
((kind(lucy)|creative(lucy)))&
((curious(lucy)|~rich(lucy))) | ~strong(alice) | [] | null | 0 |
Everyone who is either not happy or not old is either brave or creative and vice versa.
If someone is both strong and not calm then alice is either old or not calm.
If someone is calm or humble then someone is brave and vice versa.
Everyone who is not patient or not humble is both curious and not funny and vice versa.
Everyone who is not patient or humble is creative or brave.
Everyone who is not kind is not humble and vice versa.
Everyone who is not strong or calm is curious or not generous and vice versa.
Everyone who is both quiet and not creative is patient or strong and vice versa.
Everyone who is not kind is either generous or not curious.
If someone is not curious or not creative then someone is both humble and not kind.
If someone is either quiet or not generous then lucy is brave or not kind and vice versa.
Everyone who is both creative and old is both not tall and wise and vice versa.
Everyone who is either not happy or rich is tall.
If paul is old or not kind then fred is either not humble or kind.
If paul is either humble or not funny then someone is curious.
Someone is either not old or wise.
Someone is not generous or not curious.
John is not old or strong.
Someone is either generous or not kind.
Susan is calm or not funny.
Someone is kind.
Paul is not humble or strong.
Mary is rich or not kind. | Alice is curious. | entailment | (![X]:((~happy(X)<~>~old(X))<=>(brave(X)<~>creative(X))))&
((?[X]:((strong(X)&~calm(X))))=>((old(alice)<~>~calm(alice))))&
((?[X]:((calm(X)|humble(X))))<=>(?[X]:(brave(X))))&
(![X]:((~patient(X)|~humble(X))<=>(curious(X)&~funny(X))))&
(![X]:((~patient(X)|humble(X))=>(creative(X)|brave(X))))&
(![X]:(~kind(X)<=>~humble(X)))&
(![X]:((~strong(X)|calm(X))<=>(curious(X)|~generous(X))))&
(![X]:((quiet(X)&~creative(X))<=>(patient(X)|strong(X))))&
(![X]:(~kind(X)=>(generous(X)<~>~curious(X))))&
((?[X]:((~curious(X)|~creative(X))))=>(?[X]:((humble(X)&~kind(X)))))&
((?[X]:((quiet(X)<~>~generous(X))))<=>((brave(lucy)|~kind(lucy))))&
(![X]:((creative(X)&old(X))<=>(~tall(X)&wise(X))))&
(![X]:((~happy(X)<~>rich(X))=>tall(X)))&
(((old(paul)|~kind(paul)))=>((~humble(fred)<~>kind(fred))))&
(((humble(paul)<~>~funny(paul)))=>(?[X]:(curious(X))))&
(?[X]:((~old(X)<~>wise(X))))&
(?[X]:((~generous(X)|~curious(X))))&
((~old(john)|strong(john)))&
(?[X]:((generous(X)<~>~kind(X))))&
((calm(susan)|~funny(susan)))&
(?[X]:(kind(X)))&
((~humble(paul)|strong(paul)))&
((rich(mary)|~kind(mary))) | curious(alice) | [
"p5",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7416024694118449164539328
% SZS output start Proof for 7416024694118449164539328
6. ! [X0] : (~kind(X0) <=> ~humble(X0)) [input p5]
10. ? [X0] : (~creative(X0) | ~curious(X0)) => ? [X0] : (~kind(X0) & humble(X0)) [input p9]
24. ~curious(alice) [input hypothesis]
26. ? [X0] : (~creative(X0) | ~curious(X0)) => ? [X1] : (~kind(X1) & humble(X1)) [rectify 10]
31. ? [X1] : (~kind(X1) & humble(X1)) | ! [X0] : (creative(X0) & curious(X0)) [ennf transformation 26]
44. ! [X0] : ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0))) [nnf transformation 6]
50. ? [X0] : (~kind(X0) & humble(X0)) | ! [X1] : (creative(X1) & curious(X1)) [rectify 31]
51. ? [X0] : (~kind(X0) & humble(X0)) => (~kind(sK2) & humble(sK2)) [choice axiom]
52. (~kind(sK2) & humble(sK2)) | ! [X1] : (creative(X1) & curious(X1)) [skolemisation 50,51]
95. ~humble(X0) | kind(X0) [cnf transformation 44]
108. humble(sK2) | curious(X1) [cnf transformation 52]
110. ~kind(sK2) | curious(X1) [cnf transformation 52]
140. ~curious(alice) [cnf transformation 24]
182. 11 <=> kind(sK2) [avatar definition]
184. ~kind(sK2) <- (~11) [avatar component clause 182]
187. 12 <=> ! [X1] : curious(X1) [avatar definition]
188. curious(X1) <- (12) [avatar component clause 187]
189. 12 | ~11 [avatar split clause 110,182,187]
191. 13 <=> humble(sK2) [avatar definition]
193. humble(sK2) <- (13) [avatar component clause 191]
195. 12 | 13 [avatar split clause 108,191,187]
303. $false <- (12) [resolution 188,140]
304. ~12 [avatar contradiction clause 303]
307. kind(sK2) <- (13) [resolution 95,193]
309. $false <- (~11, 13) [subsumption resolution 307,184]
310. 11 | ~13 [avatar contradiction clause 309]
311. $false [avatar sat refutation 189,195,304,310]
% SZS output end Proof for 7416024694118449164539328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or humble is not humble and vice versa.
If someone is strong then someone is both not old and not wise.
Everyone who is not wise is both kind and not funny and vice versa.
Everyone who is either tall or not strong is not humble and vice versa.
If someone is both patient and not strong then someone is quiet and vice versa.
If lucy is not strong then fred is both humble and not funny.
If lucy is either rich or not patient then someone is kind and vice versa.
Everyone who is either not quiet or not curious is either not tall or not creative.
If someone is not tall then alice is not rich.
If someone is not patient or tall then someone is both not wise and not brave and vice versa.
Everyone who is not brave or not rich is both not curious and rich.
If someone is not brave then someone is both happy and rich.
Everyone who is kind is not strong or rich.
Someone is both not quiet and not creative.
Someone is both not kind and not brave.
Fred is both old and strong.
Mary is rich or old.
Susan is not tall or not calm. | Fred is patient. | neutral | (![X]:((~quiet(X)|humble(X))<=>~humble(X)))&
((?[X]:(strong(X)))=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:(~wise(X)<=>(kind(X)&~funny(X))))&
(![X]:((tall(X)<~>~strong(X))<=>~humble(X)))&
((?[X]:((patient(X)&~strong(X))))<=>(?[X]:(quiet(X))))&
((~strong(lucy))=>((humble(fred)&~funny(fred))))&
(((rich(lucy)<~>~patient(lucy)))<=>(?[X]:(kind(X))))&
(![X]:((~quiet(X)<~>~curious(X))=>(~tall(X)<~>~creative(X))))&
((?[X]:(~tall(X)))=>(~rich(alice)))&
((?[X]:((~patient(X)|tall(X))))<=>(?[X]:((~wise(X)&~brave(X)))))&
(![X]:((~brave(X)|~rich(X))=>(~curious(X)&rich(X))))&
((?[X]:(~brave(X)))=>(?[X]:((happy(X)&rich(X)))))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:((~kind(X)&~brave(X))))&
((old(fred)&strong(fred)))&
((rich(mary)|old(mary)))&
((~tall(susan)|~calm(susan))) | patient(fred) | [] | null | 0 |
If someone is both old and not old then someone is quiet or not humble and vice versa. If lucy is not creative or not patient then someone is both generous and tall and vice versa. Everyone who is either not brave or humble is not curious and vice versa. Everyone who is either funny or not funny is calm. Everyone who is both not creative and not tall is not strong or curious. If someone is wise then alice is either quiet or not funny and vice versa. Everyone who is either generous or humble is not quiet. Everyone who is not wise is calm or not quiet and vice versa. Everyone who is both calm and happy is both not quiet and not calm. If someone is kind then someone is both strong and not wise. If paul is humble or generous then susan is not happy. Everyone who is both not strong and not creative is either quiet or not humble. If someone is strong or generous then john is both not curious and kind and vice versa. Everyone who is old or not strong is either brave or not tall. Everyone who is both patient and creative is either not wise or not curious. If someone is not humble then alice is either humble or calm and vice versa. Lucy is generous. Susan is kind or old. John is both not old and not generous. Fred is either not rich or not patient. Susan is both curious and strong. Susan is quiet or not kind. | John is not strong. | neutral | ((?[X]:((old(X)&~old(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
(((~creative(lucy)|~patient(lucy)))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((~brave(X)<~>humble(X))<=>~curious(X)))&
(![X]:((funny(X)<~>~funny(X))=>calm(X)))&
(![X]:((~creative(X)&~tall(X))=>(~strong(X)|curious(X))))&
((?[X]:(wise(X)))<=>((quiet(alice)<~>~funny(alice))))&
(![X]:((generous(X)<~>humble(X))=>~quiet(X)))&
(![X]:(~wise(X)<=>(calm(X)|~quiet(X))))&
(![X]:((calm(X)&happy(X))=>(~quiet(X)&~calm(X))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)&~wise(X)))))&
(((humble(paul)|generous(paul)))=>(~happy(susan)))&
(![X]:((~strong(X)&~creative(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((strong(X)|generous(X))))<=>((~curious(john)&kind(john))))&
(![X]:((old(X)|~strong(X))=>(brave(X)<~>~tall(X))))&
(![X]:((patient(X)&creative(X))=>(~wise(X)<~>~curious(X))))&
((?[X]:(~humble(X)))<=>((humble(alice)<~>calm(alice))))&
(generous(lucy))&
((kind(susan)|old(susan)))&
((~old(john)&~generous(john)))&
((~rich(fred)<~>~patient(fred)))&
((curious(susan)&strong(susan)))&
((quiet(susan)|~kind(susan))) | ~strong(john) | [] | null | 0 |
If paul is quiet or not kind then someone is either wise or not kind and vice versa. Everyone who is both patient and not wise is strong. Everyone who is both rich and not quiet is not old or creative and vice versa. Everyone who is both happy and not kind is not humble or not tall and vice versa. Everyone who is both calm and tall is humble or old and vice versa. Everyone who is not funny is rich and vice versa. Everyone who is both not kind and not quiet is both strong and not rich and vice versa. Everyone who is curious is both rich and not curious. If someone is both not quiet and wise then fred is not strong or kind and vice versa. Everyone who is both kind and not humble is not curious or not tall. Everyone who is either not brave or curious is not happy or strong. Everyone who is either calm or not funny is either not strong or funny. Everyone who is both not old and humble is both humble and patient. If someone is both not brave and not generous then someone is creative or not strong. If someone is generous or creative then fred is both humble and creative and vice versa. Everyone who is either not generous or wise is either not kind or not curious. Lucy is patient. Someone is not wise. Someone is kind or wise. Paul is either not creative or not curious. John is either calm or brave. Someone is quiet or calm. Someone is both old and rich. | Fred is not curious. | entailment | (((quiet(paul)|~kind(paul)))<=>(?[X]:((wise(X)<~>~kind(X)))))&
(![X]:((patient(X)&~wise(X))=>strong(X)))&
(![X]:((rich(X)&~quiet(X))<=>(~old(X)|creative(X))))&
(![X]:((happy(X)&~kind(X))<=>(~humble(X)|~tall(X))))&
(![X]:((calm(X)&tall(X))<=>(humble(X)|old(X))))&
(![X]:(~funny(X)<=>rich(X)))&
(![X]:((~kind(X)&~quiet(X))<=>(strong(X)&~rich(X))))&
(![X]:(curious(X)=>(rich(X)&~curious(X))))&
((?[X]:((~quiet(X)&wise(X))))<=>((~strong(fred)|kind(fred))))&
(![X]:((kind(X)&~humble(X))=>(~curious(X)|~tall(X))))&
(![X]:((~brave(X)<~>curious(X))=>(~happy(X)|strong(X))))&
(![X]:((calm(X)<~>~funny(X))=>(~strong(X)<~>funny(X))))&
(![X]:((~old(X)&humble(X))=>(humble(X)&patient(X))))&
((?[X]:((~brave(X)&~generous(X))))=>(?[X]:((creative(X)|~strong(X)))))&
((?[X]:((generous(X)|creative(X))))<=>((humble(fred)&creative(fred))))&
(![X]:((~generous(X)<~>wise(X))=>(~kind(X)<~>~curious(X))))&
(patient(lucy))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)|wise(X))))&
((~creative(paul)<~>~curious(paul)))&
((calm(john)<~>brave(john)))&
(?[X]:((quiet(X)|calm(X))))&
(?[X]:((old(X)&rich(X)))) | ~curious(fred) | [
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8816892841181373760767637
% SZS output start Proof for 8816892841181373760767637
8. ! [X0] : (curious(X0) => (~curious(X0) & rich(X0))) [input p7]
24. curious(fred) [input hypothesis]
28. ! [X0] : ((~curious(X0) & rich(X0)) | ~curious(X0)) [ennf transformation 8]
107. ~curious(X0) | ~curious(X0) [cnf transformation 28]
142. curious(fred) [cnf transformation 24]
145. ~curious(X0) [duplicate literal removal 107]
269. $false [subsumption resolution 142,145]
% SZS output end Proof for 8816892841181373760767637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not generous or not strong then alice is either curious or not rich and vice versa. Everyone who is either rich or patient is not calm or old. Everyone who is not old is both patient and not rich and vice versa. If alice is not quiet then susan is not creative. If someone is old or not quiet then fred is brave and vice versa. Everyone who is both not old and brave is tall and vice versa. Everyone who is both not rich and happy is both not humble and kind and vice versa. Everyone who is not patient or not brave is both not creative and not wise. Everyone who is either tall or wise is not tall or quiet and vice versa. If john is either calm or not rich then someone is both not tall and not patient and vice versa. Everyone who is not patient is both generous and quiet. Everyone who is happy or strong is either tall or not wise and vice versa. Everyone who is both not kind and not tall is both patient and not brave. Everyone who is creative is either not kind or not curious. Everyone who is strong or not curious is both wise and not tall. If someone is both creative and not strong then someone is either old or not humble. Lucy is both not old and happy. Alice is not funny. Someone is both wise and rich. Alice is not quiet. Someone is either generous or quiet. Mary is either not curious or not humble. Someone is either creative or not old. Someone is generous. | Alice is not kind. | contradiction | (((~generous(susan)|~strong(susan)))<=>((curious(alice)<~>~rich(alice))))&
(![X]:((rich(X)<~>patient(X))=>(~calm(X)|old(X))))&
(![X]:(~old(X)<=>(patient(X)&~rich(X))))&
((~quiet(alice))=>(~creative(susan)))&
((?[X]:((old(X)|~quiet(X))))<=>(brave(fred)))&
(![X]:((~old(X)&brave(X))<=>tall(X)))&
(![X]:((~rich(X)&happy(X))<=>(~humble(X)&kind(X))))&
(![X]:((~patient(X)|~brave(X))=>(~creative(X)&~wise(X))))&
(![X]:((tall(X)<~>wise(X))<=>(~tall(X)|quiet(X))))&
(((calm(john)<~>~rich(john)))<=>(?[X]:((~tall(X)&~patient(X)))))&
(![X]:(~patient(X)=>(generous(X)&quiet(X))))&
(![X]:((happy(X)|strong(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~kind(X)&~tall(X))=>(patient(X)&~brave(X))))&
(![X]:(creative(X)=>(~kind(X)<~>~curious(X))))&
(![X]:((strong(X)|~curious(X))=>(wise(X)&~tall(X))))&
((?[X]:((creative(X)&~strong(X))))=>(?[X]:((old(X)<~>~humble(X)))))&
((~old(lucy)&happy(lucy)))&
(~funny(alice))&
(?[X]:((wise(X)&rich(X))))&
(~quiet(alice))&
(?[X]:((generous(X)<~>quiet(X))))&
((~curious(mary)<~>~humble(mary)))&
(?[X]:((creative(X)<~>~old(X))))&
(?[X]:(generous(X))) | ~kind(alice) | [
"p0",
"p2",
"p5",
"p7",
"p8",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 240963459005465017862539
% SZS output start Proof for 240963459005465017862539
1. (~strong(susan) | ~generous(susan)) <=> (curious(alice) <~> ~rich(alice)) [input p0]
3. ! [X0] : (~old(X0) <=> (~rich(X0) & patient(X0))) [input p2]
6. ! [X0] : ((brave(X0) & ~old(X0)) <=> tall(X0)) [input p5]
8. ! [X0] : ((~brave(X0) | ~patient(X0)) => (~wise(X0) & ~creative(X0))) [input p7]
9. ! [X0] : ((tall(X0) <~> wise(X0)) <=> (quiet(X0) | ~tall(X0))) [input p8]
12. ! [X0] : ((strong(X0) | happy(X0)) <=> (tall(X0) <~> ~wise(X0))) [input p11]
13. ! [X0] : ((~tall(X0) & ~kind(X0)) => (~brave(X0) & patient(X0))) [input p12]
15. ! [X0] : ((~curious(X0) | strong(X0)) => (~tall(X0) & wise(X0))) [input p14]
25. ~kind(alice) [input hypothesis]
31. ! [X0] : ((~wise(X0) & ~creative(X0)) | (brave(X0) & patient(X0))) [ennf transformation 8]
33. ! [X0] : ((~brave(X0) & patient(X0)) | (tall(X0) | kind(X0))) [ennf transformation 13]
34. ! [X0] : ((~brave(X0) & patient(X0)) | tall(X0) | kind(X0)) [flattening 33]
36. ! [X0] : ((~tall(X0) & wise(X0)) | (curious(X0) & ~strong(X0))) [ennf transformation 15]
38. ((~strong(susan) | ~generous(susan)) | ((curious(alice) | rich(alice)) & (~rich(alice) | ~curious(alice)))) & (((rich(alice) | ~curious(alice)) & (~rich(alice) | curious(alice))) | (strong(susan) & generous(susan))) [nnf transformation 1]
39. (~strong(susan) | ~generous(susan) | ((curious(alice) | rich(alice)) & (~rich(alice) | ~curious(alice)))) & (((rich(alice) | ~curious(alice)) & (~rich(alice) | curious(alice))) | (strong(susan) & generous(susan))) [flattening 38]
41. ! [X0] : ((~old(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | old(X0))) [nnf transformation 3]
42. ! [X0] : ((~old(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | old(X0))) [flattening 41]
47. ! [X0] : (((brave(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | (~brave(X0) | old(X0)))) [nnf transformation 6]
48. ! [X0] : (((brave(X0) & ~old(X0)) | ~tall(X0)) & (tall(X0) | ~brave(X0) | old(X0))) [flattening 47]
51. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~quiet(X0) & tall(X0))) & ((quiet(X0) | ~tall(X0)) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [nnf transformation 9]
52. ! [X0] : ((((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | (~quiet(X0) & tall(X0))) & (quiet(X0) | ~tall(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))))) [flattening 51]
57. ! [X0] : (((strong(X0) | happy(X0)) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~strong(X0) & ~happy(X0)))) [nnf transformation 12]
58. ! [X0] : ((strong(X0) | happy(X0) | ((tall(X0) | wise(X0)) & (~wise(X0) | ~tall(X0)))) & (((wise(X0) | ~tall(X0)) & (~wise(X0) | tall(X0))) | (~strong(X0) & ~happy(X0)))) [flattening 57]
78. rich(alice) | ~curious(alice) | strong(susan) [cnf transformation 39]
84. ~rich(X0) | old(X0) [cnf transformation 42]
91. ~tall(X0) | ~old(X0) [cnf transformation 48]
92. ~tall(X0) | brave(X0) [cnf transformation 48]
100. ~wise(X0) | brave(X0) [cnf transformation 31]
103. wise(X0) | tall(X0) | tall(X0) [cnf transformation 52]
116. ~wise(X0) | tall(X0) | ~strong(X0) [cnf transformation 58]
118. wise(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 58]
122. ~brave(X0) | tall(X0) | kind(X0) [cnf transformation 34]
127. ~tall(X0) | ~strong(X0) [cnf transformation 36]
128. ~tall(X0) | curious(X0) [cnf transformation 36]
143. ~kind(alice) [cnf transformation 25]
145. wise(X0) | tall(X0) [duplicate literal removal 103]
147. 1 <=> rich(alice) [avatar definition]
149. rich(alice) <- (1) [avatar component clause 147]
151. 2 <=> curious(alice) [avatar definition]
159. 4 <=> strong(susan) [avatar definition]
160. strong(susan) <- (4) [avatar component clause 159]
164. 4 | ~2 | 1 [avatar split clause 78,147,151,159]
224. ~strong(X0) | wise(X0) [subsumption resolution 118,145]
226. ~strong(X0) | tall(X0) [subsumption resolution 116,224]
228. ~strong(X0) [subsumption resolution 127,226]
287. tall(X0) | brave(X0) [resolution 145,100]
289. brave(X0) [subsumption resolution 287,92]
370. kind(X0) | tall(X0) [resolution 122,289]
411. tall(alice) [resolution 370,143]
417. curious(alice) [resolution 411,128]
419. ~old(alice) [resolution 411,91]
423. 2 [avatar split clause 417,151]
424. old(alice) <- (1) [resolution 149,84]
425. $false <- (1) [subsumption resolution 424,419]
426. ~1 [avatar contradiction clause 425]
427. $false <- (4) [subsumption resolution 160,228]
428. ~4 [avatar contradiction clause 427]
429. $false [avatar sat refutation 164,423,426,428]
% SZS output end Proof for 240963459005465017862539
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm is tall.
If fred is either kind or not strong then someone is either not kind or curious and vice versa.
If someone is both quiet and generous then someone is either rich or quiet.
If someone is both calm and strong then mary is both not humble and wise and vice versa.
Everyone who is either not funny or strong is not creative or funny.
If someone is creative or kind then someone is either rich or not curious.
If susan is either not tall or not wise then someone is not patient and vice versa.
If someone is either humble or not old then lucy is both old and funny and vice versa.
Everyone who is not brave or not curious is both tall and humble and vice versa.
If someone is not wise or not brave then someone is curious or happy and vice versa.
Everyone who is not happy is both quiet and curious and vice versa.
Everyone who is both curious and strong is both creative and not strong.
If someone is patient or calm then someone is funny or not rich.
If alice is brave or not generous then fred is curious and vice versa.
Everyone who is not brave is both happy and kind.
Everyone who is both wise and not happy is not strong and vice versa.
Fred is either kind or tall.
Someone is either not curious or not brave.
Someone is funny or not creative.
Mary is rich.
Someone is both brave and quiet.
Someone is both generous and not curious.
Someone is either curious or old. | Fred is not curious. | contradiction | (![X]:(calm(X)=>tall(X)))&
(((kind(fred)<~>~strong(fred)))<=>(?[X]:((~kind(X)<~>curious(X)))))&
((?[X]:((quiet(X)&generous(X))))=>(?[X]:((rich(X)<~>quiet(X)))))&
((?[X]:((calm(X)&strong(X))))<=>((~humble(mary)&wise(mary))))&
(![X]:((~funny(X)<~>strong(X))=>(~creative(X)|funny(X))))&
((?[X]:((creative(X)|kind(X))))=>(?[X]:((rich(X)<~>~curious(X)))))&
(((~tall(susan)<~>~wise(susan)))<=>(?[X]:(~patient(X))))&
((?[X]:((humble(X)<~>~old(X))))<=>((old(lucy)&funny(lucy))))&
(![X]:((~brave(X)|~curious(X))<=>(tall(X)&humble(X))))&
((?[X]:((~wise(X)|~brave(X))))<=>(?[X]:((curious(X)|happy(X)))))&
(![X]:(~happy(X)<=>(quiet(X)&curious(X))))&
(![X]:((curious(X)&strong(X))=>(creative(X)&~strong(X))))&
((?[X]:((patient(X)|calm(X))))=>(?[X]:((funny(X)|~rich(X)))))&
(((brave(alice)|~generous(alice)))<=>(curious(fred)))&
(![X]:(~brave(X)=>(happy(X)&kind(X))))&
(![X]:((wise(X)&~happy(X))<=>~strong(X)))&
((kind(fred)<~>tall(fred)))&
(?[X]:((~curious(X)<~>~brave(X))))&
(?[X]:((funny(X)|~creative(X))))&
(rich(mary))&
(?[X]:((brave(X)&quiet(X))))&
(?[X]:((generous(X)&~curious(X))))&
(?[X]:((curious(X)<~>old(X)))) | ~curious(fred) | [
"p1",
"p8",
"p10",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4505609172825959290156862
% SZS output start Proof for 4505609172825959290156862
2. (kind(fred) <~> ~strong(fred)) <=> ? [X0] : (~kind(X0) <~> curious(X0)) [input p1]
9. ! [X0] : ((~curious(X0) | ~brave(X0)) <=> (humble(X0) & tall(X0))) [input p8]
11. ! [X0] : (~happy(X0) <=> (curious(X0) & quiet(X0))) [input p10]
16. ! [X0] : ((~happy(X0) & wise(X0)) <=> ~strong(X0)) [input p15]
17. kind(fred) <~> tall(fred) [input p16]
24. ~curious(fred) [input hypothesis]
38. (((strong(fred) | ~kind(fred)) & (~strong(fred) | kind(fred))) | ! [X0] : ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (? [X0] : ((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | ((kind(fred) | strong(fred)) & (~strong(fred) | ~kind(fred)))) [nnf transformation 2]
39. (((strong(fred) | ~kind(fred)) & (~strong(fred) | kind(fred))) | ! [X0] : ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (? [X1] : ((~curious(X1) | kind(X1)) & (curious(X1) | ~kind(X1))) | ((kind(fred) | strong(fred)) & (~strong(fred) | ~kind(fred)))) [rectify 38]
40. ? [X1] : ((~curious(X1) | kind(X1)) & (curious(X1) | ~kind(X1))) => ((~curious(sK0) | kind(sK0)) & (curious(sK0) | ~kind(sK0))) [choice axiom]
41. (((strong(fred) | ~kind(fred)) & (~strong(fred) | kind(fred))) | ! [X0] : ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0)))) & (((~curious(sK0) | kind(sK0)) & (curious(sK0) | ~kind(sK0))) | ((kind(fred) | strong(fred)) & (~strong(fred) | ~kind(fred)))) [skolemisation 39,40]
65. ! [X0] : (((~curious(X0) | ~brave(X0)) | (~humble(X0) | ~tall(X0))) & ((humble(X0) & tall(X0)) | (curious(X0) & brave(X0)))) [nnf transformation 9]
66. ! [X0] : ((~curious(X0) | ~brave(X0) | ~humble(X0) | ~tall(X0)) & ((humble(X0) & tall(X0)) | (curious(X0) & brave(X0)))) [flattening 65]
72. ! [X0] : ((~happy(X0) | (~curious(X0) | ~quiet(X0))) & ((curious(X0) & quiet(X0)) | happy(X0))) [nnf transformation 11]
73. ! [X0] : ((~happy(X0) | ~curious(X0) | ~quiet(X0)) & ((curious(X0) & quiet(X0)) | happy(X0))) [flattening 72]
79. ! [X0] : (((~happy(X0) & wise(X0)) | strong(X0)) & (~strong(X0) | (happy(X0) | ~wise(X0)))) [nnf transformation 16]
80. ! [X0] : (((~happy(X0) & wise(X0)) | strong(X0)) & (~strong(X0) | happy(X0) | ~wise(X0))) [flattening 79]
81. (~tall(fred) | ~kind(fred)) & (tall(fred) | kind(fred)) [nnf transformation 17]
99. ~strong(fred) | kind(fred) | curious(X0) | kind(X0) [cnf transformation 41]
126. curious(X0) | tall(X0) [cnf transformation 66]
135. happy(X0) | curious(X0) [cnf transformation 73]
148. ~happy(X0) | strong(X0) [cnf transformation 80]
150. ~tall(fred) | ~kind(fred) [cnf transformation 81]
161. ~curious(fred) [cnf transformation 24]
168. 2 <=> kind(fred) [avatar definition]
170. ~kind(fred) <- (~2) [avatar component clause 168]
172. 3 <=> strong(fred) [avatar definition]
177. 4 <=> ! [X0] : (curious(X0) | kind(X0)) [avatar definition]
178. curious(X0) | kind(X0) <- (4) [avatar component clause 177]
181. 4 | 2 | ~3 [avatar split clause 99,172,168,177]
344. 41 <=> curious(fred) [avatar definition]
346. ~curious(fred) <- (~41) [avatar component clause 344]
359. 44 <=> tall(fred) [avatar definition]
362. ~2 | ~44 [avatar split clause 150,359,168]
393. ~41 [avatar split clause 161,344]
397. tall(fred) <- (~41) [resolution 126,346]
403. 44 | 41 [avatar split clause 397,344,359]
413. curious(X1) | strong(X1) [resolution 148,135]
454. strong(fred) <- (~41) [resolution 413,346]
461. 3 | 41 [avatar split clause 454,344,172]
470. kind(fred) <- (4, ~41) [resolution 178,346]
475. $false <- (~2, 4, ~41) [subsumption resolution 470,170]
476. 2 | ~4 | 41 [avatar contradiction clause 475]
479. $false [avatar sat refutation 181,362,393,403,461,476]
% SZS output end Proof for 4505609172825959290156862
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not patient then fred is either not curious or not happy and vice versa.
If someone is not quiet then someone is both generous and not quiet and vice versa.
Everyone who is not tall or tall is either patient or not happy.
Everyone who is either curious or happy is both brave and not brave and vice versa.
If mary is not creative then mary is either brave or tall and vice versa.
Everyone who is not creative is generous.
If someone is brave or creative then paul is not generous.
If someone is both calm and not brave then mary is both wise and curious.
Everyone who is either calm or curious is either generous or not funny and vice versa.
Everyone who is kind is both not brave and not funny and vice versa.
If susan is both tall and not curious then susan is both not rich and not funny and vice versa.
Everyone who is humble or patient is happy or patient and vice versa.
Everyone who is both not calm and not strong is either rich or not wise.
If john is not tall or not curious then someone is not strong or strong.
Everyone who is both not brave and creative is both not patient and quiet.
Someone is either not rich or humble.
Someone is either not creative or patient.
Mary is funny.
Someone is either old or not quiet.
Someone is generous or not happy.
Someone is generous.
Mary is tall. | Paul is kind. | contradiction | ((?[X]:(~patient(X)))<=>((~curious(fred)<~>~happy(fred))))&
((?[X]:(~quiet(X)))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)<~>~happy(X))))&
(![X]:((curious(X)<~>happy(X))<=>(brave(X)&~brave(X))))&
((~creative(mary))<=>((brave(mary)<~>tall(mary))))&
(![X]:(~creative(X)=>generous(X)))&
((?[X]:((brave(X)|creative(X))))=>(~generous(paul)))&
((?[X]:((calm(X)&~brave(X))))=>((wise(mary)&curious(mary))))&
(![X]:((calm(X)<~>curious(X))<=>(generous(X)<~>~funny(X))))&
(![X]:(kind(X)<=>(~brave(X)&~funny(X))))&
(((tall(susan)&~curious(susan)))<=>((~rich(susan)&~funny(susan))))&
(![X]:((humble(X)|patient(X))<=>(happy(X)|patient(X))))&
(![X]:((~calm(X)&~strong(X))=>(rich(X)<~>~wise(X))))&
(((~tall(john)|~curious(john)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:((~brave(X)&creative(X))=>(~patient(X)&quiet(X))))&
(?[X]:((~rich(X)<~>humble(X))))&
(?[X]:((~creative(X)<~>patient(X))))&
(funny(mary))&
(?[X]:((old(X)<~>~quiet(X))))&
(?[X]:((generous(X)|~happy(X))))&
(?[X]:(generous(X)))&
(tall(mary)) | kind(paul) | [
"p0",
"p3",
"p5",
"p6",
"p9",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8971636015013305108274758
% SZS output start Proof for 8971636015013305108274758
1. ? [X0] : ~patient(X0) <=> (~curious(fred) <~> ~happy(fred)) [input p0]
4. ! [X0] : ((curious(X0) <~> happy(X0)) <=> (~brave(X0) & brave(X0))) [input p3]
6. ! [X0] : (~creative(X0) => generous(X0)) [input p5]
7. ? [X0] : (creative(X0) | brave(X0)) => ~generous(paul) [input p6]
10. ! [X0] : (kind(X0) <=> (~funny(X0) & ~brave(X0))) [input p9]
15. ! [X0] : ((creative(X0) & ~brave(X0)) => (quiet(X0) & ~patient(X0))) [input p14]
17. ? [X0] : (~creative(X0) <~> patient(X0)) [input p16]
23. kind(paul) [input hypothesis]
25. ! [X0] : (kind(X0) => (~funny(X0) & ~brave(X0))) [unused predicate definition removal 10]
27. ! [X0] : (generous(X0) | creative(X0)) [ennf transformation 6]
28. ~generous(paul) | ! [X0] : (~creative(X0) & ~brave(X0)) [ennf transformation 7]
30. ! [X0] : ((~funny(X0) & ~brave(X0)) | ~kind(X0)) [ennf transformation 25]
34. ! [X0] : ((quiet(X0) & ~patient(X0)) | (~creative(X0) | brave(X0))) [ennf transformation 15]
35. ! [X0] : ((quiet(X0) & ~patient(X0)) | ~creative(X0) | brave(X0)) [flattening 34]
36. (? [X0] : ~patient(X0) | ((~curious(fred) | happy(fred)) & (~happy(fred) | curious(fred)))) & (((happy(fred) | curious(fred)) & (~happy(fred) | ~curious(fred))) | ! [X0] : patient(X0)) [nnf transformation 1]
37. (? [X0] : ~patient(X0) | ((~curious(fred) | happy(fred)) & (~happy(fred) | curious(fred)))) & (((happy(fred) | curious(fred)) & (~happy(fred) | ~curious(fred))) | ! [X1] : patient(X1)) [rectify 36]
38. ? [X0] : ~patient(X0) => ~patient(sK0) [choice axiom]
39. (~patient(sK0) | ((~curious(fred) | happy(fred)) & (~happy(fred) | curious(fred)))) & (((happy(fred) | curious(fred)) & (~happy(fred) | ~curious(fred))) | ! [X1] : patient(X1)) [skolemisation 37,38]
46. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [nnf transformation 4]
47. ! [X0] : ((((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0))))) [flattening 46]
60. ? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) [nnf transformation 17]
61. ? [X0] : ((~patient(X0) | creative(X0)) & (patient(X0) | ~creative(X0))) => ((~patient(sK5) | creative(sK5)) & (patient(sK5) | ~creative(sK5))) [choice axiom]
62. (~patient(sK5) | creative(sK5)) & (patient(sK5) | ~creative(sK5)) [skolemisation 60,61]
70. ~happy(fred) | ~curious(fred) | patient(X1) [cnf transformation 39]
71. happy(fred) | curious(fred) | patient(X1) [cnf transformation 39]
81. brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 47]
82. brave(X0) | curious(X0) | ~happy(X0) [cnf transformation 47]
83. ~brave(X0) | happy(X0) | ~curious(X0) [cnf transformation 47]
84. ~brave(X0) | curious(X0) | ~happy(X0) [cnf transformation 47]
91. creative(X0) | generous(X0) [cnf transformation 27]
93. ~generous(paul) | ~creative(X0) [cnf transformation 28]
104. ~kind(X0) | ~brave(X0) [cnf transformation 30]
118. ~creative(X0) | ~patient(X0) | brave(X0) [cnf transformation 35]
123. ~patient(sK5) | creative(sK5) [cnf transformation 62]
130. kind(paul) [cnf transformation 23]
132. 1 <=> happy(fred) [avatar definition]
133. ~happy(fred) <- (~1) [avatar component clause 132]
134. happy(fred) <- (1) [avatar component clause 132]
136. 2 <=> curious(fred) [avatar definition]
137. curious(fred) <- (2) [avatar component clause 136]
146. 4 <=> ! [X1] : patient(X1) [avatar definition]
147. patient(X1) <- (4) [avatar component clause 146]
148. 4 | 2 | 1 [avatar split clause 71,132,136,146]
149. 4 | ~2 | ~1 [avatar split clause 70,132,136,146]
173. ~happy(X0) | curious(X0) [subsumption resolution 82,84]
174. ~curious(X0) | happy(X0) [subsumption resolution 81,83]
192. 13 <=> ! [X0] : ~creative(X0) [avatar definition]
193. ~creative(X0) <- (13) [avatar component clause 192]
195. 14 <=> generous(paul) [avatar definition]
198. 13 | ~14 [avatar split clause 93,195,192]
248. 25 <=> creative(sK5) [avatar definition]
250. creative(sK5) <- (25) [avatar component clause 248]
252. 26 <=> patient(sK5) [avatar definition]
254. ~patient(sK5) <- (~26) [avatar component clause 252]
255. 25 | ~26 [avatar split clause 123,252,248]
283. ~brave(paul) [resolution 104,130]
291. happy(fred) <- (2) [resolution 174,137]
292. $false <- (~1, 2) [subsumption resolution 291,133]
293. 1 | ~2 [avatar contradiction clause 292]
294. curious(fred) <- (1) [resolution 134,173]
298. 2 | ~1 [avatar split clause 294,132,136]
301. $false <- (4, ~26) [resolution 147,254]
303. ~4 | 26 [avatar contradiction clause 301]
313. ~patient(X0) | brave(X0) | generous(X0) [resolution 118,91]
315. brave(X0) | generous(X0) <- (4) [subsumption resolution 313,147]
323. generous(paul) <- (4) [resolution 315,283]
328. 14 | ~4 [avatar split clause 323,146,195]
330. $false <- (13, 25) [resolution 193,250]
331. ~13 | ~25 [avatar contradiction clause 330]
332. $false [avatar sat refutation 148,149,198,255,293,298,303,328,331]
% SZS output end Proof for 8971636015013305108274758
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not tall or curious and vice versa.
If someone is quiet then someone is generous.
Everyone who is not happy or patient is either kind or old and vice versa.
Everyone who is both funny and not strong is both happy and not kind and vice versa.
If fred is not old or curious then alice is either not wise or not creative.
If someone is not generous or not funny then fred is both patient and not patient and vice versa.
Everyone who is either humble or not humble is either not humble or not curious.
If someone is old or not happy then someone is patient or humble and vice versa.
If someone is either not strong or funny then someone is not quiet.
Everyone who is generous or wise is either not humble or kind and vice versa.
Everyone who is either not wise or funny is strong and vice versa.
Everyone who is calm or not old is either patient or not humble.
Everyone who is either creative or not kind is not wise.
Everyone who is not wise is both not old and brave.
If lucy is either not strong or quiet then someone is not happy or patient and vice versa.
If john is not brave then someone is not tall or kind and vice versa.
Someone is not funny or tall.
Someone is either generous or not calm.
Someone is both old and rich.
Paul is either humble or not kind.
Susan is either not generous or not creative.
Susan is not rich.
Someone is either old or generous. | Paul is wise. | entailment | (![X]:(~generous(X)<=>(~tall(X)|curious(X))))&
((?[X]:(quiet(X)))=>(?[X]:(generous(X))))&
(![X]:((~happy(X)|patient(X))<=>(kind(X)<~>old(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)&~kind(X))))&
(((~old(fred)|curious(fred)))=>((~wise(alice)<~>~creative(alice))))&
((?[X]:((~generous(X)|~funny(X))))<=>((patient(fred)&~patient(fred))))&
(![X]:((humble(X)<~>~humble(X))=>(~humble(X)<~>~curious(X))))&
((?[X]:((old(X)|~happy(X))))<=>(?[X]:((patient(X)|humble(X)))))&
((?[X]:((~strong(X)<~>funny(X))))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)|wise(X))<=>(~humble(X)<~>kind(X))))&
(![X]:((~wise(X)<~>funny(X))<=>strong(X)))&
(![X]:((calm(X)|~old(X))=>(patient(X)<~>~humble(X))))&
(![X]:((creative(X)<~>~kind(X))=>~wise(X)))&
(![X]:(~wise(X)=>(~old(X)&brave(X))))&
(((~strong(lucy)<~>quiet(lucy)))<=>(?[X]:((~happy(X)|patient(X)))))&
((~brave(john))<=>(?[X]:((~tall(X)|kind(X)))))&
(?[X]:((~funny(X)|tall(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(?[X]:((old(X)&rich(X))))&
((humble(paul)<~>~kind(paul)))&
((~generous(susan)<~>~creative(susan)))&
(~rich(susan))&
(?[X]:((old(X)<~>generous(X)))) | wise(paul) | [
"p0",
"p3",
"p5",
"p6",
"p10",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 766480761791489825340527
% SZS output start Proof for 766480761791489825340527
1. ! [X0] : (~generous(X0) <=> (curious(X0) | ~tall(X0))) [input p0]
4. ! [X0] : ((~strong(X0) & funny(X0)) <=> (~kind(X0) & happy(X0))) [input p3]
6. ? [X0] : (~funny(X0) | ~generous(X0)) <=> (~patient(fred) & patient(fred)) [input p5]
7. ! [X0] : ((humble(X0) <~> ~humble(X0)) => (~humble(X0) <~> ~curious(X0))) [input p6]
11. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> strong(X0)) [input p10]
20. humble(paul) <~> ~kind(paul) [input p19]
24. ~wise(paul) [input hypothesis]
30. ! [X0] : ((~humble(X0) <~> ~curious(X0)) | (humble(X0) <=> ~humble(X0))) [ennf transformation 7]
35. ! [X0] : ((~generous(X0) | (~curious(X0) & tall(X0))) & ((curious(X0) | ~tall(X0)) | generous(X0))) [nnf transformation 1]
36. ! [X0] : ((~generous(X0) | (~curious(X0) & tall(X0))) & (curious(X0) | ~tall(X0) | generous(X0))) [flattening 35]
42. ! [X0] : (((~strong(X0) & funny(X0)) | (kind(X0) | ~happy(X0))) & ((~kind(X0) & happy(X0)) | (strong(X0) | ~funny(X0)))) [nnf transformation 4]
43. ! [X0] : (((~strong(X0) & funny(X0)) | kind(X0) | ~happy(X0)) & ((~kind(X0) & happy(X0)) | strong(X0) | ~funny(X0))) [flattening 42]
45. (? [X0] : (~funny(X0) | ~generous(X0)) | (patient(fred) | ~patient(fred))) & ((~patient(fred) & patient(fred)) | ! [X0] : (funny(X0) & generous(X0))) [nnf transformation 6]
46. (? [X0] : (~funny(X0) | ~generous(X0)) | patient(fred) | ~patient(fred)) & ((~patient(fred) & patient(fred)) | ! [X0] : (funny(X0) & generous(X0))) [flattening 45]
47. (? [X0] : (~funny(X0) | ~generous(X0)) | patient(fred) | ~patient(fred)) & ((~patient(fred) & patient(fred)) | ! [X1] : (funny(X1) & generous(X1))) [rectify 46]
48. ? [X0] : (~funny(X0) | ~generous(X0)) => (~funny(sK1) | ~generous(sK1)) [choice axiom]
49. ((~funny(sK1) | ~generous(sK1)) | patient(fred) | ~patient(fred)) & ((~patient(fred) & patient(fred)) | ! [X1] : (funny(X1) & generous(X1))) [skolemisation 47,48]
50. ! [X0] : (((curious(X0) | humble(X0)) & (~curious(X0) | ~humble(X0))) | ((humble(X0) | humble(X0)) & (~humble(X0) | ~humble(X0)))) [nnf transformation 30]
62. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | ~strong(X0)) & (strong(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 11]
80. (kind(paul) | ~humble(paul)) & (~kind(paul) | humble(paul)) [nnf transformation 20]
87. ~curious(X0) | ~generous(X0) [cnf transformation 36]
96. ~funny(X0) | strong(X0) | ~kind(X0) [cnf transformation 43]
103. patient(fred) | generous(X1) [cnf transformation 49]
104. patient(fred) | funny(X1) [cnf transformation 49]
105. ~patient(fred) | generous(X1) [cnf transformation 49]
106. ~patient(fred) | funny(X1) [cnf transformation 49]
111. curious(X0) | humble(X0) | humble(X0) | humble(X0) [cnf transformation 50]
127. ~strong(X0) | wise(X0) | ~funny(X0) [cnf transformation 62]
151. kind(paul) | ~humble(paul) [cnf transformation 80]
157. ~wise(paul) [cnf transformation 24]
161. humble(X0) | curious(X0) [duplicate literal removal 111]
191. 7 <=> ! [X1] : funny(X1) [avatar definition]
192. funny(X1) <- (7) [avatar component clause 191]
194. 8 <=> patient(fred) [avatar definition]
197. 7 | ~8 [avatar split clause 106,194,191]
199. 9 <=> ! [X1] : generous(X1) [avatar definition]
200. generous(X1) <- (9) [avatar component clause 199]
201. 9 | ~8 [avatar split clause 105,194,199]
202. 7 | 8 [avatar split clause 104,194,191]
203. 9 | 8 [avatar split clause 103,194,199]
311. 34 <=> humble(paul) [avatar definition]
313. ~humble(paul) <- (~34) [avatar component clause 311]
315. 35 <=> kind(paul) [avatar definition]
317. kind(paul) <- (35) [avatar component clause 315]
318. ~34 | 35 [avatar split clause 151,315,311]
352. curious(paul) <- (~34) [resolution 161,313]
354. ~generous(paul) <- (~34) [resolution 352,87]
355. $false <- (9, ~34) [subsumption resolution 354,200]
356. ~9 | 34 [avatar contradiction clause 355]
402. ~kind(X0) | strong(X0) <- (7) [resolution 96,192]
406. strong(paul) <- (7, 35) [resolution 402,317]
480. wise(paul) | ~funny(paul) <- (7, 35) [resolution 406,127]
482. ~funny(paul) <- (7, 35) [subsumption resolution 480,157]
483. $false <- (7, 35) [subsumption resolution 482,192]
484. ~7 | ~35 [avatar contradiction clause 483]
485. $false [avatar sat refutation 197,201,202,203,318,356,484]
% SZS output end Proof for 766480761791489825340527
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny or creative then fred is both calm and not happy and vice versa.
Everyone who is not humble is both not happy and creative and vice versa.
Everyone who is either old or not old is curious.
Everyone who is either wise or creative is funny and vice versa.
Everyone who is patient or not humble is both old and tall.
If someone is either brave or not curious then lucy is not brave.
Everyone who is not happy or creative is both not curious and funny and vice versa.
Everyone who is both not calm and not curious is either not funny or rich and vice versa.
If someone is either happy or not wise then someone is calm or brave.
If someone is not tall then john is either not generous or rich and vice versa.
Everyone who is not rich or curious is calm or not old and vice versa.
If alice is either brave or not humble then someone is either not curious or funny and vice versa.
Everyone who is generous is either happy or not tall and vice versa.
Alice is either patient or wise.
Someone is rich or old.
Someone is tall or wise.
Someone is either not humble or not old.
Lucy is either not quiet or humble.
Someone is either humble or not curious.
Fred is either strong or creative. | John is not generous. | neutral | (((funny(alice)|creative(alice)))<=>((calm(fred)&~happy(fred))))&
(![X]:(~humble(X)<=>(~happy(X)&creative(X))))&
(![X]:((old(X)<~>~old(X))=>curious(X)))&
(![X]:((wise(X)<~>creative(X))<=>funny(X)))&
(![X]:((patient(X)|~humble(X))=>(old(X)&tall(X))))&
((?[X]:((brave(X)<~>~curious(X))))=>(~brave(lucy)))&
(![X]:((~happy(X)|creative(X))<=>(~curious(X)&funny(X))))&
(![X]:((~calm(X)&~curious(X))<=>(~funny(X)<~>rich(X))))&
((?[X]:((happy(X)<~>~wise(X))))=>(?[X]:((calm(X)|brave(X)))))&
((?[X]:(~tall(X)))<=>((~generous(john)<~>rich(john))))&
(![X]:((~rich(X)|curious(X))<=>(calm(X)|~old(X))))&
(((brave(alice)<~>~humble(alice)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(generous(X)<=>(happy(X)<~>~tall(X))))&
((patient(alice)<~>wise(alice)))&
(?[X]:((rich(X)|old(X))))&
(?[X]:((tall(X)|wise(X))))&
(?[X]:((~humble(X)<~>~old(X))))&
((~quiet(lucy)<~>humble(lucy)))&
(?[X]:((humble(X)<~>~curious(X))))&
((strong(fred)<~>creative(fred))) | ~generous(john) | [] | null | 0 |
Everyone who is not kind is not wise or calm and vice versa.
Everyone who is either generous or not tall is calm.
If alice is either not happy or curious then someone is both not quiet and calm and vice versa.
If someone is both old and rich then lucy is both not rich and not creative and vice versa.
If mary is both funny and old then someone is either tall or not humble and vice versa.
Everyone who is both not brave and not kind is strong or generous and vice versa.
Everyone who is not patient or kind is both quiet and funny and vice versa.
Everyone who is not brave or strong is not creative or old and vice versa.
If alice is tall or not wise then someone is either not old or not funny.
Everyone who is not calm or calm is not happy.
Everyone who is either not calm or not kind is not rich or not generous and vice versa.
If john is either not happy or calm then someone is either not quiet or not old and vice versa.
If paul is either happy or not humble then someone is both calm and not kind.
If someone is both calm and old then someone is wise.
Everyone who is humble or not old is not quiet and vice versa.
If someone is happy then someone is tall and vice versa.
Someone is not patient.
Someone is not wise.
Someone is old.
Alice is both not generous and rich.
Someone is either not tall or humble.
Someone is both quiet and not strong.
Someone is both not quiet and funny.
Fred is funny or not calm. | John is tall. | contradiction | (![X]:(~kind(X)<=>(~wise(X)|calm(X))))&
(![X]:((generous(X)<~>~tall(X))=>calm(X)))&
(((~happy(alice)<~>curious(alice)))<=>(?[X]:((~quiet(X)&calm(X)))))&
((?[X]:((old(X)&rich(X))))<=>((~rich(lucy)&~creative(lucy))))&
(((funny(mary)&old(mary)))<=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:((~brave(X)&~kind(X))<=>(strong(X)|generous(X))))&
(![X]:((~patient(X)|kind(X))<=>(quiet(X)&funny(X))))&
(![X]:((~brave(X)|strong(X))<=>(~creative(X)|old(X))))&
(((tall(alice)|~wise(alice)))=>(?[X]:((~old(X)<~>~funny(X)))))&
(![X]:((~calm(X)|calm(X))=>~happy(X)))&
(![X]:((~calm(X)<~>~kind(X))<=>(~rich(X)|~generous(X))))&
(((~happy(john)<~>calm(john)))<=>(?[X]:((~quiet(X)<~>~old(X)))))&
(((happy(paul)<~>~humble(paul)))=>(?[X]:((calm(X)&~kind(X)))))&
((?[X]:((calm(X)&old(X))))=>(?[X]:(wise(X))))&
(![X]:((humble(X)|~old(X))<=>~quiet(X)))&
((?[X]:(happy(X)))<=>(?[X]:(tall(X))))&
(?[X]:(~patient(X)))&
(?[X]:(~wise(X)))&
(?[X]:(old(X)))&
((~generous(alice)&rich(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:((quiet(X)&~strong(X))))&
(?[X]:((~quiet(X)&funny(X))))&
((funny(fred)|~calm(fred))) | tall(john) | [
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4947578679315890484654288
% SZS output start Proof for 4947578679315890484654288
10. ! [X0] : ((calm(X0) | ~calm(X0)) => ~happy(X0)) [input p9]
16. ? [X0] : happy(X0) <=> ? [X0] : tall(X0) [input p15]
25. tall(john) [input hypothesis]
27. ? [X0] : happy(X0) <=> ? [X1] : tall(X1) [rectify 16]
30. ! [X0] : (~happy(X0) | (~calm(X0) & calm(X0))) [ennf transformation 10]
73. (? [X0] : happy(X0) | ! [X1] : ~tall(X1)) & (? [X1] : tall(X1) | ! [X0] : ~happy(X0)) [nnf transformation 27]
74. (? [X0] : happy(X0) | ! [X1] : ~tall(X1)) & (? [X2] : tall(X2) | ! [X3] : ~happy(X3)) [rectify 73]
75. ? [X0] : happy(X0) => happy(sK7) [choice axiom]
76. ? [X2] : tall(X2) => tall(sK8) [choice axiom]
77. (happy(sK7) | ! [X1] : ~tall(X1)) & (tall(sK8) | ! [X3] : ~happy(X3)) [skolemisation 74,76,75]
130. ~happy(X0) | calm(X0) [cnf transformation 30]
131. ~happy(X0) | ~calm(X0) [cnf transformation 30]
155. happy(sK7) | ~tall(X1) [cnf transformation 77]
168. tall(john) [cnf transformation 25]
267. ~happy(X0) [subsumption resolution 130,131]
320. ~tall(X1) [subsumption resolution 155,267]
331. $false [subsumption resolution 168,320]
% SZS output end Proof for 4947578679315890484654288
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or not humble is not old and vice versa.
If mary is both not humble and not wise then someone is not generous.
Everyone who is either not brave or happy is calm or patient and vice versa.
Everyone who is either patient or not calm is either strong or creative and vice versa.
Everyone who is not strong is old or not wise and vice versa.
If john is either patient or not rich then someone is funny.
Everyone who is either humble or happy is either not calm or funny.
If someone is either not brave or creative then fred is tall or creative and vice versa.
Everyone who is both creative and old is patient or not generous.
Everyone who is not tall or not patient is funny or not generous and vice versa.
If someone is either not humble or not old then someone is either happy or not curious.
If paul is either old or kind then someone is both not tall and not happy.
If someone is not patient then someone is creative or not humble and vice versa.
Everyone who is kind is both humble and patient.
Everyone who is not happy or funny is either calm or creative and vice versa.
Everyone who is not tall is either funny or not wise.
Fred is not curious or happy.
Alice is not happy.
Someone is not generous.
Someone is not old.
Someone is quiet or not curious.
Paul is either generous or quiet.
Someone is either creative or curious. | Paul is not strong. | neutral | (![X]:((happy(X)|~humble(X))<=>~old(X)))&
(((~humble(mary)&~wise(mary)))=>(?[X]:(~generous(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(calm(X)|patient(X))))&
(![X]:((patient(X)<~>~calm(X))<=>(strong(X)<~>creative(X))))&
(![X]:(~strong(X)<=>(old(X)|~wise(X))))&
(((patient(john)<~>~rich(john)))=>(?[X]:(funny(X))))&
(![X]:((humble(X)<~>happy(X))=>(~calm(X)<~>funny(X))))&
((?[X]:((~brave(X)<~>creative(X))))<=>((tall(fred)|creative(fred))))&
(![X]:((creative(X)&old(X))=>(patient(X)|~generous(X))))&
(![X]:((~tall(X)|~patient(X))<=>(funny(X)|~generous(X))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((old(paul)<~>kind(paul)))=>(?[X]:((~tall(X)&~happy(X)))))&
((?[X]:(~patient(X)))<=>(?[X]:((creative(X)|~humble(X)))))&
(![X]:(kind(X)=>(humble(X)&patient(X))))&
(![X]:((~happy(X)|funny(X))<=>(calm(X)<~>creative(X))))&
(![X]:(~tall(X)=>(funny(X)<~>~wise(X))))&
((~curious(fred)|happy(fred)))&
(~happy(alice))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((quiet(X)|~curious(X))))&
((generous(paul)<~>quiet(paul)))&
(?[X]:((creative(X)<~>curious(X)))) | ~strong(paul) | [] | null | 0 |
Everyone who is both humble and curious is humble and vice versa.
Everyone who is both not tall and humble is not rich or not generous and vice versa.
If mary is both happy and not old then someone is not humble.
If someone is happy then susan is both not curious and not generous.
Everyone who is generous or not brave is either not wise or tall.
If john is not patient then someone is either rich or kind.
Everyone who is either rich or humble is generous.
Everyone who is quiet is either happy or not tall and vice versa.
If someone is both not generous and brave then someone is tall and vice versa.
If susan is brave or not rich then paul is not quiet or generous and vice versa.
Everyone who is either not creative or curious is not kind.
Everyone who is not happy is both not curious and not tall and vice versa.
Everyone who is both not creative and brave is calm or tall and vice versa.
Everyone who is patient or wise is quiet and vice versa.
If lucy is old then someone is either not patient or not tall and vice versa.
Everyone who is calm is both wise and not funny.
Paul is either not funny or not rich.
Fred is both not humble and creative.
Someone is both not humble and rich.
Susan is both brave and not happy.
Someone is either creative or not wise.
Paul is either old or funny.
Someone is not wise. | Lucy is not tall. | entailment | (![X]:((humble(X)&curious(X))<=>humble(X)))&
(![X]:((~tall(X)&humble(X))<=>(~rich(X)|~generous(X))))&
(((happy(mary)&~old(mary)))=>(?[X]:(~humble(X))))&
((?[X]:(happy(X)))=>((~curious(susan)&~generous(susan))))&
(![X]:((generous(X)|~brave(X))=>(~wise(X)<~>tall(X))))&
((~patient(john))=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((rich(X)<~>humble(X))=>generous(X)))&
(![X]:(quiet(X)<=>(happy(X)<~>~tall(X))))&
((?[X]:((~generous(X)&brave(X))))<=>(?[X]:(tall(X))))&
(((brave(susan)|~rich(susan)))<=>((~quiet(paul)|generous(paul))))&
(![X]:((~creative(X)<~>curious(X))=>~kind(X)))&
(![X]:(~happy(X)<=>(~curious(X)&~tall(X))))&
(![X]:((~creative(X)&brave(X))<=>(calm(X)|tall(X))))&
(![X]:((patient(X)|wise(X))<=>quiet(X)))&
((old(lucy))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:(calm(X)=>(wise(X)&~funny(X))))&
((~funny(paul)<~>~rich(paul)))&
((~humble(fred)&creative(fred)))&
(?[X]:((~humble(X)&rich(X))))&
((brave(susan)&~happy(susan)))&
(?[X]:((creative(X)<~>~wise(X))))&
((old(paul)<~>funny(paul)))&
(?[X]:(~wise(X))) | ~tall(lucy) | [
"p0",
"p1",
"p3",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 470575124401602005620580
% SZS output start Proof for 470575124401602005620580
1. ! [X0] : ((curious(X0) & humble(X0)) <=> humble(X0)) [input p0]
2. ! [X0] : ((humble(X0) & ~tall(X0)) <=> (~generous(X0) | ~rich(X0))) [input p1]
4. ? [X0] : happy(X0) => (~generous(susan) & ~curious(susan)) [input p3]
12. ! [X0] : (~happy(X0) <=> (~tall(X0) & ~curious(X0))) [input p11]
24. tall(lucy) [input hypothesis]
28. (~generous(susan) & ~curious(susan)) | ! [X0] : ~happy(X0) [ennf transformation 4]
34. ! [X0] : (((curious(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | (~curious(X0) | ~humble(X0)))) [nnf transformation 1]
35. ! [X0] : (((curious(X0) & humble(X0)) | ~humble(X0)) & (humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 34]
36. ! [X0] : (((humble(X0) & ~tall(X0)) | (generous(X0) & rich(X0))) & ((~generous(X0) | ~rich(X0)) | (~humble(X0) | tall(X0)))) [nnf transformation 2]
37. ! [X0] : (((humble(X0) & ~tall(X0)) | (generous(X0) & rich(X0))) & (~generous(X0) | ~rich(X0) | ~humble(X0) | tall(X0))) [flattening 36]
54. ! [X0] : ((~happy(X0) | (tall(X0) | curious(X0))) & ((~tall(X0) & ~curious(X0)) | happy(X0))) [nnf transformation 12]
55. ! [X0] : ((~happy(X0) | tall(X0) | curious(X0)) & ((~tall(X0) & ~curious(X0)) | happy(X0))) [flattening 54]
75. ~humble(X0) | curious(X0) [cnf transformation 35]
80. generous(X0) | humble(X0) [cnf transformation 37]
82. ~curious(susan) | ~happy(X0) [cnf transformation 28]
83. ~generous(susan) | ~happy(X0) [cnf transformation 28]
106. ~tall(X0) | happy(X0) [cnf transformation 55]
135. tall(lucy) [cnf transformation 24]
150. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
151. ~happy(X0) <- (4) [avatar component clause 150]
153. 5 <=> generous(susan) [avatar definition]
155. ~generous(susan) <- (~5) [avatar component clause 153]
156. 4 | ~5 [avatar split clause 83,153,150]
158. 6 <=> curious(susan) [avatar definition]
160. ~curious(susan) <- (~6) [avatar component clause 158]
161. 4 | ~6 [avatar split clause 82,158,150]
274. humble(susan) <- (~5) [resolution 80,155]
276. curious(susan) <- (~5) [resolution 274,75]
277. $false <- (~5, ~6) [subsumption resolution 276,160]
278. 5 | 6 [avatar contradiction clause 277]
280. happy(lucy) [resolution 106,135]
281. $false <- (4) [subsumption resolution 280,151]
282. ~4 [avatar contradiction clause 281]
283. $false [avatar sat refutation 156,161,278,282]
% SZS output end Proof for 470575124401602005620580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not funny then someone is either not funny or generous and vice versa.
If susan is not patient then lucy is both not rich and old.
Everyone who is not brave or creative is tall.
Everyone who is not generous or tall is not old or not wise.
Everyone who is either not happy or curious is both patient and not generous.
Everyone who is old is either not strong or not humble and vice versa.
Everyone who is either rich or funny is both not strong and strong.
Everyone who is both not generous and not tall is strong or generous.
Everyone who is not brave is not wise or curious.
Everyone who is not creative or not old is curious.
Everyone who is kind or not calm is rich and vice versa.
If paul is curious or not generous then someone is either creative or not brave and vice versa.
Everyone who is either not strong or tall is either not old or kind and vice versa.
If mary is either not rich or not patient then someone is not funny or strong.
Everyone who is both not wise and not old is both not calm and not rich.
If someone is both curious and strong then someone is both not creative and not rich and vice versa.
Someone is happy.
Someone is either not brave or not funny.
Alice is not wise.
Paul is kind.
Alice is both strong and creative.
Someone is not tall or not funny.
Alice is both strong and funny.
Paul is either not old or wise. | Paul is not happy. | entailment | ((?[X]:((~patient(X)|~funny(X))))<=>(?[X]:((~funny(X)<~>generous(X)))))&
((~patient(susan))=>((~rich(lucy)&old(lucy))))&
(![X]:((~brave(X)|creative(X))=>tall(X)))&
(![X]:((~generous(X)|tall(X))=>(~old(X)|~wise(X))))&
(![X]:((~happy(X)<~>curious(X))=>(patient(X)&~generous(X))))&
(![X]:(old(X)<=>(~strong(X)<~>~humble(X))))&
(![X]:((rich(X)<~>funny(X))=>(~strong(X)&strong(X))))&
(![X]:((~generous(X)&~tall(X))=>(strong(X)|generous(X))))&
(![X]:(~brave(X)=>(~wise(X)|curious(X))))&
(![X]:((~creative(X)|~old(X))=>curious(X)))&
(![X]:((kind(X)|~calm(X))<=>rich(X)))&
(((curious(paul)|~generous(paul)))<=>(?[X]:((creative(X)<~>~brave(X)))))&
(![X]:((~strong(X)<~>tall(X))<=>(~old(X)<~>kind(X))))&
(((~rich(mary)<~>~patient(mary)))=>(?[X]:((~funny(X)|strong(X)))))&
(![X]:((~wise(X)&~old(X))=>(~calm(X)&~rich(X))))&
((?[X]:((curious(X)&strong(X))))<=>(?[X]:((~creative(X)&~rich(X)))))&
(?[X]:(happy(X)))&
(?[X]:((~brave(X)<~>~funny(X))))&
(~wise(alice))&
(kind(paul))&
((strong(alice)&creative(alice)))&
(?[X]:((~tall(X)|~funny(X))))&
((strong(alice)&funny(alice)))&
((~old(paul)<~>wise(paul))) | ~happy(paul) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3436357751466208034468777
% SZS output start Proof for 3436357751466208034468777
3. ! [X0] : ((creative(X0) | ~brave(X0)) => tall(X0)) [input p2]
4. ! [X0] : ((tall(X0) | ~generous(X0)) => (~wise(X0) | ~old(X0))) [input p3]
5. ! [X0] : ((~happy(X0) <~> curious(X0)) => (~generous(X0) & patient(X0))) [input p4]
10. ! [X0] : ((~old(X0) | ~creative(X0)) => curious(X0)) [input p9]
11. ! [X0] : ((~calm(X0) | kind(X0)) <=> rich(X0)) [input p10]
15. ! [X0] : ((~old(X0) & ~wise(X0)) => (~rich(X0) & ~calm(X0))) [input p14]
24. ~old(paul) <~> wise(paul) [input p23]
25. happy(paul) [input hypothesis]
29. ! [X0] : (tall(X0) | (~creative(X0) & brave(X0))) [ennf transformation 3]
30. ! [X0] : ((~wise(X0) | ~old(X0)) | (~tall(X0) & generous(X0))) [ennf transformation 4]
31. ! [X0] : (~wise(X0) | ~old(X0) | (~tall(X0) & generous(X0))) [flattening 30]
32. ! [X0] : ((~generous(X0) & patient(X0)) | (~happy(X0) <=> curious(X0))) [ennf transformation 5]
38. ! [X0] : (curious(X0) | (old(X0) & creative(X0))) [ennf transformation 10]
40. ! [X0] : ((~rich(X0) & ~calm(X0)) | (old(X0) | wise(X0))) [ennf transformation 15]
41. ! [X0] : ((~rich(X0) & ~calm(X0)) | old(X0) | wise(X0)) [flattening 40]
47. ! [X0] : ((~generous(X0) & patient(X0)) | ((~happy(X0) | ~curious(X0)) & (curious(X0) | happy(X0)))) [nnf transformation 32]
50. ! [X0] : (((~calm(X0) | kind(X0)) | ~rich(X0)) & (rich(X0) | (calm(X0) & ~kind(X0)))) [nnf transformation 11]
51. ! [X0] : ((~calm(X0) | kind(X0) | ~rich(X0)) & (rich(X0) | (calm(X0) & ~kind(X0)))) [flattening 50]
73. (~wise(paul) | old(paul)) & (wise(paul) | ~old(paul)) [nnf transformation 24]
83. ~creative(X0) | tall(X0) [cnf transformation 29]
84. ~wise(X0) | ~old(X0) | generous(X0) [cnf transformation 31]
85. ~wise(X0) | ~old(X0) | ~tall(X0) [cnf transformation 31]
89. ~curious(X0) | ~happy(X0) | ~generous(X0) [cnf transformation 47]
100. curious(X0) | creative(X0) [cnf transformation 38]
103. calm(X0) | rich(X0) [cnf transformation 51]
121. ~calm(X0) | old(X0) | wise(X0) [cnf transformation 41]
122. ~rich(X0) | old(X0) | wise(X0) [cnf transformation 41]
137. wise(paul) | ~old(paul) [cnf transformation 73]
138. ~wise(paul) | old(paul) [cnf transformation 73]
139. happy(paul) [cnf transformation 25]
195. 13 <=> curious(paul) [avatar definition]
196. ~curious(paul) <- (~13) [avatar component clause 195]
197. curious(paul) <- (13) [avatar component clause 195]
199. 14 <=> generous(paul) [avatar definition]
283. 32 <=> old(paul) [avatar definition]
284. ~old(paul) <- (~32) [avatar component clause 283]
285. old(paul) <- (32) [avatar component clause 283]
287. 33 <=> wise(paul) [avatar definition]
288. wise(paul) <- (33) [avatar component clause 287]
289. ~wise(paul) <- (~33) [avatar component clause 287]
290. 32 | ~33 [avatar split clause 138,287,283]
291. ~32 | 33 [avatar split clause 137,287,283]
375. ~happy(paul) | ~generous(paul) <- (13) [resolution 197,89]
377. ~generous(paul) <- (13) [subsumption resolution 375,139]
381. ~14 | ~13 [avatar split clause 377,195,199]
431. old(X0) | wise(X0) | rich(X0) [resolution 121,103]
432. wise(X0) | old(X0) [subsumption resolution 431,122]
439. old(paul) <- (~33) [resolution 432,289]
442. $false <- (~32, ~33) [subsumption resolution 439,284]
443. 32 | 33 [avatar contradiction clause 442]
447. ~old(paul) | ~tall(paul) <- (33) [resolution 288,85]
448. ~old(paul) | generous(paul) <- (33) [resolution 288,84]
449. ~tall(paul) <- (32, 33) [subsumption resolution 447,285]
450. generous(paul) <- (32, 33) [subsumption resolution 448,285]
458. 14 | ~32 | ~33 [avatar split clause 450,287,283,199]
461. creative(paul) <- (~13) [resolution 196,100]
481. tall(paul) <- (~13) [resolution 461,83]
484. $false <- (~13, 32, 33) [subsumption resolution 481,449]
485. 13 | ~32 | ~33 [avatar contradiction clause 484]
486. $false [avatar sat refutation 290,291,381,443,458,485]
% SZS output end Proof for 3436357751466208034468777
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not calm then someone is funny or not strong and vice versa.
Everyone who is both rich and wise is not humble and vice versa.
Everyone who is curious is both patient and creative and vice versa.
If john is tall or not curious then someone is both not patient and quiet.
If someone is either not patient or calm then alice is either not funny or not happy and vice versa.
Everyone who is rich or humble is old and vice versa.
Everyone who is either not old or calm is both not brave and not tall.
If someone is either happy or calm then someone is either not generous or tall and vice versa.
If lucy is not happy then someone is either kind or curious.
Everyone who is wise or generous is both not happy and creative.
Everyone who is rich or not patient is wise.
Everyone who is happy or not humble is not patient and vice versa.
Everyone who is either not rich or funny is quiet.
If mary is not curious then someone is kind or curious and vice versa.
If someone is strong then someone is either patient or not kind and vice versa.
Everyone who is tall is patient or quiet.
Someone is either patient or not patient.
Someone is not funny.
Someone is generous or not curious.
Someone is either not curious or patient.
John is either not tall or creative.
Someone is not strong or not curious. | Lucy is not creative. | neutral | ((~calm(fred))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:((rich(X)&wise(X))<=>~humble(X)))&
(![X]:(curious(X)<=>(patient(X)&creative(X))))&
(((tall(john)|~curious(john)))=>(?[X]:((~patient(X)&quiet(X)))))&
((?[X]:((~patient(X)<~>calm(X))))<=>((~funny(alice)<~>~happy(alice))))&
(![X]:((rich(X)|humble(X))<=>old(X)))&
(![X]:((~old(X)<~>calm(X))=>(~brave(X)&~tall(X))))&
((?[X]:((happy(X)<~>calm(X))))<=>(?[X]:((~generous(X)<~>tall(X)))))&
((~happy(lucy))=>(?[X]:((kind(X)<~>curious(X)))))&
(![X]:((wise(X)|generous(X))=>(~happy(X)&creative(X))))&
(![X]:((rich(X)|~patient(X))=>wise(X)))&
(![X]:((happy(X)|~humble(X))<=>~patient(X)))&
(![X]:((~rich(X)<~>funny(X))=>quiet(X)))&
((~curious(mary))<=>(?[X]:((kind(X)|curious(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((patient(X)<~>~kind(X)))))&
(![X]:(tall(X)=>(patient(X)|quiet(X))))&
(?[X]:((patient(X)<~>~patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((~curious(X)<~>patient(X))))&
((~tall(john)<~>creative(john)))&
(?[X]:((~strong(X)|~curious(X)))) | ~creative(lucy) | [] | null | 0 |
If susan is humble then john is either not wise or not patient and vice versa.
If john is either calm or curious then someone is either generous or curious.
Everyone who is either not happy or funny is brave or not strong.
Everyone who is either not wise or humble is both humble and quiet.
Everyone who is funny is either kind or funny.
If someone is both generous and calm then lucy is either not wise or not creative.
If fred is wise then mary is not calm and vice versa.
If mary is either not kind or calm then alice is both not patient and funny and vice versa.
If paul is both tall and kind then paul is quiet or not rich and vice versa.
Everyone who is either humble or old is either not rich or not patient.
Everyone who is either not calm or rich is not calm and vice versa.
If lucy is either not brave or strong then fred is not quiet and vice versa.
Everyone who is funny or not kind is both not tall and not quiet and vice versa.
Everyone who is quiet or creative is calm or not quiet.
Everyone who is patient is not kind or generous and vice versa.
Everyone who is not creative or not rich is both wise and not creative.
Someone is curious or not old.
Someone is both not old and generous.
Lucy is either calm or not creative.
Alice is both old and not funny.
Mary is either patient or tall.
Someone is either happy or funny.
Mary is brave.
Mary is either old or brave. | Lucy is calm. | contradiction | ((humble(susan))<=>((~wise(john)<~>~patient(john))))&
(((calm(john)<~>curious(john)))=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~happy(X)<~>funny(X))=>(brave(X)|~strong(X))))&
(![X]:((~wise(X)<~>humble(X))=>(humble(X)&quiet(X))))&
(![X]:(funny(X)=>(kind(X)<~>funny(X))))&
((?[X]:((generous(X)&calm(X))))=>((~wise(lucy)<~>~creative(lucy))))&
((wise(fred))<=>(~calm(mary)))&
(((~kind(mary)<~>calm(mary)))<=>((~patient(alice)&funny(alice))))&
(((tall(paul)&kind(paul)))<=>((quiet(paul)|~rich(paul))))&
(![X]:((humble(X)<~>old(X))=>(~rich(X)<~>~patient(X))))&
(![X]:((~calm(X)<~>rich(X))<=>~calm(X)))&
(((~brave(lucy)<~>strong(lucy)))<=>(~quiet(fred)))&
(![X]:((funny(X)|~kind(X))<=>(~tall(X)&~quiet(X))))&
(![X]:((quiet(X)|creative(X))=>(calm(X)|~quiet(X))))&
(![X]:(patient(X)<=>(~kind(X)|generous(X))))&
(![X]:((~creative(X)|~rich(X))=>(wise(X)&~creative(X))))&
(?[X]:((curious(X)|~old(X))))&
(?[X]:((~old(X)&generous(X))))&
((calm(lucy)<~>~creative(lucy)))&
((old(alice)&~funny(alice)))&
((patient(mary)<~>tall(mary)))&
(?[X]:((happy(X)<~>funny(X))))&
(brave(mary))&
((old(mary)<~>brave(mary))) | calm(lucy) | [
"p10",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 797902906708209581480391
% SZS output start Proof for 797902906708209581480391
11. ! [X0] : ((~calm(X0) <~> rich(X0)) <=> ~calm(X0)) [input p10]
16. ! [X0] : ((~rich(X0) | ~creative(X0)) => (~creative(X0) & wise(X0))) [input p15]
19. calm(lucy) <~> ~creative(lucy) [input p18]
25. calm(lucy) [input hypothesis]
35. ! [X0] : ((~creative(X0) & wise(X0)) | (rich(X0) & creative(X0))) [ennf transformation 16]
50. ! [X0] : ((((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | calm(X0)) & (~calm(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0))))) [nnf transformation 11]
60. (creative(lucy) | ~calm(lucy)) & (~creative(lucy) | calm(lucy)) [nnf transformation 19]
102. ~calm(X0) | ~calm(X0) | ~rich(X0) [cnf transformation 50]
104. ~rich(X0) | calm(X0) | calm(X0) [cnf transformation 50]
122. ~creative(X0) | rich(X0) [cnf transformation 35]
127. creative(lucy) | ~calm(lucy) [cnf transformation 60]
137. calm(lucy) [cnf transformation 25]
139. ~calm(X0) | ~rich(X0) [duplicate literal removal 102]
140. ~rich(X0) | calm(X0) [duplicate literal removal 104]
241. ~rich(X0) [subsumption resolution 139,140]
259. ~creative(X0) [subsumption resolution 122,241]
270. ~calm(lucy) [subsumption resolution 127,259]
293. $false [subsumption resolution 137,270]
% SZS output end Proof for 797902906708209581480391
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not creative or calm then someone is either not old or not calm. If someone is not curious then mary is not curious. Everyone who is not patient or happy is both quiet and rich. Everyone who is both not tall and curious is curious or not calm. If paul is both happy and not rich then someone is brave. Everyone who is not wise or not quiet is tall. If paul is wise then fred is not curious. If someone is either not funny or rich then john is humble or not brave and vice versa. Everyone who is either quiet or wise is both not humble and not old and vice versa. If mary is patient or quiet then lucy is not patient or strong. If someone is rich or kind then fred is not old or not creative and vice versa. If someone is not patient or old then mary is generous or not happy. If someone is not curious then someone is curious and vice versa. Everyone who is both not old and not brave is strong and vice versa. Everyone who is kind or not kind is not wise and vice versa. If someone is not old then fred is both not strong and not calm and vice versa. Susan is not wise. Someone is rich or old. Someone is either not curious or brave. Someone is patient. Someone is either rich or not strong. Someone is humble. | Lucy is not old. | entailment | ((?[X]:((~creative(X)<~>calm(X))))=>(?[X]:((~old(X)<~>~calm(X)))))&
((?[X]:(~curious(X)))=>(~curious(mary)))&
(![X]:((~patient(X)|happy(X))=>(quiet(X)&rich(X))))&
(![X]:((~tall(X)&curious(X))=>(curious(X)|~calm(X))))&
(((happy(paul)&~rich(paul)))=>(?[X]:(brave(X))))&
(![X]:((~wise(X)|~quiet(X))=>tall(X)))&
((wise(paul))=>(~curious(fred)))&
((?[X]:((~funny(X)<~>rich(X))))<=>((humble(john)|~brave(john))))&
(![X]:((quiet(X)<~>wise(X))<=>(~humble(X)&~old(X))))&
(((patient(mary)|quiet(mary)))=>((~patient(lucy)|strong(lucy))))&
((?[X]:((rich(X)|kind(X))))<=>((~old(fred)|~creative(fred))))&
((?[X]:((~patient(X)|old(X))))=>((generous(mary)|~happy(mary))))&
((?[X]:(~curious(X)))<=>(?[X]:(curious(X))))&
(![X]:((~old(X)&~brave(X))<=>strong(X)))&
(![X]:((kind(X)|~kind(X))<=>~wise(X)))&
((?[X]:(~old(X)))<=>((~strong(fred)&~calm(fred))))&
(~wise(susan))&
(?[X]:((rich(X)|old(X))))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:(patient(X)))&
(?[X]:((rich(X)<~>~strong(X))))&
(?[X]:(humble(X))) | ~old(lucy) | [
"p2",
"p8",
"p9",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2657111179628927931872854
% SZS output start Proof for 2657111179628927931872854
3. ! [X0] : ((happy(X0) | ~patient(X0)) => (rich(X0) & quiet(X0))) [input p2]
9. ! [X0] : ((quiet(X0) <~> wise(X0)) <=> (~old(X0) & ~humble(X0))) [input p8]
10. (quiet(mary) | patient(mary)) => (strong(lucy) | ~patient(lucy)) [input p9]
14. ! [X0] : ((~brave(X0) & ~old(X0)) <=> strong(X0)) [input p13]
15. ! [X0] : ((~kind(X0) | kind(X0)) <=> ~wise(X0)) [input p14]
23. old(lucy) [input hypothesis]
29. ! [X0] : (~patient(X0) => (rich(X0) & quiet(X0))) [pure predicate removal 3]
33. ! [X0] : ((rich(X0) & quiet(X0)) | patient(X0)) [ennf transformation 29]
35. (strong(lucy) | ~patient(lucy)) | (~quiet(mary) & ~patient(mary)) [ennf transformation 10]
36. strong(lucy) | ~patient(lucy) | (~quiet(mary) & ~patient(mary)) [flattening 35]
46. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (old(X0) | humble(X0))) & ((~old(X0) & ~humble(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | old(X0) | humble(X0)) & ((~old(X0) & ~humble(X0)) | ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))))) [flattening 46]
58. ! [X0] : (((~brave(X0) & ~old(X0)) | ~strong(X0)) & (strong(X0) | (brave(X0) | old(X0)))) [nnf transformation 14]
59. ! [X0] : (((~brave(X0) & ~old(X0)) | ~strong(X0)) & (strong(X0) | brave(X0) | old(X0))) [flattening 58]
60. ! [X0] : (((~kind(X0) | kind(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) & ~kind(X0)))) [nnf transformation 15]
61. ! [X0] : ((~kind(X0) | kind(X0) | wise(X0)) & (~wise(X0) | (kind(X0) & ~kind(X0)))) [flattening 60]
84. quiet(X0) | patient(X0) [cnf transformation 33]
95. ~quiet(X0) | wise(X0) | ~old(X0) [cnf transformation 47]
99. strong(lucy) | ~patient(lucy) | ~patient(mary) [cnf transformation 36]
100. strong(lucy) | ~patient(lucy) | ~quiet(mary) [cnf transformation 36]
108. ~strong(X0) | ~old(X0) [cnf transformation 59]
110. ~wise(X0) | ~kind(X0) [cnf transformation 61]
111. ~wise(X0) | kind(X0) [cnf transformation 61]
124. old(lucy) [cnf transformation 23]
189. 15 <=> quiet(mary) [avatar definition]
191. ~quiet(mary) <- (~15) [avatar component clause 189]
193. 16 <=> patient(lucy) [avatar definition]
197. 17 <=> strong(lucy) [avatar definition]
199. strong(lucy) <- (17) [avatar component clause 197]
200. ~15 | ~16 | 17 [avatar split clause 100,197,193,189]
202. 18 <=> patient(mary) [avatar definition]
204. ~patient(mary) <- (~18) [avatar component clause 202]
205. ~18 | ~16 | 17 [avatar split clause 99,197,193,202]
245. ~wise(X0) [subsumption resolution 110,111]
305. wise(X0) | ~old(X0) | patient(X0) [resolution 95,84]
306. ~old(X0) | patient(X0) [subsumption resolution 305,245]
307. patient(lucy) [resolution 306,124]
311. 16 [avatar split clause 307,193]
312. patient(mary) <- (~15) [resolution 191,84]
313. $false <- (~15, ~18) [subsumption resolution 312,204]
314. 15 | 18 [avatar contradiction clause 313]
318. ~old(lucy) <- (17) [resolution 199,108]
319. $false <- (17) [subsumption resolution 318,124]
320. ~17 [avatar contradiction clause 319]
321. $false [avatar sat refutation 200,205,311,314,320]
% SZS output end Proof for 2657111179628927931872854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not funny then someone is either strong or brave and vice versa.
If lucy is not humble or generous then someone is either not creative or not wise.
If paul is wise or kind then someone is humble or old and vice versa.
Everyone who is not wise or generous is both not strong and quiet and vice versa.
Everyone who is both kind and humble is either humble or not old and vice versa.
If someone is either kind or old then mary is tall or not kind.
Everyone who is not calm or not happy is both strong and not tall.
Everyone who is calm is curious or strong.
If alice is both not humble and brave then someone is both not happy and calm.
Everyone who is patient is either not quiet or strong and vice versa.
Everyone who is funny or wise is happy.
Everyone who is both patient and rich is not funny and vice versa.
If lucy is not humble or happy then susan is either not wise or happy and vice versa.
If someone is not brave or brave then lucy is either not quiet or curious.
Everyone who is either old or wise is both not creative and not funny and vice versa.
Everyone who is either not quiet or curious is kind and vice versa.
Paul is either not humble or not old.
Someone is funny or not rich.
Lucy is not creative or not funny.
Paul is not kind.
Someone is kind.
John is either curious or not brave.
Someone is both curious and not calm.
Someone is calm or not calm. | John is not wise. | contradiction | ((?[X]:((quiet(X)<~>~funny(X))))<=>(?[X]:((strong(X)<~>brave(X)))))&
(((~humble(lucy)|generous(lucy)))=>(?[X]:((~creative(X)<~>~wise(X)))))&
(((wise(paul)|kind(paul)))<=>(?[X]:((humble(X)|old(X)))))&
(![X]:((~wise(X)|generous(X))<=>(~strong(X)&quiet(X))))&
(![X]:((kind(X)&humble(X))<=>(humble(X)<~>~old(X))))&
((?[X]:((kind(X)<~>old(X))))=>((tall(mary)|~kind(mary))))&
(![X]:((~calm(X)|~happy(X))=>(strong(X)&~tall(X))))&
(![X]:(calm(X)=>(curious(X)|strong(X))))&
(((~humble(alice)&brave(alice)))=>(?[X]:((~happy(X)&calm(X)))))&
(![X]:(patient(X)<=>(~quiet(X)<~>strong(X))))&
(![X]:((funny(X)|wise(X))=>happy(X)))&
(![X]:((patient(X)&rich(X))<=>~funny(X)))&
(((~humble(lucy)|happy(lucy)))<=>((~wise(susan)<~>happy(susan))))&
((?[X]:((~brave(X)|brave(X))))=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((old(X)<~>wise(X))<=>(~creative(X)&~funny(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>kind(X)))&
((~humble(paul)<~>~old(paul)))&
(?[X]:((funny(X)|~rich(X))))&
((~creative(lucy)|~funny(lucy)))&
(~kind(paul))&
(?[X]:(kind(X)))&
((curious(john)<~>~brave(john)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:((calm(X)|~calm(X)))) | ~wise(john) | [
"p3",
"p4",
"p6",
"p7",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8798333870667754669301718
% SZS output start Proof for 8798333870667754669301718
4. ! [X0] : ((generous(X0) | ~wise(X0)) <=> (quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((humble(X0) & kind(X0)) <=> (humble(X0) <~> ~old(X0))) [input p4]
7. ! [X0] : ((~happy(X0) | ~calm(X0)) => (~tall(X0) & strong(X0))) [input p6]
8. ! [X0] : (calm(X0) => (strong(X0) | curious(X0))) [input p7]
10. ! [X0] : (patient(X0) <=> (~quiet(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((rich(X0) & patient(X0)) <=> ~funny(X0)) [input p11]
15. ! [X0] : ((old(X0) <~> wise(X0)) <=> (~funny(X0) & ~creative(X0))) [input p14]
16. ! [X0] : ((~quiet(X0) <~> curious(X0)) <=> kind(X0)) [input p15]
25. ~wise(john) [input hypothesis]
30. ! [X0] : ((~tall(X0) & strong(X0)) | (happy(X0) & calm(X0))) [ennf transformation 7]
31. ! [X0] : ((strong(X0) | curious(X0)) | ~calm(X0)) [ennf transformation 8]
32. ! [X0] : (strong(X0) | curious(X0) | ~calm(X0)) [flattening 31]
50. ! [X0] : (((generous(X0) | ~wise(X0)) | (~quiet(X0) | strong(X0))) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [nnf transformation 4]
51. ! [X0] : ((generous(X0) | ~wise(X0) | ~quiet(X0) | strong(X0)) & ((quiet(X0) & ~strong(X0)) | (~generous(X0) & wise(X0)))) [flattening 50]
52. ! [X0] : (((humble(X0) & kind(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | (~humble(X0) | ~kind(X0)))) [nnf transformation 5]
53. ! [X0] : (((humble(X0) & kind(X0)) | ((humble(X0) | old(X0)) & (~old(X0) | ~humble(X0)))) & (((old(X0) | ~humble(X0)) & (~old(X0) | humble(X0))) | ~humble(X0) | ~kind(X0))) [flattening 52]
57. ! [X0] : ((patient(X0) | ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) & (((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ~patient(X0))) [nnf transformation 10]
58. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | (~rich(X0) | ~patient(X0)))) [nnf transformation 12]
59. ! [X0] : (((rich(X0) & patient(X0)) | funny(X0)) & (~funny(X0) | ~rich(X0) | ~patient(X0))) [flattening 58]
63. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | (funny(X0) | creative(X0))) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [nnf transformation 15]
64. ! [X0] : ((((~wise(X0) | ~old(X0)) & (wise(X0) | old(X0))) | funny(X0) | creative(X0)) & ((~funny(X0) & ~creative(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0))))) [flattening 63]
65. ! [X0] : ((((~curious(X0) | quiet(X0)) & (curious(X0) | ~quiet(X0))) | ~kind(X0)) & (kind(X0) | ((~quiet(X0) | ~curious(X0)) & (curious(X0) | quiet(X0))))) [nnf transformation 16]
92. ~strong(X0) | wise(X0) [cnf transformation 51]
94. wise(X0) | quiet(X0) [cnf transformation 51]
98. old(X0) | ~humble(X0) | ~humble(X0) | ~kind(X0) [cnf transformation 53]
102. humble(X0) | humble(X0) | old(X0) [cnf transformation 53]
105. calm(X0) | strong(X0) [cnf transformation 30]
109. strong(X0) | curious(X0) | ~calm(X0) [cnf transformation 32]
112. ~patient(X0) | ~quiet(X0) | strong(X0) [cnf transformation 57]
119. patient(X0) | funny(X0) [cnf transformation 59]
133. ~old(X0) | wise(X0) | ~funny(X0) [cnf transformation 64]
138. ~curious(X0) | ~quiet(X0) | kind(X0) [cnf transformation 65]
152. ~wise(john) [cnf transformation 25]
153. old(X0) | ~humble(X0) | ~kind(X0) [duplicate literal removal 98]
154. old(X0) | humble(X0) [duplicate literal removal 102]
237. ~kind(X0) | old(X0) [subsumption resolution 153,154]
250. curious(X0) | strong(X0) [subsumption resolution 109,105]
326. 37 <=> curious(john) [avatar definition]
327. curious(john) <- (37) [avatar component clause 326]
328. ~curious(john) <- (~37) [avatar component clause 326]
336. quiet(john) [resolution 94,152]
364. strong(john) <- (~37) [resolution 250,328]
368. wise(john) <- (~37) [resolution 364,92]
369. $false <- (~37) [subsumption resolution 368,152]
370. 37 [avatar contradiction clause 369]
371. ~quiet(X0) | strong(X0) | funny(X0) [resolution 112,119]
485. ~quiet(john) | kind(john) <- (37) [resolution 138,327]
487. kind(john) <- (37) [subsumption resolution 485,336]
511. old(john) <- (37) [resolution 487,237]
559. strong(john) | funny(john) [resolution 371,336]
563. 64 <=> funny(john) [avatar definition]
567. 65 <=> strong(john) [avatar definition]
569. strong(john) <- (65) [avatar component clause 567]
570. 64 | 65 [avatar split clause 559,567,563]
632. wise(john) | ~funny(john) <- (37) [resolution 511,133]
635. ~funny(john) <- (37) [subsumption resolution 632,152]
639. ~64 | ~37 [avatar split clause 635,326,563]
653. wise(john) <- (65) [resolution 569,92]
655. $false <- (65) [subsumption resolution 653,152]
656. ~65 [avatar contradiction clause 655]
657. $false [avatar sat refutation 370,570,639,656]
% SZS output end Proof for 8798333870667754669301718
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong or quiet is rich or strong and vice versa.
If fred is brave or generous then susan is either kind or rich.
Everyone who is old or tall is kind and vice versa.
Everyone who is both wise and not humble is kind and vice versa.
If john is funny or not curious then someone is both not calm and not patient.
Everyone who is not quiet or generous is either creative or tall and vice versa.
Everyone who is both kind and not happy is generous or happy and vice versa.
If lucy is either not creative or not happy then someone is quiet and vice versa.
Everyone who is funny is not humble and vice versa.
If someone is either not tall or funny then someone is not brave and vice versa.
Everyone who is either not kind or happy is not brave.
If someone is both curious and not quiet then someone is not strong and vice versa.
Everyone who is not quiet is both not tall and not kind.
Everyone who is tall is not curious or generous and vice versa.
Everyone who is not quiet or not creative is not tall.
If alice is not patient then someone is either kind or not tall.
Paul is not happy.
Susan is not funny or generous.
Someone is humble or not patient.
Someone is either not humble or quiet.
Someone is not tall or brave. | Paul is curious. | entailment | (![X]:((~strong(X)|quiet(X))<=>(rich(X)|strong(X))))&
(((brave(fred)|generous(fred)))=>((kind(susan)<~>rich(susan))))&
(![X]:((old(X)|tall(X))<=>kind(X)))&
(![X]:((wise(X)&~humble(X))<=>kind(X)))&
(((funny(john)|~curious(john)))=>(?[X]:((~calm(X)&~patient(X)))))&
(![X]:((~quiet(X)|generous(X))<=>(creative(X)<~>tall(X))))&
(![X]:((kind(X)&~happy(X))<=>(generous(X)|happy(X))))&
(((~creative(lucy)<~>~happy(lucy)))<=>(?[X]:(quiet(X))))&
(![X]:(funny(X)<=>~humble(X)))&
((?[X]:((~tall(X)<~>funny(X))))<=>(?[X]:(~brave(X))))&
(![X]:((~kind(X)<~>happy(X))=>~brave(X)))&
((?[X]:((curious(X)&~quiet(X))))<=>(?[X]:(~strong(X))))&
(![X]:(~quiet(X)=>(~tall(X)&~kind(X))))&
(![X]:(tall(X)<=>(~curious(X)|generous(X))))&
(![X]:((~quiet(X)|~creative(X))=>~tall(X)))&
((~patient(alice))=>(?[X]:((kind(X)<~>~tall(X)))))&
(~happy(paul))&
((~funny(susan)|generous(susan)))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(?[X]:((~tall(X)|brave(X)))) | curious(paul) | [
"p2",
"p5",
"p6",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 254651502935321368476733
% SZS output start Proof for 254651502935321368476733
3. ! [X0] : ((tall(X0) | old(X0)) <=> kind(X0)) [input p2]
6. ! [X0] : ((generous(X0) | ~quiet(X0)) <=> (creative(X0) <~> tall(X0))) [input p5]
7. ! [X0] : ((~happy(X0) & kind(X0)) <=> (happy(X0) | generous(X0))) [input p6]
14. ! [X0] : (tall(X0) <=> (generous(X0) | ~curious(X0))) [input p13]
15. ! [X0] : ((~creative(X0) | ~quiet(X0)) => ~tall(X0)) [input p14]
22. ~curious(paul) [input hypothesis]
30. ! [X0] : (~tall(X0) | (creative(X0) & quiet(X0))) [ennf transformation 15]
35. ! [X0] : (((tall(X0) | old(X0)) | ~kind(X0)) & (kind(X0) | (~tall(X0) & ~old(X0)))) [nnf transformation 3]
36. ! [X0] : ((tall(X0) | old(X0) | ~kind(X0)) & (kind(X0) | (~tall(X0) & ~old(X0)))) [flattening 35]
41. ! [X0] : (((generous(X0) | ~quiet(X0)) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [nnf transformation 6]
42. ! [X0] : ((generous(X0) | ~quiet(X0) | ((creative(X0) | ~tall(X0)) & (tall(X0) | ~creative(X0)))) & (((~tall(X0) | ~creative(X0)) & (tall(X0) | creative(X0))) | (~generous(X0) & quiet(X0)))) [flattening 41]
43. ! [X0] : (((~happy(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & ((happy(X0) | generous(X0)) | (happy(X0) | ~kind(X0)))) [nnf transformation 7]
44. ! [X0] : (((~happy(X0) & kind(X0)) | (~happy(X0) & ~generous(X0))) & (happy(X0) | generous(X0) | happy(X0) | ~kind(X0))) [flattening 43]
61. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & ((generous(X0) | ~curious(X0)) | ~tall(X0))) [nnf transformation 14]
62. ! [X0] : ((tall(X0) | (~generous(X0) & curious(X0))) & (generous(X0) | ~curious(X0) | ~tall(X0))) [flattening 61]
82. ~tall(X0) | kind(X0) [cnf transformation 36]
92. ~creative(X0) | ~tall(X0) | ~generous(X0) [cnf transformation 42]
95. happy(X0) | generous(X0) | happy(X0) | ~kind(X0) [cnf transformation 44]
99. ~happy(X0) | ~happy(X0) [cnf transformation 44]
118. curious(X0) | tall(X0) [cnf transformation 62]
121. ~tall(X0) | creative(X0) [cnf transformation 30]
130. ~curious(paul) [cnf transformation 22]
131. happy(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 95]
132. ~happy(X0) [duplicate literal removal 99]
169. ~kind(X0) | generous(X0) [subsumption resolution 131,132]
290. tall(paul) [resolution 118,130]
292. kind(paul) [resolution 290,82]
295. creative(paul) [resolution 121,290]
298. generous(paul) [resolution 169,292]
311. ~tall(paul) | ~generous(paul) [resolution 92,295]
314. ~generous(paul) [subsumption resolution 311,290]
315. $false [subsumption resolution 314,298]
% SZS output end Proof for 254651502935321368476733
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both not humble and not kind. If someone is not patient or not rich then lucy is either happy or patient and vice versa. Everyone who is either not kind or not strong is both calm and not calm. Everyone who is not curious is tall. Everyone who is either not kind or not rich is either kind or not old and vice versa. Everyone who is funny is either not rich or not calm and vice versa. Everyone who is not wise or patient is both creative and funny and vice versa. If lucy is both kind and creative then alice is both happy and creative. Everyone who is either not curious or curious is humble. Everyone who is not kind or quiet is not happy. If someone is either quiet or tall then someone is not patient or not kind and vice versa. Everyone who is happy is humble or not curious and vice versa. Everyone who is either not rich or not old is either not creative or not strong. If susan is humble or generous then fred is both not creative and strong. If someone is both not strong and generous then someone is both not humble and humble and vice versa. Everyone who is both generous and not old is happy and vice versa. Lucy is generous. Alice is quiet or wise. Lucy is not curious. Paul is not brave. | Paul is not strong. | contradiction | (![X]:(creative(X)=>(~humble(X)&~kind(X))))&
((?[X]:((~patient(X)|~rich(X))))<=>((happy(lucy)<~>patient(lucy))))&
(![X]:((~kind(X)<~>~strong(X))=>(calm(X)&~calm(X))))&
(![X]:(~curious(X)=>tall(X)))&
(![X]:((~kind(X)<~>~rich(X))<=>(kind(X)<~>~old(X))))&
(![X]:(funny(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((~wise(X)|patient(X))<=>(creative(X)&funny(X))))&
(((kind(lucy)&creative(lucy)))=>((happy(alice)&creative(alice))))&
(![X]:((~curious(X)<~>curious(X))=>humble(X)))&
(![X]:((~kind(X)|quiet(X))=>~happy(X)))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:((~patient(X)|~kind(X)))))&
(![X]:(happy(X)<=>(humble(X)|~curious(X))))&
(![X]:((~rich(X)<~>~old(X))=>(~creative(X)<~>~strong(X))))&
(((humble(susan)|generous(susan)))=>((~creative(fred)&strong(fred))))&
((?[X]:((~strong(X)&generous(X))))<=>(?[X]:((~humble(X)&humble(X)))))&
(![X]:((generous(X)&~old(X))<=>happy(X)))&
(generous(lucy))&
((quiet(alice)|wise(alice)))&
(~curious(lucy))&
(~brave(paul)) | ~strong(paul) | [
"p2",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 60237009928104923396125
% SZS output start Proof for 60237009928104923396125
3. ! [X0] : ((~kind(X0) <~> ~strong(X0)) => (~calm(X0) & calm(X0))) [input p2]
9. ! [X0] : ((~curious(X0) <~> curious(X0)) => humble(X0)) [input p8]
10. ! [X0] : ((quiet(X0) | ~kind(X0)) => ~happy(X0)) [input p9]
12. ! [X0] : (happy(X0) <=> (~curious(X0) | humble(X0))) [input p11]
21. ~strong(paul) [input hypothesis]
26. ! [X0] : ((~calm(X0) & calm(X0)) | (~kind(X0) <=> ~strong(X0))) [ennf transformation 3]
30. ! [X0] : (humble(X0) | (~curious(X0) <=> curious(X0))) [ennf transformation 9]
31. ! [X0] : (~happy(X0) | (~quiet(X0) & kind(X0))) [ennf transformation 10]
38. ! [X0] : ((~calm(X0) & calm(X0)) | ((~kind(X0) | strong(X0)) & (~strong(X0) | kind(X0)))) [nnf transformation 26]
43. ! [X0] : (humble(X0) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 30]
49. ! [X0] : ((happy(X0) | (curious(X0) & ~humble(X0))) & ((~curious(X0) | humble(X0)) | ~happy(X0))) [nnf transformation 12]
50. ! [X0] : ((happy(X0) | (curious(X0) & ~humble(X0))) & (~curious(X0) | humble(X0) | ~happy(X0))) [flattening 49]
68. calm(X0) | ~kind(X0) | strong(X0) [cnf transformation 38]
70. ~calm(X0) | ~kind(X0) | strong(X0) [cnf transformation 38]
91. humble(X0) | curious(X0) | curious(X0) [cnf transformation 43]
92. humble(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
93. ~happy(X0) | kind(X0) [cnf transformation 31]
102. happy(X0) | ~humble(X0) [cnf transformation 50]
122. ~strong(paul) [cnf transformation 21]
123. humble(X0) | curious(X0) [duplicate literal removal 91]
124. ~curious(X0) | humble(X0) [duplicate literal removal 92]
157. ~kind(X0) | strong(X0) [subsumption resolution 68,70]
161. humble(X0) [subsumption resolution 123,124]
163. 7 <=> ! [X1] : kind(X1) [avatar definition]
164. kind(X1) <- (7) [avatar component clause 163]
193. happy(X0) [subsumption resolution 102,161]
235. kind(X0) [resolution 93,193]
244. strong(X0) <- (7) [resolution 157,164]
246. $false <- (7) [resolution 244,122]
248. ~7 [avatar contradiction clause 246]
249. 7 [avatar split clause 235,163]
250. $false [avatar sat refutation 248,249]
% SZS output end Proof for 60237009928104923396125
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not calm and happy is not kind or not old and vice versa.
Everyone who is either not funny or rich is not curious.
If lucy is either not old or calm then someone is both not curious and creative.
If someone is not tall or not calm then someone is strong and vice versa.
Everyone who is not happy or not quiet is not generous or not calm and vice versa.
Everyone who is not humble is not wise and vice versa.
Everyone who is either creative or not kind is either curious or wise.
If someone is either not rich or not wise then lucy is patient or not humble and vice versa.
If mary is brave then john is both not kind and not brave.
Everyone who is both not tall and not brave is not creative or rich and vice versa.
Everyone who is not wise is not patient and vice versa.
Everyone who is not old is both not funny and patient.
Everyone who is calm or funny is patient.
Everyone who is both wise and not kind is rich and vice versa.
Everyone who is both funny and not wise is tall or brave and vice versa.
If someone is both happy and not happy then paul is either not quiet or humble and vice versa.
Paul is either not tall or not rich.
Someone is generous or not brave.
Someone is either kind or not quiet.
Someone is calm.
Someone is not wise.
Paul is not old.
Mary is generous or not happy.
Someone is happy or generous. | Paul is not wise. | contradiction | (![X]:((~calm(X)&happy(X))<=>(~kind(X)|~old(X))))&
(![X]:((~funny(X)<~>rich(X))=>~curious(X)))&
(((~old(lucy)<~>calm(lucy)))=>(?[X]:((~curious(X)&creative(X)))))&
((?[X]:((~tall(X)|~calm(X))))<=>(?[X]:(strong(X))))&
(![X]:((~happy(X)|~quiet(X))<=>(~generous(X)|~calm(X))))&
(![X]:(~humble(X)<=>~wise(X)))&
(![X]:((creative(X)<~>~kind(X))=>(curious(X)<~>wise(X))))&
((?[X]:((~rich(X)<~>~wise(X))))<=>((patient(lucy)|~humble(lucy))))&
((brave(mary))=>((~kind(john)&~brave(john))))&
(![X]:((~tall(X)&~brave(X))<=>(~creative(X)|rich(X))))&
(![X]:(~wise(X)<=>~patient(X)))&
(![X]:(~old(X)=>(~funny(X)&patient(X))))&
(![X]:((calm(X)|funny(X))=>patient(X)))&
(![X]:((wise(X)&~kind(X))<=>rich(X)))&
(![X]:((funny(X)&~wise(X))<=>(tall(X)|brave(X))))&
((?[X]:((happy(X)&~happy(X))))<=>((~quiet(paul)<~>humble(paul))))&
((~tall(paul)<~>~rich(paul)))&
(?[X]:((generous(X)|~brave(X))))&
(?[X]:((kind(X)<~>~quiet(X))))&
(?[X]:(calm(X)))&
(?[X]:(~wise(X)))&
(~old(paul))&
((generous(mary)|~happy(mary)))&
(?[X]:((happy(X)|generous(X)))) | ~wise(paul) | [
"p11",
"p13",
"p14",
"p16",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 736690366964928694771542
% SZS output start Proof for 736690366964928694771542
12. ! [X0] : (~old(X0) => (patient(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((~kind(X0) & wise(X0)) <=> rich(X0)) [input p13]
15. ! [X0] : ((~wise(X0) & funny(X0)) <=> (brave(X0) | tall(X0))) [input p14]
17. ~tall(paul) <~> ~rich(paul) [input p16]
22. ~old(paul) [input p21]
25. ~wise(paul) [input hypothesis]
31. ! [X0] : ((patient(X0) & ~funny(X0)) | old(X0)) [ennf transformation 12]
56. ! [X0] : (((~kind(X0) & wise(X0)) | ~rich(X0)) & (rich(X0) | (kind(X0) | ~wise(X0)))) [nnf transformation 14]
57. ! [X0] : (((~kind(X0) & wise(X0)) | ~rich(X0)) & (rich(X0) | kind(X0) | ~wise(X0))) [flattening 56]
58. ! [X0] : (((~wise(X0) & funny(X0)) | (~brave(X0) & ~tall(X0))) & ((brave(X0) | tall(X0)) | (wise(X0) | ~funny(X0)))) [nnf transformation 15]
59. ! [X0] : (((~wise(X0) & funny(X0)) | (~brave(X0) & ~tall(X0))) & (brave(X0) | tall(X0) | wise(X0) | ~funny(X0))) [flattening 58]
64. (rich(paul) | tall(paul)) & (~rich(paul) | ~tall(paul)) [nnf transformation 17]
115. ~funny(X0) | old(X0) [cnf transformation 31]
120. wise(X0) | ~rich(X0) [cnf transformation 57]
123. ~tall(X0) | funny(X0) [cnf transformation 59]
134. rich(paul) | tall(paul) [cnf transformation 64]
140. ~old(paul) [cnf transformation 22]
143. ~wise(paul) [cnf transformation 25]
213. 15 <=> ! [X1] : (~rich(X1) | wise(X1)) [avatar definition]
214. ~rich(X1) | wise(X1) <- (15) [avatar component clause 213]
234. 15 [avatar split clause 120,213]
252. 23 <=> tall(paul) [avatar definition]
254. tall(paul) <- (23) [avatar component clause 252]
256. 24 <=> rich(paul) [avatar definition]
258. rich(paul) <- (24) [avatar component clause 256]
259. 23 | 24 [avatar split clause 134,256,252]
312. funny(paul) <- (23) [resolution 123,254]
314. old(paul) <- (23) [resolution 312,115]
315. $false <- (23) [subsumption resolution 314,140]
316. ~23 [avatar contradiction clause 315]
323. wise(paul) <- (15, 24) [resolution 214,258]
326. $false <- (15, 24) [subsumption resolution 323,143]
327. ~15 | ~24 [avatar contradiction clause 326]
328. $false [avatar sat refutation 234,259,316,327]
% SZS output end Proof for 736690366964928694771542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative then someone is strong and vice versa.
If alice is both curious and calm then someone is either not creative or not quiet and vice versa.
If someone is old or quiet then someone is old.
Everyone who is old or humble is both kind and generous.
Everyone who is both brave and strong is either old or brave and vice versa.
If someone is happy then mary is not calm or brave and vice versa.
If mary is either not old or kind then susan is both generous and humble.
Everyone who is not rich is either funny or not strong.
Everyone who is both funny and not rich is both not generous and not kind.
Everyone who is calm is both not wise and not quiet.
Everyone who is both not brave and curious is both tall and not creative and vice versa.
Everyone who is happy is brave.
If susan is not kind or not happy then paul is either not creative or not tall.
Everyone who is not wise or not rich is not humble or quiet.
If susan is not happy or not strong then alice is both not kind and calm.
If someone is both humble and not calm then mary is tall and vice versa.
Someone is both not rich and wise.
Alice is quiet.
Lucy is either not happy or rich.
Someone is strong.
Someone is not funny.
Someone is either patient or wise.
Someone is calm.
Mary is creative. | Mary is not quiet. | contradiction | ((creative(fred))<=>(?[X]:(strong(X))))&
(((curious(alice)&calm(alice)))<=>(?[X]:((~creative(X)<~>~quiet(X)))))&
((?[X]:((old(X)|quiet(X))))=>(?[X]:(old(X))))&
(![X]:((old(X)|humble(X))=>(kind(X)&generous(X))))&
(![X]:((brave(X)&strong(X))<=>(old(X)<~>brave(X))))&
((?[X]:(happy(X)))<=>((~calm(mary)|brave(mary))))&
(((~old(mary)<~>kind(mary)))=>((generous(susan)&humble(susan))))&
(![X]:(~rich(X)=>(funny(X)<~>~strong(X))))&
(![X]:((funny(X)&~rich(X))=>(~generous(X)&~kind(X))))&
(![X]:(calm(X)=>(~wise(X)&~quiet(X))))&
(![X]:((~brave(X)&curious(X))<=>(tall(X)&~creative(X))))&
(![X]:(happy(X)=>brave(X)))&
(((~kind(susan)|~happy(susan)))=>((~creative(paul)<~>~tall(paul))))&
(![X]:((~wise(X)|~rich(X))=>(~humble(X)|quiet(X))))&
(((~happy(susan)|~strong(susan)))=>((~kind(alice)&calm(alice))))&
((?[X]:((humble(X)&~calm(X))))<=>(tall(mary)))&
(?[X]:((~rich(X)&wise(X))))&
(quiet(alice))&
((~happy(lucy)<~>rich(lucy)))&
(?[X]:(strong(X)))&
(?[X]:(~funny(X)))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:(calm(X)))&
(creative(mary)) | ~quiet(mary) | [
"p1",
"p9",
"p17",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8985188990739698076492087
% SZS output start Proof for 8985188990739698076492087
2. (calm(alice) & curious(alice)) <=> ? [X0] : (~creative(X0) <~> ~quiet(X0)) [input p1]
10. ! [X0] : (calm(X0) => (~quiet(X0) & ~wise(X0))) [input p9]
18. quiet(alice) [input p17]
24. creative(mary) [input p23]
25. ~quiet(mary) [input hypothesis]
33. ! [X0] : ((~quiet(X0) & ~wise(X0)) | ~calm(X0)) [ennf transformation 10]
43. ((calm(alice) & curious(alice)) | ! [X0] : ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (? [X0] : ((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~calm(alice) | ~curious(alice))) [nnf transformation 2]
44. ((calm(alice) & curious(alice)) | ! [X0] : ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (? [X0] : ((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~calm(alice) | ~curious(alice)) [flattening 43]
45. ((calm(alice) & curious(alice)) | ! [X0] : ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (? [X1] : ((quiet(X1) | creative(X1)) & (~quiet(X1) | ~creative(X1))) | ~calm(alice) | ~curious(alice)) [rectify 44]
46. ? [X1] : ((quiet(X1) | creative(X1)) & (~quiet(X1) | ~creative(X1))) => ((quiet(sK1) | creative(sK1)) & (~quiet(sK1) | ~creative(sK1))) [choice axiom]
47. ((calm(alice) & curious(alice)) | ! [X0] : ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(sK1) | creative(sK1)) & (~quiet(sK1) | ~creative(sK1))) | ~calm(alice) | ~curious(alice)) [skolemisation 45,46]
86. calm(alice) | ~creative(X0) | quiet(X0) [cnf transformation 47]
111. ~quiet(X0) | ~calm(X0) [cnf transformation 33]
132. quiet(alice) [cnf transformation 18]
140. creative(mary) [cnf transformation 24]
141. ~quiet(mary) [cnf transformation 25]
158. 4 <=> ! [X0] : (~creative(X0) | quiet(X0)) [avatar definition]
159. ~creative(X0) | quiet(X0) <- (4) [avatar component clause 158]
161. 5 <=> calm(alice) [avatar definition]
164. 4 | 5 [avatar split clause 86,161,158]
315. ~calm(alice) [resolution 111,132]
318. ~5 [avatar split clause 315,161]
322. quiet(mary) <- (4) [resolution 159,140]
325. $false <- (4) [subsumption resolution 322,141]
326. ~4 [avatar contradiction clause 325]
327. $false [avatar sat refutation 164,318,326]
% SZS output end Proof for 8985188990739698076492087
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 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. | Susan is wise. | 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)))) | wise(susan) | [
"p0",
"p3",
"p7",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2123923015196776103660541
% SZS output start Proof for 2123923015196776103660541
1. ! [X0] : (wise(X0) => (~quiet(X0) & ~kind(X0))) [input p0]
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]
25. wise(susan) [input hypothesis]
27. ! [X0] : ((~quiet(X0) & ~kind(X0)) | ~wise(X0)) [ennf transformation 1]
34. ! [X0] : ((~rich(X0) & strong(X0)) | (~curious(X0) & kind(X0))) [ennf transformation 13]
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]
72. ~kind(X0) | ~wise(X0) [cnf transformation 27]
73. ~quiet(X0) | ~wise(X0) [cnf transformation 27]
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]
105. ~rich(X0) | kind(X0) | ~tall(X0) [cnf transformation 49]
107. tall(X0) | kind(X0) | rich(X0) | kind(X0) [cnf transformation 49]
114. ~rich(X0) | kind(X0) [cnf transformation 34]
139. wise(susan) [cnf transformation 25]
141. ~kind(X0) | rich(X0) [duplicate literal removal 102]
142. rich(X0) | kind(X0) | tall(X0) [duplicate literal removal 107]
181. ~creative(X0) | rich(X0) [subsumption resolution 92,93]
446. kind(X4) | tall(X4) | kind(X4) [resolution 142,114]
447. tall(X4) | kind(X4) [duplicate literal removal 446]
522. creative(X1) | kind(X1) | quiet(X1) [resolution 447,86]
557. kind(X2) | quiet(X2) | rich(X2) [resolution 522,181]
564. rich(X2) | quiet(X2) [subsumption resolution 557,141]
578. quiet(X0) | kind(X0) | ~tall(X0) [resolution 564,105]
583. quiet(X0) | kind(X0) [subsumption resolution 578,447]
607. kind(X3) | ~wise(X3) [resolution 583,73]
610. ~wise(X3) [subsumption resolution 607,72]
619. $false [resolution 610,139]
% SZS output end Proof for 2123923015196776103660541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not tall is either funny or not brave.
Everyone who is both not rich and not curious is not wise or not strong.
Everyone who is either old or brave is not humble or tall and vice versa.
If paul is both patient and creative then someone is not rich and vice versa.
If paul is not humble then someone is not creative or calm and vice versa.
Everyone who is tall is not old and vice versa.
If someone is either not happy or not old then someone is both patient and not generous and vice versa.
If paul is not funny or not kind then john is either not wise or strong.
Everyone who is not calm or not rich is both not tall and strong.
If john is not calm or not strong then alice is both wise and not rich.
If lucy is both not strong and not tall then someone is both not creative and not calm.
Everyone who is both not calm and not quiet is either not tall or rich and vice versa.
If fred is both old and kind then someone is generous.
Everyone who is either not strong or not rich is tall.
If someone is quiet then susan is curious or calm and vice versa.
If someone is either not curious or not happy then someone is both kind and not creative.
Someone is either not calm or not old.
John is either not strong or wise.
Someone is patient.
Someone is either not rich or humble.
Alice is not brave or not humble.
Lucy is both rich and not wise. | John is wise. | entailment | (![X]:((curious(X)&~tall(X))=>(funny(X)<~>~brave(X))))&
(![X]:((~rich(X)&~curious(X))=>(~wise(X)|~strong(X))))&
(![X]:((old(X)<~>brave(X))<=>(~humble(X)|tall(X))))&
(((patient(paul)&creative(paul)))<=>(?[X]:(~rich(X))))&
((~humble(paul))<=>(?[X]:((~creative(X)|calm(X)))))&
(![X]:(tall(X)<=>~old(X)))&
((?[X]:((~happy(X)<~>~old(X))))<=>(?[X]:((patient(X)&~generous(X)))))&
(((~funny(paul)|~kind(paul)))=>((~wise(john)<~>strong(john))))&
(![X]:((~calm(X)|~rich(X))=>(~tall(X)&strong(X))))&
(((~calm(john)|~strong(john)))=>((wise(alice)&~rich(alice))))&
(((~strong(lucy)&~tall(lucy)))=>(?[X]:((~creative(X)&~calm(X)))))&
(![X]:((~calm(X)&~quiet(X))<=>(~tall(X)<~>rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:(generous(X))))&
(![X]:((~strong(X)<~>~rich(X))=>tall(X)))&
((?[X]:(quiet(X)))<=>((curious(susan)|calm(susan))))&
((?[X]:((~curious(X)<~>~happy(X))))=>(?[X]:((kind(X)&~creative(X)))))&
(?[X]:((~calm(X)<~>~old(X))))&
((~strong(john)<~>wise(john)))&
(?[X]:(patient(X)))&
(?[X]:((~rich(X)<~>humble(X))))&
((~brave(alice)|~humble(alice)))&
((rich(lucy)&~wise(lucy))) | wise(john) | [
"p8",
"p11",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1827724953498746576597048
% SZS output start Proof for 1827724953498746576597048
9. ! [X0] : ((~rich(X0) | ~calm(X0)) => (strong(X0) & ~tall(X0))) [input p8]
12. ! [X0] : ((~quiet(X0) & ~calm(X0)) <=> (~tall(X0) <~> rich(X0))) [input p11]
14. ! [X0] : ((~strong(X0) <~> ~rich(X0)) => tall(X0)) [input p13]
18. ~strong(john) <~> wise(john) [input p17]
23. ~wise(john) [input hypothesis]
31. ! [X0] : ((strong(X0) & ~tall(X0)) | (rich(X0) & calm(X0))) [ennf transformation 9]
37. ! [X0] : (tall(X0) | (~strong(X0) <=> ~rich(X0))) [ennf transformation 14]
60. ! [X0] : (((~quiet(X0) & ~calm(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (quiet(X0) | calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((~quiet(X0) & ~calm(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0)))) & (((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | quiet(X0) | calm(X0))) [flattening 60]
64. ! [X0] : (tall(X0) | ((~strong(X0) | rich(X0)) & (~rich(X0) | strong(X0)))) [nnf transformation 37]
77. (~wise(john) | strong(john)) & (wise(john) | ~strong(john)) [nnf transformation 18]
110. ~tall(X0) | calm(X0) [cnf transformation 31]
111. ~tall(X0) | rich(X0) [cnf transformation 31]
113. strong(X0) | rich(X0) [cnf transformation 31]
123. ~calm(X0) | ~tall(X0) | ~rich(X0) [cnf transformation 61]
127. tall(X0) | ~rich(X0) | strong(X0) [cnf transformation 64]
138. wise(john) | ~strong(john) [cnf transformation 77]
146. ~wise(john) [cnf transformation 23]
222. 18 <=> wise(john) [avatar definition]
273. ~tall(X0) | ~rich(X0) [subsumption resolution 123,110]
274. ~tall(X0) [subsumption resolution 273,111]
293. ~rich(X0) | strong(X0) [subsumption resolution 127,274]
294. strong(X0) [subsumption resolution 293,113]
341. wise(john) [subsumption resolution 138,294]
342. 18 [avatar split clause 341,222]
362. ~18 [avatar split clause 146,222]
363. $false [avatar sat refutation 342,362]
% SZS output end Proof for 1827724953498746576597048
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall then mary is not creative or creative.
Everyone who is humble is either not kind or funny and vice versa.
If fred is strong or not tall then someone is generous and vice versa.
If susan is strong then alice is tall or not old and vice versa.
If alice is both generous and not wise then lucy is not quiet and vice versa.
Everyone who is not tall is not calm and vice versa.
If paul is both not humble and not patient then someone is strong or not quiet and vice versa.
Everyone who is either rich or not funny is both not calm and calm and vice versa.
If someone is both not strong and tall then someone is old.
Everyone who is quiet or wise is patient or not curious.
Everyone who is not happy or not calm is generous or creative and vice versa.
Everyone who is both not happy and rich is humble or not funny.
Everyone who is patient is not wise or curious and vice versa.
Everyone who is funny is tall or generous.
If lucy is both creative and not strong then mary is kind and vice versa.
Everyone who is both curious and strong is either strong or not curious.
Paul is either generous or not rich.
John is not patient or not funny.
Alice is either funny or not curious.
Lucy is kind or funny.
Someone is strong or not creative.
Fred is funny.
John is not old. | Fred is strong. | neutral | ((~tall(alice))=>((~creative(mary)|creative(mary))))&
(![X]:(humble(X)<=>(~kind(X)<~>funny(X))))&
(((strong(fred)|~tall(fred)))<=>(?[X]:(generous(X))))&
((strong(susan))<=>((tall(alice)|~old(alice))))&
(((generous(alice)&~wise(alice)))<=>(~quiet(lucy)))&
(![X]:(~tall(X)<=>~calm(X)))&
(((~humble(paul)&~patient(paul)))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((rich(X)<~>~funny(X))<=>(~calm(X)&calm(X))))&
((?[X]:((~strong(X)&tall(X))))=>(?[X]:(old(X))))&
(![X]:((quiet(X)|wise(X))=>(patient(X)|~curious(X))))&
(![X]:((~happy(X)|~calm(X))<=>(generous(X)|creative(X))))&
(![X]:((~happy(X)&rich(X))=>(humble(X)|~funny(X))))&
(![X]:(patient(X)<=>(~wise(X)|curious(X))))&
(![X]:(funny(X)=>(tall(X)|generous(X))))&
(((creative(lucy)&~strong(lucy)))<=>(kind(mary)))&
(![X]:((curious(X)&strong(X))=>(strong(X)<~>~curious(X))))&
((generous(paul)<~>~rich(paul)))&
((~patient(john)|~funny(john)))&
((funny(alice)<~>~curious(alice)))&
((kind(lucy)|funny(lucy)))&
(?[X]:((strong(X)|~creative(X))))&
(funny(fred))&
(~old(john)) | strong(fred) | [] | null | 0 |
Everyone who is brave is wise and vice versa.
Everyone who is not quiet is either creative or not tall and vice versa.
If john is either not wise or not strong then someone is both happy and curious and vice versa.
If lucy is not generous or humble then someone is not generous or not old and vice versa.
If susan is not humble then paul is both funny and humble and vice versa.
Everyone who is both not patient and generous is either calm or wise.
Everyone who is both not tall and not calm is not funny or not generous and vice versa.
If someone is wise or funny then paul is not funny and vice versa.
Everyone who is not funny is not funny or not patient and vice versa.
If susan is not creative then someone is calm and vice versa.
Everyone who is either creative or brave is both not calm and patient.
Everyone who is not kind or not creative is both old and wise.
Everyone who is not calm or not brave is not rich or not kind and vice versa.
If fred is not generous or rich then someone is either not curious or happy.
Everyone who is both not tall and not funny is either not kind or not strong.
If alice is either old or kind then someone is either not tall or strong.
John is wise.
Paul is tall or not generous.
Alice is tall or wise.
Lucy is creative or brave.
Fred is not calm or generous.
Fred is not brave.
John is creative.
Someone is both humble and not funny. | Fred is not rich. | entailment | (![X]:(brave(X)<=>wise(X)))&
(![X]:(~quiet(X)<=>(creative(X)<~>~tall(X))))&
(((~wise(john)<~>~strong(john)))<=>(?[X]:((happy(X)&curious(X)))))&
(((~generous(lucy)|humble(lucy)))<=>(?[X]:((~generous(X)|~old(X)))))&
((~humble(susan))<=>((funny(paul)&humble(paul))))&
(![X]:((~patient(X)&generous(X))=>(calm(X)<~>wise(X))))&
(![X]:((~tall(X)&~calm(X))<=>(~funny(X)|~generous(X))))&
((?[X]:((wise(X)|funny(X))))<=>(~funny(paul)))&
(![X]:(~funny(X)<=>(~funny(X)|~patient(X))))&
((~creative(susan))<=>(?[X]:(calm(X))))&
(![X]:((creative(X)<~>brave(X))=>(~calm(X)&patient(X))))&
(![X]:((~kind(X)|~creative(X))=>(old(X)&wise(X))))&
(![X]:((~calm(X)|~brave(X))<=>(~rich(X)|~kind(X))))&
(((~generous(fred)|rich(fred)))=>(?[X]:((~curious(X)<~>happy(X)))))&
(![X]:((~tall(X)&~funny(X))=>(~kind(X)<~>~strong(X))))&
(((old(alice)<~>kind(alice)))=>(?[X]:((~tall(X)<~>strong(X)))))&
(wise(john))&
((tall(paul)|~generous(paul)))&
((tall(alice)|wise(alice)))&
((creative(lucy)|brave(lucy)))&
((~calm(fred)|generous(fred)))&
(~brave(fred))&
(creative(john))&
(?[X]:((humble(X)&~funny(X)))) | ~rich(fred) | [
"p0",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2578732831924029991413228
% SZS output start Proof for 2578732831924029991413228
1. ! [X0] : (brave(X0) <=> wise(X0)) [input p0]
12. ! [X0] : ((~creative(X0) | ~kind(X0)) => (wise(X0) & old(X0))) [input p11]
13. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~kind(X0) | ~rich(X0))) [input p12]
22. ~brave(fred) [input p21]
25. rich(fred) [input hypothesis]
29. ! [X0] : ((wise(X0) & old(X0)) | (creative(X0) & kind(X0))) [ennf transformation 12]
34. ! [X0] : ((brave(X0) | ~wise(X0)) & (wise(X0) | ~brave(X0))) [nnf transformation 1]
60. ! [X0] : (((~brave(X0) | ~calm(X0)) | (kind(X0) & rich(X0))) & ((~kind(X0) | ~rich(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 13]
61. ! [X0] : ((~brave(X0) | ~calm(X0) | (kind(X0) & rich(X0))) & (~kind(X0) | ~rich(X0) | (brave(X0) & calm(X0)))) [flattening 60]
72. ~wise(X0) | brave(X0) [cnf transformation 34]
107. kind(X0) | wise(X0) [cnf transformation 29]
110. ~rich(X0) | ~kind(X0) | brave(X0) [cnf transformation 61]
128. ~brave(fred) [cnf transformation 22]
132. rich(fred) [cnf transformation 25]
230. 22 <=> rich(fred) [avatar definition]
231. rich(fred) <- (22) [avatar component clause 230]
303. 22 [avatar split clause 132,230]
368. 44 <=> kind(fred) [avatar definition]
370. ~kind(fred) <- (~44) [avatar component clause 368]
378. ~kind(fred) | brave(fred) <- (22) [resolution 110,231]
381. wise(fred) <- (~44) [resolution 370,107]
405. brave(fred) <- (~44) [resolution 381,72]
406. $false <- (~44) [subsumption resolution 405,128]
407. 44 [avatar contradiction clause 406]
408. ~kind(fred) <- (22) [subsumption resolution 378,128]
409. ~44 | ~22 [avatar split clause 408,230,368]
412. $false [avatar sat refutation 303,407,409]
% SZS output end Proof for 2578732831924029991413228
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not generous then someone is brave or not creative and vice versa.
Everyone who is both funny and happy is both not humble and calm and vice versa.
If susan is generous or kind then paul is not creative or not generous.
Everyone who is humble is either rich or not happy and vice versa.
Everyone who is wise or calm is both brave and not wise.
Everyone who is both patient and not strong is not patient and vice versa.
Everyone who is not strong is patient or not tall.
Everyone who is either generous or tall is rich or not wise.
Everyone who is rich or not tall is either generous or not tall.
Everyone who is either not rich or kind is either patient or quiet.
If john is both not old and not generous then someone is calm or not rich and vice versa.
If lucy is wise then john is either quiet or kind.
If alice is not old or creative then someone is not tall or not calm.
If someone is not patient or not quiet then lucy is curious or strong.
If someone is either not old or not strong then someone is old or wise and vice versa.
Mary is both humble and patient.
Paul is tall or strong.
Someone is not calm or not old.
Someone is either calm or quiet.
Lucy is either not creative or humble.
Lucy is both not calm and patient.
Susan is brave or creative. | Paul is not patient. | contradiction | ((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((brave(X)|~creative(X)))))&
(![X]:((funny(X)&happy(X))<=>(~humble(X)&calm(X))))&
(((generous(susan)|kind(susan)))=>((~creative(paul)|~generous(paul))))&
(![X]:(humble(X)<=>(rich(X)<~>~happy(X))))&
(![X]:((wise(X)|calm(X))=>(brave(X)&~wise(X))))&
(![X]:((patient(X)&~strong(X))<=>~patient(X)))&
(![X]:(~strong(X)=>(patient(X)|~tall(X))))&
(![X]:((generous(X)<~>tall(X))=>(rich(X)|~wise(X))))&
(![X]:((rich(X)|~tall(X))=>(generous(X)<~>~tall(X))))&
(![X]:((~rich(X)<~>kind(X))=>(patient(X)<~>quiet(X))))&
(((~old(john)&~generous(john)))<=>(?[X]:((calm(X)|~rich(X)))))&
((wise(lucy))=>((quiet(john)<~>kind(john))))&
(((~old(alice)|creative(alice)))=>(?[X]:((~tall(X)|~calm(X)))))&
((?[X]:((~patient(X)|~quiet(X))))=>((curious(lucy)|strong(lucy))))&
((?[X]:((~old(X)<~>~strong(X))))<=>(?[X]:((old(X)|wise(X)))))&
((humble(mary)&patient(mary)))&
((tall(paul)|strong(paul)))&
(?[X]:((~calm(X)|~old(X))))&
(?[X]:((calm(X)<~>quiet(X))))&
((~creative(lucy)<~>humble(lucy)))&
((~calm(lucy)&patient(lucy)))&
((brave(susan)|creative(susan))) | ~patient(paul) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 8773838493734695470645421
% SZS output start Proof for 8773838493734695470645421
6. ! [X0] : ((~strong(X0) & patient(X0)) <=> ~patient(X0)) [input p5]
23. ~patient(paul) [input hypothesis]
46. ! [X0] : (((~strong(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | (strong(X0) | ~patient(X0)))) [nnf transformation 6]
47. ! [X0] : (((~strong(X0) & patient(X0)) | patient(X0)) & (~patient(X0) | strong(X0) | ~patient(X0))) [flattening 46]
90. patient(X0) | patient(X0) [cnf transformation 47]
129. ~patient(paul) [cnf transformation 23]
132. patient(X0) [duplicate literal removal 90]
287. $false [subsumption resolution 129,132]
% SZS output end Proof for 8773838493734695470645421
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not wise or kind then mary is not generous or not happy and vice versa.
Everyone who is curious is both not tall and not kind and vice versa.
If someone is either strong or old then john is not curious and vice versa.
Everyone who is not strong or strong is not rich.
Everyone who is both not wise and not old is not happy.
Everyone who is either not strong or kind is both not strong and strong and vice versa.
If someone is patient or not funny then someone is either happy or not funny.
Everyone who is not brave is both not generous and not rich and vice versa.
If lucy is happy or quiet then alice is not curious and vice versa.
If mary is either not strong or rich then someone is both old and quiet.
If paul is either not curious or not kind then someone is not patient or humble and vice versa.
If john is not rich or patient then someone is not strong or not funny.
Everyone who is rich or not funny is humble or not creative and vice versa.
Everyone who is either not happy or not humble is either not brave or not quiet.
Everyone who is humble or not patient is not generous or not kind and vice versa.
Everyone who is not brave is either not wise or not tall and vice versa.
Fred is either not humble or not calm.
Lucy is not happy.
Someone is either not calm or not curious.
Mary is curious or not wise.
Someone is either creative or tall.
Susan is kind or not brave.
Someone is both not tall and quiet.
Lucy is humble. | Susan is not happy. | neutral | (((~wise(lucy)<~>kind(lucy)))<=>((~generous(mary)|~happy(mary))))&
(![X]:(curious(X)<=>(~tall(X)&~kind(X))))&
((?[X]:((strong(X)<~>old(X))))<=>(~curious(john)))&
(![X]:((~strong(X)|strong(X))=>~rich(X)))&
(![X]:((~wise(X)&~old(X))=>~happy(X)))&
(![X]:((~strong(X)<~>kind(X))<=>(~strong(X)&strong(X))))&
((?[X]:((patient(X)|~funny(X))))=>(?[X]:((happy(X)<~>~funny(X)))))&
(![X]:(~brave(X)<=>(~generous(X)&~rich(X))))&
(((happy(lucy)|quiet(lucy)))<=>(~curious(alice)))&
(((~strong(mary)<~>rich(mary)))=>(?[X]:((old(X)&quiet(X)))))&
(((~curious(paul)<~>~kind(paul)))<=>(?[X]:((~patient(X)|humble(X)))))&
(((~rich(john)|patient(john)))=>(?[X]:((~strong(X)|~funny(X)))))&
(![X]:((rich(X)|~funny(X))<=>(humble(X)|~creative(X))))&
(![X]:((~happy(X)<~>~humble(X))=>(~brave(X)<~>~quiet(X))))&
(![X]:((humble(X)|~patient(X))<=>(~generous(X)|~kind(X))))&
(![X]:(~brave(X)<=>(~wise(X)<~>~tall(X))))&
((~humble(fred)<~>~calm(fred)))&
(~happy(lucy))&
(?[X]:((~calm(X)<~>~curious(X))))&
((curious(mary)|~wise(mary)))&
(?[X]:((creative(X)<~>tall(X))))&
((kind(susan)|~brave(susan)))&
(?[X]:((~tall(X)&quiet(X))))&
(humble(lucy)) | ~happy(susan) | [] | null | 0 |
Everyone who is curious or not rich is not kind or strong and vice versa. If susan is either rich or not patient then fred is not strong or calm. Everyone who is both generous and not generous is patient or strong. If susan is generous or not rich then someone is either strong or not wise and vice versa. If someone is not curious or tall then someone is either not wise or happy. If someone is happy or rich then someone is both not old and not brave. If someone is not generous then someone is kind or old. Everyone who is both brave and old is both not curious and rich. Everyone who is either old or humble is not curious or not patient. Everyone who is patient or rich is kind. Everyone who is old or not curious is not old. Everyone who is not patient is not strong or not funny and vice versa. If susan is curious or not patient then fred is not rich or not patient and vice versa. Everyone who is either curious or calm is both old and not calm and vice versa. Everyone who is funny or kind is not happy or not funny. Everyone who is curious is not old or strong. Fred is not patient. Susan is not brave or not strong. Susan is both strong and not brave. Someone is quiet or not old. Mary is strong or funny. Someone is both not generous and patient. Someone is kind. Mary is both patient and not wise. | Mary is generous. | neutral | (![X]:((curious(X)|~rich(X))<=>(~kind(X)|strong(X))))&
(((rich(susan)<~>~patient(susan)))=>((~strong(fred)|calm(fred))))&
(![X]:((generous(X)&~generous(X))=>(patient(X)|strong(X))))&
(((generous(susan)|~rich(susan)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
((?[X]:((~curious(X)|tall(X))))=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((happy(X)|rich(X))))=>(?[X]:((~old(X)&~brave(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((kind(X)|old(X)))))&
(![X]:((brave(X)&old(X))=>(~curious(X)&rich(X))))&
(![X]:((old(X)<~>humble(X))=>(~curious(X)|~patient(X))))&
(![X]:((patient(X)|rich(X))=>kind(X)))&
(![X]:((old(X)|~curious(X))=>~old(X)))&
(![X]:(~patient(X)<=>(~strong(X)|~funny(X))))&
(((curious(susan)|~patient(susan)))<=>((~rich(fred)|~patient(fred))))&
(![X]:((curious(X)<~>calm(X))<=>(old(X)&~calm(X))))&
(![X]:((funny(X)|kind(X))=>(~happy(X)|~funny(X))))&
(![X]:(curious(X)=>(~old(X)|strong(X))))&
(~patient(fred))&
((~brave(susan)|~strong(susan)))&
((strong(susan)&~brave(susan)))&
(?[X]:((quiet(X)|~old(X))))&
((strong(mary)|funny(mary)))&
(?[X]:((~generous(X)&patient(X))))&
(?[X]:(kind(X)))&
((patient(mary)&~wise(mary))) | generous(mary) | [] | null | 0 |
Everyone who is either not humble or creative is not brave or curious and vice versa. If susan is either rich or not happy then someone is either not rich or funny. Everyone who is either kind or funny is not wise and vice versa. Everyone who is both not old and quiet is both not quiet and patient and vice versa. Everyone who is quiet is creative and vice versa. Everyone who is not quiet is both not wise and not quiet. Everyone who is not patient is not quiet. If someone is both strong and not rich then john is both not tall and not happy. Everyone who is not brave or not quiet is either strong or happy and vice versa. If someone is patient or brave then someone is either not patient or not old and vice versa. Everyone who is quiet or old is patient and vice versa. If susan is either wise or curious then someone is not creative or not strong and vice versa. Everyone who is either not tall or quiet is strong and vice versa. Everyone who is patient is either not funny or strong. If susan is both not wise and not patient then someone is not humble or generous and vice versa. If someone is both not generous and not tall then alice is both not happy and curious. Lucy is not tall. Someone is either wise or not creative. Someone is either rich or kind. Susan is both not patient and not rich. Alice is not old. Someone is not humble or humble. | John is not funny. | neutral | (![X]:((~humble(X)<~>creative(X))<=>(~brave(X)|curious(X))))&
(((rich(susan)<~>~happy(susan)))=>(?[X]:((~rich(X)<~>funny(X)))))&
(![X]:((kind(X)<~>funny(X))<=>~wise(X)))&
(![X]:((~old(X)&quiet(X))<=>(~quiet(X)&patient(X))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:(~quiet(X)=>(~wise(X)&~quiet(X))))&
(![X]:(~patient(X)=>~quiet(X)))&
((?[X]:((strong(X)&~rich(X))))=>((~tall(john)&~happy(john))))&
(![X]:((~brave(X)|~quiet(X))<=>(strong(X)<~>happy(X))))&
((?[X]:((patient(X)|brave(X))))<=>(?[X]:((~patient(X)<~>~old(X)))))&
(![X]:((quiet(X)|old(X))<=>patient(X)))&
(((wise(susan)<~>curious(susan)))<=>(?[X]:((~creative(X)|~strong(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>strong(X)))&
(![X]:(patient(X)=>(~funny(X)<~>strong(X))))&
(((~wise(susan)&~patient(susan)))<=>(?[X]:((~humble(X)|generous(X)))))&
((?[X]:((~generous(X)&~tall(X))))=>((~happy(alice)&curious(alice))))&
(~tall(lucy))&
(?[X]:((wise(X)<~>~creative(X))))&
(?[X]:((rich(X)<~>kind(X))))&
((~patient(susan)&~rich(susan)))&
(~old(alice))&
(?[X]:((~humble(X)|humble(X)))) | ~funny(john) | [] | null | 0 |
If someone is old then susan is either not calm or not creative and vice versa. Everyone who is not humble is either not quiet or patient. Everyone who is not quiet or not old is quiet and vice versa. Everyone who is both not humble and not quiet is not generous and vice versa. Everyone who is either curious or not tall is both funny and tall. If someone is both tall and strong then susan is either generous or not curious and vice versa. Everyone who is both rich and happy is either curious or strong. If susan is both not calm and funny then alice is not tall or not funny and vice versa. Everyone who is both old and kind is both not patient and not rich. Everyone who is not happy is not old. If john is both not generous and rich then someone is not strong and vice versa. Everyone who is both not curious and not humble is not wise. If someone is not strong or not humble then paul is either funny or quiet. If someone is both not happy and calm then john is either not calm or happy and vice versa. Everyone who is happy or humble is either kind or curious. Everyone who is not generous is not creative or old. Lucy is not creative. Someone is both not calm and wise. Someone is either happy or not curious. Someone is not tall or generous. Someone is both funny and calm. Lucy is happy or curious. | Paul is creative. | neutral | ((?[X]:(old(X)))<=>((~calm(susan)<~>~creative(susan))))&
(![X]:(~humble(X)=>(~quiet(X)<~>patient(X))))&
(![X]:((~quiet(X)|~old(X))<=>quiet(X)))&
(![X]:((~humble(X)&~quiet(X))<=>~generous(X)))&
(![X]:((curious(X)<~>~tall(X))=>(funny(X)&tall(X))))&
((?[X]:((tall(X)&strong(X))))<=>((generous(susan)<~>~curious(susan))))&
(![X]:((rich(X)&happy(X))=>(curious(X)<~>strong(X))))&
(((~calm(susan)&funny(susan)))<=>((~tall(alice)|~funny(alice))))&
(![X]:((old(X)&kind(X))=>(~patient(X)&~rich(X))))&
(![X]:(~happy(X)=>~old(X)))&
(((~generous(john)&rich(john)))<=>(?[X]:(~strong(X))))&
(![X]:((~curious(X)&~humble(X))=>~wise(X)))&
((?[X]:((~strong(X)|~humble(X))))=>((funny(paul)<~>quiet(paul))))&
((?[X]:((~happy(X)&calm(X))))<=>((~calm(john)<~>happy(john))))&
(![X]:((happy(X)|humble(X))=>(kind(X)<~>curious(X))))&
(![X]:(~generous(X)=>(~creative(X)|old(X))))&
(~creative(lucy))&
(?[X]:((~calm(X)&wise(X))))&
(?[X]:((happy(X)<~>~curious(X))))&
(?[X]:((~tall(X)|generous(X))))&
(?[X]:((funny(X)&calm(X))))&
((happy(lucy)|curious(lucy))) | creative(paul) | [] | null | 0 |
If someone is not generous or not calm then someone is either wise or brave.
If someone is both not quiet and humble then alice is curious.
If john is wise or not brave then fred is not wise or not curious.
If john is creative then someone is happy or not wise and vice versa.
Everyone who is not creative is not calm or humble and vice versa.
If mary is both strong and not wise then someone is either not funny or rich.
Everyone who is either brave or generous is calm or kind and vice versa.
If someone is either not rich or patient then someone is both generous and not generous and vice versa.
Everyone who is strong is not funny or happy.
If fred is not funny or quiet then someone is both not curious and tall and vice versa.
Everyone who is tall is both happy and not wise.
Everyone who is not creative or not kind is either not quiet or not curious.
If someone is both not old and not curious then someone is either not strong or not funny.
Everyone who is either quiet or happy is either not humble or wise and vice versa.
If someone is both not wise and funny then fred is both wise and old and vice versa.
Everyone who is not humble is both not funny and not wise.
Someone is patient or creative.
Someone is kind.
Paul is either not generous or brave.
Someone is not patient or not humble.
Someone is patient or old.
Someone is curious.
Someone is not funny. | John is not humble. | entailment | ((?[X]:((~generous(X)|~calm(X))))=>(?[X]:((wise(X)<~>brave(X)))))&
((?[X]:((~quiet(X)&humble(X))))=>(curious(alice)))&
(((wise(john)|~brave(john)))=>((~wise(fred)|~curious(fred))))&
((creative(john))<=>(?[X]:((happy(X)|~wise(X)))))&
(![X]:(~creative(X)<=>(~calm(X)|humble(X))))&
(((strong(mary)&~wise(mary)))=>(?[X]:((~funny(X)<~>rich(X)))))&
(![X]:((brave(X)<~>generous(X))<=>(calm(X)|kind(X))))&
((?[X]:((~rich(X)<~>patient(X))))<=>(?[X]:((generous(X)&~generous(X)))))&
(![X]:(strong(X)=>(~funny(X)|happy(X))))&
(((~funny(fred)|quiet(fred)))<=>(?[X]:((~curious(X)&tall(X)))))&
(![X]:(tall(X)=>(happy(X)&~wise(X))))&
(![X]:((~creative(X)|~kind(X))=>(~quiet(X)<~>~curious(X))))&
((?[X]:((~old(X)&~curious(X))))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(![X]:((quiet(X)<~>happy(X))<=>(~humble(X)<~>wise(X))))&
((?[X]:((~wise(X)&funny(X))))<=>((wise(fred)&old(fred))))&
(![X]:(~humble(X)=>(~funny(X)&~wise(X))))&
(?[X]:((patient(X)|creative(X))))&
(?[X]:(kind(X)))&
((~generous(paul)<~>brave(paul)))&
(?[X]:((~patient(X)|~humble(X))))&
(?[X]:((patient(X)|old(X))))&
(?[X]:(curious(X)))&
(?[X]:(~funny(X))) | ~humble(john) | [
"p2",
"p3",
"p4",
"p9",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4107395144505691791838808
% SZS output start Proof for 4107395144505691791838808
3. (~brave(john) | wise(john)) => (~curious(fred) | ~wise(fred)) [input p2]
4. creative(john) <=> ? [X0] : (~wise(X0) | happy(X0)) [input p3]
5. ! [X0] : (~creative(X0) <=> (humble(X0) | ~calm(X0))) [input p4]
10. (quiet(fred) | ~funny(fred)) <=> ? [X0] : (tall(X0) & ~curious(X0)) [input p9]
11. ! [X0] : (tall(X0) => (~wise(X0) & happy(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | ~creative(X0)) => (~quiet(X0) <~> ~curious(X0))) [input p11]
16. ! [X0] : (~humble(X0) => (~wise(X0) & ~funny(X0))) [input p15]
24. humble(john) [input hypothesis]
30. (~curious(fred) | ~wise(fred)) | (brave(john) & ~wise(john)) [ennf transformation 3]
31. ~curious(fred) | ~wise(fred) | (brave(john) & ~wise(john)) [flattening 30]
36. ! [X0] : ((~wise(X0) & happy(X0)) | ~tall(X0)) [ennf transformation 11]
37. ! [X0] : ((~quiet(X0) <~> ~curious(X0)) | (kind(X0) & creative(X0))) [ennf transformation 12]
39. ! [X0] : ((~wise(X0) & ~funny(X0)) | humble(X0)) [ennf transformation 16]
44. (creative(john) | ! [X0] : (wise(X0) & ~happy(X0))) & (? [X0] : (~wise(X0) | happy(X0)) | ~creative(john)) [nnf transformation 4]
45. (creative(john) | ! [X0] : (wise(X0) & ~happy(X0))) & (? [X1] : (~wise(X1) | happy(X1)) | ~creative(john)) [rectify 44]
46. ? [X1] : (~wise(X1) | happy(X1)) => (~wise(sK1) | happy(sK1)) [choice axiom]
47. (creative(john) | ! [X0] : (wise(X0) & ~happy(X0))) & ((~wise(sK1) | happy(sK1)) | ~creative(john)) [skolemisation 45,46]
48. ! [X0] : ((~creative(X0) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | creative(X0))) [nnf transformation 5]
49. ! [X0] : ((~creative(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | creative(X0))) [flattening 48]
60. ((quiet(fred) | ~funny(fred)) | ! [X0] : (~tall(X0) | curious(X0))) & (? [X0] : (tall(X0) & ~curious(X0)) | (~quiet(fred) & funny(fred))) [nnf transformation 10]
61. (quiet(fred) | ~funny(fred) | ! [X0] : (~tall(X0) | curious(X0))) & (? [X0] : (tall(X0) & ~curious(X0)) | (~quiet(fred) & funny(fred))) [flattening 60]
62. (quiet(fred) | ~funny(fred) | ! [X0] : (~tall(X0) | curious(X0))) & (? [X1] : (tall(X1) & ~curious(X1)) | (~quiet(fred) & funny(fred))) [rectify 61]
63. ? [X1] : (tall(X1) & ~curious(X1)) => (tall(sK5) & ~curious(sK5)) [choice axiom]
64. (quiet(fred) | ~funny(fred) | ! [X0] : (~tall(X0) | curious(X0))) & ((tall(sK5) & ~curious(sK5)) | (~quiet(fred) & funny(fred))) [skolemisation 62,63]
65. ! [X0] : (((curious(X0) | quiet(X0)) & (~curious(X0) | ~quiet(X0))) | (kind(X0) & creative(X0))) [nnf transformation 37]
94. ~curious(fred) | ~wise(fred) | ~wise(john) [cnf transformation 31]
97. creative(john) | ~happy(X0) [cnf transformation 47]
98. creative(john) | wise(X0) [cnf transformation 47]
101. ~creative(X0) | ~humble(X0) [cnf transformation 49]
120. tall(sK5) | ~quiet(fred) [cnf transformation 64]
122. ~tall(X0) | happy(X0) [cnf transformation 36]
126. creative(X0) | quiet(X0) | curious(X0) [cnf transformation 65]
143. ~wise(X0) | humble(X0) [cnf transformation 39]
152. humble(john) [cnf transformation 24]
184. 8 <=> wise(fred) [avatar definition]
186. ~wise(fred) <- (~8) [avatar component clause 184]
188. 9 <=> curious(fred) [avatar definition]
190. ~curious(fred) <- (~9) [avatar component clause 188]
193. 10 <=> wise(john) [avatar definition]
195. ~wise(john) <- (~10) [avatar component clause 193]
196. ~10 | ~8 | ~9 [avatar split clause 94,188,184,193]
198. 11 <=> ! [X0] : wise(X0) [avatar definition]
199. wise(X0) <- (11) [avatar component clause 198]
201. 12 <=> creative(john) [avatar definition]
203. creative(john) <- (12) [avatar component clause 201]
204. 11 | 12 [avatar split clause 98,201,198]
206. 13 <=> ! [X0] : ~happy(X0) [avatar definition]
207. ~happy(X0) <- (13) [avatar component clause 206]
208. 13 | 12 [avatar split clause 97,201,206]
258. 25 <=> quiet(fred) [avatar definition]
263. 26 <=> tall(sK5) [avatar definition]
265. tall(sK5) <- (26) [avatar component clause 263]
266. ~25 | 26 [avatar split clause 120,263,258]
344. ~humble(john) <- (12) [resolution 101,203]
345. $false <- (12) [subsumption resolution 344,152]
346. ~12 [avatar contradiction clause 345]
358. humble(X0) <- (11) [resolution 143,199]
367. $false <- (~10, 11) [subsumption resolution 195,199]
368. 10 | ~11 [avatar contradiction clause 367]
424. quiet(X0) | curious(X0) | ~humble(X0) [resolution 126,101]
427. curious(X0) | quiet(X0) <- (11) [subsumption resolution 424,358]
445. quiet(fred) <- (~9, 11) [resolution 427,190]
450. 25 | 9 | ~11 [avatar split clause 445,198,188,258]
453. happy(sK5) <- (26) [resolution 265,122]
458. $false <- (13, 26) [subsumption resolution 453,207]
459. ~13 | ~26 [avatar contradiction clause 458]
460. $false <- (~8, 11) [subsumption resolution 186,199]
461. 8 | ~11 [avatar contradiction clause 460]
462. $false [avatar sat refutation 196,204,208,266,346,368,450,459,461]
% SZS output end Proof for 4107395144505691791838808
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not generous or not humble then lucy is either not old or humble.
If lucy is both not curious and not quiet then someone is rich and vice versa.
Everyone who is both strong and not strong is not happy and vice versa.
Everyone who is either curious or not generous is calm or curious and vice versa.
If paul is either not old or not funny then someone is both happy and old.
Everyone who is not rich or not generous is not old and vice versa.
Everyone who is not funny is either not brave or not funny.
Everyone who is not old is either not curious or not humble and vice versa.
Everyone who is strong or not tall is not strong or generous and vice versa.
If paul is either not wise or strong then someone is both not funny and funny.
If someone is curious then someone is quiet.
If someone is not kind then someone is either generous or old.
Everyone who is either not creative or not tall is both quiet and not generous.
If someone is not curious then someone is either not calm or not tall and vice versa.
Everyone who is kind is either not generous or not strong.
If john is creative or generous then someone is both generous and not generous.
Mary is not tall.
Mary is not creative or not old.
Someone is either not patient or funny.
Someone is tall.
Mary is kind.
Someone is either patient or not strong.
Someone is happy.
Lucy is strong or not quiet. | John is not kind. | entailment | ((?[X]:((~generous(X)|~humble(X))))=>((~old(lucy)<~>humble(lucy))))&
(((~curious(lucy)&~quiet(lucy)))<=>(?[X]:(rich(X))))&
(![X]:((strong(X)&~strong(X))<=>~happy(X)))&
(![X]:((curious(X)<~>~generous(X))<=>(calm(X)|curious(X))))&
(((~old(paul)<~>~funny(paul)))=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~rich(X)|~generous(X))<=>~old(X)))&
(![X]:(~funny(X)=>(~brave(X)<~>~funny(X))))&
(![X]:(~old(X)<=>(~curious(X)<~>~humble(X))))&
(![X]:((strong(X)|~tall(X))<=>(~strong(X)|generous(X))))&
(((~wise(paul)<~>strong(paul)))=>(?[X]:((~funny(X)&funny(X)))))&
((?[X]:(curious(X)))=>(?[X]:(quiet(X))))&
((?[X]:(~kind(X)))=>(?[X]:((generous(X)<~>old(X)))))&
(![X]:((~creative(X)<~>~tall(X))=>(quiet(X)&~generous(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~calm(X)<~>~tall(X)))))&
(![X]:(kind(X)=>(~generous(X)<~>~strong(X))))&
(((creative(john)|generous(john)))=>(?[X]:((generous(X)&~generous(X)))))&
(~tall(mary))&
((~creative(mary)|~old(mary)))&
(?[X]:((~patient(X)<~>funny(X))))&
(?[X]:(tall(X)))&
(kind(mary))&
(?[X]:((patient(X)<~>~strong(X))))&
(?[X]:(happy(X)))&
((strong(lucy)|~quiet(lucy))) | ~kind(john) | [
"p8",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5971098781898282998475144
% SZS output start Proof for 5971098781898282998475144
9. ! [X0] : ((~tall(X0) | strong(X0)) <=> (generous(X0) | ~strong(X0))) [input p8]
15. ! [X0] : (kind(X0) => (~generous(X0) <~> ~strong(X0))) [input p14]
16. (generous(john) | creative(john)) => ? [X0] : (~generous(X0) & generous(X0)) [input p15]
25. kind(john) [input hypothesis]
39. ! [X0] : ((~generous(X0) <~> ~strong(X0)) | ~kind(X0)) [ennf transformation 15]
40. ? [X0] : (~generous(X0) & generous(X0)) | (~generous(john) & ~creative(john)) [ennf transformation 16]
56. ! [X0] : (((~tall(X0) | strong(X0)) | (~generous(X0) & strong(X0))) & ((generous(X0) | ~strong(X0)) | (tall(X0) & ~strong(X0)))) [nnf transformation 9]
57. ! [X0] : ((~tall(X0) | strong(X0) | (~generous(X0) & strong(X0))) & (generous(X0) | ~strong(X0) | (tall(X0) & ~strong(X0)))) [flattening 56]
74. ! [X0] : (((strong(X0) | generous(X0)) & (~strong(X0) | ~generous(X0))) | ~kind(X0)) [nnf transformation 39]
75. ? [X0] : (~generous(X0) & generous(X0)) => (~generous(sK7) & generous(sK7)) [choice axiom]
76. (~generous(sK7) & generous(sK7)) | (~generous(john) & ~creative(john)) [skolemisation 40,75]
114. generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 57]
134. strong(X0) | generous(X0) | ~kind(X0) [cnf transformation 74]
136. generous(sK7) | ~generous(john) [cnf transformation 76]
138. ~generous(sK7) | ~generous(john) [cnf transformation 76]
149. kind(john) [cnf transformation 25]
150. ~strong(X0) | generous(X0) [duplicate literal removal 114]
276. ~kind(X0) | generous(X0) [subsumption resolution 134,150]
279. 27 <=> generous(john) [avatar definition]
281. ~generous(john) <- (~27) [avatar component clause 279]
283. 28 <=> generous(sK7) [avatar definition]
286. ~27 | ~28 [avatar split clause 138,283,279]
292. ~27 | 28 [avatar split clause 136,283,279]
345. generous(john) [resolution 276,149]
347. $false <- (~27) [subsumption resolution 345,281]
348. 27 [avatar contradiction clause 347]
350. $false [avatar sat refutation 286,292,348]
% SZS output end Proof for 5971098781898282998475144
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not patient and not creative is not kind.
If mary is not wise or patient then mary is not tall and vice versa.
Everyone who is old is both not curious and not old.
Everyone who is not happy is kind or not wise and vice versa.
If fred is either not tall or not funny then paul is either rich or humble and vice versa.
Everyone who is either generous or not creative is either not patient or creative and vice versa.
If someone is creative or not funny then someone is both not generous and humble.
If mary is either calm or old then someone is either patient or happy and vice versa.
If someone is both calm and not humble then someone is not rich or wise and vice versa.
If someone is generous or happy then someone is either not tall or creative and vice versa.
Everyone who is either generous or not kind is either not happy or happy and vice versa.
Everyone who is not kind is not happy and vice versa.
If mary is both funny and not generous then john is curious and vice versa.
Everyone who is not generous or not calm is not rich or not curious and vice versa.
Everyone who is either not humble or not strong is not generous or not kind.
Everyone who is not humble is either not creative or not funny.
Someone is either not creative or humble.
Lucy is not curious or not rich.
Someone is creative or humble.
Lucy is brave or not tall.
Someone is either not curious or funny.
John is not creative or not happy.
Paul is brave. | Mary is not patient. | entailment | (![X]:((~patient(X)&~creative(X))=>~kind(X)))&
(((~wise(mary)|patient(mary)))<=>(~tall(mary)))&
(![X]:(old(X)=>(~curious(X)&~old(X))))&
(![X]:(~happy(X)<=>(kind(X)|~wise(X))))&
(((~tall(fred)<~>~funny(fred)))<=>((rich(paul)<~>humble(paul))))&
(![X]:((generous(X)<~>~creative(X))<=>(~patient(X)<~>creative(X))))&
((?[X]:((creative(X)|~funny(X))))=>(?[X]:((~generous(X)&humble(X)))))&
(((calm(mary)<~>old(mary)))<=>(?[X]:((patient(X)<~>happy(X)))))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~rich(X)|wise(X)))))&
((?[X]:((generous(X)|happy(X))))<=>(?[X]:((~tall(X)<~>creative(X)))))&
(![X]:((generous(X)<~>~kind(X))<=>(~happy(X)<~>happy(X))))&
(![X]:(~kind(X)<=>~happy(X)))&
(((funny(mary)&~generous(mary)))<=>(curious(john)))&
(![X]:((~generous(X)|~calm(X))<=>(~rich(X)|~curious(X))))&
(![X]:((~humble(X)<~>~strong(X))=>(~generous(X)|~kind(X))))&
(![X]:(~humble(X)=>(~creative(X)<~>~funny(X))))&
(?[X]:((~creative(X)<~>humble(X))))&
((~curious(lucy)|~rich(lucy)))&
(?[X]:((creative(X)|humble(X))))&
((brave(lucy)|~tall(lucy)))&
(?[X]:((~curious(X)<~>funny(X))))&
((~creative(john)|~happy(john)))&
(brave(paul)) | ~patient(mary) | [
"p3",
"p5",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4146724486918079833625315
% SZS output start Proof for 4146724486918079833625315
4. ! [X0] : (~happy(X0) <=> (~wise(X0) | kind(X0))) [input p3]
6. ! [X0] : ((generous(X0) <~> ~creative(X0)) <=> (~patient(X0) <~> creative(X0))) [input p5]
11. ! [X0] : ((generous(X0) <~> ~kind(X0)) <=> (~happy(X0) <~> happy(X0))) [input p10]
12. ! [X0] : (~kind(X0) <=> ~happy(X0)) [input p11]
24. patient(mary) [input hypothesis]
39. ! [X0] : ((~happy(X0) | (wise(X0) & ~kind(X0))) & ((~wise(X0) | kind(X0)) | happy(X0))) [nnf transformation 4]
40. ! [X0] : ((~happy(X0) | (wise(X0) & ~kind(X0))) & (~wise(X0) | kind(X0) | happy(X0))) [flattening 39]
42. ! [X0] : ((((creative(X0) | ~generous(X0)) & (~creative(X0) | generous(X0))) | ((~patient(X0) | ~creative(X0)) & (creative(X0) | patient(X0)))) & (((~creative(X0) | patient(X0)) & (creative(X0) | ~patient(X0))) | ((generous(X0) | creative(X0)) & (~creative(X0) | ~generous(X0))))) [nnf transformation 6]
60. ! [X0] : ((((kind(X0) | ~generous(X0)) & (~kind(X0) | generous(X0))) | ((~happy(X0) | ~happy(X0)) & (happy(X0) | happy(X0)))) & (((~happy(X0) | happy(X0)) & (happy(X0) | ~happy(X0))) | ((generous(X0) | kind(X0)) & (~kind(X0) | ~generous(X0))))) [nnf transformation 11]
61. ! [X0] : ((~kind(X0) | happy(X0)) & (~happy(X0) | kind(X0))) [nnf transformation 12]
83. ~happy(X0) | ~kind(X0) [cnf transformation 40]
94. creative(X0) | ~patient(X0) | generous(X0) | creative(X0) [cnf transformation 42]
98. ~creative(X0) | generous(X0) | ~patient(X0) | ~creative(X0) [cnf transformation 42]
130. kind(X0) | ~generous(X0) | happy(X0) | happy(X0) [cnf transformation 60]
131. kind(X0) | ~generous(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 60]
133. ~kind(X0) | happy(X0) [cnf transformation 61]
152. patient(mary) [cnf transformation 24]
155. kind(X0) | ~generous(X0) | happy(X0) [duplicate literal removal 130]
156. kind(X0) | ~generous(X0) | ~happy(X0) [duplicate literal removal 131]
157. creative(X0) | ~patient(X0) | generous(X0) [duplicate literal removal 94]
159. ~creative(X0) | generous(X0) | ~patient(X0) [duplicate literal removal 98]
171. 3 <=> patient(mary) [avatar definition]
173. patient(mary) <- (3) [avatar component clause 171]
202. ~patient(X0) | generous(X0) [subsumption resolution 157,159]
311. ~generous(X0) | ~happy(X0) [subsumption resolution 156,83]
312. ~generous(X0) | kind(X0) [subsumption resolution 155,311]
314. ~kind(X0) [subsumption resolution 133,83]
322. 33 <=> generous(mary) [avatar definition]
323. generous(mary) <- (33) [avatar component clause 322]
379. 3 [avatar split clause 152,171]
388. generous(mary) <- (3) [resolution 202,173]
390. 33 | ~3 [avatar split clause 388,171,322]
396. kind(mary) <- (33) [resolution 312,323]
399. $false <- (33) [subsumption resolution 396,314]
400. ~33 [avatar contradiction clause 399]
401. $false [avatar sat refutation 379,390,400]
% SZS output end Proof for 4146724486918079833625315
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not humble then fred is creative.
Everyone who is both generous and happy is funny.
If john is not creative or not old then alice is either not humble or not quiet.
If paul is not rich or curious then mary is not humble or not quiet.
Everyone who is not old or not humble is not happy or funny and vice versa.
If fred is both not rich and curious then someone is both not brave and calm.
If someone is both not old and calm then paul is either not humble or funny.
If susan is both rich and not curious then mary is not humble.
Everyone who is not patient is quiet and vice versa.
If someone is not creative or brave then lucy is both funny and not old and vice versa.
Everyone who is not generous is both rich and kind and vice versa.
Everyone who is both not wise and not quiet is patient or wise and vice versa.
Everyone who is curious is patient or not creative and vice versa.
Everyone who is either generous or happy is not kind.
Everyone who is both not strong and not old is both not humble and not funny and vice versa.
If lucy is both calm and wise then someone is happy.
John is both strong and not kind.
Fred is not kind.
Lucy is brave or creative.
Susan is happy or not calm.
Someone is not patient.
Fred is both not quiet and not creative.
Someone is calm.
John is brave. | Mary is generous. | neutral | ((?[X]:(~humble(X)))=>(creative(fred)))&
(![X]:((generous(X)&happy(X))=>funny(X)))&
(((~creative(john)|~old(john)))=>((~humble(alice)<~>~quiet(alice))))&
(((~rich(paul)|curious(paul)))=>((~humble(mary)|~quiet(mary))))&
(![X]:((~old(X)|~humble(X))<=>(~happy(X)|funny(X))))&
(((~rich(fred)&curious(fred)))=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((~old(X)&calm(X))))=>((~humble(paul)<~>funny(paul))))&
(((rich(susan)&~curious(susan)))=>(~humble(mary)))&
(![X]:(~patient(X)<=>quiet(X)))&
((?[X]:((~creative(X)|brave(X))))<=>((funny(lucy)&~old(lucy))))&
(![X]:(~generous(X)<=>(rich(X)&kind(X))))&
(![X]:((~wise(X)&~quiet(X))<=>(patient(X)|wise(X))))&
(![X]:(curious(X)<=>(patient(X)|~creative(X))))&
(![X]:((generous(X)<~>happy(X))=>~kind(X)))&
(![X]:((~strong(X)&~old(X))<=>(~humble(X)&~funny(X))))&
(((calm(lucy)&wise(lucy)))=>(?[X]:(happy(X))))&
((strong(john)&~kind(john)))&
(~kind(fred))&
((brave(lucy)|creative(lucy)))&
((happy(susan)|~calm(susan)))&
(?[X]:(~patient(X)))&
((~quiet(fred)&~creative(fred)))&
(?[X]:(calm(X)))&
(brave(john)) | generous(mary) | [] | null | 0 |
If lucy is either not happy or old then someone is not tall or tall.
If mary is not quiet then john is both curious and not funny and vice versa.
If someone is not tall then someone is both not kind and rich.
Everyone who is not funny is either generous or tall and vice versa.
Everyone who is either old or not kind is either not patient or funny.
If susan is strong then john is either funny or not brave and vice versa.
If someone is either quiet or not rich then alice is either not kind or quiet and vice versa.
If susan is both quiet and patient then someone is both not patient and wise and vice versa.
Everyone who is patient or not generous is strong and vice versa.
If paul is not rich or funny then paul is either not brave or not creative.
Everyone who is not quiet or not tall is both funny and not funny and vice versa.
Everyone who is wise or not quiet is both not rich and not strong.
Everyone who is patient or strong is strong and vice versa.
If someone is both creative and not happy then someone is not old and vice versa.
If someone is both not humble and quiet then lucy is rich and vice versa.
Everyone who is old is not tall and vice versa.
Someone is strong.
Someone is not brave.
Someone is not humble.
Someone is both not kind and quiet.
John is creative or humble.
Lucy is not creative or generous.
Fred is either strong or calm. | Mary is quiet. | entailment | (((~happy(lucy)<~>old(lucy)))=>(?[X]:((~tall(X)|tall(X)))))&
((~quiet(mary))<=>((curious(john)&~funny(john))))&
((?[X]:(~tall(X)))=>(?[X]:((~kind(X)&rich(X)))))&
(![X]:(~funny(X)<=>(generous(X)<~>tall(X))))&
(![X]:((old(X)<~>~kind(X))=>(~patient(X)<~>funny(X))))&
((strong(susan))<=>((funny(john)<~>~brave(john))))&
((?[X]:((quiet(X)<~>~rich(X))))<=>((~kind(alice)<~>quiet(alice))))&
(((quiet(susan)&patient(susan)))<=>(?[X]:((~patient(X)&wise(X)))))&
(![X]:((patient(X)|~generous(X))<=>strong(X)))&
(((~rich(paul)|funny(paul)))=>((~brave(paul)<~>~creative(paul))))&
(![X]:((~quiet(X)|~tall(X))<=>(funny(X)&~funny(X))))&
(![X]:((wise(X)|~quiet(X))=>(~rich(X)&~strong(X))))&
(![X]:((patient(X)|strong(X))<=>strong(X)))&
((?[X]:((creative(X)&~happy(X))))<=>(?[X]:(~old(X))))&
((?[X]:((~humble(X)&quiet(X))))<=>(rich(lucy)))&
(![X]:(old(X)<=>~tall(X)))&
(?[X]:(strong(X)))&
(?[X]:(~brave(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~kind(X)&quiet(X))))&
((creative(john)|humble(john)))&
((~creative(lucy)|generous(lucy)))&
((strong(fred)<~>calm(fred))) | quiet(mary) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 298325854935823665748330
% SZS output start Proof for 298325854935823665748330
11. ! [X0] : ((~tall(X0) | ~quiet(X0)) <=> (~funny(X0) & funny(X0))) [input p10]
24. ~quiet(mary) [input hypothesis]
55. ! [X0] : (((~tall(X0) | ~quiet(X0)) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | (tall(X0) & quiet(X0)))) [nnf transformation 11]
56. ! [X0] : ((~tall(X0) | ~quiet(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | (tall(X0) & quiet(X0)))) [flattening 55]
116. funny(X0) | quiet(X0) [cnf transformation 56]
118. ~funny(X0) | quiet(X0) [cnf transformation 56]
145. ~quiet(mary) [cnf transformation 24]
261. quiet(X0) [subsumption resolution 116,118]
325. $false [subsumption resolution 145,261]
% SZS output end Proof for 298325854935823665748330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is either not tall or old and vice versa.
If someone is not strong or old then someone is either curious or not creative.
If someone is calm then john is not humble and vice versa.
If someone is quiet or old then someone is both not tall and calm.
Everyone who is not wise is either strong or not quiet and vice versa.
Everyone who is both curious and generous is funny or not strong and vice versa.
Everyone who is either not tall or strong is both not curious and funny.
If john is not rich or not old then mary is both quiet and not calm and vice versa.
Everyone who is both not creative and old is quiet or not humble and vice versa.
Everyone who is kind or not wise is both wise and not strong and vice versa.
If someone is kind or not creative then someone is both not happy and strong and vice versa.
Everyone who is not tall is not strong or calm.
If someone is both patient and curious then john is patient.
Everyone who is both not strong and not funny is either not funny or brave.
Everyone who is not brave is either not old or humble.
Everyone who is either old or funny is either creative or wise.
Someone is both curious and not generous.
Someone is happy.
Paul is funny.
Someone is not old or not strong.
Someone is either not strong or not wise.
Paul is not rich or not generous.
Someone is not patient or not quiet.
Someone is either not generous or not patient. | John is humble. | contradiction | (![X]:((creative(X)|brave(X))<=>(~tall(X)<~>old(X))))&
((?[X]:((~strong(X)|old(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
((?[X]:(calm(X)))<=>(~humble(john)))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
(?[X]:((curious(X)&~generous(X))))&
(?[X]:(happy(X)))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X)))) | humble(john) | [
"p2",
"p3",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6887096913394088561865255
% SZS output start Proof for 6887096913394088561865255
3. ? [X0] : calm(X0) <=> ~humble(john) [input p2]
4. ? [X0] : (old(X0) | quiet(X0)) => ? [X0] : (calm(X0) & ~tall(X0)) [input p3]
8. (~old(john) | ~rich(john)) <=> (~calm(mary) & quiet(mary)) [input p7]
25. humble(john) [input hypothesis]
27. ? [X0] : (old(X0) | quiet(X0)) => ? [X1] : (calm(X1) & ~tall(X1)) [rectify 4]
30. ? [X1] : (calm(X1) & ~tall(X1)) | ! [X0] : (~old(X0) & ~quiet(X0)) [ennf transformation 27]
45. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X0] : ~calm(X0)) [nnf transformation 3]
46. (? [X0] : calm(X0) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [rectify 45]
47. ? [X0] : calm(X0) => calm(sK1) [choice axiom]
48. (calm(sK1) | humble(john)) & (~humble(john) | ! [X1] : ~calm(X1)) [skolemisation 46,47]
49. ? [X0] : (calm(X0) & ~tall(X0)) | ! [X1] : (~old(X1) & ~quiet(X1)) [rectify 30]
50. ? [X0] : (calm(X0) & ~tall(X0)) => (calm(sK2) & ~tall(sK2)) [choice axiom]
51. (calm(sK2) & ~tall(sK2)) | ! [X1] : (~old(X1) & ~quiet(X1)) [skolemisation 49,50]
56. ((~old(john) | ~rich(john)) | (calm(mary) | ~quiet(mary))) & ((~calm(mary) & quiet(mary)) | (old(john) & rich(john))) [nnf transformation 8]
57. (~old(john) | ~rich(john) | calm(mary) | ~quiet(mary)) & ((~calm(mary) & quiet(mary)) | (old(john) & rich(john))) [flattening 56]
94. ~humble(john) | ~calm(X1) [cnf transformation 48]
98. calm(sK2) | ~quiet(X1) [cnf transformation 51]
99. calm(sK2) | ~old(X1) [cnf transformation 51]
114. quiet(mary) | old(john) [cnf transformation 57]
154. humble(john) [cnf transformation 25]
159. 1 <=> ! [X1] : ~old(X1) [avatar definition]
160. ~old(X1) <- (1) [avatar component clause 159]
177. 5 <=> humble(john) [avatar definition]
186. 7 <=> ! [X1] : ~calm(X1) [avatar definition]
187. ~calm(X1) <- (7) [avatar component clause 186]
188. 7 | ~5 [avatar split clause 94,177,186]
190. 8 <=> calm(sK2) [avatar definition]
192. calm(sK2) <- (8) [avatar component clause 190]
193. 1 | 8 [avatar split clause 99,190,159]
195. 9 <=> ! [X1] : ~quiet(X1) [avatar definition]
196. ~quiet(X1) <- (9) [avatar component clause 195]
197. 9 | 8 [avatar split clause 98,190,195]
206. 11 <=> quiet(mary) [avatar definition]
207. quiet(mary) <- (11) [avatar component clause 206]
218. 14 <=> old(john) [avatar definition]
219. old(john) <- (14) [avatar component clause 218]
224. 14 | 11 [avatar split clause 114,206,218]
307. 5 [avatar split clause 154,177]
308. $false <- (7, 8) [resolution 192,187]
309. ~7 | ~8 [avatar contradiction clause 308]
310. $false <- (9, 11) [resolution 207,196]
311. ~9 | ~11 [avatar contradiction clause 310]
312. $false <- (1, 14) [subsumption resolution 219,160]
313. ~1 | ~14 [avatar contradiction clause 312]
314. $false [avatar sat refutation 188,193,197,224,307,309,311,313]
% SZS output end Proof for 6887096913394088561865255
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is either not kind or not creative and vice versa.
If someone is both curious and not generous then john is not wise or brave and vice versa.
If fred is not patient or not rich then someone is generous.
If john is either old or quiet then someone is happy or quiet.
Everyone who is creative is either not strong or creative and vice versa.
Everyone who is not rich is tall.
If someone is humble then john is both patient and generous.
If susan is not creative or strong then paul is quiet and vice versa.
If paul is not creative then paul is either wise or not brave and vice versa.
Everyone who is both not creative and not old is both not strong and not rich and vice versa.
If john is not rich or not funny then someone is both not wise and calm.
If alice is either humble or not strong then someone is not calm or humble and vice versa.
Everyone who is either not kind or not patient is both strong and tall.
If someone is not rich or calm then alice is not strong and vice versa.
Everyone who is both not old and humble is not brave or not kind and vice versa.
If someone is both not generous and not humble then alice is either rich or not old and vice versa.
John is both old and wise.
Susan is not curious.
Susan is either brave or generous.
Someone is kind.
Someone is both kind and old.
Alice is not old or brave.
Alice is generous. | Susan is not rich. | contradiction | (![X]:(~kind(X)<=>(~kind(X)<~>~creative(X))))&
((?[X]:((curious(X)&~generous(X))))<=>((~wise(john)|brave(john))))&
(((~patient(fred)|~rich(fred)))=>(?[X]:(generous(X))))&
(((old(john)<~>quiet(john)))=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:(creative(X)<=>(~strong(X)<~>creative(X))))&
(![X]:(~rich(X)=>tall(X)))&
((?[X]:(humble(X)))=>((patient(john)&generous(john))))&
(((~creative(susan)|strong(susan)))<=>(quiet(paul)))&
((~creative(paul))<=>((wise(paul)<~>~brave(paul))))&
(![X]:((~creative(X)&~old(X))<=>(~strong(X)&~rich(X))))&
(((~rich(john)|~funny(john)))=>(?[X]:((~wise(X)&calm(X)))))&
(((humble(alice)<~>~strong(alice)))<=>(?[X]:((~calm(X)|humble(X)))))&
(![X]:((~kind(X)<~>~patient(X))=>(strong(X)&tall(X))))&
((?[X]:((~rich(X)|calm(X))))<=>(~strong(alice)))&
(![X]:((~old(X)&humble(X))<=>(~brave(X)|~kind(X))))&
((?[X]:((~generous(X)&~humble(X))))<=>((rich(alice)<~>~old(alice))))&
((old(john)&wise(john)))&
(~curious(susan))&
((brave(susan)<~>generous(susan)))&
(?[X]:(kind(X)))&
(?[X]:((kind(X)&old(X))))&
((~old(alice)|brave(alice)))&
(generous(alice)) | ~rich(susan) | [
"p0",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4379843641514309294176619
% SZS output start Proof for 4379843641514309294176619
1. ! [X0] : (~kind(X0) <=> (~kind(X0) <~> ~creative(X0))) [input p0]
5. ! [X0] : (creative(X0) <=> (~strong(X0) <~> creative(X0))) [input p4]
14. ? [X0] : (calm(X0) | ~rich(X0)) <=> ~strong(alice) [input p13]
24. ~rich(susan) [input hypothesis]
33. ! [X0] : ((~kind(X0) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0)))) & (((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | kind(X0))) [nnf transformation 1]
41. ! [X0] : ((creative(X0) | ((~strong(X0) | ~creative(X0)) & (creative(X0) | strong(X0)))) & (((~creative(X0) | strong(X0)) & (creative(X0) | ~strong(X0))) | ~creative(X0))) [nnf transformation 5]
54. (? [X0] : (calm(X0) | ~rich(X0)) | strong(alice)) & (~strong(alice) | ! [X0] : (~calm(X0) & rich(X0))) [nnf transformation 14]
55. (? [X0] : (calm(X0) | ~rich(X0)) | strong(alice)) & (~strong(alice) | ! [X1] : (~calm(X1) & rich(X1))) [rectify 54]
56. ? [X0] : (calm(X0) | ~rich(X0)) => (calm(sK4) | ~rich(sK4)) [choice axiom]
57. ((calm(sK4) | ~rich(sK4)) | strong(alice)) & (~strong(alice) | ! [X1] : (~calm(X1) & rich(X1))) [skolemisation 55,56]
70. creative(X0) | kind(X0) | kind(X0) [cnf transformation 33]
72. ~kind(X0) | ~kind(X0) | creative(X0) [cnf transformation 33]
81. ~creative(X0) | strong(X0) | ~creative(X0) [cnf transformation 41]
107. ~strong(alice) | rich(X1) [cnf transformation 57]
131. ~rich(susan) [cnf transformation 24]
132. ~creative(X0) | strong(X0) [duplicate literal removal 81]
134. creative(X0) | kind(X0) [duplicate literal removal 70]
135. ~kind(X0) | creative(X0) [duplicate literal removal 72]
136. creative(X0) [subsumption resolution 134,135]
175. strong(X0) [subsumption resolution 132,136]
238. rich(X1) [subsumption resolution 107,175]
271. $false [subsumption resolution 131,238]
% SZS output end Proof for 4379843641514309294176619
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not humble then someone is both quiet and tall and vice versa.
If paul is either kind or generous then someone is not brave or not kind.
Everyone who is both not happy and tall is both old and not brave and vice versa.
Everyone who is not generous is curious or not happy.
If someone is kind then fred is both not kind and not rich.
Everyone who is both not calm and not patient is either funny or generous.
Everyone who is wise is either strong or not tall.
Everyone who is either strong or calm is not happy.
Everyone who is both quiet and brave is not creative and vice versa.
Everyone who is quiet is both old and quiet and vice versa.
Everyone who is not happy or not strong is generous or patient.
If alice is not funny or not patient then susan is happy or not brave and vice versa.
Everyone who is brave or not old is both not brave and not happy.
Everyone who is not quiet is humble.
Everyone who is not quiet is not brave or happy and vice versa.
If fred is not curious then someone is not generous or not curious.
Someone is both old and not calm.
Someone is either not humble or rich.
Lucy is tall or not wise.
Someone is not calm.
Alice is either funny or not brave.
Someone is either not wise or quiet. | Paul is brave. | contradiction | ((?[X]:((~creative(X)<~>~humble(X))))<=>(?[X]:((quiet(X)&tall(X)))))&
(((kind(paul)<~>generous(paul)))=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((~happy(X)&tall(X))<=>(old(X)&~brave(X))))&
(![X]:(~generous(X)=>(curious(X)|~happy(X))))&
((?[X]:(kind(X)))=>((~kind(fred)&~rich(fred))))&
(![X]:((~calm(X)&~patient(X))=>(funny(X)<~>generous(X))))&
(![X]:(wise(X)=>(strong(X)<~>~tall(X))))&
(![X]:((strong(X)<~>calm(X))=>~happy(X)))&
(![X]:((quiet(X)&brave(X))<=>~creative(X)))&
(![X]:(quiet(X)<=>(old(X)&quiet(X))))&
(![X]:((~happy(X)|~strong(X))=>(generous(X)|patient(X))))&
(((~funny(alice)|~patient(alice)))<=>((happy(susan)|~brave(susan))))&
(![X]:((brave(X)|~old(X))=>(~brave(X)&~happy(X))))&
(![X]:(~quiet(X)=>humble(X)))&
(![X]:(~quiet(X)<=>(~brave(X)|happy(X))))&
((~curious(fred))=>(?[X]:((~generous(X)|~curious(X)))))&
(?[X]:((old(X)&~calm(X))))&
(?[X]:((~humble(X)<~>rich(X))))&
((tall(lucy)|~wise(lucy)))&
(?[X]:(~calm(X)))&
((funny(alice)<~>~brave(alice)))&
(?[X]:((~wise(X)<~>quiet(X)))) | brave(paul) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2594229241055253522869619
% SZS output start Proof for 2594229241055253522869619
13. ! [X0] : ((~old(X0) | brave(X0)) => (~happy(X0) & ~brave(X0))) [input p12]
23. brave(paul) [input hypothesis]
35. ! [X0] : ((~happy(X0) & ~brave(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 13]
105. ~brave(X0) | ~brave(X0) [cnf transformation 35]
124. brave(paul) [cnf transformation 23]
125. ~brave(X0) [duplicate literal removal 105]
244. $false [subsumption resolution 124,125]
% SZS output end Proof for 2594229241055253522869619
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is both not tall and creative then mary is not creative or kind and vice versa. Everyone who is not old or generous is either curious or not calm and vice versa. Everyone who is both brave and patient is tall or curious. If someone is both not curious and strong then someone is not humble. Everyone who is either not rich or funny is either not creative or tall. Everyone who is either wise or patient is calm and vice versa. Everyone who is either creative or not quiet is both not happy and not humble. If someone is both not old and brave then someone is both not quiet and brave. Everyone who is either tall or not quiet is not funny. Everyone who is either not calm or not tall is brave and vice versa. Everyone who is either generous or curious is not curious and vice versa. Everyone who is both not calm and not generous is not rich or wise and vice versa. Everyone who is curious is either old or not calm. Everyone who is generous is not funny and vice versa. If mary is either quiet or happy then mary is not brave or generous and vice versa. If lucy is happy then someone is wise and vice versa. Alice is both not funny and not kind. Someone is rich or not wise. Someone is not kind or not patient. Susan is not tall or calm. Susan is funny or creative. Alice is not quiet or not brave. Paul is brave. John is curious or not kind. | John is not curious. | neutral | (((~tall(paul)&creative(paul)))<=>((~creative(mary)|kind(mary))))&
(![X]:((~old(X)|generous(X))<=>(curious(X)<~>~calm(X))))&
(![X]:((brave(X)&patient(X))=>(tall(X)|curious(X))))&
((?[X]:((~curious(X)&strong(X))))=>(?[X]:(~humble(X))))&
(![X]:((~rich(X)<~>funny(X))=>(~creative(X)<~>tall(X))))&
(![X]:((wise(X)<~>patient(X))<=>calm(X)))&
(![X]:((creative(X)<~>~quiet(X))=>(~happy(X)&~humble(X))))&
((?[X]:((~old(X)&brave(X))))=>(?[X]:((~quiet(X)&brave(X)))))&
(![X]:((tall(X)<~>~quiet(X))=>~funny(X)))&
(![X]:((~calm(X)<~>~tall(X))<=>brave(X)))&
(![X]:((generous(X)<~>curious(X))<=>~curious(X)))&
(![X]:((~calm(X)&~generous(X))<=>(~rich(X)|wise(X))))&
(![X]:(curious(X)=>(old(X)<~>~calm(X))))&
(![X]:(generous(X)<=>~funny(X)))&
(((quiet(mary)<~>happy(mary)))<=>((~brave(mary)|generous(mary))))&
((happy(lucy))<=>(?[X]:(wise(X))))&
((~funny(alice)&~kind(alice)))&
(?[X]:((rich(X)|~wise(X))))&
(?[X]:((~kind(X)|~patient(X))))&
((~tall(susan)|calm(susan)))&
((funny(susan)|creative(susan)))&
((~quiet(alice)|~brave(alice)))&
(brave(paul))&
((curious(john)|~kind(john))) | ~curious(john) | [] | null | 0 |
Everyone who is not funny is both patient and not old and vice versa. Everyone who is humble is either not tall or not old. If someone is not old then someone is either not brave or quiet and vice versa. Everyone who is old is both wise and not rich and vice versa. Everyone who is patient or old is both quiet and not kind. Everyone who is not patient or not wise is either quiet or old and vice versa. Everyone who is both not calm and calm is either calm or humble. Everyone who is calm is either not old or rich. Everyone who is not curious or rich is either not rich or tall. Everyone who is not wise or not patient is either kind or humble and vice versa. Everyone who is happy is either not curious or not old and vice versa. Everyone who is both not humble and happy is humble or curious and vice versa. Everyone who is not wise is not curious. If fred is either calm or not quiet then lucy is both not patient and wise. Everyone who is not wise is either not kind or not creative and vice versa. If john is rich then someone is not brave and vice versa. Mary is either not humble or strong. John is not wise. Someone is not generous. Lucy is not strong or not creative. Someone is both wise and not brave. Someone is either not rich or curious. | Fred is not rich. | neutral | (![X]:(~funny(X)<=>(patient(X)&~old(X))))&
(![X]:(humble(X)=>(~tall(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(old(X)<=>(wise(X)&~rich(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~kind(X))))&
(![X]:((~patient(X)|~wise(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~calm(X)&calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
((rich(john))<=>(?[X]:(~brave(X))))&
((~humble(mary)<~>strong(mary)))&
(~wise(john))&
(?[X]:(~generous(X)))&
((~strong(lucy)|~creative(lucy)))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:((~rich(X)<~>curious(X)))) | ~rich(fred) | [] | null | 0 |
Everyone who is both patient and not wise is both not generous and not quiet and vice versa.
If someone is either old or rich then paul is not old or strong and vice versa.
Everyone who is old is patient and vice versa.
If someone is not strong or strong then someone is creative or happy.
Everyone who is not rich is either not quiet or creative.
If someone is not tall then someone is either humble or strong and vice versa.
If someone is generous or not curious then someone is either not old or wise and vice versa.
Everyone who is not curious is happy or strong.
If fred is not quiet then lucy is either not generous or funny.
Everyone who is both not brave and curious is either strong or not generous and vice versa.
If mary is not old then someone is both generous and brave.
If someone is rich then alice is both not tall and curious.
Everyone who is both tall and not rich is not wise or not rich and vice versa.
If paul is either wise or creative then someone is quiet and vice versa.
Everyone who is not brave or not humble is strong or not wise and vice versa.
If alice is either not curious or not kind then mary is happy or funny and vice versa.
Someone is not brave.
John is not brave or not creative.
Someone is either not creative or not quiet.
Paul is not quiet.
Susan is not generous.
Fred is either funny or curious.
Susan is rich. | Fred is not rich. | neutral | (![X]:((patient(X)&~wise(X))<=>(~generous(X)&~quiet(X))))&
((?[X]:((old(X)<~>rich(X))))<=>((~old(paul)|strong(paul))))&
(![X]:(old(X)<=>patient(X)))&
((?[X]:((~strong(X)|strong(X))))=>(?[X]:((creative(X)|happy(X)))))&
(![X]:(~rich(X)=>(~quiet(X)<~>creative(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((humble(X)<~>strong(X)))))&
((?[X]:((generous(X)|~curious(X))))<=>(?[X]:((~old(X)<~>wise(X)))))&
(![X]:(~curious(X)=>(happy(X)|strong(X))))&
((~quiet(fred))=>((~generous(lucy)<~>funny(lucy))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)<~>~generous(X))))&
((~old(mary))=>(?[X]:((generous(X)&brave(X)))))&
((?[X]:(rich(X)))=>((~tall(alice)&curious(alice))))&
(![X]:((tall(X)&~rich(X))<=>(~wise(X)|~rich(X))))&
(((wise(paul)<~>creative(paul)))<=>(?[X]:(quiet(X))))&
(![X]:((~brave(X)|~humble(X))<=>(strong(X)|~wise(X))))&
(((~curious(alice)<~>~kind(alice)))<=>((happy(mary)|funny(mary))))&
(?[X]:(~brave(X)))&
((~brave(john)|~creative(john)))&
(?[X]:((~creative(X)<~>~quiet(X))))&
(~quiet(paul))&
(~generous(susan))&
((funny(fred)<~>curious(fred)))&
(rich(susan)) | ~rich(fred) | [] | null | 0 |
If paul is either brave or not wise then alice is patient. Everyone who is not funny is either old or not patient and vice versa. If someone is either not brave or creative then someone is not funny. Everyone who is both tall and quiet is curious or not curious. Everyone who is both not generous and creative is not brave or not rich and vice versa. Everyone who is both not rich and not quiet is both not brave and not generous and vice versa. Everyone who is both curious and not brave is not curious. Everyone who is both creative and not happy is calm and vice versa. Everyone who is either old or not rich is either not rich or not brave. Everyone who is both strong and not strong is either tall or curious and vice versa. Everyone who is brave or not old is both not calm and not brave. Everyone who is not kind is not calm. Everyone who is strong is either not happy or not curious and vice versa. Everyone who is rich is both creative and strong and vice versa. If mary is quiet or not funny then alice is both happy and creative and vice versa. If john is either not quiet or not kind then someone is either not wise or curious and vice versa. John is not strong or not tall. Paul is either funny or calm. Someone is not wise. Alice is creative. John is happy or not funny. | Paul is curious. | contradiction | (((brave(paul)<~>~wise(paul)))=>(patient(alice)))&
(![X]:(~funny(X)<=>(old(X)<~>~patient(X))))&
((?[X]:((~brave(X)<~>creative(X))))=>(?[X]:(~funny(X))))&
(![X]:((tall(X)&quiet(X))=>(curious(X)|~curious(X))))&
(![X]:((~generous(X)&creative(X))<=>(~brave(X)|~rich(X))))&
(![X]:((~rich(X)&~quiet(X))<=>(~brave(X)&~generous(X))))&
(![X]:((curious(X)&~brave(X))=>~curious(X)))&
(![X]:((creative(X)&~happy(X))<=>calm(X)))&
(![X]:((old(X)<~>~rich(X))=>(~rich(X)<~>~brave(X))))&
(![X]:((strong(X)&~strong(X))<=>(tall(X)<~>curious(X))))&
(![X]:((brave(X)|~old(X))=>(~calm(X)&~brave(X))))&
(![X]:(~kind(X)=>~calm(X)))&
(![X]:(strong(X)<=>(~happy(X)<~>~curious(X))))&
(![X]:(rich(X)<=>(creative(X)&strong(X))))&
(((quiet(mary)|~funny(mary)))<=>((happy(alice)&creative(alice))))&
(((~quiet(john)<~>~kind(john)))<=>(?[X]:((~wise(X)<~>curious(X)))))&
((~strong(john)|~tall(john)))&
((funny(paul)<~>calm(paul)))&
(?[X]:(~wise(X)))&
(creative(alice))&
((happy(john)|~funny(john))) | curious(paul) | [
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2563389341813440719682612
% SZS output start Proof for 2563389341813440719682612
7. ! [X0] : ((~brave(X0) & curious(X0)) => ~curious(X0)) [input p6]
11. ! [X0] : ((~old(X0) | brave(X0)) => (~brave(X0) & ~calm(X0))) [input p10]
22. curious(paul) [input hypothesis]
28. ! [X0] : (~curious(X0) | (brave(X0) | ~curious(X0))) [ennf transformation 7]
29. ! [X0] : (~curious(X0) | brave(X0) | ~curious(X0)) [flattening 28]
31. ! [X0] : ((~brave(X0) & ~calm(X0)) | (old(X0) & ~brave(X0))) [ennf transformation 11]
78. ~curious(X0) | brave(X0) | ~curious(X0) [cnf transformation 29]
94. ~brave(X0) | ~brave(X0) [cnf transformation 31]
123. curious(paul) [cnf transformation 22]
124. ~brave(X0) [duplicate literal removal 94]
127. ~curious(X0) | brave(X0) [duplicate literal removal 78]
241. brave(paul) [resolution 127,123]
242. $false [subsumption resolution 241,124]
% SZS output end Proof for 2563389341813440719682612
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or brave is kind and vice versa.
Everyone who is not brave or rich is either not quiet or not rich.
If john is quiet then susan is either not humble or not happy and vice versa.
If someone is not funny then paul is quiet or not tall.
Everyone who is not calm is happy or not creative and vice versa.
Everyone who is either funny or generous is patient.
Everyone who is not curious is both brave and not kind.
Everyone who is both not wise and not humble is patient or rich and vice versa.
If someone is not wise or brave then john is both strong and patient and vice versa.
Everyone who is either not happy or wise is both not old and not humble.
If someone is either tall or calm then lucy is happy and vice versa.
If lucy is not wise then paul is not funny or not old and vice versa.
If someone is not patient then someone is both not humble and brave and vice versa.
Everyone who is not old is not tall or wise.
Everyone who is both tall and not quiet is not happy.
If alice is either quiet or old then susan is not wise and vice versa.
Someone is happy.
Fred is both tall and happy.
Fred is both not wise and not calm.
Someone is tall.
Someone is both wise and kind.
Someone is not happy.
Someone is generous or happy.
John is both patient and quiet. | Fred is rich. | contradiction | (![X]:((funny(X)|brave(X))<=>kind(X)))&
(![X]:((~brave(X)|rich(X))=>(~quiet(X)<~>~rich(X))))&
((quiet(john))<=>((~humble(susan)<~>~happy(susan))))&
((?[X]:(~funny(X)))=>((quiet(paul)|~tall(paul))))&
(![X]:(~calm(X)<=>(happy(X)|~creative(X))))&
(![X]:((funny(X)<~>generous(X))=>patient(X)))&
(![X]:(~curious(X)=>(brave(X)&~kind(X))))&
(![X]:((~wise(X)&~humble(X))<=>(patient(X)|rich(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((strong(john)&patient(john))))&
(![X]:((~happy(X)<~>wise(X))=>(~old(X)&~humble(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>(happy(lucy)))&
((~wise(lucy))<=>((~funny(paul)|~old(paul))))&
((?[X]:(~patient(X)))<=>(?[X]:((~humble(X)&brave(X)))))&
(![X]:(~old(X)=>(~tall(X)|wise(X))))&
(![X]:((tall(X)&~quiet(X))=>~happy(X)))&
(((quiet(alice)<~>old(alice)))<=>(~wise(susan)))&
(?[X]:(happy(X)))&
((tall(fred)&happy(fred)))&
((~wise(fred)&~calm(fred)))&
(?[X]:(tall(X)))&
(?[X]:((wise(X)&kind(X))))&
(?[X]:(~happy(X)))&
(?[X]:((generous(X)|happy(X))))&
((patient(john)&quiet(john))) | rich(fred) | [
"p1",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1166881703038070731829181
% SZS output start Proof for 1166881703038070731829181
2. ! [X0] : ((rich(X0) | ~brave(X0)) => (~quiet(X0) <~> ~rich(X0))) [input p1]
15. ! [X0] : ((~quiet(X0) & tall(X0)) => ~happy(X0)) [input p14]
18. happy(fred) & tall(fred) [input p17]
25. rich(fred) [input hypothesis]
31. ! [X0] : ((~quiet(X0) <~> ~rich(X0)) | (~rich(X0) & brave(X0))) [ennf transformation 2]
38. ! [X0] : (~happy(X0) | (quiet(X0) | ~tall(X0))) [ennf transformation 15]
39. ! [X0] : (~happy(X0) | quiet(X0) | ~tall(X0)) [flattening 38]
40. ! [X0] : (((rich(X0) | quiet(X0)) & (~rich(X0) | ~quiet(X0))) | (~rich(X0) & brave(X0))) [nnf transformation 31]
77. ~rich(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 40]
115. ~tall(X0) | quiet(X0) | ~happy(X0) [cnf transformation 39]
121. tall(fred) [cnf transformation 18]
122. happy(fred) [cnf transformation 18]
132. rich(fred) [cnf transformation 25]
133. ~quiet(X0) | ~rich(X0) [duplicate literal removal 77]
376. quiet(fred) | ~happy(fred) [resolution 115,121]
379. quiet(fred) [subsumption resolution 376,122]
499. ~rich(fred) [resolution 379,133]
500. $false [subsumption resolution 499,132]
% SZS output end Proof for 1166881703038070731829181
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy and not strong is either happy or brave.
If paul is calm or curious then paul is either not patient or not curious and vice versa.
If john is either not calm or kind then someone is both quiet and not patient.
If john is both not curious and not quiet then someone is not patient.
Everyone who is both strong and not rich is both tall and not strong and vice versa.
If someone is either happy or not quiet then someone is both not humble and not kind and vice versa.
If someone is calm or creative then someone is quiet or funny.
If mary is not creative or not quiet then john is not wise and vice versa.
If susan is not kind or tall then someone is not generous or happy and vice versa.
Everyone who is kind or happy is not tall or curious and vice versa.
Everyone who is either not calm or old is not wise.
Everyone who is creative or wise is wise or not humble.
If someone is happy then someone is either not quiet or not strong and vice versa.
If someone is wise or not strong then someone is either creative or brave.
Everyone who is kind or rich is not curious or not calm.
Everyone who is not old or not kind is both kind and not curious.
John is not generous.
Paul is funny or not generous.
Someone is happy.
Someone is quiet or patient.
Mary is quiet or not happy.
Someone is calm or funny.
Someone is both creative and happy.
Paul is not curious. | Mary is not quiet. | contradiction | (![X]:((happy(X)&~strong(X))=>(happy(X)<~>brave(X))))&
(((calm(paul)|curious(paul)))<=>((~patient(paul)<~>~curious(paul))))&
(((~calm(john)<~>kind(john)))=>(?[X]:((quiet(X)&~patient(X)))))&
(((~curious(john)&~quiet(john)))=>(?[X]:(~patient(X))))&
(![X]:((strong(X)&~rich(X))<=>(tall(X)&~strong(X))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>(?[X]:((~humble(X)&~kind(X)))))&
((?[X]:((calm(X)|creative(X))))=>(?[X]:((quiet(X)|funny(X)))))&
(((~creative(mary)|~quiet(mary)))<=>(~wise(john)))&
(((~kind(susan)|tall(susan)))<=>(?[X]:((~generous(X)|happy(X)))))&
(![X]:((kind(X)|happy(X))<=>(~tall(X)|curious(X))))&
(![X]:((~calm(X)<~>old(X))=>~wise(X)))&
(![X]:((creative(X)|wise(X))=>(wise(X)|~humble(X))))&
((?[X]:(happy(X)))<=>(?[X]:((~quiet(X)<~>~strong(X)))))&
((?[X]:((wise(X)|~strong(X))))=>(?[X]:((creative(X)<~>brave(X)))))&
(![X]:((kind(X)|rich(X))=>(~curious(X)|~calm(X))))&
(![X]:((~old(X)|~kind(X))=>(kind(X)&~curious(X))))&
(~generous(john))&
((funny(paul)|~generous(paul)))&
(?[X]:(happy(X)))&
(?[X]:((quiet(X)|patient(X))))&
((quiet(mary)|~happy(mary)))&
(?[X]:((calm(X)|funny(X))))&
(?[X]:((creative(X)&happy(X))))&
(~curious(paul)) | ~quiet(mary) | [
"p5",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4383124326061898059705497
% SZS output start Proof for 4383124326061898059705497
6. ? [X0] : (happy(X0) <~> ~quiet(X0)) <=> ? [X0] : (~kind(X0) & ~humble(X0)) [input p5]
16. ! [X0] : ((~kind(X0) | ~old(X0)) => (~curious(X0) & kind(X0))) [input p15]
21. ~happy(mary) | quiet(mary) [input p20]
25. ~quiet(mary) [input hypothesis]
26. ? [X0] : (happy(X0) <~> ~quiet(X0)) <=> ? [X1] : (~kind(X1) & ~humble(X1)) [rectify 6]
44. ! [X0] : ((~curious(X0) & kind(X0)) | (kind(X0) & old(X0))) [ennf transformation 16]
55. (? [X0] : ((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ! [X1] : (kind(X1) | humble(X1))) & (? [X1] : (~kind(X1) & ~humble(X1)) | ! [X0] : ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) [nnf transformation 26]
56. (? [X0] : ((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ! [X1] : (kind(X1) | humble(X1))) & (? [X2] : (~kind(X2) & ~humble(X2)) | ! [X3] : ((happy(X3) | quiet(X3)) & (~quiet(X3) | ~happy(X3)))) [rectify 55]
57. ? [X0] : ((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) => ((quiet(sK2) | ~happy(sK2)) & (~quiet(sK2) | happy(sK2))) [choice axiom]
58. ? [X2] : (~kind(X2) & ~humble(X2)) => (~kind(sK3) & ~humble(sK3)) [choice axiom]
59. (((quiet(sK2) | ~happy(sK2)) & (~quiet(sK2) | happy(sK2))) | ! [X1] : (kind(X1) | humble(X1))) & ((~kind(sK3) & ~humble(sK3)) | ! [X3] : ((happy(X3) | quiet(X3)) & (~quiet(X3) | ~happy(X3)))) [skolemisation 56,58,57]
105. ~kind(sK3) | happy(X3) | quiet(X3) [cnf transformation 59]
134. kind(X0) | kind(X0) [cnf transformation 44]
140. ~happy(mary) | quiet(mary) [cnf transformation 21]
144. ~quiet(mary) [cnf transformation 25]
145. kind(X0) [duplicate literal removal 134]
214. 14 <=> ! [X3] : (happy(X3) | quiet(X3)) [avatar definition]
215. quiet(X3) | happy(X3) <- (14) [avatar component clause 214]
217. 15 <=> kind(sK3) [avatar definition]
219. ~kind(sK3) <- (~15) [avatar component clause 217]
220. 14 | ~15 [avatar split clause 105,217,214]
240. 20 <=> quiet(mary) [avatar definition]
242. ~quiet(mary) <- (~20) [avatar component clause 240]
322. 38 <=> happy(mary) [avatar definition]
324. ~happy(mary) <- (~38) [avatar component clause 322]
325. 20 | ~38 [avatar split clause 140,322,240]
327. ~20 [avatar split clause 144,240]
330. $false <- (~15) [subsumption resolution 219,145]
331. 15 [avatar contradiction clause 330]
339. happy(mary) <- (14, ~20) [resolution 215,242]
342. $false <- (14, ~20, ~38) [subsumption resolution 339,324]
343. ~14 | 20 | 38 [avatar contradiction clause 342]
344. $false [avatar sat refutation 220,325,327,331,343]
% SZS output end Proof for 4383124326061898059705497
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not patient or not creative then john is both brave and kind. Everyone who is brave is creative. If someone is both not wise and generous then someone is both funny and tall and vice versa. If susan is not curious or wise then alice is generous or happy and vice versa. Everyone who is both curious and not humble is not curious and vice versa. If someone is curious then someone is both not old and not brave. If alice is kind or not creative then john is both tall and rich and vice versa. If alice is both brave and kind then mary is either not wise or rich and vice versa. Everyone who is both happy and generous is not old and vice versa. If paul is either humble or happy then someone is both not humble and wise. If someone is not humble then someone is not rich and vice versa. If john is creative then someone is wise or strong and vice versa. Everyone who is not generous or not tall is rich or not brave and vice versa. Everyone who is not patient or not old is either wise or tall. Everyone who is not funny or funny is not funny or old and vice versa. Everyone who is both not wise and creative is either wise or kind and vice versa. Mary is either kind or not patient. Someone is either humble or not happy. Someone is both funny and calm. Fred is either wise or rich. Mary is not strong. Mary is both calm and curious. Someone is patient. Someone is brave. | John is not old. | contradiction | (((~patient(mary)|~creative(mary)))=>((brave(john)&kind(john))))&
(![X]:(brave(X)=>creative(X)))&
((?[X]:((~wise(X)&generous(X))))<=>(?[X]:((funny(X)&tall(X)))))&
(((~curious(susan)|wise(susan)))<=>((generous(alice)|happy(alice))))&
(![X]:((curious(X)&~humble(X))<=>~curious(X)))&
((?[X]:(curious(X)))=>(?[X]:((~old(X)&~brave(X)))))&
(((kind(alice)|~creative(alice)))<=>((tall(john)&rich(john))))&
(((brave(alice)&kind(alice)))<=>((~wise(mary)<~>rich(mary))))&
(![X]:((happy(X)&generous(X))<=>~old(X)))&
(((humble(paul)<~>happy(paul)))=>(?[X]:((~humble(X)&wise(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~rich(X))))&
((creative(john))<=>(?[X]:((wise(X)|strong(X)))))&
(![X]:((~generous(X)|~tall(X))<=>(rich(X)|~brave(X))))&
(![X]:((~patient(X)|~old(X))=>(wise(X)<~>tall(X))))&
(![X]:((~funny(X)|funny(X))<=>(~funny(X)|old(X))))&
(![X]:((~wise(X)&creative(X))<=>(wise(X)<~>kind(X))))&
((kind(mary)<~>~patient(mary)))&
(?[X]:((humble(X)<~>~happy(X))))&
(?[X]:((funny(X)&calm(X))))&
((wise(fred)<~>rich(fred)))&
(~strong(mary))&
((calm(mary)&curious(mary)))&
(?[X]:(patient(X)))&
(?[X]:(brave(X))) | ~old(john) | [
"p4",
"p6",
"p8",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6060203980516731509879982
% SZS output start Proof for 6060203980516731509879982
5. ! [X0] : ((~humble(X0) & curious(X0)) <=> ~curious(X0)) [input p4]
7. (~creative(alice) | kind(alice)) <=> (rich(john) & tall(john)) [input p6]
9. ! [X0] : ((generous(X0) & happy(X0)) <=> ~old(X0)) [input p8]
11. ? [X0] : ~humble(X0) <=> ? [X0] : ~rich(X0) [input p10]
13. ! [X0] : ((~tall(X0) | ~generous(X0)) <=> (~brave(X0) | rich(X0))) [input p12]
16. ! [X0] : ((creative(X0) & ~wise(X0)) <=> (wise(X0) <~> kind(X0))) [input p15]
25. ~old(john) [input hypothesis]
28. ? [X0] : ~humble(X0) <=> ? [X1] : ~rich(X1) [rectify 11]
43. ! [X0] : (((~humble(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | (humble(X0) | ~curious(X0)))) [nnf transformation 5]
44. ! [X0] : (((~humble(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | humble(X0) | ~curious(X0))) [flattening 43]
48. ((~creative(alice) | kind(alice)) | (~rich(john) | ~tall(john))) & ((rich(john) & tall(john)) | (creative(alice) & ~kind(alice))) [nnf transformation 7]
49. (~creative(alice) | kind(alice) | ~rich(john) | ~tall(john)) & ((rich(john) & tall(john)) | (creative(alice) & ~kind(alice))) [flattening 48]
52. ! [X0] : (((generous(X0) & happy(X0)) | old(X0)) & (~old(X0) | (~generous(X0) | ~happy(X0)))) [nnf transformation 9]
53. ! [X0] : (((generous(X0) & happy(X0)) | old(X0)) & (~old(X0) | ~generous(X0) | ~happy(X0))) [flattening 52]
57. (? [X0] : ~humble(X0) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : humble(X0)) [nnf transformation 28]
58. (? [X0] : ~humble(X0) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : humble(X3)) [rectify 57]
59. ? [X0] : ~humble(X0) => ~humble(sK4) [choice axiom]
60. ? [X2] : ~rich(X2) => ~rich(sK5) [choice axiom]
61. (~humble(sK4) | ! [X1] : rich(X1)) & (~rich(sK5) | ! [X3] : humble(X3)) [skolemisation 58,60,59]
66. ! [X0] : (((~tall(X0) | ~generous(X0)) | (brave(X0) & ~rich(X0))) & ((~brave(X0) | rich(X0)) | (tall(X0) & generous(X0)))) [nnf transformation 13]
67. ! [X0] : ((~tall(X0) | ~generous(X0) | (brave(X0) & ~rich(X0))) & (~brave(X0) | rich(X0) | (tall(X0) & generous(X0)))) [flattening 66]
71. ! [X0] : (((creative(X0) & ~wise(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | (~creative(X0) | wise(X0)))) [nnf transformation 16]
72. ! [X0] : (((creative(X0) & ~wise(X0)) | ((wise(X0) | ~kind(X0)) & (kind(X0) | ~wise(X0)))) & (((~kind(X0) | ~wise(X0)) & (kind(X0) | wise(X0))) | ~creative(X0) | wise(X0))) [flattening 71]
97. ~curious(X0) | humble(X0) | ~curious(X0) [cnf transformation 44]
98. curious(X0) | curious(X0) [cnf transformation 44]
102. tall(john) | ~kind(alice) [cnf transformation 49]
103. tall(john) | creative(alice) [cnf transformation 49]
115. old(X0) | generous(X0) [cnf transformation 53]
121. ~humble(sK4) | rich(X1) [cnf transformation 61]
127. ~tall(X0) | ~generous(X0) | ~rich(X0) [cnf transformation 67]
137. kind(X0) | wise(X0) | ~creative(X0) | wise(X0) [cnf transformation 72]
139. ~wise(X0) | kind(X0) | ~wise(X0) [cnf transformation 72]
154. ~old(john) [cnf transformation 25]
155. kind(X0) | wise(X0) | ~creative(X0) [duplicate literal removal 137]
156. ~wise(X0) | kind(X0) [duplicate literal removal 139]
159. ~curious(X0) | humble(X0) [duplicate literal removal 97]
160. curious(X0) [duplicate literal removal 98]
227. humble(X0) [subsumption resolution 159,160]
231. 15 <=> tall(john) [avatar definition]
232. tall(john) <- (15) [avatar component clause 231]
239. 17 <=> kind(alice) [avatar definition]
240. ~kind(alice) <- (~17) [avatar component clause 239]
243. 18 <=> creative(alice) [avatar definition]
244. creative(alice) <- (18) [avatar component clause 243]
249. 18 | 15 [avatar split clause 103,231,243]
250. ~17 | 15 [avatar split clause 102,231,239]
282. rich(X1) [subsumption resolution 121,227]
304. ~tall(X0) | ~generous(X0) [subsumption resolution 127,282]
305. ~creative(X0) | kind(X0) [subsumption resolution 155,156]
327. generous(john) [resolution 115,154]
334. ~generous(john) <- (15) [resolution 304,232]
335. $false <- (15) [subsumption resolution 334,327]
336. ~15 [avatar contradiction clause 335]
340. kind(alice) <- (18) [resolution 305,244]
341. $false <- (~17, 18) [subsumption resolution 340,240]
342. 17 | ~18 [avatar contradiction clause 341]
343. $false [avatar sat refutation 249,250,336,342]
% SZS output end Proof for 6060203980516731509879982
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both kind and rich then john is calm or kind.
Everyone who is old or kind is both old and creative and vice versa.
Everyone who is not generous is brave or not rich and vice versa.
Everyone who is either funny or not creative is either calm or wise and vice versa.
Everyone who is either quiet or not old is both not strong and not quiet.
Everyone who is happy is either happy or strong.
If someone is either creative or patient then someone is creative.
If someone is either not generous or not wise then someone is either humble or not happy and vice versa.
Everyone who is creative or not calm is both creative and generous.
If john is not funny or brave then someone is either kind or not curious and vice versa.
Everyone who is either not tall or not funny is both generous and quiet and vice versa.
If someone is not creative or not tall then susan is not brave and vice versa.
Everyone who is creative or kind is both patient and not creative and vice versa.
Everyone who is brave is not funny or not wise and vice versa.
Everyone who is either not rich or curious is not patient or generous and vice versa.
Everyone who is either not funny or curious is both not rich and strong.
Someone is quiet or old.
Paul is either brave or calm.
Paul is kind or humble.
Someone is not strong.
Someone is both calm and rich.
Mary is not rich.
Someone is both strong and quiet. | Susan is not rich. | entailment | (((kind(susan)&rich(susan)))=>((calm(john)|kind(john))))&
(![X]:((old(X)|kind(X))<=>(old(X)&creative(X))))&
(![X]:(~generous(X)<=>(brave(X)|~rich(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(calm(X)<~>wise(X))))&
(![X]:((quiet(X)<~>~old(X))=>(~strong(X)&~quiet(X))))&
(![X]:(happy(X)=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)<~>patient(X))))=>(?[X]:(creative(X))))&
((?[X]:((~generous(X)<~>~wise(X))))<=>(?[X]:((humble(X)<~>~happy(X)))))&
(![X]:((creative(X)|~calm(X))=>(creative(X)&generous(X))))&
(((~funny(john)|brave(john)))<=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((~tall(X)<~>~funny(X))<=>(generous(X)&quiet(X))))&
((?[X]:((~creative(X)|~tall(X))))<=>(~brave(susan)))&
(![X]:((creative(X)|kind(X))<=>(patient(X)&~creative(X))))&
(![X]:(brave(X)<=>(~funny(X)|~wise(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~patient(X)|generous(X))))&
(![X]:((~funny(X)<~>curious(X))=>(~rich(X)&strong(X))))&
(?[X]:((quiet(X)|old(X))))&
((brave(paul)<~>calm(paul)))&
((kind(paul)|humble(paul)))&
(?[X]:(~strong(X)))&
(?[X]:((calm(X)&rich(X))))&
(~rich(mary))&
(?[X]:((strong(X)&quiet(X)))) | ~rich(susan) | [
"p2",
"p11",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5627932440135911052846047
% SZS output start Proof for 5627932440135911052846047
3. ! [X0] : (~generous(X0) <=> (~rich(X0) | brave(X0))) [input p2]
12. ? [X0] : (~tall(X0) | ~creative(X0)) <=> ~brave(susan) [input p11]
13. ! [X0] : ((kind(X0) | creative(X0)) <=> (~creative(X0) & patient(X0))) [input p12]
14. ! [X0] : (brave(X0) <=> (~wise(X0) | ~funny(X0))) [input p13]
15. ! [X0] : ((~rich(X0) <~> curious(X0)) <=> (generous(X0) | ~patient(X0))) [input p14]
16. ! [X0] : ((~funny(X0) <~> curious(X0)) => (strong(X0) & ~rich(X0))) [input p15]
24. rich(susan) [input hypothesis]
33. ! [X0] : ((strong(X0) & ~rich(X0)) | (~funny(X0) <=> curious(X0))) [ennf transformation 16]
36. ! [X0] : ((~generous(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | generous(X0))) [nnf transformation 3]
37. ! [X0] : ((~generous(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | generous(X0))) [flattening 36]
57. (? [X0] : (~tall(X0) | ~creative(X0)) | brave(susan)) & (~brave(susan) | ! [X0] : (tall(X0) & creative(X0))) [nnf transformation 12]
58. (? [X0] : (~tall(X0) | ~creative(X0)) | brave(susan)) & (~brave(susan) | ! [X1] : (tall(X1) & creative(X1))) [rectify 57]
59. ? [X0] : (~tall(X0) | ~creative(X0)) => (~tall(sK4) | ~creative(sK4)) [choice axiom]
60. ((~tall(sK4) | ~creative(sK4)) | brave(susan)) & (~brave(susan) | ! [X1] : (tall(X1) & creative(X1))) [skolemisation 58,59]
61. ! [X0] : (((kind(X0) | creative(X0)) | (creative(X0) | ~patient(X0))) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [nnf transformation 13]
62. ! [X0] : ((kind(X0) | creative(X0) | creative(X0) | ~patient(X0)) & ((~creative(X0) & patient(X0)) | (~kind(X0) & ~creative(X0)))) [flattening 61]
63. ! [X0] : ((brave(X0) | (wise(X0) & funny(X0))) & ((~wise(X0) | ~funny(X0)) | ~brave(X0))) [nnf transformation 14]
64. ! [X0] : ((brave(X0) | (wise(X0) & funny(X0))) & (~wise(X0) | ~funny(X0) | ~brave(X0))) [flattening 63]
65. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (~generous(X0) & patient(X0))) & ((generous(X0) | ~patient(X0)) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [nnf transformation 15]
66. ! [X0] : ((((~curious(X0) | rich(X0)) & (curious(X0) | ~rich(X0))) | (~generous(X0) & patient(X0))) & (generous(X0) | ~patient(X0) | ((~rich(X0) | ~curious(X0)) & (curious(X0) | rich(X0))))) [flattening 65]
67. ! [X0] : ((strong(X0) & ~rich(X0)) | ((~funny(X0) | ~curious(X0)) & (curious(X0) | funny(X0)))) [nnf transformation 33]
83. ~rich(X0) | brave(X0) | generous(X0) [cnf transformation 37]
85. ~generous(X0) | rich(X0) [cnf transformation 37]
126. ~brave(susan) | creative(X1) [cnf transformation 60]
131. ~creative(X0) | ~creative(X0) [cnf transformation 62]
135. funny(X0) | brave(X0) [cnf transformation 64]
140. curious(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 66]
144. ~curious(X0) | ~funny(X0) | ~rich(X0) [cnf transformation 67]
157. rich(susan) [cnf transformation 24]
158. ~creative(X0) [duplicate literal removal 131]
167. 2 <=> rich(susan) [avatar definition]
168. rich(susan) <- (2) [avatar component clause 167]
256. 22 <=> brave(susan) [avatar definition]
257. ~brave(susan) <- (~22) [avatar component clause 256]
273. 26 <=> ! [X1] : creative(X1) [avatar definition]
274. creative(X1) <- (26) [avatar component clause 273]
275. 26 | ~22 [avatar split clause 126,256,273]
279. ~generous(X0) | curious(X0) [subsumption resolution 140,85]
301. 2 [avatar split clause 157,167]
328. brave(susan) | generous(susan) <- (2) [resolution 83,168]
338. generous(susan) <- (2, ~22) [subsumption resolution 328,257]
343. curious(susan) <- (2, ~22) [resolution 338,279]
364. ~funny(susan) | ~rich(susan) <- (2, ~22) [resolution 144,343]
366. ~funny(susan) <- (2, ~22) [subsumption resolution 364,168]
464. brave(susan) <- (2, ~22) [resolution 366,135]
465. $false <- (2, ~22) [subsumption resolution 464,257]
466. ~2 | 22 [avatar contradiction clause 465]
483. $false <- (26) [subsumption resolution 274,158]
484. ~26 [avatar contradiction clause 483]
485. $false [avatar sat refutation 275,301,466,484]
% SZS output end Proof for 5627932440135911052846047
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave then someone is both strong and not curious and vice versa. If paul is funny then lucy is both strong and quiet. Everyone who is not strong is happy or not curious and vice versa. Everyone who is funny is wise or not rich and vice versa. If someone is either not happy or not rich then paul is both not rich and strong. Everyone who is not creative or not old is either not tall or not patient. Everyone who is either strong or calm is both curious and not happy. Everyone who is not strong or happy is old or not generous. Everyone who is not quiet is not rich or not brave. Everyone who is either rich or creative is either not generous or funny and vice versa. Everyone who is both not patient and not quiet is either not tall or not creative. Everyone who is both not generous and creative is either not creative or not tall. Everyone who is not quiet is quiet. Everyone who is either not humble or creative is either not tall or not old and vice versa. If someone is wise or not wise then someone is tall or generous. Everyone who is not happy is both not strong and not tall. Lucy is not happy or not generous. Someone is not brave or brave. Someone is not creative. Someone is not happy or not quiet. Someone is humble or not happy. Someone is not wise or not patient. Mary is either not creative or old. | Mary is quiet. | entailment | ((?[X]:(~brave(X)))<=>(?[X]:((strong(X)&~curious(X)))))&
((funny(paul))=>((strong(lucy)&quiet(lucy))))&
(![X]:(~strong(X)<=>(happy(X)|~curious(X))))&
(![X]:(funny(X)<=>(wise(X)|~rich(X))))&
((?[X]:((~happy(X)<~>~rich(X))))=>((~rich(paul)&strong(paul))))&
(![X]:((~creative(X)|~old(X))=>(~tall(X)<~>~patient(X))))&
(![X]:((strong(X)<~>calm(X))=>(curious(X)&~happy(X))))&
(![X]:((~strong(X)|happy(X))=>(old(X)|~generous(X))))&
(![X]:(~quiet(X)=>(~rich(X)|~brave(X))))&
(![X]:((rich(X)<~>creative(X))<=>(~generous(X)<~>funny(X))))&
(![X]:((~patient(X)&~quiet(X))=>(~tall(X)<~>~creative(X))))&
(![X]:((~generous(X)&creative(X))=>(~creative(X)<~>~tall(X))))&
(![X]:(~quiet(X)=>quiet(X)))&
(![X]:((~humble(X)<~>creative(X))<=>(~tall(X)<~>~old(X))))&
((?[X]:((wise(X)|~wise(X))))=>(?[X]:((tall(X)|generous(X)))))&
(![X]:(~happy(X)=>(~strong(X)&~tall(X))))&
((~happy(lucy)|~generous(lucy)))&
(?[X]:((~brave(X)|brave(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~happy(X)|~quiet(X))))&
(?[X]:((humble(X)|~happy(X))))&
(?[X]:((~wise(X)|~patient(X))))&
((~creative(mary)<~>old(mary))) | quiet(mary) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7058946304735707355868638
% SZS output start Proof for 7058946304735707355868638
13. ! [X0] : (~quiet(X0) => quiet(X0)) [input p12]
24. ~quiet(mary) [input hypothesis]
39. ! [X0] : (quiet(X0) | quiet(X0)) [ennf transformation 13]
110. quiet(X0) | quiet(X0) [cnf transformation 39]
131. ~quiet(mary) [cnf transformation 24]
132. quiet(X0) [duplicate literal removal 110]
248. $false [subsumption resolution 131,132]
% SZS output end Proof for 7058946304735707355868638
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not old and patient then someone is either not generous or happy.
Everyone who is not happy or not humble is happy and vice versa.
Everyone who is creative or not quiet is both not brave and brave and vice versa.
If someone is both patient and humble then someone is both quiet and not calm.
If someone is both old and patient then susan is both creative and old.
Everyone who is not old is both creative and not curious and vice versa.
Everyone who is tall is wise and vice versa.
Everyone who is both humble and calm is calm and vice versa.
Everyone who is both strong and not old is either patient or wise and vice versa.
If someone is either rich or curious then someone is patient or tall.
Everyone who is both quiet and strong is either not happy or quiet and vice versa.
Everyone who is rich is both rich and not patient.
Everyone who is either not generous or not strong is curious or quiet.
If someone is tall then someone is humble.
Someone is not calm or not creative.
Someone is not rich or creative.
Lucy is wise or not creative.
Lucy is either tall or not brave.
Someone is not generous or not kind.
Paul is both not generous and not calm.
Someone is both not generous and not rich. | Lucy is not wise. | entailment | (((~old(alice)&patient(alice)))=>(?[X]:((~generous(X)<~>happy(X)))))&
(![X]:((~happy(X)|~humble(X))<=>happy(X)))&
(![X]:((creative(X)|~quiet(X))<=>(~brave(X)&brave(X))))&
((?[X]:((patient(X)&humble(X))))=>(?[X]:((quiet(X)&~calm(X)))))&
((?[X]:((old(X)&patient(X))))=>((creative(susan)&old(susan))))&
(![X]:(~old(X)<=>(creative(X)&~curious(X))))&
(![X]:(tall(X)<=>wise(X)))&
(![X]:((humble(X)&calm(X))<=>calm(X)))&
(![X]:((strong(X)&~old(X))<=>(patient(X)<~>wise(X))))&
((?[X]:((rich(X)<~>curious(X))))=>(?[X]:((patient(X)|tall(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)<~>quiet(X))))&
(![X]:(rich(X)=>(rich(X)&~patient(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(curious(X)|quiet(X))))&
((?[X]:(tall(X)))=>(?[X]:(humble(X))))&
(?[X]:((~calm(X)|~creative(X))))&
(?[X]:((~rich(X)|creative(X))))&
((wise(lucy)|~creative(lucy)))&
((tall(lucy)<~>~brave(lucy)))&
(?[X]:((~generous(X)|~kind(X))))&
((~generous(paul)&~calm(paul)))&
(?[X]:((~generous(X)&~rich(X)))) | ~wise(lucy) | [
"p1",
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4691419870534833328608475
% SZS output start Proof for 4691419870534833328608475
2. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> happy(X0)) [input p1]
7. ! [X0] : (tall(X0) <=> wise(X0)) [input p6]
14. ? [X0] : tall(X0) => ? [X0] : humble(X0) [input p13]
22. wise(lucy) [input hypothesis]
25. ? [X0] : tall(X0) => ? [X1] : humble(X1) [rectify 14]
35. ? [X1] : humble(X1) | ! [X0] : ~tall(X0) [ennf transformation 25]
39. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (humble(X0) & happy(X0)))) [nnf transformation 2]
40. ! [X0] : ((~humble(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (humble(X0) & happy(X0)))) [flattening 39]
48. ! [X0] : ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0))) [nnf transformation 7]
60. ? [X0] : humble(X0) | ! [X1] : ~tall(X1) [rectify 35]
61. ? [X0] : humble(X0) => humble(sK3) [choice axiom]
62. humble(sK3) | ! [X1] : ~tall(X1) [skolemisation 60,61]
72. happy(X0) | happy(X0) [cnf transformation 40]
74. ~humble(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 40]
88. ~wise(X0) | tall(X0) [cnf transformation 48]
110. humble(sK3) | ~tall(X1) [cnf transformation 62]
120. wise(lucy) [cnf transformation 22]
123. happy(X0) [duplicate literal removal 72]
124. ~humble(X0) | ~happy(X0) [duplicate literal removal 74]
185. 13 <=> ! [X1] : ~tall(X1) [avatar definition]
186. ~tall(X1) <- (13) [avatar component clause 185]
188. 14 <=> humble(sK3) [avatar definition]
190. humble(sK3) <- (14) [avatar component clause 188]
191. 13 | 14 [avatar split clause 110,188,185]
209. tall(lucy) [resolution 88,120]
212. $false <- (13) [subsumption resolution 209,186]
213. ~13 [avatar contradiction clause 212]
218. ~happy(sK3) <- (14) [resolution 124,190]
219. $false <- (14) [subsumption resolution 218,123]
220. ~14 [avatar contradiction clause 219]
221. $false [avatar sat refutation 191,213,220]
% SZS output end Proof for 4691419870534833328608475
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is either not kind or not humble and vice versa.
If someone is brave then paul is either not funny or not calm and vice versa.
If someone is not tall then someone is funny or brave.
Everyone who is patient or not quiet is both not brave and curious.
If susan is both not curious and calm then someone is both not patient and not rich and vice versa.
If someone is both creative and curious then someone is patient or not funny and vice versa.
If someone is humble or not quiet then someone is both rich and old and vice versa.
If susan is either not funny or not generous then fred is both not calm and not happy.
Everyone who is creative or not strong is not creative.
Everyone who is creative is tall.
Everyone who is both patient and not kind is kind or not generous and vice versa.
Everyone who is both not kind and not creative is either curious or not humble and vice versa.
Everyone who is both brave and not rich is either curious or not wise and vice versa.
Everyone who is both wise and not rich is both not happy and not kind.
Everyone who is either curious or kind is not old and vice versa.
Someone is either quiet or strong.
Someone is not brave or creative.
Someone is not rich.
Someone is both strong and not rich.
Someone is not creative. | Susan is rich. | contradiction | (![X]:(~funny(X)<=>(~kind(X)<~>~humble(X))))&
((?[X]:(brave(X)))<=>((~funny(paul)<~>~calm(paul))))&
((?[X]:(~tall(X)))=>(?[X]:((funny(X)|brave(X)))))&
(![X]:((patient(X)|~quiet(X))=>(~brave(X)&curious(X))))&
(((~curious(susan)&calm(susan)))<=>(?[X]:((~patient(X)&~rich(X)))))&
((?[X]:((creative(X)&curious(X))))<=>(?[X]:((patient(X)|~funny(X)))))&
((?[X]:((humble(X)|~quiet(X))))<=>(?[X]:((rich(X)&old(X)))))&
(((~funny(susan)<~>~generous(susan)))=>((~calm(fred)&~happy(fred))))&
(![X]:((creative(X)|~strong(X))=>~creative(X)))&
(![X]:(creative(X)=>tall(X)))&
(![X]:((patient(X)&~kind(X))<=>(kind(X)|~generous(X))))&
(![X]:((~kind(X)&~creative(X))<=>(curious(X)<~>~humble(X))))&
(![X]:((brave(X)&~rich(X))<=>(curious(X)<~>~wise(X))))&
(![X]:((wise(X)&~rich(X))=>(~happy(X)&~kind(X))))&
(![X]:((curious(X)<~>kind(X))<=>~old(X)))&
(?[X]:((quiet(X)<~>strong(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:(~rich(X)))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:(~creative(X))) | rich(susan) | [
"p0",
"p3",
"p4",
"p5",
"p6",
"p8",
"p10",
"p11",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1746988826035307330182551
% SZS output start Proof for 1746988826035307330182551
1. ! [X0] : (~funny(X0) <=> (~kind(X0) <~> ~humble(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | patient(X0)) => (curious(X0) & ~brave(X0))) [input p3]
5. (calm(susan) & ~curious(susan)) <=> ? [X0] : (~rich(X0) & ~patient(X0)) [input p4]
6. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X0] : (~funny(X0) | patient(X0)) [input p5]
7. ? [X0] : (~quiet(X0) | humble(X0)) <=> ? [X0] : (old(X0) & rich(X0)) [input p6]
9. ! [X0] : ((~strong(X0) | creative(X0)) => ~creative(X0)) [input p8]
11. ! [X0] : ((~kind(X0) & patient(X0)) <=> (~generous(X0) | kind(X0))) [input p10]
12. ! [X0] : ((~creative(X0) & ~kind(X0)) <=> (curious(X0) <~> ~humble(X0))) [input p11]
15. ! [X0] : ((curious(X0) <~> kind(X0)) <=> ~old(X0)) [input p14]
18. ? [X0] : ~rich(X0) [input p17]
21. rich(susan) [input hypothesis]
23. ? [X0] : (curious(X0) & creative(X0)) <=> ? [X1] : (~funny(X1) | patient(X1)) [rectify 6]
24. ? [X0] : (~quiet(X0) | humble(X0)) <=> ? [X1] : (old(X1) & rich(X1)) [rectify 7]
29. ! [X0] : ((curious(X0) & ~brave(X0)) | (quiet(X0) & ~patient(X0))) [ennf transformation 4]
31. ! [X0] : (~creative(X0) | (strong(X0) & ~creative(X0))) [ennf transformation 9]
34. ! [X0] : ((~funny(X0) | ((~kind(X0) | humble(X0)) & (~humble(X0) | kind(X0)))) & (((humble(X0) | kind(X0)) & (~humble(X0) | ~kind(X0))) | funny(X0))) [nnf transformation 1]
39. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X0] : (~rich(X0) & ~patient(X0)) | (~calm(susan) | curious(susan))) [nnf transformation 5]
40. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X0] : (~rich(X0) & ~patient(X0)) | ~calm(susan) | curious(susan)) [flattening 39]
41. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & (? [X1] : (~rich(X1) & ~patient(X1)) | ~calm(susan) | curious(susan)) [rectify 40]
42. ? [X1] : (~rich(X1) & ~patient(X1)) => (~rich(sK1) & ~patient(sK1)) [choice axiom]
43. ((calm(susan) & ~curious(susan)) | ! [X0] : (rich(X0) | patient(X0))) & ((~rich(sK1) & ~patient(sK1)) | ~calm(susan) | curious(susan)) [skolemisation 41,42]
44. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X1] : (~funny(X1) | patient(X1)) | ! [X0] : (~curious(X0) | ~creative(X0))) [nnf transformation 23]
45. (? [X0] : (curious(X0) & creative(X0)) | ! [X1] : (funny(X1) & ~patient(X1))) & (? [X2] : (~funny(X2) | patient(X2)) | ! [X3] : (~curious(X3) | ~creative(X3))) [rectify 44]
46. ? [X0] : (curious(X0) & creative(X0)) => (curious(sK2) & creative(sK2)) [choice axiom]
47. ? [X2] : (~funny(X2) | patient(X2)) => (~funny(sK3) | patient(sK3)) [choice axiom]
48. ((curious(sK2) & creative(sK2)) | ! [X1] : (funny(X1) & ~patient(X1))) & ((~funny(sK3) | patient(sK3)) | ! [X3] : (~curious(X3) | ~creative(X3))) [skolemisation 45,47,46]
49. (? [X0] : (~quiet(X0) | humble(X0)) | ! [X1] : (~old(X1) | ~rich(X1))) & (? [X1] : (old(X1) & rich(X1)) | ! [X0] : (quiet(X0) & ~humble(X0))) [nnf transformation 24]
50. (? [X0] : (~quiet(X0) | humble(X0)) | ! [X1] : (~old(X1) | ~rich(X1))) & (? [X2] : (old(X2) & rich(X2)) | ! [X3] : (quiet(X3) & ~humble(X3))) [rectify 49]
51. ? [X0] : (~quiet(X0) | humble(X0)) => (~quiet(sK4) | humble(sK4)) [choice axiom]
52. ? [X2] : (old(X2) & rich(X2)) => (old(sK5) & rich(sK5)) [choice axiom]
53. ((~quiet(sK4) | humble(sK4)) | ! [X1] : (~old(X1) | ~rich(X1))) & ((old(sK5) & rich(sK5)) | ! [X3] : (quiet(X3) & ~humble(X3))) [skolemisation 50,52,51]
55. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & ((~generous(X0) | kind(X0)) | (kind(X0) | ~patient(X0)))) [nnf transformation 11]
56. ! [X0] : (((~kind(X0) & patient(X0)) | (generous(X0) & ~kind(X0))) & (~generous(X0) | kind(X0) | kind(X0) | ~patient(X0))) [flattening 55]
57. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | (creative(X0) | kind(X0)))) [nnf transformation 12]
58. ! [X0] : (((~creative(X0) & ~kind(X0)) | ((curious(X0) | humble(X0)) & (~humble(X0) | ~curious(X0)))) & (((humble(X0) | ~curious(X0)) & (~humble(X0) | curious(X0))) | creative(X0) | kind(X0))) [flattening 57]
61. ! [X0] : ((((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | old(X0)) & (~old(X0) | ((curious(X0) | ~kind(X0)) & (kind(X0) | ~curious(X0))))) [nnf transformation 15]
67. ? [X0] : ~rich(X0) => ~rich(sK8) [choice axiom]
68. ~rich(sK8) [skolemisation 18,67]
75. ~humble(X0) | ~funny(X0) | kind(X0) [cnf transformation 34]
84. curious(X0) | quiet(X0) [cnf transformation 29]
87. ~curious(susan) | rich(X0) | patient(X0) [cnf transformation 43]
90. creative(sK2) | ~patient(X1) [cnf transformation 48]
91. creative(sK2) | funny(X1) [cnf transformation 48]
98. ~quiet(sK4) | humble(sK4) | ~old(X1) | ~rich(X1) [cnf transformation 53]
101. ~creative(X0) | ~creative(X0) [cnf transformation 31]
106. ~kind(X0) | ~kind(X0) [cnf transformation 56]
109. humble(X0) | ~curious(X0) | creative(X0) | kind(X0) [cnf transformation 58]
123. kind(X0) | curious(X0) | old(X0) [cnf transformation 61]
128. ~rich(sK8) [cnf transformation 68]
132. rich(susan) [cnf transformation 21]
134. ~kind(X0) [duplicate literal removal 106]
135. ~creative(X0) [duplicate literal removal 101]
156. 5 <=> ! [X0] : (rich(X0) | patient(X0)) [avatar definition]
157. rich(X0) | patient(X0) <- (5) [avatar component clause 156]
164. 7 <=> curious(susan) [avatar definition]
166. ~curious(susan) <- (~7) [avatar component clause 164]
167. 5 | ~7 [avatar split clause 87,164,156]
179. 10 <=> ! [X1] : funny(X1) [avatar definition]
180. funny(X1) <- (10) [avatar component clause 179]
187. 12 <=> ! [X1] : ~patient(X1) [avatar definition]
188. ~patient(X1) <- (12) [avatar component clause 187]
191. 13 <=> creative(sK2) [avatar definition]
193. creative(sK2) <- (13) [avatar component clause 191]
194. 10 | 13 [avatar split clause 91,191,179]
195. 12 | 13 [avatar split clause 90,191,187]
209. 17 <=> ! [X1] : (~old(X1) | ~rich(X1)) [avatar definition]
210. ~old(X1) | ~rich(X1) <- (17) [avatar component clause 209]
212. 18 <=> humble(sK4) [avatar definition]
214. humble(sK4) <- (18) [avatar component clause 212]
216. 19 <=> quiet(sK4) [avatar definition]
218. ~quiet(sK4) <- (~19) [avatar component clause 216]
219. 17 | 18 | ~19 [avatar split clause 98,216,212,209]
253. humble(X0) | ~curious(X0) | kind(X0) [subsumption resolution 109,135]
254. ~curious(X0) | humble(X0) [subsumption resolution 253,134]
257. old(X0) | curious(X0) [subsumption resolution 123,134]
272. rich(X0) <- (5, 12) [subsumption resolution 157,188]
276. $false <- (13) [subsumption resolution 193,135]
277. ~13 [avatar contradiction clause 276]
278. $false <- (5, 12) [resolution 272,128]
281. ~5 | ~12 [avatar contradiction clause 278]
286. quiet(X0) | humble(X0) [resolution 254,84]
290. ~rich(X0) | curious(X0) <- (17) [resolution 257,210]
292. curious(susan) <- (17) [resolution 290,132]
293. $false <- (~7, 17) [subsumption resolution 292,166]
294. 7 | ~17 [avatar contradiction clause 293]
309. humble(sK4) <- (~19) [resolution 286,218]
312. 18 | 19 [avatar split clause 309,216,212]
313. ~funny(sK4) | kind(sK4) <- (18) [resolution 214,75]
316. kind(sK4) <- (10, 18) [subsumption resolution 313,180]
317. $false <- (10, 18) [subsumption resolution 316,134]
318. ~10 | ~18 [avatar contradiction clause 317]
319. $false [avatar sat refutation 167,194,195,219,277,281,294,312,318]
% SZS output end Proof for 1746988826035307330182551
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and calm is either not rich or brave and vice versa.
Everyone who is not curious or not humble is either not creative or not calm and vice versa.
If someone is not old then susan is not calm and vice versa.
Everyone who is strong or not creative is not curious.
Everyone who is either not rich or brave is humble or old and vice versa.
Everyone who is both not rich and not kind is generous or not funny and vice versa.
If someone is either not creative or happy then mary is both not tall and not generous and vice versa.
If someone is brave then fred is both kind and not rich and vice versa.
Everyone who is both not funny and not brave is not old and vice versa.
Everyone who is either not creative or old is either humble or generous.
If paul is either not funny or not calm then susan is both not quiet and not creative and vice versa.
Everyone who is not strong is brave.
Everyone who is either happy or patient is either kind or strong.
If lucy is both old and tall then lucy is humble.
Everyone who is both curious and patient is either not humble or not happy and vice versa.
Fred is humble or not quiet.
Fred is creative or not curious.
Lucy is either brave or not patient.
Someone is either not rich or not happy.
Someone is funny or tall. | Paul is not funny. | contradiction | (![X]:((generous(X)&calm(X))<=>(~rich(X)<~>brave(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~creative(X)<~>~calm(X))))&
((?[X]:(~old(X)))<=>(~calm(susan)))&
(![X]:((strong(X)|~creative(X))=>~curious(X)))&
(![X]:((~rich(X)<~>brave(X))<=>(humble(X)|old(X))))&
(![X]:((~rich(X)&~kind(X))<=>(generous(X)|~funny(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>((~tall(mary)&~generous(mary))))&
((?[X]:(brave(X)))<=>((kind(fred)&~rich(fred))))&
(![X]:((~funny(X)&~brave(X))<=>~old(X)))&
(![X]:((~creative(X)<~>old(X))=>(humble(X)<~>generous(X))))&
(((~funny(paul)<~>~calm(paul)))<=>((~quiet(susan)&~creative(susan))))&
(![X]:(~strong(X)=>brave(X)))&
(![X]:((happy(X)<~>patient(X))=>(kind(X)<~>strong(X))))&
(((old(lucy)&tall(lucy)))=>(humble(lucy)))&
(![X]:((curious(X)&patient(X))<=>(~humble(X)<~>~happy(X))))&
((humble(fred)|~quiet(fred)))&
((creative(fred)|~curious(fred)))&
((brave(lucy)<~>~patient(lucy)))&
(?[X]:((~rich(X)<~>~happy(X))))&
(?[X]:((funny(X)|tall(X)))) | ~funny(paul) | [
"p0",
"p1",
"p2",
"p3",
"p4",
"p5",
"p7",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2597314663851810193532504
% SZS output start Proof for 2597314663851810193532504
1. ! [X0] : ((calm(X0) & generous(X0)) <=> (~rich(X0) <~> brave(X0))) [input p0]
2. ! [X0] : ((~humble(X0) | ~curious(X0)) <=> (~creative(X0) <~> ~calm(X0))) [input p1]
3. ? [X0] : ~old(X0) <=> ~calm(susan) [input p2]
4. ! [X0] : ((~creative(X0) | strong(X0)) => ~curious(X0)) [input p3]
5. ! [X0] : ((~rich(X0) <~> brave(X0)) <=> (old(X0) | humble(X0))) [input p4]
6. ! [X0] : ((~kind(X0) & ~rich(X0)) <=> (~funny(X0) | generous(X0))) [input p5]
8. ? [X0] : brave(X0) <=> (~rich(fred) & kind(fred)) [input p7]
9. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> ~old(X0)) [input p8]
10. ! [X0] : ((~creative(X0) <~> old(X0)) => (humble(X0) <~> generous(X0))) [input p9]
12. ! [X0] : (~strong(X0) => brave(X0)) [input p11]
21. ~funny(paul) [input hypothesis]
22. ! [X0] : (~curious(X0) | (creative(X0) & ~strong(X0))) [ennf transformation 4]
23. ! [X0] : ((humble(X0) <~> generous(X0)) | (~creative(X0) <=> old(X0))) [ennf transformation 10]
24. ! [X0] : (brave(X0) | strong(X0)) [ennf transformation 12]
28. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~calm(X0) | ~generous(X0)))) [nnf transformation 1]
29. ! [X0] : (((calm(X0) & generous(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0)))) & (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ~calm(X0) | ~generous(X0))) [flattening 28]
30. ! [X0] : (((~humble(X0) | ~curious(X0)) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [nnf transformation 2]
31. ! [X0] : ((~humble(X0) | ~curious(X0) | ((~creative(X0) | calm(X0)) & (~calm(X0) | creative(X0)))) & (((calm(X0) | creative(X0)) & (~calm(X0) | ~creative(X0))) | (humble(X0) & curious(X0)))) [flattening 30]
32. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X0] : old(X0)) [nnf transformation 3]
33. (? [X0] : ~old(X0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [rectify 32]
34. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
35. (~old(sK0) | calm(susan)) & (~calm(susan) | ! [X1] : old(X1)) [skolemisation 33,34]
36. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & ((old(X0) | humble(X0)) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [nnf transformation 5]
37. ! [X0] : ((((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | (~old(X0) & ~humble(X0))) & (old(X0) | humble(X0) | ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))))) [flattening 36]
38. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & ((~funny(X0) | generous(X0)) | (kind(X0) | rich(X0)))) [nnf transformation 6]
39. ! [X0] : (((~kind(X0) & ~rich(X0)) | (funny(X0) & ~generous(X0))) & (~funny(X0) | generous(X0) | kind(X0) | rich(X0))) [flattening 38]
45. (? [X0] : brave(X0) | (rich(fred) | ~kind(fred))) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [nnf transformation 8]
46. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X0] : ~brave(X0)) [flattening 45]
47. (? [X0] : brave(X0) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [rectify 46]
48. ? [X0] : brave(X0) => brave(sK2) [choice axiom]
49. (brave(sK2) | rich(fred) | ~kind(fred)) & ((~rich(fred) & kind(fred)) | ! [X1] : ~brave(X1)) [skolemisation 47,48]
50. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | (brave(X0) | funny(X0)))) [nnf transformation 9]
51. ! [X0] : (((~brave(X0) & ~funny(X0)) | old(X0)) & (~old(X0) | brave(X0) | funny(X0))) [flattening 50]
52. ! [X0] : (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0)))) [nnf transformation 23]
66. brave(X0) | generous(X0) | rich(X0) [cnf transformation 29]
67. ~brave(X0) | ~rich(X0) | generous(X0) [cnf transformation 29]
68. brave(X0) | calm(X0) | rich(X0) [cnf transformation 29]
70. ~creative(X0) | ~calm(X0) | curious(X0) [cnf transformation 31]
76. ~calm(susan) | old(X1) [cnf transformation 35]
77. ~old(sK0) | calm(susan) [cnf transformation 35]
78. ~strong(X0) | ~curious(X0) [cnf transformation 22]
80. old(X0) | humble(X0) | brave(X0) | rich(X0) [cnf transformation 37]
85. ~old(X0) | rich(X0) | ~brave(X0) [cnf transformation 37]
87. ~rich(X0) | ~generous(X0) [cnf transformation 39]
88. ~rich(X0) | funny(X0) [cnf transformation 39]
97. kind(fred) | ~brave(X1) [cnf transformation 49]
98. ~rich(fred) | ~brave(X1) [cnf transformation 49]
99. brave(sK2) | rich(fred) | ~kind(fred) [cnf transformation 49]
100. ~old(X0) | brave(X0) | funny(X0) [cnf transformation 51]
101. ~funny(X0) | old(X0) [cnf transformation 51]
102. ~brave(X0) | old(X0) [cnf transformation 51]
105. ~humble(X0) | ~generous(X0) | old(X0) | creative(X0) [cnf transformation 52]
113. strong(X0) | brave(X0) [cnf transformation 24]
132. ~funny(paul) [cnf transformation 21]
134. 1 <=> calm(susan) [avatar definition]
138. 2 <=> old(sK0) [avatar definition]
140. ~old(sK0) <- (~2) [avatar component clause 138]
141. 1 | ~2 [avatar split clause 77,138,134]
143. 3 <=> ! [X1] : old(X1) [avatar definition]
144. old(X1) <- (3) [avatar component clause 143]
145. 3 | ~1 [avatar split clause 76,134,143]
175. 10 <=> kind(fred) [avatar definition]
179. 11 <=> rich(fred) [avatar definition]
183. 12 <=> brave(sK2) [avatar definition]
185. brave(sK2) <- (12) [avatar component clause 183]
186. ~10 | 11 | 12 [avatar split clause 99,183,179,175]
188. 13 <=> ! [X1] : ~brave(X1) [avatar definition]
189. ~brave(X1) <- (13) [avatar component clause 188]
190. 13 | ~11 [avatar split clause 98,179,188]
191. 13 | 10 [avatar split clause 97,175,188]
201. 16 <=> funny(paul) [avatar definition]
202. ~funny(paul) <- (~16) [avatar component clause 201]
265. ~16 [avatar split clause 132,201]
273. old(sK2) <- (12) [resolution 102,185]
274. ~curious(X0) | brave(X0) [resolution 113,78]
288. ~rich(sK2) | generous(sK2) <- (12) [resolution 67,185]
292. ~rich(sK2) <- (12) [subsumption resolution 288,87]
343. rich(sK2) | ~brave(sK2) <- (12) [resolution 85,273]
350. ~brave(sK2) <- (12) [subsumption resolution 343,292]
351. $false <- (12) [subsumption resolution 350,185]
352. ~12 [avatar contradiction clause 351]
367. rich(X0) | calm(X0) <- (13) [resolution 189,68]
368. rich(X1) | generous(X1) <- (13) [resolution 189,66]
430. humble(sK0) | brave(sK0) | rich(sK0) <- (~2) [resolution 80,140]
437. humble(sK0) | rich(sK0) <- (~2, 13) [subsumption resolution 430,189]
439. 40 <=> rich(sK0) [avatar definition]
440. ~rich(sK0) <- (~40) [avatar component clause 439]
441. rich(sK0) <- (40) [avatar component clause 439]
443. 41 <=> humble(sK0) [avatar definition]
445. humble(sK0) <- (41) [avatar component clause 443]
446. 40 | 41 | 2 | ~13 [avatar split clause 437,188,138,443,439]
450. funny(sK0) <- (40) [resolution 441,88]
454. 42 <=> generous(sK0) [avatar definition]
458. 43 <=> calm(sK0) [avatar definition]
459. calm(sK0) <- (43) [avatar component clause 458]
465. old(sK0) <- (40) [resolution 450,101]
466. $false <- (~2, 40) [subsumption resolution 465,140]
467. 2 | ~40 [avatar contradiction clause 466]
491. 46 <=> curious(sK0) [avatar definition]
493. curious(sK0) <- (46) [avatar component clause 491]
583. calm(sK0) <- (13, ~40) [resolution 367,440]
586. 43 | ~13 | 40 [avatar split clause 583,439,188,458]
593. brave(X2) | funny(X2) <- (3) [resolution 144,100]
597. funny(X2) <- (3, 13) [subsumption resolution 593,189]
600. ~generous(sK0) | old(sK0) | creative(sK0) <- (41) [resolution 445,105]
606. $false <- (3, 13, ~16) [resolution 597,202]
609. ~3 | ~13 | 16 [avatar contradiction clause 606]
617. generous(sK0) <- (13, ~40) [resolution 368,440]
624. 42 | ~13 | 40 [avatar split clause 617,439,188,454]
625. ~generous(sK0) | creative(sK0) <- (~2, 41) [subsumption resolution 600,140]
627. 58 <=> creative(sK0) [avatar definition]
629. creative(sK0) <- (58) [avatar component clause 627]
630. 58 | ~42 | 2 | ~41 [avatar split clause 625,443,138,454,627]
680. ~calm(sK0) | curious(sK0) <- (58) [resolution 629,70]
681. curious(sK0) <- (43, 58) [subsumption resolution 680,459]
682. 46 | ~43 | ~58 [avatar split clause 681,627,458,491]
683. brave(sK0) <- (46) [resolution 493,274]
685. $false <- (13, 46) [subsumption resolution 683,189]
686. ~13 | ~46 [avatar contradiction clause 685]
687. $false [avatar sat refutation 141,145,186,190,191,265,352,446,467,586,609,624,630,682,686]
% SZS output end Proof for 2597314663851810193532504
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If mary is both funny and humble then someone is either humble or strong.
If someone is patient then mary is not strong or not creative.
If someone is either humble or not wise then susan is both not brave and happy and vice versa.
If fred is happy or not tall then someone is both tall and creative and vice versa.
If lucy is both not calm and not creative then paul is not curious or curious and vice versa.
Everyone who is not funny is not rich or happy and vice versa.
Everyone who is either not wise or not calm is both patient and rich.
If someone is either not rich or not funny then someone is rich or strong.
Everyone who is both not calm and curious is not rich or not happy and vice versa.
Everyone who is either wise or humble is not wise and vice versa.
If someone is both not rich and calm then susan is both generous and not old and vice versa.
If someone is both not curious and creative then someone is both not quiet and not strong and vice versa.
If john is both not funny and not wise then paul is both generous and not tall and vice versa.
Everyone who is kind or funny is both not kind and quiet.
Everyone who is both not generous and creative is both not funny and not creative and vice versa.
Everyone who is not wise or not happy is not patient or tall.
Alice is either not patient or not quiet.
Someone is either not curious or humble.
Fred is either not quiet or strong.
Someone is calm.
Lucy is not strong or old.
John is not humble or creative.
Someone is not rich.
Someone is not curious or not patient. | Mary is not strong. | neutral | (((funny(mary)&humble(mary)))=>(?[X]:((humble(X)<~>strong(X)))))&
((?[X]:(patient(X)))=>((~strong(mary)|~creative(mary))))&
((?[X]:((humble(X)<~>~wise(X))))<=>((~brave(susan)&happy(susan))))&
(((happy(fred)|~tall(fred)))<=>(?[X]:((tall(X)&creative(X)))))&
(((~calm(lucy)&~creative(lucy)))<=>((~curious(paul)|curious(paul))))&
(![X]:(~funny(X)<=>(~rich(X)|happy(X))))&
(![X]:((~wise(X)<~>~calm(X))=>(patient(X)&rich(X))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:((rich(X)|strong(X)))))&
(![X]:((~calm(X)&curious(X))<=>(~rich(X)|~happy(X))))&
(![X]:((wise(X)<~>humble(X))<=>~wise(X)))&
((?[X]:((~rich(X)&calm(X))))<=>((generous(susan)&~old(susan))))&
((?[X]:((~curious(X)&creative(X))))<=>(?[X]:((~quiet(X)&~strong(X)))))&
(((~funny(john)&~wise(john)))<=>((generous(paul)&~tall(paul))))&
(![X]:((kind(X)|funny(X))=>(~kind(X)&quiet(X))))&
(![X]:((~generous(X)&creative(X))<=>(~funny(X)&~creative(X))))&
(![X]:((~wise(X)|~happy(X))=>(~patient(X)|tall(X))))&
((~patient(alice)<~>~quiet(alice)))&
(?[X]:((~curious(X)<~>humble(X))))&
((~quiet(fred)<~>strong(fred)))&
(?[X]:(calm(X)))&
((~strong(lucy)|old(lucy)))&
((~humble(john)|creative(john)))&
(?[X]:(~rich(X)))&
(?[X]:((~curious(X)|~patient(X)))) | ~strong(mary) | [] | null | 0 |
If someone is humble then john is either not tall or not brave and vice versa.
Everyone who is either not strong or rich is both not funny and not creative and vice versa.
If someone is not patient or not tall then someone is not wise and vice versa.
If mary is either humble or brave then alice is not strong or not tall and vice versa.
If alice is either not strong or generous then someone is both not old and rich.
Everyone who is both not generous and not creative is humble and vice versa.
Everyone who is brave or not strong is both old and not patient and vice versa.
If someone is both not old and tall then someone is both not tall and not brave.
Everyone who is rich is not wise and vice versa.
Everyone who is strong is both not tall and not strong and vice versa.
Everyone who is old or quiet is either humble or creative and vice versa.
If susan is either not curious or not creative then susan is both patient and wise.
Everyone who is not quiet is both not old and not brave.
If john is tall or not patient then someone is rich or tall.
Everyone who is not calm or not strong is old or tall.
Everyone who is both calm and not strong is tall or brave and vice versa.
Alice is brave or not strong.
Someone is not rich.
Mary is either tall or curious.
Mary is either patient or creative.
Someone is humble.
Someone is happy or brave. | Alice is not wise. | entailment | ((?[X]:(humble(X)))<=>((~tall(john)<~>~brave(john))))&
(![X]:((~strong(X)<~>rich(X))<=>(~funny(X)&~creative(X))))&
((?[X]:((~patient(X)|~tall(X))))<=>(?[X]:(~wise(X))))&
(((humble(mary)<~>brave(mary)))<=>((~strong(alice)|~tall(alice))))&
(((~strong(alice)<~>generous(alice)))=>(?[X]:((~old(X)&rich(X)))))&
(![X]:((~generous(X)&~creative(X))<=>humble(X)))&
(![X]:((brave(X)|~strong(X))<=>(old(X)&~patient(X))))&
((?[X]:((~old(X)&tall(X))))=>(?[X]:((~tall(X)&~brave(X)))))&
(![X]:(rich(X)<=>~wise(X)))&
(![X]:(strong(X)<=>(~tall(X)&~strong(X))))&
(![X]:((old(X)|quiet(X))<=>(humble(X)<~>creative(X))))&
(((~curious(susan)<~>~creative(susan)))=>((patient(susan)&wise(susan))))&
(![X]:(~quiet(X)=>(~old(X)&~brave(X))))&
(((tall(john)|~patient(john)))=>(?[X]:((rich(X)|tall(X)))))&
(![X]:((~calm(X)|~strong(X))=>(old(X)|tall(X))))&
(![X]:((calm(X)&~strong(X))<=>(tall(X)|brave(X))))&
((brave(alice)|~strong(alice)))&
(?[X]:(~rich(X)))&
((tall(mary)<~>curious(mary)))&
((patient(mary)<~>creative(mary)))&
(?[X]:(humble(X)))&
(?[X]:((happy(X)|brave(X)))) | ~wise(alice) | [
"p1",
"p4",
"p5",
"p7",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 8876196842273544076548694
% SZS output start Proof for 8876196842273544076548694
2. ! [X0] : ((~strong(X0) <~> rich(X0)) <=> (~creative(X0) & ~funny(X0))) [input p1]
5. (~strong(alice) <~> generous(alice)) => ? [X0] : (rich(X0) & ~old(X0)) [input p4]
6. ! [X0] : ((~creative(X0) & ~generous(X0)) <=> humble(X0)) [input p5]
8. ? [X0] : (tall(X0) & ~old(X0)) => ? [X0] : (~brave(X0) & ~tall(X0)) [input p7]
9. ! [X0] : (rich(X0) <=> ~wise(X0)) [input p8]
10. ! [X0] : (strong(X0) <=> (~strong(X0) & ~tall(X0))) [input p9]
11. ! [X0] : ((quiet(X0) | old(X0)) <=> (humble(X0) <~> creative(X0))) [input p10]
23. wise(alice) [input hypothesis]
25. ? [X0] : (tall(X0) & ~old(X0)) => ? [X1] : (~brave(X1) & ~tall(X1)) [rectify 8]
27. ? [X0] : (rich(X0) & ~old(X0)) | (~strong(alice) <=> generous(alice)) [ennf transformation 5]
28. ? [X1] : (~brave(X1) & ~tall(X1)) | ! [X0] : (~tall(X0) | old(X0)) [ennf transformation 25]
38. ! [X0] : ((((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | (creative(X0) | funny(X0))) & ((~creative(X0) & ~funny(X0)) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~rich(X0) | strong(X0)) & (rich(X0) | ~strong(X0))) | creative(X0) | funny(X0)) & ((~creative(X0) & ~funny(X0)) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0))))) [flattening 38]
47. ? [X0] : (rich(X0) & ~old(X0)) | ((~strong(alice) | ~generous(alice)) & (generous(alice) | strong(alice))) [nnf transformation 27]
48. ? [X0] : (rich(X0) & ~old(X0)) => (rich(sK3) & ~old(sK3)) [choice axiom]
49. (rich(sK3) & ~old(sK3)) | ((~strong(alice) | ~generous(alice)) & (generous(alice) | strong(alice))) [skolemisation 47,48]
50. ! [X0] : (((~creative(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | (creative(X0) | generous(X0)))) [nnf transformation 6]
51. ! [X0] : (((~creative(X0) & ~generous(X0)) | ~humble(X0)) & (humble(X0) | creative(X0) | generous(X0))) [flattening 50]
54. ? [X0] : (~brave(X0) & ~tall(X0)) | ! [X1] : (~tall(X1) | old(X1)) [rectify 28]
55. ? [X0] : (~brave(X0) & ~tall(X0)) => (~brave(sK4) & ~tall(sK4)) [choice axiom]
56. (~brave(sK4) & ~tall(sK4)) | ! [X1] : (~tall(X1) | old(X1)) [skolemisation 54,55]
57. ! [X0] : ((rich(X0) | wise(X0)) & (~wise(X0) | ~rich(X0))) [nnf transformation 9]
58. ! [X0] : ((strong(X0) | (strong(X0) | tall(X0))) & ((~strong(X0) & ~tall(X0)) | ~strong(X0))) [nnf transformation 10]
59. ! [X0] : ((strong(X0) | strong(X0) | tall(X0)) & ((~strong(X0) & ~tall(X0)) | ~strong(X0))) [flattening 58]
60. ! [X0] : (((quiet(X0) | old(X0)) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~quiet(X0) & ~old(X0)))) [nnf transformation 11]
61. ! [X0] : ((quiet(X0) | old(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) & (((~creative(X0) | ~humble(X0)) & (creative(X0) | humble(X0))) | (~quiet(X0) & ~old(X0)))) [flattening 60]
79. ~creative(X0) | rich(X0) | strong(X0) [cnf transformation 39]
92. ~old(sK3) | generous(alice) | strong(alice) [cnf transformation 49]
97. ~generous(X0) | ~humble(X0) [cnf transformation 51]
104. ~tall(sK4) | ~tall(X1) | old(X1) [cnf transformation 56]
106. ~wise(X0) | ~rich(X0) [cnf transformation 57]
109. ~strong(X0) | ~strong(X0) [cnf transformation 59]
110. strong(X0) | strong(X0) | tall(X0) [cnf transformation 59]
111. ~old(X0) | humble(X0) | creative(X0) [cnf transformation 61]
139. wise(alice) [cnf transformation 23]
140. ~strong(X0) [duplicate literal removal 109]
141. strong(X0) | tall(X0) [duplicate literal removal 110]
174. 8 <=> ! [X3] : tall(X3) [avatar definition]
175. tall(X3) <- (8) [avatar component clause 174]
199. 14 <=> strong(alice) [avatar definition]
201. strong(alice) <- (14) [avatar component clause 199]
208. 15 <=> generous(alice) [avatar definition]
209. generous(alice) <- (15) [avatar component clause 208]
218. 17 <=> old(sK3) [avatar definition]
220. ~old(sK3) <- (~17) [avatar component clause 218]
222. 14 | 15 | ~17 [avatar split clause 92,218,208,199]
224. 18 <=> ! [X1] : (~tall(X1) | old(X1)) [avatar definition]
225. ~tall(X1) | old(X1) <- (18) [avatar component clause 224]
232. 20 <=> tall(sK4) [avatar definition]
234. ~tall(sK4) <- (~20) [avatar component clause 232]
235. 18 | ~20 [avatar split clause 104,232,224]
292. $false <- (14) [subsumption resolution 201,140]
293. ~14 [avatar contradiction clause 292]
298. ~humble(alice) <- (15) [resolution 97,209]
316. ~rich(alice) [resolution 106,139]
327. tall(X0) [resolution 141,140]
328. 8 [avatar split clause 327,174]
330. $false <- (8, ~20) [resolution 175,234]
332. ~8 | 20 [avatar contradiction clause 330]
334. old(X1) <- (8, 18) [subsumption resolution 225,175]
340. creative(X0) | humble(X0) <- (8, 18) [resolution 111,334]
346. humble(X1) | rich(X1) | strong(X1) <- (8, 18) [resolution 340,79]
348. rich(X1) | humble(X1) <- (8, 18) [subsumption resolution 346,140]
352. humble(alice) <- (8, 18) [resolution 348,316]
353. $false <- (8, 15, 18) [subsumption resolution 352,298]
354. ~8 | ~15 | ~18 [avatar contradiction clause 353]
355. $false <- (8, ~17, 18) [subsumption resolution 220,334]
356. ~8 | 17 | ~18 [avatar contradiction clause 355]
357. $false [avatar sat refutation 222,235,293,328,332,354,356]
% SZS output end Proof for 8876196842273544076548694
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not wise is not rich.
If john is humble or happy then someone is both not rich and not brave.
If fred is generous then paul is generous and vice versa.
If someone is either kind or not quiet then john is either not creative or strong.
Everyone who is not quiet is wise or not tall and vice versa.
Everyone who is not old is both not humble and generous.
Everyone who is not old or not tall is not generous.
Everyone who is not brave or not funny is not tall and vice versa.
Everyone who is not brave or curious is both not humble and not old.
Everyone who is not humble or calm is not rich and vice versa.
If someone is calm or not funny then someone is both not old and wise.
If susan is both happy and creative then lucy is tall.
Everyone who is both strong and old is either happy or not patient and vice versa.
Everyone who is both not kind and old is both patient and strong.
If john is both not creative and brave then lucy is both not rich and kind.
Someone is happy.
Someone is wise.
Someone is not wise or happy.
Someone is either not generous or creative.
Someone is either rich or not creative.
Someone is both not humble and not wise. | Paul is not tall. | contradiction | (![X]:((~calm(X)|~wise(X))=>~rich(X)))&
(((humble(john)|happy(john)))=>(?[X]:((~rich(X)&~brave(X)))))&
((generous(fred))<=>(generous(paul)))&
((?[X]:((kind(X)<~>~quiet(X))))=>((~creative(john)<~>strong(john))))&
(![X]:(~quiet(X)<=>(wise(X)|~tall(X))))&
(![X]:(~old(X)=>(~humble(X)&generous(X))))&
(![X]:((~old(X)|~tall(X))=>~generous(X)))&
(![X]:((~brave(X)|~funny(X))<=>~tall(X)))&
(![X]:((~brave(X)|curious(X))=>(~humble(X)&~old(X))))&
(![X]:((~humble(X)|calm(X))<=>~rich(X)))&
((?[X]:((calm(X)|~funny(X))))=>(?[X]:((~old(X)&wise(X)))))&
(((happy(susan)&creative(susan)))=>(tall(lucy)))&
(![X]:((strong(X)&old(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((~kind(X)&old(X))=>(patient(X)&strong(X))))&
(((~creative(john)&brave(john)))=>((~rich(lucy)&kind(lucy))))&
(?[X]:(happy(X)))&
(?[X]:(wise(X)))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~creative(X))))&
(?[X]:((~humble(X)&~wise(X)))) | ~tall(paul) | [
"p5",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6316400508468369613953152
% SZS output start Proof for 6316400508468369613953152
6. ! [X0] : (~old(X0) => (generous(X0) & ~humble(X0))) [input p5]
7. ! [X0] : ((~tall(X0) | ~old(X0)) => ~generous(X0)) [input p6]
8. ! [X0] : ((~funny(X0) | ~brave(X0)) <=> ~tall(X0)) [input p7]
9. ! [X0] : ((curious(X0) | ~brave(X0)) => (~old(X0) & ~humble(X0))) [input p8]
11. ? [X0] : (~funny(X0) | calm(X0)) => ? [X0] : (wise(X0) & ~old(X0)) [input p10]
22. ~tall(paul) [input hypothesis]
23. ? [X0] : (~funny(X0) | calm(X0)) => ? [X1] : (wise(X1) & ~old(X1)) [rectify 11]
24. ! [X0] : (~brave(X0) => (~old(X0) & ~humble(X0))) [pure predicate removal 9]
28. ! [X0] : ((generous(X0) & ~humble(X0)) | old(X0)) [ennf transformation 6]
29. ! [X0] : (~generous(X0) | (tall(X0) & old(X0))) [ennf transformation 7]
30. ! [X0] : ((~old(X0) & ~humble(X0)) | brave(X0)) [ennf transformation 24]
31. ? [X1] : (wise(X1) & ~old(X1)) | ! [X0] : (funny(X0) & ~calm(X0)) [ennf transformation 23]
44. ! [X0] : (((~funny(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (funny(X0) & brave(X0)))) [nnf transformation 8]
45. ! [X0] : ((~funny(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (funny(X0) & brave(X0)))) [flattening 44]
48. ? [X0] : (wise(X0) & ~old(X0)) | ! [X1] : (funny(X1) & ~calm(X1)) [rectify 31]
49. ? [X0] : (wise(X0) & ~old(X0)) => (wise(sK1) & ~old(sK1)) [choice axiom]
50. (wise(sK1) & ~old(sK1)) | ! [X1] : (funny(X1) & ~calm(X1)) [skolemisation 48,49]
83. old(X0) | generous(X0) [cnf transformation 28]
84. ~generous(X0) | old(X0) [cnf transformation 29]
88. ~funny(X0) | ~brave(X0) | tall(X0) [cnf transformation 45]
90. ~old(X0) | brave(X0) [cnf transformation 30]
95. ~old(sK1) | funny(X1) [cnf transformation 50]
118. ~tall(paul) [cnf transformation 22]
167. old(X0) [subsumption resolution 84,83]
168. brave(X0) [subsumption resolution 90,167]
172. 11 <=> ! [X1] : funny(X1) [avatar definition]
173. funny(X1) <- (11) [avatar component clause 172]
183. funny(X1) [subsumption resolution 95,167]
184. 11 [avatar split clause 183,172]
232. ~brave(X0) | tall(X0) <- (11) [resolution 88,173]
233. tall(X0) <- (11) [subsumption resolution 232,168]
235. $false <- (11) [resolution 233,118]
239. ~11 [avatar contradiction clause 235]
240. $false [avatar sat refutation 184,239]
% SZS output end Proof for 6316400508468369613953152
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not patient is curious and vice versa.
Everyone who is creative is both strong and generous.
Everyone who is not creative or funny is kind or not funny.
Everyone who is either not quiet or old is not quiet or creative and vice versa.
If someone is either kind or not brave then someone is both happy and not rich and vice versa.
Everyone who is either not funny or rich is either not creative or humble and vice versa.
If someone is either not humble or generous then someone is both not brave and calm and vice versa.
Everyone who is either not funny or funny is not creative or strong and vice versa.
Everyone who is both calm and funny is both kind and not kind.
Everyone who is either not old or not kind is both not patient and not wise.
Everyone who is both patient and funny is not creative or not kind and vice versa.
If someone is both creative and happy then someone is either not kind or old.
If mary is both not generous and not funny then lucy is not funny or not tall.
If john is generous or not tall then someone is either not kind or not tall.
Everyone who is either humble or not funny is both not calm and not strong and vice versa.
Everyone who is either calm or wise is brave or strong and vice versa.
Paul is either not wise or old.
Someone is not creative or not rich.
Someone is both not old and not happy.
Fred is kind or not happy.
Fred is patient.
Fred is not calm. | Lucy is not creative. | contradiction | (![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
(((~generous(mary)&~funny(mary)))=>((~funny(lucy)|~tall(lucy))))&
(((generous(john)|~tall(john)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
(![X]:((humble(X)<~>~funny(X))<=>(~calm(X)&~strong(X))))&
(![X]:((calm(X)<~>wise(X))<=>(brave(X)|strong(X))))&
((~wise(paul)<~>old(paul)))&
(?[X]:((~creative(X)|~rich(X))))&
(?[X]:((~old(X)&~happy(X))))&
((kind(fred)|~happy(fred)))&
(patient(fred))&
(~calm(fred)) | ~creative(lucy) | [
"p2",
"p3",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7379056278373746954345793
% SZS output start Proof for 7379056278373746954345793
3. ! [X0] : ((funny(X0) | ~creative(X0)) => (~funny(X0) | kind(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (creative(X0) | ~quiet(X0))) [input p3]
10. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (~wise(X0) & ~patient(X0))) [input p9]
11. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p10]
23. ~creative(lucy) [input hypothesis]
28. ! [X0] : ((~funny(X0) | kind(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 3]
29. ! [X0] : (~funny(X0) | kind(X0) | (~funny(X0) & creative(X0))) [flattening 28]
32. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 10]
37. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 4]
38. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 37]
52. ! [X0] : ((~wise(X0) & ~patient(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 32]
53. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 11]
54. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 53]
74. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 29]
76. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 38]
79. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
109. ~kind(X0) | ~patient(X0) | old(X0) [cnf transformation 52]
114. creative(X0) | patient(X0) [cnf transformation 54]
117. funny(X0) | kind(X0) [cnf transformation 54]
145. ~creative(lucy) [cnf transformation 23]
148. creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 76]
149. ~old(X0) | quiet(X0) [duplicate literal removal 79]
150. ~funny(X0) | kind(X0) [duplicate literal removal 74]
151. ~old(X0) | creative(X0) [subsumption resolution 148,149]
215. kind(X0) [subsumption resolution 117,150]
285. patient(lucy) [resolution 114,145]
297. ~patient(X0) | old(X0) [resolution 109,215]
318. old(lucy) [resolution 297,285]
327. creative(lucy) [resolution 318,151]
329. $false [subsumption resolution 327,145]
% SZS output end Proof for 7379056278373746954345793
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either not brave or wise then someone is either curious or not funny and vice versa.
If someone is not old or generous then someone is both not generous and not humble.
Everyone who is both not happy and funny is strong or not strong and vice versa.
If someone is not rich then someone is old or kind.
Everyone who is both not rich and wise is either not humble or not brave.
Everyone who is generous or calm is tall.
If mary is not strong or wise then paul is not wise or generous and vice versa.
If mary is not rich or not calm then alice is patient and vice versa.
Everyone who is creative is not patient or funny and vice versa.
Everyone who is both not kind and not brave is not happy or brave.
Everyone who is not humble is either creative or not humble.
If susan is not tall or not calm then someone is either not quiet or not wise and vice versa.
Everyone who is both wise and not happy is strong and vice versa.
Everyone who is either not happy or funny is not strong.
If someone is either kind or not funny then someone is either not happy or humble and vice versa.
If someone is not curious or not rich then someone is brave.
Alice is either generous or calm.
Someone is either curious or not generous.
Someone is both not rich and calm.
Someone is wise or kind.
Alice is rich or not calm. | Susan is happy. | contradiction | (((~brave(lucy)<~>wise(lucy)))<=>(?[X]:((curious(X)<~>~funny(X)))))&
((?[X]:((~old(X)|generous(X))))=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((~happy(X)&funny(X))<=>(strong(X)|~strong(X))))&
((?[X]:(~rich(X)))=>(?[X]:((old(X)|kind(X)))))&
(![X]:((~rich(X)&wise(X))=>(~humble(X)<~>~brave(X))))&
(![X]:((generous(X)|calm(X))=>tall(X)))&
(((~strong(mary)|wise(mary)))<=>((~wise(paul)|generous(paul))))&
(((~rich(mary)|~calm(mary)))<=>(patient(alice)))&
(![X]:(creative(X)<=>(~patient(X)|funny(X))))&
(![X]:((~kind(X)&~brave(X))=>(~happy(X)|brave(X))))&
(![X]:(~humble(X)=>(creative(X)<~>~humble(X))))&
(((~tall(susan)|~calm(susan)))<=>(?[X]:((~quiet(X)<~>~wise(X)))))&
(![X]:((wise(X)&~happy(X))<=>strong(X)))&
(![X]:((~happy(X)<~>funny(X))=>~strong(X)))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((~happy(X)<~>humble(X)))))&
((?[X]:((~curious(X)|~rich(X))))=>(?[X]:(brave(X))))&
((generous(alice)<~>calm(alice)))&
(?[X]:((curious(X)<~>~generous(X))))&
(?[X]:((~rich(X)&calm(X))))&
(?[X]:((wise(X)|kind(X))))&
((rich(alice)|~calm(alice))) | happy(susan) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 4004442314935577699575300
% SZS output start Proof for 4004442314935577699575300
3. ! [X0] : ((funny(X0) & ~happy(X0)) <=> (~strong(X0) | strong(X0))) [input p2]
22. happy(susan) [input hypothesis]
45. ! [X0] : (((funny(X0) & ~happy(X0)) | (strong(X0) & ~strong(X0))) & ((~strong(X0) | strong(X0)) | (~funny(X0) | happy(X0)))) [nnf transformation 3]
46. ! [X0] : (((funny(X0) & ~happy(X0)) | (strong(X0) & ~strong(X0))) & (~strong(X0) | strong(X0) | ~funny(X0) | happy(X0))) [flattening 45]
90. ~happy(X0) | ~strong(X0) [cnf transformation 46]
91. ~happy(X0) | strong(X0) [cnf transformation 46]
140. happy(susan) [cnf transformation 22]
187. ~happy(X0) [subsumption resolution 90,91]
297. $false [subsumption resolution 140,187]
% SZS output end Proof for 4004442314935577699575300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not curious then someone is patient or happy and vice versa. Everyone who is either curious or quiet is both not wise and creative and vice versa. Everyone who is either not quiet or creative is not old and vice versa. Everyone who is wise is humble and vice versa. If john is not rich or not happy then someone is both not strong and brave and vice versa. Everyone who is both not patient and old is curious or not funny and vice versa. If mary is either rich or not funny then someone is both calm and not brave and vice versa. Everyone who is not strong or brave is either old or not strong. If lucy is wise or not kind then someone is both not creative and tall and vice versa. Everyone who is strong is both happy and not funny. Everyone who is either brave or creative is either not patient or creative. If someone is either not happy or not curious then susan is both generous and calm. Everyone who is not funny or not rich is either curious or strong and vice versa. If someone is either not wise or generous then someone is not humble or rich. Everyone who is either not quiet or not calm is curious or not creative and vice versa. If alice is not rich then someone is both not happy and not tall and vice versa. Someone is both not creative and humble. Fred is not wise. Mary is not old. Someone is either brave or not funny. Someone is both funny and not tall. Someone is both funny and not patient. Fred is happy or kind. Someone is either strong or not wise. | Fred is funny. | entailment | ((?[X]:(~curious(X)))<=>(?[X]:((patient(X)|happy(X)))))&
(![X]:((curious(X)<~>quiet(X))<=>(~wise(X)&creative(X))))&
(![X]:((~quiet(X)<~>creative(X))<=>~old(X)))&
(![X]:(wise(X)<=>humble(X)))&
(((~rich(john)|~happy(john)))<=>(?[X]:((~strong(X)&brave(X)))))&
(![X]:((~patient(X)&old(X))<=>(curious(X)|~funny(X))))&
(((rich(mary)<~>~funny(mary)))<=>(?[X]:((calm(X)&~brave(X)))))&
(![X]:((~strong(X)|brave(X))=>(old(X)<~>~strong(X))))&
(((wise(lucy)|~kind(lucy)))<=>(?[X]:((~creative(X)&tall(X)))))&
(![X]:(strong(X)=>(happy(X)&~funny(X))))&
(![X]:((brave(X)<~>creative(X))=>(~patient(X)<~>creative(X))))&
((?[X]:((~happy(X)<~>~curious(X))))=>((generous(susan)&calm(susan))))&
(![X]:((~funny(X)|~rich(X))<=>(curious(X)<~>strong(X))))&
((?[X]:((~wise(X)<~>generous(X))))=>(?[X]:((~humble(X)|rich(X)))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(curious(X)|~creative(X))))&
((~rich(alice))<=>(?[X]:((~happy(X)&~tall(X)))))&
(?[X]:((~creative(X)&humble(X))))&
(~wise(fred))&
(~old(mary))&
(?[X]:((brave(X)<~>~funny(X))))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:((funny(X)&~patient(X))))&
((happy(fred)|kind(fred)))&
(?[X]:((strong(X)<~>~wise(X)))) | funny(fred) | [
"p1",
"p2",
"p5",
"p7",
"p9",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5102959754934271662987592
% SZS output start Proof for 5102959754934271662987592
2. ! [X0] : ((curious(X0) <~> quiet(X0)) <=> (creative(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((~quiet(X0) <~> creative(X0)) <=> ~old(X0)) [input p2]
6. ! [X0] : ((old(X0) & ~patient(X0)) <=> (~funny(X0) | curious(X0))) [input p5]
8. ! [X0] : ((brave(X0) | ~strong(X0)) => (old(X0) <~> ~strong(X0))) [input p7]
10. ! [X0] : (strong(X0) => (~funny(X0) & happy(X0))) [input p9]
13. ! [X0] : ((~rich(X0) | ~funny(X0)) <=> (curious(X0) <~> strong(X0))) [input p12]
18. ~wise(fred) [input p17]
25. ~funny(fred) [input hypothesis]
28. ! [X0] : ((old(X0) <~> ~strong(X0)) | (~brave(X0) & strong(X0))) [ennf transformation 8]
29. ! [X0] : ((~funny(X0) & happy(X0)) | ~strong(X0)) [ennf transformation 10]
38. ! [X0] : ((((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | (~creative(X0) | wise(X0))) & ((creative(X0) & ~wise(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0))))) [nnf transformation 2]
39. ! [X0] : ((((~quiet(X0) | ~curious(X0)) & (quiet(X0) | curious(X0))) | ~creative(X0) | wise(X0)) & ((creative(X0) & ~wise(X0)) | ((curious(X0) | ~quiet(X0)) & (quiet(X0) | ~curious(X0))))) [flattening 38]
40. ! [X0] : ((((~creative(X0) | quiet(X0)) & (creative(X0) | ~quiet(X0))) | old(X0)) & (~old(X0) | ((~quiet(X0) | ~creative(X0)) & (creative(X0) | quiet(X0))))) [nnf transformation 3]
47. ! [X0] : (((old(X0) & ~patient(X0)) | (funny(X0) & ~curious(X0))) & ((~funny(X0) | curious(X0)) | (~old(X0) | patient(X0)))) [nnf transformation 6]
48. ! [X0] : (((old(X0) & ~patient(X0)) | (funny(X0) & ~curious(X0))) & (~funny(X0) | curious(X0) | ~old(X0) | patient(X0))) [flattening 47]
53. ! [X0] : (((strong(X0) | ~old(X0)) & (~strong(X0) | old(X0))) | (~brave(X0) & strong(X0))) [nnf transformation 28]
61. ! [X0] : (((~rich(X0) | ~funny(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (rich(X0) & funny(X0)))) [nnf transformation 13]
62. ! [X0] : ((~rich(X0) | ~funny(X0) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (rich(X0) & funny(X0)))) [flattening 61]
91. ~quiet(X0) | curious(X0) | creative(X0) [cnf transformation 39]
92. ~creative(X0) | curious(X0) | quiet(X0) | wise(X0) [cnf transformation 39]
94. ~old(X0) | creative(X0) | quiet(X0) [cnf transformation 40]
95. ~old(X0) | ~quiet(X0) | ~creative(X0) [cnf transformation 40]
109. funny(X0) | old(X0) [cnf transformation 48]
118. strong(X0) | ~old(X0) | strong(X0) [cnf transformation 53]
126. ~funny(X0) | ~strong(X0) [cnf transformation 29]
137. ~strong(X0) | ~curious(X0) | funny(X0) [cnf transformation 62]
154. ~wise(fred) [cnf transformation 18]
165. ~funny(fred) [cnf transformation 25]
168. ~old(X0) | strong(X0) [duplicate literal removal 118]
285. ~strong(X0) | ~curious(X0) [subsumption resolution 137,126]
356. old(fred) [resolution 109,165]
366. strong(fred) [resolution 168,356]
374. ~curious(fred) [resolution 366,285]
395. creative(fred) | quiet(fred) [resolution 94,356]
398. 42 <=> quiet(fred) [avatar definition]
399. ~quiet(fred) <- (~42) [avatar component clause 398]
400. quiet(fred) <- (42) [avatar component clause 398]
402. 43 <=> creative(fred) [avatar definition]
403. ~creative(fred) <- (~43) [avatar component clause 402]
404. creative(fred) <- (43) [avatar component clause 402]
405. 42 | 43 [avatar split clause 395,402,398]
422. ~quiet(fred) | ~creative(fred) [resolution 95,356]
431. curious(fred) | creative(fred) <- (42) [resolution 400,91]
432. creative(fred) <- (42) [subsumption resolution 431,374]
433. $false <- (42, ~43) [subsumption resolution 432,403]
434. ~42 | 43 [avatar contradiction clause 433]
435. ~43 | ~42 [avatar split clause 422,398,402]
578. curious(fred) | quiet(fred) | wise(fred) <- (43) [resolution 92,404]
580. quiet(fred) | wise(fred) <- (43) [subsumption resolution 578,374]
581. wise(fred) <- (~42, 43) [subsumption resolution 580,399]
582. $false <- (~42, 43) [subsumption resolution 581,154]
583. 42 | ~43 [avatar contradiction clause 582]
586. $false [avatar sat refutation 405,434,435,583]
% SZS output end Proof for 5102959754934271662987592
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny then someone is both not patient and not humble. Everyone who is both kind and humble is humble and vice versa. If john is both not quiet and not creative then someone is not happy or not patient and vice versa. If someone is both not rich and not creative then someone is rich. If alice is either kind or funny then someone is not strong or not humble and vice versa. Everyone who is both not strong and not curious is both old and creative and vice versa. Everyone who is either not tall or not generous is both not wise and not calm. If someone is both patient and old then someone is both generous and not strong and vice versa. If someone is both wise and quiet then fred is rich or old and vice versa. Everyone who is either not tall or creative is not kind or not strong and vice versa. If paul is not brave or not quiet then susan is funny and vice versa. If mary is not tall or generous then someone is either calm or strong and vice versa. Everyone who is either wise or tall is both brave and kind. If someone is both not funny and rich then fred is not kind and vice versa. Everyone who is either not old or quiet is not curious or not kind and vice versa. Everyone who is curious is both not brave and old and vice versa. Alice is either not patient or funny. Lucy is patient or not strong. Lucy is kind. Someone is wise. Someone is not patient or not quiet. Someone is either not curious or wise. Fred is both happy and curious. | Susan is rich. | neutral | ((?[X]:(~funny(X)))=>(?[X]:((~patient(X)&~humble(X)))))&
(![X]:((kind(X)&humble(X))<=>humble(X)))&
(((~quiet(john)&~creative(john)))<=>(?[X]:((~happy(X)|~patient(X)))))&
((?[X]:((~rich(X)&~creative(X))))=>(?[X]:(rich(X))))&
(((kind(alice)<~>funny(alice)))<=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((~strong(X)&~curious(X))<=>(old(X)&creative(X))))&
(![X]:((~tall(X)<~>~generous(X))=>(~wise(X)&~calm(X))))&
((?[X]:((patient(X)&old(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:((wise(X)&quiet(X))))<=>((rich(fred)|old(fred))))&
(![X]:((~tall(X)<~>creative(X))<=>(~kind(X)|~strong(X))))&
(((~brave(paul)|~quiet(paul)))<=>(funny(susan)))&
(((~tall(mary)|generous(mary)))<=>(?[X]:((calm(X)<~>strong(X)))))&
(![X]:((wise(X)<~>tall(X))=>(brave(X)&kind(X))))&
((?[X]:((~funny(X)&rich(X))))<=>(~kind(fred)))&
(![X]:((~old(X)<~>quiet(X))<=>(~curious(X)|~kind(X))))&
(![X]:(curious(X)<=>(~brave(X)&old(X))))&
((~patient(alice)<~>funny(alice)))&
((patient(lucy)|~strong(lucy)))&
(kind(lucy))&
(?[X]:(wise(X)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~curious(X)<~>wise(X))))&
((happy(fred)&curious(fred))) | rich(susan) | [] | null | 0 |
Everyone who is not funny is both patient and not old and vice versa. Everyone who is humble is either not tall or not old. If someone is not old then someone is either not brave or quiet and vice versa. Everyone who is old is both wise and not rich and vice versa. Everyone who is patient or old is both quiet and not kind. Everyone who is not patient or not wise is either quiet or old and vice versa. Everyone who is both not calm and calm is either calm or humble. Everyone who is calm is either not old or rich. Everyone who is not curious or rich is either not rich or tall. Everyone who is not wise or not patient is either kind or humble and vice versa. Everyone who is happy is either not curious or not old and vice versa. Everyone who is both not humble and happy is humble or curious and vice versa. Everyone who is not wise is not curious. If fred is either calm or not quiet then lucy is both not patient and wise. Everyone who is not wise is either not kind or not creative and vice versa. If john is rich then someone is not brave and vice versa. Mary is either not humble or strong. John is not wise. Someone is not generous. Lucy is not strong or not creative. Someone is both wise and not brave. Someone is either not rich or curious. | Lucy is kind. | entailment | (![X]:(~funny(X)<=>(patient(X)&~old(X))))&
(![X]:(humble(X)=>(~tall(X)<~>~old(X))))&
((?[X]:(~old(X)))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(old(X)<=>(wise(X)&~rich(X))))&
(![X]:((patient(X)|old(X))=>(quiet(X)&~kind(X))))&
(![X]:((~patient(X)|~wise(X))<=>(quiet(X)<~>old(X))))&
(![X]:((~calm(X)&calm(X))=>(calm(X)<~>humble(X))))&
(![X]:(calm(X)=>(~old(X)<~>rich(X))))&
(![X]:((~curious(X)|rich(X))=>(~rich(X)<~>tall(X))))&
(![X]:((~wise(X)|~patient(X))<=>(kind(X)<~>humble(X))))&
(![X]:(happy(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~humble(X)&happy(X))<=>(humble(X)|curious(X))))&
(![X]:(~wise(X)=>~curious(X)))&
(((calm(fred)<~>~quiet(fred)))=>((~patient(lucy)&wise(lucy))))&
(![X]:(~wise(X)<=>(~kind(X)<~>~creative(X))))&
((rich(john))<=>(?[X]:(~brave(X))))&
((~humble(mary)<~>strong(mary)))&
(~wise(john))&
(?[X]:(~generous(X)))&
((~strong(lucy)|~creative(lucy)))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:((~rich(X)<~>curious(X)))) | kind(lucy) | [
"p4",
"p5",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 2489299374676974055536231
% SZS output start Proof for 2489299374676974055536231
5. ! [X0] : ((old(X0) | patient(X0)) => (~kind(X0) & quiet(X0))) [input p4]
6. ! [X0] : ((~wise(X0) | ~patient(X0)) <=> (quiet(X0) <~> old(X0))) [input p5]
10. ! [X0] : ((~patient(X0) | ~wise(X0)) <=> (kind(X0) <~> humble(X0))) [input p9]
11. ! [X0] : (happy(X0) <=> (~curious(X0) <~> ~old(X0))) [input p10]
12. ! [X0] : ((happy(X0) & ~humble(X0)) <=> (curious(X0) | humble(X0))) [input p11]
23. ~kind(lucy) [input hypothesis]
27. ! [X0] : ((~kind(X0) & quiet(X0)) | (~old(X0) & ~patient(X0))) [ennf transformation 5]
42. ! [X0] : (((~wise(X0) | ~patient(X0)) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) & (((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (wise(X0) & patient(X0)))) [nnf transformation 6]
43. ! [X0] : ((~wise(X0) | ~patient(X0) | ((quiet(X0) | ~old(X0)) & (old(X0) | ~quiet(X0)))) & (((~old(X0) | ~quiet(X0)) & (old(X0) | quiet(X0))) | (wise(X0) & patient(X0)))) [flattening 42]
47. ! [X0] : (((~patient(X0) | ~wise(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & wise(X0)))) [nnf transformation 10]
48. ! [X0] : ((~patient(X0) | ~wise(X0) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (patient(X0) & wise(X0)))) [flattening 47]
49. ! [X0] : ((happy(X0) | ((~curious(X0) | old(X0)) & (~old(X0) | curious(X0)))) & (((old(X0) | curious(X0)) & (~old(X0) | ~curious(X0))) | ~happy(X0))) [nnf transformation 11]
50. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & ((curious(X0) | humble(X0)) | (~happy(X0) | humble(X0)))) [nnf transformation 12]
51. ! [X0] : (((happy(X0) & ~humble(X0)) | (~curious(X0) & ~humble(X0))) & (curious(X0) | humble(X0) | ~happy(X0) | humble(X0))) [flattening 50]
73. ~patient(X0) | quiet(X0) [cnf transformation 27]
81. ~wise(X0) | ~patient(X0) | old(X0) | ~quiet(X0) [cnf transformation 43]
91. kind(X0) | humble(X0) | wise(X0) [cnf transformation 48]
92. kind(X0) | humble(X0) | patient(X0) [cnf transformation 48]
97. ~happy(X0) | ~curious(X0) | ~old(X0) [cnf transformation 49]
99. ~old(X0) | happy(X0) | curious(X0) [cnf transformation 49]
101. curious(X0) | humble(X0) | ~happy(X0) | humble(X0) [cnf transformation 51]
102. ~humble(X0) | ~humble(X0) [cnf transformation 51]
105. ~curious(X0) | happy(X0) [cnf transformation 51]
125. ~kind(lucy) [cnf transformation 23]
126. curious(X0) | humble(X0) | ~happy(X0) [duplicate literal removal 101]
127. ~humble(X0) [duplicate literal removal 102]
156. ~wise(X0) | ~patient(X0) | old(X0) [subsumption resolution 81,73]
165. ~happy(X0) | curious(X0) [subsumption resolution 126,127]
172. 8 <=> wise(lucy) [avatar definition]
174. wise(lucy) <- (8) [avatar component clause 172]
178. 9 <=> patient(lucy) [avatar definition]
179. patient(lucy) <- (9) [avatar component clause 178]
241. humble(lucy) | wise(lucy) [resolution 91,125]
245. wise(lucy) [subsumption resolution 241,127]
246. 8 [avatar split clause 245,172]
250. 19 <=> old(lucy) [avatar definition]
251. ~old(lucy) <- (~19) [avatar component clause 250]
252. old(lucy) <- (19) [avatar component clause 250]
258. humble(lucy) | patient(lucy) [resolution 92,125]
262. patient(lucy) [subsumption resolution 258,127]
263. 9 [avatar split clause 262,178]
271. happy(lucy) | curious(lucy) <- (19) [resolution 99,252]
273. happy(lucy) <- (19) [subsumption resolution 271,105]
285. ~curious(lucy) | ~old(lucy) <- (19) [resolution 273,97]
286. curious(lucy) <- (19) [resolution 273,165]
287. ~curious(lucy) <- (19) [subsumption resolution 285,252]
288. $false <- (19) [subsumption resolution 286,287]
289. ~19 [avatar contradiction clause 288]
299. ~patient(lucy) | old(lucy) <- (8) [resolution 156,174]
301. old(lucy) <- (8, 9) [subsumption resolution 299,179]
302. $false <- (8, 9, ~19) [subsumption resolution 301,251]
303. ~8 | ~9 | 19 [avatar contradiction clause 302]
304. $false [avatar sat refutation 246,263,289,303]
% SZS output end Proof for 2489299374676974055536231
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is kind or not generous then someone is both wise and not brave and vice versa. Everyone who is not curious is funny and vice versa. Everyone who is both generous and kind is both not wise and not old and vice versa. If mary is either tall or quiet then someone is both not old and not quiet. Everyone who is either curious or not curious is not old or kind and vice versa. Everyone who is not brave or curious is not curious and vice versa. If someone is curious or humble then john is creative. If someone is either not kind or not happy then alice is both funny and not humble and vice versa. Everyone who is both generous and not generous is generous. Everyone who is both brave and not patient is either wise or not quiet. Everyone who is either tall or patient is both not quiet and not creative. Everyone who is either not funny or not kind is curious or not patient and vice versa. If someone is either creative or brave then someone is wise or kind. Everyone who is both creative and strong is patient or old and vice versa. If someone is quiet or not strong then fred is both quiet and not strong and vice versa. Everyone who is funny or creative is not tall or not rich and vice versa. Someone is both calm and not brave. Paul is not tall or creative. Alice is both not calm and kind. Someone is either tall or not strong. Someone is either not creative or kind. Paul is not strong. | Paul is not brave. | entailment | (((kind(lucy)|~generous(lucy)))<=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(![X]:((creative(X)&strong(X))<=>(patient(X)|old(X))))&
((?[X]:((quiet(X)|~strong(X))))<=>((quiet(fred)&~strong(fred))))&
(![X]:((funny(X)|creative(X))<=>(~tall(X)|~rich(X))))&
(?[X]:((calm(X)&~brave(X))))&
((~tall(paul)|creative(paul)))&
((~calm(alice)&kind(alice)))&
(?[X]:((tall(X)<~>~strong(X))))&
(?[X]:((~creative(X)<~>kind(X))))&
(~strong(paul)) | ~brave(paul) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5963277413697528930727202
% SZS output start Proof for 5963277413697528930727202
6. ! [X0] : ((curious(X0) | ~brave(X0)) <=> ~curious(X0)) [input p5]
23. brave(paul) [input hypothesis]
46. ! [X0] : (((curious(X0) | ~brave(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [nnf transformation 6]
47. ! [X0] : ((curious(X0) | ~brave(X0) | curious(X0)) & (~curious(X0) | (~curious(X0) & brave(X0)))) [flattening 46]
100. ~curious(X0) | ~curious(X0) [cnf transformation 47]
101. curious(X0) | ~brave(X0) | curious(X0) [cnf transformation 47]
149. brave(paul) [cnf transformation 23]
151. ~curious(X0) [duplicate literal removal 100]
152. ~brave(X0) | curious(X0) [duplicate literal removal 101]
311. curious(paul) [resolution 152,149]
312. $false [subsumption resolution 311,151]
% SZS output end Proof for 5963277413697528930727202
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not tall is either rich or patient.
If someone is either not happy or not creative then someone is not funny and vice versa.
Everyone who is both not curious and kind is both tall and not generous.
Everyone who is happy or not generous is either not tall or not funny and vice versa.
If someone is both not strong and rich then paul is both old and patient.
If someone is kind or happy then alice is both happy and not happy and vice versa.
Everyone who is not brave or not rich is not brave or not tall and vice versa.
Everyone who is either not wise or not happy is not generous.
If alice is not quiet then mary is either brave or funny and vice versa.
If someone is creative or not rich then someone is not tall or old.
Everyone who is both wise and brave is either not rich or patient and vice versa.
Everyone who is both not patient and kind is not wise and vice versa.
Everyone who is not funny is curious.
If paul is curious then lucy is not tall.
Everyone who is both not tall and funny is wise and vice versa.
Everyone who is both not tall and happy is either not quiet or humble.
Someone is not tall or not strong.
Someone is not quiet.
Someone is not rich or brave.
Lucy is brave or not strong.
Someone is both not creative and not humble.
Someone is not quiet or wise.
Paul is old. | Mary is patient. | neutral | (![X]:((~strong(X)<~>~tall(X))=>(rich(X)<~>patient(X))))&
((?[X]:((~happy(X)<~>~creative(X))))<=>(?[X]:(~funny(X))))&
(![X]:((~curious(X)&kind(X))=>(tall(X)&~generous(X))))&
(![X]:((happy(X)|~generous(X))<=>(~tall(X)<~>~funny(X))))&
((?[X]:((~strong(X)&rich(X))))=>((old(paul)&patient(paul))))&
((?[X]:((kind(X)|happy(X))))<=>((happy(alice)&~happy(alice))))&
(![X]:((~brave(X)|~rich(X))<=>(~brave(X)|~tall(X))))&
(![X]:((~wise(X)<~>~happy(X))=>~generous(X)))&
((~quiet(alice))<=>((brave(mary)<~>funny(mary))))&
((?[X]:((creative(X)|~rich(X))))=>(?[X]:((~tall(X)|old(X)))))&
(![X]:((wise(X)&brave(X))<=>(~rich(X)<~>patient(X))))&
(![X]:((~patient(X)&kind(X))<=>~wise(X)))&
(![X]:(~funny(X)=>curious(X)))&
((curious(paul))=>(~tall(lucy)))&
(![X]:((~tall(X)&funny(X))<=>wise(X)))&
(![X]:((~tall(X)&happy(X))=>(~quiet(X)<~>humble(X))))&
(?[X]:((~tall(X)|~strong(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~rich(X)|brave(X))))&
((brave(lucy)|~strong(lucy)))&
(?[X]:((~creative(X)&~humble(X))))&
(?[X]:((~quiet(X)|wise(X))))&
(old(paul)) | patient(mary) | [] | null | 0 |
If someone is both old and not kind then someone is rich or happy.
Everyone who is either not calm or happy is not patient or happy and vice versa.
Everyone who is tall or happy is either patient or quiet and vice versa.
If susan is not generous then someone is both rich and brave and vice versa.
Everyone who is both not rich and not wise is either strong or not calm.
Everyone who is both tall and humble is either humble or not calm.
Everyone who is either rich or happy is both wise and not creative.
Everyone who is either old or not calm is both not rich and not tall.
Everyone who is kind or not rich is both calm and brave and vice versa.
If lucy is both not patient and brave then mary is not patient and vice versa.
If lucy is both not generous and not kind then john is funny.
If mary is either not happy or quiet then someone is not rich.
If lucy is not strong or patient then someone is either not quiet or not patient and vice versa.
Everyone who is not old or curious is both rich and wise and vice versa.
If someone is either not quiet or curious then someone is either not curious or not brave and vice versa.
Everyone who is not kind or quiet is both not brave and not kind and vice versa.
John is either not wise or not patient.
Someone is either not wise or funny.
Alice is strong or creative.
Someone is either not happy or kind.
Mary is curious or not tall.
Fred is either not quiet or funny.
Someone is both not strong and curious. | Mary is not calm. | contradiction | ((?[X]:((old(X)&~kind(X))))=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((~calm(X)<~>happy(X))<=>(~patient(X)|happy(X))))&
(![X]:((tall(X)|happy(X))<=>(patient(X)<~>quiet(X))))&
((~generous(susan))<=>(?[X]:((rich(X)&brave(X)))))&
(![X]:((~rich(X)&~wise(X))=>(strong(X)<~>~calm(X))))&
(![X]:((tall(X)&humble(X))=>(humble(X)<~>~calm(X))))&
(![X]:((rich(X)<~>happy(X))=>(wise(X)&~creative(X))))&
(![X]:((old(X)<~>~calm(X))=>(~rich(X)&~tall(X))))&
(![X]:((kind(X)|~rich(X))<=>(calm(X)&brave(X))))&
(((~patient(lucy)&brave(lucy)))<=>(~patient(mary)))&
(((~generous(lucy)&~kind(lucy)))=>(funny(john)))&
(((~happy(mary)<~>quiet(mary)))=>(?[X]:(~rich(X))))&
(((~strong(lucy)|patient(lucy)))<=>(?[X]:((~quiet(X)<~>~patient(X)))))&
(![X]:((~old(X)|curious(X))<=>(rich(X)&wise(X))))&
((?[X]:((~quiet(X)<~>curious(X))))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((~kind(X)|quiet(X))<=>(~brave(X)&~kind(X))))&
((~wise(john)<~>~patient(john)))&
(?[X]:((~wise(X)<~>funny(X))))&
((strong(alice)|creative(alice)))&
(?[X]:((~happy(X)<~>kind(X))))&
((curious(mary)|~tall(mary)))&
((~quiet(fred)<~>funny(fred)))&
(?[X]:((~strong(X)&curious(X)))) | ~calm(mary) | [
"p1",
"p2",
"p8",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 460948358124001833845832
% SZS output start Proof for 460948358124001833845832
2. ! [X0] : ((~calm(X0) <~> happy(X0)) <=> (happy(X0) | ~patient(X0))) [input p1]
3. ! [X0] : ((happy(X0) | tall(X0)) <=> (patient(X0) <~> quiet(X0))) [input p2]
9. ! [X0] : ((~rich(X0) | kind(X0)) <=> (brave(X0) & calm(X0))) [input p8]
10. (brave(lucy) & ~patient(lucy)) <=> ~patient(mary) [input p9]
16. ! [X0] : ((quiet(X0) | ~kind(X0)) <=> (~kind(X0) & ~brave(X0))) [input p15]
24. ~calm(mary) [input hypothesis]
40. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [nnf transformation 2]
41. ! [X0] : ((((~happy(X0) | calm(X0)) & (happy(X0) | ~calm(X0))) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | ((~calm(X0) | ~happy(X0)) & (happy(X0) | calm(X0))))) [flattening 40]
42. ! [X0] : (((happy(X0) | tall(X0)) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~happy(X0) & ~tall(X0)))) [nnf transformation 3]
43. ! [X0] : ((happy(X0) | tall(X0) | ((patient(X0) | ~quiet(X0)) & (quiet(X0) | ~patient(X0)))) & (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~happy(X0) & ~tall(X0)))) [flattening 42]
52. ! [X0] : (((~rich(X0) | kind(X0)) | (~brave(X0) | ~calm(X0))) & ((brave(X0) & calm(X0)) | (rich(X0) & ~kind(X0)))) [nnf transformation 9]
53. ! [X0] : ((~rich(X0) | kind(X0) | ~brave(X0) | ~calm(X0)) & ((brave(X0) & calm(X0)) | (rich(X0) & ~kind(X0)))) [flattening 52]
54. ((brave(lucy) & ~patient(lucy)) | patient(mary)) & (~patient(mary) | (~brave(lucy) | patient(lucy))) [nnf transformation 10]
55. ((brave(lucy) & ~patient(lucy)) | patient(mary)) & (~patient(mary) | ~brave(lucy) | patient(lucy)) [flattening 54]
71. ! [X0] : (((quiet(X0) | ~kind(X0)) | (kind(X0) | brave(X0))) & ((~kind(X0) & ~brave(X0)) | (~quiet(X0) & kind(X0)))) [nnf transformation 16]
72. ! [X0] : ((quiet(X0) | ~kind(X0) | kind(X0) | brave(X0)) & ((~kind(X0) & ~brave(X0)) | (~quiet(X0) & kind(X0)))) [flattening 71]
84. happy(X0) | ~patient(X0) | happy(X0) | calm(X0) [cnf transformation 41]
86. ~calm(X0) | happy(X0) | patient(X0) [cnf transformation 41]
89. ~happy(X0) | calm(X0) | ~happy(X0) [cnf transformation 41]
91. ~happy(X0) | patient(X0) | quiet(X0) [cnf transformation 43]
111. ~kind(X0) | calm(X0) [cnf transformation 53]
117. ~patient(lucy) | patient(mary) [cnf transformation 55]
118. brave(lucy) | patient(mary) [cnf transformation 55]
141. ~brave(X0) | kind(X0) [cnf transformation 72]
142. ~brave(X0) | ~quiet(X0) [cnf transformation 72]
158. ~calm(mary) [cnf transformation 24]
160. happy(X0) | ~patient(X0) | calm(X0) [duplicate literal removal 84]
161. ~happy(X0) | calm(X0) [duplicate literal removal 89]
174. ~patient(X0) | calm(X0) [subsumption resolution 160,161]
194. 8 <=> patient(mary) [avatar definition]
196. patient(mary) <- (8) [avatar component clause 194]
198. 9 <=> brave(lucy) [avatar definition]
200. brave(lucy) <- (9) [avatar component clause 198]
201. 8 | 9 [avatar split clause 118,198,194]
203. 10 <=> patient(lucy) [avatar definition]
205. ~patient(lucy) <- (~10) [avatar component clause 203]
206. 8 | ~10 [avatar split clause 117,203,194]
213. 12 <=> kind(lucy) [avatar definition]
215. kind(lucy) <- (12) [avatar component clause 213]
364. calm(mary) <- (8) [resolution 174,196]
365. $false <- (8) [subsumption resolution 364,158]
366. ~8 [avatar contradiction clause 365]
367. ~quiet(lucy) <- (9) [resolution 200,142]
368. kind(lucy) <- (9) [resolution 200,141]
369. 12 | ~9 [avatar split clause 368,198,213]
371. calm(lucy) <- (12) [resolution 215,111]
376. happy(lucy) | patient(lucy) <- (12) [resolution 86,371]
377. happy(lucy) <- (~10, 12) [subsumption resolution 376,205]
379. patient(lucy) | quiet(lucy) <- (~10, 12) [resolution 91,377]
380. quiet(lucy) <- (~10, 12) [subsumption resolution 379,205]
381. $false <- (9, ~10, 12) [subsumption resolution 380,367]
382. ~9 | 10 | ~12 [avatar contradiction clause 381]
383. $false [avatar sat refutation 201,206,366,369,382]
% SZS output end Proof for 460948358124001833845832
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either kind or not curious then someone is creative or patient.
Everyone who is either not creative or rich is brave or not wise and vice versa.
If susan is funny or happy then john is either not strong or not rich and vice versa.
Everyone who is either not funny or calm is not brave or rich and vice versa.
Everyone who is not calm is funny or brave and vice versa.
Everyone who is not patient is either rich or not curious.
Everyone who is not quiet is generous or not generous.
If alice is rich or not patient then someone is not funny or not patient and vice versa.
Everyone who is not strong or creative is wise and vice versa.
Everyone who is creative is not old.
If fred is quiet or not funny then alice is both wise and not happy.
Everyone who is either not wise or not tall is either patient or not strong.
Everyone who is not brave is not wise and vice versa.
If paul is not wise or happy then someone is not quiet and vice versa.
Everyone who is either not kind or funny is both funny and not tall and vice versa.
Everyone who is kind or patient is either not rich or wise.
Susan is both wise and not curious.
Someone is tall.
Paul is both happy and not rich.
Someone is not happy.
Mary is not generous.
Someone is not wise or old.
John is either brave or not quiet.
Someone is either calm or tall. | Fred is wise. | entailment | (((kind(paul)<~>~curious(paul)))=>(?[X]:((creative(X)|patient(X)))))&
(![X]:((~creative(X)<~>rich(X))<=>(brave(X)|~wise(X))))&
(((funny(susan)|happy(susan)))<=>((~strong(john)<~>~rich(john))))&
(![X]:((~funny(X)<~>calm(X))<=>(~brave(X)|rich(X))))&
(![X]:(~calm(X)<=>(funny(X)|brave(X))))&
(![X]:(~patient(X)=>(rich(X)<~>~curious(X))))&
(![X]:(~quiet(X)=>(generous(X)|~generous(X))))&
(((rich(alice)|~patient(alice)))<=>(?[X]:((~funny(X)|~patient(X)))))&
(![X]:((~strong(X)|creative(X))<=>wise(X)))&
(![X]:(creative(X)=>~old(X)))&
(((quiet(fred)|~funny(fred)))=>((wise(alice)&~happy(alice))))&
(![X]:((~wise(X)<~>~tall(X))=>(patient(X)<~>~strong(X))))&
(![X]:(~brave(X)<=>~wise(X)))&
(((~wise(paul)|happy(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(funny(X)&~tall(X))))&
(![X]:((kind(X)|patient(X))=>(~rich(X)<~>wise(X))))&
((wise(susan)&~curious(susan)))&
(?[X]:(tall(X)))&
((happy(paul)&~rich(paul)))&
(?[X]:(~happy(X)))&
(~generous(mary))&
(?[X]:((~wise(X)|old(X))))&
((brave(john)<~>~quiet(john)))&
(?[X]:((calm(X)<~>tall(X)))) | wise(fred) | [
"p3",
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1814679499370692630911117
% SZS output start Proof for 1814679499370692630911117
4. ! [X0] : ((~funny(X0) <~> calm(X0)) <=> (rich(X0) | ~brave(X0))) [input p3]
5. ! [X0] : (~calm(X0) <=> (brave(X0) | funny(X0))) [input p4]
13. ! [X0] : (~brave(X0) <=> ~wise(X0)) [input p12]
25. ~wise(fred) [input hypothesis]
41. ! [X0] : ((((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~rich(X0) & brave(X0))) & ((rich(X0) | ~brave(X0)) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0))))) [nnf transformation 4]
42. ! [X0] : ((((~calm(X0) | funny(X0)) & (calm(X0) | ~funny(X0))) | (~rich(X0) & brave(X0))) & (rich(X0) | ~brave(X0) | ((~funny(X0) | ~calm(X0)) & (calm(X0) | funny(X0))))) [flattening 41]
43. ! [X0] : ((~calm(X0) | (~brave(X0) & ~funny(X0))) & ((brave(X0) | funny(X0)) | calm(X0))) [nnf transformation 5]
44. ! [X0] : ((~calm(X0) | (~brave(X0) & ~funny(X0))) & (brave(X0) | funny(X0) | calm(X0))) [flattening 43]
54. ! [X0] : ((~brave(X0) | wise(X0)) & (~wise(X0) | brave(X0))) [nnf transformation 13]
89. ~funny(X0) | calm(X0) | brave(X0) [cnf transformation 42]
91. ~calm(X0) | funny(X0) | brave(X0) [cnf transformation 42]
93. brave(X0) | funny(X0) | calm(X0) [cnf transformation 44]
94. ~calm(X0) | ~funny(X0) [cnf transformation 44]
116. ~brave(X0) | wise(X0) [cnf transformation 54]
142. ~wise(fred) [cnf transformation 25]
185. calm(X0) | brave(X0) [subsumption resolution 93,89]
294. brave(X1) | ~funny(X1) [resolution 185,94]
334. funny(X0) | brave(X0) | brave(X0) [resolution 91,185]
335. funny(X0) | brave(X0) [duplicate literal removal 334]
339. brave(X0) [subsumption resolution 335,294]
343. wise(X2) [resolution 339,116]
345. $false [resolution 343,142]
% SZS output end Proof for 1814679499370692630911117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not rich is both not brave and humble and vice versa.
Everyone who is tall or not curious is old.
If paul is not curious then someone is not strong.
Everyone who is generous is either quiet or not wise and vice versa.
Everyone who is either brave or quiet is either quiet or not calm.
Everyone who is not creative or old is both generous and creative.
If someone is both curious and rich then susan is not curious or not humble.
Everyone who is both not rich and patient is not calm or not curious.
Everyone who is funny is both not generous and not quiet and vice versa.
Everyone who is tall is curious or happy and vice versa.
Everyone who is kind or not creative is either happy or curious.
Everyone who is brave or funny is either creative or humble.
Everyone who is either generous or not tall is both not creative and not happy and vice versa.
If someone is either not rich or not kind then someone is both not happy and not old.
Paul is not quiet.
John is not quiet or not rich.
Paul is old or not humble.
Alice is both not curious and strong. | John is wise. | neutral | (![X]:((brave(X)|~rich(X))<=>(~brave(X)&humble(X))))&
(![X]:((tall(X)|~curious(X))=>old(X)))&
((~curious(paul))=>(?[X]:(~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~wise(X))))&
(![X]:((brave(X)<~>quiet(X))=>(quiet(X)<~>~calm(X))))&
(![X]:((~creative(X)|old(X))=>(generous(X)&creative(X))))&
((?[X]:((curious(X)&rich(X))))=>((~curious(susan)|~humble(susan))))&
(![X]:((~rich(X)&patient(X))=>(~calm(X)|~curious(X))))&
(![X]:(funny(X)<=>(~generous(X)&~quiet(X))))&
(![X]:(tall(X)<=>(curious(X)|happy(X))))&
(![X]:((kind(X)|~creative(X))=>(happy(X)<~>curious(X))))&
(![X]:((brave(X)|funny(X))=>(creative(X)<~>humble(X))))&
(![X]:((generous(X)<~>~tall(X))<=>(~creative(X)&~happy(X))))&
((?[X]:((~rich(X)<~>~kind(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(~quiet(paul))&
((~quiet(john)|~rich(john)))&
((old(paul)|~humble(paul)))&
((~curious(alice)&strong(alice))) | wise(john) | [] | null | 0 |
Everyone who is both not calm and creative is either not quiet or not tall and vice versa. If someone is not curious or not generous then john is not tall or not quiet and vice versa. Everyone who is either not kind or not funny is curious or wise and vice versa. If someone is not creative then someone is both kind and wise and vice versa. If fred is both not kind and not rich then someone is not curious and vice versa. Everyone who is rich or not wise is not brave and vice versa. Everyone who is not creative or old is both wise and not kind. Everyone who is both not calm and creative is not quiet or generous and vice versa. Everyone who is both wise and patient is brave or not happy and vice versa. If fred is brave or not rich then someone is tall and vice versa. If someone is generous or happy then lucy is not creative or not generous. Everyone who is both not creative and humble is both not old and curious and vice versa. If someone is not happy or not kind then john is both generous and not quiet. Everyone who is not wise is not patient or happy. Everyone who is curious or not strong is either not old or wise. Everyone who is wise or not wise is both not curious and not wise. Mary is both not kind and calm. Someone is generous. Someone is old or rich. Alice is both not curious and not strong. John is creative or wise. Lucy is not quiet or not wise. John is either not kind or not humble. | John is tall. | entailment | (![X]:((~calm(X)&creative(X))<=>(~quiet(X)<~>~tall(X))))&
((?[X]:((~curious(X)|~generous(X))))<=>((~tall(john)|~quiet(john))))&
(![X]:((~kind(X)<~>~funny(X))<=>(curious(X)|wise(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((kind(X)&wise(X)))))&
(((~kind(fred)&~rich(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((rich(X)|~wise(X))<=>~brave(X)))&
(![X]:((~creative(X)|old(X))=>(wise(X)&~kind(X))))&
(![X]:((~calm(X)&creative(X))<=>(~quiet(X)|generous(X))))&
(![X]:((wise(X)&patient(X))<=>(brave(X)|~happy(X))))&
(((brave(fred)|~rich(fred)))<=>(?[X]:(tall(X))))&
((?[X]:((generous(X)|happy(X))))=>((~creative(lucy)|~generous(lucy))))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
((~kind(mary)&calm(mary)))&
(?[X]:(generous(X)))&
(?[X]:((old(X)|rich(X))))&
((~curious(alice)&~strong(alice)))&
((creative(john)|wise(john)))&
((~quiet(lucy)|~wise(lucy)))&
((~kind(john)<~>~humble(john))) | tall(john) | [
"p0",
"p4",
"p6",
"p7",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6408114623481558794421316
% SZS output start Proof for 6408114623481558794421316
1. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (~quiet(X0) <~> ~tall(X0))) [input p0]
5. (~rich(fred) & ~kind(fred)) <=> ? [X0] : ~curious(X0) [input p4]
7. ! [X0] : ((old(X0) | ~creative(X0)) => (~kind(X0) & wise(X0))) [input p6]
8. ! [X0] : ((creative(X0) & ~calm(X0)) <=> (generous(X0) | ~quiet(X0))) [input p7]
13. ? [X0] : (~kind(X0) | ~happy(X0)) => (~quiet(john) & generous(john)) [input p12]
16. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p15]
24. ~tall(john) [input hypothesis]
26. ! [X0] : ((~kind(X0) & wise(X0)) | (~old(X0) & creative(X0))) [ennf transformation 7]
29. (~quiet(john) & generous(john)) | ! [X0] : (kind(X0) & happy(X0)) [ennf transformation 13]
33. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 16]
34. ! [X0] : (((creative(X0) & ~calm(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | (~creative(X0) | calm(X0)))) [nnf transformation 1]
35. ! [X0] : (((creative(X0) & ~calm(X0)) | ((~quiet(X0) | tall(X0)) & (~tall(X0) | quiet(X0)))) & (((tall(X0) | quiet(X0)) & (~tall(X0) | ~quiet(X0))) | ~creative(X0) | calm(X0))) [flattening 34]
48. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | (rich(fred) | kind(fred))) [nnf transformation 5]
49. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (? [X0] : ~curious(X0) | rich(fred) | kind(fred)) [flattening 48]
50. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (? [X1] : ~curious(X1) | rich(fred) | kind(fred)) [rectify 49]
51. ? [X1] : ~curious(X1) => ~curious(sK3) [choice axiom]
52. ((~rich(fred) & ~kind(fred)) | ! [X0] : curious(X0)) & (~curious(sK3) | rich(fred) | kind(fred)) [skolemisation 50,51]
55. ! [X0] : (((creative(X0) & ~calm(X0)) | (~generous(X0) & quiet(X0))) & ((generous(X0) | ~quiet(X0)) | (~creative(X0) | calm(X0)))) [nnf transformation 8]
56. ! [X0] : (((creative(X0) & ~calm(X0)) | (~generous(X0) & quiet(X0))) & (generous(X0) | ~quiet(X0) | ~creative(X0) | calm(X0))) [flattening 55]
73. ~creative(X0) | quiet(X0) | tall(X0) | calm(X0) [cnf transformation 35]
92. ~kind(fred) | curious(X0) [cnf transformation 52]
97. wise(X0) | creative(X0) [cnf transformation 26]
102. ~calm(X0) | quiet(X0) [cnf transformation 56]
123. ~quiet(john) | kind(X0) [cnf transformation 29]
130. ~curious(X0) | wise(X0) [cnf transformation 33]
131. ~wise(X0) | ~wise(X0) [cnf transformation 33]
143. ~tall(john) [cnf transformation 24]
144. ~wise(X0) [duplicate literal removal 131]
146. 1 <=> quiet(john) [avatar definition]
147. ~quiet(john) <- (~1) [avatar component clause 146]
159. 4 <=> tall(john) [avatar definition]
160. ~tall(john) <- (~4) [avatar component clause 159]
168. 6 <=> ! [X1] : curious(X1) [avatar definition]
169. curious(X1) <- (6) [avatar component clause 168]
180. 9 <=> ! [X3] : creative(X3) [avatar definition]
181. creative(X3) <- (9) [avatar component clause 180]
198. 13 <=> kind(fred) [avatar definition]
200. ~kind(fred) <- (~13) [avatar component clause 198]
201. 6 | ~13 [avatar split clause 92,198,168]
237. 21 <=> ! [X0] : kind(X0) [avatar definition]
238. kind(X0) <- (21) [avatar component clause 237]
239. 21 | ~1 [avatar split clause 123,146,237]
250. ~curious(X0) [subsumption resolution 130,144]
270. ~4 [avatar split clause 143,159]
273. $false <- (6) [subsumption resolution 169,250]
274. ~6 [avatar contradiction clause 273]
277. $false <- (~13, 21) [subsumption resolution 200,238]
278. 13 | ~21 [avatar contradiction clause 277]
279. creative(X0) [resolution 97,144]
318. quiet(X0) | tall(X0) | calm(X0) <- (9) [resolution 73,181]
319. tall(X0) | quiet(X0) <- (9) [subsumption resolution 318,102]
320. quiet(john) <- (~4, 9) [resolution 319,160]
326. $false <- (~1, ~4, 9) [subsumption resolution 320,147]
327. 1 | 4 | ~9 [avatar contradiction clause 326]
329. 9 [avatar split clause 279,180]
332. $false [avatar sat refutation 201,239,270,274,278,327,329]
% SZS output end Proof for 6408114623481558794421316
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is both patient and not creative. If someone is both not funny and not patient then alice is rich or not quiet and vice versa. If someone is not calm or not tall then mary is both brave and tall. If susan is either rich or brave then lucy is humble or not brave and vice versa. Everyone who is either rich or not tall is not strong or not brave and vice versa. If someone is not creative then someone is curious or not quiet and vice versa. If someone is humble then someone is not strong or funny and vice versa. If fred is not wise then someone is either not wise or not old. If susan is strong or not curious then susan is both not funny and not quiet and vice versa. If someone is both happy and patient then mary is both strong and not wise. Everyone who is either not generous or not tall is both creative and not generous. If someone is both calm and not humble then someone is either not old or not quiet and vice versa. Everyone who is curious or generous is both quiet and not calm. Everyone who is rich or wise is either not old or happy. Everyone who is either not kind or not strong is both brave and not calm. If someone is kind or not happy then alice is both not happy and creative. Someone is not funny. Someone is funny. Someone is not generous. Fred is kind or not happy. Someone is both not creative and strong. John is not tall. Someone is happy or funny. Someone is both patient and not calm. | Mary is brave. | entailment | (![X]:(strong(X)=>(patient(X)&~creative(X))))&
((?[X]:((~funny(X)&~patient(X))))<=>((rich(alice)|~quiet(alice))))&
((?[X]:((~calm(X)|~tall(X))))=>((brave(mary)&tall(mary))))&
(((rich(susan)<~>brave(susan)))<=>((humble(lucy)|~brave(lucy))))&
(![X]:((rich(X)<~>~tall(X))<=>(~strong(X)|~brave(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((curious(X)|~quiet(X)))))&
((?[X]:(humble(X)))<=>(?[X]:((~strong(X)|funny(X)))))&
((~wise(fred))=>(?[X]:((~wise(X)<~>~old(X)))))&
(((strong(susan)|~curious(susan)))<=>((~funny(susan)&~quiet(susan))))&
((?[X]:((happy(X)&patient(X))))=>((strong(mary)&~wise(mary))))&
(![X]:((~generous(X)<~>~tall(X))=>(creative(X)&~generous(X))))&
((?[X]:((calm(X)&~humble(X))))<=>(?[X]:((~old(X)<~>~quiet(X)))))&
(![X]:((curious(X)|generous(X))=>(quiet(X)&~calm(X))))&
(![X]:((rich(X)|wise(X))=>(~old(X)<~>happy(X))))&
(![X]:((~kind(X)<~>~strong(X))=>(brave(X)&~calm(X))))&
((?[X]:((kind(X)|~happy(X))))=>((~happy(alice)&creative(alice))))&
(?[X]:(~funny(X)))&
(?[X]:(funny(X)))&
(?[X]:(~generous(X)))&
((kind(fred)|~happy(fred)))&
(?[X]:((~creative(X)&strong(X))))&
(~tall(john))&
(?[X]:((happy(X)|funny(X))))&
(?[X]:((patient(X)&~calm(X)))) | brave(mary) | [
"p2",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1590461584229672631279136
% SZS output start Proof for 1590461584229672631279136
3. ? [X0] : (~tall(X0) | ~calm(X0)) => (tall(mary) & brave(mary)) [input p2]
22. ~tall(john) [input p21]
25. ~brave(mary) [input hypothesis]
30. (tall(mary) & brave(mary)) | ! [X0] : (tall(X0) & calm(X0)) [ennf transformation 3]
90. brave(mary) | tall(X0) [cnf transformation 30]
152. ~tall(john) [cnf transformation 22]
156. ~brave(mary) [cnf transformation 25]
183. 6 <=> ! [X0] : tall(X0) [avatar definition]
184. tall(X0) <- (6) [avatar component clause 183]
195. 9 <=> brave(mary) [avatar definition]
198. 6 | 9 [avatar split clause 90,195,183]
385. ~9 [avatar split clause 156,195]
386. $false <- (6) [resolution 184,152]
387. ~6 [avatar contradiction clause 386]
388. $false [avatar sat refutation 198,385,387]
% SZS output end Proof for 1590461584229672631279136
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is either kind or humble and vice versa.
Everyone who is either not tall or rich is not wise or humble and vice versa.
Everyone who is creative or calm is funny.
Everyone who is brave or not strong is either not patient or kind.
If john is not tall or strong then alice is both wise and brave.
Everyone who is both not funny and patient is both quiet and kind.
If someone is either not patient or not calm then mary is either quiet or not patient and vice versa.
If someone is both not brave and not generous then mary is patient and vice versa.
Everyone who is not patient is not funny or curious and vice versa.
Everyone who is not funny or tall is not rich and vice versa.
If someone is not humble then alice is both happy and not brave.
Everyone who is happy or patient is rich.
If mary is not tall then someone is happy and vice versa.
Everyone who is both patient and not quiet is either creative or calm.
If someone is either kind or not calm then mary is not creative.
If someone is both not funny and not quiet then mary is either not kind or kind.
Someone is either curious or not calm.
Someone is either rich or strong.
Someone is both not quiet and not generous.
Someone is both not curious and happy.
Fred is either not calm or not strong.
Susan is either calm or happy.
Fred is not kind.
Lucy is humble. | Alice is wise. | entailment | (![X]:(~old(X)<=>(kind(X)<~>humble(X))))&
(![X]:((~tall(X)<~>rich(X))<=>(~wise(X)|humble(X))))&
(![X]:((creative(X)|calm(X))=>funny(X)))&
(![X]:((brave(X)|~strong(X))=>(~patient(X)<~>kind(X))))&
(((~tall(john)|strong(john)))=>((wise(alice)&brave(alice))))&
(![X]:((~funny(X)&patient(X))=>(quiet(X)&kind(X))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>((quiet(mary)<~>~patient(mary))))&
((?[X]:((~brave(X)&~generous(X))))<=>(patient(mary)))&
(![X]:(~patient(X)<=>(~funny(X)|curious(X))))&
(![X]:((~funny(X)|tall(X))<=>~rich(X)))&
((?[X]:(~humble(X)))=>((happy(alice)&~brave(alice))))&
(![X]:((happy(X)|patient(X))=>rich(X)))&
((~tall(mary))<=>(?[X]:(happy(X))))&
(![X]:((patient(X)&~quiet(X))=>(creative(X)<~>calm(X))))&
((?[X]:((kind(X)<~>~calm(X))))=>(~creative(mary)))&
((?[X]:((~funny(X)&~quiet(X))))=>((~kind(mary)<~>kind(mary))))&
(?[X]:((curious(X)<~>~calm(X))))&
(?[X]:((rich(X)<~>strong(X))))&
(?[X]:((~quiet(X)&~generous(X))))&
(?[X]:((~curious(X)&happy(X))))&
((~calm(fred)<~>~strong(fred)))&
((calm(susan)<~>happy(susan)))&
(~kind(fred))&
(humble(lucy)) | wise(alice) | [
"p1",
"p4",
"p9",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4178213725119127969206600
% SZS output start Proof for 4178213725119127969206600
2. ! [X0] : ((~tall(X0) <~> rich(X0)) <=> (humble(X0) | ~wise(X0))) [input p1]
5. (strong(john) | ~tall(john)) => (brave(alice) & wise(alice)) [input p4]
10. ! [X0] : ((tall(X0) | ~funny(X0)) <=> ~rich(X0)) [input p9]
11. ? [X0] : ~humble(X0) => (~brave(alice) & happy(alice)) [input p10]
12. ! [X0] : ((patient(X0) | happy(X0)) => rich(X0)) [input p11]
25. ~wise(alice) [input hypothesis]
28. (brave(alice) & wise(alice)) | (~strong(john) & tall(john)) [ennf transformation 5]
31. (~brave(alice) & happy(alice)) | ! [X0] : humble(X0) [ennf transformation 11]
32. ! [X0] : (rich(X0) | (~patient(X0) & ~happy(X0))) [ennf transformation 12]
37. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~humble(X0) & wise(X0))) & ((humble(X0) | ~wise(X0)) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~rich(X0) | tall(X0)) & (rich(X0) | ~tall(X0))) | (~humble(X0) & wise(X0))) & (humble(X0) | ~wise(X0) | ((~tall(X0) | ~rich(X0)) & (rich(X0) | tall(X0))))) [flattening 37]
50. ! [X0] : (((tall(X0) | ~funny(X0)) | rich(X0)) & (~rich(X0) | (~tall(X0) & funny(X0)))) [nnf transformation 10]
51. ! [X0] : ((tall(X0) | ~funny(X0) | rich(X0)) & (~rich(X0) | (~tall(X0) & funny(X0)))) [flattening 50]
74. ~tall(X0) | rich(X0) | ~humble(X0) [cnf transformation 38]
75. ~rich(X0) | tall(X0) | wise(X0) [cnf transformation 38]
83. wise(alice) | tall(john) [cnf transformation 28]
104. ~rich(X0) | ~tall(X0) [cnf transformation 51]
106. happy(alice) | humble(X0) [cnf transformation 31]
108. ~happy(X0) | rich(X0) [cnf transformation 32]
132. ~wise(alice) [cnf transformation 25]
143. 3 <=> tall(john) [avatar definition]
145. tall(john) <- (3) [avatar component clause 143]
148. 4 <=> wise(alice) [avatar definition]
149. ~wise(alice) <- (~4) [avatar component clause 148]
152. 3 | 4 [avatar split clause 83,148,143]
198. 14 <=> ! [X0] : humble(X0) [avatar definition]
199. humble(X0) <- (14) [avatar component clause 198]
202. 15 <=> happy(alice) [avatar definition]
204. happy(alice) <- (15) [avatar component clause 202]
205. 14 | 15 [avatar split clause 106,202,198]
271. ~4 [avatar split clause 132,148]
292. 31 <=> rich(john) [avatar definition]
294. rich(john) <- (31) [avatar component clause 292]
298. rich(john) | ~humble(john) <- (3) [resolution 74,145]
299. rich(john) <- (3, 14) [subsumption resolution 298,199]
300. 31 | ~3 | ~14 [avatar split clause 299,198,143,292]
306. rich(alice) <- (15) [resolution 204,108]
356. tall(alice) | wise(alice) <- (15) [resolution 306,75]
357. ~tall(alice) <- (15) [resolution 306,104]
364. 39 <=> tall(alice) [avatar definition]
368. tall(alice) <- (~4, 15) [subsumption resolution 356,149]
369. 39 | 4 | ~15 [avatar split clause 368,202,148,364]
370. ~39 | ~15 [avatar split clause 357,202,364]
383. ~tall(john) <- (31) [resolution 294,104]
385. $false <- (3, 31) [subsumption resolution 383,145]
386. ~3 | ~31 [avatar contradiction clause 385]
387. $false [avatar sat refutation 152,205,271,300,369,370,386]
% SZS output end Proof for 4178213725119127969206600
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and not old then john is either brave or old.
Everyone who is quiet is both not generous and not patient.
If mary is strong then susan is not curious or quiet and vice versa.
Everyone who is not kind is calm.
If john is both brave and not quiet then lucy is not curious.
Everyone who is not old or humble is not generous and vice versa.
Everyone who is both not strong and kind is calm.
If someone is not humble then john is kind or not rich and vice versa.
If someone is happy or not humble then someone is both not humble and not quiet.
Everyone who is either happy or not rich is not brave or not patient and vice versa.
If lucy is old or not happy then someone is happy and vice versa.
Everyone who is both not brave and not generous is not brave or curious.
If someone is wise then susan is happy and vice versa.
Everyone who is either kind or not generous is not quiet and vice versa.
Everyone who is calm is not kind or not generous and vice versa.
If mary is calm or not old then someone is tall or not curious.
Someone is either wise or happy.
Someone is either not brave or not tall.
Lucy is not creative.
Susan is either happy or strong.
Someone is both funny and not generous.
Someone is both creative and calm.
Someone is both not wise and creative.
Someone is either not generous or creative. | Susan is curious. | neutral | ((?[X]:((curious(X)&~old(X))))=>((brave(john)<~>old(john))))&
(![X]:(quiet(X)=>(~generous(X)&~patient(X))))&
((strong(mary))<=>((~curious(susan)|quiet(susan))))&
(![X]:(~kind(X)=>calm(X)))&
(((brave(john)&~quiet(john)))=>(~curious(lucy)))&
(![X]:((~old(X)|humble(X))<=>~generous(X)))&
(![X]:((~strong(X)&kind(X))=>calm(X)))&
((?[X]:(~humble(X)))<=>((kind(john)|~rich(john))))&
((?[X]:((happy(X)|~humble(X))))=>(?[X]:((~humble(X)&~quiet(X)))))&
(![X]:((happy(X)<~>~rich(X))<=>(~brave(X)|~patient(X))))&
(((old(lucy)|~happy(lucy)))<=>(?[X]:(happy(X))))&
(![X]:((~brave(X)&~generous(X))=>(~brave(X)|curious(X))))&
((?[X]:(wise(X)))<=>(happy(susan)))&
(![X]:((kind(X)<~>~generous(X))<=>~quiet(X)))&
(![X]:(calm(X)<=>(~kind(X)|~generous(X))))&
(((calm(mary)|~old(mary)))=>(?[X]:((tall(X)|~curious(X)))))&
(?[X]:((wise(X)<~>happy(X))))&
(?[X]:((~brave(X)<~>~tall(X))))&
(~creative(lucy))&
((happy(susan)<~>strong(susan)))&
(?[X]:((funny(X)&~generous(X))))&
(?[X]:((creative(X)&calm(X))))&
(?[X]:((~wise(X)&creative(X))))&
(?[X]:((~generous(X)<~>creative(X)))) | curious(susan) | [] | null | 0 |
Everyone who is funny is not creative or not kind and vice versa.
Everyone who is either strong or not wise is both not patient and old and vice versa.
If mary is both generous and not brave then paul is not calm or not tall and vice versa.
Everyone who is both not funny and creative is either patient or old.
If fred is quiet then john is not happy and vice versa.
Everyone who is either not calm or wise is tall.
Everyone who is either not generous or tall is not kind.
Everyone who is both generous and not quiet is either generous or not funny.
If mary is both quiet and humble then alice is both not humble and happy and vice versa.
Everyone who is either not patient or happy is not creative.
If alice is both not tall and creative then someone is creative or calm.
Everyone who is either wise or creative is quiet or not creative and vice versa.
Everyone who is either wise or curious is either happy or not funny and vice versa.
If someone is not old then paul is both not patient and not wise and vice versa.
If someone is both not happy and humble then someone is not funny and vice versa.
If john is not kind or tall then someone is both not curious and humble.
Susan is either not curious or not strong.
Someone is not calm or old.
Alice is not rich.
Someone is patient or not kind.
Lucy is both not patient and happy.
John is both not funny and wise.
Someone is either brave or not creative.
Mary is both not patient and not old. | Fred is not generous. | neutral | (![X]:(funny(X)<=>(~creative(X)|~kind(X))))&
(![X]:((strong(X)<~>~wise(X))<=>(~patient(X)&old(X))))&
(((generous(mary)&~brave(mary)))<=>((~calm(paul)|~tall(paul))))&
(![X]:((~funny(X)&creative(X))=>(patient(X)<~>old(X))))&
((quiet(fred))<=>(~happy(john)))&
(![X]:((~calm(X)<~>wise(X))=>tall(X)))&
(![X]:((~generous(X)<~>tall(X))=>~kind(X)))&
(![X]:((generous(X)&~quiet(X))=>(generous(X)<~>~funny(X))))&
(((quiet(mary)&humble(mary)))<=>((~humble(alice)&happy(alice))))&
(![X]:((~patient(X)<~>happy(X))=>~creative(X)))&
(((~tall(alice)&creative(alice)))=>(?[X]:((creative(X)|calm(X)))))&
(![X]:((wise(X)<~>creative(X))<=>(quiet(X)|~creative(X))))&
(![X]:((wise(X)<~>curious(X))<=>(happy(X)<~>~funny(X))))&
((?[X]:(~old(X)))<=>((~patient(paul)&~wise(paul))))&
((?[X]:((~happy(X)&humble(X))))<=>(?[X]:(~funny(X))))&
(((~kind(john)|tall(john)))=>(?[X]:((~curious(X)&humble(X)))))&
((~curious(susan)<~>~strong(susan)))&
(?[X]:((~calm(X)|old(X))))&
(~rich(alice))&
(?[X]:((patient(X)|~kind(X))))&
((~patient(lucy)&happy(lucy)))&
((~funny(john)&wise(john)))&
(?[X]:((brave(X)<~>~creative(X))))&
((~patient(mary)&~old(mary))) | ~generous(fred) | [] | null | 0 |
If someone is either wise or creative then paul is both not humble and rich.
Everyone who is either quiet or not tall is both kind and humble and vice versa.
Everyone who is both humble and not funny is both wise and not rich.
Everyone who is rich is both not strong and not quiet and vice versa.
Everyone who is not rich or not curious is not old or not patient.
If someone is both not kind and not strong then mary is not brave.
Everyone who is either not quiet or not tall is generous or happy.
Everyone who is both not curious and not patient is either tall or not creative.
Everyone who is both not brave and not funny is either tall or not generous and vice versa.
If mary is both curious and calm then someone is calm and vice versa.
Everyone who is both not strong and rich is either brave or not rich and vice versa.
If someone is either happy or humble then john is not rich or not calm.
Everyone who is patient or curious is both not wise and old and vice versa.
If someone is creative or quiet then mary is not humble or not strong and vice versa.
Everyone who is not generous or not kind is both patient and creative and vice versa.
Everyone who is both not calm and brave is not kind.
Fred is calm or old.
Mary is rich or not kind.
Paul is both strong and quiet.
Someone is not patient.
Someone is not old.
Alice is not happy or not creative.
Someone is funny or calm.
Someone is either tall or calm. | Paul is humble. | contradiction | ((?[X]:((wise(X)<~>creative(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((quiet(X)<~>~tall(X))<=>(kind(X)&humble(X))))&
(![X]:((humble(X)&~funny(X))=>(wise(X)&~rich(X))))&
(![X]:(rich(X)<=>(~strong(X)&~quiet(X))))&
(![X]:((~rich(X)|~curious(X))=>(~old(X)|~patient(X))))&
((?[X]:((~kind(X)&~strong(X))))=>(~brave(mary)))&
(![X]:((~quiet(X)<~>~tall(X))=>(generous(X)|happy(X))))&
(![X]:((~curious(X)&~patient(X))=>(tall(X)<~>~creative(X))))&
(![X]:((~brave(X)&~funny(X))<=>(tall(X)<~>~generous(X))))&
(((curious(mary)&calm(mary)))<=>(?[X]:(calm(X))))&
(![X]:((~strong(X)&rich(X))<=>(brave(X)<~>~rich(X))))&
((?[X]:((happy(X)<~>humble(X))))=>((~rich(john)|~calm(john))))&
(![X]:((patient(X)|curious(X))<=>(~wise(X)&old(X))))&
((?[X]:((creative(X)|quiet(X))))<=>((~humble(mary)|~strong(mary))))&
(![X]:((~generous(X)|~kind(X))<=>(patient(X)&creative(X))))&
(![X]:((~calm(X)&brave(X))=>~kind(X)))&
((calm(fred)|old(fred)))&
((rich(mary)|~kind(mary)))&
((strong(paul)&quiet(paul)))&
(?[X]:(~patient(X)))&
(?[X]:(~old(X)))&
((~happy(alice)|~creative(alice)))&
(?[X]:((funny(X)|calm(X))))&
(?[X]:((tall(X)<~>calm(X)))) | humble(paul) | [
"p1",
"p3",
"p4",
"p5",
"p8",
"p10",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7386761870892989030566408
% SZS output start Proof for 7386761870892989030566408
2. ! [X0] : ((quiet(X0) <~> ~tall(X0)) <=> (humble(X0) & kind(X0))) [input p1]
4. ! [X0] : (rich(X0) <=> (~quiet(X0) & ~strong(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | ~rich(X0)) => (~patient(X0) | ~old(X0))) [input p4]
6. ? [X0] : (~strong(X0) & ~kind(X0)) => ~brave(mary) [input p5]
9. ! [X0] : ((~funny(X0) & ~brave(X0)) <=> (tall(X0) <~> ~generous(X0))) [input p8]
11. ! [X0] : ((rich(X0) & ~strong(X0)) <=> (brave(X0) <~> ~rich(X0))) [input p10]
13. ! [X0] : ((curious(X0) | patient(X0)) <=> (old(X0) & ~wise(X0))) [input p12]
15. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (creative(X0) & patient(X0))) [input p14]
19. quiet(paul) & strong(paul) [input p18]
25. humble(paul) [input hypothesis]
29. ! [X0] : ((~patient(X0) | ~old(X0)) | (curious(X0) & rich(X0))) [ennf transformation 5]
30. ! [X0] : (~patient(X0) | ~old(X0) | (curious(X0) & rich(X0))) [flattening 29]
31. ~brave(mary) | ! [X0] : (strong(X0) | kind(X0)) [ennf transformation 6]
41. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | (~humble(X0) | ~kind(X0))) & ((humble(X0) & kind(X0)) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [nnf transformation 2]
42. ! [X0] : ((((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | ~humble(X0) | ~kind(X0)) & ((humble(X0) & kind(X0)) | ((quiet(X0) | tall(X0)) & (~tall(X0) | ~quiet(X0))))) [flattening 41]
43. ! [X0] : ((rich(X0) | (quiet(X0) | strong(X0))) & ((~quiet(X0) & ~strong(X0)) | ~rich(X0))) [nnf transformation 4]
44. ! [X0] : ((rich(X0) | quiet(X0) | strong(X0)) & ((~quiet(X0) & ~strong(X0)) | ~rich(X0))) [flattening 43]
47. ! [X0] : (((~funny(X0) & ~brave(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | (funny(X0) | brave(X0)))) [nnf transformation 9]
48. ! [X0] : (((~funny(X0) & ~brave(X0)) | ((tall(X0) | generous(X0)) & (~generous(X0) | ~tall(X0)))) & (((generous(X0) | ~tall(X0)) & (~generous(X0) | tall(X0))) | funny(X0) | brave(X0))) [flattening 47]
54. ! [X0] : (((rich(X0) & ~strong(X0)) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | (~rich(X0) | strong(X0)))) [nnf transformation 11]
55. ! [X0] : (((rich(X0) & ~strong(X0)) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0)))) & (((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ~rich(X0) | strong(X0))) [flattening 54]
57. ! [X0] : (((curious(X0) | patient(X0)) | (~old(X0) | wise(X0))) & ((old(X0) & ~wise(X0)) | (~curious(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((curious(X0) | patient(X0) | ~old(X0) | wise(X0)) & ((old(X0) & ~wise(X0)) | (~curious(X0) & ~patient(X0)))) [flattening 57]
64. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~creative(X0) | ~patient(X0))) & ((creative(X0) & patient(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 15]
65. ! [X0] : ((~kind(X0) | ~generous(X0) | ~creative(X0) | ~patient(X0)) & ((creative(X0) & patient(X0)) | (kind(X0) & generous(X0)))) [flattening 64]
84. ~kind(X0) | ~quiet(X0) | ~humble(X0) | tall(X0) [cnf transformation 42]
87. ~strong(X0) | ~rich(X0) [cnf transformation 44]
90. ~patient(X0) | ~old(X0) | rich(X0) [cnf transformation 30]
92. ~brave(mary) | strong(X0) | kind(X0) [cnf transformation 31]
99. ~generous(X0) | ~brave(X0) | ~tall(X0) [cnf transformation 48]
106. ~rich(X0) | brave(X0) | ~rich(X0) | strong(X0) [cnf transformation 55]
111. rich(X0) | brave(X0) | rich(X0) [cnf transformation 55]
116. ~patient(X0) | old(X0) [cnf transformation 58]
123. generous(X0) | patient(X0) [cnf transformation 65]
124. patient(X0) | kind(X0) [cnf transformation 65]
131. strong(paul) [cnf transformation 19]
132. quiet(paul) [cnf transformation 19]
139. humble(paul) [cnf transformation 25]
140. ~rich(X0) | brave(X0) | strong(X0) [duplicate literal removal 106]
141. brave(X0) | rich(X0) [duplicate literal removal 111]
146. 2 <=> rich(paul) [avatar definition]
147. ~rich(paul) <- (~2) [avatar component clause 146]
155. 4 <=> humble(paul) [avatar definition]
156. humble(paul) <- (4) [avatar component clause 155]
161. 5 <=> ! [X0] : (strong(X0) | kind(X0)) [avatar definition]
162. strong(X0) | kind(X0) <- (5) [avatar component clause 161]
164. 6 <=> brave(mary) [avatar definition]
166. ~brave(mary) <- (~6) [avatar component clause 164]
167. 5 | ~6 [avatar split clause 92,164,161]
186. brave(X0) | strong(X0) [subsumption resolution 140,141]
205. 15 <=> strong(mary) [avatar definition]
207. strong(mary) <- (15) [avatar component clause 205]
240. 23 <=> rich(mary) [avatar definition]
242. rich(mary) <- (23) [avatar component clause 240]
276. 4 [avatar split clause 139,155]
279. ~rich(paul) [resolution 87,131]
280. ~2 [avatar split clause 279,146]
285. old(X0) | kind(X0) [resolution 124,116]
288. rich(mary) <- (~6) [resolution 141,166]
289. 23 | 6 [avatar split clause 288,164,240]
300. strong(mary) <- (~6) [resolution 186,166]
301. 15 | 6 [avatar split clause 300,164,205]
302. ~rich(mary) <- (15) [resolution 207,87]
303. $false <- (15, 23) [subsumption resolution 302,242]
304. ~15 | ~23 [avatar contradiction clause 303]
305. ~rich(X0) | kind(X0) <- (5) [resolution 162,87]
340. ~old(X0) | rich(X0) | kind(X0) [resolution 90,124]
341. rich(X0) | kind(X0) [subsumption resolution 340,285]
342. kind(X0) <- (5) [subsumption resolution 341,305]
345. ~brave(X1) | ~tall(X1) | patient(X1) [resolution 99,123]
379. 40 <=> tall(paul) [avatar definition]
381. tall(paul) <- (40) [avatar component clause 379]
415. ~quiet(X0) | ~humble(X0) | tall(X0) <- (5) [resolution 84,342]
526. 59 <=> patient(paul) [avatar definition]
528. patient(paul) <- (59) [avatar component clause 526]
565. ~tall(X1) | patient(X1) | rich(X1) [resolution 345,141]
813. ~humble(paul) | tall(paul) <- (5) [resolution 415,132]
815. tall(paul) <- (4, 5) [subsumption resolution 813,156]
826. 40 | ~4 | ~5 [avatar split clause 815,161,155,379]
862. patient(paul) | rich(paul) <- (40) [resolution 565,381]
869. patient(paul) <- (~2, 40) [subsumption resolution 862,147]
870. 59 | 2 | ~40 [avatar split clause 869,379,146,526]
882. ~old(paul) | rich(paul) <- (59) [resolution 528,90]
883. old(paul) <- (59) [resolution 528,116]
886. 81 <=> old(paul) [avatar definition]
890. ~old(paul) <- (~2, 59) [subsumption resolution 882,147]
891. ~81 | 2 | ~59 [avatar split clause 890,526,146,886]
892. 81 | ~59 [avatar split clause 883,526,886]
895. $false [avatar sat refutation 167,276,280,289,301,304,826,870,891,892]
% SZS output end Proof for 7386761870892989030566408
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.041 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not creative then alice is not patient and vice versa.
Everyone who is tall is patient.
Everyone who is both not strong and not quiet is curious or not tall.
Everyone who is both not kind and not old is rich or not old and vice versa.
If someone is not happy then someone is both funny and strong and vice versa.
Everyone who is both rich and not old is either not funny or brave.
Everyone who is either kind or not kind is either brave or creative and vice versa.
If someone is quiet or not rich then john is either happy or not strong and vice versa.
Everyone who is not kind is both not wise and not kind.
Everyone who is both old and not brave is curious and vice versa.
If someone is not happy or not calm then john is not rich or not curious and vice versa.
If someone is either old or not creative then susan is strong.
If fred is either funny or not calm then someone is both generous and not funny.
Everyone who is humble is creative or not brave.
Everyone who is either not patient or funny is patient and vice versa.
Everyone who is not happy is not kind or strong and vice versa.
Mary is either not patient or not humble.
Paul is either not brave or kind.
Someone is humble.
Someone is not creative or rich.
Someone is either not kind or not calm.
Someone is humble or not kind.
Alice is both humble and not curious.
Paul is both creative and patient. | Paul is not rich. | entailment | ((~creative(alice))<=>(~patient(alice)))&
(![X]:(tall(X)=>patient(X)))&
(![X]:((~strong(X)&~quiet(X))=>(curious(X)|~tall(X))))&
(![X]:((~kind(X)&~old(X))<=>(rich(X)|~old(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((funny(X)&strong(X)))))&
(![X]:((rich(X)&~old(X))=>(~funny(X)<~>brave(X))))&
(![X]:((kind(X)<~>~kind(X))<=>(brave(X)<~>creative(X))))&
((?[X]:((quiet(X)|~rich(X))))<=>((happy(john)<~>~strong(john))))&
(![X]:(~kind(X)=>(~wise(X)&~kind(X))))&
(![X]:((old(X)&~brave(X))<=>curious(X)))&
((?[X]:((~happy(X)|~calm(X))))<=>((~rich(john)|~curious(john))))&
((?[X]:((old(X)<~>~creative(X))))=>(strong(susan)))&
(((funny(fred)<~>~calm(fred)))=>(?[X]:((generous(X)&~funny(X)))))&
(![X]:(humble(X)=>(creative(X)|~brave(X))))&
(![X]:((~patient(X)<~>funny(X))<=>patient(X)))&
(![X]:(~happy(X)<=>(~kind(X)|strong(X))))&
((~patient(mary)<~>~humble(mary)))&
((~brave(paul)<~>kind(paul)))&
(?[X]:(humble(X)))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:((~kind(X)<~>~calm(X))))&
(?[X]:((humble(X)|~kind(X))))&
((humble(alice)&~curious(alice)))&
((creative(paul)&patient(paul))) | ~rich(paul) | [
"p3",
"p5",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2582075096148354256324766
% SZS output start Proof for 2582075096148354256324766
4. ! [X0] : ((~old(X0) & ~kind(X0)) <=> (~old(X0) | rich(X0))) [input p3]
6. ! [X0] : ((~old(X0) & rich(X0)) => (~funny(X0) <~> brave(X0))) [input p5]
15. ! [X0] : ((~patient(X0) <~> funny(X0)) <=> patient(X0)) [input p14]
18. ~brave(paul) <~> kind(paul) [input p17]
25. rich(paul) [input hypothesis]
31. ! [X0] : ((~funny(X0) <~> brave(X0)) | (old(X0) | ~rich(X0))) [ennf transformation 6]
32. ! [X0] : ((~funny(X0) <~> brave(X0)) | old(X0) | ~rich(X0)) [flattening 31]
39. ! [X0] : (((~old(X0) & ~kind(X0)) | (old(X0) & ~rich(X0))) & ((~old(X0) | rich(X0)) | (old(X0) | kind(X0)))) [nnf transformation 4]
40. ! [X0] : (((~old(X0) & ~kind(X0)) | (old(X0) & ~rich(X0))) & (~old(X0) | rich(X0) | old(X0) | kind(X0))) [flattening 39]
46. ! [X0] : (((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | old(X0) | ~rich(X0)) [nnf transformation 32]
63. ! [X0] : ((((~funny(X0) | patient(X0)) & (funny(X0) | ~patient(X0))) | ~patient(X0)) & (patient(X0) | ((~patient(X0) | ~funny(X0)) & (funny(X0) | patient(X0))))) [nnf transformation 15]
67. (~kind(paul) | brave(paul)) & (kind(paul) | ~brave(paul)) [nnf transformation 18]
80. ~rich(X0) | ~kind(X0) [cnf transformation 40]
82. ~rich(X0) | ~old(X0) [cnf transformation 40]
87. brave(X0) | ~funny(X0) | old(X0) | ~rich(X0) [cnf transformation 46]
116. patient(X0) | funny(X0) | patient(X0) [cnf transformation 63]
118. funny(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 63]
125. kind(paul) | ~brave(paul) [cnf transformation 67]
136. rich(paul) [cnf transformation 25]
137. patient(X0) | funny(X0) [duplicate literal removal 116]
138. ~patient(X0) | funny(X0) [duplicate literal removal 118]
175. ~funny(X0) | brave(X0) | ~rich(X0) [subsumption resolution 87,82]
256. funny(X0) [subsumption resolution 137,138]
268. 27 <=> brave(paul) [avatar definition]
272. 28 <=> kind(paul) [avatar definition]
276. ~27 | 28 [avatar split clause 125,272,268]
311. ~kind(paul) [resolution 80,136]
343. ~rich(X0) | brave(X0) [resolution 175,256]
344. brave(paul) [resolution 343,136]
347. 27 [avatar split clause 344,268]
348. ~28 [avatar split clause 311,272]
349. $false [avatar sat refutation 276,347,348]
% SZS output end Proof for 2582075096148354256324766
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble is both not strong and not creative and vice versa.
If alice is not wise then susan is brave or not old and vice versa.
Everyone who is both not strong and not rich is either not tall or funny and vice versa.
If susan is not calm then alice is either not calm or not funny and vice versa.
Everyone who is tall or brave is not wise and vice versa.
If someone is not calm then someone is not tall or not rich.
If alice is either wise or not brave then someone is both generous and not wise and vice versa.
If someone is calm then someone is calm or not funny and vice versa.
Everyone who is patient is tall or not old and vice versa.
Everyone who is generous is both rich and not quiet and vice versa.
Everyone who is not funny is either not old or patient and vice versa.
If someone is not tall then someone is not brave or not generous and vice versa.
Everyone who is either curious or not quiet is both not patient and not rich.
If fred is either generous or not patient then fred is not brave.
Everyone who is old is both creative and not funny and vice versa.
Everyone who is both not quiet and not curious is wise or not funny and vice versa.
Mary is either calm or patient.
Someone is brave.
John is either not funny or tall.
Susan is not curious.
Someone is tall. | Alice is not old. | entailment | (![X]:(~humble(X)<=>(~strong(X)&~creative(X))))&
((~wise(alice))<=>((brave(susan)|~old(susan))))&
(![X]:((~strong(X)&~rich(X))<=>(~tall(X)<~>funny(X))))&
((~calm(susan))<=>((~calm(alice)<~>~funny(alice))))&
(![X]:((tall(X)|brave(X))<=>~wise(X)))&
((?[X]:(~calm(X)))=>(?[X]:((~tall(X)|~rich(X)))))&
(((wise(alice)<~>~brave(alice)))<=>(?[X]:((generous(X)&~wise(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((calm(X)|~funny(X)))))&
(![X]:(patient(X)<=>(tall(X)|~old(X))))&
(![X]:(generous(X)<=>(rich(X)&~quiet(X))))&
(![X]:(~funny(X)<=>(~old(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))=>(~patient(X)&~rich(X))))&
(((generous(fred)<~>~patient(fred)))=>(~brave(fred)))&
(![X]:(old(X)<=>(creative(X)&~funny(X))))&
(![X]:((~quiet(X)&~curious(X))<=>(wise(X)|~funny(X))))&
((calm(mary)<~>patient(mary)))&
(?[X]:(brave(X)))&
((~funny(john)<~>tall(john)))&
(~curious(susan))&
(?[X]:(tall(X))) | ~old(alice) | [
"p8",
"p10",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5363165653276727245153889
% SZS output start Proof for 5363165653276727245153889
9. ! [X0] : (patient(X0) <=> (~old(X0) | tall(X0))) [input p8]
11. ! [X0] : (~funny(X0) <=> (~old(X0) <~> patient(X0))) [input p10]
13. ! [X0] : ((curious(X0) <~> ~quiet(X0)) => (~rich(X0) & ~patient(X0))) [input p12]
15. ! [X0] : (old(X0) <=> (~funny(X0) & creative(X0))) [input p14]
16. ! [X0] : ((~curious(X0) & ~quiet(X0)) <=> (~funny(X0) | wise(X0))) [input p15]
22. old(alice) [input hypothesis]
27. ! [X0] : ((~rich(X0) & ~patient(X0)) | (curious(X0) <=> ~quiet(X0))) [ennf transformation 13]
48. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & ((~old(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 9]
49. ! [X0] : ((patient(X0) | (old(X0) & ~tall(X0))) & (~old(X0) | tall(X0) | ~patient(X0))) [flattening 48]
52. ! [X0] : ((~funny(X0) | ((~old(X0) | ~patient(X0)) & (patient(X0) | old(X0)))) & (((~patient(X0) | old(X0)) & (patient(X0) | ~old(X0))) | funny(X0))) [nnf transformation 11]
58. ! [X0] : ((~rich(X0) & ~patient(X0)) | ((curious(X0) | quiet(X0)) & (~quiet(X0) | ~curious(X0)))) [nnf transformation 27]
60. ! [X0] : ((old(X0) | (funny(X0) | ~creative(X0))) & ((~funny(X0) & creative(X0)) | ~old(X0))) [nnf transformation 15]
61. ! [X0] : ((old(X0) | funny(X0) | ~creative(X0)) & ((~funny(X0) & creative(X0)) | ~old(X0))) [flattening 60]
62. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (funny(X0) & ~wise(X0))) & ((~funny(X0) | wise(X0)) | (curious(X0) | quiet(X0)))) [nnf transformation 16]
63. ! [X0] : (((~curious(X0) & ~quiet(X0)) | (funny(X0) & ~wise(X0))) & (~funny(X0) | wise(X0) | curious(X0) | quiet(X0))) [flattening 62]
98. patient(X0) | old(X0) [cnf transformation 49]
102. patient(X0) | ~old(X0) | funny(X0) [cnf transformation 52]
103. ~patient(X0) | old(X0) | funny(X0) [cnf transformation 52]
110. ~patient(X0) | curious(X0) | quiet(X0) [cnf transformation 58]
116. ~funny(X0) | ~old(X0) [cnf transformation 61]
120. ~quiet(X0) | funny(X0) [cnf transformation 63]
122. ~curious(X0) | funny(X0) [cnf transformation 63]
130. old(alice) [cnf transformation 22]
147. 4 <=> funny(alice) [avatar definition]
148. ~funny(alice) <- (~4) [avatar component clause 147]
149. funny(alice) <- (4) [avatar component clause 147]
196. 14 <=> ! [X1] : funny(X1) [avatar definition]
197. funny(X1) <- (14) [avatar component clause 196]
216. funny(X0) | old(X0) [subsumption resolution 103,98]
217. patient(X0) | funny(X0) [subsumption resolution 102,216]
283. ~old(alice) <- (4) [resolution 116,149]
284. $false <- (4) [subsumption resolution 283,130]
285. ~4 [avatar contradiction clause 284]
352. curious(X0) | quiet(X0) | funny(X0) [resolution 110,217]
356. quiet(X0) | funny(X0) [subsumption resolution 352,122]
357. funny(X0) [subsumption resolution 356,120]
358. 14 [avatar split clause 357,196]
380. $false <- (~4, 14) [resolution 197,148]
385. 4 | ~14 [avatar contradiction clause 380]
387. $false [avatar sat refutation 285,358,385]
% SZS output end Proof for 5363165653276727245153889
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not brave is both curious and brave and vice versa.
If someone is curious or not calm then someone is curious and vice versa.
Everyone who is kind is not happy and vice versa.
If someone is brave or not quiet then someone is either patient or not strong and vice versa.
Everyone who is both not wise and strong is both not creative and not tall.
If alice is not curious then fred is not calm and vice versa.
Everyone who is either rich or not humble is funny and vice versa.
Everyone who is either creative or not kind is brave or happy.
If someone is not tall or not generous then someone is either quiet or happy.
Everyone who is patient is either quiet or not wise and vice versa.
If someone is not kind then someone is not humble.
If john is rich then someone is either not calm or old.
Everyone who is either funny or wise is kind or not calm.
Everyone who is not creative or not calm is both not kind and tall and vice versa.
If mary is both wise and not kind then someone is both humble and not happy.
Everyone who is not patient is brave.
John is not curious.
Fred is not old or patient.
John is not tall or not generous.
Lucy is either funny or humble.
Fred is happy or not tall.
Someone is both not happy and not generous.
Lucy is not quiet or rich.
Someone is either strong or not happy. | Lucy is funny. | neutral | (![X]:((funny(X)|~brave(X))<=>(curious(X)&brave(X))))&
((?[X]:((curious(X)|~calm(X))))<=>(?[X]:(curious(X))))&
(![X]:(kind(X)<=>~happy(X)))&
((?[X]:((brave(X)|~quiet(X))))<=>(?[X]:((patient(X)<~>~strong(X)))))&
(![X]:((~wise(X)&strong(X))=>(~creative(X)&~tall(X))))&
((~curious(alice))<=>(~calm(fred)))&
(![X]:((rich(X)<~>~humble(X))<=>funny(X)))&
(![X]:((creative(X)<~>~kind(X))=>(brave(X)|happy(X))))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((quiet(X)<~>happy(X)))))&
(![X]:(patient(X)<=>(quiet(X)<~>~wise(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~humble(X))))&
((rich(john))=>(?[X]:((~calm(X)<~>old(X)))))&
(![X]:((funny(X)<~>wise(X))=>(kind(X)|~calm(X))))&
(![X]:((~creative(X)|~calm(X))<=>(~kind(X)&tall(X))))&
(((wise(mary)&~kind(mary)))=>(?[X]:((humble(X)&~happy(X)))))&
(![X]:(~patient(X)=>brave(X)))&
(~curious(john))&
((~old(fred)|patient(fred)))&
((~tall(john)|~generous(john)))&
((funny(lucy)<~>humble(lucy)))&
((happy(fred)|~tall(fred)))&
(?[X]:((~happy(X)&~generous(X))))&
((~quiet(lucy)|rich(lucy)))&
(?[X]:((strong(X)<~>~happy(X)))) | funny(lucy) | [] | null | 0 |
If fred is not humble then someone is not old or not kind and vice versa. Everyone who is tall or not patient is either not brave or quiet. Everyone who is generous is not old and vice versa. Everyone who is not kind is not funny or not old. Everyone who is both generous and old is both not calm and kind. Everyone who is not patient is brave and vice versa. Everyone who is brave is both not strong and not happy and vice versa. If someone is both not creative and wise then mary is both not brave and calm. If john is funny or curious then paul is curious or tall and vice versa. If someone is both not patient and patient then someone is not happy. If lucy is either not wise or not humble then paul is both not happy and old. Everyone who is not brave is both not calm and not curious and vice versa. If someone is both not kind and brave then alice is either curious or creative. If fred is either not old or tall then lucy is not generous or not rich and vice versa. If someone is either not brave or humble then alice is not curious or not brave. Everyone who is both not patient and not humble is curious or creative. Someone is both strong and not generous. Someone is strong or not wise. Someone is not kind. Mary is not funny or old. Someone is both not rich and tall. Someone is both curious and wise. Susan is either quiet or calm. John is both not tall and not happy. | John is not kind. | neutral | ((~humble(fred))<=>(?[X]:((~old(X)|~kind(X)))))&
(![X]:((tall(X)|~patient(X))=>(~brave(X)<~>quiet(X))))&
(![X]:(generous(X)<=>~old(X)))&
(![X]:(~kind(X)=>(~funny(X)|~old(X))))&
(![X]:((generous(X)&old(X))=>(~calm(X)&kind(X))))&
(![X]:(~patient(X)<=>brave(X)))&
(![X]:(brave(X)<=>(~strong(X)&~happy(X))))&
((?[X]:((~creative(X)&wise(X))))=>((~brave(mary)&calm(mary))))&
(((funny(john)|curious(john)))<=>((curious(paul)|tall(paul))))&
((?[X]:((~patient(X)&patient(X))))=>(?[X]:(~happy(X))))&
(((~wise(lucy)<~>~humble(lucy)))=>((~happy(paul)&old(paul))))&
(![X]:(~brave(X)<=>(~calm(X)&~curious(X))))&
((?[X]:((~kind(X)&brave(X))))=>((curious(alice)<~>creative(alice))))&
(((~old(fred)<~>tall(fred)))<=>((~generous(lucy)|~rich(lucy))))&
((?[X]:((~brave(X)<~>humble(X))))=>((~curious(alice)|~brave(alice))))&
(![X]:((~patient(X)&~humble(X))=>(curious(X)|creative(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((strong(X)|~wise(X))))&
(?[X]:(~kind(X)))&
((~funny(mary)|old(mary)))&
(?[X]:((~rich(X)&tall(X))))&
(?[X]:((curious(X)&wise(X))))&
((quiet(susan)<~>calm(susan)))&
((~tall(john)&~happy(john))) | ~kind(john) | [] | null | 0 |
Everyone who is happy or brave is both funny and creative and vice versa.
Everyone who is both kind and humble is both kind and brave.
Everyone who is either not patient or old is either not rich or tall and vice versa.
Everyone who is not happy or calm is strong or not curious.
Everyone who is both not humble and old is not brave and vice versa.
Everyone who is either curious or not curious is not happy.
If john is curious then someone is strong or not calm.
Everyone who is both quiet and strong is not strong or humble.
If someone is not wise then someone is both wise and not creative.
If paul is both happy and not rich then someone is not happy.
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.
Someone is either not happy or not strong.
Mary is either not patient or tall.
Someone is not quiet.
Alice is not calm or not brave.
Paul is kind.
Someone is either not curious or not patient.
Mary is either not brave or generous.
Susan is either not kind or rich. | Mary is wise. | entailment | (![X]:((happy(X)|brave(X))<=>(funny(X)&creative(X))))&
(![X]:((kind(X)&humble(X))=>(kind(X)&brave(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~happy(X)|calm(X))=>(strong(X)|~curious(X))))&
(![X]:((~humble(X)&old(X))<=>~brave(X)))&
(![X]:((curious(X)<~>~curious(X))=>~happy(X)))&
((curious(john))=>(?[X]:((strong(X)|~calm(X)))))&
(![X]:((quiet(X)&strong(X))=>(~strong(X)|humble(X))))&
((?[X]:(~wise(X)))=>(?[X]:((wise(X)&~creative(X)))))&
(((happy(paul)&~rich(paul)))=>(?[X]:(~happy(X))))&
((?[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))))&
(?[X]:((~happy(X)<~>~strong(X))))&
((~patient(mary)<~>tall(mary)))&
(?[X]:(~quiet(X)))&
((~calm(alice)|~brave(alice)))&
(kind(paul))&
(?[X]:((~curious(X)<~>~patient(X))))&
((~brave(mary)<~>generous(mary)))&
((~kind(susan)<~>rich(susan))) | wise(mary) | [
"p0",
"p5",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3105025949830615508470496
% SZS output start Proof for 3105025949830615508470496
1. ! [X0] : ((brave(X0) | happy(X0)) <=> (creative(X0) & funny(X0))) [input p0]
6. ! [X0] : ((curious(X0) <~> ~curious(X0)) => ~happy(X0)) [input p5]
9. ? [X0] : ~wise(X0) => ? [X0] : (~creative(X0) & wise(X0)) [input p8]
11. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X0] : (happy(X0) & old(X0)) [input p10]
24. ~wise(mary) [input hypothesis]
25. ? [X0] : ~wise(X0) => ? [X1] : (~creative(X1) & wise(X1)) [rectify 9]
26. ? [X0] : (creative(X0) <~> ~brave(X0)) => ? [X1] : (happy(X1) & old(X1)) [rectify 11]
33. ! [X0] : (~happy(X0) | (curious(X0) <=> ~curious(X0))) [ennf transformation 6]
35. ? [X1] : (~creative(X1) & wise(X1)) | ! [X0] : wise(X0) [ennf transformation 25]
38. ? [X1] : (happy(X1) & old(X1)) | ! [X0] : (creative(X0) <=> ~brave(X0)) [ennf transformation 26]
44. ! [X0] : (((brave(X0) | happy(X0)) | (~creative(X0) | ~funny(X0))) & ((creative(X0) & funny(X0)) | (~brave(X0) & ~happy(X0)))) [nnf transformation 1]
45. ! [X0] : ((brave(X0) | happy(X0) | ~creative(X0) | ~funny(X0)) & ((creative(X0) & funny(X0)) | (~brave(X0) & ~happy(X0)))) [flattening 44]
49. ! [X0] : (~happy(X0) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0)))) [nnf transformation 33]
52. ? [X0] : (~creative(X0) & wise(X0)) | ! [X1] : wise(X1) [rectify 35]
53. ? [X0] : (~creative(X0) & wise(X0)) => (~creative(sK1) & wise(sK1)) [choice axiom]
54. (~creative(sK1) & wise(sK1)) | ! [X1] : wise(X1) [skolemisation 52,53]
57. ? [X1] : (happy(X1) & old(X1)) | ! [X0] : ((creative(X0) | brave(X0)) & (~brave(X0) | ~creative(X0))) [nnf transformation 38]
58. ? [X0] : (happy(X0) & old(X0)) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [rectify 57]
59. ? [X0] : (happy(X0) & old(X0)) => (happy(sK3) & old(sK3)) [choice axiom]
60. (happy(sK3) & old(sK3)) | ! [X1] : ((creative(X1) | brave(X1)) & (~brave(X1) | ~creative(X1))) [skolemisation 58,59]
77. creative(X0) | ~brave(X0) [cnf transformation 45]
94. ~happy(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 49]
95. ~happy(X0) | curious(X0) | curious(X0) [cnf transformation 49]
98. ~creative(sK1) | wise(X1) [cnf transformation 54]
103. happy(sK3) | creative(X1) | brave(X1) [cnf transformation 60]
128. ~wise(mary) [cnf transformation 24]
131. ~happy(X0) | ~curious(X0) [duplicate literal removal 94]
132. ~happy(X0) | curious(X0) [duplicate literal removal 95]
133. ~happy(X0) [subsumption resolution 131,132]
148. 4 <=> ! [X1] : wise(X1) [avatar definition]
149. wise(X1) <- (4) [avatar component clause 148]
151. 5 <=> creative(sK1) [avatar definition]
153. ~creative(sK1) <- (~5) [avatar component clause 151]
154. 4 | ~5 [avatar split clause 98,151,148]
160. creative(X1) | brave(X1) [subsumption resolution 103,133]
161. creative(X1) [subsumption resolution 160,77]
197. $false <- (4) [resolution 149,128]
198. ~4 [avatar contradiction clause 197]
199. $false <- (~5) [subsumption resolution 153,161]
200. 5 [avatar contradiction clause 199]
201. $false [avatar sat refutation 154,198,200]
% SZS output end Proof for 3105025949830615508470496
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either creative or not kind then mary is both creative and strong.
Everyone who is both wise and not old is both not quiet and wise and vice versa.
Everyone who is both humble and quiet is calm.
If lucy is not quiet or not creative then mary is both not patient and quiet.
Everyone who is not wise is not kind and vice versa.
Everyone who is either tall or not curious is calm or not patient.
If paul is happy then fred is either not creative or generous and vice versa.
Everyone who is both quiet and curious is either rich or not brave and vice versa.
If lucy is not kind or not curious then alice is tall.
Everyone who is both wise and not patient is not funny or strong and vice versa.
Everyone who is either not tall or curious is not tall.
If susan is generous then mary is quiet or not funny and vice versa.
Everyone who is patient is strong and vice versa.
Everyone who is either rich or calm is not quiet.
Everyone who is both not creative and patient is not brave and vice versa.
Everyone who is quiet is kind or strong and vice versa.
John is quiet.
Fred is happy.
Someone is not curious.
Lucy is not generous or funny.
Someone is not quiet or not old.
Someone is kind or not wise.
Mary is generous or not generous.
Someone is either not brave or curious. | John is not brave. | contradiction | ((?[X]:((creative(X)<~>~kind(X))))=>((creative(mary)&strong(mary))))&
(![X]:((wise(X)&~old(X))<=>(~quiet(X)&wise(X))))&
(![X]:((humble(X)&quiet(X))=>calm(X)))&
(((~quiet(lucy)|~creative(lucy)))=>((~patient(mary)&quiet(mary))))&
(![X]:(~wise(X)<=>~kind(X)))&
(![X]:((tall(X)<~>~curious(X))=>(calm(X)|~patient(X))))&
((happy(paul))<=>((~creative(fred)<~>generous(fred))))&
(![X]:((quiet(X)&curious(X))<=>(rich(X)<~>~brave(X))))&
(((~kind(lucy)|~curious(lucy)))=>(tall(alice)))&
(![X]:((wise(X)&~patient(X))<=>(~funny(X)|strong(X))))&
(![X]:((~tall(X)<~>curious(X))=>~tall(X)))&
((generous(susan))<=>((quiet(mary)|~funny(mary))))&
(![X]:(patient(X)<=>strong(X)))&
(![X]:((rich(X)<~>calm(X))=>~quiet(X)))&
(![X]:((~creative(X)&patient(X))<=>~brave(X)))&
(![X]:(quiet(X)<=>(kind(X)|strong(X))))&
(quiet(john))&
(happy(fred))&
(?[X]:(~curious(X)))&
((~generous(lucy)|funny(lucy)))&
(?[X]:((~quiet(X)|~old(X))))&
(?[X]:((kind(X)|~wise(X))))&
((generous(mary)|~generous(mary)))&
(?[X]:((~brave(X)<~>curious(X)))) | ~brave(john) | [
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5259830828879449737987081
% SZS output start Proof for 5259830828879449737987081
10. ! [X0] : ((~patient(X0) & wise(X0)) <=> (strong(X0) | ~funny(X0))) [input p9]
13. ! [X0] : (patient(X0) <=> strong(X0)) [input p12]
15. ! [X0] : ((patient(X0) & ~creative(X0)) <=> ~brave(X0)) [input p14]
25. ~brave(john) [input hypothesis]
42. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (patient(X0) | ~wise(X0)))) [nnf transformation 10]
43. ! [X0] : (((~patient(X0) & wise(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | patient(X0) | ~wise(X0))) [flattening 42]
47. ! [X0] : ((patient(X0) | ~strong(X0)) & (strong(X0) | ~patient(X0))) [nnf transformation 13]
49. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | (~patient(X0) | creative(X0)))) [nnf transformation 15]
50. ! [X0] : (((patient(X0) & ~creative(X0)) | brave(X0)) & (~brave(X0) | ~patient(X0) | creative(X0))) [flattening 49]
94. ~patient(X0) | ~strong(X0) [cnf transformation 43]
100. strong(X0) | ~patient(X0) [cnf transformation 47]
101. patient(X0) | ~strong(X0) [cnf transformation 47]
106. patient(X0) | brave(X0) [cnf transformation 50]
119. ~brave(john) [cnf transformation 25]
200. ~strong(X0) [subsumption resolution 101,94]
201. ~patient(X0) [subsumption resolution 100,200]
202. brave(X0) [subsumption resolution 106,201]
223. $false [subsumption resolution 119,202]
% SZS output end Proof for 5259830828879449737987081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or not strong is both not creative and curious and vice versa.
If fred is both not funny and not wise then someone is curious and vice versa.
Everyone who is both curious and brave is not creative or not brave.
Everyone who is curious or not strong is kind or curious and vice versa.
If someone is either rich or quiet then someone is both wise and not curious.
If paul is strong or patient then someone is either calm or creative.
Everyone who is both curious and brave is either tall or not humble.
If someone is both old and strong then lucy is both patient and not generous and vice versa.
Everyone who is not tall or not strong is not generous or humble and vice versa.
Everyone who is not funny or not generous is both not quiet and wise.
If someone is either calm or not curious then someone is not wise or funny and vice versa.
Everyone who is not curious or not generous is not creative or not wise and vice versa.
If someone is not humble then someone is both not old and strong.
Everyone who is not patient is brave or not calm.
If someone is tall then lucy is either not brave or not strong.
Everyone who is not brave is old or quiet and vice versa.
Someone is either brave or generous.
Someone is not old.
Someone is either generous or not calm.
Lucy is both not humble and not kind.
Susan is both creative and quiet.
Alice is strong.
Fred is brave.
John is not curious or kind. | Susan is not funny. | contradiction | (![X]:((~rich(X)|~strong(X))<=>(~creative(X)&curious(X))))&
(((~funny(fred)&~wise(fred)))<=>(?[X]:(curious(X))))&
(![X]:((curious(X)&brave(X))=>(~creative(X)|~brave(X))))&
(![X]:((curious(X)|~strong(X))<=>(kind(X)|curious(X))))&
((?[X]:((rich(X)<~>quiet(X))))=>(?[X]:((wise(X)&~curious(X)))))&
(((strong(paul)|patient(paul)))=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((curious(X)&brave(X))=>(tall(X)<~>~humble(X))))&
((?[X]:((old(X)&strong(X))))<=>((patient(lucy)&~generous(lucy))))&
(![X]:((~tall(X)|~strong(X))<=>(~generous(X)|humble(X))))&
(![X]:((~funny(X)|~generous(X))=>(~quiet(X)&wise(X))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:((~wise(X)|funny(X)))))&
(![X]:((~curious(X)|~generous(X))<=>(~creative(X)|~wise(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~old(X)&strong(X)))))&
(![X]:(~patient(X)=>(brave(X)|~calm(X))))&
((?[X]:(tall(X)))=>((~brave(lucy)<~>~strong(lucy))))&
(![X]:(~brave(X)<=>(old(X)|quiet(X))))&
(?[X]:((brave(X)<~>generous(X))))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>~calm(X))))&
((~humble(lucy)&~kind(lucy)))&
((creative(susan)&quiet(susan)))&
(strong(alice))&
(brave(fred))&
((~curious(john)|kind(john))) | ~funny(susan) | [
"p9",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 661418040969903588652898
% SZS output start Proof for 661418040969903588652898
10. ! [X0] : ((~generous(X0) | ~funny(X0)) => (wise(X0) & ~quiet(X0))) [input p9]
21. quiet(susan) & creative(susan) [input p20]
25. ~funny(susan) [input hypothesis]
35. ! [X0] : ((wise(X0) & ~quiet(X0)) | (generous(X0) & funny(X0))) [ennf transformation 10]
116. ~quiet(X0) | funny(X0) [cnf transformation 35]
146. quiet(susan) [cnf transformation 21]
150. ~funny(susan) [cnf transformation 25]
329. funny(susan) [resolution 116,146]
330. $false [subsumption resolution 329,150]
% SZS output end Proof for 661418040969903588652898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is not brave or not patient then someone is either wise or happy.
Everyone who is either not patient or creative is not funny and vice versa.
Everyone who is calm or not funny is either strong or not rich.
If someone is either not funny or not curious then someone is not creative and vice versa.
Everyone who is old or not brave is brave and vice versa.
If someone is not old then fred is both not patient and creative and vice versa.
Everyone who is either generous or kind is either not quiet or not generous.
If john is both not patient and not brave then someone is both not wise and not creative.
If someone is both not tall and calm then paul is not curious or not kind.
Everyone who is either not calm or creative is creative.
If lucy is either not tall or strong then fred is not funny or not calm and vice versa.
If someone is either not curious or humble then someone is either not kind or not funny and vice versa.
If someone is not calm then fred is either not brave or not kind.
Everyone who is not rich or kind is not tall.
If someone is not generous or not rich then paul is either funny or not kind.
Everyone who is not wise or patient is either not curious or quiet.
Someone is brave or old.
Susan is either funny or humble.
Someone is strong or not strong.
John is both brave and not rich.
Mary is old or not brave.
Someone is both not wise and not kind.
Paul is either creative or not creative. | Paul is not calm. | neutral | (((~brave(paul)|~patient(paul)))=>(?[X]:((wise(X)<~>happy(X)))))&
(![X]:((~patient(X)<~>creative(X))<=>~funny(X)))&
(![X]:((calm(X)|~funny(X))=>(strong(X)<~>~rich(X))))&
((?[X]:((~funny(X)<~>~curious(X))))<=>(?[X]:(~creative(X))))&
(![X]:((old(X)|~brave(X))<=>brave(X)))&
((?[X]:(~old(X)))<=>((~patient(fred)&creative(fred))))&
(![X]:((generous(X)<~>kind(X))=>(~quiet(X)<~>~generous(X))))&
(((~patient(john)&~brave(john)))=>(?[X]:((~wise(X)&~creative(X)))))&
((?[X]:((~tall(X)&calm(X))))=>((~curious(paul)|~kind(paul))))&
(![X]:((~calm(X)<~>creative(X))=>creative(X)))&
(((~tall(lucy)<~>strong(lucy)))<=>((~funny(fred)|~calm(fred))))&
((?[X]:((~curious(X)<~>humble(X))))<=>(?[X]:((~kind(X)<~>~funny(X)))))&
((?[X]:(~calm(X)))=>((~brave(fred)<~>~kind(fred))))&
(![X]:((~rich(X)|kind(X))=>~tall(X)))&
((?[X]:((~generous(X)|~rich(X))))=>((funny(paul)<~>~kind(paul))))&
(![X]:((~wise(X)|patient(X))=>(~curious(X)<~>quiet(X))))&
(?[X]:((brave(X)|old(X))))&
((funny(susan)<~>humble(susan)))&
(?[X]:((strong(X)|~strong(X))))&
((brave(john)&~rich(john)))&
((old(mary)|~brave(mary)))&
(?[X]:((~wise(X)&~kind(X))))&
((creative(paul)<~>~creative(paul))) | ~calm(paul) | [] | null | 0 |
Everyone who is either strong or not strong is either generous or creative and vice versa.
If paul is brave or not quiet then someone is both not old and not calm and vice versa.
If alice is kind then someone is both kind and calm and vice versa.
If alice is wise then lucy is not happy or not patient.
If someone is rich then someone is both not quiet and not generous and vice versa.
Everyone who is not old is both creative and not tall and vice versa.
Everyone who is not creative is either not wise or quiet.
Everyone who is either not brave or brave is strong and vice versa.
Everyone who is not rich is both not strong and strong and vice versa.
If someone is both not happy and not tall then paul is tall and vice versa.
Everyone who is both not brave and patient is either humble or not rich and vice versa.
Everyone who is not funny is not strong and vice versa.
Everyone who is either quiet or not tall is not generous and vice versa.
Everyone who is patient or happy is both not happy and not funny.
If alice is either not quiet or not tall then susan is not humble or not happy.
Someone is creative.
Someone is happy or generous.
Someone is kind.
Paul is both not quiet and not patient.
John is humble or quiet.
Someone is either calm or not quiet. | Alice is not creative. | neutral | (![X]:((strong(X)<~>~strong(X))<=>(generous(X)<~>creative(X))))&
(((brave(paul)|~quiet(paul)))<=>(?[X]:((~old(X)&~calm(X)))))&
((kind(alice))<=>(?[X]:((kind(X)&calm(X)))))&
((wise(alice))=>((~happy(lucy)|~patient(lucy))))&
((?[X]:(rich(X)))<=>(?[X]:((~quiet(X)&~generous(X)))))&
(![X]:(~old(X)<=>(creative(X)&~tall(X))))&
(![X]:(~creative(X)=>(~wise(X)<~>quiet(X))))&
(![X]:((~brave(X)<~>brave(X))<=>strong(X)))&
(![X]:(~rich(X)<=>(~strong(X)&strong(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(tall(paul)))&
(![X]:((~brave(X)&patient(X))<=>(humble(X)<~>~rich(X))))&
(![X]:(~funny(X)<=>~strong(X)))&
(![X]:((quiet(X)<~>~tall(X))<=>~generous(X)))&
(![X]:((patient(X)|happy(X))=>(~happy(X)&~funny(X))))&
(((~quiet(alice)<~>~tall(alice)))=>((~humble(susan)|~happy(susan))))&
(?[X]:(creative(X)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:(kind(X)))&
((~quiet(paul)&~patient(paul)))&
((humble(john)|quiet(john)))&
(?[X]:((calm(X)<~>~quiet(X)))) | ~creative(alice) | [] | null | 0 |
Everyone who is not strong is brave and vice versa.
If paul is either not wise or not kind then john is not creative or not calm.
Everyone who is not generous is either generous or creative and vice versa.
Everyone who is strong is either not rich or not kind and vice versa.
If someone is either funny or kind then someone is either not kind or patient and vice versa.
Everyone who is either wise or strong is either creative or strong and vice versa.
If susan is both tall and old then mary is not patient.
Everyone who is not brave is not old or not calm.
If susan is either happy or not quiet then someone is either not creative or not funny and vice versa.
Everyone who is not old or happy is both not funny and humble and vice versa.
If someone is not creative or not brave then someone is not funny or patient.
If someone is not funny or not kind then someone is not humble or kind and vice versa.
Everyone who is both creative and not patient is wise or not brave.
Everyone who is not brave is either kind or wise and vice versa.
If someone is patient or not creative then someone is either not calm or patient and vice versa.
Everyone who is not generous or funny is either not funny or not tall.
Paul is generous.
John is not strong or not curious.
Mary is kind or funny.
Susan is both not kind and not generous.
Someone is either brave or not wise.
Someone is not funny.
Susan is wise.
Susan is both not happy and not funny. | John is not patient. | neutral | (![X]:(~strong(X)<=>brave(X)))&
(((~wise(paul)<~>~kind(paul)))=>((~creative(john)|~calm(john))))&
(![X]:(~generous(X)<=>(generous(X)<~>creative(X))))&
(![X]:(strong(X)<=>(~rich(X)<~>~kind(X))))&
((?[X]:((funny(X)<~>kind(X))))<=>(?[X]:((~kind(X)<~>patient(X)))))&
(![X]:((wise(X)<~>strong(X))<=>(creative(X)<~>strong(X))))&
(((tall(susan)&old(susan)))=>(~patient(mary)))&
(![X]:(~brave(X)=>(~old(X)|~calm(X))))&
(((happy(susan)<~>~quiet(susan)))<=>(?[X]:((~creative(X)<~>~funny(X)))))&
(![X]:((~old(X)|happy(X))<=>(~funny(X)&humble(X))))&
((?[X]:((~creative(X)|~brave(X))))=>(?[X]:((~funny(X)|patient(X)))))&
((?[X]:((~funny(X)|~kind(X))))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((creative(X)&~patient(X))=>(wise(X)|~brave(X))))&
(![X]:(~brave(X)<=>(kind(X)<~>wise(X))))&
((?[X]:((patient(X)|~creative(X))))<=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:((~generous(X)|funny(X))=>(~funny(X)<~>~tall(X))))&
(generous(paul))&
((~strong(john)|~curious(john)))&
((kind(mary)|funny(mary)))&
((~kind(susan)&~generous(susan)))&
(?[X]:((brave(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
(wise(susan))&
((~happy(susan)&~funny(susan))) | ~patient(john) | [] | null | 0 |
If someone is not strong then susan is not curious or old and vice versa.
If fred is both not wise and kind then fred is either quiet or funny.
If susan is both creative and not creative then someone is not old.
If mary is both not brave and not strong then paul is either not old or generous.
If someone is not generous or kind then paul is either not brave or not generous and vice versa.
Everyone who is either not old or quiet is either creative or quiet.
Everyone who is not strong or not brave is not wise and vice versa.
Everyone who is both not happy and wise is old and vice versa.
Everyone who is quiet or strong is both not wise and not strong.
If someone is either generous or not rich then fred is not funny or not creative and vice versa.
Everyone who is not kind is both not curious and not old and vice versa.
Everyone who is both not tall and patient is happy or not calm and vice versa.
Everyone who is not brave is either generous or curious and vice versa.
If lucy is rich or kind then someone is brave or not wise and vice versa.
Everyone who is not wise is both not funny and not generous.
Everyone who is calm is both funny and rich.
Alice is creative or not patient.
Paul is patient.
Someone is not generous.
Alice is both patient and not humble.
Someone is either not tall or not happy.
Someone is not old or not kind.
Someone is either not generous or tall. | Fred is generous. | contradiction | ((?[X]:(~strong(X)))<=>((~curious(susan)|old(susan))))&
(((~wise(fred)&kind(fred)))=>((quiet(fred)<~>funny(fred))))&
(((creative(susan)&~creative(susan)))=>(?[X]:(~old(X))))&
(((~brave(mary)&~strong(mary)))=>((~old(paul)<~>generous(paul))))&
((?[X]:((~generous(X)|kind(X))))<=>((~brave(paul)<~>~generous(paul))))&
(![X]:((~old(X)<~>quiet(X))=>(creative(X)<~>quiet(X))))&
(![X]:((~strong(X)|~brave(X))<=>~wise(X)))&
(![X]:((~happy(X)&wise(X))<=>old(X)))&
(![X]:((quiet(X)|strong(X))=>(~wise(X)&~strong(X))))&
((?[X]:((generous(X)<~>~rich(X))))<=>((~funny(fred)|~creative(fred))))&
(![X]:(~kind(X)<=>(~curious(X)&~old(X))))&
(![X]:((~tall(X)&patient(X))<=>(happy(X)|~calm(X))))&
(![X]:(~brave(X)<=>(generous(X)<~>curious(X))))&
(((rich(lucy)|kind(lucy)))<=>(?[X]:((brave(X)|~wise(X)))))&
(![X]:(~wise(X)=>(~funny(X)&~generous(X))))&
(![X]:(calm(X)=>(funny(X)&rich(X))))&
((creative(alice)|~patient(alice)))&
(patient(paul))&
(?[X]:(~generous(X)))&
((patient(alice)&~humble(alice)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~old(X)|~kind(X))))&
(?[X]:((~generous(X)<~>tall(X)))) | generous(fred) | [
"p6",
"p8",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3064872899913931093457686
% SZS output start Proof for 3064872899913931093457686
7. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> ~wise(X0)) [input p6]
9. ! [X0] : ((strong(X0) | quiet(X0)) => (~strong(X0) & ~wise(X0))) [input p8]
15. ! [X0] : (~wise(X0) => (~generous(X0) & ~funny(X0))) [input p14]
24. generous(fred) [input hypothesis]
33. ! [X0] : ((~strong(X0) & ~wise(X0)) | (~strong(X0) & ~quiet(X0))) [ennf transformation 9]
34. ! [X0] : ((~generous(X0) & ~funny(X0)) | wise(X0)) [ennf transformation 15]
50. ! [X0] : (((~brave(X0) | ~strong(X0)) | wise(X0)) & (~wise(X0) | (brave(X0) & strong(X0)))) [nnf transformation 7]
51. ! [X0] : ((~brave(X0) | ~strong(X0) | wise(X0)) & (~wise(X0) | (brave(X0) & strong(X0)))) [flattening 50]
97. ~wise(X0) | strong(X0) [cnf transformation 51]
106. ~strong(X0) | ~strong(X0) [cnf transformation 33]
130. ~generous(X0) | wise(X0) [cnf transformation 34]
142. generous(fred) [cnf transformation 24]
143. ~strong(X0) [duplicate literal removal 106]
165. 5 <=> wise(fred) [avatar definition]
167. wise(fred) <- (5) [avatar component clause 165]
297. wise(fred) [resolution 130,142]
299. 5 [avatar split clause 297,165]
301. strong(fred) <- (5) [resolution 167,97]
302. $false <- (5) [subsumption resolution 301,143]
303. ~5 [avatar contradiction clause 302]
304. $false [avatar sat refutation 299,303]
% SZS output end Proof for 3064872899913931093457686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not creative or patient is generous or rich and vice versa.
Everyone who is both not generous and generous is quiet and vice versa.
If someone is both kind and not kind then john is not calm or patient.
Everyone who is brave is either rich or curious.
If susan is either wise or not strong then john is either not quiet or kind and vice versa.
Everyone who is both not wise and not brave is not humble and vice versa.
Everyone who is either not wise or curious is both not strong and strong and vice versa.
Everyone who is kind or brave is kind and vice versa.
If someone is generous then someone is both not happy and generous and vice versa.
If lucy is curious then fred is quiet or not brave and vice versa.
Everyone who is either not curious or quiet is both humble and not calm.
Everyone who is not wise is not happy.
Everyone who is not humble is both not calm and kind and vice versa.
Everyone who is either brave or quiet is either curious or not wise and vice versa.
If someone is either brave or generous then someone is either not happy or rich.
Someone is both not curious and funny.
Someone is curious.
Someone is not generous or not funny.
Someone is not patient or not calm.
Alice is not curious or generous.
John is old or not old.
Someone is both not brave and not tall.
Someone is rich or kind. | Fred is not calm. | entailment | (![X]:((~creative(X)<~>patient(X))<=>(generous(X)|rich(X))))&
(![X]:((~generous(X)&generous(X))<=>quiet(X)))&
((?[X]:((kind(X)&~kind(X))))=>((~calm(john)|patient(john))))&
(![X]:(brave(X)=>(rich(X)<~>curious(X))))&
(((wise(susan)<~>~strong(susan)))<=>((~quiet(john)<~>kind(john))))&
(![X]:((~wise(X)&~brave(X))<=>~humble(X)))&
(![X]:((~wise(X)<~>curious(X))<=>(~strong(X)&strong(X))))&
(![X]:((kind(X)|brave(X))<=>kind(X)))&
((?[X]:(generous(X)))<=>(?[X]:((~happy(X)&generous(X)))))&
((curious(lucy))<=>((quiet(fred)|~brave(fred))))&
(![X]:((~curious(X)<~>quiet(X))=>(humble(X)&~calm(X))))&
(![X]:(~wise(X)=>~happy(X)))&
(![X]:(~humble(X)<=>(~calm(X)&kind(X))))&
(![X]:((brave(X)<~>quiet(X))<=>(curious(X)<~>~wise(X))))&
((?[X]:((brave(X)<~>generous(X))))=>(?[X]:((~happy(X)<~>rich(X)))))&
(?[X]:((~curious(X)&funny(X))))&
(?[X]:(curious(X)))&
(?[X]:((~generous(X)|~funny(X))))&
(?[X]:((~patient(X)|~calm(X))))&
((~curious(alice)|generous(alice)))&
((old(john)|~old(john)))&
(?[X]:((~brave(X)&~tall(X))))&
(?[X]:((rich(X)|kind(X)))) | ~calm(fred) | [
"p1",
"p5",
"p6",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 773695538699462174164264
% SZS output start Proof for 773695538699462174164264
2. ! [X0] : ((generous(X0) & ~generous(X0)) <=> quiet(X0)) [input p1]
6. ! [X0] : ((~brave(X0) & ~wise(X0)) <=> ~humble(X0)) [input p5]
7. ! [X0] : ((~wise(X0) <~> curious(X0)) <=> (strong(X0) & ~strong(X0))) [input p6]
11. ! [X0] : ((~curious(X0) <~> quiet(X0)) => (~calm(X0) & humble(X0))) [input p10]
13. ! [X0] : (~humble(X0) <=> (kind(X0) & ~calm(X0))) [input p12]
14. ! [X0] : ((brave(X0) <~> quiet(X0)) <=> (curious(X0) <~> ~wise(X0))) [input p13]
24. calm(fred) [input hypothesis]
31. ! [X0] : ((~calm(X0) & humble(X0)) | (~curious(X0) <=> quiet(X0))) [ennf transformation 11]
36. ! [X0] : (((generous(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | (~generous(X0) | generous(X0)))) [nnf transformation 2]
37. ! [X0] : (((generous(X0) & ~generous(X0)) | ~quiet(X0)) & (quiet(X0) | ~generous(X0) | generous(X0))) [flattening 36]
40. ! [X0] : (((~brave(X0) & ~wise(X0)) | humble(X0)) & (~humble(X0) | (brave(X0) | wise(X0)))) [nnf transformation 6]
41. ! [X0] : (((~brave(X0) & ~wise(X0)) | humble(X0)) & (~humble(X0) | brave(X0) | wise(X0))) [flattening 40]
42. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | (~strong(X0) | strong(X0))) & ((strong(X0) & ~strong(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [nnf transformation 7]
43. ! [X0] : ((((~curious(X0) | wise(X0)) & (curious(X0) | ~wise(X0))) | ~strong(X0) | strong(X0)) & ((strong(X0) & ~strong(X0)) | ((~wise(X0) | ~curious(X0)) & (curious(X0) | wise(X0))))) [flattening 42]
53. ! [X0] : ((~calm(X0) & humble(X0)) | ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0)))) [nnf transformation 31]
54. ! [X0] : ((~humble(X0) | (~kind(X0) | calm(X0))) & ((kind(X0) & ~calm(X0)) | humble(X0))) [nnf transformation 13]
55. ! [X0] : ((~humble(X0) | ~kind(X0) | calm(X0)) & ((kind(X0) & ~calm(X0)) | humble(X0))) [flattening 54]
56. ! [X0] : ((((~quiet(X0) | ~brave(X0)) & (quiet(X0) | brave(X0))) | ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0)))) & (((wise(X0) | ~curious(X0)) & (~wise(X0) | curious(X0))) | ((brave(X0) | ~quiet(X0)) & (quiet(X0) | ~brave(X0))))) [nnf transformation 14]
80. ~generous(X0) | ~quiet(X0) [cnf transformation 37]
81. ~quiet(X0) | generous(X0) [cnf transformation 37]
93. ~humble(X0) | brave(X0) | wise(X0) [cnf transformation 41]
96. ~strong(X0) | curious(X0) | wise(X0) [cnf transformation 43]
97. ~strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 43]
98. strong(X0) | curious(X0) | wise(X0) [cnf transformation 43]
99. strong(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 43]
113. ~calm(X0) | quiet(X0) | curious(X0) [cnf transformation 53]
116. ~calm(X0) | humble(X0) [cnf transformation 55]
119. ~wise(X0) | curious(X0) | quiet(X0) | ~brave(X0) [cnf transformation 56]
121. wise(X0) | ~curious(X0) | quiet(X0) | ~brave(X0) [cnf transformation 56]
140. calm(fred) [cnf transformation 24]
141. ~quiet(X0) [subsumption resolution 80,81]
162. ~wise(X0) | ~curious(X0) [subsumption resolution 97,99]
163. wise(X0) | curious(X0) [subsumption resolution 96,98]
196. ~calm(X0) | curious(X0) [subsumption resolution 113,141]
198. wise(X0) | ~curious(X0) | ~brave(X0) [subsumption resolution 121,141]
199. ~curious(X0) | ~brave(X0) [subsumption resolution 198,162]
200. ~wise(X0) | curious(X0) | ~brave(X0) [subsumption resolution 119,141]
201. curious(X0) | ~brave(X0) [subsumption resolution 200,163]
202. ~brave(X0) [subsumption resolution 201,199]
253. humble(fred) [resolution 116,140]
257. curious(fred) [resolution 196,140]
281. brave(fred) | wise(fred) [resolution 93,253]
283. wise(fred) [subsumption resolution 281,202]
285. ~curious(fred) [resolution 283,162]
287. $false [subsumption resolution 285,257]
% SZS output end Proof for 773695538699462174164264
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich is both brave and not kind.
Everyone who is both not generous and wise is calm and vice versa.
Everyone who is either not calm or not tall is either humble or brave and vice versa.
Everyone who is either not rich or not generous is both not old and not rich.
If someone is either not quiet or not humble then someone is both not calm and not funny and vice versa.
Everyone who is either brave or not rich is not funny and vice versa.
Everyone who is brave is either creative or rich and vice versa.
If paul is not kind then susan is either not creative or humble.
Everyone who is either not creative or creative is patient or not rich and vice versa.
Everyone who is calm is both not creative and not quiet.
Everyone who is both not curious and not humble is both not humble and not strong and vice versa.
If someone is either not rich or calm then alice is either not happy or not patient.
If lucy is both not calm and not quiet then susan is both not curious and strong and vice versa.
If someone is not kind then someone is not curious.
If paul is not kind or not calm then alice is funny or not tall and vice versa.
If someone is either old or brave then someone is both not happy and humble.
Someone is either not patient or tall.
Alice is both strong and rich.
Someone is not rich or happy.
Fred is not strong or strong.
Someone is not creative or not tall.
Mary is both patient and not tall.
Someone is not humble.
Paul is both not calm and not patient. | Paul is funny. | entailment | (![X]:(~rich(X)=>(brave(X)&~kind(X))))&
(![X]:((~generous(X)&wise(X))<=>calm(X)))&
(![X]:((~calm(X)<~>~tall(X))<=>(humble(X)<~>brave(X))))&
(![X]:((~rich(X)<~>~generous(X))=>(~old(X)&~rich(X))))&
((?[X]:((~quiet(X)<~>~humble(X))))<=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((brave(X)<~>~rich(X))<=>~funny(X)))&
(![X]:(brave(X)<=>(creative(X)<~>rich(X))))&
((~kind(paul))=>((~creative(susan)<~>humble(susan))))&
(![X]:((~creative(X)<~>creative(X))<=>(patient(X)|~rich(X))))&
(![X]:(calm(X)=>(~creative(X)&~quiet(X))))&
(![X]:((~curious(X)&~humble(X))<=>(~humble(X)&~strong(X))))&
((?[X]:((~rich(X)<~>calm(X))))=>((~happy(alice)<~>~patient(alice))))&
(((~calm(lucy)&~quiet(lucy)))<=>((~curious(susan)&strong(susan))))&
((?[X]:(~kind(X)))=>(?[X]:(~curious(X))))&
(((~kind(paul)|~calm(paul)))<=>((funny(alice)|~tall(alice))))&
((?[X]:((old(X)<~>brave(X))))=>(?[X]:((~happy(X)&humble(X)))))&
(?[X]:((~patient(X)<~>tall(X))))&
((strong(alice)&rich(alice)))&
(?[X]:((~rich(X)|happy(X))))&
((~strong(fred)|strong(fred)))&
(?[X]:((~creative(X)|~tall(X))))&
((patient(mary)&~tall(mary)))&
(?[X]:(~humble(X)))&
((~calm(paul)&~patient(paul))) | funny(paul) | [
"p0",
"p5",
"p6",
"p8",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7299004417187907543395051
% SZS output start Proof for 7299004417187907543395051
1. ! [X0] : (~rich(X0) => (~kind(X0) & brave(X0))) [input p0]
6. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> ~funny(X0)) [input p5]
7. ! [X0] : (brave(X0) <=> (creative(X0) <~> rich(X0))) [input p6]
9. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (~rich(X0) | patient(X0))) [input p8]
24. ~patient(paul) & ~calm(paul) [input p23]
25. ~funny(paul) [input hypothesis]
29. ! [X0] : ((~kind(X0) & brave(X0)) | rich(X0)) [ennf transformation 1]
45. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | funny(X0)) & (~funny(X0) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 6]
46. ! [X0] : ((brave(X0) | ((creative(X0) | ~rich(X0)) & (rich(X0) | ~creative(X0)))) & (((~rich(X0) | ~creative(X0)) & (rich(X0) | creative(X0))) | ~brave(X0))) [nnf transformation 7]
48. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (rich(X0) & ~patient(X0))) & ((~rich(X0) | patient(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 9]
49. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (rich(X0) & ~patient(X0))) & (~rich(X0) | patient(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 48]
73. brave(X0) | rich(X0) [cnf transformation 29]
98. ~rich(X0) | brave(X0) | funny(X0) [cnf transformation 45]
99. rich(X0) | ~brave(X0) | funny(X0) [cnf transformation 45]
100. rich(X0) | creative(X0) | ~brave(X0) [cnf transformation 46]
101. ~creative(X0) | ~rich(X0) | ~brave(X0) [cnf transformation 46]
103. brave(X0) | creative(X0) | ~rich(X0) [cnf transformation 46]
106. ~rich(X0) | patient(X0) | creative(X0) | creative(X0) [cnf transformation 49]
146. ~patient(paul) [cnf transformation 24]
147. ~funny(paul) [cnf transformation 25]
148. ~rich(X0) | patient(X0) | creative(X0) [duplicate literal removal 106]
182. funny(X0) | rich(X0) [subsumption resolution 99,73]
183. funny(X0) | brave(X0) [subsumption resolution 98,182]
184. creative(X0) | brave(X0) [subsumption resolution 103,73]
185. creative(X0) | rich(X0) [subsumption resolution 100,184]
200. patient(X0) | creative(X0) [subsumption resolution 148,185]
312. rich(paul) [resolution 182,147]
315. brave(paul) [resolution 183,147]
322. creative(paul) [resolution 200,146]
332. ~rich(paul) | ~brave(paul) [resolution 101,322]
334. ~brave(paul) [subsumption resolution 332,312]
335. $false [subsumption resolution 334,315]
% SZS output end Proof for 7299004417187907543395051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is not rich or calm then susan is either not quiet or not creative and vice versa.
Everyone who is both not funny and curious is either not generous or not wise and vice versa.
Everyone who is either rich or not humble is not old or tall and vice versa.
Everyone who is both strong and happy is not funny or humble and vice versa.
If mary is either brave or not brave then john is not calm or not quiet.
Everyone who is either not funny or not humble is both not calm and not patient and vice versa.
If someone is rich then paul is tall or happy and vice versa.
If someone is both not rich and humble then someone is not rich or humble and vice versa.
Everyone who is not generous or not humble is either not humble or old and vice versa.
If john is both not quiet and not calm then lucy is either not calm or funny.
If someone is either strong or happy then someone is old or quiet and vice versa.
If lucy is either tall or calm then john is both not humble and funny.
If someone is either tall or funny then someone is both generous and not quiet and vice versa.
Everyone who is both not creative and curious is both not generous and not quiet and vice versa.
If susan is either funny or not funny then someone is either not creative or not strong and vice versa.
Someone is wise or calm.
Someone is kind.
Someone is generous or not curious.
Someone is both strong and not quiet.
Alice is either creative or strong.
Someone is either happy or not kind.
John is tall or generous. | Fred is humble. | neutral | (((~rich(fred)|calm(fred)))<=>((~quiet(susan)<~>~creative(susan))))&
(![X]:((~funny(X)&curious(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((rich(X)<~>~humble(X))<=>(~old(X)|tall(X))))&
(![X]:((strong(X)&happy(X))<=>(~funny(X)|humble(X))))&
(((brave(mary)<~>~brave(mary)))=>((~calm(john)|~quiet(john))))&
(![X]:((~funny(X)<~>~humble(X))<=>(~calm(X)&~patient(X))))&
((?[X]:(rich(X)))<=>((tall(paul)|happy(paul))))&
((?[X]:((~rich(X)&humble(X))))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((~generous(X)|~humble(X))<=>(~humble(X)<~>old(X))))&
(((~quiet(john)&~calm(john)))=>((~calm(lucy)<~>funny(lucy))))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((old(X)|quiet(X)))))&
(((tall(lucy)<~>calm(lucy)))=>((~humble(john)&funny(john))))&
((?[X]:((tall(X)<~>funny(X))))<=>(?[X]:((generous(X)&~quiet(X)))))&
(![X]:((~creative(X)&curious(X))<=>(~generous(X)&~quiet(X))))&
(((funny(susan)<~>~funny(susan)))<=>(?[X]:((~creative(X)<~>~strong(X)))))&
(?[X]:((wise(X)|calm(X))))&
(?[X]:(kind(X)))&
(?[X]:((generous(X)|~curious(X))))&
(?[X]:((strong(X)&~quiet(X))))&
((creative(alice)<~>strong(alice)))&
(?[X]:((happy(X)<~>~kind(X))))&
((tall(john)|generous(john))) | humble(fred) | [] | null | 0 |
If someone is both not rich and calm then alice is either quiet or not kind and vice versa. If john is either not happy or quiet then someone is both curious and happy and vice versa. Everyone who is either happy or tall is both curious and not creative and vice versa. Everyone who is either not wise or not strong is both humble and calm. Everyone who is either not old or not creative is both not humble and quiet. Everyone who is brave is both humble and calm and vice versa. Everyone who is not curious or patient is either funny or not kind. If paul is strong then someone is either not quiet or wise and vice versa. Everyone who is calm is not brave. If someone is old or creative then someone is either not patient or patient and vice versa. If someone is both not brave and not patient then fred is either not rich or wise. Everyone who is either not strong or quiet is either not strong or patient. If alice is either wise or brave then someone is brave. If someone is either not happy or not kind then fred is not creative and vice versa. Everyone who is either not strong or kind is both curious and old. If someone is either not patient or not curious then someone is both not kind and not calm and vice versa. Someone is both calm and not happy. Someone is both not creative and generous. Mary is either not humble or not rich. Someone is quiet. Paul is both kind and humble. Someone is not humble. Someone is either not quiet or tall. Susan is not funny or not creative. | Alice is not rich. | neutral | ((?[X]:((~rich(X)&calm(X))))<=>((quiet(alice)<~>~kind(alice))))&
(((~happy(john)<~>quiet(john)))<=>(?[X]:((curious(X)&happy(X)))))&
(![X]:((happy(X)<~>tall(X))<=>(curious(X)&~creative(X))))&
(![X]:((~wise(X)<~>~strong(X))=>(humble(X)&calm(X))))&
(![X]:((~old(X)<~>~creative(X))=>(~humble(X)&quiet(X))))&
(![X]:(brave(X)<=>(humble(X)&calm(X))))&
(![X]:((~curious(X)|patient(X))=>(funny(X)<~>~kind(X))))&
((strong(paul))<=>(?[X]:((~quiet(X)<~>wise(X)))))&
(![X]:(calm(X)=>~brave(X)))&
((?[X]:((old(X)|creative(X))))<=>(?[X]:((~patient(X)<~>patient(X)))))&
((?[X]:((~brave(X)&~patient(X))))=>((~rich(fred)<~>wise(fred))))&
(![X]:((~strong(X)<~>quiet(X))=>(~strong(X)<~>patient(X))))&
(((wise(alice)<~>brave(alice)))=>(?[X]:(brave(X))))&
((?[X]:((~happy(X)<~>~kind(X))))<=>(~creative(fred)))&
(![X]:((~strong(X)<~>kind(X))=>(curious(X)&old(X))))&
((?[X]:((~patient(X)<~>~curious(X))))<=>(?[X]:((~kind(X)&~calm(X)))))&
(?[X]:((calm(X)&~happy(X))))&
(?[X]:((~creative(X)&generous(X))))&
((~humble(mary)<~>~rich(mary)))&
(?[X]:(quiet(X)))&
((kind(paul)&humble(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((~quiet(X)<~>tall(X))))&
((~funny(susan)|~creative(susan))) | ~rich(alice) | [] | null | 0 |
Everyone who is strong or not patient is rich or not calm and vice versa.
Everyone who is not brave or not humble is both not tall and humble.
If fred is not kind then lucy is both not tall and generous and vice versa.
Everyone who is not generous is curious.
Everyone who is either not funny or kind is either patient or kind.
Everyone who is either not strong or humble is both not wise and not patient.
Everyone who is old is both not generous and strong.
If someone is both humble and rich then paul is not brave and vice versa.
If someone is both not patient and wise then john is kind.
Everyone who is not humble or not curious is either not generous or not funny and vice versa.
Everyone who is either not generous or humble is either generous or kind and vice versa.
Everyone who is both humble and old is either not brave or quiet and vice versa.
If mary is both not calm and not strong then paul is both brave and rich.
Everyone who is either old or kind is quiet or not generous and vice versa.
If someone is both not old and old then someone is not creative or not wise.
Everyone who is either not patient or not brave is either generous or kind.
Mary is funny.
Lucy is brave or strong.
Alice is not kind.
Susan is either strong or generous.
Someone is not quiet.
Lucy is either curious or quiet.
John is brave. | Susan is not old. | entailment | (![X]:((strong(X)|~patient(X))<=>(rich(X)|~calm(X))))&
(![X]:((~brave(X)|~humble(X))=>(~tall(X)&humble(X))))&
((~kind(fred))<=>((~tall(lucy)&generous(lucy))))&
(![X]:(~generous(X)=>curious(X)))&
(![X]:((~funny(X)<~>kind(X))=>(patient(X)<~>kind(X))))&
(![X]:((~strong(X)<~>humble(X))=>(~wise(X)&~patient(X))))&
(![X]:(old(X)=>(~generous(X)&strong(X))))&
((?[X]:((humble(X)&rich(X))))<=>(~brave(paul)))&
((?[X]:((~patient(X)&wise(X))))=>(kind(john)))&
(![X]:((~humble(X)|~curious(X))<=>(~generous(X)<~>~funny(X))))&
(![X]:((~generous(X)<~>humble(X))<=>(generous(X)<~>kind(X))))&
(![X]:((humble(X)&old(X))<=>(~brave(X)<~>quiet(X))))&
(((~calm(mary)&~strong(mary)))=>((brave(paul)&rich(paul))))&
(![X]:((old(X)<~>kind(X))<=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)&old(X))))=>(?[X]:((~creative(X)|~wise(X)))))&
(![X]:((~patient(X)<~>~brave(X))=>(generous(X)<~>kind(X))))&
(funny(mary))&
((brave(lucy)|strong(lucy)))&
(~kind(alice))&
((strong(susan)<~>generous(susan)))&
(?[X]:(~quiet(X)))&
((curious(lucy)<~>quiet(lucy)))&
(brave(john)) | ~old(susan) | [
"p1",
"p3",
"p4",
"p5",
"p6",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6570517074084411633968038
% SZS output start Proof for 6570517074084411633968038
2. ! [X0] : ((~humble(X0) | ~brave(X0)) => (humble(X0) & ~tall(X0))) [input p1]
4. ! [X0] : (~generous(X0) => curious(X0)) [input p3]
5. ! [X0] : ((~funny(X0) <~> kind(X0)) => (patient(X0) <~> kind(X0))) [input p4]
6. ! [X0] : ((~strong(X0) <~> humble(X0)) => (~patient(X0) & ~wise(X0))) [input p5]
7. ! [X0] : (old(X0) => (strong(X0) & ~generous(X0))) [input p6]
10. ! [X0] : ((~curious(X0) | ~humble(X0)) <=> (~generous(X0) <~> ~funny(X0))) [input p9]
11. ! [X0] : ((~generous(X0) <~> humble(X0)) <=> (generous(X0) <~> kind(X0))) [input p10]
24. old(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) <~> humble(X0)) => ~patient(X0)) [pure predicate removal 6]
29. ! [X0] : ((humble(X0) & ~tall(X0)) | (humble(X0) & brave(X0))) [ennf transformation 2]
30. ! [X0] : (curious(X0) | generous(X0)) [ennf transformation 4]
31. ! [X0] : ((patient(X0) <~> kind(X0)) | (~funny(X0) <=> kind(X0))) [ennf transformation 5]
32. ! [X0] : (~patient(X0) | (~strong(X0) <=> humble(X0))) [ennf transformation 27]
33. ! [X0] : ((strong(X0) & ~generous(X0)) | ~old(X0)) [ennf transformation 7]
41. ! [X0] : (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | ((~funny(X0) | ~kind(X0)) & (kind(X0) | funny(X0)))) [nnf transformation 31]
42. ! [X0] : (~patient(X0) | ((~strong(X0) | ~humble(X0)) & (humble(X0) | strong(X0)))) [nnf transformation 32]
47. ! [X0] : (((~curious(X0) | ~humble(X0)) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0)))) & (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (curious(X0) & humble(X0)))) [nnf transformation 10]
48. ! [X0] : ((~curious(X0) | ~humble(X0) | ((~generous(X0) | funny(X0)) & (~funny(X0) | generous(X0)))) & (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | (curious(X0) & humble(X0)))) [flattening 47]
49. ! [X0] : ((((~humble(X0) | generous(X0)) & (humble(X0) | ~generous(X0))) | ((generous(X0) | ~kind(X0)) & (kind(X0) | ~generous(X0)))) & (((~kind(X0) | ~generous(X0)) & (kind(X0) | generous(X0))) | ((~generous(X0) | ~humble(X0)) & (humble(X0) | generous(X0))))) [nnf transformation 11]
66. humble(X0) | humble(X0) [cnf transformation 29]
70. curious(X0) | generous(X0) [cnf transformation 30]
71. kind(X0) | patient(X0) | kind(X0) | funny(X0) [cnf transformation 41]
76. ~patient(X0) | ~strong(X0) | ~humble(X0) [cnf transformation 42]
77. ~old(X0) | ~generous(X0) [cnf transformation 33]
78. ~old(X0) | strong(X0) [cnf transformation 33]
86. ~curious(X0) | ~humble(X0) | ~funny(X0) | generous(X0) [cnf transformation 48]
91. ~kind(X0) | ~generous(X0) | ~generous(X0) | ~humble(X0) [cnf transformation 49]
95. ~humble(X0) | generous(X0) | generous(X0) | ~kind(X0) [cnf transformation 49]
123. old(susan) [cnf transformation 24]
125. ~kind(X0) | ~generous(X0) | ~humble(X0) [duplicate literal removal 91]
127. ~humble(X0) | generous(X0) | ~kind(X0) [duplicate literal removal 95]
128. funny(X0) | patient(X0) | kind(X0) [duplicate literal removal 71]
130. humble(X0) [duplicate literal removal 66]
146. ~patient(X0) | ~strong(X0) [subsumption resolution 76,130]
162. ~curious(X0) | ~funny(X0) | generous(X0) [subsumption resolution 86,130]
163. ~funny(X0) | generous(X0) [subsumption resolution 162,70]
165. ~kind(X0) | generous(X0) [subsumption resolution 127,130]
166. ~kind(X0) | ~generous(X0) [subsumption resolution 125,130]
167. ~kind(X0) [subsumption resolution 166,165]
198. 12 <=> strong(susan) [avatar definition]
199. strong(susan) <- (12) [avatar component clause 198]
202. 13 <=> generous(susan) [avatar definition]
204. ~generous(susan) <- (~13) [avatar component clause 202]
217. ~generous(susan) [resolution 77,123]
218. strong(susan) [resolution 78,123]
256. patient(X1) | kind(X1) | generous(X1) [resolution 128,163]
258. generous(X1) | patient(X1) [subsumption resolution 256,167]
261. patient(susan) <- (~13) [resolution 258,204]
274. ~strong(susan) <- (~13) [resolution 261,146]
275. $false <- (12, ~13) [subsumption resolution 274,199]
276. ~12 | 13 [avatar contradiction clause 275]
277. 12 [avatar split clause 218,198]
278. ~13 [avatar split clause 217,202]
279. $false [avatar sat refutation 276,277,278]
% SZS output end Proof for 6570517074084411633968038
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is both not creative and not humble then fred is not tall and vice versa.
If john is both not brave and creative then someone is not patient or humble.
If someone is creative then someone is both old and rich.
If someone is either quiet or strong then someone is calm or happy and vice versa.
If paul is not humble then paul is not brave and vice versa.
Everyone who is humble or strong is both curious and not generous and vice versa.
If someone is not patient then someone is not strong.
Everyone who is not old is either not brave or not curious and vice versa.
Everyone who is either not generous or happy is both kind and not creative.
If lucy is not quiet or calm then someone is both not humble and not patient.
Everyone who is both not generous and tall is either rich or not happy and vice versa.
If alice is not patient then someone is either wise or strong.
Everyone who is both not tall and not rich is curious and vice versa.
Everyone who is not happy is both not tall and wise.
If lucy is either humble or happy then someone is both quiet and not old.
Everyone who is tall or creative is both patient and creative.
Fred is not patient or humble.
Lucy is not old.
Someone is not patient or rich.
Someone is either not calm or quiet.
Someone is not funny or old.
John is both funny and kind.
John is both happy and not calm.
John is both not creative and not wise. | John is rich. | contradiction | (((~creative(alice)&~humble(alice)))<=>(~tall(fred)))&
(((~brave(john)&creative(john)))=>(?[X]:((~patient(X)|humble(X)))))&
((?[X]:(creative(X)))=>(?[X]:((old(X)&rich(X)))))&
((?[X]:((quiet(X)<~>strong(X))))<=>(?[X]:((calm(X)|happy(X)))))&
((~humble(paul))<=>(~brave(paul)))&
(![X]:((humble(X)|strong(X))<=>(curious(X)&~generous(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~strong(X))))&
(![X]:(~old(X)<=>(~brave(X)<~>~curious(X))))&
(![X]:((~generous(X)<~>happy(X))=>(kind(X)&~creative(X))))&
(((~quiet(lucy)|calm(lucy)))=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((~generous(X)&tall(X))<=>(rich(X)<~>~happy(X))))&
((~patient(alice))=>(?[X]:((wise(X)<~>strong(X)))))&
(![X]:((~tall(X)&~rich(X))<=>curious(X)))&
(![X]:(~happy(X)=>(~tall(X)&wise(X))))&
(((humble(lucy)<~>happy(lucy)))=>(?[X]:((quiet(X)&~old(X)))))&
(![X]:((tall(X)|creative(X))=>(patient(X)&creative(X))))&
((~patient(fred)|humble(fred)))&
(~old(lucy))&
(?[X]:((~patient(X)|rich(X))))&
(?[X]:((~calm(X)<~>quiet(X))))&
(?[X]:((~funny(X)|old(X))))&
((funny(john)&kind(john)))&
((happy(john)&~calm(john)))&
((~creative(john)&~wise(john))) | rich(john) | [
"p10",
"p15",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4145023385772231556613230
% SZS output start Proof for 4145023385772231556613230
11. ! [X0] : ((tall(X0) & ~generous(X0)) <=> (rich(X0) <~> ~happy(X0))) [input p10]
16. ! [X0] : ((creative(X0) | tall(X0)) => (creative(X0) & patient(X0))) [input p15]
23. ~calm(john) & happy(john) [input p22]
24. ~wise(john) & ~creative(john) [input p23]
25. rich(john) [input hypothesis]
40. ! [X0] : ((creative(X0) & patient(X0)) | (~creative(X0) & ~tall(X0))) [ennf transformation 16]
63. ! [X0] : (((tall(X0) & ~generous(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) & (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (~tall(X0) | generous(X0)))) [nnf transformation 11]
64. ! [X0] : (((tall(X0) & ~generous(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0)))) & (((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | ~tall(X0) | generous(X0))) [flattening 63]
114. ~happy(X0) | tall(X0) | ~rich(X0) [cnf transformation 64]
129. ~tall(X0) | creative(X0) [cnf transformation 40]
138. happy(john) [cnf transformation 23]
140. ~creative(john) [cnf transformation 24]
142. rich(john) [cnf transformation 25]
163. 5 <=> creative(john) [avatar definition]
331. ~5 [avatar split clause 140,163]
339. tall(john) | ~rich(john) [resolution 114,138]
340. tall(john) [subsumption resolution 339,142]
341. creative(john) [resolution 340,129]
346. 5 [avatar split clause 341,163]
347. $false [avatar sat refutation 331,346]
% SZS output end Proof for 4145023385772231556613230
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is wise then someone is both generous and calm and vice versa.
If someone is both kind and not rich then someone is either not brave or not kind.
If someone is generous then someone is tall or not curious.
Everyone who is not funny or old is both brave and not kind.
Everyone who is both not creative and humble is not humble and vice versa.
Everyone who is not rich or rich is not old or not kind and vice versa.
Everyone who is not brave or not old is either old or not generous.
Everyone who is strong is old or not tall and vice versa.
Everyone who is calm is kind or happy and vice versa.
Everyone who is both not patient and not humble is either not generous or not old.
Everyone who is both strong and not rich is either not brave or kind.
Everyone who is curious is both happy and not brave and vice versa.
Everyone who is both quiet and not calm is either old or not tall.
Everyone who is either not quiet or curious is either quiet or not funny and vice versa.
If susan is not happy then someone is either not patient or not curious and vice versa.
Everyone who is wise or not brave is quiet or funny and vice versa.
Someone is not kind or strong.
Paul is old or not quiet.
Someone is old.
Susan is both not happy and not wise.
Susan is either not funny or old.
Lucy is not humble or not tall.
Alice is quiet or wise.
Paul is both not patient and tall. | Lucy is not kind. | neutral | ((?[X]:(wise(X)))<=>(?[X]:((generous(X)&calm(X)))))&
((?[X]:((kind(X)&~rich(X))))=>(?[X]:((~brave(X)<~>~kind(X)))))&
((?[X]:(generous(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(![X]:((~funny(X)|old(X))=>(brave(X)&~kind(X))))&
(![X]:((~creative(X)&humble(X))<=>~humble(X)))&
(![X]:((~rich(X)|rich(X))<=>(~old(X)|~kind(X))))&
(![X]:((~brave(X)|~old(X))=>(old(X)<~>~generous(X))))&
(![X]:(strong(X)<=>(old(X)|~tall(X))))&
(![X]:(calm(X)<=>(kind(X)|happy(X))))&
(![X]:((~patient(X)&~humble(X))=>(~generous(X)<~>~old(X))))&
(![X]:((strong(X)&~rich(X))=>(~brave(X)<~>kind(X))))&
(![X]:(curious(X)<=>(happy(X)&~brave(X))))&
(![X]:((quiet(X)&~calm(X))=>(old(X)<~>~tall(X))))&
(![X]:((~quiet(X)<~>curious(X))<=>(quiet(X)<~>~funny(X))))&
((~happy(susan))<=>(?[X]:((~patient(X)<~>~curious(X)))))&
(![X]:((wise(X)|~brave(X))<=>(quiet(X)|funny(X))))&
(?[X]:((~kind(X)|strong(X))))&
((old(paul)|~quiet(paul)))&
(?[X]:(old(X)))&
((~happy(susan)&~wise(susan)))&
((~funny(susan)<~>old(susan)))&
((~humble(lucy)|~tall(lucy)))&
((quiet(alice)|wise(alice)))&
((~patient(paul)&tall(paul))) | ~kind(lucy) | [] | null | 0 |
If alice is either old or not tall then someone is both patient and calm. Everyone who is either rich or not happy is both not rich and not old and vice versa. Everyone who is either creative or not tall is both strong and not old. If susan is both not funny and wise then john is either not happy or brave. Everyone who is both humble and not strong is either not old or not creative and vice versa. Everyone who is either brave or not tall is both not brave and not humble. If john is either old or not kind then someone is either strong or brave. If mary is both not kind and curious then someone is tall or not brave and vice versa. Everyone who is either strong or not patient is either tall or wise and vice versa. Everyone who is not brave is not wise or funny and vice versa. If paul is both not calm and curious then fred is quiet or not strong. Everyone who is not wise is not kind. Everyone who is not funny or not humble is curious or not old. Everyone who is both not funny and not old is both not funny and not tall and vice versa. Everyone who is not humble is not old and vice versa. Everyone who is both not creative and generous is happy or not brave. Someone is not patient. Someone is not curious. Fred is not curious or not generous. Someone is both not creative and calm. Someone is both patient and not happy. Fred is either kind or wise. Someone is either not tall or not generous. Fred is either funny or wise. | Fred is generous. | contradiction | (((old(alice)<~>~tall(alice)))=>(?[X]:((patient(X)&calm(X)))))&
(![X]:((rich(X)<~>~happy(X))<=>(~rich(X)&~old(X))))&
(![X]:((creative(X)<~>~tall(X))=>(strong(X)&~old(X))))&
(((~funny(susan)&wise(susan)))=>((~happy(john)<~>brave(john))))&
(![X]:((humble(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(![X]:((brave(X)<~>~tall(X))=>(~brave(X)&~humble(X))))&
(((old(john)<~>~kind(john)))=>(?[X]:((strong(X)<~>brave(X)))))&
(((~kind(mary)&curious(mary)))<=>(?[X]:((tall(X)|~brave(X)))))&
(![X]:((strong(X)<~>~patient(X))<=>(tall(X)<~>wise(X))))&
(![X]:(~brave(X)<=>(~wise(X)|funny(X))))&
(((~calm(paul)&curious(paul)))=>((quiet(fred)|~strong(fred))))&
(![X]:(~wise(X)=>~kind(X)))&
(![X]:((~funny(X)|~humble(X))=>(curious(X)|~old(X))))&
(![X]:((~funny(X)&~old(X))<=>(~funny(X)&~tall(X))))&
(![X]:(~humble(X)<=>~old(X)))&
(![X]:((~creative(X)&generous(X))=>(happy(X)|~brave(X))))&
(?[X]:(~patient(X)))&
(?[X]:(~curious(X)))&
((~curious(fred)|~generous(fred)))&
(?[X]:((~creative(X)&calm(X))))&
(?[X]:((patient(X)&~happy(X))))&
((kind(fred)<~>wise(fred)))&
(?[X]:((~tall(X)<~>~generous(X))))&
((funny(fred)<~>wise(fred))) | generous(fred) | [
"p1",
"p4",
"p5",
"p9",
"p11",
"p13",
"p14",
"p15",
"p21",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 7453073670672010546831542
% SZS output start Proof for 7453073670672010546831542
2. ! [X0] : ((rich(X0) <~> ~happy(X0)) <=> (~old(X0) & ~rich(X0))) [input p1]
5. ! [X0] : ((~strong(X0) & humble(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p4]
6. ! [X0] : ((brave(X0) <~> ~tall(X0)) => (~humble(X0) & ~brave(X0))) [input p5]
10. ! [X0] : (~brave(X0) <=> (funny(X0) | ~wise(X0))) [input p9]
12. ! [X0] : (~wise(X0) => ~kind(X0)) [input p11]
14. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (~tall(X0) & ~funny(X0))) [input p13]
15. ! [X0] : (~humble(X0) <=> ~old(X0)) [input p14]
16. ! [X0] : ((generous(X0) & ~creative(X0)) => (~brave(X0) | happy(X0))) [input p15]
22. kind(fred) <~> wise(fred) [input p21]
24. funny(fred) <~> wise(fred) [input p23]
25. generous(fred) [input hypothesis]
33. ! [X0] : ((~humble(X0) & ~brave(X0)) | (brave(X0) <=> ~tall(X0))) [ennf transformation 6]
35. ! [X0] : (~kind(X0) | wise(X0)) [ennf transformation 12]
38. ! [X0] : ((~brave(X0) | happy(X0)) | (~generous(X0) | creative(X0))) [ennf transformation 16]
39. ! [X0] : (~brave(X0) | happy(X0) | ~generous(X0) | creative(X0)) [flattening 38]
43. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | (old(X0) | rich(X0))) & ((~old(X0) & ~rich(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [nnf transformation 2]
44. ! [X0] : ((((happy(X0) | ~rich(X0)) & (~happy(X0) | rich(X0))) | old(X0) | rich(X0)) & ((~old(X0) & ~rich(X0)) | ((rich(X0) | happy(X0)) & (~happy(X0) | ~rich(X0))))) [flattening 43]
47. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (strong(X0) | ~humble(X0)))) [nnf transformation 5]
48. ! [X0] : (((~strong(X0) & humble(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | strong(X0) | ~humble(X0))) [flattening 47]
49. ! [X0] : ((~humble(X0) & ~brave(X0)) | ((brave(X0) | tall(X0)) & (~tall(X0) | ~brave(X0)))) [nnf transformation 33]
59. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & ((funny(X0) | ~wise(X0)) | brave(X0))) [nnf transformation 10]
60. ! [X0] : ((~brave(X0) | (~funny(X0) & wise(X0))) & (funny(X0) | ~wise(X0) | brave(X0))) [flattening 59]
61. ! [X0] : (((~old(X0) & ~funny(X0)) | (tall(X0) | funny(X0))) & ((~tall(X0) & ~funny(X0)) | (old(X0) | funny(X0)))) [nnf transformation 14]
62. ! [X0] : (((~old(X0) & ~funny(X0)) | tall(X0) | funny(X0)) & ((~tall(X0) & ~funny(X0)) | old(X0) | funny(X0))) [flattening 61]
63. ! [X0] : ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0))) [nnf transformation 15]
72. (~wise(fred) | ~kind(fred)) & (wise(fred) | kind(fred)) [nnf transformation 22]
76. (~wise(fred) | ~funny(fred)) & (wise(fred) | funny(fred)) [nnf transformation 24]
79. ~rich(X0) | ~happy(X0) | ~rich(X0) [cnf transformation 44]
83. ~happy(X0) | rich(X0) | old(X0) | rich(X0) [cnf transformation 44]
91. ~humble(X0) | ~old(X0) | strong(X0) | ~creative(X0) [cnf transformation 48]
93. ~creative(X0) | humble(X0) | old(X0) [cnf transformation 48]
95. ~strong(X0) | ~creative(X0) | old(X0) [cnf transformation 48]
97. ~brave(X0) | ~tall(X0) | ~brave(X0) [cnf transformation 49]
118. ~wise(X0) | funny(X0) | brave(X0) [cnf transformation 60]
121. ~kind(X0) | wise(X0) [cnf transformation 35]
127. ~old(X0) | tall(X0) | funny(X0) [cnf transformation 62]
128. ~old(X0) | humble(X0) [cnf transformation 63]
129. ~humble(X0) | old(X0) [cnf transformation 63]
130. ~generous(X0) | happy(X0) | ~brave(X0) | creative(X0) [cnf transformation 39]
137. wise(fred) | kind(fred) [cnf transformation 72]
138. ~wise(fred) | ~kind(fred) [cnf transformation 72]
142. ~wise(fred) | ~funny(fred) [cnf transformation 76]
143. generous(fred) [cnf transformation 25]
144. ~brave(X0) | ~tall(X0) [duplicate literal removal 97]
145. ~happy(X0) | ~rich(X0) [duplicate literal removal 79]
146. ~happy(X0) | rich(X0) | old(X0) [duplicate literal removal 83]
228. 18 <=> generous(fred) [avatar definition]
229. generous(fred) <- (18) [avatar component clause 228]
232. ~kind(fred) [subsumption resolution 138,121]
233. wise(fred) [subsumption resolution 137,232]
244. ~funny(fred) [subsumption resolution 142,233]
245. 18 [avatar split clause 143,228]
298. funny(fred) | brave(fred) [resolution 118,233]
300. brave(fred) [subsumption resolution 298,244]
306. ~tall(fred) [resolution 300,144]
402. 40 <=> strong(fred) [avatar definition]
403. ~strong(fred) <- (~40) [avatar component clause 402]
404. strong(fred) <- (40) [avatar component clause 402]
420. happy(fred) | ~brave(fred) | creative(fred) <- (18) [resolution 130,229]
422. happy(fred) | creative(fred) <- (18) [subsumption resolution 420,300]
424. 41 <=> creative(fred) [avatar definition]
426. creative(fred) <- (41) [avatar component clause 424]
428. 42 <=> happy(fred) [avatar definition]
430. happy(fred) <- (42) [avatar component clause 428]
431. 41 | 42 | ~18 [avatar split clause 422,228,428,424]
446. humble(fred) | old(fred) <- (41) [resolution 426,93]
449. humble(fred) <- (41) [subsumption resolution 446,128]
642. ~old(fred) | strong(fred) | ~creative(fred) <- (41) [resolution 449,91]
645. old(fred) <- (41) [resolution 449,129]
646. ~old(fred) | ~creative(fred) <- (~40, 41) [subsumption resolution 642,403]
647. ~old(fred) <- (~40, 41) [subsumption resolution 646,426]
648. $false <- (~40, 41) [subsumption resolution 645,647]
649. 40 | ~41 [avatar contradiction clause 648]
658. ~creative(fred) | old(fred) <- (40) [resolution 404,95]
660. rich(fred) | old(fred) <- (42) [resolution 430,146]
662. ~rich(fred) <- (42) [resolution 430,145]
666. old(fred) <- (42) [subsumption resolution 660,662]
766. tall(fred) | funny(fred) <- (42) [resolution 666,127]
772. funny(fred) <- (42) [subsumption resolution 766,306]
773. $false <- (42) [subsumption resolution 772,244]
774. ~42 [avatar contradiction clause 773]
776. old(fred) <- (40, 41) [subsumption resolution 658,426]
817. tall(fred) | funny(fred) <- (40, 41) [resolution 776,127]
823. funny(fred) <- (40, 41) [subsumption resolution 817,306]
824. $false <- (40, 41) [subsumption resolution 823,244]
825. ~40 | ~41 [avatar contradiction clause 824]
826. $false [avatar sat refutation 245,431,649,774,825]
% SZS output end Proof for 7453073670672010546831542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is either happy or not humble. Everyone who is both not calm and creative is both not patient and not calm and vice versa. Everyone who is not calm or brave is not quiet and vice versa. Everyone who is either not quiet or generous is either calm or patient. If john is both not tall and wise then john is both humble and old. Everyone who is either not rich or calm is wise or not happy. Everyone who is both curious and not strong is both calm and not happy. Everyone who is wise is both not funny and not wise. If alice is not quiet or funny then fred is old or not kind and vice versa. If alice is happy or not happy then susan is either not funny or not brave and vice versa. Everyone who is not strong or not happy is both not rich and happy. If susan is both happy and humble then alice is brave. Everyone who is not humble or creative is not wise or not calm and vice versa. If someone is kind or not curious then paul is both happy and not happy. Everyone who is either tall or humble is not calm and vice versa. Everyone who is not humble is both not generous and not patient and vice versa. Paul is patient or not generous. Someone is both tall and strong. Someone is either not generous or not creative. Paul is both not wise and not quiet. Fred is either not wise or old. Paul is both not quiet and patient. | Alice is happy. | entailment | (![X]:(brave(X)=>(happy(X)<~>~humble(X))))&
(![X]:((~calm(X)&creative(X))<=>(~patient(X)&~calm(X))))&
(![X]:((~calm(X)|brave(X))<=>~quiet(X)))&
(![X]:((~quiet(X)<~>generous(X))=>(calm(X)<~>patient(X))))&
(((~tall(john)&wise(john)))=>((humble(john)&old(john))))&
(![X]:((~rich(X)<~>calm(X))=>(wise(X)|~happy(X))))&
(![X]:((curious(X)&~strong(X))=>(calm(X)&~happy(X))))&
(![X]:(wise(X)=>(~funny(X)&~wise(X))))&
(((~quiet(alice)|funny(alice)))<=>((old(fred)|~kind(fred))))&
(((happy(alice)|~happy(alice)))<=>((~funny(susan)<~>~brave(susan))))&
(![X]:((~strong(X)|~happy(X))=>(~rich(X)&happy(X))))&
(((happy(susan)&humble(susan)))=>(brave(alice)))&
(![X]:((~humble(X)|creative(X))<=>(~wise(X)|~calm(X))))&
((?[X]:((kind(X)|~curious(X))))=>((happy(paul)&~happy(paul))))&
(![X]:((tall(X)<~>humble(X))<=>~calm(X)))&
(![X]:(~humble(X)<=>(~generous(X)&~patient(X))))&
((patient(paul)|~generous(paul)))&
(?[X]:((tall(X)&strong(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
((~wise(paul)&~quiet(paul)))&
((~wise(fred)<~>old(fred)))&
((~quiet(paul)&patient(paul))) | happy(alice) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 832006255594711845032392
% SZS output start Proof for 832006255594711845032392
11. ! [X0] : ((~happy(X0) | ~strong(X0)) => (happy(X0) & ~rich(X0))) [input p10]
23. ~happy(alice) [input hypothesis]
24. ! [X0] : (~happy(X0) => (happy(X0) & ~rich(X0))) [pure predicate removal 11]
35. ! [X0] : ((happy(X0) & ~rich(X0)) | happy(X0)) [ennf transformation 24]
91. happy(X0) | happy(X0) [cnf transformation 35]
116. ~happy(alice) [cnf transformation 23]
117. happy(X0) [duplicate literal removal 91]
209. $false [subsumption resolution 116,117]
% SZS output end Proof for 832006255594711845032392
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or humble then alice is calm.
If someone is not generous or not happy then someone is not strong.
Everyone who is both humble and not calm is happy or rich and vice versa.
Everyone who is curious is both not strong and quiet and vice versa.
Everyone who is not humble or calm is either creative or happy and vice versa.
Everyone who is both calm and not humble is not rich and vice versa.
If someone is both not funny and creative then someone is both not calm and not old.
Everyone who is both kind and old is both funny and not wise.
Everyone who is kind is both not kind and not strong.
Everyone who is both not quiet and not patient is both humble and not strong and vice versa.
If someone is both patient and humble then someone is either not patient or not tall and vice versa.
Everyone who is not curious or humble is brave or not funny.
If someone is not wise or curious then someone is not rich or humble and vice versa.
Everyone who is either not rich or old is not rich and vice versa.
Someone is either not generous or curious.
Fred is wise or not quiet.
Lucy is not strong.
Someone is not calm.
Alice is curious.
Someone is both not creative and rich.
Someone is brave or humble. | Alice is not wise. | neutral | ((?[X]:((calm(X)|humble(X))))=>(calm(alice)))&
((?[X]:((~generous(X)|~happy(X))))=>(?[X]:(~strong(X))))&
(![X]:((humble(X)&~calm(X))<=>(happy(X)|rich(X))))&
(![X]:(curious(X)<=>(~strong(X)&quiet(X))))&
(![X]:((~humble(X)|calm(X))<=>(creative(X)<~>happy(X))))&
(![X]:((calm(X)&~humble(X))<=>~rich(X)))&
((?[X]:((~funny(X)&creative(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(![X]:((kind(X)&old(X))=>(funny(X)&~wise(X))))&
(![X]:(kind(X)=>(~kind(X)&~strong(X))))&
(![X]:((~quiet(X)&~patient(X))<=>(humble(X)&~strong(X))))&
((?[X]:((patient(X)&humble(X))))<=>(?[X]:((~patient(X)<~>~tall(X)))))&
(![X]:((~curious(X)|humble(X))=>(brave(X)|~funny(X))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((~rich(X)|humble(X)))))&
(![X]:((~rich(X)<~>old(X))<=>~rich(X)))&
(?[X]:((~generous(X)<~>curious(X))))&
((wise(fred)|~quiet(fred)))&
(~strong(lucy))&
(?[X]:(~calm(X)))&
(curious(alice))&
(?[X]:((~creative(X)&rich(X))))&
(?[X]:((brave(X)|humble(X)))) | ~wise(alice) | [] | null | 0 |
Everyone who is both not wise and creative is not kind. If fred is funny or old then someone is both happy and kind and vice versa. Everyone who is not quiet or wise is either not curious or not tall and vice versa. Everyone who is not quiet or not patient is not patient or generous. Everyone who is happy or not patient is curious and vice versa. Everyone who is creative is both strong and generous. Everyone who is not creative or funny is kind or not funny. Everyone who is either not quiet or old is not quiet or creative and vice versa. If someone is either kind or not brave then someone is both happy and not rich and vice versa. Everyone who is either not funny or rich is either not creative or humble and vice versa. If someone is either not humble or generous then someone is both not brave and calm and vice versa. Everyone who is either not funny or funny is not creative or strong and vice versa. Everyone who is both calm and funny is both kind and not kind. Everyone who is either not old or not kind is both not patient and not wise. Everyone who is both patient and funny is not creative or not kind and vice versa. If someone is both creative and happy then someone is either not kind or old. Lucy is not funny or not tall. Susan is either not funny or not tall. Someone is either not kind or not tall. Paul is both funny and humble. Someone is not patient. Someone is either happy or not curious. Lucy is curious. | Paul is not curious. | contradiction | (![X]:((~wise(X)&creative(X))=>~kind(X)))&
(((funny(fred)|old(fred)))<=>(?[X]:((happy(X)&kind(X)))))&
(![X]:((~quiet(X)|wise(X))<=>(~curious(X)<~>~tall(X))))&
(![X]:((~quiet(X)|~patient(X))=>(~patient(X)|generous(X))))&
(![X]:((happy(X)|~patient(X))<=>curious(X)))&
(![X]:(creative(X)=>(strong(X)&generous(X))))&
(![X]:((~creative(X)|funny(X))=>(kind(X)|~funny(X))))&
(![X]:((~quiet(X)<~>old(X))<=>(~quiet(X)|creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((happy(X)&~rich(X)))))&
(![X]:((~funny(X)<~>rich(X))<=>(~creative(X)<~>humble(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>(?[X]:((~brave(X)&calm(X)))))&
(![X]:((~funny(X)<~>funny(X))<=>(~creative(X)|strong(X))))&
(![X]:((calm(X)&funny(X))=>(kind(X)&~kind(X))))&
(![X]:((~old(X)<~>~kind(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)&funny(X))<=>(~creative(X)|~kind(X))))&
((?[X]:((creative(X)&happy(X))))=>(?[X]:((~kind(X)<~>old(X)))))&
((~funny(lucy)|~tall(lucy)))&
((~funny(susan)<~>~tall(susan)))&
(?[X]:((~kind(X)<~>~tall(X))))&
((funny(paul)&humble(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
(curious(lucy)) | ~curious(paul) | [
"p4",
"p6",
"p7",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 190070859820429672189482
% SZS output start Proof for 190070859820429672189482
5. ! [X0] : ((~patient(X0) | happy(X0)) <=> curious(X0)) [input p4]
7. ! [X0] : ((funny(X0) | ~creative(X0)) => (~funny(X0) | kind(X0))) [input p6]
8. ! [X0] : ((~quiet(X0) <~> old(X0)) <=> (creative(X0) | ~quiet(X0))) [input p7]
14. ! [X0] : ((~old(X0) <~> ~kind(X0)) => (~wise(X0) & ~patient(X0))) [input p13]
15. ! [X0] : ((funny(X0) & patient(X0)) <=> (~kind(X0) | ~creative(X0))) [input p14]
20. humble(paul) & funny(paul) [input p19]
24. ~curious(paul) [input hypothesis]
33. ! [X0] : ((~funny(X0) | kind(X0)) | (~funny(X0) & creative(X0))) [ennf transformation 7]
34. ! [X0] : (~funny(X0) | kind(X0) | (~funny(X0) & creative(X0))) [flattening 33]
37. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~old(X0) <=> ~kind(X0))) [ennf transformation 14]
46. ! [X0] : (((~patient(X0) | happy(X0)) | ~curious(X0)) & (curious(X0) | (patient(X0) & ~happy(X0)))) [nnf transformation 5]
47. ! [X0] : ((~patient(X0) | happy(X0) | ~curious(X0)) & (curious(X0) | (patient(X0) & ~happy(X0)))) [flattening 46]
48. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & ((creative(X0) | ~quiet(X0)) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [nnf transformation 8]
49. ! [X0] : ((((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | (~creative(X0) & quiet(X0))) & (creative(X0) | ~quiet(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0))))) [flattening 48]
63. ! [X0] : ((~wise(X0) & ~patient(X0)) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 37]
64. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & ((~kind(X0) | ~creative(X0)) | (~funny(X0) | ~patient(X0)))) [nnf transformation 15]
65. ! [X0] : (((funny(X0) & patient(X0)) | (kind(X0) & creative(X0))) & (~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0))) [flattening 64]
94. patient(X0) | curious(X0) [cnf transformation 47]
99. ~funny(X0) | kind(X0) | ~funny(X0) [cnf transformation 34]
101. creative(X0) | ~quiet(X0) | ~quiet(X0) | ~old(X0) [cnf transformation 49]
104. ~old(X0) | quiet(X0) | quiet(X0) [cnf transformation 49]
134. ~patient(X0) | ~kind(X0) | old(X0) [cnf transformation 63]
138. ~kind(X0) | ~creative(X0) | ~funny(X0) | ~patient(X0) [cnf transformation 65]
139. patient(X0) | creative(X0) [cnf transformation 65]
142. funny(X0) | kind(X0) [cnf transformation 65]
150. funny(paul) [cnf transformation 20]
156. ~curious(paul) [cnf transformation 24]
159. creative(X0) | ~quiet(X0) | ~old(X0) [duplicate literal removal 101]
160. ~old(X0) | quiet(X0) [duplicate literal removal 104]
161. ~funny(X0) | kind(X0) [duplicate literal removal 99]
186. ~old(X0) | creative(X0) [subsumption resolution 159,160]
250. kind(X0) [subsumption resolution 142,161]
251. ~patient(X0) | ~funny(X0) | ~creative(X0) [subsumption resolution 138,250]
354. ~kind(X0) | old(X0) | creative(X0) [resolution 134,139]
356. old(X0) | creative(X0) [subsumption resolution 354,250]
357. creative(X0) [subsumption resolution 356,186]
392. ~funny(X1) | ~creative(X1) | curious(X1) [resolution 251,94]
393. ~funny(X1) | curious(X1) [subsumption resolution 392,357]
457. curious(paul) [resolution 393,150]
460. $false [subsumption resolution 457,156]
% SZS output end Proof for 190070859820429672189482
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or not quiet is both wise and not calm. Everyone who is not calm or not kind is rich and vice versa. If someone is both happy and funny then lucy is both not strong and rich. Everyone who is both generous and kind is not brave and vice versa. If mary is kind or wise then susan is either not calm or humble and vice versa. Everyone who is both not old and old is both quiet and creative. If john is both not calm and brave then someone is not creative. If alice is both not creative and tall then someone is both quiet and brave. Everyone who is both not quiet and not tall is not old and vice versa. Everyone who is not happy or happy is patient or creative. Everyone who is either not funny or kind is either calm or creative and vice versa. If someone is not calm then lucy is either not quiet or curious and vice versa. Everyone who is either rich or not happy is both not tall and wise and vice versa. Everyone who is calm or creative is both happy and generous and vice versa. If someone is patient or not brave then someone is either rich or tall and vice versa. Everyone who is not curious is both happy and wise. Someone is either not old or not rich. John is old. Susan is either happy or rich. Someone is calm or curious. Susan is happy or brave. Someone is brave. Someone is creative. Fred is either happy or not humble. | Susan is not creative. | neutral | (![X]:((old(X)<~>~quiet(X))=>(wise(X)&~calm(X))))&
(![X]:((~calm(X)|~kind(X))<=>rich(X)))&
((?[X]:((happy(X)&funny(X))))=>((~strong(lucy)&rich(lucy))))&
(![X]:((generous(X)&kind(X))<=>~brave(X)))&
(((kind(mary)|wise(mary)))<=>((~calm(susan)<~>humble(susan))))&
(![X]:((~old(X)&old(X))=>(quiet(X)&creative(X))))&
(((~calm(john)&brave(john)))=>(?[X]:(~creative(X))))&
(((~creative(alice)&tall(alice)))=>(?[X]:((quiet(X)&brave(X)))))&
(![X]:((~quiet(X)&~tall(X))<=>~old(X)))&
(![X]:((~happy(X)|happy(X))=>(patient(X)|creative(X))))&
(![X]:((~funny(X)<~>kind(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(~calm(X)))<=>((~quiet(lucy)<~>curious(lucy))))&
(![X]:((rich(X)<~>~happy(X))<=>(~tall(X)&wise(X))))&
(![X]:((calm(X)|creative(X))<=>(happy(X)&generous(X))))&
((?[X]:((patient(X)|~brave(X))))<=>(?[X]:((rich(X)<~>tall(X)))))&
(![X]:(~curious(X)=>(happy(X)&wise(X))))&
(?[X]:((~old(X)<~>~rich(X))))&
(old(john))&
((happy(susan)<~>rich(susan)))&
(?[X]:((calm(X)|curious(X))))&
((happy(susan)|brave(susan)))&
(?[X]:(brave(X)))&
(?[X]:(creative(X)))&
((happy(fred)<~>~humble(fred))) | ~creative(susan) | [] | 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 funny. Everyone who is patient is curious. If someone is not creative then someone is patient. Everyone who is not creative is either not curious or not patient. If lucy is either curious or not funny then susan is not quiet. 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 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. Lucy is both not funny and not kind. Alice is funny or old. John is both wise and funny. Someone is not happy. Paul is happy. Lucy is either not generous or patient. | Susan is not humble. | contradiction | (![X]:(~funny(X)<=>brave(X)))&
((?[X]:((~kind(X)|old(X))))=>(?[X]:(creative(X))))&
(![X]:(~creative(X)=>(kind(X)|funny(X))))&
(![X]:(patient(X)=>curious(X)))&
((?[X]:(~creative(X)))=>(?[X]:(patient(X))))&
(![X]:(~creative(X)=>(~curious(X)<~>~patient(X))))&
(((curious(lucy)<~>~funny(lucy)))=>(~quiet(susan)))&
(![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]:((~wise(X)&tall(X))))<=>(?[X]:(tall(X))))&
(((creative(lucy)|~creative(lucy)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
((~funny(lucy)&~kind(lucy)))&
((funny(alice)|old(alice)))&
((wise(john)&funny(john)))&
(?[X]:(~happy(X)))&
(happy(paul))&
((~generous(lucy)<~>patient(lucy))) | ~humble(susan) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7551858272399084567919640
% SZS output start Proof for 7551858272399084567919640
13. ! [X0] : ((curious(X0) & humble(X0)) <=> (~patient(X0) | ~humble(X0))) [input p12]
22. ~humble(susan) [input hypothesis]
50. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & ((~patient(X0) | ~humble(X0)) | (~curious(X0) | ~humble(X0)))) [nnf transformation 13]
51. ! [X0] : (((curious(X0) & humble(X0)) | (patient(X0) & humble(X0))) & (~patient(X0) | ~humble(X0) | ~curious(X0) | ~humble(X0))) [flattening 50]
104. humble(X0) | humble(X0) [cnf transformation 51]
126. ~humble(susan) [cnf transformation 22]
128. humble(X0) [duplicate literal removal 104]
251. $false [subsumption resolution 126,128]
% SZS output end Proof for 7551858272399084567919640
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either calm or tall is tall or not creative and vice versa. Everyone who is both happy and not kind is not old. If fred is quiet then alice is both funny and not wise. Everyone who is either not quiet or curious is humble and vice versa. Everyone who is funny is happy and vice versa. If lucy is either not old or not calm then alice is either brave or not rich. If susan is either not humble or not funny then paul is not humble or wise and vice versa. If someone is both not creative and wise then someone is not rich or strong. Everyone who is not patient or quiet is old or not patient and vice versa. If someone is either not wise or not rich then paul is either happy or patient. Everyone who is not brave or not tall is either tall or not happy. If someone is not humble or brave then someone is both generous and creative. Everyone who is either creative or happy is both not funny and not kind. Everyone who is either creative or curious is either curious or happy and vice versa. Everyone who is either not curious or creative is both not curious and not rich. Everyone who is tall or not calm is either curious or not tall. Someone is wise or not old. Someone is either not generous or quiet. Alice is both rich and old. Paul is tall or strong. Someone is either creative or kind. Lucy is patient or not kind. Paul is either not calm or kind. Someone is either not patient or not happy. | Paul is not creative. | entailment | (![X]:((calm(X)<~>tall(X))<=>(tall(X)|~creative(X))))&
(![X]:((happy(X)&~kind(X))=>~old(X)))&
((quiet(fred))=>((funny(alice)&~wise(alice))))&
(![X]:((~quiet(X)<~>curious(X))<=>humble(X)))&
(![X]:(funny(X)<=>happy(X)))&
(((~old(lucy)<~>~calm(lucy)))=>((brave(alice)<~>~rich(alice))))&
(((~humble(susan)<~>~funny(susan)))<=>((~humble(paul)|wise(paul))))&
((?[X]:((~creative(X)&wise(X))))=>(?[X]:((~rich(X)|strong(X)))))&
(![X]:((~patient(X)|quiet(X))<=>(old(X)|~patient(X))))&
((?[X]:((~wise(X)<~>~rich(X))))=>((happy(paul)<~>patient(paul))))&
(![X]:((~brave(X)|~tall(X))=>(tall(X)<~>~happy(X))))&
((?[X]:((~humble(X)|brave(X))))=>(?[X]:((generous(X)&creative(X)))))&
(![X]:((creative(X)<~>happy(X))=>(~funny(X)&~kind(X))))&
(![X]:((creative(X)<~>curious(X))<=>(curious(X)<~>happy(X))))&
(![X]:((~curious(X)<~>creative(X))=>(~curious(X)&~rich(X))))&
(![X]:((tall(X)|~calm(X))=>(curious(X)<~>~tall(X))))&
(?[X]:((wise(X)|~old(X))))&
(?[X]:((~generous(X)<~>quiet(X))))&
((rich(alice)&old(alice)))&
((tall(paul)|strong(paul)))&
(?[X]:((creative(X)<~>kind(X))))&
((patient(lucy)|~kind(lucy)))&
((~calm(paul)<~>kind(paul)))&
(?[X]:((~patient(X)<~>~happy(X)))) | ~creative(paul) | [
"p0",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6299260324208949666657226
% SZS output start Proof for 6299260324208949666657226
1. ! [X0] : ((calm(X0) <~> tall(X0)) <=> (~creative(X0) | tall(X0))) [input p0]
11. ! [X0] : ((~tall(X0) | ~brave(X0)) => (tall(X0) <~> ~happy(X0))) [input p10]
14. ! [X0] : ((creative(X0) <~> curious(X0)) <=> (curious(X0) <~> happy(X0))) [input p13]
15. ! [X0] : ((~curious(X0) <~> creative(X0)) => (~rich(X0) & ~curious(X0))) [input p14]
16. ! [X0] : ((~calm(X0) | tall(X0)) => (curious(X0) <~> ~tall(X0))) [input p15]
25. creative(paul) [input hypothesis]
35. ! [X0] : ((tall(X0) <~> ~happy(X0)) | (tall(X0) & brave(X0))) [ennf transformation 11]
38. ! [X0] : ((~rich(X0) & ~curious(X0)) | (~curious(X0) <=> creative(X0))) [ennf transformation 15]
39. ! [X0] : ((curious(X0) <~> ~tall(X0)) | (calm(X0) & ~tall(X0))) [ennf transformation 16]
40. ! [X0] : ((((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (creative(X0) & ~tall(X0))) & ((~creative(X0) | tall(X0)) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0))))) [nnf transformation 1]
41. ! [X0] : ((((~tall(X0) | ~calm(X0)) & (tall(X0) | calm(X0))) | (creative(X0) & ~tall(X0))) & (~creative(X0) | tall(X0) | ((calm(X0) | ~tall(X0)) & (tall(X0) | ~calm(X0))))) [flattening 40]
50. ! [X0] : (((happy(X0) | ~tall(X0)) & (~happy(X0) | tall(X0))) | (tall(X0) & brave(X0))) [nnf transformation 35]
55. ! [X0] : ((((~curious(X0) | ~creative(X0)) & (curious(X0) | creative(X0))) | ((curious(X0) | ~happy(X0)) & (happy(X0) | ~curious(X0)))) & (((~happy(X0) | ~curious(X0)) & (happy(X0) | curious(X0))) | ((creative(X0) | ~curious(X0)) & (curious(X0) | ~creative(X0))))) [nnf transformation 14]
56. ! [X0] : ((~rich(X0) & ~curious(X0)) | ((~curious(X0) | ~creative(X0)) & (creative(X0) | curious(X0)))) [nnf transformation 38]
57. ! [X0] : (((tall(X0) | ~curious(X0)) & (~tall(X0) | curious(X0))) | (calm(X0) & ~tall(X0))) [nnf transformation 39]
74. ~tall(X0) | ~calm(X0) | ~tall(X0) [cnf transformation 41]
104. ~happy(X0) | tall(X0) | tall(X0) [cnf transformation 50]
115. happy(X0) | curious(X0) | curious(X0) | ~creative(X0) [cnf transformation 55]
121. ~curious(X0) | ~creative(X0) | happy(X0) | ~curious(X0) [cnf transformation 55]
124. ~curious(X0) | ~curious(X0) | ~creative(X0) [cnf transformation 56]
128. ~tall(X0) | curious(X0) | calm(X0) [cnf transformation 57]
143. creative(paul) [cnf transformation 25]
145. ~curious(X0) | ~creative(X0) [duplicate literal removal 124]
146. happy(X0) | curious(X0) | ~creative(X0) [duplicate literal removal 115]
149. ~curious(X0) | ~creative(X0) | happy(X0) [duplicate literal removal 121]
150. ~happy(X0) | tall(X0) [duplicate literal removal 104]
152. ~tall(X0) | ~calm(X0) [duplicate literal removal 74]
214. 13 <=> happy(paul) [avatar definition]
215. happy(paul) <- (13) [avatar component clause 214]
247. ~creative(X0) | happy(X0) [subsumption resolution 146,149]
248. ~tall(X0) | curious(X0) [subsumption resolution 128,152]
312. tall(paul) <- (13) [resolution 150,215]
317. happy(paul) [resolution 247,143]
319. curious(paul) <- (13) [resolution 248,312]
326. ~creative(paul) <- (13) [resolution 319,145]
327. $false <- (13) [subsumption resolution 326,143]
328. ~13 [avatar contradiction clause 327]
329. 13 [avatar split clause 317,214]
330. $false [avatar sat refutation 328,329]
% SZS output end Proof for 6299260324208949666657226
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either quiet or not strong then someone is old or not wise and vice versa.
Everyone who is not happy is either not wise or not curious.
Everyone who is funny is both not old and humble and vice versa.
Everyone who is strong is either patient or not rich and vice versa.
Everyone who is either not old or not funny is not rich or wise and vice versa.
If someone is old or rich then mary is not generous or not kind.
If lucy is creative then alice is not strong.
Everyone who is strong or not patient is not rich or curious and vice versa.
Everyone who is old or not tall is happy or funny and vice versa.
If someone is both not quiet and quiet then mary is both curious and not funny.
Everyone who is both not calm and creative is either not wise or rich.
If someone is both not humble and not generous then someone is not strong or not tall and vice versa.
If someone is not humble then someone is either creative or not patient and vice versa.
If someone is either rich or not rich then john is both not strong and funny.
Everyone who is quiet is either not happy or kind and vice versa.
Alice is either not humble or strong.
John is not curious or generous.
Someone is curious or not humble.
Someone is both not quiet and not kind.
Someone is either funny or not humble.
Someone is both happy and curious.
Someone is both creative and brave.
Paul is either calm or not old. | John is tall. | contradiction | ((?[X]:((quiet(X)<~>~strong(X))))<=>(?[X]:((old(X)|~wise(X)))))&
(![X]:(~happy(X)=>(~wise(X)<~>~curious(X))))&
(![X]:(funny(X)<=>(~old(X)&humble(X))))&
(![X]:(strong(X)<=>(patient(X)<~>~rich(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(~rich(X)|wise(X))))&
((?[X]:((old(X)|rich(X))))=>((~generous(mary)|~kind(mary))))&
((creative(lucy))=>(~strong(alice)))&
(![X]:((strong(X)|~patient(X))<=>(~rich(X)|curious(X))))&
(![X]:((old(X)|~tall(X))<=>(happy(X)|funny(X))))&
((?[X]:((~quiet(X)&quiet(X))))=>((curious(mary)&~funny(mary))))&
(![X]:((~calm(X)&creative(X))=>(~wise(X)<~>rich(X))))&
((?[X]:((~humble(X)&~generous(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:((creative(X)<~>~patient(X)))))&
((?[X]:((rich(X)<~>~rich(X))))=>((~strong(john)&funny(john))))&
(![X]:(quiet(X)<=>(~happy(X)<~>kind(X))))&
((~humble(alice)<~>strong(alice)))&
((~curious(john)|generous(john)))&
(?[X]:((curious(X)|~humble(X))))&
(?[X]:((~quiet(X)&~kind(X))))&
(?[X]:((funny(X)<~>~humble(X))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((creative(X)&brave(X))))&
((calm(paul)<~>~old(paul))) | tall(john) | [
"p2",
"p3",
"p7",
"p8",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8605152111458037772672429
% SZS output start Proof for 8605152111458037772672429
3. ! [X0] : (funny(X0) <=> (humble(X0) & ~old(X0))) [input p2]
4. ! [X0] : (strong(X0) <=> (patient(X0) <~> ~rich(X0))) [input p3]
8. ! [X0] : ((~patient(X0) | strong(X0)) <=> (curious(X0) | ~rich(X0))) [input p7]
9. ! [X0] : ((~tall(X0) | old(X0)) <=> (funny(X0) | happy(X0))) [input p8]
14. ? [X0] : (rich(X0) <~> ~rich(X0)) => (funny(john) & ~strong(john)) [input p13]
24. tall(john) [input hypothesis]
36. (funny(john) & ~strong(john)) | ! [X0] : (rich(X0) <=> ~rich(X0)) [ennf transformation 14]
43. ! [X0] : ((funny(X0) | (~humble(X0) | old(X0))) & ((humble(X0) & ~old(X0)) | ~funny(X0))) [nnf transformation 3]
44. ! [X0] : ((funny(X0) | ~humble(X0) | old(X0)) & ((humble(X0) & ~old(X0)) | ~funny(X0))) [flattening 43]
45. ! [X0] : ((strong(X0) | ((patient(X0) | rich(X0)) & (~rich(X0) | ~patient(X0)))) & (((rich(X0) | ~patient(X0)) & (~rich(X0) | patient(X0))) | ~strong(X0))) [nnf transformation 4]
48. ! [X0] : (((~patient(X0) | strong(X0)) | (~curious(X0) & rich(X0))) & ((curious(X0) | ~rich(X0)) | (patient(X0) & ~strong(X0)))) [nnf transformation 8]
49. ! [X0] : ((~patient(X0) | strong(X0) | (~curious(X0) & rich(X0))) & (curious(X0) | ~rich(X0) | (patient(X0) & ~strong(X0)))) [flattening 48]
50. ! [X0] : (((~tall(X0) | old(X0)) | (~funny(X0) & ~happy(X0))) & ((funny(X0) | happy(X0)) | (tall(X0) & ~old(X0)))) [nnf transformation 9]
51. ! [X0] : ((~tall(X0) | old(X0) | (~funny(X0) & ~happy(X0))) & (funny(X0) | happy(X0) | (tall(X0) & ~old(X0)))) [flattening 50]
63. (funny(john) & ~strong(john)) | ! [X0] : ((rich(X0) | rich(X0)) & (~rich(X0) | ~rich(X0))) [nnf transformation 36]
86. ~funny(X0) | ~old(X0) [cnf transformation 44]
92. strong(X0) | patient(X0) | rich(X0) [cnf transformation 45]
104. ~patient(X0) | strong(X0) | rich(X0) [cnf transformation 49]
109. ~tall(X0) | old(X0) | ~funny(X0) [cnf transformation 51]
124. ~strong(john) | rich(X0) | rich(X0) [cnf transformation 63]
125. funny(john) | ~rich(X0) | ~rich(X0) [cnf transformation 63]
144. tall(john) [cnf transformation 24]
146. ~strong(john) | rich(X0) [duplicate literal removal 124]
147. funny(john) | ~rich(X0) [duplicate literal removal 125]
186. 9 <=> ! [X0] : ~rich(X0) [avatar definition]
187. ~rich(X0) <- (9) [avatar component clause 186]
207. rich(X0) | strong(X0) [subsumption resolution 104,92]
208. ~tall(X0) | ~funny(X0) [subsumption resolution 109,86]
219. 16 <=> ! [X1] : strong(X1) [avatar definition]
220. strong(X1) <- (16) [avatar component clause 219]
266. 27 <=> ! [X0] : rich(X0) [avatar definition]
267. rich(X0) <- (27) [avatar component clause 266]
269. 28 <=> funny(john) [avatar definition]
271. funny(john) <- (28) [avatar component clause 269]
273. 9 | 28 [avatar split clause 147,269,186]
275. 29 <=> strong(john) [avatar definition]
277. ~strong(john) <- (~29) [avatar component clause 275]
278. 27 | ~29 [avatar split clause 146,275,266]
323. $false <- (9, 27) [subsumption resolution 187,267]
324. ~9 | ~27 [avatar contradiction clause 323]
327. strong(X0) <- (9) [resolution 207,187]
328. 16 | ~9 [avatar split clause 327,186,219]
330. $false <- (16, ~29) [resolution 220,277]
335. ~16 | 29 [avatar contradiction clause 330]
337. ~funny(john) [resolution 208,144]
338. $false <- (28) [subsumption resolution 337,271]
339. ~28 [avatar contradiction clause 338]
340. $false [avatar sat refutation 273,278,324,328,335,339]
% SZS output end Proof for 8605152111458037772672429
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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