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
|
|---|---|---|---|---|---|---|---|
If someone is rich or not old then someone is both not humble and tall and vice versa.
Everyone who is creative or not wise is kind.
Everyone who is not happy is not quiet or funny and vice versa.
Everyone who is funny or not quiet is kind.
If someone is rich then fred is either curious or not old and vice versa.
Everyone who is both wise and not creative is kind or not creative and vice versa.
If paul is not kind or brave then paul is not humble and vice versa.
Everyone who is either not old or not funny is kind and vice versa.
Everyone who is either not calm or tall is either generous or strong.
Everyone who is not old or not curious is both brave and not funny.
If someone is both not brave and brave then someone is either not creative or not happy and vice versa.
Everyone who is funny or creative is both happy and not rich.
If paul is either funny or not creative then someone is not happy and vice versa.
If susan is not humble then someone is both humble and not calm.
Everyone who is either not strong or not wise is both not generous and not quiet and vice versa.
Susan is not funny.
Alice is creative or patient.
Someone is both rich and not calm.
Alice is funny or not happy.
Paul is humble. | Alice is not kind. | contradiction | ((?[X]:((rich(X)|~old(X))))<=>(?[X]:((~humble(X)&tall(X)))))&
(![X]:((creative(X)|~wise(X))=>kind(X)))&
(![X]:(~happy(X)<=>(~quiet(X)|funny(X))))&
(![X]:((funny(X)|~quiet(X))=>kind(X)))&
((?[X]:(rich(X)))<=>((curious(fred)<~>~old(fred))))&
(![X]:((wise(X)&~creative(X))<=>(kind(X)|~creative(X))))&
(((~kind(paul)|brave(paul)))<=>(~humble(paul)))&
(![X]:((~old(X)<~>~funny(X))<=>kind(X)))&
(![X]:((~calm(X)<~>tall(X))=>(generous(X)<~>strong(X))))&
(![X]:((~old(X)|~curious(X))=>(brave(X)&~funny(X))))&
((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((~creative(X)<~>~happy(X)))))&
(![X]:((funny(X)|creative(X))=>(happy(X)&~rich(X))))&
(((funny(paul)<~>~creative(paul)))<=>(?[X]:(~happy(X))))&
((~humble(susan))=>(?[X]:((humble(X)&~calm(X)))))&
(![X]:((~strong(X)<~>~wise(X))<=>(~generous(X)&~quiet(X))))&
(~funny(susan))&
((creative(alice)|patient(alice)))&
(?[X]:((rich(X)&~calm(X))))&
((funny(alice)|~happy(alice)))&
(humble(paul)) | ~kind(alice) | [
"p1",
"p2",
"p3",
"p5",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 3602271156161140581217664
% SZS output start Proof for 3602271156161140581217664
2. ! [X0] : ((~wise(X0) | creative(X0)) => kind(X0)) [input p1]
3. ! [X0] : (~happy(X0) <=> (funny(X0) | ~quiet(X0))) [input p2]
4. ! [X0] : ((~quiet(X0) | funny(X0)) => kind(X0)) [input p3]
6. ! [X0] : ((~creative(X0) & wise(X0)) <=> (~creative(X0) | kind(X0))) [input p5]
8. ! [X0] : ((~old(X0) <~> ~funny(X0)) <=> kind(X0)) [input p7]
10. ! [X0] : ((~curious(X0) | ~old(X0)) => (~funny(X0) & brave(X0))) [input p9]
11. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X0] : (~creative(X0) <~> ~happy(X0)) [input p10]
21. ~kind(alice) [input hypothesis]
23. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X1] : (~creative(X1) <~> ~happy(X1)) [rectify 11]
25. ! [X0] : (kind(X0) | (wise(X0) & ~creative(X0))) [ennf transformation 2]
26. ! [X0] : (kind(X0) | (quiet(X0) & ~funny(X0))) [ennf transformation 4]
28. ! [X0] : ((~funny(X0) & brave(X0)) | (curious(X0) & old(X0))) [ennf transformation 10]
36. ! [X0] : ((~happy(X0) | (~funny(X0) & quiet(X0))) & ((funny(X0) | ~quiet(X0)) | happy(X0))) [nnf transformation 3]
37. ! [X0] : ((~happy(X0) | (~funny(X0) & quiet(X0))) & (funny(X0) | ~quiet(X0) | happy(X0))) [flattening 36]
42. ! [X0] : (((~creative(X0) & wise(X0)) | (creative(X0) & ~kind(X0))) & ((~creative(X0) | kind(X0)) | (creative(X0) | ~wise(X0)))) [nnf transformation 6]
43. ! [X0] : (((~creative(X0) & wise(X0)) | (creative(X0) & ~kind(X0))) & (~creative(X0) | kind(X0) | creative(X0) | ~wise(X0))) [flattening 42]
46. ! [X0] : ((((funny(X0) | old(X0)) & (~funny(X0) | ~old(X0))) | ~kind(X0)) & (kind(X0) | ((~old(X0) | funny(X0)) & (~funny(X0) | old(X0))))) [nnf transformation 8]
48. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : ((~creative(X1) | happy(X1)) & (~happy(X1) | creative(X1)))) & (? [X1] : ((happy(X1) | creative(X1)) & (~happy(X1) | ~creative(X1))) | ! [X0] : (~brave(X0) | brave(X0))) [nnf transformation 23]
49. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : ((~creative(X1) | happy(X1)) & (~happy(X1) | creative(X1)))) & (? [X2] : ((happy(X2) | creative(X2)) & (~happy(X2) | ~creative(X2))) | ! [X3] : (~brave(X3) | brave(X3))) [rectify 48]
50. ? [X0] : (brave(X0) & ~brave(X0)) => (brave(sK3) & ~brave(sK3)) [choice axiom]
51. ? [X2] : ((happy(X2) | creative(X2)) & (~happy(X2) | ~creative(X2))) => ((happy(sK4) | creative(sK4)) & (~happy(sK4) | ~creative(sK4))) [choice axiom]
52. ((brave(sK3) & ~brave(sK3)) | ! [X1] : ((~creative(X1) | happy(X1)) & (~happy(X1) | creative(X1)))) & (((happy(sK4) | creative(sK4)) & (~happy(sK4) | ~creative(sK4))) | ! [X3] : (~brave(X3) | brave(X3))) [skolemisation 49,51,50]
68. ~creative(X0) | kind(X0) [cnf transformation 25]
70. ~quiet(X0) | funny(X0) | happy(X0) [cnf transformation 37]
73. ~funny(X0) | kind(X0) [cnf transformation 26]
74. quiet(X0) | kind(X0) [cnf transformation 26]
82. ~creative(X0) | ~kind(X0) [cnf transformation 43]
89. ~funny(X0) | ~old(X0) | ~kind(X0) [cnf transformation 46]
97. ~funny(X0) | old(X0) [cnf transformation 28]
101. ~brave(sK3) | ~happy(X1) | creative(X1) [cnf transformation 52]
103. brave(sK3) | ~happy(X1) | creative(X1) [cnf transformation 52]
126. ~kind(alice) [cnf transformation 21]
173. ~creative(X0) [subsumption resolution 82,68]
190. ~funny(X0) | ~old(X0) [subsumption resolution 89,73]
192. ~funny(X0) [subsumption resolution 97,190]
193. brave(sK3) | ~happy(X1) [subsumption resolution 103,173]
195. 14 <=> ! [X1] : ~happy(X1) [avatar definition]
196. ~happy(X1) <- (14) [avatar component clause 195]
198. 15 <=> brave(sK3) [avatar definition]
201. 14 | 15 [avatar split clause 193,198,195]
202. ~brave(sK3) | ~happy(X1) [subsumption resolution 101,173]
203. 14 | ~15 [avatar split clause 202,198,195]
234. funny(X0) | happy(X0) | kind(X0) [resolution 70,74]
235. happy(X0) | kind(X0) [subsumption resolution 234,192]
236. kind(X0) <- (14) [subsumption resolution 235,196]
237. $false <- (14) [resolution 236,126]
238. ~14 [avatar contradiction clause 237]
239. $false [avatar sat refutation 201,203,238]
% SZS output end Proof for 3602271156161140581217664
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not calm is either not old or curious and vice versa. If mary is either not strong or rich then someone is either not humble or not brave and vice versa. If john is either creative or tall then someone is not happy. If susan is not curious or creative then paul is not creative and vice versa. Everyone who is curious is both calm and not quiet and vice versa. Everyone who is either generous or not calm is not kind and vice versa. If paul is rich then lucy is either kind or rich and vice versa. If john is both wise and calm then someone is not humble or brave and vice versa. If someone is not kind then someone is both not funny and not creative. Everyone who is either not strong or calm is either curious or not kind. If fred is not curious or not old then susan is not curious. Everyone who is not curious or not generous is kind. If someone is not happy or creative then someone is not quiet. Everyone who is either not old or not quiet is both happy and not funny and vice versa. Everyone who is not creative or not old is both not tall and not calm and vice versa. If someone is both not humble and patient then someone is rich or not quiet. Someone is kind or not funny. Someone is either not creative or not strong. Someone is happy or not rich. Someone is both not funny and happy. John is kind or strong. Someone is either patient or not curious. | Lucy is rich. | neutral | (![X]:((~old(X)|~calm(X))<=>(~old(X)<~>curious(X))))&
(((~strong(mary)<~>rich(mary)))<=>(?[X]:((~humble(X)<~>~brave(X)))))&
(((creative(john)<~>tall(john)))=>(?[X]:(~happy(X))))&
(((~curious(susan)|creative(susan)))<=>(~creative(paul)))&
(![X]:(curious(X)<=>(calm(X)&~quiet(X))))&
(![X]:((generous(X)<~>~calm(X))<=>~kind(X)))&
((rich(paul))<=>((kind(lucy)<~>rich(lucy))))&
(((wise(john)&calm(john)))<=>(?[X]:((~humble(X)|brave(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((~strong(X)<~>calm(X))=>(curious(X)<~>~kind(X))))&
(((~curious(fred)|~old(fred)))=>(~curious(susan)))&
(![X]:((~curious(X)|~generous(X))=>kind(X)))&
((?[X]:((~happy(X)|creative(X))))=>(?[X]:(~quiet(X))))&
(![X]:((~old(X)<~>~quiet(X))<=>(happy(X)&~funny(X))))&
(![X]:((~creative(X)|~old(X))<=>(~tall(X)&~calm(X))))&
((?[X]:((~humble(X)&patient(X))))=>(?[X]:((rich(X)|~quiet(X)))))&
(?[X]:((kind(X)|~funny(X))))&
(?[X]:((~creative(X)<~>~strong(X))))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:((~funny(X)&happy(X))))&
((kind(john)|strong(john)))&
(?[X]:((patient(X)<~>~curious(X)))) | rich(lucy) | [] | null | 0 |
If someone is both brave and happy then susan is kind or not humble.
Everyone who is both creative and not generous is generous.
Everyone who is both tall and wise is both not creative and generous.
Everyone who is funny or not generous is both calm and creative.
If someone is generous then lucy is either patient or creative.
Everyone who is humble is both brave and not curious.
Everyone who is either not creative or quiet is tall and vice versa.
Everyone who is not strong or not tall is brave or not tall.
If lucy is not tall or brave then fred is either wise or generous and vice versa.
If paul is both not creative and creative then someone is not strong or not patient and vice versa.
If someone is both not tall and generous then fred is both not happy and old and vice versa.
If someone is not kind then someone is creative or happy and vice versa.
If paul is either not rich or not tall then someone is both not wise and tall.
If someone is both not old and old then someone is brave and vice versa.
Everyone who is patient or tall is both tall and strong and vice versa.
If someone is both funny and calm then someone is not strong or quiet.
Someone is old.
Fred is either patient or not rich.
Someone is not quiet or funny.
Someone is curious or not calm.
Fred is patient.
Someone is not humble or wise.
Paul is either creative or wise. | Lucy is creative. | contradiction | ((?[X]:((brave(X)&happy(X))))=>((kind(susan)|~humble(susan))))&
(![X]:((creative(X)&~generous(X))=>generous(X)))&
(![X]:((tall(X)&wise(X))=>(~creative(X)&generous(X))))&
(![X]:((funny(X)|~generous(X))=>(calm(X)&creative(X))))&
((?[X]:(generous(X)))=>((patient(lucy)<~>creative(lucy))))&
(![X]:(humble(X)=>(brave(X)&~curious(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>tall(X)))&
(![X]:((~strong(X)|~tall(X))=>(brave(X)|~tall(X))))&
(((~tall(lucy)|brave(lucy)))<=>((wise(fred)<~>generous(fred))))&
(((~creative(paul)&creative(paul)))<=>(?[X]:((~strong(X)|~patient(X)))))&
((?[X]:((~tall(X)&generous(X))))<=>((~happy(fred)&old(fred))))&
((?[X]:(~kind(X)))<=>(?[X]:((creative(X)|happy(X)))))&
(((~rich(paul)<~>~tall(paul)))=>(?[X]:((~wise(X)&tall(X)))))&
((?[X]:((~old(X)&old(X))))<=>(?[X]:(brave(X))))&
(![X]:((patient(X)|tall(X))<=>(tall(X)&strong(X))))&
((?[X]:((funny(X)&calm(X))))=>(?[X]:((~strong(X)|quiet(X)))))&
(?[X]:(old(X)))&
((patient(fred)<~>~rich(fred)))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((curious(X)|~calm(X))))&
(patient(fred))&
(?[X]:((~humble(X)|wise(X))))&
((creative(paul)<~>wise(paul))) | creative(lucy) | [
"p1",
"p3",
"p4",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8849513553230599649930983
% SZS output start Proof for 8849513553230599649930983
2. ! [X0] : ((~generous(X0) & creative(X0)) => generous(X0)) [input p1]
4. ! [X0] : ((~generous(X0) | funny(X0)) => (creative(X0) & calm(X0))) [input p3]
5. ? [X0] : generous(X0) => (patient(lucy) <~> creative(lucy)) [input p4]
10. (creative(paul) & ~creative(paul)) <=> ? [X0] : (~patient(X0) | ~strong(X0)) [input p9]
24. creative(lucy) [input hypothesis]
32. ! [X0] : (generous(X0) | (generous(X0) | ~creative(X0))) [ennf transformation 2]
33. ! [X0] : (generous(X0) | generous(X0) | ~creative(X0)) [flattening 32]
36. ! [X0] : ((creative(X0) & calm(X0)) | (generous(X0) & ~funny(X0))) [ennf transformation 4]
37. (patient(lucy) <~> creative(lucy)) | ! [X0] : ~generous(X0) [ennf transformation 5]
42. ((~creative(lucy) | ~patient(lucy)) & (creative(lucy) | patient(lucy))) | ! [X0] : ~generous(X0) [nnf transformation 37]
46. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & (? [X0] : (~patient(X0) | ~strong(X0)) | (~creative(paul) | creative(paul))) [nnf transformation 10]
47. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & (? [X0] : (~patient(X0) | ~strong(X0)) | ~creative(paul) | creative(paul)) [flattening 46]
48. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & (? [X1] : (~patient(X1) | ~strong(X1)) | ~creative(paul) | creative(paul)) [rectify 47]
49. ? [X1] : (~patient(X1) | ~strong(X1)) => (~patient(sK0) | ~strong(sK0)) [choice axiom]
50. ((creative(paul) & ~creative(paul)) | ! [X0] : (patient(X0) & strong(X0))) & ((~patient(sK0) | ~strong(sK0)) | ~creative(paul) | creative(paul)) [skolemisation 48,49]
80. generous(X0) | generous(X0) | ~creative(X0) [cnf transformation 33]
86. creative(X0) | generous(X0) [cnf transformation 36]
88. ~creative(lucy) | ~patient(lucy) | ~generous(X0) [cnf transformation 42]
103. ~creative(paul) | patient(X0) [cnf transformation 50]
105. creative(paul) | patient(X0) [cnf transformation 50]
133. creative(lucy) [cnf transformation 24]
134. generous(X0) | ~creative(X0) [duplicate literal removal 80]
135. generous(X0) [subsumption resolution 86,134]
136. ~creative(lucy) | ~patient(lucy) [subsumption resolution 88,135]
138. 1 <=> patient(lucy) [avatar definition]
140. ~patient(lucy) <- (~1) [avatar component clause 138]
142. 2 <=> creative(lucy) [avatar definition]
145. ~1 | ~2 [avatar split clause 136,142,138]
167. 6 <=> ! [X0] : patient(X0) [avatar definition]
168. patient(X0) <- (6) [avatar component clause 167]
170. 7 <=> creative(paul) [avatar definition]
173. 6 | 7 [avatar split clause 105,170,167]
178. 6 | ~7 [avatar split clause 103,170,167]
292. 2 [avatar split clause 133,142]
295. $false <- (~1, 6) [subsumption resolution 140,168]
296. 1 | ~6 [avatar contradiction clause 295]
297. $false [avatar sat refutation 145,173,178,292,296]
% SZS output end Proof for 8849513553230599649930983
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not quiet then someone is strong or not tall. If paul is strong then someone is either old or curious and vice versa. Everyone who is not happy is not brave. Everyone who is either not curious or rich is kind or not happy and vice versa. If someone is funny or not quiet then fred is both not creative and not kind and vice versa. If john is old or not rich then john is either patient or not funny and vice versa. Everyone who is either not wise or not curious is curious and vice versa. Everyone who is kind or tall is not rich. Everyone who is both funny and patient is both rich and brave. If alice is not happy then mary is not old or generous and vice versa. Everyone who is either not old or not generous is patient or quiet and vice versa. Everyone who is either humble or happy is rich and vice versa. Everyone who is not humble or not rich is humble. If someone is either quiet or wise then fred is old or funny and vice versa. If someone is both calm and quiet then someone is both not creative and brave and vice versa. If someone is not patient then fred is either not patient or not kind. Alice is not creative. Lucy is either funny or not quiet. Someone is either not tall or funny. Fred is both happy and generous. Someone is calm or not curious. Susan is either not happy or strong. Someone is either not creative or patient. | John is quiet. | contradiction | (((~humble(paul)|~quiet(paul)))=>(?[X]:((strong(X)|~tall(X)))))&
((strong(paul))<=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:(~happy(X)=>~brave(X)))&
(![X]:((~curious(X)<~>rich(X))<=>(kind(X)|~happy(X))))&
((?[X]:((funny(X)|~quiet(X))))<=>((~creative(fred)&~kind(fred))))&
(((old(john)|~rich(john)))<=>((patient(john)<~>~funny(john))))&
(![X]:((~wise(X)<~>~curious(X))<=>curious(X)))&
(![X]:((kind(X)|tall(X))=>~rich(X)))&
(![X]:((funny(X)&patient(X))=>(rich(X)&brave(X))))&
((~happy(alice))<=>((~old(mary)|generous(mary))))&
(![X]:((~old(X)<~>~generous(X))<=>(patient(X)|quiet(X))))&
(![X]:((humble(X)<~>happy(X))<=>rich(X)))&
(![X]:((~humble(X)|~rich(X))=>humble(X)))&
((?[X]:((quiet(X)<~>wise(X))))<=>((old(fred)|funny(fred))))&
((?[X]:((calm(X)&quiet(X))))<=>(?[X]:((~creative(X)&brave(X)))))&
((?[X]:(~patient(X)))=>((~patient(fred)<~>~kind(fred))))&
(~creative(alice))&
((funny(lucy)<~>~quiet(lucy)))&
(?[X]:((~tall(X)<~>funny(X))))&
((happy(fred)&generous(fred)))&
(?[X]:((calm(X)|~curious(X))))&
((~happy(susan)<~>strong(susan)))&
(?[X]:((~creative(X)<~>patient(X)))) | quiet(john) | [
"p4",
"p6",
"p8",
"p10",
"p11",
"p12",
"p13",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 508033684973330082416134
% SZS output start Proof for 508033684973330082416134
5. ? [X0] : (~quiet(X0) | funny(X0)) <=> (~kind(fred) & ~creative(fred)) [input p4]
7. ! [X0] : ((~wise(X0) <~> ~curious(X0)) <=> curious(X0)) [input p6]
9. ! [X0] : ((patient(X0) & funny(X0)) => (brave(X0) & rich(X0))) [input p8]
11. ! [X0] : ((~old(X0) <~> ~generous(X0)) <=> (quiet(X0) | patient(X0))) [input p10]
12. ! [X0] : ((humble(X0) <~> happy(X0)) <=> rich(X0)) [input p11]
13. ! [X0] : ((~rich(X0) | ~humble(X0)) => humble(X0)) [input p12]
14. ? [X0] : (quiet(X0) <~> wise(X0)) <=> (funny(fred) | old(fred)) [input p13]
16. ? [X0] : ~patient(X0) => (~patient(fred) <~> ~kind(fred)) [input p15]
20. generous(fred) & happy(fred) [input p19]
24. quiet(john) [input hypothesis]
29. ! [X0] : ((brave(X0) & rich(X0)) | (~patient(X0) | ~funny(X0))) [ennf transformation 9]
30. ! [X0] : ((brave(X0) & rich(X0)) | ~patient(X0) | ~funny(X0)) [flattening 29]
31. ! [X0] : (humble(X0) | (rich(X0) & humble(X0))) [ennf transformation 13]
32. (~patient(fred) <~> ~kind(fred)) | ! [X0] : patient(X0) [ennf transformation 16]
41. (? [X0] : (~quiet(X0) | funny(X0)) | (kind(fred) | creative(fred))) & ((~kind(fred) & ~creative(fred)) | ! [X0] : (quiet(X0) & ~funny(X0))) [nnf transformation 5]
42. (? [X0] : (~quiet(X0) | funny(X0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X0] : (quiet(X0) & ~funny(X0))) [flattening 41]
43. (? [X0] : (~quiet(X0) | funny(X0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X1] : (quiet(X1) & ~funny(X1))) [rectify 42]
44. ? [X0] : (~quiet(X0) | funny(X0)) => (~quiet(sK2) | funny(sK2)) [choice axiom]
45. ((~quiet(sK2) | funny(sK2)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X1] : (quiet(X1) & ~funny(X1))) [skolemisation 43,44]
48. ! [X0] : ((((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | ~curious(X0)) & (curious(X0) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0))))) [nnf transformation 7]
51. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [nnf transformation 11]
52. ! [X0] : ((((generous(X0) | old(X0)) & (~generous(X0) | ~old(X0))) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ((~old(X0) | generous(X0)) & (~generous(X0) | old(X0))))) [flattening 51]
53. ! [X0] : ((((~happy(X0) | ~humble(X0)) & (happy(X0) | humble(X0))) | ~rich(X0)) & (rich(X0) | ((humble(X0) | ~happy(X0)) & (happy(X0) | ~humble(X0))))) [nnf transformation 12]
54. (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~funny(fred) & ~old(fred))) & ((funny(fred) | old(fred)) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) [nnf transformation 14]
55. (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~funny(fred) & ~old(fred))) & (funny(fred) | old(fred) | ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0)))) [flattening 54]
56. (? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) | (~funny(fred) & ~old(fred))) & (funny(fred) | old(fred) | ! [X1] : ((quiet(X1) | ~wise(X1)) & (wise(X1) | ~quiet(X1)))) [rectify 55]
57. ? [X0] : ((~wise(X0) | ~quiet(X0)) & (wise(X0) | quiet(X0))) => ((~wise(sK3) | ~quiet(sK3)) & (wise(sK3) | quiet(sK3))) [choice axiom]
58. (((~wise(sK3) | ~quiet(sK3)) & (wise(sK3) | quiet(sK3))) | (~funny(fred) & ~old(fred))) & (funny(fred) | old(fred) | ! [X1] : ((quiet(X1) | ~wise(X1)) & (wise(X1) | ~quiet(X1)))) [skolemisation 56,57]
64. ((kind(fred) | patient(fred)) & (~kind(fred) | ~patient(fred))) | ! [X0] : patient(X0) [nnf transformation 32]
90. ~kind(fred) | ~funny(X1) [cnf transformation 45]
91. ~kind(fred) | quiet(X1) [cnf transformation 45]
100. curious(X0) | ~wise(X0) | curious(X0) [cnf transformation 48]
101. ~curious(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 48]
105. ~patient(X0) | rich(X0) | ~funny(X0) [cnf transformation 30]
112. ~generous(X0) | ~old(X0) | ~patient(X0) [cnf transformation 52]
113. ~generous(X0) | ~old(X0) | ~quiet(X0) [cnf transformation 52]
119. ~rich(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 53]
120. humble(X0) | humble(X0) [cnf transformation 31]
122. funny(fred) | old(fred) | wise(X1) | ~quiet(X1) [cnf transformation 58]
133. kind(fred) | patient(fred) | patient(X0) [cnf transformation 64]
139. happy(fred) [cnf transformation 20]
140. generous(fred) [cnf transformation 20]
146. quiet(john) [cnf transformation 24]
147. humble(X0) [duplicate literal removal 120]
148. curious(X0) | ~wise(X0) [duplicate literal removal 100]
149. ~wise(X0) | ~curious(X0) [duplicate literal removal 101]
195. 11 <=> kind(fred) [avatar definition]
208. 14 <=> ! [X1] : quiet(X1) [avatar definition]
209. quiet(X1) <- (14) [avatar component clause 208]
210. 14 | ~11 [avatar split clause 91,195,208]
212. 15 <=> ! [X1] : ~funny(X1) [avatar definition]
213. ~funny(X1) <- (15) [avatar component clause 212]
214. 15 | ~11 [avatar split clause 90,195,212]
239. ~wise(X0) [subsumption resolution 148,149]
257. 23 <=> funny(fred) [avatar definition]
258. funny(fred) <- (23) [avatar component clause 257]
267. 25 <=> old(fred) [avatar definition]
271. funny(fred) | old(fred) | ~quiet(X1) [subsumption resolution 122,239]
273. 26 <=> ! [X1] : ~quiet(X1) [avatar definition]
274. ~quiet(X1) <- (26) [avatar component clause 273]
275. 26 | 25 | 23 [avatar split clause 271,257,267,273]
303. 33 <=> ! [X0] : patient(X0) [avatar definition]
304. patient(X0) <- (33) [avatar component clause 303]
306. 34 <=> patient(fred) [avatar definition]
308. patient(fred) <- (34) [avatar component clause 306]
309. 33 | 34 | 11 [avatar split clause 133,195,306,303]
360. $false <- (15, 23) [resolution 258,213]
361. ~15 | ~23 [avatar contradiction clause 360]
388. ~funny(X0) | rich(X0) <- (33) [resolution 105,304]
390. ~old(fred) | ~patient(fred) [resolution 112,140]
394. ~old(fred) <- (33) [subsumption resolution 390,304]
395. ~25 | ~33 [avatar split clause 394,303,267]
396. $false <- (26) [resolution 274,146]
399. ~26 [avatar contradiction clause 396]
400. ~old(fred) | ~quiet(fred) [resolution 113,140]
401. rich(fred) <- (23, 33) [resolution 388,258]
427. ~humble(fred) | ~happy(fred) <- (23, 33) [resolution 119,401]
431. ~happy(fred) <- (23, 33) [subsumption resolution 427,147]
432. $false <- (23, 33) [subsumption resolution 431,139]
433. ~23 | ~33 [avatar contradiction clause 432]
435. 47 <=> quiet(fred) [avatar definition]
437. ~quiet(fred) <- (~47) [avatar component clause 435]
438. ~47 | ~25 [avatar split clause 400,267,435]
458. ~34 | ~25 [avatar split clause 390,267,306]
464. 52 <=> rich(fred) [avatar definition]
465. rich(fred) <- (52) [avatar component clause 464]
491. rich(fred) | ~funny(fred) <- (34) [resolution 308,105]
496. rich(fred) <- (23, 34) [subsumption resolution 491,258]
497. 52 | ~23 | ~34 [avatar split clause 496,306,257,464]
534. $false <- (14, ~47) [resolution 437,209]
535. ~14 | 47 [avatar contradiction clause 534]
552. ~humble(fred) | ~happy(fred) <- (52) [resolution 465,119]
556. ~happy(fred) <- (52) [subsumption resolution 552,147]
557. $false <- (52) [subsumption resolution 556,139]
558. ~52 [avatar contradiction clause 557]
559. $false [avatar sat refutation 210,214,275,309,361,395,399,433,438,458,497,535,558]
% SZS output end Proof for 508033684973330082416134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both quiet and not rich then mary is kind or generous and vice versa.
Everyone who is calm or happy is not funny.
Everyone who is old is both wise and generous.
Everyone who is both creative and not creative is happy or not happy.
If someone is either not old or not quiet then someone is quiet or rich and vice versa.
Everyone who is happy or not kind is not wise and vice versa.
Everyone who is either curious or tall is not kind and vice versa.
If mary is not patient then someone is not rich or not creative.
Everyone who is not wise is both not strong and wise and vice versa.
Everyone who is either not generous or not calm is both not kind and not tall.
Everyone who is both kind and quiet is not humble or not curious.
Everyone who is happy or not wise is not calm or patient and vice versa.
Everyone who is not quiet is either not old or rich.
If john is either not wise or generous then fred is rich.
If lucy is either not curious or happy then someone is curious or strong.
Everyone who is both not quiet and not wise is either old or curious and vice versa.
John is curious or not old.
Someone is wise or not strong.
Someone is either not quiet or not funny.
Susan is not humble or not calm.
Someone is either not rich or creative.
Someone is either not wise or wise. | Fred is not rich. | contradiction | (((quiet(paul)&~rich(paul)))<=>((kind(mary)|generous(mary))))&
(![X]:((calm(X)|happy(X))=>~funny(X)))&
(![X]:(old(X)=>(wise(X)&generous(X))))&
(![X]:((creative(X)&~creative(X))=>(happy(X)|~happy(X))))&
((?[X]:((~old(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|rich(X)))))&
(![X]:((happy(X)|~kind(X))<=>~wise(X)))&
(![X]:((curious(X)<~>tall(X))<=>~kind(X)))&
((~patient(mary))=>(?[X]:((~rich(X)|~creative(X)))))&
(![X]:(~wise(X)<=>(~strong(X)&wise(X))))&
(![X]:((~generous(X)<~>~calm(X))=>(~kind(X)&~tall(X))))&
(![X]:((kind(X)&quiet(X))=>(~humble(X)|~curious(X))))&
(![X]:((happy(X)|~wise(X))<=>(~calm(X)|patient(X))))&
(![X]:(~quiet(X)=>(~old(X)<~>rich(X))))&
(((~wise(john)<~>generous(john)))=>(rich(fred)))&
(((~curious(lucy)<~>happy(lucy)))=>(?[X]:((curious(X)|strong(X)))))&
(![X]:((~quiet(X)&~wise(X))<=>(old(X)<~>curious(X))))&
((curious(john)|~old(john)))&
(?[X]:((wise(X)|~strong(X))))&
(?[X]:((~quiet(X)<~>~funny(X))))&
((~humble(susan)|~calm(susan)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((~wise(X)<~>wise(X)))) | ~rich(fred) | [
"p5",
"p8",
"p9",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1707471953326928438717880
% SZS output start Proof for 1707471953326928438717880
6. ! [X0] : ((~kind(X0) | happy(X0)) <=> ~wise(X0)) [input p5]
9. ! [X0] : (~wise(X0) <=> (wise(X0) & ~strong(X0))) [input p8]
10. ! [X0] : ((~generous(X0) <~> ~calm(X0)) => (~tall(X0) & ~kind(X0))) [input p9]
12. ! [X0] : ((~wise(X0) | happy(X0)) <=> (patient(X0) | ~calm(X0))) [input p11]
14. (~wise(john) <~> generous(john)) => rich(fred) [input p13]
23. ~rich(fred) [input hypothesis]
32. ! [X0] : ((~tall(X0) & ~kind(X0)) | (~generous(X0) <=> ~calm(X0))) [ennf transformation 10]
34. rich(fred) | (~wise(john) <=> generous(john)) [ennf transformation 14]
43. ! [X0] : (((~kind(X0) | happy(X0)) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [nnf transformation 6]
44. ! [X0] : ((~kind(X0) | happy(X0) | wise(X0)) & (~wise(X0) | (kind(X0) & ~happy(X0)))) [flattening 43]
48. ! [X0] : ((~wise(X0) | (~wise(X0) | strong(X0))) & ((wise(X0) & ~strong(X0)) | wise(X0))) [nnf transformation 9]
49. ! [X0] : ((~wise(X0) | ~wise(X0) | strong(X0)) & ((wise(X0) & ~strong(X0)) | wise(X0))) [flattening 48]
50. ! [X0] : ((~tall(X0) & ~kind(X0)) | ((~generous(X0) | calm(X0)) & (~calm(X0) | generous(X0)))) [nnf transformation 32]
51. ! [X0] : (((~wise(X0) | happy(X0)) | (~patient(X0) & calm(X0))) & ((patient(X0) | ~calm(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 12]
52. ! [X0] : ((~wise(X0) | happy(X0) | (~patient(X0) & calm(X0))) & (patient(X0) | ~calm(X0) | (wise(X0) & ~happy(X0)))) [flattening 51]
54. rich(fred) | ((~wise(john) | ~generous(john)) & (generous(john) | wise(john))) [nnf transformation 34]
87. ~wise(X0) | ~happy(X0) [cnf transformation 44]
88. ~wise(X0) | kind(X0) [cnf transformation 44]
96. wise(X0) | wise(X0) [cnf transformation 49]
98. ~calm(X0) | ~kind(X0) | generous(X0) [cnf transformation 50]
104. ~wise(X0) | happy(X0) | calm(X0) [cnf transformation 52]
109. rich(fred) | ~wise(john) | ~generous(john) [cnf transformation 54]
126. ~rich(fred) [cnf transformation 23]
127. wise(X0) [duplicate literal removal 96]
198. happy(X0) | calm(X0) [subsumption resolution 104,127]
199. rich(fred) | ~generous(john) [subsumption resolution 109,127]
201. 16 <=> generous(john) [avatar definition]
203. ~generous(john) <- (~16) [avatar component clause 201]
205. 17 <=> rich(fred) [avatar definition]
208. ~16 | 17 [avatar split clause 199,205,201]
249. ~17 [avatar split clause 126,205]
252. ~happy(X0) [resolution 87,127]
255. kind(X0) [resolution 88,127]
259. calm(X0) [resolution 198,252]
279. ~kind(X0) | generous(X0) [resolution 98,259]
280. generous(X0) [subsumption resolution 279,255]
282. $false <- (~16) [resolution 280,203]
283. 16 [avatar contradiction clause 282]
285. $false [avatar sat refutation 208,249,283]
% SZS output end Proof for 1707471953326928438717880
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both rich and not curious and vice versa. If someone is not tall or brave then someone is tall or quiet and vice versa. Everyone who is not happy or not wise is rich or tall and vice versa. If someone is either tall or not strong then mary is both not tall and funny. If someone is not wise or not kind then someone is not rich. If someone is brave or curious then fred is either not happy or not brave. If john is both patient and not funny then someone is not old or not tall and vice versa. Everyone who is both not brave and happy is humble or not tall and vice versa. If john is both brave and generous then susan is not funny. Everyone who is both not humble and not strong is kind and vice versa. If john is either tall or not funny then someone is old. If someone is not old then fred is happy or patient. Everyone who is not generous is patient or not old and vice versa. Everyone who is either kind or not creative is not humble and vice versa. Everyone who is either strong or happy is creative and vice versa. If susan is patient then someone is both not curious and not rich and vice versa. Someone is not kind. Someone is both old and tall. Someone is generous or not kind. Someone is either wise or patient. Mary is quiet. Mary is calm. Someone is either rich or not old. John is humble or strong. | Fred is humble. | neutral | (![X]:(creative(X)<=>(rich(X)&~curious(X))))&
((?[X]:((~tall(X)|brave(X))))<=>(?[X]:((tall(X)|quiet(X)))))&
(![X]:((~happy(X)|~wise(X))<=>(rich(X)|tall(X))))&
((?[X]:((tall(X)<~>~strong(X))))=>((~tall(mary)&funny(mary))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:(~rich(X))))&
((?[X]:((brave(X)|curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((patient(john)&~funny(john)))<=>(?[X]:((~old(X)|~tall(X)))))&
(![X]:((~brave(X)&happy(X))<=>(humble(X)|~tall(X))))&
(((brave(john)&generous(john)))=>(~funny(susan)))&
(![X]:((~humble(X)&~strong(X))<=>kind(X)))&
(((tall(john)<~>~funny(john)))=>(?[X]:(old(X))))&
((?[X]:(~old(X)))=>((happy(fred)|patient(fred))))&
(![X]:(~generous(X)<=>(patient(X)|~old(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~humble(X)))&
(![X]:((strong(X)<~>happy(X))<=>creative(X)))&
((patient(susan))<=>(?[X]:((~curious(X)&~rich(X)))))&
(?[X]:(~kind(X)))&
(?[X]:((old(X)&tall(X))))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((wise(X)<~>patient(X))))&
(quiet(mary))&
(calm(mary))&
(?[X]:((rich(X)<~>~old(X))))&
((humble(john)|strong(john))) | humble(fred) | [] | null | 0 |
Everyone who is not happy or wise is not rich or funny.
If someone is both humble and not calm then lucy is strong.
If fred is not brave then someone is old or not generous.
If someone is either quiet or calm then lucy is not quiet and vice versa.
If someone is either curious or tall then alice is either funny or quiet.
If susan is not creative or not tall then alice is not humble.
If mary is not funny or not rich then someone is patient and vice versa.
Everyone who is not funny is calm or not tall.
Everyone who is both not strong and not rich is not kind and vice versa.
If someone is funny or not wise then fred is patient.
If fred is not tall or old then fred is tall.
If someone is both brave and not wise then lucy is both not quiet and quiet and vice versa.
Everyone who is either not strong or not generous is not humble.
Everyone who is both humble and not calm is calm and vice versa.
Everyone who is either strong or not rich is both not rich and curious.
If lucy is humble then fred is either not generous or not calm and vice versa.
Someone is not creative or creative.
Someone is brave.
Someone is not strong or patient.
Someone is patient.
Alice is not brave. | Alice is not happy. | neutral | (![X]:((~happy(X)|wise(X))=>(~rich(X)|funny(X))))&
((?[X]:((humble(X)&~calm(X))))=>(strong(lucy)))&
((~brave(fred))=>(?[X]:((old(X)|~generous(X)))))&
((?[X]:((quiet(X)<~>calm(X))))<=>(~quiet(lucy)))&
((?[X]:((curious(X)<~>tall(X))))=>((funny(alice)<~>quiet(alice))))&
(((~creative(susan)|~tall(susan)))=>(~humble(alice)))&
(((~funny(mary)|~rich(mary)))<=>(?[X]:(patient(X))))&
(![X]:(~funny(X)=>(calm(X)|~tall(X))))&
(![X]:((~strong(X)&~rich(X))<=>~kind(X)))&
((?[X]:((funny(X)|~wise(X))))=>(patient(fred)))&
(((~tall(fred)|old(fred)))=>(tall(fred)))&
((?[X]:((brave(X)&~wise(X))))<=>((~quiet(lucy)&quiet(lucy))))&
(![X]:((~strong(X)<~>~generous(X))=>~humble(X)))&
(![X]:((humble(X)&~calm(X))<=>calm(X)))&
(![X]:((strong(X)<~>~rich(X))=>(~rich(X)&curious(X))))&
((humble(lucy))<=>((~generous(fred)<~>~calm(fred))))&
(?[X]:((~creative(X)|creative(X))))&
(?[X]:(brave(X)))&
(?[X]:((~strong(X)|patient(X))))&
(?[X]:(patient(X)))&
(~brave(alice)) | ~happy(alice) | [] | null | 0 |
Everyone who is tall or funny is not patient or not curious and vice versa.
Everyone who is not strong is either curious or not funny.
Everyone who is not wise or happy is not happy or creative and vice versa.
Everyone who is either happy or not quiet is not patient.
Everyone who is either not tall or not brave is strong or not creative.
If alice is quiet or funny then someone is either not quiet or quiet and vice versa.
If someone is old or not old then susan is both not creative and generous and vice versa.
Everyone who is both creative and funny is calm.
Everyone who is humble or quiet is both not creative and not rich.
If someone is either old or not creative then someone is either strong or not tall and vice versa.
Everyone who is either tall or not quiet is either humble or generous and vice versa.
Everyone who is both not humble and old is both not quiet and curious and vice versa.
Everyone who is not brave is not happy.
Everyone who is curious is both not funny and not old.
If susan is both happy and not wise then someone is both not strong and not curious.
Everyone who is either not quiet or rich is wise or patient and vice versa.
Lucy is not creative or tall.
Someone is either kind or not happy.
Someone is either old or not brave.
Paul is either happy or not humble.
Someone is either not wise or happy.
Someone is both not creative and tall.
Someone is not tall or not generous.
Paul is both not rich and not generous. | Paul is not quiet. | contradiction | (![X]:((tall(X)|funny(X))<=>(~patient(X)|~curious(X))))&
(![X]:(~strong(X)=>(curious(X)<~>~funny(X))))&
(![X]:((~wise(X)|happy(X))<=>(~happy(X)|creative(X))))&
(![X]:((happy(X)<~>~quiet(X))=>~patient(X)))&
(![X]:((~tall(X)<~>~brave(X))=>(strong(X)|~creative(X))))&
(((quiet(alice)|funny(alice)))<=>(?[X]:((~quiet(X)<~>quiet(X)))))&
((?[X]:((old(X)|~old(X))))<=>((~creative(susan)&generous(susan))))&
(![X]:((creative(X)&funny(X))=>calm(X)))&
(![X]:((humble(X)|quiet(X))=>(~creative(X)&~rich(X))))&
((?[X]:((old(X)<~>~creative(X))))<=>(?[X]:((strong(X)<~>~tall(X)))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~humble(X)&old(X))<=>(~quiet(X)&curious(X))))&
(![X]:(~brave(X)=>~happy(X)))&
(![X]:(curious(X)=>(~funny(X)&~old(X))))&
(((happy(susan)&~wise(susan)))=>(?[X]:((~strong(X)&~curious(X)))))&
(![X]:((~quiet(X)<~>rich(X))<=>(wise(X)|patient(X))))&
((~creative(lucy)|tall(lucy)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((old(X)<~>~brave(X))))&
((happy(paul)<~>~humble(paul)))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((~creative(X)&tall(X))))&
(?[X]:((~tall(X)|~generous(X))))&
((~rich(paul)&~generous(paul))) | ~quiet(paul) | [
"p2",
"p3",
"p8",
"p15",
"p19",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 732558380009911522955195
% SZS output start Proof for 732558380009911522955195
3. ! [X0] : ((happy(X0) | ~wise(X0)) <=> (creative(X0) | ~happy(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~quiet(X0)) => ~patient(X0)) [input p3]
9. ! [X0] : ((quiet(X0) | humble(X0)) => (~rich(X0) & ~creative(X0))) [input p8]
16. ! [X0] : ((~quiet(X0) <~> rich(X0)) <=> (patient(X0) | wise(X0))) [input p15]
20. happy(paul) <~> ~humble(paul) [input p19]
24. ~generous(paul) & ~rich(paul) [input p23]
25. ~quiet(paul) [input hypothesis]
29. ! [X0] : (~patient(X0) | (happy(X0) <=> ~quiet(X0))) [ennf transformation 4]
32. ! [X0] : ((~rich(X0) & ~creative(X0)) | (~quiet(X0) & ~humble(X0))) [ennf transformation 9]
40. ! [X0] : (((happy(X0) | ~wise(X0)) | (~creative(X0) & happy(X0))) & ((creative(X0) | ~happy(X0)) | (~happy(X0) & wise(X0)))) [nnf transformation 3]
41. ! [X0] : ((happy(X0) | ~wise(X0) | (~creative(X0) & happy(X0))) & (creative(X0) | ~happy(X0) | (~happy(X0) & wise(X0)))) [flattening 40]
42. ! [X0] : (~patient(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) [nnf transformation 29]
64. ! [X0] : ((((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0))))) [nnf transformation 16]
65. ! [X0] : ((((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0))))) [flattening 64]
72. (humble(paul) | ~happy(paul)) & (~humble(paul) | happy(paul)) [nnf transformation 20]
87. creative(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 41]
88. happy(X0) | ~wise(X0) | happy(X0) [cnf transformation 41]
91. ~patient(X0) | happy(X0) | quiet(X0) [cnf transformation 42]
105. ~humble(X0) | ~creative(X0) [cnf transformation 32]
134. rich(X0) | wise(X0) | patient(X0) | quiet(X0) [cnf transformation 65]
146. humble(paul) | ~happy(paul) [cnf transformation 72]
152. ~rich(paul) [cnf transformation 24]
154. ~quiet(paul) [cnf transformation 25]
157. ~happy(X0) | creative(X0) [duplicate literal removal 87]
158. ~wise(X0) | happy(X0) [duplicate literal removal 88]
281. 27 <=> happy(paul) [avatar definition]
282. happy(paul) <- (27) [avatar component clause 281]
283. ~happy(paul) <- (~27) [avatar component clause 281]
285. 28 <=> humble(paul) [avatar definition]
287. humble(paul) <- (28) [avatar component clause 285]
288. ~27 | 28 [avatar split clause 146,285,281]
400. wise(paul) | patient(paul) | quiet(paul) [resolution 134,152]
405. wise(paul) | patient(paul) [subsumption resolution 400,154]
407. 43 <=> patient(paul) [avatar definition]
409. patient(paul) <- (43) [avatar component clause 407]
411. 44 <=> wise(paul) [avatar definition]
413. wise(paul) <- (44) [avatar component clause 411]
414. 43 | 44 [avatar split clause 405,411,407]
415. happy(paul) | quiet(paul) <- (43) [resolution 409,91]
416. quiet(paul) <- (~27, 43) [subsumption resolution 415,283]
417. $false <- (~27, 43) [subsumption resolution 416,154]
418. 27 | ~43 [avatar contradiction clause 417]
420. happy(paul) <- (44) [resolution 413,158]
423. 27 | ~44 [avatar split clause 420,411,281]
433. creative(paul) <- (27) [resolution 282,157]
440. ~creative(paul) <- (28) [resolution 287,105]
445. $false <- (27, 28) [subsumption resolution 440,433]
446. ~27 | ~28 [avatar contradiction clause 445]
447. $false [avatar sat refutation 288,414,418,423,446]
% SZS output end Proof for 732558380009911522955195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is not creative.
Everyone who is not quiet is strong.
Everyone who is calm or not generous is not humble and vice versa.
Everyone who is not humble is not wise and vice versa.
If someone is not humble or quiet then paul is calm and vice versa.
If susan is both quiet and not calm then fred is both kind and happy.
Everyone who is not tall or tall is both patient and curious.
If someone is not creative then someone is both generous and kind.
Everyone who is rich or happy is both not happy and old and vice versa.
If someone is not funny or generous then someone is not happy or patient and vice versa.
If someone is either curious or not creative then someone is not kind.
If lucy is strong or not brave then fred is both not creative and humble and vice versa.
If someone is not patient or not strong then someone is either not calm or generous.
If someone is both tall and not generous then someone is not quiet or not generous.
Everyone who is either brave or calm is not strong or not happy and vice versa.
Everyone who is both patient and not funny is rich or not humble and vice versa.
Lucy is calm.
Susan is not wise or not quiet.
Someone is not patient or not strong.
Someone is not old or not patient.
Mary is either kind or not tall.
Fred is not quiet or curious. | Lucy is wise. | contradiction | (![X]:(~generous(X)=>~creative(X)))&
(![X]:(~quiet(X)=>strong(X)))&
(![X]:((calm(X)|~generous(X))<=>~humble(X)))&
(![X]:(~humble(X)<=>~wise(X)))&
((?[X]:((~humble(X)|quiet(X))))<=>(calm(paul)))&
(((quiet(susan)&~calm(susan)))=>((kind(fred)&happy(fred))))&
(![X]:((~tall(X)|tall(X))=>(patient(X)&curious(X))))&
((?[X]:(~creative(X)))=>(?[X]:((generous(X)&kind(X)))))&
(![X]:((rich(X)|happy(X))<=>(~happy(X)&old(X))))&
((?[X]:((~funny(X)|generous(X))))<=>(?[X]:((~happy(X)|patient(X)))))&
((?[X]:((curious(X)<~>~creative(X))))=>(?[X]:(~kind(X))))&
(((strong(lucy)|~brave(lucy)))<=>((~creative(fred)&humble(fred))))&
((?[X]:((~patient(X)|~strong(X))))=>(?[X]:((~calm(X)<~>generous(X)))))&
((?[X]:((tall(X)&~generous(X))))=>(?[X]:((~quiet(X)|~generous(X)))))&
(![X]:((brave(X)<~>calm(X))<=>(~strong(X)|~happy(X))))&
(![X]:((patient(X)&~funny(X))<=>(rich(X)|~humble(X))))&
(calm(lucy))&
((~wise(susan)|~quiet(susan)))&
(?[X]:((~patient(X)|~strong(X))))&
(?[X]:((~old(X)|~patient(X))))&
((kind(mary)<~>~tall(mary)))&
((~quiet(fred)|curious(fred))) | wise(lucy) | [
"p2",
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2931165541496894659416196
% SZS output start Proof for 2931165541496894659416196
3. ! [X0] : ((~generous(X0) | calm(X0)) <=> ~humble(X0)) [input p2]
4. ! [X0] : (~humble(X0) <=> ~wise(X0)) [input p3]
17. calm(lucy) [input p16]
23. wise(lucy) [input hypothesis]
38. ! [X0] : (((~generous(X0) | calm(X0)) | humble(X0)) & (~humble(X0) | (generous(X0) & ~calm(X0)))) [nnf transformation 3]
39. ! [X0] : ((~generous(X0) | calm(X0) | humble(X0)) & (~humble(X0) | (generous(X0) & ~calm(X0)))) [flattening 38]
40. ! [X0] : ((~humble(X0) | wise(X0)) & (~wise(X0) | humble(X0))) [nnf transformation 4]
79. ~humble(X0) | ~calm(X0) [cnf transformation 39]
82. ~wise(X0) | humble(X0) [cnf transformation 40]
127. calm(lucy) [cnf transformation 17]
134. wise(lucy) [cnf transformation 23]
287. humble(lucy) [resolution 82,134]
289. ~calm(lucy) [resolution 287,79]
290. $false [subsumption resolution 289,127]
% SZS output end Proof for 2931165541496894659416196
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If john is not curious or not rich then someone is not creative. Everyone who is both not tall and not generous is not rich and vice versa. Everyone who is wise is not rich. If susan is quiet or not curious then lucy is not old or humble. If someone is rich or creative then someone is not rich or not calm. If paul is either not humble or wise then mary is kind. Everyone who is both not creative and not calm is strong or kind and vice versa. Everyone who is both funny and calm is both not funny and patient and vice versa. If john is either not humble or calm then lucy is not generous or strong and vice versa. If someone is both brave and not generous then someone is either strong or not kind and vice versa. Everyone who is wise or not quiet is either curious or not funny. Everyone who is both humble and not patient is both funny and curious and vice versa. If someone is happy then someone is either not curious or humble. Everyone who is both not curious and not rich is either wise or patient. Everyone who is either not creative or not kind is kind and vice versa. Everyone who is old is not wise or patient. Alice is both not patient and not old. Someone is patient or rich. Someone is curious. Someone is not humble or curious. Someone is not old or kind. Someone is both funny and happy. Someone is either rich or not strong. Fred is both not kind and not funny. | Lucy is creative. | contradiction | (((~curious(john)|~rich(john)))=>(?[X]:(~creative(X))))&
(![X]:((~tall(X)&~generous(X))<=>~rich(X)))&
(![X]:(wise(X)=>~rich(X)))&
(((quiet(susan)|~curious(susan)))=>((~old(lucy)|humble(lucy))))&
((?[X]:((rich(X)|creative(X))))=>(?[X]:((~rich(X)|~calm(X)))))&
(((~humble(paul)<~>wise(paul)))=>(kind(mary)))&
(![X]:((~creative(X)&~calm(X))<=>(strong(X)|kind(X))))&
(![X]:((funny(X)&calm(X))<=>(~funny(X)&patient(X))))&
(((~humble(john)<~>calm(john)))<=>((~generous(lucy)|strong(lucy))))&
((?[X]:((brave(X)&~generous(X))))<=>(?[X]:((strong(X)<~>~kind(X)))))&
(![X]:((wise(X)|~quiet(X))=>(curious(X)<~>~funny(X))))&
(![X]:((humble(X)&~patient(X))<=>(funny(X)&curious(X))))&
((?[X]:(happy(X)))=>(?[X]:((~curious(X)<~>humble(X)))))&
(![X]:((~curious(X)&~rich(X))=>(wise(X)<~>patient(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>kind(X)))&
(![X]:(old(X)=>(~wise(X)|patient(X))))&
((~patient(alice)&~old(alice)))&
(?[X]:((patient(X)|rich(X))))&
(?[X]:(curious(X)))&
(?[X]:((~humble(X)|curious(X))))&
(?[X]:((~old(X)|kind(X))))&
(?[X]:((funny(X)&happy(X))))&
(?[X]:((rich(X)<~>~strong(X))))&
((~kind(fred)&~funny(fred))) | creative(lucy) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6152407246383535589751500
% SZS output start Proof for 6152407246383535589751500
7. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (kind(X0) | strong(X0))) [input p6]
15. ! [X0] : ((~creative(X0) <~> ~kind(X0)) <=> kind(X0)) [input p14]
25. creative(lucy) [input hypothesis]
50. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~kind(X0) & ~strong(X0))) & ((kind(X0) | strong(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 7]
51. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~kind(X0) & ~strong(X0))) & (kind(X0) | strong(X0) | calm(X0) | creative(X0))) [flattening 50]
69. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [nnf transformation 15]
93. ~creative(X0) | ~kind(X0) [cnf transformation 51]
123. kind(X0) | ~creative(X0) | kind(X0) [cnf transformation 69]
136. creative(lucy) [cnf transformation 25]
137. kind(X0) | ~creative(X0) [duplicate literal removal 123]
156. 4 <=> ! [X1] : ~creative(X1) [avatar definition]
157. ~creative(X1) <- (4) [avatar component clause 156]
255. ~creative(X0) [subsumption resolution 137,93]
256. 4 [avatar split clause 255,156]
285. $false <- (4) [resolution 157,136]
286. ~4 [avatar contradiction clause 285]
287. $false [avatar sat refutation 256,286]
% SZS output end Proof for 6152407246383535589751500
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall or not brave is both old and not patient. If alice is either patient or not generous then fred is not funny. If someone is not creative then john is humble and vice versa. Everyone who is not curious is not quiet. If someone is either tall or not wise then someone is tall or not happy. Everyone who is both creative and quiet is both creative and not strong and vice versa. Everyone who is brave is not curious and vice versa. Everyone who is not brave or not funny is not humble. If someone is not humble or not strong then alice is not humble. Everyone who is not happy or not brave is both quiet and not happy. If someone is not brave or not wise then someone is both generous and strong. If john is both not happy and creative then someone is generous and vice versa. Everyone who is wise is strong. If someone is both not calm and brave then fred is both old and not funny. If someone is both old and quiet then mary is not happy or humble and vice versa. If john is either not brave or generous then susan is kind and vice versa. Fred is brave. Someone is tall. Mary is both not funny and generous. Paul is both humble and calm. Someone is either old or brave. Alice is either not old or not brave. Susan is not calm or not funny. | Fred is not strong. | contradiction | (![X]:((tall(X)|~brave(X))=>(old(X)&~patient(X))))&
(((patient(alice)<~>~generous(alice)))=>(~funny(fred)))&
((?[X]:(~creative(X)))<=>(humble(john)))&
(![X]:(~curious(X)=>~quiet(X)))&
((?[X]:((tall(X)<~>~wise(X))))=>(?[X]:((tall(X)|~happy(X)))))&
(![X]:((creative(X)&quiet(X))<=>(creative(X)&~strong(X))))&
(![X]:(brave(X)<=>~curious(X)))&
(![X]:((~brave(X)|~funny(X))=>~humble(X)))&
((?[X]:((~humble(X)|~strong(X))))=>(~humble(alice)))&
(![X]:((~happy(X)|~brave(X))=>(quiet(X)&~happy(X))))&
((?[X]:((~brave(X)|~wise(X))))=>(?[X]:((generous(X)&strong(X)))))&
(((~happy(john)&creative(john)))<=>(?[X]:(generous(X))))&
(![X]:(wise(X)=>strong(X)))&
((?[X]:((~calm(X)&brave(X))))=>((old(fred)&~funny(fred))))&
((?[X]:((old(X)&quiet(X))))<=>((~happy(mary)|humble(mary))))&
(((~brave(john)<~>generous(john)))<=>(kind(susan)))&
(brave(fred))&
(?[X]:(tall(X)))&
((~funny(mary)&generous(mary)))&
((humble(paul)&calm(paul)))&
(?[X]:((old(X)<~>brave(X))))&
((~old(alice)<~>~brave(alice)))&
((~calm(susan)|~funny(susan))) | ~strong(fred) | [
"p2",
"p3",
"p5",
"p6",
"p7",
"p9",
"p11",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 3897714342894754522123063
% SZS output start Proof for 3897714342894754522123063
3. ? [X0] : ~creative(X0) <=> humble(john) [input p2]
4. ! [X0] : (~curious(X0) => ~quiet(X0)) [input p3]
6. ! [X0] : ((quiet(X0) & creative(X0)) <=> (~strong(X0) & creative(X0))) [input p5]
7. ! [X0] : (brave(X0) <=> ~curious(X0)) [input p6]
8. ! [X0] : ((~funny(X0) | ~brave(X0)) => ~humble(X0)) [input p7]
10. ! [X0] : ((~brave(X0) | ~happy(X0)) => (~happy(X0) & quiet(X0))) [input p9]
12. (creative(john) & ~happy(john)) <=> ? [X0] : generous(X0) [input p11]
17. brave(fred) [input p16]
19. generous(mary) & ~funny(mary) [input p18]
24. ~strong(fred) [input hypothesis]
29. ! [X0] : (~quiet(X0) | curious(X0)) [ennf transformation 4]
31. ! [X0] : (~humble(X0) | (funny(X0) & brave(X0))) [ennf transformation 8]
33. ! [X0] : ((~happy(X0) & quiet(X0)) | (brave(X0) & happy(X0))) [ennf transformation 10]
38. (? [X0] : ~creative(X0) | ~humble(john)) & (humble(john) | ! [X0] : creative(X0)) [nnf transformation 3]
39. (? [X0] : ~creative(X0) | ~humble(john)) & (humble(john) | ! [X1] : creative(X1)) [rectify 38]
40. ? [X0] : ~creative(X0) => ~creative(sK0) [choice axiom]
41. (~creative(sK0) | ~humble(john)) & (humble(john) | ! [X1] : creative(X1)) [skolemisation 39,40]
46. ! [X0] : (((quiet(X0) & creative(X0)) | (strong(X0) | ~creative(X0))) & ((~strong(X0) & creative(X0)) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 6]
47. ! [X0] : (((quiet(X0) & creative(X0)) | strong(X0) | ~creative(X0)) & ((~strong(X0) & creative(X0)) | ~quiet(X0) | ~creative(X0))) [flattening 46]
48. ! [X0] : ((brave(X0) | curious(X0)) & (~curious(X0) | ~brave(X0))) [nnf transformation 7]
52. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (~creative(john) | happy(john))) [nnf transformation 12]
53. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | ~creative(john) | happy(john)) [flattening 52]
54. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | ~creative(john) | happy(john)) [rectify 53]
55. ? [X1] : generous(X1) => generous(sK3) [choice axiom]
56. ((creative(john) & ~happy(john)) | ! [X0] : ~generous(X0)) & (generous(sK3) | ~creative(john) | happy(john)) [skolemisation 54,55]
75. humble(john) | creative(X1) [cnf transformation 41]
77. ~quiet(X0) | curious(X0) [cnf transformation 29]
83. ~creative(X0) | strong(X0) | quiet(X0) [cnf transformation 47]
84. ~curious(X0) | ~brave(X0) [cnf transformation 48]
86. ~humble(X0) | brave(X0) [cnf transformation 31]
90. happy(X0) | quiet(X0) [cnf transformation 33]
99. ~happy(john) | ~generous(X0) [cnf transformation 56]
113. brave(fred) [cnf transformation 17]
116. generous(mary) [cnf transformation 19]
124. ~strong(fred) [cnf transformation 24]
140. 4 <=> humble(john) [avatar definition]
141. humble(john) <- (4) [avatar component clause 140]
149. 6 <=> ! [X1] : creative(X1) [avatar definition]
150. creative(X1) <- (6) [avatar component clause 149]
151. 6 | 4 [avatar split clause 75,140,149]
199. 18 <=> ! [X0] : ~generous(X0) [avatar definition]
200. ~generous(X0) <- (18) [avatar component clause 199]
207. 20 <=> happy(john) [avatar definition]
209. ~happy(john) <- (~20) [avatar component clause 207]
210. 18 | ~20 [avatar split clause 99,207,199]
254. 30 <=> brave(john) [avatar definition]
255. ~brave(john) <- (~30) [avatar component clause 254]
292. $false <- (18) [resolution 200,116]
293. ~18 [avatar contradiction clause 292]
301. brave(john) <- (4) [resolution 86,141]
303. $false <- (4, ~30) [subsumption resolution 301,255]
304. ~4 | 30 [avatar contradiction clause 303]
312. quiet(john) <- (~20) [resolution 90,209]
319. curious(john) <- (~20) [resolution 312,77]
346. strong(X0) | quiet(X0) <- (6) [resolution 83,150]
352. ~brave(john) <- (~20) [resolution 319,84]
357. ~30 | 20 [avatar split clause 352,207,254]
365. quiet(fred) <- (6) [resolution 346,124]
369. curious(fred) <- (6) [resolution 365,77]
370. ~brave(fred) <- (6) [resolution 369,84]
371. $false <- (6) [subsumption resolution 370,113]
372. ~6 [avatar contradiction clause 371]
373. $false [avatar sat refutation 151,210,293,304,357,372]
% SZS output end Proof for 3897714342894754522123063
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both not wise and not happy. If alice is either not creative or not strong then mary is strong or tall. If someone is either calm or not old then john is not generous. Everyone who is kind or not old is either tall or calm. If someone is either not old or not calm then someone is not humble. Everyone who is both not kind and humble is either generous or not humble and vice versa. Everyone who is strong is not humble. Everyone who is not curious is not brave or not calm. If susan is both not happy and kind then someone is not funny or tall. If susan is not happy then paul is humble. Everyone who is both not strong and not tall is quiet or patient and vice versa. Everyone who is not tall is creative or not humble. Everyone who is not patient is either tall or not calm. Everyone who is both not patient and patient is not quiet. If lucy is not brave or not rich then someone is both not rich and not funny. Everyone who is both generous and patient is not kind or strong and vice versa. Someone is either creative or not patient. Someone is not tall. Someone is both creative and funny. Susan is generous. Fred is not strong or funny. Someone is old or kind. John is both not wise and funny. Someone is both not humble and not rich. | Fred is not tall. | entailment | (![X]:(~funny(X)=>(~wise(X)&~happy(X))))&
(((~creative(alice)<~>~strong(alice)))=>((strong(mary)|tall(mary))))&
((?[X]:((calm(X)<~>~old(X))))=>(~generous(john)))&
(![X]:((kind(X)|~old(X))=>(tall(X)<~>calm(X))))&
((?[X]:((~old(X)<~>~calm(X))))=>(?[X]:(~humble(X))))&
(![X]:((~kind(X)&humble(X))<=>(generous(X)<~>~humble(X))))&
(![X]:(strong(X)=>~humble(X)))&
(![X]:(~curious(X)=>(~brave(X)|~calm(X))))&
(((~happy(susan)&kind(susan)))=>(?[X]:((~funny(X)|tall(X)))))&
((~happy(susan))=>(humble(paul)))&
(![X]:((~strong(X)&~tall(X))<=>(quiet(X)|patient(X))))&
(![X]:(~tall(X)=>(creative(X)|~humble(X))))&
(![X]:(~patient(X)=>(tall(X)<~>~calm(X))))&
(![X]:((~patient(X)&patient(X))=>~quiet(X)))&
(((~brave(lucy)|~rich(lucy)))=>(?[X]:((~rich(X)&~funny(X)))))&
(![X]:((generous(X)&patient(X))<=>(~kind(X)|strong(X))))&
(?[X]:((creative(X)<~>~patient(X))))&
(?[X]:(~tall(X)))&
(?[X]:((creative(X)&funny(X))))&
(generous(susan))&
((~strong(fred)|funny(fred)))&
(?[X]:((old(X)|kind(X))))&
((~wise(john)&funny(john)))&
(?[X]:((~humble(X)&~rich(X)))) | ~tall(fred) | [
"p3",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6649680017398153627277761
% SZS output start Proof for 6649680017398153627277761
4. ! [X0] : ((~old(X0) | kind(X0)) => (tall(X0) <~> calm(X0))) [input p3]
11. ! [X0] : ((~tall(X0) & ~strong(X0)) <=> (patient(X0) | quiet(X0))) [input p10]
13. ! [X0] : (~patient(X0) => (tall(X0) <~> ~calm(X0))) [input p12]
16. ! [X0] : ((patient(X0) & generous(X0)) <=> (strong(X0) | ~kind(X0))) [input p15]
25. tall(fred) [input hypothesis]
35. ! [X0] : ((tall(X0) <~> calm(X0)) | (old(X0) & ~kind(X0))) [ennf transformation 4]
43. ! [X0] : ((tall(X0) <~> ~calm(X0)) | patient(X0)) [ennf transformation 13]
49. ! [X0] : (((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (old(X0) & ~kind(X0))) [nnf transformation 35]
58. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | (tall(X0) | strong(X0)))) [nnf transformation 11]
59. ! [X0] : (((~tall(X0) & ~strong(X0)) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | tall(X0) | strong(X0))) [flattening 58]
60. ! [X0] : (((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | patient(X0)) [nnf transformation 43]
63. ! [X0] : (((patient(X0) & generous(X0)) | (~strong(X0) & kind(X0))) & ((strong(X0) | ~kind(X0)) | (~patient(X0) | ~generous(X0)))) [nnf transformation 16]
64. ! [X0] : (((patient(X0) & generous(X0)) | (~strong(X0) & kind(X0))) & (strong(X0) | ~kind(X0) | ~patient(X0) | ~generous(X0))) [flattening 63]
83. ~kind(X0) | ~tall(X0) | ~calm(X0) [cnf transformation 49]
100. ~patient(X0) | ~tall(X0) [cnf transformation 59]
103. calm(X0) | ~tall(X0) | patient(X0) [cnf transformation 60]
110. patient(X0) | kind(X0) [cnf transformation 64]
123. tall(fred) [cnf transformation 25]
191. ~tall(X0) | calm(X0) [subsumption resolution 103,100]
229. ~tall(X0) | kind(X0) [resolution 110,100]
234. calm(fred) [resolution 191,123]
239. kind(fred) [resolution 229,123]
244. ~tall(fred) | ~calm(fred) [resolution 239,83]
246. ~calm(fred) [subsumption resolution 244,123]
247. $false [subsumption resolution 246,234]
% SZS output end Proof for 6649680017398153627277761
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or rich is not brave or not calm. Everyone who is not kind or calm is wise. If fred is not patient then someone is strong and vice versa. If someone is not happy or rich then paul is not creative and vice versa. Everyone who is not calm is either not calm or kind. Everyone who is not creative is calm or curious and vice versa. Everyone who is either not wise or creative is old. If susan is not patient or not creative then lucy is either not humble or not brave and vice versa. Everyone who is not creative is both not rich and rich. Everyone who is either brave or curious is not wise or brave. Everyone who is both not rich and rich is quiet or wise. Everyone who is both humble and not patient is both not humble and not brave. Everyone who is both funny and curious is humble or strong. Everyone who is either not old or not patient is generous or not patient and vice versa. Everyone who is either not strong or brave is brave and vice versa. If susan is either wise or humble then mary is both strong and brave. Paul is not patient or tall. Someone is not rich. Paul is both funny and quiet. Alice is either funny or old. Paul is either not tall or funny. Lucy is either strong or kind. Mary is not humble. | Fred is not happy. | contradiction | (![X]:((~quiet(X)|rich(X))=>(~brave(X)|~calm(X))))&
(![X]:((~kind(X)|calm(X))=>wise(X)))&
((~patient(fred))<=>(?[X]:(strong(X))))&
((?[X]:((~happy(X)|rich(X))))<=>(~creative(paul)))&
(![X]:(~calm(X)=>(~calm(X)<~>kind(X))))&
(![X]:(~creative(X)<=>(calm(X)|curious(X))))&
(![X]:((~wise(X)<~>creative(X))=>old(X)))&
(((~patient(susan)|~creative(susan)))<=>((~humble(lucy)<~>~brave(lucy))))&
(![X]:(~creative(X)=>(~rich(X)&rich(X))))&
(![X]:((brave(X)<~>curious(X))=>(~wise(X)|brave(X))))&
(![X]:((~rich(X)&rich(X))=>(quiet(X)|wise(X))))&
(![X]:((humble(X)&~patient(X))=>(~humble(X)&~brave(X))))&
(![X]:((funny(X)&curious(X))=>(humble(X)|strong(X))))&
(![X]:((~old(X)<~>~patient(X))<=>(generous(X)|~patient(X))))&
(![X]:((~strong(X)<~>brave(X))<=>brave(X)))&
(((wise(susan)<~>humble(susan)))=>((strong(mary)&brave(mary))))&
((~patient(paul)|tall(paul)))&
(?[X]:(~rich(X)))&
((funny(paul)&quiet(paul)))&
((funny(alice)<~>old(alice)))&
((~tall(paul)<~>funny(paul)))&
((strong(lucy)<~>kind(lucy)))&
(~humble(mary)) | ~happy(fred) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 3243459685737168854130013
% SZS output start Proof for 3243459685737168854130013
4. ? [X0] : (rich(X0) | ~happy(X0)) <=> ~creative(paul) [input p3]
9. ! [X0] : (~creative(X0) => (rich(X0) & ~rich(X0))) [input p8]
24. ~happy(fred) [input hypothesis]
33. ! [X0] : ((rich(X0) & ~rich(X0)) | creative(X0)) [ennf transformation 9]
45. (? [X0] : (rich(X0) | ~happy(X0)) | creative(paul)) & (~creative(paul) | ! [X0] : (~rich(X0) & happy(X0))) [nnf transformation 4]
46. (? [X0] : (rich(X0) | ~happy(X0)) | creative(paul)) & (~creative(paul) | ! [X1] : (~rich(X1) & happy(X1))) [rectify 45]
47. ? [X0] : (rich(X0) | ~happy(X0)) => (rich(sK1) | ~happy(sK1)) [choice axiom]
48. ((rich(sK1) | ~happy(sK1)) | creative(paul)) & (~creative(paul) | ! [X1] : (~rich(X1) & happy(X1))) [skolemisation 46,47]
70. ~creative(paul) | happy(X1) [cnf transformation 48]
86. ~rich(X0) | creative(X0) [cnf transformation 33]
87. rich(X0) | creative(X0) [cnf transformation 33]
117. ~happy(fred) [cnf transformation 24]
139. 4 <=> creative(paul) [avatar definition]
140. ~creative(paul) <- (~4) [avatar component clause 139]
156. 8 <=> ! [X1] : happy(X1) [avatar definition]
157. happy(X1) <- (8) [avatar component clause 156]
158. 8 | ~4 [avatar split clause 70,139,156]
181. creative(X0) [subsumption resolution 86,87]
220. $false <- (~4) [subsumption resolution 140,181]
221. 4 [avatar contradiction clause 220]
222. $false <- (8) [resolution 157,117]
225. ~8 [avatar contradiction clause 222]
226. $false [avatar sat refutation 158,221,225]
% SZS output end Proof for 3243459685737168854130013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or old then lucy is not brave and vice versa. Everyone who is either curious or not old is not old or strong and vice versa. Everyone who is kind or calm is either not happy or brave and vice versa. If someone is both not brave and quiet then someone is kind or brave and vice versa. Everyone who is both kind and not happy is kind or patient and vice versa. If someone is both not strong and not curious then fred is calm. Everyone who is humble or not wise is both wise and not calm and vice versa. Everyone who is either creative or not patient is either not quiet or not wise and vice versa. If someone is quiet then someone is both calm and brave and vice versa. If someone is both humble and not humble then someone is both not quiet and kind. Everyone who is either rich or not wise is patient or not creative and vice versa. Everyone who is not curious is not quiet or tall and vice versa. Everyone who is either not happy or creative is not happy or kind. Everyone who is funny or creative is either not creative or patient. If susan is both not creative and not old then someone is either kind or happy and vice versa. Everyone who is both not funny and not tall is not generous and vice versa. Mary is tall. John is both humble and not tall. Mary is calm or not brave. Mary is not quiet. Alice is not funny. Mary is either curious or not funny. | Mary is generous. | entailment | ((?[X]:((creative(X)|old(X))))<=>(~brave(lucy)))&
(![X]:((curious(X)<~>~old(X))<=>(~old(X)|strong(X))))&
(![X]:((kind(X)|calm(X))<=>(~happy(X)<~>brave(X))))&
((?[X]:((~brave(X)&quiet(X))))<=>(?[X]:((kind(X)|brave(X)))))&
(![X]:((kind(X)&~happy(X))<=>(kind(X)|patient(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(calm(fred)))&
(![X]:((humble(X)|~wise(X))<=>(wise(X)&~calm(X))))&
(![X]:((creative(X)<~>~patient(X))<=>(~quiet(X)<~>~wise(X))))&
((?[X]:(quiet(X)))<=>(?[X]:((calm(X)&brave(X)))))&
((?[X]:((humble(X)&~humble(X))))=>(?[X]:((~quiet(X)&kind(X)))))&
(![X]:((rich(X)<~>~wise(X))<=>(patient(X)|~creative(X))))&
(![X]:(~curious(X)<=>(~quiet(X)|tall(X))))&
(![X]:((~happy(X)<~>creative(X))=>(~happy(X)|kind(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>patient(X))))&
(((~creative(susan)&~old(susan)))<=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~funny(X)&~tall(X))<=>~generous(X)))&
(tall(mary))&
((humble(john)&~tall(john)))&
((calm(mary)|~brave(mary)))&
(~quiet(mary))&
(~funny(alice))&
((curious(mary)<~>~funny(mary))) | generous(mary) | [
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1342765110160286886966531
% SZS output start Proof for 1342765110160286886966531
16. ! [X0] : ((~tall(X0) & ~funny(X0)) <=> ~generous(X0)) [input p15]
17. tall(mary) [input p16]
23. ~generous(mary) [input hypothesis]
27. ! [X0] : (~generous(X0) => (~tall(X0) & ~funny(X0))) [unused predicate definition removal 16]
33. ! [X0] : ((~tall(X0) & ~funny(X0)) | generous(X0)) [ennf transformation 27]
138. ~tall(X0) | generous(X0) [cnf transformation 33]
139. tall(mary) [cnf transformation 17]
147. ~generous(mary) [cnf transformation 23]
293. generous(mary) [resolution 138,139]
294. $false [subsumption resolution 293,147]
% SZS output end Proof for 1342765110160286886966531
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall is rich or kind.
Everyone who is patient is not humble and vice versa.
Everyone who is creative is not funny.
Everyone who is not happy is either not quiet or not rich.
If mary is either old or not rich then someone is both not quiet and not patient.
If someone is not brave or strong then susan is either wise or not rich.
If someone is either old or rich then lucy is either not happy or curious and vice versa.
If someone is both not rich and not old then someone is either calm or tall and vice versa.
Everyone who is not rich or patient is both generous and patient and vice versa.
Everyone who is both not rich and funny is patient.
Everyone who is rich is patient or not wise and vice versa.
If someone is either not kind or creative then someone is strong or not creative and vice versa.
If john is not kind then fred is either quiet or not generous and vice versa.
Everyone who is both wise and not kind is not calm or humble.
If someone is both generous and not old then lucy is rich.
Fred is both not happy and not wise.
John is not tall.
Mary is curious or not happy.
Someone is either not creative or not patient.
Someone is not humble or wise.
Someone is quiet or not generous.
Someone is either tall or generous. | John is not calm. | entailment | (![X]:(~tall(X)=>(rich(X)|kind(X))))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:(creative(X)=>~funny(X)))&
(![X]:(~happy(X)=>(~quiet(X)<~>~rich(X))))&
(((old(mary)<~>~rich(mary)))=>(?[X]:((~quiet(X)&~patient(X)))))&
((?[X]:((~brave(X)|strong(X))))=>((wise(susan)<~>~rich(susan))))&
((?[X]:((old(X)<~>rich(X))))<=>((~happy(lucy)<~>curious(lucy))))&
((?[X]:((~rich(X)&~old(X))))<=>(?[X]:((calm(X)<~>tall(X)))))&
(![X]:((~rich(X)|patient(X))<=>(generous(X)&patient(X))))&
(![X]:((~rich(X)&funny(X))=>patient(X)))&
(![X]:(rich(X)<=>(patient(X)|~wise(X))))&
((?[X]:((~kind(X)<~>creative(X))))<=>(?[X]:((strong(X)|~creative(X)))))&
((~kind(john))<=>((quiet(fred)<~>~generous(fred))))&
(![X]:((wise(X)&~kind(X))=>(~calm(X)|humble(X))))&
((?[X]:((generous(X)&~old(X))))=>(rich(lucy)))&
((~happy(fred)&~wise(fred)))&
(~tall(john))&
((curious(mary)|~happy(mary)))&
(?[X]:((~creative(X)<~>~patient(X))))&
(?[X]:((~humble(X)|wise(X))))&
(?[X]:((quiet(X)|~generous(X))))&
(?[X]:((tall(X)<~>generous(X)))) | ~calm(john) | [
"p7",
"p8",
"p10",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 8035605282617300292533128
% SZS output start Proof for 8035605282617300292533128
8. ? [X0] : (~old(X0) & ~rich(X0)) <=> ? [X0] : (calm(X0) <~> tall(X0)) [input p7]
9. ! [X0] : ((patient(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p8]
11. ! [X0] : (rich(X0) <=> (~wise(X0) | patient(X0))) [input p10]
17. ~tall(john) [input p16]
23. calm(john) [input hypothesis]
24. ? [X0] : (~old(X0) & ~rich(X0)) <=> ? [X1] : (calm(X1) <~> tall(X1)) [rectify 8]
47. (? [X0] : (~old(X0) & ~rich(X0)) | ! [X1] : ((calm(X1) | ~tall(X1)) & (tall(X1) | ~calm(X1)))) & (? [X1] : ((~tall(X1) | ~calm(X1)) & (tall(X1) | calm(X1))) | ! [X0] : (old(X0) | rich(X0))) [nnf transformation 24]
48. (? [X0] : (~old(X0) & ~rich(X0)) | ! [X1] : ((calm(X1) | ~tall(X1)) & (tall(X1) | ~calm(X1)))) & (? [X2] : ((~tall(X2) | ~calm(X2)) & (tall(X2) | calm(X2))) | ! [X3] : (old(X3) | rich(X3))) [rectify 47]
49. ? [X0] : (~old(X0) & ~rich(X0)) => (~old(sK2) & ~rich(sK2)) [choice axiom]
50. ? [X2] : ((~tall(X2) | ~calm(X2)) & (tall(X2) | calm(X2))) => ((~tall(sK3) | ~calm(sK3)) & (tall(sK3) | calm(sK3))) [choice axiom]
51. ((~old(sK2) & ~rich(sK2)) | ! [X1] : ((calm(X1) | ~tall(X1)) & (tall(X1) | ~calm(X1)))) & (((~tall(sK3) | ~calm(sK3)) & (tall(sK3) | calm(sK3))) | ! [X3] : (old(X3) | rich(X3))) [skolemisation 48,50,49]
52. ! [X0] : (((patient(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (~patient(X0) & rich(X0)))) [nnf transformation 9]
53. ! [X0] : ((patient(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (~patient(X0) & rich(X0)))) [flattening 52]
54. ! [X0] : ((rich(X0) | (wise(X0) & ~patient(X0))) & ((~wise(X0) | patient(X0)) | ~rich(X0))) [nnf transformation 11]
55. ! [X0] : ((rich(X0) | (wise(X0) & ~patient(X0))) & (~wise(X0) | patient(X0) | ~rich(X0))) [flattening 54]
93. ~rich(sK2) | tall(X1) | ~calm(X1) [cnf transformation 51]
99. patient(X0) | rich(X0) [cnf transformation 53]
103. rich(X0) | ~patient(X0) [cnf transformation 55]
119. ~tall(john) [cnf transformation 17]
127. calm(john) [cnf transformation 23]
200. 16 <=> ! [X1] : (tall(X1) | ~calm(X1)) [avatar definition]
201. ~calm(X1) | tall(X1) <- (16) [avatar component clause 200]
204. 17 <=> rich(sK2) [avatar definition]
206. ~rich(sK2) <- (~17) [avatar component clause 204]
208. 16 | ~17 [avatar split clause 93,204,200]
222. rich(X0) [subsumption resolution 103,99]
318. $false <- (~17) [subsumption resolution 206,222]
319. 17 [avatar contradiction clause 318]
338. tall(john) <- (16) [resolution 201,127]
339. $false <- (16) [subsumption resolution 338,119]
340. ~16 [avatar contradiction clause 339]
341. $false [avatar sat refutation 208,319,340]
% SZS output end Proof for 8035605282617300292533128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If john is brave or not creative then paul is not tall and vice versa.
Everyone who is not wise or strong is either not generous or patient and vice versa.
Everyone who is not old is curious or not humble and vice versa.
If mary is either quiet or old then someone is both brave and generous.
If alice is both not generous and not rich then someone is either strong or not brave and vice versa.
Everyone who is either not happy or brave is curious or creative and vice versa.
If someone is both not wise and rich then someone is humble and vice versa.
Everyone who is either patient or kind is calm and vice versa.
Everyone who is both not creative and wise is not brave or rich and vice versa.
Everyone who is not funny or wise is both quiet and not kind and vice versa.
Everyone who is either not curious or happy is either humble or not generous.
If someone is not wise or brave then lucy is not humble and vice versa.
If someone is both strong and quiet then susan is calm and vice versa.
Everyone who is either tall or not brave is both strong and not generous and vice versa.
If someone is humble then alice is wise and vice versa.
If someone is not calm or not creative then someone is patient.
Susan is either humble or not curious.
Fred is brave or not kind.
John is not funny.
Mary is quiet.
Paul is not creative or kind.
Alice is not quiet or not old.
Someone is either not humble or brave. | Paul is generous. | neutral | (((brave(john)|~creative(john)))<=>(~tall(paul)))&
(![X]:((~wise(X)|strong(X))<=>(~generous(X)<~>patient(X))))&
(![X]:(~old(X)<=>(curious(X)|~humble(X))))&
(((quiet(mary)<~>old(mary)))=>(?[X]:((brave(X)&generous(X)))))&
(((~generous(alice)&~rich(alice)))<=>(?[X]:((strong(X)<~>~brave(X)))))&
(![X]:((~happy(X)<~>brave(X))<=>(curious(X)|creative(X))))&
((?[X]:((~wise(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((patient(X)<~>kind(X))<=>calm(X)))&
(![X]:((~creative(X)&wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(quiet(X)&~kind(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~generous(X))))&
((?[X]:((~wise(X)|brave(X))))<=>(~humble(lucy)))&
((?[X]:((strong(X)&quiet(X))))<=>(calm(susan)))&
(![X]:((tall(X)<~>~brave(X))<=>(strong(X)&~generous(X))))&
((?[X]:(humble(X)))<=>(wise(alice)))&
((?[X]:((~calm(X)|~creative(X))))=>(?[X]:(patient(X))))&
((humble(susan)<~>~curious(susan)))&
((brave(fred)|~kind(fred)))&
(~funny(john))&
(quiet(mary))&
((~creative(paul)|kind(paul)))&
((~quiet(alice)|~old(alice)))&
(?[X]:((~humble(X)<~>brave(X)))) | generous(paul) | [] | null | 0 |
If someone is both not funny and happy then someone is either humble or not rich and vice versa. If susan is both not calm and happy then john is both not tall and not curious and vice versa. Everyone who is curious is patient. If paul is either not old or curious then someone is both funny and creative and vice versa. If paul is creative or curious then someone is either strong or quiet. Everyone who is not strong is not curious and vice versa. If someone is creative then someone is not happy and vice versa. If someone is not patient or not strong then susan is either generous or wise. Everyone who is creative or not funny is both not tall and patient and vice versa. If someone is humble or not quiet then someone is tall. If someone is tall or not quiet then susan is both generous and kind. If paul is both not wise and not funny then someone is both not generous and not patient. If someone is not quiet or not strong then john is either patient or tall and vice versa. Everyone who is both not happy and calm is both funny and not funny. Everyone who is both brave and not old is not generous or humble and vice versa. If fred is both wise and not quiet then alice is both patient and not brave and vice versa. John is either happy or not humble. Someone is not happy. John is both not wise and not curious. John is patient or wise. Lucy is either happy or calm. Fred is both patient and not quiet. Alice is generous. Someone is both not generous and tall. | Susan is generous. | entailment | ((?[X]:((~funny(X)&happy(X))))<=>(?[X]:((humble(X)<~>~rich(X)))))&
(((~calm(susan)&happy(susan)))<=>((~tall(john)&~curious(john))))&
(![X]:(curious(X)=>patient(X)))&
(((~old(paul)<~>curious(paul)))<=>(?[X]:((funny(X)&creative(X)))))&
(((creative(paul)|curious(paul)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~strong(X)<=>~curious(X)))&
((?[X]:(creative(X)))<=>(?[X]:(~happy(X))))&
((?[X]:((~patient(X)|~strong(X))))=>((generous(susan)<~>wise(susan))))&
(![X]:((creative(X)|~funny(X))<=>(~tall(X)&patient(X))))&
((?[X]:((humble(X)|~quiet(X))))=>(?[X]:(tall(X))))&
((?[X]:((tall(X)|~quiet(X))))=>((generous(susan)&kind(susan))))&
(((~wise(paul)&~funny(paul)))=>(?[X]:((~generous(X)&~patient(X)))))&
((?[X]:((~quiet(X)|~strong(X))))<=>((patient(john)<~>tall(john))))&
(![X]:((~happy(X)&calm(X))=>(funny(X)&~funny(X))))&
(![X]:((brave(X)&~old(X))<=>(~generous(X)|humble(X))))&
(((wise(fred)&~quiet(fred)))<=>((patient(alice)&~brave(alice))))&
((happy(john)<~>~humble(john)))&
(?[X]:(~happy(X)))&
((~wise(john)&~curious(john)))&
((patient(john)|wise(john)))&
((happy(lucy)<~>calm(lucy)))&
((patient(fred)&~quiet(fred)))&
(generous(alice))&
(?[X]:((~generous(X)&tall(X)))) | generous(susan) | [
"p10",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 1465609849741312265196535
% SZS output start Proof for 1465609849741312265196535
11. ? [X0] : (~quiet(X0) | tall(X0)) => (kind(susan) & generous(susan)) [input p10]
24. ? [X0] : (tall(X0) & ~generous(X0)) [input p23]
25. ~generous(susan) [input hypothesis]
29. ? [X0] : (~quiet(X0) | tall(X0)) => generous(susan) [pure predicate removal 11]
34. generous(susan) | ! [X0] : (quiet(X0) & ~tall(X0)) [ennf transformation 29]
79. ? [X0] : (tall(X0) & ~generous(X0)) => (tall(sK10) & ~generous(sK10)) [choice axiom]
80. tall(sK10) & ~generous(sK10) [skolemisation 24,79]
117. generous(susan) | ~tall(X0) [cnf transformation 34]
150. tall(sK10) [cnf transformation 80]
151. ~generous(susan) [cnf transformation 25]
264. 25 <=> generous(susan) [avatar definition]
292. 31 <=> ! [X0] : ~tall(X0) [avatar definition]
293. ~tall(X0) <- (31) [avatar component clause 292]
294. 31 | 25 [avatar split clause 117,264,292]
368. ~25 [avatar split clause 151,264]
373. $false <- (31) [resolution 293,150]
374. ~31 [avatar contradiction clause 373]
375. $false [avatar sat refutation 294,368,374]
% SZS output end Proof for 1465609849741312265196535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or not humble is humble and vice versa.
Everyone who is both old and creative is both tall and curious.
If paul is both not kind and not humble then lucy is not kind or not old and vice versa.
Everyone who is both not kind and not curious is both not strong and humble and vice versa.
Everyone who is patient is both brave and not quiet and vice versa.
If mary is brave or quiet then mary is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
Everyone who is not calm is old.
If alice is both not humble and funny then someone is not curious and vice versa.
If susan is not strong then someone is not happy or curious and vice versa.
Everyone who is wise is not patient.
Someone is brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave.
Mary is old.
Lucy is either not rich or quiet.
John is both funny and not kind. | John is not old. | neutral | (![X]:((~curious(X)<~>~humble(X))<=>humble(X)))&
(![X]:((old(X)&creative(X))=>(tall(X)&curious(X))))&
(((~kind(paul)&~humble(paul)))<=>((~kind(lucy)|~old(lucy))))&
(![X]:((~kind(X)&~curious(X))<=>(~strong(X)&humble(X))))&
(![X]:(patient(X)<=>(brave(X)&~quiet(X))))&
(((brave(mary)|quiet(mary)))<=>((rich(mary)<~>~patient(mary))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:(wise(X)=>~patient(X)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy)))&
((funny(john)&~kind(john))) | ~old(john) | [] | null | 0 |
Everyone who is either not quiet or calm is either quiet or not humble.
If someone is brave or not calm then lucy is both not curious and not funny.
Everyone who is both curious and patient is strong or not creative and vice versa.
Everyone who is not strong is not kind or rich and vice versa.
If someone is not rich then someone is both not kind and not creative and vice versa.
If alice is old or not humble then susan is either not tall or not brave and vice versa.
If someone is not generous then someone is both kind and not old and vice versa.
Everyone who is either not rich or patient is both not happy and not calm and vice versa.
If fred is strong or quiet then someone is not kind or tall.
If someone is both tall and not generous then susan is either not calm or tall and vice versa.
If fred is not old then someone is both old and not brave and vice versa.
Everyone who is both patient and not tall is both creative and not funny and vice versa.
If lucy is humble then mary is both humble and brave.
If someone is not rich then someone is calm or not wise and vice versa.
Everyone who is not curious or not rich is either wise or brave.
Everyone who is not humble is not kind or strong.
Fred is creative.
Fred is wise or generous.
John is humble or brave.
Someone is not strong or not patient.
Susan is both not kind and rich.
Someone is either strong or not patient.
Fred is either curious or kind.
Susan is strong or not kind. | Lucy is quiet. | neutral | (![X]:((~quiet(X)<~>calm(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((brave(X)|~calm(X))))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((curious(X)&patient(X))<=>(strong(X)|~creative(X))))&
(![X]:(~strong(X)<=>(~kind(X)|rich(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~kind(X)&~creative(X)))))&
(((old(alice)|~humble(alice)))<=>((~tall(susan)<~>~brave(susan))))&
((?[X]:(~generous(X)))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~rich(X)<~>patient(X))<=>(~happy(X)&~calm(X))))&
(((strong(fred)|quiet(fred)))=>(?[X]:((~kind(X)|tall(X)))))&
((?[X]:((tall(X)&~generous(X))))<=>((~calm(susan)<~>tall(susan))))&
((~old(fred))<=>(?[X]:((old(X)&~brave(X)))))&
(![X]:((patient(X)&~tall(X))<=>(creative(X)&~funny(X))))&
((humble(lucy))=>((humble(mary)&brave(mary))))&
((?[X]:(~rich(X)))<=>(?[X]:((calm(X)|~wise(X)))))&
(![X]:((~curious(X)|~rich(X))=>(wise(X)<~>brave(X))))&
(![X]:(~humble(X)=>(~kind(X)|strong(X))))&
(creative(fred))&
((wise(fred)|generous(fred)))&
((humble(john)|brave(john)))&
(?[X]:((~strong(X)|~patient(X))))&
((~kind(susan)&rich(susan)))&
(?[X]:((strong(X)<~>~patient(X))))&
((curious(fred)<~>kind(fred)))&
((strong(susan)|~kind(susan))) | quiet(lucy) | [] | null | 0 |
Everyone who is either not tall or not creative is creative.
If mary is either strong or not quiet then lucy is either wise or curious and vice versa.
Everyone who is either wise or brave is not wise or not strong and vice versa.
If someone is either quiet or creative then john is either rich or not curious and vice versa.
Everyone who is not rich or brave is both calm and not calm.
If lucy is either not brave or not creative then someone is old or happy.
If lucy is both brave and not curious then someone is not happy and vice versa.
Everyone who is either not strong or patient is not rich and vice versa.
Everyone who is either not humble or not creative is either not generous or not happy and vice versa.
If paul is brave then someone is not strong.
Everyone who is either not brave or rich is not happy or happy.
Everyone who is kind or not brave is not creative and vice versa.
Everyone who is not kind or curious is not humble.
Everyone who is both not curious and funny is either not happy or brave and vice versa.
Everyone who is either curious or creative is either brave or kind.
If someone is either not happy or not calm then paul is both funny and kind and vice versa.
Someone is funny or happy.
Paul is either happy or not rich.
Someone is both not brave and generous.
Someone is happy.
Paul is kind. | Lucy is humble. | neutral | (![X]:((~tall(X)<~>~creative(X))=>creative(X)))&
(((strong(mary)<~>~quiet(mary)))<=>((wise(lucy)<~>curious(lucy))))&
(![X]:((wise(X)<~>brave(X))<=>(~wise(X)|~strong(X))))&
((?[X]:((quiet(X)<~>creative(X))))<=>((rich(john)<~>~curious(john))))&
(![X]:((~rich(X)|brave(X))=>(calm(X)&~calm(X))))&
(((~brave(lucy)<~>~creative(lucy)))=>(?[X]:((old(X)|happy(X)))))&
(((brave(lucy)&~curious(lucy)))<=>(?[X]:(~happy(X))))&
(![X]:((~strong(X)<~>patient(X))<=>~rich(X)))&
(![X]:((~humble(X)<~>~creative(X))<=>(~generous(X)<~>~happy(X))))&
((brave(paul))=>(?[X]:(~strong(X))))&
(![X]:((~brave(X)<~>rich(X))=>(~happy(X)|happy(X))))&
(![X]:((kind(X)|~brave(X))<=>~creative(X)))&
(![X]:((~kind(X)|curious(X))=>~humble(X)))&
(![X]:((~curious(X)&funny(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((curious(X)<~>creative(X))=>(brave(X)<~>kind(X))))&
((?[X]:((~happy(X)<~>~calm(X))))<=>((funny(paul)&kind(paul))))&
(?[X]:((funny(X)|happy(X))))&
((happy(paul)<~>~rich(paul)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(happy(X)))&
(kind(paul)) | humble(lucy) | [] | null | 0 |
If lucy is either old or not strong then alice is both kind and not funny and vice versa.
If someone is not calm then someone is either not quiet or happy.
If fred is both happy and not wise then someone is not funny and vice versa.
If fred is funny then someone is not wise and vice versa.
If someone is either not quiet or not happy then fred is not brave and vice versa.
Everyone who is both not wise and patient is curious or not old and vice versa.
If someone is either not wise or not funny then someone is strong or not quiet and vice versa.
Everyone who is creative or not generous is kind and vice versa.
Everyone who is not patient is both not happy and creative.
Everyone who is not generous or calm is either not calm or generous and vice versa.
Everyone who is both not funny and strong is both not kind and old and vice versa.
Everyone who is either not kind or brave is both humble and creative and vice versa.
Everyone who is either tall or not quiet is both humble and not wise and vice versa.
If someone is not wise then alice is both happy and not curious and vice versa.
Everyone who is quiet is quiet or strong and vice versa.
Everyone who is humble or curious is either old or calm and vice versa.
Alice is either not calm or rich.
Someone is both not generous and not happy.
Someone is either not wise or not curious.
Alice is not quiet or not strong.
Susan is both not strong and not rich.
Someone is not humble.
Someone is either creative or happy.
Susan is either not rich or tall. | Susan is rich. | contradiction | (((old(lucy)<~>~strong(lucy)))<=>((kind(alice)&~funny(alice))))&
((?[X]:(~calm(X)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(((happy(fred)&~wise(fred)))<=>(?[X]:(~funny(X))))&
((funny(fred))<=>(?[X]:(~wise(X))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>(~brave(fred)))&
(![X]:((~wise(X)&patient(X))<=>(curious(X)|~old(X))))&
((?[X]:((~wise(X)<~>~funny(X))))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((creative(X)|~generous(X))<=>kind(X)))&
(![X]:(~patient(X)=>(~happy(X)&creative(X))))&
(![X]:((~generous(X)|calm(X))<=>(~calm(X)<~>generous(X))))&
(![X]:((~funny(X)&strong(X))<=>(~kind(X)&old(X))))&
(![X]:((~kind(X)<~>brave(X))<=>(humble(X)&creative(X))))&
(![X]:((tall(X)<~>~quiet(X))<=>(humble(X)&~wise(X))))&
((?[X]:(~wise(X)))<=>((happy(alice)&~curious(alice))))&
(![X]:(quiet(X)<=>(quiet(X)|strong(X))))&
(![X]:((humble(X)|curious(X))<=>(old(X)<~>calm(X))))&
((~calm(alice)<~>rich(alice)))&
(?[X]:((~generous(X)&~happy(X))))&
(?[X]:((~wise(X)<~>~curious(X))))&
((~quiet(alice)|~strong(alice)))&
((~strong(susan)&~rich(susan)))&
(?[X]:(~humble(X)))&
(?[X]:((creative(X)<~>happy(X))))&
((~rich(susan)<~>tall(susan))) | rich(susan) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5393259814993703345715781
% SZS output start Proof for 5393259814993703345715781
21. ~rich(susan) & ~strong(susan) [input p20]
25. rich(susan) [input hypothesis]
162. ~rich(susan) [cnf transformation 21]
168. rich(susan) [cnf transformation 25]
343. $false [subsumption resolution 168,162]
% SZS output end Proof for 5393259814993703345715781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or strong is not humble and vice versa.
Everyone who is either not old or not curious is patient.
If alice is kind then susan is either wise or not tall and vice versa.
Everyone who is either tall or not patient is either wise or not wise and vice versa.
Everyone who is either not rich or curious is either not strong or not humble and vice versa.
If fred is wise then someone is wise or humble and vice versa.
Everyone who is both not creative and not wise is either quiet or tall and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is either funny or generous is generous or not wise and vice versa.
Everyone who is either not happy or funny is both quiet and happy and vice versa.
If someone is both not kind and not creative then someone is either not quiet or not humble and vice versa.
Everyone who is both strong and not quiet is either quiet or not calm.
Everyone who is either humble or not calm is tall or not strong.
Everyone who is tall or calm is both not calm and creative and vice versa.
If john is not kind or not patient then lucy is both humble and creative and vice versa.
Someone is strong.
Someone is either not funny or curious.
Susan is strong.
Fred is either not creative or not brave.
Someone is not happy. | Susan is patient. | entailment | (![X]:((~creative(X)|strong(X))<=>~humble(X)))&
(![X]:((~old(X)<~>~curious(X))=>patient(X)))&
((kind(alice))<=>((wise(susan)<~>~tall(susan))))&
(![X]:((tall(X)<~>~patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((~rich(X)<~>curious(X))<=>(~strong(X)<~>~humble(X))))&
((wise(fred))<=>(?[X]:((wise(X)|humble(X)))))&
(![X]:((~creative(X)&~wise(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((funny(X)<~>generous(X))<=>(generous(X)|~wise(X))))&
(![X]:((~happy(X)<~>funny(X))<=>(quiet(X)&happy(X))))&
((?[X]:((~kind(X)&~creative(X))))<=>(?[X]:((~quiet(X)<~>~humble(X)))))&
(![X]:((strong(X)&~quiet(X))=>(quiet(X)<~>~calm(X))))&
(![X]:((humble(X)<~>~calm(X))=>(tall(X)|~strong(X))))&
(![X]:((tall(X)|calm(X))<=>(~calm(X)&creative(X))))&
(((~kind(john)|~patient(john)))<=>((humble(lucy)&creative(lucy))))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)<~>curious(X))))&
(strong(susan))&
((~creative(fred)<~>~brave(fred)))&
(?[X]:(~happy(X))) | patient(susan) | [
"p0",
"p3",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1046785361896825873400578
% SZS output start Proof for 1046785361896825873400578
1. ! [X0] : ((strong(X0) | ~creative(X0)) <=> ~humble(X0)) [input p0]
4. ! [X0] : ((tall(X0) <~> ~patient(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p3]
13. ! [X0] : ((humble(X0) <~> ~calm(X0)) => (~strong(X0) | tall(X0))) [input p12]
14. ! [X0] : ((calm(X0) | tall(X0)) <=> (creative(X0) & ~calm(X0))) [input p13]
18. strong(susan) [input p17]
21. ~patient(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) | tall(X0)) | (humble(X0) <=> ~calm(X0))) [ennf transformation 13]
28. ! [X0] : (~strong(X0) | tall(X0) | (humble(X0) <=> ~calm(X0))) [flattening 27]
29. ! [X0] : (((strong(X0) | ~creative(X0)) | humble(X0)) & (~humble(X0) | (~strong(X0) & creative(X0)))) [nnf transformation 1]
30. ! [X0] : ((strong(X0) | ~creative(X0) | humble(X0)) & (~humble(X0) | (~strong(X0) & creative(X0)))) [flattening 29]
33. ! [X0] : ((((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0))))) [nnf transformation 4]
56. ! [X0] : (~strong(X0) | tall(X0) | ((humble(X0) | calm(X0)) & (~calm(X0) | ~humble(X0)))) [nnf transformation 28]
57. ! [X0] : (((calm(X0) | tall(X0)) | (~creative(X0) | calm(X0))) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [nnf transformation 14]
58. ! [X0] : ((calm(X0) | tall(X0) | ~creative(X0) | calm(X0)) & ((creative(X0) & ~calm(X0)) | (~calm(X0) & ~tall(X0)))) [flattening 57]
70. ~humble(X0) | ~strong(X0) [cnf transformation 30]
84. patient(X0) | ~tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 33]
85. patient(X0) | ~tall(X0) | wise(X0) | wise(X0) [cnf transformation 33]
126. ~strong(X0) | tall(X0) | humble(X0) | calm(X0) [cnf transformation 56]
128. ~calm(X0) | ~calm(X0) [cnf transformation 58]
140. strong(susan) [cnf transformation 18]
144. ~patient(susan) [cnf transformation 21]
145. ~calm(X0) [duplicate literal removal 128]
154. patient(X0) | ~tall(X0) | ~wise(X0) [duplicate literal removal 84]
155. ~tall(X0) | patient(X0) | wise(X0) [duplicate literal removal 85]
157. 1 <=> tall(susan) [avatar definition]
159. tall(susan) <- (1) [avatar component clause 157]
172. ~tall(X0) | patient(X0) [subsumption resolution 154,155]
247. ~strong(X0) | tall(X0) | calm(X0) [subsumption resolution 126,70]
364. tall(susan) | calm(susan) [resolution 247,140]
371. tall(susan) [subsumption resolution 364,145]
372. 1 [avatar split clause 371,157]
376. patient(susan) <- (1) [resolution 159,172]
379. $false <- (1) [subsumption resolution 376,144]
380. ~1 [avatar contradiction clause 379]
381. $false [avatar sat refutation 372,380]
% SZS output end Proof for 1046785361896825873400578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If paul is patient or not creative then someone is both not tall and kind and vice versa.
Everyone who is not old is both creative and not curious and vice versa.
Everyone who is not humble or creative is generous or not tall and vice versa.
Everyone who is calm or brave is either funny or tall.
If someone is not funny or not tall then alice is curious or not generous and vice versa.
If mary is either not wise or wise then alice is both not funny and quiet.
If john is tall then susan is either not curious or old.
Everyone who is not creative is not patient or happy.
If mary is both not tall and not curious then mary is either not generous or not happy and vice versa.
Everyone who is not old is not quiet.
Everyone who is not brave is either not curious or not old and vice versa.
Everyone who is either not tall or generous is either kind or not patient and vice versa.
Everyone who is either not curious or not generous is both not kind and wise and vice versa.
Everyone who is both kind and generous is generous or curious.
If john is not patient then john is quiet or not strong.
If paul is both quiet and funny then susan is strong and vice versa.
John is humble.
Paul is both generous and funny.
John is creative.
Someone is calm.
Mary is both strong and quiet.
Someone is either rich or strong.
Paul is both not patient and happy.
Someone is not creative or creative. | John is quiet. | neutral | (((patient(paul)|~creative(paul)))<=>(?[X]:((~tall(X)&kind(X)))))&
(![X]:(~old(X)<=>(creative(X)&~curious(X))))&
(![X]:((~humble(X)|creative(X))<=>(generous(X)|~tall(X))))&
(![X]:((calm(X)|brave(X))=>(funny(X)<~>tall(X))))&
((?[X]:((~funny(X)|~tall(X))))<=>((curious(alice)|~generous(alice))))&
(((~wise(mary)<~>wise(mary)))=>((~funny(alice)&quiet(alice))))&
((tall(john))=>((~curious(susan)<~>old(susan))))&
(![X]:(~creative(X)=>(~patient(X)|happy(X))))&
(((~tall(mary)&~curious(mary)))<=>((~generous(mary)<~>~happy(mary))))&
(![X]:(~old(X)=>~quiet(X)))&
(![X]:(~brave(X)<=>(~curious(X)<~>~old(X))))&
(![X]:((~tall(X)<~>generous(X))<=>(kind(X)<~>~patient(X))))&
(![X]:((~curious(X)<~>~generous(X))<=>(~kind(X)&wise(X))))&
(![X]:((kind(X)&generous(X))=>(generous(X)|curious(X))))&
((~patient(john))=>((quiet(john)|~strong(john))))&
(((quiet(paul)&funny(paul)))<=>(strong(susan)))&
(humble(john))&
((generous(paul)&funny(paul)))&
(creative(john))&
(?[X]:(calm(X)))&
((strong(mary)&quiet(mary)))&
(?[X]:((rich(X)<~>strong(X))))&
((~patient(paul)&happy(paul)))&
(?[X]:((~creative(X)|creative(X)))) | quiet(john) | [] | null | 0 |
Everyone who is either old or calm is curious and vice versa.
Everyone who is creative is not strong or not happy.
Everyone who is funny or curious is not humble.
Everyone who is calm or not generous is both not strong and humble and vice versa.
If someone is both not kind and not happy then mary is funny or happy and vice versa.
Everyone who is both tall and humble is patient.
Everyone who is both not strong and not creative is both calm and tall.
If lucy is either generous or not generous then paul is patient and vice versa.
If mary is either not kind or calm then paul is either not generous or not old.
If someone is humble then alice is creative or not wise.
If someone is both funny and not calm then lucy is either wise or patient and vice versa.
Everyone who is either creative or not calm is either creative or not funny and vice versa.
If someone is not tall or not creative then someone is both generous and quiet and vice versa.
Everyone who is either not old or not funny is not humble and vice versa.
Fred is either not kind or not tall.
Someone is either not happy or wise.
Mary is tall or not creative.
Someone is not curious or kind.
Someone is not kind or not strong.
Fred is not quiet. | Alice is happy. | neutral | (![X]:((old(X)<~>calm(X))<=>curious(X)))&
(![X]:(creative(X)=>(~strong(X)|~happy(X))))&
(![X]:((funny(X)|curious(X))=>~humble(X)))&
(![X]:((calm(X)|~generous(X))<=>(~strong(X)&humble(X))))&
((?[X]:((~kind(X)&~happy(X))))<=>((funny(mary)|happy(mary))))&
(![X]:((tall(X)&humble(X))=>patient(X)))&
(![X]:((~strong(X)&~creative(X))=>(calm(X)&tall(X))))&
(((generous(lucy)<~>~generous(lucy)))<=>(patient(paul)))&
(((~kind(mary)<~>calm(mary)))=>((~generous(paul)<~>~old(paul))))&
((?[X]:(humble(X)))=>((creative(alice)|~wise(alice))))&
((?[X]:((funny(X)&~calm(X))))<=>((wise(lucy)<~>patient(lucy))))&
(![X]:((creative(X)<~>~calm(X))<=>(creative(X)<~>~funny(X))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:((~old(X)<~>~funny(X))<=>~humble(X)))&
((~kind(fred)<~>~tall(fred)))&
(?[X]:((~happy(X)<~>wise(X))))&
((tall(mary)|~creative(mary)))&
(?[X]:((~curious(X)|kind(X))))&
(?[X]:((~kind(X)|~strong(X))))&
(~quiet(fred)) | happy(alice) | [] | null | 0 |
If someone is not kind then susan is not wise or strong. Everyone who is either not wise or calm is funny or not patient and vice versa. Everyone who is either not creative or generous is both not old and patient and vice versa. Everyone who is creative is not funny and vice versa. Everyone who is kind or creative is both creative and calm and vice versa. If alice is wise or not humble then john is either not wise or not curious. Everyone who is calm is brave or happy and vice versa. If someone is not wise then alice is wise and vice versa. Everyone who is both funny and tall is both strong and quiet. If susan is wise or not quiet then someone is both patient and old. Everyone who is either kind or not quiet is not quiet or not happy. If alice is both creative and strong then someone is both kind and humble and vice versa. If someone is either wise or not happy then fred is both patient and kind. If someone is funny or not creative then someone is not patient. Everyone who is both not calm and not rich is either creative or generous and vice versa. If mary is not wise then paul is both not generous and not brave and vice versa. Someone is either not calm or calm. Someone is calm or patient. Mary is either wise or not old. Someone is either quiet or tall. Someone is both creative and not brave. Alice is not curious or calm. Someone is not brave or quiet. John is either happy or wise. | Fred is not funny. | entailment | ((?[X]:(~kind(X)))=>((~wise(susan)|strong(susan))))&
(![X]:((~wise(X)<~>calm(X))<=>(funny(X)|~patient(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(~old(X)&patient(X))))&
(![X]:(creative(X)<=>~funny(X)))&
(![X]:((kind(X)|creative(X))<=>(creative(X)&calm(X))))&
(((wise(alice)|~humble(alice)))=>((~wise(john)<~>~curious(john))))&
(![X]:(calm(X)<=>(brave(X)|happy(X))))&
((?[X]:(~wise(X)))<=>(wise(alice)))&
(![X]:((funny(X)&tall(X))=>(strong(X)&quiet(X))))&
(((wise(susan)|~quiet(susan)))=>(?[X]:((patient(X)&old(X)))))&
(![X]:((kind(X)<~>~quiet(X))=>(~quiet(X)|~happy(X))))&
(((creative(alice)&strong(alice)))<=>(?[X]:((kind(X)&humble(X)))))&
((?[X]:((wise(X)<~>~happy(X))))=>((patient(fred)&kind(fred))))&
((?[X]:((funny(X)|~creative(X))))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)&~rich(X))<=>(creative(X)<~>generous(X))))&
((~wise(mary))<=>((~generous(paul)&~brave(paul))))&
(?[X]:((~calm(X)<~>calm(X))))&
(?[X]:((calm(X)|patient(X))))&
((wise(mary)<~>~old(mary)))&
(?[X]:((quiet(X)<~>tall(X))))&
(?[X]:((creative(X)&~brave(X))))&
((~curious(alice)|calm(alice)))&
(?[X]:((~brave(X)|quiet(X))))&
((happy(john)<~>wise(john))) | ~funny(fred) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8935732838831480755618060
% SZS output start Proof for 8935732838831480755618060
2. ! [X0] : ((~wise(X0) <~> calm(X0)) <=> (~patient(X0) | funny(X0))) [input p1]
3. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (patient(X0) & ~old(X0))) [input p2]
4. ! [X0] : (creative(X0) <=> ~funny(X0)) [input p3]
5. ! [X0] : ((creative(X0) | kind(X0)) <=> (calm(X0) & creative(X0))) [input p4]
7. ! [X0] : (calm(X0) <=> (happy(X0) | brave(X0))) [input p6]
13. ? [X0] : (wise(X0) <~> ~happy(X0)) => (kind(fred) & patient(fred)) [input p12]
14. ? [X0] : (~creative(X0) | funny(X0)) => ? [X0] : ~patient(X0) [input p13]
15. ! [X0] : ((~rich(X0) & ~calm(X0)) <=> (creative(X0) <~> generous(X0))) [input p14]
25. funny(fred) [input hypothesis]
26. ? [X0] : (~creative(X0) | funny(X0)) => ? [X1] : ~patient(X1) [rectify 14]
35. (kind(fred) & patient(fred)) | ! [X0] : (wise(X0) <=> ~happy(X0)) [ennf transformation 13]
36. ? [X1] : ~patient(X1) | ! [X0] : (creative(X0) & ~funny(X0)) [ennf transformation 26]
37. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (patient(X0) & ~funny(X0))) & ((~patient(X0) | funny(X0)) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [nnf transformation 2]
38. ! [X0] : ((((~calm(X0) | wise(X0)) & (calm(X0) | ~wise(X0))) | (patient(X0) & ~funny(X0))) & (~patient(X0) | funny(X0) | ((~wise(X0) | ~calm(X0)) & (calm(X0) | wise(X0))))) [flattening 37]
39. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~patient(X0) | old(X0))) & ((patient(X0) & ~old(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | ~patient(X0) | old(X0)) & ((patient(X0) & ~old(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [flattening 39]
41. ! [X0] : ((creative(X0) | funny(X0)) & (~funny(X0) | ~creative(X0))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) | kind(X0)) | (~calm(X0) | ~creative(X0))) & ((calm(X0) & creative(X0)) | (~creative(X0) & ~kind(X0)))) [nnf transformation 5]
43. ! [X0] : ((creative(X0) | kind(X0) | ~calm(X0) | ~creative(X0)) & ((calm(X0) & creative(X0)) | (~creative(X0) & ~kind(X0)))) [flattening 42]
45. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & ((happy(X0) | brave(X0)) | ~calm(X0))) [nnf transformation 7]
46. ! [X0] : ((calm(X0) | (~happy(X0) & ~brave(X0))) & (happy(X0) | brave(X0) | ~calm(X0))) [flattening 45]
59. (kind(fred) & patient(fred)) | ! [X0] : ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))) [nnf transformation 35]
60. ? [X0] : ~patient(X0) | ! [X1] : (creative(X1) & ~funny(X1)) [rectify 36]
61. ? [X0] : ~patient(X0) => ~patient(sK3) [choice axiom]
62. ~patient(sK3) | ! [X1] : (creative(X1) & ~funny(X1)) [skolemisation 60,61]
63. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | (rich(X0) | calm(X0)))) [nnf transformation 15]
64. ! [X0] : (((~rich(X0) & ~calm(X0)) | ((creative(X0) | ~generous(X0)) & (generous(X0) | ~creative(X0)))) & (((~generous(X0) | ~creative(X0)) & (generous(X0) | creative(X0))) | rich(X0) | calm(X0))) [flattening 63]
84. ~funny(X0) | ~wise(X0) | calm(X0) [cnf transformation 38]
90. generous(X0) | patient(X0) | creative(X0) [cnf transformation 40]
91. ~generous(X0) | ~creative(X0) | patient(X0) [cnf transformation 40]
94. ~creative(X0) | ~funny(X0) [cnf transformation 41]
95. creative(X0) | funny(X0) [cnf transformation 41]
96. ~kind(X0) | creative(X0) [cnf transformation 43]
99. ~creative(X0) | calm(X0) [cnf transformation 43]
107. ~happy(X0) | calm(X0) [cnf transformation 46]
125. kind(fred) | wise(X0) | happy(X0) [cnf transformation 59]
126. ~patient(sK3) | ~funny(X1) [cnf transformation 62]
130. ~calm(X0) | generous(X0) | ~creative(X0) [cnf transformation 64]
131. ~generous(X0) | creative(X0) | ~calm(X0) [cnf transformation 64]
150. funny(fred) [cnf transformation 25]
233. 18 <=> ! [X0] : (wise(X0) | happy(X0)) [avatar definition]
234. happy(X0) | wise(X0) <- (18) [avatar component clause 233]
236. 19 <=> kind(fred) [avatar definition]
238. kind(fred) <- (19) [avatar component clause 236]
239. 18 | 19 [avatar split clause 125,236,233]
254. 23 <=> patient(sK3) [avatar definition]
256. ~patient(sK3) <- (~23) [avatar component clause 254]
259. 24 <=> ! [X1] : ~funny(X1) [avatar definition]
260. ~funny(X1) <- (24) [avatar component clause 259]
261. 24 | ~23 [avatar split clause 126,254,259]
262. ~creative(X0) | generous(X0) [subsumption resolution 130,99]
331. funny(X0) | calm(X0) [resolution 99,95]
333. calm(X0) | wise(X0) <- (18) [resolution 234,107]
336. generous(X0) | funny(X0) [resolution 262,95]
460. creative(X0) | ~calm(X0) | patient(X0) | creative(X0) [resolution 131,90]
464. ~calm(X0) | creative(X0) | patient(X0) [duplicate literal removal 460]
527. calm(X1) | ~wise(X1) | calm(X1) [resolution 331,84]
528. calm(X1) | ~wise(X1) [duplicate literal removal 527]
529. calm(X1) <- (18) [subsumption resolution 528,333]
543. funny(X2) | ~creative(X2) | patient(X2) [resolution 336,91]
544. ~creative(X2) | patient(X2) [subsumption resolution 543,94]
569. creative(X0) | patient(X0) <- (18) [resolution 529,464]
576. patient(X0) <- (18) [subsumption resolution 569,544]
588. $false <- (18, ~23) [resolution 576,256]
591. ~18 | 23 [avatar contradiction clause 588]
623. creative(fred) <- (19) [resolution 238,96]
626. $false <- (24) [resolution 260,150]
627. ~24 [avatar contradiction clause 626]
652. ~funny(fred) <- (19) [resolution 623,94]
664. $false <- (19) [subsumption resolution 652,150]
665. ~19 [avatar contradiction clause 664]
666. $false [avatar sat refutation 239,261,591,627,665]
% SZS output end Proof for 8935732838831480755618060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If alice is both not generous and strong then alice is either not wise or not generous and vice versa.
If john is both funny and strong then fred is curious or not strong.
Everyone who is wise or not rich is both patient and not patient and vice versa.
Everyone who is calm is curious or generous.
Everyone who is quiet or rich is either not wise or happy.
Everyone who is calm is either funny or not curious and vice versa.
Everyone who is either funny or not wise is both not happy and not calm and vice versa.
Everyone who is wise or not creative is either happy or not patient and vice versa.
Everyone who is either not curious or not quiet is either brave or funny and vice versa.
If lucy is creative then fred is calm and vice versa.
If paul is creative then someone is both not happy and not quiet.
Everyone who is not funny is both not tall and creative.
Everyone who is not happy or quiet is not humble.
If someone is both not old and not funny then someone is both not happy and not old.
If mary is not old or not quiet then someone is humble or not quiet and vice versa.
If lucy is old then someone is both not strong and not humble.
Someone is either strong or not tall.
Susan is either rich or quiet.
Paul is patient.
Susan is not humble or kind.
Fred is not strong.
Susan is either not rich or strong. | Susan is funny. | neutral | (((~generous(alice)&strong(alice)))<=>((~wise(alice)<~>~generous(alice))))&
(((funny(john)&strong(john)))=>((curious(fred)|~strong(fred))))&
(![X]:((wise(X)|~rich(X))<=>(patient(X)&~patient(X))))&
(![X]:(calm(X)=>(curious(X)|generous(X))))&
(![X]:((quiet(X)|rich(X))=>(~wise(X)<~>happy(X))))&
(![X]:(calm(X)<=>(funny(X)<~>~curious(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(~happy(X)&~calm(X))))&
(![X]:((wise(X)|~creative(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(brave(X)<~>funny(X))))&
((creative(lucy))<=>(calm(fred)))&
((creative(paul))=>(?[X]:((~happy(X)&~quiet(X)))))&
(![X]:(~funny(X)=>(~tall(X)&creative(X))))&
(![X]:((~happy(X)|quiet(X))=>~humble(X)))&
((?[X]:((~old(X)&~funny(X))))=>(?[X]:((~happy(X)&~old(X)))))&
(((~old(mary)|~quiet(mary)))<=>(?[X]:((humble(X)|~quiet(X)))))&
((old(lucy))=>(?[X]:((~strong(X)&~humble(X)))))&
(?[X]:((strong(X)<~>~tall(X))))&
((rich(susan)<~>quiet(susan)))&
(patient(paul))&
((~humble(susan)|kind(susan)))&
(~strong(fred))&
((~rich(susan)<~>strong(susan))) | funny(susan) | [] | null | 0 |
If paul is wise then someone is either not tall or not old and vice versa.
Everyone who is not calm is either calm or not old.
If someone is brave or rich then lucy is both tall and not kind.
If fred is quiet or old then someone is tall or humble and vice versa.
If someone is not quiet or humble then john is either not kind or kind.
Everyone who is both not strong and not wise is either happy or not quiet and vice versa.
If someone is calm or rich then fred is both kind and brave.
Everyone who is either rich or tall is wise.
Everyone who is either tall or generous is either humble or old.
If mary is either not curious or not calm then fred is both not tall and not generous and vice versa.
If alice is not creative or not strong then someone is not tall and vice versa.
Everyone who is not wise is either calm or wise and vice versa.
If someone is both not funny and not quiet then alice is humble and vice versa.
Everyone who is humble or not strong is not curious or not happy.
Everyone who is either quiet or not humble is both not patient and brave.
Everyone who is not old is both not tall and not wise.
Alice is both not kind and creative.
Mary is either not kind or rich.
Paul is not tall or calm.
Someone is both rich and not brave.
Lucy is not old or curious.
John is not strong or generous.
Susan is not creative or curious.
Someone is either not kind or not generous. | Fred is brave. | entailment | ((wise(paul))<=>(?[X]:((~tall(X)<~>~old(X)))))&
(![X]:(~calm(X)=>(calm(X)<~>~old(X))))&
((?[X]:((brave(X)|rich(X))))=>((tall(lucy)&~kind(lucy))))&
(((quiet(fred)|old(fred)))<=>(?[X]:((tall(X)|humble(X)))))&
((?[X]:((~quiet(X)|humble(X))))=>((~kind(john)<~>kind(john))))&
(![X]:((~strong(X)&~wise(X))<=>(happy(X)<~>~quiet(X))))&
((?[X]:((calm(X)|rich(X))))=>((kind(fred)&brave(fred))))&
(![X]:((rich(X)<~>tall(X))=>wise(X)))&
(![X]:((tall(X)<~>generous(X))=>(humble(X)<~>old(X))))&
(((~curious(mary)<~>~calm(mary)))<=>((~tall(fred)&~generous(fred))))&
(((~creative(alice)|~strong(alice)))<=>(?[X]:(~tall(X))))&
(![X]:(~wise(X)<=>(calm(X)<~>wise(X))))&
((?[X]:((~funny(X)&~quiet(X))))<=>(humble(alice)))&
(![X]:((humble(X)|~strong(X))=>(~curious(X)|~happy(X))))&
(![X]:((quiet(X)<~>~humble(X))=>(~patient(X)&brave(X))))&
(![X]:(~old(X)=>(~tall(X)&~wise(X))))&
((~kind(alice)&creative(alice)))&
((~kind(mary)<~>rich(mary)))&
((~tall(paul)|calm(paul)))&
(?[X]:((rich(X)&~brave(X))))&
((~old(lucy)|curious(lucy)))&
((~strong(john)|generous(john)))&
((~creative(susan)|curious(susan)))&
(?[X]:((~kind(X)<~>~generous(X)))) | brave(fred) | [
"p6",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7867387283513047893173296
% SZS output start Proof for 7867387283513047893173296
7. ? [X0] : (rich(X0) | calm(X0)) => (brave(fred) & kind(fred)) [input p6]
12. ! [X0] : (~wise(X0) <=> (calm(X0) <~> wise(X0))) [input p11]
25. ~brave(fred) [input hypothesis]
30. (brave(fred) & kind(fred)) | ! [X0] : (~rich(X0) & ~calm(X0)) [ennf transformation 7]
59. ! [X0] : ((~wise(X0) | ((calm(X0) | ~wise(X0)) & (wise(X0) | ~calm(X0)))) & (((~wise(X0) | ~calm(X0)) & (wise(X0) | calm(X0))) | wise(X0))) [nnf transformation 12]
97. brave(fred) | ~calm(X0) [cnf transformation 30]
114. wise(X0) | calm(X0) | wise(X0) [cnf transformation 59]
117. ~wise(X0) | calm(X0) | ~wise(X0) [cnf transformation 59]
139. ~brave(fred) [cnf transformation 25]
140. wise(X0) | calm(X0) [duplicate literal removal 114]
141. ~wise(X0) | calm(X0) [duplicate literal removal 117]
210. 16 <=> brave(fred) [avatar definition]
215. 17 <=> ! [X0] : ~calm(X0) [avatar definition]
216. ~calm(X0) <- (17) [avatar component clause 215]
217. 17 | 16 [avatar split clause 97,210,215]
264. calm(X0) [subsumption resolution 140,141]
332. ~16 [avatar split clause 139,210]
335. $false <- (17) [subsumption resolution 216,264]
336. ~17 [avatar contradiction clause 335]
338. $false [avatar sat refutation 217,332,336]
% SZS output end Proof for 7867387283513047893173296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both generous and brave then alice is not wise or not kind and vice versa.
If someone is both not rich and quiet then paul is old and vice versa.
Everyone who is both not funny and not humble is both not strong and wise and vice versa.
If someone is both strong and not generous then someone is not patient or quiet and vice versa.
Everyone who is either not strong or not quiet is strong and vice versa.
Everyone who is calm or not wise is not wise or strong and vice versa.
Everyone who is both kind and generous is calm.
Everyone who is both wise and creative is not tall or tall and vice versa.
If someone is not humble then someone is not strong or strong.
Everyone who is funny is either not rich or not curious.
If someone is both not calm and happy then someone is not tall or not funny and vice versa.
Everyone who is not humble is both funny and not kind and vice versa.
If susan is both not brave and not quiet then lucy is both not generous and not tall and vice versa.
If fred is both old and calm then someone is either not tall or not wise and vice versa.
If someone is both brave and rich then fred is humble and vice versa.
Mary is either creative or rich.
Paul is either generous or not old.
Someone is creative or not happy.
Mary is both not kind and calm.
Someone is both generous and not kind. | Fred is happy. | neutral | (((generous(mary)&brave(mary)))<=>((~wise(alice)|~kind(alice))))&
((?[X]:((~rich(X)&quiet(X))))<=>(old(paul)))&
(![X]:((~funny(X)&~humble(X))<=>(~strong(X)&wise(X))))&
((?[X]:((strong(X)&~generous(X))))<=>(?[X]:((~patient(X)|quiet(X)))))&
(![X]:((~strong(X)<~>~quiet(X))<=>strong(X)))&
(![X]:((calm(X)|~wise(X))<=>(~wise(X)|strong(X))))&
(![X]:((kind(X)&generous(X))=>calm(X)))&
(![X]:((wise(X)&creative(X))<=>(~tall(X)|tall(X))))&
((?[X]:(~humble(X)))=>(?[X]:((~strong(X)|strong(X)))))&
(![X]:(funny(X)=>(~rich(X)<~>~curious(X))))&
((?[X]:((~calm(X)&happy(X))))<=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:(~humble(X)<=>(funny(X)&~kind(X))))&
(((~brave(susan)&~quiet(susan)))<=>((~generous(lucy)&~tall(lucy))))&
(((old(fred)&calm(fred)))<=>(?[X]:((~tall(X)<~>~wise(X)))))&
((?[X]:((brave(X)&rich(X))))<=>(humble(fred)))&
((creative(mary)<~>rich(mary)))&
((generous(paul)<~>~old(paul)))&
(?[X]:((creative(X)|~happy(X))))&
((~kind(mary)&calm(mary)))&
(?[X]:((generous(X)&~kind(X)))) | happy(fred) | [] | null | 0 |
Everyone who is not generous is not brave and vice versa.
Everyone who is strong or calm is either not quiet or not calm and vice versa.
Everyone who is either strong or not strong is both generous and strong.
Everyone who is either creative or tall is humble.
Everyone who is either humble or curious is not rich or not tall.
Everyone who is old or not funny is funny or generous.
Everyone who is funny or brave is rich and vice versa.
If susan is brave then someone is rich or not kind.
Everyone who is not tall or humble is not rich or not funny and vice versa.
Everyone who is not brave or not wise is old and vice versa.
Everyone who is not humble is not quiet.
If fred is happy then someone is brave or happy and vice versa.
Everyone who is both not old and old is not calm or not curious.
If fred is both patient and not old then someone is both calm and not creative.
Everyone who is both not rich and not brave is not strong.
If someone is quiet then someone is not calm or rich.
Lucy is happy or humble.
Mary is not calm or humble.
Someone is either not calm or not tall.
Paul is both happy and not tall.
Someone is old or strong.
Someone is wise or not happy.
Someone is both strong and happy.
Fred is both quiet and not patient. | Mary is not calm. | neutral | (![X]:(~generous(X)<=>~brave(X)))&
(![X]:((strong(X)|calm(X))<=>(~quiet(X)<~>~calm(X))))&
(![X]:((strong(X)<~>~strong(X))=>(generous(X)&strong(X))))&
(![X]:((creative(X)<~>tall(X))=>humble(X)))&
(![X]:((humble(X)<~>curious(X))=>(~rich(X)|~tall(X))))&
(![X]:((old(X)|~funny(X))=>(funny(X)|generous(X))))&
(![X]:((funny(X)|brave(X))<=>rich(X)))&
((brave(susan))=>(?[X]:((rich(X)|~kind(X)))))&
(![X]:((~tall(X)|humble(X))<=>(~rich(X)|~funny(X))))&
(![X]:((~brave(X)|~wise(X))<=>old(X)))&
(![X]:(~humble(X)=>~quiet(X)))&
((happy(fred))<=>(?[X]:((brave(X)|happy(X)))))&
(![X]:((~old(X)&old(X))=>(~calm(X)|~curious(X))))&
(((patient(fred)&~old(fred)))=>(?[X]:((calm(X)&~creative(X)))))&
(![X]:((~rich(X)&~brave(X))=>~strong(X)))&
((?[X]:(quiet(X)))=>(?[X]:((~calm(X)|rich(X)))))&
((happy(lucy)|humble(lucy)))&
((~calm(mary)|humble(mary)))&
(?[X]:((~calm(X)<~>~tall(X))))&
((happy(paul)&~tall(paul)))&
(?[X]:((old(X)|strong(X))))&
(?[X]:((wise(X)|~happy(X))))&
(?[X]:((strong(X)&happy(X))))&
((quiet(fred)&~patient(fred))) | ~calm(mary) | [] | null | 0 |
If fred is not creative or curious then alice is patient or curious and vice versa.
Everyone who is not happy or creative is both not happy and kind.
Everyone who is not creative is not patient or not brave.
If someone is generous or not curious then someone is both not generous and not kind.
Everyone who is calm is not humble or brave and vice versa.
Everyone who is either happy or wise is both humble and curious and vice versa.
Everyone who is not generous or rich is creative or quiet and vice versa.
If someone is either not strong or not tall then someone is calm or wise.
If someone is not rich or not kind then someone is both generous and strong and vice versa.
Everyone who is both funny and not curious is either patient or wise and vice versa.
If someone is old or rich then alice is not wise.
If someone is not funny then fred is not curious and vice versa.
If fred is not strong or not quiet then someone is strong and vice versa.
Everyone who is happy or not calm is not brave and vice versa.
Everyone who is either creative or humble is either rich or not rich and vice versa.
If lucy is old or strong then lucy is patient or not funny and vice versa.
Someone is happy.
Fred is not old.
John is either not curious or not brave.
Someone is not old.
Someone is not creative or not old.
Someone is not rich.
Someone is either brave or not creative.
Someone is tall. | Alice is not curious. | neutral | (((~creative(fred)|curious(fred)))<=>((patient(alice)|curious(alice))))&
(![X]:((~happy(X)|creative(X))=>(~happy(X)&kind(X))))&
(![X]:(~creative(X)=>(~patient(X)|~brave(X))))&
((?[X]:((generous(X)|~curious(X))))=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:(calm(X)<=>(~humble(X)|brave(X))))&
(![X]:((happy(X)<~>wise(X))<=>(humble(X)&curious(X))))&
(![X]:((~generous(X)|rich(X))<=>(creative(X)|quiet(X))))&
((?[X]:((~strong(X)<~>~tall(X))))=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:((~rich(X)|~kind(X))))<=>(?[X]:((generous(X)&strong(X)))))&
(![X]:((funny(X)&~curious(X))<=>(patient(X)<~>wise(X))))&
((?[X]:((old(X)|rich(X))))=>(~wise(alice)))&
((?[X]:(~funny(X)))<=>(~curious(fred)))&
(((~strong(fred)|~quiet(fred)))<=>(?[X]:(strong(X))))&
(![X]:((happy(X)|~calm(X))<=>~brave(X)))&
(![X]:((creative(X)<~>humble(X))<=>(rich(X)<~>~rich(X))))&
(((old(lucy)|strong(lucy)))<=>((patient(lucy)|~funny(lucy))))&
(?[X]:(happy(X)))&
(~old(fred))&
((~curious(john)<~>~brave(john)))&
(?[X]:(~old(X)))&
(?[X]:((~creative(X)|~old(X))))&
(?[X]:(~rich(X)))&
(?[X]:((brave(X)<~>~creative(X))))&
(?[X]:(tall(X))) | ~curious(alice) | [] | null | 0 |
If paul is both happy and not generous then someone is humble and vice versa.
If someone is not strong or not creative then john is both not rich and not strong.
If someone is both not quiet and kind then lucy is either calm or not generous.
If someone is not wise or not calm then john is both happy and not creative and vice versa.
If someone is generous then someone is both not tall and not wise.
If susan is not funny or old then someone is either not wise or not calm.
If lucy is either not funny or not humble then paul is happy and vice versa.
Everyone who is not brave or not kind is patient and vice versa.
If john is calm or old then someone is either not brave or not funny and vice versa.
If someone is both not patient and not kind then someone is not rich and vice versa.
Everyone who is both not old and strong is rich or creative.
If lucy is either not curious or not humble then paul is rich.
Everyone who is both not generous and happy is both rich and not kind and vice versa.
Everyone who is either tall or funny is kind or tall and vice versa.
Everyone who is both tall and happy is either not calm or not quiet.
Everyone who is generous or funny is both strong and patient and vice versa.
Lucy is kind.
Fred is not tall.
John is kind or not generous.
Someone is both creative and not funny.
Someone is creative or not tall. | Fred is funny. | entailment | (((happy(paul)&~generous(paul)))<=>(?[X]:(humble(X))))&
((?[X]:((~strong(X)|~creative(X))))=>((~rich(john)&~strong(john))))&
((?[X]:((~quiet(X)&kind(X))))=>((calm(lucy)<~>~generous(lucy))))&
((?[X]:((~wise(X)|~calm(X))))<=>((happy(john)&~creative(john))))&
((?[X]:(generous(X)))=>(?[X]:((~tall(X)&~wise(X)))))&
(((~funny(susan)|old(susan)))=>(?[X]:((~wise(X)<~>~calm(X)))))&
(((~funny(lucy)<~>~humble(lucy)))<=>(happy(paul)))&
(![X]:((~brave(X)|~kind(X))<=>patient(X)))&
(((calm(john)|old(john)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
((?[X]:((~patient(X)&~kind(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~old(X)&strong(X))=>(rich(X)|creative(X))))&
(((~curious(lucy)<~>~humble(lucy)))=>(rich(paul)))&
(![X]:((~generous(X)&happy(X))<=>(rich(X)&~kind(X))))&
(![X]:((tall(X)<~>funny(X))<=>(kind(X)|tall(X))))&
(![X]:((tall(X)&happy(X))=>(~calm(X)<~>~quiet(X))))&
(![X]:((generous(X)|funny(X))<=>(strong(X)&patient(X))))&
(kind(lucy))&
(~tall(fred))&
((kind(john)|~generous(john)))&
(?[X]:((creative(X)&~funny(X))))&
(?[X]:((creative(X)|~tall(X)))) | funny(fred) | [
"p1",
"p3",
"p4",
"p7",
"p9",
"p13",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 1961416671538700090347736
% SZS output start Proof for 1961416671538700090347736
2. ? [X0] : (~creative(X0) | ~strong(X0)) => (~strong(john) & ~rich(john)) [input p1]
4. ? [X0] : (~calm(X0) | ~wise(X0)) <=> (~creative(john) & happy(john)) [input p3]
5. ? [X0] : generous(X0) => ? [X0] : (~wise(X0) & ~tall(X0)) [input p4]
8. ! [X0] : ((~kind(X0) | ~brave(X0)) <=> patient(X0)) [input p7]
10. ? [X0] : (~kind(X0) & ~patient(X0)) <=> ? [X0] : ~rich(X0) [input p9]
14. ! [X0] : ((tall(X0) <~> funny(X0)) <=> (tall(X0) | kind(X0))) [input p13]
16. ! [X0] : ((funny(X0) | generous(X0)) <=> (patient(X0) & strong(X0))) [input p15]
18. ~tall(fred) [input p17]
22. ~funny(fred) [input hypothesis]
23. ? [X0] : generous(X0) => ? [X1] : (~wise(X1) & ~tall(X1)) [rectify 5]
24. ? [X0] : (~kind(X0) & ~patient(X0)) <=> ? [X1] : ~rich(X1) [rectify 10]
25. (~strong(john) & ~rich(john)) | ! [X0] : (creative(X0) & strong(X0)) [ennf transformation 2]
27. ? [X1] : (~wise(X1) & ~tall(X1)) | ! [X0] : ~generous(X0) [ennf transformation 23]
40. (? [X0] : (~calm(X0) | ~wise(X0)) | (creative(john) | ~happy(john))) & ((~creative(john) & happy(john)) | ! [X0] : (calm(X0) & wise(X0))) [nnf transformation 4]
41. (? [X0] : (~calm(X0) | ~wise(X0)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X0] : (calm(X0) & wise(X0))) [flattening 40]
42. (? [X0] : (~calm(X0) | ~wise(X0)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X1] : (calm(X1) & wise(X1))) [rectify 41]
43. ? [X0] : (~calm(X0) | ~wise(X0)) => (~calm(sK1) | ~wise(sK1)) [choice axiom]
44. ((~calm(sK1) | ~wise(sK1)) | creative(john) | ~happy(john)) & ((~creative(john) & happy(john)) | ! [X1] : (calm(X1) & wise(X1))) [skolemisation 42,43]
45. ? [X0] : (~wise(X0) & ~tall(X0)) | ! [X1] : ~generous(X1) [rectify 27]
46. ? [X0] : (~wise(X0) & ~tall(X0)) => (~wise(sK2) & ~tall(sK2)) [choice axiom]
47. (~wise(sK2) & ~tall(sK2)) | ! [X1] : ~generous(X1) [skolemisation 45,46]
52. ! [X0] : (((~kind(X0) | ~brave(X0)) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [nnf transformation 8]
53. ! [X0] : ((~kind(X0) | ~brave(X0) | ~patient(X0)) & (patient(X0) | (kind(X0) & brave(X0)))) [flattening 52]
59. (? [X0] : (~kind(X0) & ~patient(X0)) | ! [X1] : rich(X1)) & (? [X1] : ~rich(X1) | ! [X0] : (kind(X0) | patient(X0))) [nnf transformation 24]
60. (? [X0] : (~kind(X0) & ~patient(X0)) | ! [X1] : rich(X1)) & (? [X2] : ~rich(X2) | ! [X3] : (kind(X3) | patient(X3))) [rectify 59]
61. ? [X0] : (~kind(X0) & ~patient(X0)) => (~kind(sK5) & ~patient(sK5)) [choice axiom]
62. ? [X2] : ~rich(X2) => ~rich(sK6) [choice axiom]
63. ((~kind(sK5) & ~patient(sK5)) | ! [X1] : rich(X1)) & (~rich(sK6) | ! [X3] : (kind(X3) | patient(X3))) [skolemisation 60,62,61]
67. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~tall(X0) & ~kind(X0))) & ((tall(X0) | kind(X0)) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [nnf transformation 14]
68. ! [X0] : ((((~funny(X0) | ~tall(X0)) & (funny(X0) | tall(X0))) | (~tall(X0) & ~kind(X0))) & (tall(X0) | kind(X0) | ((tall(X0) | ~funny(X0)) & (funny(X0) | ~tall(X0))))) [flattening 67]
70. ! [X0] : (((funny(X0) | generous(X0)) | (~patient(X0) | ~strong(X0))) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [nnf transformation 16]
71. ! [X0] : ((funny(X0) | generous(X0) | ~patient(X0) | ~strong(X0)) & ((patient(X0) & strong(X0)) | (~funny(X0) & ~generous(X0)))) [flattening 70]
79. ~rich(john) | strong(X0) [cnf transformation 25]
80. ~rich(john) | creative(X0) [cnf transformation 25]
87. ~creative(john) | wise(X1) [cnf transformation 44]
91. ~wise(sK2) | ~generous(X1) [cnf transformation 47]
101. patient(X0) | kind(X0) [cnf transformation 53]
110. ~patient(sK5) | rich(X1) [cnf transformation 63]
111. ~kind(sK5) | rich(X1) [cnf transformation 63]
120. tall(X0) | kind(X0) | tall(X0) | ~funny(X0) [cnf transformation 68]
121. ~kind(X0) | tall(X0) | funny(X0) [cnf transformation 68]
124. ~funny(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 68]
131. ~patient(X0) | generous(X0) | funny(X0) | ~strong(X0) [cnf transformation 71]
133. ~tall(fred) [cnf transformation 18]
138. ~funny(fred) [cnf transformation 22]
139. tall(X0) | kind(X0) | ~funny(X0) [duplicate literal removal 120]
140. ~funny(X0) | ~tall(X0) [duplicate literal removal 124]
160. 5 <=> ! [X0] : creative(X0) [avatar definition]
161. creative(X0) <- (5) [avatar component clause 160]
168. 7 <=> ! [X0] : strong(X0) [avatar definition]
169. strong(X0) <- (7) [avatar component clause 168]
172. 8 <=> rich(john) [avatar definition]
174. ~rich(john) <- (~8) [avatar component clause 172]
175. 5 | ~8 [avatar split clause 80,172,160]
176. 7 | ~8 [avatar split clause 79,172,168]
195. 13 <=> creative(john) [avatar definition]
196. ~creative(john) <- (~13) [avatar component clause 195]
212. 17 <=> ! [X1] : wise(X1) [avatar definition]
213. wise(X1) <- (17) [avatar component clause 212]
214. 17 | ~13 [avatar split clause 87,195,212]
218. 18 <=> ! [X1] : ~generous(X1) [avatar definition]
219. ~generous(X1) <- (18) [avatar component clause 218]
221. 19 <=> wise(sK2) [avatar definition]
223. ~wise(sK2) <- (~19) [avatar component clause 221]
224. 18 | ~19 [avatar split clause 91,221,218]
291. 33 <=> ! [X1] : rich(X1) [avatar definition]
292. rich(X1) <- (33) [avatar component clause 291]
294. 34 <=> kind(sK5) [avatar definition]
297. 33 | ~34 [avatar split clause 111,294,291]
299. 35 <=> patient(sK5) [avatar definition]
301. ~patient(sK5) <- (~35) [avatar component clause 299]
302. 33 | ~35 [avatar split clause 110,299,291]
313. ~funny(X0) | kind(X0) [subsumption resolution 139,140]
333. kind(sK5) <- (~35) [resolution 101,301]
336. 34 | 35 [avatar split clause 333,299,294]
337. $false <- (~8, 33) [resolution 292,174]
338. 8 | ~33 [avatar contradiction clause 337]
339. $false <- (5, ~13) [resolution 161,196]
340. ~5 | 13 [avatar contradiction clause 339]
352. $false <- (17, ~19) [resolution 213,223]
353. ~17 | 19 [avatar contradiction clause 352]
404. generous(X0) | funny(X0) | ~strong(X0) | kind(X0) [resolution 131,101]
409. funny(X0) | ~strong(X0) | kind(X0) <- (18) [subsumption resolution 404,219]
410. funny(X0) | kind(X0) <- (7, 18) [subsumption resolution 409,169]
411. kind(X0) <- (7, 18) [subsumption resolution 410,313]
416. funny(X0) | tall(X0) <- (7, 18) [resolution 411,121]
440. tall(fred) <- (7, 18) [resolution 416,138]
443. $false <- (7, 18) [subsumption resolution 440,133]
444. ~7 | ~18 [avatar contradiction clause 443]
445. $false [avatar sat refutation 175,176,214,224,297,302,336,338,340,353,444]
% SZS output end Proof for 1961416671538700090347736
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and generous is both wise and creative. Everyone who is both calm and happy is both strong and not tall and vice versa. Everyone who is rich is both wise and kind and vice versa. Everyone who is not creative or not humble is funny and vice versa. Everyone who is either curious or kind is brave and vice versa. Everyone who is wise or curious is humble or not calm. If lucy is quiet or brave then someone is funny. If someone is both not funny and not curious then alice is funny and vice versa. Everyone who is not wise or quiet is both curious and not humble and vice versa. If john is both calm and not tall then paul is both calm and happy. If mary is both not strong and old then fred is both funny and not brave and vice versa. If someone is patient or not humble then paul is happy or wise. Everyone who is either humble or funny is not kind or not strong. If susan is not kind then susan is both generous and not old and vice versa. Everyone who is funny or tall is patient and vice versa. Everyone who is either happy or humble is either not brave or not calm. Someone is not humble or not kind. Someone is both funny and strong. Paul is wise. Someone is not humble. Someone is humble. Someone is generous. Mary is not generous. Lucy is both creative and not patient. | Susan is not wise. | neutral | (![X]:((patient(X)&generous(X))=>(wise(X)&creative(X))))&
(![X]:((calm(X)&happy(X))<=>(strong(X)&~tall(X))))&
(![X]:(rich(X)<=>(wise(X)&kind(X))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)<~>~calm(X))))&
(?[X]:((~humble(X)|~kind(X))))&
(?[X]:((funny(X)&strong(X))))&
(wise(paul))&
(?[X]:(~humble(X)))&
(?[X]:(humble(X)))&
(?[X]:(generous(X)))&
(~generous(mary))&
((creative(lucy)&~patient(lucy))) | ~wise(susan) | [] | null | 0 |
Everyone who is either not curious or not humble is humble and vice versa.
Everyone who is both old and creative is both tall and curious.
If paul is both not kind and not humble then lucy is not kind or not old and vice versa.
Everyone who is both not kind and not curious is both not strong and humble and vice versa.
Everyone who is patient is both brave and not quiet and vice versa.
If mary is brave or quiet then mary is either rich or not patient and vice versa.
Everyone who is both generous and not patient is both not kind and humble.
If someone is either strong or tall then alice is humble.
Everyone who is both not calm and not curious is old or rich and vice versa.
If someone is funny or not brave then someone is not curious or not kind and vice versa.
If someone is not wise or not old then lucy is curious or not calm and vice versa.
Everyone who is not calm is old.
If alice is both not humble and funny then someone is not curious and vice versa.
If susan is not strong then someone is not happy or curious and vice versa.
Everyone who is wise is not patient.
Someone is brave.
Someone is either happy or funny.
Someone is not quiet or strong.
Lucy is not calm or brave.
Mary is old.
Lucy is either not rich or quiet.
John is both funny and not kind. | Paul is happy. | neutral | (![X]:((~curious(X)<~>~humble(X))<=>humble(X)))&
(![X]:((old(X)&creative(X))=>(tall(X)&curious(X))))&
(((~kind(paul)&~humble(paul)))<=>((~kind(lucy)|~old(lucy))))&
(![X]:((~kind(X)&~curious(X))<=>(~strong(X)&humble(X))))&
(![X]:(patient(X)<=>(brave(X)&~quiet(X))))&
(((brave(mary)|quiet(mary)))<=>((rich(mary)<~>~patient(mary))))&
(![X]:((generous(X)&~patient(X))=>(~kind(X)&humble(X))))&
((?[X]:((strong(X)<~>tall(X))))=>(humble(alice)))&
(![X]:((~calm(X)&~curious(X))<=>(old(X)|rich(X))))&
((?[X]:((funny(X)|~brave(X))))<=>(?[X]:((~curious(X)|~kind(X)))))&
((?[X]:((~wise(X)|~old(X))))<=>((curious(lucy)|~calm(lucy))))&
(![X]:(~calm(X)=>old(X)))&
(((~humble(alice)&funny(alice)))<=>(?[X]:(~curious(X))))&
((~strong(susan))<=>(?[X]:((~happy(X)|curious(X)))))&
(![X]:(wise(X)=>~patient(X)))&
(?[X]:(brave(X)))&
(?[X]:((happy(X)<~>funny(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((~calm(lucy)|brave(lucy)))&
(old(mary))&
((~rich(lucy)<~>quiet(lucy)))&
((funny(john)&~kind(john))) | happy(paul) | [] | null | 0 |
Everyone who is both brave and patient is calm and vice versa. Everyone who is not calm is either not wise or generous. If susan is patient then someone is both kind and creative and vice versa. Everyone who is both not strong and tall is either generous or wise. Everyone who is both humble and curious is both not kind and funny. Everyone who is either creative or patient is both patient and not funny and vice versa. If mary is both not strong and wise then someone is wise or not calm and vice versa. If someone is creative then paul is not generous or not funny and vice versa. If john is either not curious or strong then susan is both not happy and not humble and vice versa. If someone is either happy or not quiet then lucy is both humble and calm and vice versa. Everyone who is either not wise or kind is both curious and old and vice versa. Everyone who is both generous and not curious is not rich and vice versa. Everyone who is tall or happy is not rich or quiet and vice versa. Everyone who is either not generous or funny is either curious or not tall and vice versa. Everyone who is both not brave and not kind is kind. Everyone who is either curious or not patient is either not quiet or not old. Someone is wise or not curious. Someone is not generous or not strong. Mary is either generous or not strong. Someone is either not rich or not wise. Lucy is both quiet and creative. Alice is not kind. Alice is strong or not calm. Lucy is not strong. | Alice is creative. | neutral | (![X]:((brave(X)&patient(X))<=>calm(X)))&
(![X]:(~calm(X)=>(~wise(X)<~>generous(X))))&
((patient(susan))<=>(?[X]:((kind(X)&creative(X)))))&
(![X]:((~strong(X)&tall(X))=>(generous(X)<~>wise(X))))&
(![X]:((humble(X)&curious(X))=>(~kind(X)&funny(X))))&
(![X]:((creative(X)<~>patient(X))<=>(patient(X)&~funny(X))))&
(((~strong(mary)&wise(mary)))<=>(?[X]:((wise(X)|~calm(X)))))&
((?[X]:(creative(X)))<=>((~generous(paul)|~funny(paul))))&
(((~curious(john)<~>strong(john)))<=>((~happy(susan)&~humble(susan))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((humble(lucy)&calm(lucy))))&
(![X]:((~wise(X)<~>kind(X))<=>(curious(X)&old(X))))&
(![X]:((generous(X)&~curious(X))<=>~rich(X)))&
(![X]:((tall(X)|happy(X))<=>(~rich(X)|quiet(X))))&
(![X]:((~generous(X)<~>funny(X))<=>(curious(X)<~>~tall(X))))&
(![X]:((~brave(X)&~kind(X))=>kind(X)))&
(![X]:((curious(X)<~>~patient(X))=>(~quiet(X)<~>~old(X))))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((~generous(X)|~strong(X))))&
((generous(mary)<~>~strong(mary)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((quiet(lucy)&creative(lucy)))&
(~kind(alice))&
((strong(alice)|~calm(alice)))&
(~strong(lucy)) | creative(alice) | [] | null | 0 |
If someone is not strong then paul is either not curious or not creative and vice versa.
Everyone who is both not strong and not old is calm and vice versa.
Everyone who is either wise or generous is either wise or not funny.
Everyone who is both old and not humble is funny or rich.
If someone is brave or not rich then someone is not calm and vice versa.
If someone is not quiet then someone is either tall or not brave and vice versa.
If john is either not curious or happy then mary is not humble and vice versa.
If mary is both brave and not creative then john is either curious or not quiet.
If someone is not curious then someone is rich.
If alice is either curious or wise then susan is humble and vice versa.
Everyone who is not quiet or not old is kind or funny and vice versa.
If someone is not creative or not funny then john is not quiet and vice versa.
If someone is brave or not creative then someone is rich or not quiet and vice versa.
If john is either not tall or not quiet then someone is either generous or not creative and vice versa.
If susan is either not brave or funny then mary is both not kind and not patient and vice versa.
If someone is both brave and not rich then someone is not tall or not patient.
Someone is not funny.
John is strong.
Someone is both tall and humble.
Paul is either not rich or not funny.
Someone is both creative and patient.
Someone is both not funny and rich.
Mary is not brave. | John is not quiet. | entailment | ((?[X]:(~strong(X)))<=>((~curious(paul)<~>~creative(paul))))&
(![X]:((~strong(X)&~old(X))<=>calm(X)))&
(![X]:((wise(X)<~>generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((old(X)&~humble(X))=>(funny(X)|rich(X))))&
((?[X]:((brave(X)|~rich(X))))<=>(?[X]:(~calm(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((tall(X)<~>~brave(X)))))&
(((~curious(john)<~>happy(john)))<=>(~humble(mary)))&
(((brave(mary)&~creative(mary)))=>((curious(john)<~>~quiet(john))))&
((?[X]:(~curious(X)))=>(?[X]:(rich(X))))&
(((curious(alice)<~>wise(alice)))<=>(humble(susan)))&
(![X]:((~quiet(X)|~old(X))<=>(kind(X)|funny(X))))&
((?[X]:((~creative(X)|~funny(X))))<=>(~quiet(john)))&
((?[X]:((brave(X)|~creative(X))))<=>(?[X]:((rich(X)|~quiet(X)))))&
(((~tall(john)<~>~quiet(john)))<=>(?[X]:((generous(X)<~>~creative(X)))))&
(((~brave(susan)<~>funny(susan)))<=>((~kind(mary)&~patient(mary))))&
((?[X]:((brave(X)&~rich(X))))=>(?[X]:((~tall(X)|~patient(X)))))&
(?[X]:(~funny(X)))&
(strong(john))&
(?[X]:((tall(X)&humble(X))))&
((~rich(paul)<~>~funny(paul)))&
(?[X]:((creative(X)&patient(X))))&
(?[X]:((~funny(X)&rich(X))))&
(~brave(mary)) | ~quiet(john) | [
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 148232557533309686406150
% SZS output start Proof for 148232557533309686406150
12. ? [X0] : (~funny(X0) | ~creative(X0)) <=> ~quiet(john) [input p11]
17. ? [X0] : ~funny(X0) [input p16]
24. quiet(john) [input hypothesis]
62. (? [X0] : (~funny(X0) | ~creative(X0)) | quiet(john)) & (~quiet(john) | ! [X0] : (funny(X0) & creative(X0))) [nnf transformation 12]
63. (? [X0] : (~funny(X0) | ~creative(X0)) | quiet(john)) & (~quiet(john) | ! [X1] : (funny(X1) & creative(X1))) [rectify 62]
64. ? [X0] : (~funny(X0) | ~creative(X0)) => (~funny(sK6) | ~creative(sK6)) [choice axiom]
65. ((~funny(sK6) | ~creative(sK6)) | quiet(john)) & (~quiet(john) | ! [X1] : (funny(X1) & creative(X1))) [skolemisation 63,64]
80. ? [X0] : ~funny(X0) => ~funny(sK11) [choice axiom]
81. ~funny(sK11) [skolemisation 17,80]
124. ~quiet(john) | funny(X1) [cnf transformation 65]
145. ~funny(sK11) [cnf transformation 81]
156. quiet(john) [cnf transformation 24]
252. 22 <=> quiet(john) [avatar definition]
291. 30 <=> ! [X1] : funny(X1) [avatar definition]
292. funny(X1) <- (30) [avatar component clause 291]
293. 30 | ~22 [avatar split clause 124,252,291]
392. 22 [avatar split clause 156,252]
399. $false <- (30) [resolution 292,145]
402. ~30 [avatar contradiction clause 399]
403. $false [avatar sat refutation 293,392,402]
% SZS output end Proof for 148232557533309686406150
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not 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 5363165653276727245543698
% SZS output start Proof for 5363165653276727245543698
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 5363165653276727245543698
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is calm.
If someone is brave then susan is calm or humble and vice versa.
If paul is funny or generous then paul is not wise or not patient.
Everyone who is both not wise and creative is not wise and vice versa.
Everyone who is quiet is humble and vice versa.
Everyone who is not tall or curious is both not old and not kind and vice versa.
If paul is not strong then someone is creative and vice versa.
Everyone who is humble or not quiet is both not old and tall and vice versa.
If mary is not creative or curious then paul is tall or wise and vice versa.
Everyone who is either not funny or quiet is either quiet or not wise and vice versa.
Everyone who is not old or not strong is tall.
Everyone who is rich is not kind.
Everyone who is either curious or not creative is old and vice versa.
Everyone who is either not calm or not curious is strong or not kind.
If mary is not curious or not rich then john is not calm and vice versa.
If someone is either not rich or brave then alice is not calm and vice versa.
Someone is either not happy or not creative.
Alice is rich.
John is either not humble or kind.
Someone is both patient and not calm.
Someone is calm.
Someone is either kind or not happy.
Someone is either calm or not happy.
Someone is patient or not old. | Mary is not funny. | contradiction | (![X]:(~humble(X)=>calm(X)))&
((?[X]:(brave(X)))<=>((calm(susan)|humble(susan))))&
(((funny(paul)|generous(paul)))=>((~wise(paul)|~patient(paul))))&
(![X]:((~wise(X)&creative(X))<=>~wise(X)))&
(![X]:(quiet(X)<=>humble(X)))&
(![X]:((~tall(X)|curious(X))<=>(~old(X)&~kind(X))))&
((~strong(paul))<=>(?[X]:(creative(X))))&
(![X]:((humble(X)|~quiet(X))<=>(~old(X)&tall(X))))&
(((~creative(mary)|curious(mary)))<=>((tall(paul)|wise(paul))))&
(![X]:((~funny(X)<~>quiet(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~old(X)|~strong(X))=>tall(X)))&
(![X]:(rich(X)=>~kind(X)))&
(![X]:((curious(X)<~>~creative(X))<=>old(X)))&
(![X]:((~calm(X)<~>~curious(X))=>(strong(X)|~kind(X))))&
(((~curious(mary)|~rich(mary)))<=>(~calm(john)))&
((?[X]:((~rich(X)<~>brave(X))))<=>(~calm(alice)))&
(?[X]:((~happy(X)<~>~creative(X))))&
(rich(alice))&
((~humble(john)<~>kind(john)))&
(?[X]:((patient(X)&~calm(X))))&
(?[X]:(calm(X)))&
(?[X]:((kind(X)<~>~happy(X))))&
(?[X]:((calm(X)<~>~happy(X))))&
(?[X]:((patient(X)|~old(X)))) | ~funny(mary) | [
"p3",
"p5",
"p8",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8628406612078730599597263
% SZS output start Proof for 8628406612078730599597263
4. ! [X0] : ((creative(X0) & ~wise(X0)) <=> ~wise(X0)) [input p3]
6. ! [X0] : ((curious(X0) | ~tall(X0)) <=> (~kind(X0) & ~old(X0))) [input p5]
9. (curious(mary) | ~creative(mary)) <=> (wise(paul) | tall(paul)) [input p8]
10. ! [X0] : ((~funny(X0) <~> quiet(X0)) <=> (quiet(X0) <~> ~wise(X0))) [input p9]
11. ! [X0] : ((~strong(X0) | ~old(X0)) => tall(X0)) [input p10]
13. ! [X0] : ((curious(X0) <~> ~creative(X0)) <=> old(X0)) [input p12]
25. ~funny(mary) [input hypothesis]
30. ! [X0] : (tall(X0) | (strong(X0) & old(X0))) [ennf transformation 11]
39. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | (~creative(X0) | wise(X0)))) [nnf transformation 4]
40. ! [X0] : (((creative(X0) & ~wise(X0)) | wise(X0)) & (~wise(X0) | ~creative(X0) | wise(X0))) [flattening 39]
42. ! [X0] : (((curious(X0) | ~tall(X0)) | (kind(X0) | old(X0))) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [nnf transformation 6]
43. ! [X0] : ((curious(X0) | ~tall(X0) | kind(X0) | old(X0)) & ((~kind(X0) & ~old(X0)) | (~curious(X0) & tall(X0)))) [flattening 42]
50. ((curious(mary) | ~creative(mary)) | (~wise(paul) & ~tall(paul))) & ((wise(paul) | tall(paul)) | (~curious(mary) & creative(mary))) [nnf transformation 9]
51. (curious(mary) | ~creative(mary) | (~wise(paul) & ~tall(paul))) & (wise(paul) | tall(paul) | (~curious(mary) & creative(mary))) [flattening 50]
52. ! [X0] : ((((~quiet(X0) | funny(X0)) & (quiet(X0) | ~funny(X0))) | ((quiet(X0) | wise(X0)) & (~wise(X0) | ~quiet(X0)))) & (((wise(X0) | ~quiet(X0)) & (~wise(X0) | quiet(X0))) | ((~funny(X0) | ~quiet(X0)) & (quiet(X0) | funny(X0))))) [nnf transformation 10]
53. ! [X0] : ((((creative(X0) | ~curious(X0)) & (~creative(X0) | curious(X0))) | ~old(X0)) & (old(X0) | ((curious(X0) | creative(X0)) & (~creative(X0) | ~curious(X0))))) [nnf transformation 13]
84. creative(X0) | wise(X0) [cnf transformation 40]
87. ~old(X0) | tall(X0) [cnf transformation 43]
88. ~old(X0) | ~curious(X0) [cnf transformation 43]
101. curious(mary) | ~creative(mary) | ~tall(paul) [cnf transformation 51]
103. ~wise(X0) | quiet(X0) | quiet(X0) | funny(X0) [cnf transformation 52]
109. ~quiet(X0) | funny(X0) | ~wise(X0) | ~quiet(X0) [cnf transformation 52]
111. tall(X0) | old(X0) [cnf transformation 30]
114. old(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 53]
140. ~funny(mary) [cnf transformation 25]
141. ~wise(X0) | quiet(X0) | funny(X0) [duplicate literal removal 103]
144. ~quiet(X0) | funny(X0) | ~wise(X0) [duplicate literal removal 109]
186. 10 <=> creative(mary) [avatar definition]
187. creative(mary) <- (10) [avatar component clause 186]
188. ~creative(mary) <- (~10) [avatar component clause 186]
190. 11 <=> curious(mary) [avatar definition]
192. curious(mary) <- (11) [avatar component clause 190]
195. 12 <=> tall(paul) [avatar definition]
197. ~tall(paul) <- (~12) [avatar component clause 195]
198. ~12 | ~10 | 11 [avatar split clause 101,190,186,195]
202. ~wise(X0) | funny(X0) [subsumption resolution 141,144]
203. tall(X0) [subsumption resolution 111,87]
205. ~curious(X0) | ~creative(X0) [subsumption resolution 114,88]
300. wise(mary) <- (~10) [resolution 84,188]
324. funny(mary) <- (~10) [resolution 300,202]
325. $false <- (~10) [subsumption resolution 324,140]
326. 10 [avatar contradiction clause 325]
329. ~creative(mary) <- (11) [resolution 205,192]
330. $false <- (10, 11) [subsumption resolution 329,187]
331. ~10 | ~11 [avatar contradiction clause 330]
333. $false <- (~12) [subsumption resolution 197,203]
334. 12 [avatar contradiction clause 333]
335. $false [avatar sat refutation 198,326,331,334]
% SZS output end Proof for 8628406612078730599597263
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or not rich is not curious or not rich and vice versa. If alice is humble then john is both rich and not creative. If someone is quiet then john is either creative or kind. If someone is curious then someone is humble or funny. Everyone who is creative or curious is rich or not calm and vice versa. If alice is not generous then someone is both not tall and humble. Everyone who is either not happy or kind is happy or wise. Everyone who is creative is both not kind and kind. If john is brave or funny then susan is strong or not strong and vice versa. If alice is either old or patient then someone is strong. Everyone who is either not quiet or calm is both not quiet and not funny. Everyone who is either not wise or humble is funny and vice versa. Everyone who is either not curious or not strong is either not wise or not brave and vice versa. Everyone who is tall is happy. Everyone who is both not kind and not quiet is either rich or tall. Everyone who is not wise is not generous. Someone is both not brave and not generous. Lucy is kind. Mary is tall. Susan is not curious. Fred is rich or creative. John is not patient or not funny. | John is not patient. | neutral | (![X]:((~old(X)<~>~rich(X))<=>(~curious(X)|~rich(X))))&
((humble(alice))=>((rich(john)&~creative(john))))&
((?[X]:(quiet(X)))=>((creative(john)<~>kind(john))))&
((?[X]:(curious(X)))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((creative(X)|curious(X))<=>(rich(X)|~calm(X))))&
((~generous(alice))=>(?[X]:((~tall(X)&humble(X)))))&
(![X]:((~happy(X)<~>kind(X))=>(happy(X)|wise(X))))&
(![X]:(creative(X)=>(~kind(X)&kind(X))))&
(((brave(john)|funny(john)))<=>((strong(susan)|~strong(susan))))&
(((old(alice)<~>patient(alice)))=>(?[X]:(strong(X))))&
(![X]:((~quiet(X)<~>calm(X))=>(~quiet(X)&~funny(X))))&
(![X]:((~wise(X)<~>humble(X))<=>funny(X)))&
(![X]:((~curious(X)<~>~strong(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(tall(X)=>happy(X)))&
(![X]:((~kind(X)&~quiet(X))=>(rich(X)<~>tall(X))))&
(![X]:(~wise(X)=>~generous(X)))&
(?[X]:((~brave(X)&~generous(X))))&
(kind(lucy))&
(tall(mary))&
(~curious(susan))&
((rich(fred)|creative(fred)))&
((~patient(john)|~funny(john))) | ~patient(john) | [] | null | 0 |
Everyone who is either not strong or not curious is either rich or not quiet and vice versa. Everyone who is not tall or not curious is both quiet and strong and vice versa. Everyone who is tall or not rich is either old or not calm. Everyone who is either kind or not creative is both rich and not creative and vice versa. Everyone who is both wise and funny is either not calm or creative and vice versa. If someone is not generous then someone is both not brave and tall and vice versa. Everyone who is not curious is either quiet or calm and vice versa. Everyone who is either humble or not wise is both rich and not curious and vice versa. Everyone who is both not quiet and kind is wise and vice versa. Everyone who is calm or not humble is both not funny and old. If someone is both not wise and happy then paul is both old and not brave and vice versa. Everyone who is either not rich or humble is both not kind and tall and vice versa. If fred is quiet then mary is either rich or not wise. Everyone who is funny or calm is either not generous or kind. Everyone who is not strong is funny and vice versa. If fred is not curious or funny then someone is happy or rich and vice versa. Someone is either not generous or not wise. Susan is strong. Someone is humble. Someone is creative. Someone is either happy or not curious. Mary is old or not rich. Mary is kind. | Fred is calm. | contradiction | (![X]:((~strong(X)<~>~curious(X))<=>(rich(X)<~>~quiet(X))))&
(![X]:((~tall(X)|~curious(X))<=>(quiet(X)&strong(X))))&
(![X]:((tall(X)|~rich(X))=>(old(X)<~>~calm(X))))&
(![X]:((kind(X)<~>~creative(X))<=>(rich(X)&~creative(X))))&
(![X]:((wise(X)&funny(X))<=>(~calm(X)<~>creative(X))))&
((?[X]:(~generous(X)))<=>(?[X]:((~brave(X)&tall(X)))))&
(![X]:(~curious(X)<=>(quiet(X)<~>calm(X))))&
(![X]:((humble(X)<~>~wise(X))<=>(rich(X)&~curious(X))))&
(![X]:((~quiet(X)&kind(X))<=>wise(X)))&
(![X]:((calm(X)|~humble(X))=>(~funny(X)&old(X))))&
((?[X]:((~wise(X)&happy(X))))<=>((old(paul)&~brave(paul))))&
(![X]:((~rich(X)<~>humble(X))<=>(~kind(X)&tall(X))))&
((quiet(fred))=>((rich(mary)<~>~wise(mary))))&
(![X]:((funny(X)|calm(X))=>(~generous(X)<~>kind(X))))&
(![X]:(~strong(X)<=>funny(X)))&
(((~curious(fred)|funny(fred)))<=>(?[X]:((happy(X)|rich(X)))))&
(?[X]:((~generous(X)<~>~wise(X))))&
(strong(susan))&
(?[X]:(humble(X)))&
(?[X]:(creative(X)))&
(?[X]:((happy(X)<~>~curious(X))))&
((old(mary)|~rich(mary)))&
(kind(mary)) | calm(fred) | [
"p0",
"p1",
"p6",
"p9",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1365266602846693349663409
% SZS output start Proof for 1365266602846693349663409
1. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> (rich(X0) <~> ~quiet(X0))) [input p0]
2. ! [X0] : ((~curious(X0) | ~tall(X0)) <=> (strong(X0) & quiet(X0))) [input p1]
7. ! [X0] : (~curious(X0) <=> (quiet(X0) <~> calm(X0))) [input p6]
10. ! [X0] : ((~humble(X0) | calm(X0)) => (old(X0) & ~funny(X0))) [input p9]
16. (funny(fred) | ~curious(fred)) <=> ? [X0] : (rich(X0) | happy(X0)) [input p15]
21. ? [X0] : (happy(X0) <~> ~curious(X0)) [input p20]
24. calm(fred) [input hypothesis]
27. ! [X0] : ((old(X0) & ~funny(X0)) | (humble(X0) & ~calm(X0))) [ennf transformation 10]
30. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0)))) & (((quiet(X0) | ~rich(X0)) & (~quiet(X0) | rich(X0))) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 1]
31. ! [X0] : (((~curious(X0) | ~tall(X0)) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | (curious(X0) & tall(X0)))) [nnf transformation 2]
32. ! [X0] : ((~curious(X0) | ~tall(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | (curious(X0) & tall(X0)))) [flattening 31]
43. ! [X0] : ((~curious(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0)))) & (((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | curious(X0))) [nnf transformation 7]
58. ((funny(fred) | ~curious(fred)) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | (~funny(fred) & curious(fred))) [nnf transformation 16]
59. (funny(fred) | ~curious(fred) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | (~funny(fred) & curious(fred))) [flattening 58]
60. (funny(fred) | ~curious(fred) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X1] : (rich(X1) | happy(X1)) | (~funny(fred) & curious(fred))) [rectify 59]
61. ? [X1] : (rich(X1) | happy(X1)) => (rich(sK3) | happy(sK3)) [choice axiom]
62. (funny(fred) | ~curious(fred) | ! [X0] : (~rich(X0) & ~happy(X0))) & ((rich(sK3) | happy(sK3)) | (~funny(fred) & curious(fred))) [skolemisation 60,61]
70. ? [X0] : ((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) [nnf transformation 21]
71. ? [X0] : ((curious(X0) | ~happy(X0)) & (~curious(X0) | happy(X0))) => ((curious(sK7) | ~happy(sK7)) & (~curious(sK7) | happy(sK7))) [choice axiom]
72. (curious(sK7) | ~happy(sK7)) & (~curious(sK7) | happy(sK7)) [skolemisation 70,71]
74. ~quiet(X0) | rich(X0) | ~strong(X0) | curious(X0) [cnf transformation 30]
82. quiet(X0) | curious(X0) [cnf transformation 32]
84. curious(X0) | strong(X0) [cnf transformation 32]
106. ~calm(X0) | ~quiet(X0) | curious(X0) [cnf transformation 43]
108. ~curious(X0) | quiet(X0) | ~calm(X0) [cnf transformation 43]
118. ~funny(X0) | ~calm(X0) [cnf transformation 27]
142. funny(fred) | ~curious(fred) | ~happy(X0) [cnf transformation 62]
143. funny(fred) | ~curious(fred) | ~rich(X0) [cnf transformation 62]
149. ~curious(sK7) | happy(sK7) [cnf transformation 72]
153. calm(fred) [cnf transformation 24]
177. ~calm(X0) | quiet(X0) [subsumption resolution 108,82]
178. ~calm(X0) | curious(X0) [subsumption resolution 106,177]
217. 14 <=> ! [X0] : ~rich(X0) [avatar definition]
218. ~rich(X0) <- (14) [avatar component clause 217]
220. 15 <=> curious(fred) [avatar definition]
224. 16 <=> funny(fred) [avatar definition]
226. funny(fred) <- (16) [avatar component clause 224]
227. 14 | ~15 | 16 [avatar split clause 143,224,220,217]
229. 17 <=> ! [X0] : ~happy(X0) [avatar definition]
230. ~happy(X0) <- (17) [avatar component clause 229]
231. 17 | ~15 | 16 [avatar split clause 142,224,220,229]
253. 22 <=> happy(sK7) [avatar definition]
254. happy(sK7) <- (22) [avatar component clause 253]
257. 23 <=> curious(sK7) [avatar definition]
258. ~curious(sK7) <- (~23) [avatar component clause 257]
261. 22 | ~23 [avatar split clause 149,257,253]
285. curious(fred) [resolution 178,153]
353. ~calm(fred) <- (16) [resolution 226,118]
356. $false <- (16) [subsumption resolution 353,153]
357. ~16 [avatar contradiction clause 356]
358. 15 [avatar split clause 285,220]
528. rich(X0) | ~strong(X0) | curious(X0) | curious(X0) [resolution 74,82]
532. rich(X0) | ~strong(X0) | curious(X0) [duplicate literal removal 528]
533. ~strong(X0) | curious(X0) <- (14) [subsumption resolution 532,218]
534. curious(X0) <- (14) [subsumption resolution 533,84]
535. $false <- (14, ~23) [resolution 534,258]
537. ~14 | 23 [avatar contradiction clause 535]
538. $false <- (17, 22) [subsumption resolution 254,230]
539. ~17 | ~22 [avatar contradiction clause 538]
540. $false [avatar sat refutation 227,231,261,357,358,537,539]
% SZS output end Proof for 1365266602846693349663409
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is either curious or not patient then someone is strong or generous and vice versa.
Everyone who is not calm or quiet is either curious or kind.
If someone is wise then lucy is wise and vice versa.
Everyone who is both not tall and not humble is both not wise and not creative and vice versa.
Everyone who is not patient is both generous and humble and vice versa.
If someone is both not brave and not calm then someone is either not brave or happy and vice versa.
Everyone who is not curious or not kind is both not rich and not funny.
If susan is happy then someone is not patient or patient and vice versa.
If fred is old or generous then someone is both quiet and not happy.
If someone is not funny or not happy then mary is not creative or not curious.
Everyone who is either not kind or not calm is wise or not wise and vice versa.
Everyone who is not happy is either curious or not creative.
If someone is humble or creative then someone is both rich and not old.
Everyone who is either not brave or not kind is either not rich or brave.
Everyone who is not tall is not creative and vice versa.
Everyone who is not calm is not patient or wise and vice versa.
Fred is either not patient or not creative.
Someone is both not brave and not funny.
Someone is not brave.
Someone is either not kind or not quiet.
Someone is both not curious and not rich. | Susan is not brave. | entailment | (((curious(lucy)<~>~patient(lucy)))<=>(?[X]:((strong(X)|generous(X)))))&
(![X]:((~calm(X)|quiet(X))=>(curious(X)<~>kind(X))))&
((?[X]:(wise(X)))<=>(wise(lucy)))&
(![X]:((~tall(X)&~humble(X))<=>(~wise(X)&~creative(X))))&
(![X]:(~patient(X)<=>(generous(X)&humble(X))))&
((?[X]:((~brave(X)&~calm(X))))<=>(?[X]:((~brave(X)<~>happy(X)))))&
(![X]:((~curious(X)|~kind(X))=>(~rich(X)&~funny(X))))&
((happy(susan))<=>(?[X]:((~patient(X)|patient(X)))))&
(((old(fred)|generous(fred)))=>(?[X]:((quiet(X)&~happy(X)))))&
((?[X]:((~funny(X)|~happy(X))))=>((~creative(mary)|~curious(mary))))&
(![X]:((~kind(X)<~>~calm(X))<=>(wise(X)|~wise(X))))&
(![X]:(~happy(X)=>(curious(X)<~>~creative(X))))&
((?[X]:((humble(X)|creative(X))))=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((~brave(X)<~>~kind(X))=>(~rich(X)<~>brave(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
(![X]:(~calm(X)<=>(~patient(X)|wise(X))))&
((~patient(fred)<~>~creative(fred)))&
(?[X]:((~brave(X)&~funny(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~kind(X)<~>~quiet(X))))&
(?[X]:((~curious(X)&~rich(X)))) | ~brave(susan) | [
"p1",
"p2",
"p3",
"p4",
"p6",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6649692425804872142959716
% SZS output start Proof for 6649692425804872142959716
2. ! [X0] : ((quiet(X0) | ~calm(X0)) => (curious(X0) <~> kind(X0))) [input p1]
3. ? [X0] : wise(X0) <=> wise(lucy) [input p2]
4. ! [X0] : ((~humble(X0) & ~tall(X0)) <=> (~creative(X0) & ~wise(X0))) [input p3]
5. ! [X0] : (~patient(X0) <=> (humble(X0) & generous(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | ~curious(X0)) => (~funny(X0) & ~rich(X0))) [input p6]
11. ! [X0] : ((~kind(X0) <~> ~calm(X0)) <=> (~wise(X0) | wise(X0))) [input p10]
13. ? [X0] : (creative(X0) | humble(X0)) => ? [X0] : (~old(X0) & rich(X0)) [input p12]
14. ! [X0] : ((~brave(X0) <~> ~kind(X0)) => (~rich(X0) <~> brave(X0))) [input p13]
15. ! [X0] : (~tall(X0) <=> ~creative(X0)) [input p14]
16. ! [X0] : (~calm(X0) <=> (wise(X0) | ~patient(X0))) [input p15]
22. brave(susan) [input hypothesis]
24. ? [X0] : (creative(X0) | humble(X0)) => ? [X1] : (~old(X1) & rich(X1)) [rectify 13]
26. ? [X0] : (creative(X0) | humble(X0)) => ? [X1] : rich(X1) [pure predicate removal 24]
27. ! [X0] : ((curious(X0) <~> kind(X0)) | (~quiet(X0) & calm(X0))) [ennf transformation 2]
28. ! [X0] : ((~funny(X0) & ~rich(X0)) | (kind(X0) & curious(X0))) [ennf transformation 7]
33. ? [X1] : rich(X1) | ! [X0] : (~creative(X0) & ~humble(X0)) [ennf transformation 26]
34. ! [X0] : ((~rich(X0) <~> brave(X0)) | (~brave(X0) <=> ~kind(X0))) [ennf transformation 14]
39. ! [X0] : (((~kind(X0) | ~curious(X0)) & (kind(X0) | curious(X0))) | (~quiet(X0) & calm(X0))) [nnf transformation 27]
40. (? [X0] : wise(X0) | ~wise(lucy)) & (wise(lucy) | ! [X0] : ~wise(X0)) [nnf transformation 3]
41. (? [X0] : wise(X0) | ~wise(lucy)) & (wise(lucy) | ! [X1] : ~wise(X1)) [rectify 40]
42. ? [X0] : wise(X0) => wise(sK1) [choice axiom]
43. (wise(sK1) | ~wise(lucy)) & (wise(lucy) | ! [X1] : ~wise(X1)) [skolemisation 41,42]
44. ! [X0] : (((~humble(X0) & ~tall(X0)) | (creative(X0) | wise(X0))) & ((~creative(X0) & ~wise(X0)) | (humble(X0) | tall(X0)))) [nnf transformation 4]
45. ! [X0] : (((~humble(X0) & ~tall(X0)) | creative(X0) | wise(X0)) & ((~creative(X0) & ~wise(X0)) | humble(X0) | tall(X0))) [flattening 44]
46. ! [X0] : ((~patient(X0) | (~humble(X0) | ~generous(X0))) & ((humble(X0) & generous(X0)) | patient(X0))) [nnf transformation 5]
47. ! [X0] : ((~patient(X0) | ~humble(X0) | ~generous(X0)) & ((humble(X0) & generous(X0)) | patient(X0))) [flattening 46]
59. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (wise(X0) & ~wise(X0))) & ((~wise(X0) | wise(X0)) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [nnf transformation 11]
60. ! [X0] : ((((calm(X0) | kind(X0)) & (~calm(X0) | ~kind(X0))) | (wise(X0) & ~wise(X0))) & (~wise(X0) | wise(X0) | ((~kind(X0) | calm(X0)) & (~calm(X0) | kind(X0))))) [flattening 59]
62. ? [X0] : rich(X0) | ! [X1] : (~creative(X1) & ~humble(X1)) [rectify 33]
63. ? [X0] : rich(X0) => rich(sK6) [choice axiom]
64. rich(sK6) | ! [X1] : (~creative(X1) & ~humble(X1)) [skolemisation 62,63]
65. ! [X0] : (((~brave(X0) | rich(X0)) & (brave(X0) | ~rich(X0))) | ((~brave(X0) | kind(X0)) & (~kind(X0) | brave(X0)))) [nnf transformation 34]
66. ! [X0] : ((~tall(X0) | creative(X0)) & (~creative(X0) | tall(X0))) [nnf transformation 15]
67. ! [X0] : ((~calm(X0) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | calm(X0))) [nnf transformation 16]
68. ! [X0] : ((~calm(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | calm(X0))) [flattening 67]
87. ~kind(X0) | ~curious(X0) | calm(X0) [cnf transformation 39]
89. wise(lucy) | ~wise(X1) [cnf transformation 43]
91. ~wise(X0) | humble(X0) | tall(X0) [cnf transformation 45]
96. humble(X0) | patient(X0) [cnf transformation 47]
104. ~rich(X0) | curious(X0) [cnf transformation 28]
105. ~rich(X0) | kind(X0) [cnf transformation 28]
117. ~calm(X0) | ~kind(X0) | ~wise(X0) [cnf transformation 60]
118. ~kind(X0) | ~calm(X0) | wise(X0) [cnf transformation 60]
119. calm(X0) | kind(X0) | ~wise(X0) [cnf transformation 60]
120. wise(X0) | kind(X0) | calm(X0) [cnf transformation 60]
123. rich(sK6) | ~humble(X1) [cnf transformation 64]
124. rich(sK6) | ~creative(X1) [cnf transformation 64]
128. ~brave(X0) | rich(X0) | ~brave(X0) | kind(X0) [cnf transformation 65]
130. ~tall(X0) | creative(X0) [cnf transformation 66]
131. ~patient(X0) | wise(X0) | calm(X0) [cnf transformation 68]
143. brave(susan) [cnf transformation 22]
145. ~brave(X0) | rich(X0) | kind(X0) [duplicate literal removal 128]
175. 7 <=> wise(lucy) [avatar definition]
176. wise(lucy) <- (7) [avatar component clause 175]
184. 9 <=> ! [X1] : ~wise(X1) [avatar definition]
185. ~wise(X1) <- (9) [avatar component clause 184]
186. 9 | 7 [avatar split clause 89,175,184]
227. 19 <=> ! [X0] : patient(X0) [avatar definition]
228. patient(X0) <- (19) [avatar component clause 227]
260. kind(X0) | calm(X0) [subsumption resolution 119,120]
261. ~kind(X0) | ~calm(X0) [subsumption resolution 117,118]
263. 27 <=> ! [X1] : ~creative(X1) [avatar definition]
264. ~creative(X1) <- (27) [avatar component clause 263]
266. 28 <=> rich(sK6) [avatar definition]
268. rich(sK6) <- (28) [avatar component clause 266]
269. 27 | 28 [avatar split clause 124,266,263]
271. 29 <=> ! [X1] : ~humble(X1) [avatar definition]
272. ~humble(X1) <- (29) [avatar component clause 271]
273. 29 | 28 [avatar split clause 123,266,271]
274. ~brave(X0) | kind(X0) [subsumption resolution 145,105]
297. curious(sK6) <- (28) [resolution 104,268]
298. kind(sK6) <- (28) [resolution 105,268]
302. ~calm(sK6) <- (28) [resolution 261,298]
304. kind(susan) [resolution 274,143]
306. ~calm(susan) [resolution 304,261]
310. ~curious(X1) | calm(X1) | calm(X1) [resolution 87,260]
314. ~curious(X1) | calm(X1) [duplicate literal removal 310]
331. humble(lucy) | tall(lucy) <- (7) [resolution 91,176]
334. 36 <=> tall(lucy) [avatar definition]
336. tall(lucy) <- (36) [avatar component clause 334]
338. 37 <=> humble(lucy) [avatar definition]
340. humble(lucy) <- (37) [avatar component clause 338]
341. 36 | 37 | ~7 [avatar split clause 331,175,338,334]
351. creative(lucy) <- (36) [resolution 336,130]
366. calm(sK6) <- (28) [resolution 314,297]
367. $false <- (28) [subsumption resolution 366,302]
368. ~28 [avatar contradiction clause 367]
369. $false <- (27, 36) [resolution 264,351]
372. ~27 | ~36 [avatar contradiction clause 369]
373. patient(X0) <- (29) [resolution 272,96]
374. 19 | ~29 [avatar split clause 373,271,227]
384. wise(X0) | calm(X0) <- (19) [resolution 131,228]
386. calm(X0) <- (9, 19) [subsumption resolution 384,185]
389. $false <- (9, 19) [resolution 386,306]
394. ~9 | ~19 [avatar contradiction clause 389]
397. $false <- (29, 37) [subsumption resolution 340,272]
398. ~29 | ~37 [avatar contradiction clause 397]
399. $false [avatar sat refutation 186,269,273,341,368,372,374,394,398]
% SZS output end Proof for 6649692425804872142959716
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not old or kind then someone is both funny and calm and vice versa.
Everyone who is not kind is either curious or funny.
Everyone who is humble or not humble is tall.
Everyone who is not tall is brave or not creative.
Everyone who is happy is not kind and vice versa.
If someone is either funny or happy then lucy is either not strong or strong and vice versa.
If someone is quiet then paul is either not tall or kind.
Everyone who is either humble or rich is both not brave and brave and vice versa.
If someone is not wise or not curious then someone is quiet or not wise.
Everyone who is quiet or not wise is both not kind and kind.
Everyone who is either funny or not tall is both not strong and not wise.
If lucy is either happy or not humble then alice is either not humble or not quiet.
Everyone who is both curious and not generous is strong.
If someone is either calm or creative then lucy is either strong or tall and vice versa.
Lucy is either not strong or strong.
John is either patient or calm.
Someone is either not wise or not creative.
John is not brave. | Alice is wise. | entailment | (((~old(fred)<~>kind(fred)))<=>(?[X]:((funny(X)&calm(X)))))&
(![X]:(~kind(X)=>(curious(X)<~>funny(X))))&
(![X]:((humble(X)|~humble(X))=>tall(X)))&
(![X]:(~tall(X)=>(brave(X)|~creative(X))))&
(![X]:(happy(X)<=>~kind(X)))&
((?[X]:((funny(X)<~>happy(X))))<=>((~strong(lucy)<~>strong(lucy))))&
((?[X]:(quiet(X)))=>((~tall(paul)<~>kind(paul))))&
(![X]:((humble(X)<~>rich(X))<=>(~brave(X)&brave(X))))&
((?[X]:((~wise(X)|~curious(X))))=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:((quiet(X)|~wise(X))=>(~kind(X)&kind(X))))&
(![X]:((funny(X)<~>~tall(X))=>(~strong(X)&~wise(X))))&
(((happy(lucy)<~>~humble(lucy)))=>((~humble(alice)<~>~quiet(alice))))&
(![X]:((curious(X)&~generous(X))=>strong(X)))&
((?[X]:((calm(X)<~>creative(X))))<=>((strong(lucy)<~>tall(lucy))))&
((~strong(lucy)<~>strong(lucy)))&
((patient(john)<~>calm(john)))&
(?[X]:((~wise(X)<~>~creative(X))))&
(~brave(john)) | wise(alice) | [
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 4685842876133108593230702
% SZS output start Proof for 4685842876133108593230702
10. ! [X0] : ((~wise(X0) | quiet(X0)) => (kind(X0) & ~kind(X0))) [input p9]
19. ~wise(alice) [input hypothesis]
28. ! [X0] : ((kind(X0) & ~kind(X0)) | (wise(X0) & ~quiet(X0))) [ennf transformation 10]
90. ~kind(X0) | wise(X0) [cnf transformation 28]
92. kind(X0) | wise(X0) [cnf transformation 28]
116. ~wise(alice) [cnf transformation 19]
187. 14 <=> ! [X1] : wise(X1) [avatar definition]
188. wise(X1) <- (14) [avatar component clause 187]
190. wise(X0) [subsumption resolution 90,92]
191. 14 [avatar split clause 190,187]
262. $false <- (14) [resolution 188,116]
263. ~14 [avatar contradiction clause 262]
264. $false [avatar sat refutation 191,263]
% SZS output end Proof for 4685842876133108593230702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is not brave and vice versa. If fred is not rich or not old then john is quiet or not tall and vice versa. If someone is either not curious or happy then someone is both old and creative. If someone is not kind then someone is both tall and not strong and vice versa. If mary is not funny or strong then fred is curious and vice versa. If someone is either not quiet or not rich then john is both rich and not tall. Everyone who is creative is both not kind and tall. Everyone who is either calm or not strong is tall. Everyone who is both not strong and old is not rich. If someone is not generous then someone is both quiet and humble. If lucy is not happy then someone is both not quiet and strong and vice versa. If someone is both not happy and funny then someone is curious or generous. If someone is both not wise and not rich then someone is both humble and tall and vice versa. If susan is patient or not patient then fred is both strong and happy. If someone is quiet then someone is either not tall or not rich and vice versa. Someone is either not funny or not rich. Someone is both curious and not tall. Someone is brave or not wise. Someone is rich. Someone is not creative or happy. Alice is both not generous and creative. Someone is either humble or not rich. John is either not wise or not kind. | Fred is strong. | entailment | (![X]:(old(X)<=>~brave(X)))&
(((~rich(fred)|~old(fred)))<=>((quiet(john)|~tall(john))))&
((?[X]:((~curious(X)<~>happy(X))))=>(?[X]:((old(X)&creative(X)))))&
((?[X]:(~kind(X)))<=>(?[X]:((tall(X)&~strong(X)))))&
(((~funny(mary)|strong(mary)))<=>(curious(fred)))&
((?[X]:((~quiet(X)<~>~rich(X))))=>((rich(john)&~tall(john))))&
(![X]:(creative(X)=>(~kind(X)&tall(X))))&
(![X]:((calm(X)<~>~strong(X))=>tall(X)))&
(![X]:((~strong(X)&old(X))=>~rich(X)))&
((?[X]:(~generous(X)))=>(?[X]:((quiet(X)&humble(X)))))&
((~happy(lucy))<=>(?[X]:((~quiet(X)&strong(X)))))&
((?[X]:((~happy(X)&funny(X))))=>(?[X]:((curious(X)|generous(X)))))&
((?[X]:((~wise(X)&~rich(X))))<=>(?[X]:((humble(X)&tall(X)))))&
(((patient(susan)|~patient(susan)))=>((strong(fred)&happy(fred))))&
((?[X]:(quiet(X)))<=>(?[X]:((~tall(X)<~>~rich(X)))))&
(?[X]:((~funny(X)<~>~rich(X))))&
(?[X]:((curious(X)&~tall(X))))&
(?[X]:((brave(X)|~wise(X))))&
(?[X]:(rich(X)))&
(?[X]:((~creative(X)|happy(X))))&
((~generous(alice)&creative(alice)))&
(?[X]:((humble(X)<~>~rich(X))))&
((~wise(john)<~>~kind(john))) | strong(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 439735282068684658117578
% SZS output start Proof for 439735282068684658117578
14. (~patient(susan) | patient(susan)) => (happy(fred) & strong(fred)) [input p13]
24. ~strong(fred) [input hypothesis]
39. (happy(fred) & strong(fred)) | (patient(susan) & ~patient(susan)) [ennf transformation 14]
126. strong(fred) | ~patient(susan) [cnf transformation 39]
127. strong(fred) | patient(susan) [cnf transformation 39]
147. ~strong(fred) [cnf transformation 24]
306. 36 <=> patient(susan) [avatar definition]
316. 38 <=> strong(fred) [avatar definition]
319. 36 | 38 [avatar split clause 127,316,306]
320. ~36 | 38 [avatar split clause 126,316,306]
394. ~38 [avatar split clause 147,316]
395. $false [avatar sat refutation 319,320,394]
% SZS output end Proof for 439735282068684658117578
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old or strong then someone is not generous or not funny.
If susan is not old then someone is both not generous and creative.
If lucy is happy then someone is not curious and vice versa.
Everyone who is both generous and old is either rich or not calm and vice versa.
If someone is quiet or not calm then paul is not old.
If someone is not calm or not happy then susan is either not rich or creative and vice versa.
Everyone who is either creative or not curious is both not rich and happy and vice versa.
Everyone who is kind is either generous or not quiet.
Everyone who is patient or wise is tall or not rich and vice versa.
Everyone who is not generous is patient and vice versa.
Everyone who is generous is either calm or kind and vice versa.
Everyone who is calm or not kind is both not generous and generous.
Everyone who is not brave is either not calm or brave and vice versa.
If someone is either not rich or generous then someone is either quiet or brave.
Everyone who is old is both not happy and tall.
Someone is not happy.
Someone is not humble.
Someone is either not creative or not curious.
Someone is either humble or not old.
Someone is either not humble or happy.
Someone is not strong. | Susan is generous. | entailment | (((~old(alice)|strong(alice)))=>(?[X]:((~generous(X)|~funny(X)))))&
((~old(susan))=>(?[X]:((~generous(X)&creative(X)))))&
((happy(lucy))<=>(?[X]:(~curious(X))))&
(![X]:((generous(X)&old(X))<=>(rich(X)<~>~calm(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(~old(paul)))&
((?[X]:((~calm(X)|~happy(X))))<=>((~rich(susan)<~>creative(susan))))&
(![X]:((creative(X)<~>~curious(X))<=>(~rich(X)&happy(X))))&
(![X]:(kind(X)=>(generous(X)<~>~quiet(X))))&
(![X]:((patient(X)|wise(X))<=>(tall(X)|~rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(generous(X)<=>(calm(X)<~>kind(X))))&
(![X]:((calm(X)|~kind(X))=>(~generous(X)&generous(X))))&
(![X]:(~brave(X)<=>(~calm(X)<~>brave(X))))&
((?[X]:((~rich(X)<~>generous(X))))=>(?[X]:((quiet(X)<~>brave(X)))))&
(![X]:(old(X)=>(~happy(X)&tall(X))))&
(?[X]:(~happy(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~creative(X)<~>~curious(X))))&
(?[X]:((humble(X)<~>~old(X))))&
(?[X]:((~humble(X)<~>happy(X))))&
(?[X]:(~strong(X))) | generous(susan) | [
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8163595360944508421289971
% SZS output start Proof for 8163595360944508421289971
11. ! [X0] : (generous(X0) <=> (calm(X0) <~> kind(X0))) [input p10]
12. ! [X0] : ((~kind(X0) | calm(X0)) => (generous(X0) & ~generous(X0))) [input p11]
22. ~generous(susan) [input hypothesis]
29. ! [X0] : ((generous(X0) & ~generous(X0)) | (kind(X0) & ~calm(X0))) [ennf transformation 12]
50. ! [X0] : ((generous(X0) | ((calm(X0) | ~kind(X0)) & (kind(X0) | ~calm(X0)))) & (((~kind(X0) | ~calm(X0)) & (kind(X0) | calm(X0))) | ~generous(X0))) [nnf transformation 11]
104. ~kind(X0) | calm(X0) | generous(X0) [cnf transformation 50]
105. ~generous(X0) | ~calm(X0) [cnf transformation 29]
107. ~calm(X0) | generous(X0) [cnf transformation 29]
108. kind(X0) | generous(X0) [cnf transformation 29]
127. ~generous(susan) [cnf transformation 22]
195. ~calm(X0) [subsumption resolution 105,107]
331. calm(X0) | generous(X0) | generous(X0) [resolution 104,108]
333. calm(X0) | generous(X0) [duplicate literal removal 331]
334. generous(X0) [subsumption resolution 333,195]
335. $false [resolution 334,127]
% SZS output end Proof for 8163595360944508421289971
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich then someone is either not quiet or quiet. If susan is not kind or not funny then someone is not rich or creative and vice versa. Everyone who is not strong is both humble and calm. Everyone who is wise or humble is both quiet and not funny and vice versa. Everyone who is not generous is not old. If paul is creative then lucy is both rich and not wise and vice versa. Everyone who is either tall or wise is either not strong or not calm. Everyone who is strong or creative is both not curious and generous. If someone is both wise and kind then alice is both humble and tall and vice versa. If someone is either not wise or not happy then paul is not humble or kind and vice versa. If someone is not happy or not rich then someone is both patient and generous and vice versa. Everyone who is patient is rich or not wise and vice versa. If fred is both funny and not patient then lucy is tall and vice versa. Everyone who is strong or not humble is not quiet or not generous and vice versa. Everyone who is not tall is both happy and not wise. Someone is either not strong or not quiet. Fred is both not calm and brave. Someone is both rich and not tall. Someone is either not humble or not generous. Someone is both wise and rich. | Lucy is quiet. | neutral | ((?[X]:(~rich(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(((~kind(susan)|~funny(susan)))<=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:(~strong(X)=>(humble(X)&calm(X))))&
(![X]:((wise(X)|humble(X))<=>(quiet(X)&~funny(X))))&
(![X]:(~generous(X)=>~old(X)))&
((creative(paul))<=>((rich(lucy)&~wise(lucy))))&
(![X]:((tall(X)<~>wise(X))=>(~strong(X)<~>~calm(X))))&
(![X]:((strong(X)|creative(X))=>(~curious(X)&generous(X))))&
((?[X]:((wise(X)&kind(X))))<=>((humble(alice)&tall(alice))))&
((?[X]:((~wise(X)<~>~happy(X))))<=>((~humble(paul)|kind(paul))))&
((?[X]:((~happy(X)|~rich(X))))<=>(?[X]:((patient(X)&generous(X)))))&
(![X]:(patient(X)<=>(rich(X)|~wise(X))))&
(((funny(fred)&~patient(fred)))<=>(tall(lucy)))&
(![X]:((strong(X)|~humble(X))<=>(~quiet(X)|~generous(X))))&
(![X]:(~tall(X)=>(happy(X)&~wise(X))))&
(?[X]:((~strong(X)<~>~quiet(X))))&
((~calm(fred)&brave(fred)))&
(?[X]:((rich(X)&~tall(X))))&
(?[X]:((~humble(X)<~>~generous(X))))&
(?[X]:((wise(X)&rich(X)))) | quiet(lucy) | [] | null | 0 |
Everyone who is both tall and not quiet is curious and vice versa. If mary is both not creative and not calm then someone is both not happy and not funny and vice versa. If paul is wise then someone is either happy or not calm. Everyone who is both not kind and humble is both patient and generous and vice versa. Everyone who is old or brave is either funny or brave. If alice is both calm and funny then susan is curious. Everyone who is not patient is not kind and vice versa. Everyone who is either not curious or humble is not patient. If mary is funny then fred is either funny or brave. If someone is either not curious or brave then john is either not humble or calm. Everyone who is wise is not creative or not strong and vice versa. Everyone who is either wise or not patient is curious or not calm. If someone is both wise and not curious then someone is either curious or humble. Everyone who is either patient or not kind is both not brave and not creative. If susan is both humble and happy then someone is calm or not curious and vice versa. Everyone who is not rich or humble is wise. John is both strong and happy. Lucy is calm. Lucy is both wise and quiet. Mary is curious. Lucy is either not curious or not wise. John is rich. | Fred is creative. | contradiction | (![X]:((tall(X)&~quiet(X))<=>curious(X)))&
(((~creative(mary)&~calm(mary)))<=>(?[X]:((~happy(X)&~funny(X)))))&
((wise(paul))=>(?[X]:((happy(X)<~>~calm(X)))))&
(![X]:((~kind(X)&humble(X))<=>(patient(X)&generous(X))))&
(![X]:((old(X)|brave(X))=>(funny(X)<~>brave(X))))&
(((calm(alice)&funny(alice)))=>(curious(susan)))&
(![X]:(~patient(X)<=>~kind(X)))&
(![X]:((~curious(X)<~>humble(X))=>~patient(X)))&
((funny(mary))=>((funny(fred)<~>brave(fred))))&
((?[X]:((~curious(X)<~>brave(X))))=>((~humble(john)<~>calm(john))))&
(![X]:(wise(X)<=>(~creative(X)|~strong(X))))&
(![X]:((wise(X)<~>~patient(X))=>(curious(X)|~calm(X))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((curious(X)<~>humble(X)))))&
(![X]:((patient(X)<~>~kind(X))=>(~brave(X)&~creative(X))))&
(((humble(susan)&happy(susan)))<=>(?[X]:((calm(X)|~curious(X)))))&
(![X]:((~rich(X)|humble(X))=>wise(X)))&
((strong(john)&happy(john)))&
(calm(lucy))&
((wise(lucy)&quiet(lucy)))&
(curious(mary))&
((~curious(lucy)<~>~wise(lucy)))&
(rich(john)) | creative(fred) | [
"p6",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1874991024502186543576538
% SZS output start Proof for 1874991024502186543576538
7. ! [X0] : (~patient(X0) <=> ~kind(X0)) [input p6]
14. ! [X0] : ((patient(X0) <~> ~kind(X0)) => (~creative(X0) & ~brave(X0))) [input p13]
23. creative(fred) [input hypothesis]
38. ! [X0] : ((~creative(X0) & ~brave(X0)) | (patient(X0) <=> ~kind(X0))) [ennf transformation 14]
53. ! [X0] : ((~patient(X0) | kind(X0)) & (~kind(X0) | patient(X0))) [nnf transformation 7]
64. ! [X0] : ((~creative(X0) & ~brave(X0)) | ((patient(X0) | kind(X0)) & (~kind(X0) | ~patient(X0)))) [nnf transformation 38]
87. ~kind(X0) | patient(X0) [cnf transformation 53]
88. ~patient(X0) | kind(X0) [cnf transformation 53]
106. ~creative(X0) | ~kind(X0) | ~patient(X0) [cnf transformation 64]
107. ~creative(X0) | patient(X0) | kind(X0) [cnf transformation 64]
122. creative(fred) [cnf transformation 23]
218. ~creative(X0) | patient(X0) [subsumption resolution 107,87]
219. ~creative(X0) | ~patient(X0) [subsumption resolution 106,88]
220. ~creative(X0) [subsumption resolution 219,218]
252. $false [subsumption resolution 122,220]
% SZS output end Proof for 1874991024502186543576538
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or brave is both strong and not brave.
If someone is wise or brave then susan is funny and vice versa.
If paul is not rich then someone is both not creative and creative and vice versa.
Everyone who is not rich is both not old and not patient.
If someone is both not funny and not kind then alice is both not creative and not old.
Everyone who is both not humble and curious is not funny or not strong and vice versa.
Everyone who is creative or not patient is funny and vice versa.
If someone is curious then paul is strong and vice versa.
Everyone who is either brave or happy is either quiet or not curious.
If mary is not rich or not creative then someone is old and vice versa.
Everyone who is either wise or kind is brave or humble and vice versa.
If someone is happy then john is happy or tall and vice versa.
If someone is not tall or not old then lucy is not patient and vice versa.
If paul is not funny then lucy is either not happy or calm.
If someone is either humble or rich then lucy is patient or brave.
Everyone who is not happy or brave is not kind and vice versa.
Someone is either kind or generous.
Susan is both calm and not creative.
Paul is not quiet or brave.
Lucy is not rich or not wise.
Someone is both not generous and not happy.
Lucy is patient.
Someone is funny.
Alice is not brave or not patient. | Susan is tall. | entailment | (![X]:((old(X)|brave(X))=>(strong(X)&~brave(X))))&
((?[X]:((wise(X)|brave(X))))<=>(funny(susan)))&
((~rich(paul))<=>(?[X]:((~creative(X)&creative(X)))))&
(![X]:(~rich(X)=>(~old(X)&~patient(X))))&
((?[X]:((~funny(X)&~kind(X))))=>((~creative(alice)&~old(alice))))&
(![X]:((~humble(X)&curious(X))<=>(~funny(X)|~strong(X))))&
(![X]:((creative(X)|~patient(X))<=>funny(X)))&
((?[X]:(curious(X)))<=>(strong(paul)))&
(![X]:((brave(X)<~>happy(X))=>(quiet(X)<~>~curious(X))))&
(((~rich(mary)|~creative(mary)))<=>(?[X]:(old(X))))&
(![X]:((wise(X)<~>kind(X))<=>(brave(X)|humble(X))))&
((?[X]:(happy(X)))<=>((happy(john)|tall(john))))&
((?[X]:((~tall(X)|~old(X))))<=>(~patient(lucy)))&
((~funny(paul))=>((~happy(lucy)<~>calm(lucy))))&
((?[X]:((humble(X)<~>rich(X))))=>((patient(lucy)|brave(lucy))))&
(![X]:((~happy(X)|brave(X))<=>~kind(X)))&
(?[X]:((kind(X)<~>generous(X))))&
((calm(susan)&~creative(susan)))&
((~quiet(paul)|brave(paul)))&
((~rich(lucy)|~wise(lucy)))&
(?[X]:((~generous(X)&~happy(X))))&
(patient(lucy))&
(?[X]:(funny(X)))&
((~brave(alice)|~patient(alice))) | tall(susan) | [
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 63006326110776833450691
% SZS output start Proof for 63006326110776833450691
13. ? [X0] : (~old(X0) | ~tall(X0)) <=> ~patient(lucy) [input p12]
22. patient(lucy) [input p21]
25. ~tall(susan) [input hypothesis]
62. (? [X0] : (~old(X0) | ~tall(X0)) | patient(lucy)) & (~patient(lucy) | ! [X0] : (old(X0) & tall(X0))) [nnf transformation 13]
63. (? [X0] : (~old(X0) | ~tall(X0)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (old(X1) & tall(X1))) [rectify 62]
64. ? [X0] : (~old(X0) | ~tall(X0)) => (~old(sK5) | ~tall(sK5)) [choice axiom]
65. ((~old(sK5) | ~tall(sK5)) | patient(lucy)) & (~patient(lucy) | ! [X1] : (old(X1) & tall(X1))) [skolemisation 63,64]
117. ~patient(lucy) | tall(X1) [cnf transformation 65]
135. patient(lucy) [cnf transformation 22]
138. ~tall(susan) [cnf transformation 25]
231. 20 <=> patient(lucy) [avatar definition]
248. 24 <=> ! [X1] : tall(X1) [avatar definition]
249. tall(X1) <- (24) [avatar component clause 248]
250. 24 | ~20 [avatar split clause 117,231,248]
296. 20 [avatar split clause 135,231]
301. $false <- (24) [resolution 249,138]
302. ~24 [avatar contradiction clause 301]
303. $false [avatar sat refutation 250,296,302]
% SZS output end Proof for 63006326110776833450691
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is either humble or not patient and vice versa. Everyone who is not tall or not generous is either not curious or not tall. If lucy is kind or not quiet then lucy is patient or humble. Everyone who is calm is both brave and funny and vice versa. If paul is both funny and not calm then someone is not patient. Everyone who is calm is both not curious and creative. If alice is both calm and not strong then someone is both not quiet and not brave. Everyone who is not strong or strong is both wise and not patient. If john is both brave and not generous then susan is either not creative or humble. Everyone who is either brave or not happy is not creative or old and vice versa. If paul is both not generous and not curious then someone is either wise or not happy. If someone is either not curious or patient then paul is not calm and vice versa. Everyone who is either not old or patient is both not happy and not kind. Everyone who is not patient is both happy and kind and vice versa. If lucy is calm then someone is calm or funny. Fred is either happy or not tall. Mary is strong or not tall. | Mary is kind. | entailment | (![X]:(calm(X)<=>(humble(X)<~>~patient(X))))&
(![X]:((~tall(X)|~generous(X))=>(~curious(X)<~>~tall(X))))&
(((kind(lucy)|~quiet(lucy)))=>((patient(lucy)|humble(lucy))))&
(![X]:(calm(X)<=>(brave(X)&funny(X))))&
(((funny(paul)&~calm(paul)))=>(?[X]:(~patient(X))))&
(![X]:(calm(X)=>(~curious(X)&creative(X))))&
(((calm(alice)&~strong(alice)))=>(?[X]:((~quiet(X)&~brave(X)))))&
(![X]:((~strong(X)|strong(X))=>(wise(X)&~patient(X))))&
(((brave(john)&~generous(john)))=>((~creative(susan)<~>humble(susan))))&
(![X]:((brave(X)<~>~happy(X))<=>(~creative(X)|old(X))))&
(((~generous(paul)&~curious(paul)))=>(?[X]:((wise(X)<~>~happy(X)))))&
((?[X]:((~curious(X)<~>patient(X))))<=>(~calm(paul)))&
(![X]:((~old(X)<~>patient(X))=>(~happy(X)&~kind(X))))&
(![X]:(~patient(X)<=>(happy(X)&kind(X))))&
((calm(lucy))=>(?[X]:((calm(X)|funny(X)))))&
((happy(fred)<~>~tall(fred)))&
((strong(mary)|~tall(mary))) | kind(mary) | [
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2682591971437601484606882
% SZS output start Proof for 2682591971437601484606882
8. ! [X0] : ((strong(X0) | ~strong(X0)) => (~patient(X0) & wise(X0))) [input p7]
14. ! [X0] : (~patient(X0) <=> (kind(X0) & happy(X0))) [input p13]
18. ~kind(mary) [input hypothesis]
22. ! [X0] : ((strong(X0) | ~strong(X0)) => ~patient(X0)) [pure predicate removal 8]
31. ! [X0] : (~patient(X0) | (~strong(X0) & strong(X0))) [ennf transformation 22]
49. ! [X0] : ((~patient(X0) | (~kind(X0) | ~happy(X0))) & ((kind(X0) & happy(X0)) | patient(X0))) [nnf transformation 14]
50. ! [X0] : ((~patient(X0) | ~kind(X0) | ~happy(X0)) & ((kind(X0) & happy(X0)) | patient(X0))) [flattening 49]
70. ~patient(X0) | strong(X0) [cnf transformation 31]
71. ~patient(X0) | ~strong(X0) [cnf transformation 31]
87. kind(X0) | patient(X0) [cnf transformation 50]
93. ~kind(mary) [cnf transformation 18]
144. ~patient(X0) [subsumption resolution 70,71]
158. kind(X0) [subsumption resolution 87,144]
180. $false [subsumption resolution 93,158]
% SZS output end Proof for 2682591971437601484606882
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either tall or strong then someone is calm or not patient and vice versa.
If someone is not generous or not tall then susan is both funny and tall and vice versa.
If lucy is not kind then alice is kind.
Everyone who is not happy or calm is either not creative or not brave.
If fred is rich or not rich then someone is quiet or not calm.
Everyone who is curious is brave or humble.
Everyone who is not wise is tall or not kind.
If someone is both tall and not brave then fred is both not curious and patient.
If lucy is calm then someone is either not happy or funny and vice versa.
Everyone who is not rich or not kind is kind and vice versa.
If susan is strong then someone is wise or humble.
If someone is both not happy and calm then someone is either not calm or rich.
Everyone who is either not humble or calm is patient and vice versa.
If someone is both not funny and rich then susan is either humble or not brave and vice versa.
If lucy is not rich then john is not wise and vice versa.
Everyone who is either not brave or not humble is either not brave or wise.
Someone is strong or kind.
Lucy is either calm or not humble.
Paul is either old or not old.
Fred is both tall and not calm.
Someone is both not patient and not wise.
Lucy is both not tall and not rich.
Alice is both not patient and strong. | Lucy is patient. | entailment | ((?[X]:((tall(X)<~>strong(X))))<=>(?[X]:((calm(X)|~patient(X)))))&
((?[X]:((~generous(X)|~tall(X))))<=>((funny(susan)&tall(susan))))&
((~kind(lucy))=>(kind(alice)))&
(![X]:((~happy(X)|calm(X))=>(~creative(X)<~>~brave(X))))&
(((rich(fred)|~rich(fred)))=>(?[X]:((quiet(X)|~calm(X)))))&
(![X]:(curious(X)=>(brave(X)|humble(X))))&
(![X]:(~wise(X)=>(tall(X)|~kind(X))))&
((?[X]:((tall(X)&~brave(X))))=>((~curious(fred)&patient(fred))))&
((calm(lucy))<=>(?[X]:((~happy(X)<~>funny(X)))))&
(![X]:((~rich(X)|~kind(X))<=>kind(X)))&
((strong(susan))=>(?[X]:((wise(X)|humble(X)))))&
((?[X]:((~happy(X)&calm(X))))=>(?[X]:((~calm(X)<~>rich(X)))))&
(![X]:((~humble(X)<~>calm(X))<=>patient(X)))&
((?[X]:((~funny(X)&rich(X))))<=>((humble(susan)<~>~brave(susan))))&
((~rich(lucy))<=>(~wise(john)))&
(![X]:((~brave(X)<~>~humble(X))=>(~brave(X)<~>wise(X))))&
(?[X]:((strong(X)|kind(X))))&
((calm(lucy)<~>~humble(lucy)))&
((old(paul)<~>~old(paul)))&
((tall(fred)&~calm(fred)))&
(?[X]:((~patient(X)&~wise(X))))&
((~tall(lucy)&~rich(lucy)))&
((~patient(alice)&strong(alice))) | patient(lucy) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 753293120407019167668085
% SZS output start Proof for 753293120407019167668085
13. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> patient(X0)) [input p12]
18. calm(lucy) <~> ~humble(lucy) [input p17]
24. ~patient(lucy) [input hypothesis]
61. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | ~patient(X0)) & (patient(X0) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 13]
70. (humble(lucy) | ~calm(lucy)) & (~humble(lucy) | calm(lucy)) [nnf transformation 18]
102. humble(X0) | calm(X0) | patient(X0) [cnf transformation 61]
103. ~humble(X0) | patient(X0) | ~calm(X0) [cnf transformation 61]
119. ~humble(lucy) | calm(lucy) [cnf transformation 70]
120. humble(lucy) | ~calm(lucy) [cnf transformation 70]
131. ~patient(lucy) [cnf transformation 24]
218. 20 <=> calm(lucy) [avatar definition]
219. ~calm(lucy) <- (~20) [avatar component clause 218]
220. calm(lucy) <- (20) [avatar component clause 218]
298. 37 <=> humble(lucy) [avatar definition]
299. ~humble(lucy) <- (~37) [avatar component clause 298]
300. humble(lucy) <- (37) [avatar component clause 298]
301. ~20 | 37 [avatar split clause 120,298,218]
302. 20 | ~37 [avatar split clause 119,298,218]
349. calm(lucy) | patient(lucy) <- (~37) [resolution 102,299]
359. patient(lucy) <- (~20, ~37) [subsumption resolution 349,219]
360. $false <- (~20, ~37) [subsumption resolution 359,131]
361. 20 | 37 [avatar contradiction clause 360]
377. patient(lucy) | ~calm(lucy) <- (37) [resolution 103,300]
379. ~calm(lucy) <- (37) [subsumption resolution 377,131]
380. $false <- (20, 37) [subsumption resolution 379,220]
381. ~20 | ~37 [avatar contradiction clause 380]
382. $false [avatar sat refutation 301,302,361,381]
% SZS output end Proof for 753293120407019167668085
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or curious then someone is either old or humble and vice versa.
Everyone who is old is either kind or calm and vice versa.
Everyone who is not old or generous is either not generous or not strong.
If someone is not creative or not quiet then lucy is both not patient and not generous and vice versa.
Everyone who is not calm is not humble or old and vice versa.
Everyone who is both kind and creative is both not tall and not humble and vice versa.
If someone is either not tall or not patient then fred is kind or humble.
Everyone who is not strong or quiet is not calm and vice versa.
If someone is either calm or curious then someone is both generous and curious.
If john is generous or not creative then paul is both not kind and not calm.
If mary is both strong and not brave then alice is either not humble or rich and vice versa.
Everyone who is not generous is either patient or not generous and vice versa.
Everyone who is not quiet is not patient.
If someone is brave then susan is both not strong and not funny and vice versa.
If lucy is rich then someone is either not tall or not old.
Someone is either not calm or not creative.
Someone is not humble.
Someone is both not brave and generous.
Someone is not calm.
Alice is either not strong or funny. | Alice is not kind. | neutral | ((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((old(X)<~>humble(X)))))&
(![X]:(old(X)<=>(kind(X)<~>calm(X))))&
(![X]:((~old(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~creative(X)|~quiet(X))))<=>((~patient(lucy)&~generous(lucy))))&
(![X]:(~calm(X)<=>(~humble(X)|old(X))))&
(![X]:((kind(X)&creative(X))<=>(~tall(X)&~humble(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(fred)|humble(fred))))&
(![X]:((~strong(X)|quiet(X))<=>~calm(X)))&
((?[X]:((calm(X)<~>curious(X))))=>(?[X]:((generous(X)&curious(X)))))&
(((generous(john)|~creative(john)))=>((~kind(paul)&~calm(paul))))&
(((strong(mary)&~brave(mary)))<=>((~humble(alice)<~>rich(alice))))&
(![X]:(~generous(X)<=>(patient(X)<~>~generous(X))))&
(![X]:(~quiet(X)=>~patient(X)))&
((?[X]:(brave(X)))<=>((~strong(susan)&~funny(susan))))&
((rich(lucy))=>(?[X]:((~tall(X)<~>~old(X)))))&
(?[X]:((~calm(X)<~>~creative(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:(~calm(X)))&
((~strong(alice)<~>funny(alice))) | ~kind(alice) | [] | null | 0 |
If lucy is patient or not humble then someone is not brave or curious and vice versa.
If someone is creative then susan is either strong or calm and vice versa.
If someone is both not calm and rich then someone is not strong.
If alice is either rich or not humble then susan is not strong or not generous and vice versa.
If mary is both generous and kind then mary is happy or not calm.
If fred is creative then someone is both old and not rich and vice versa.
Everyone who is both creative and not curious is not strong or wise.
If lucy is either not humble or not tall then john is either not creative or not rich and vice versa.
Everyone who is not wise or not funny is either generous or patient and vice versa.
If someone is quiet or not calm then someone is either happy or not wise.
Everyone who is either humble or not strong is not funny or quiet.
If someone is either not tall or old then someone is not calm or not humble.
Everyone who is not quiet or not generous is not creative or wise and vice versa.
Everyone who is either generous or wise is either happy or strong.
Everyone who is quiet or kind is generous.
Everyone who is not wise or not calm is not quiet.
Paul is both humble and not curious.
Fred is either not rich or humble.
Someone is both wise and not rich.
Fred is either patient or quiet. | John is not happy. | neutral | (((patient(lucy)|~humble(lucy)))<=>(?[X]:((~brave(X)|curious(X)))))&
((?[X]:(creative(X)))<=>((strong(susan)<~>calm(susan))))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:(~strong(X))))&
(((rich(alice)<~>~humble(alice)))<=>((~strong(susan)|~generous(susan))))&
(((generous(mary)&kind(mary)))=>((happy(mary)|~calm(mary))))&
((creative(fred))<=>(?[X]:((old(X)&~rich(X)))))&
(![X]:((creative(X)&~curious(X))=>(~strong(X)|wise(X))))&
(((~humble(lucy)<~>~tall(lucy)))<=>((~creative(john)<~>~rich(john))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)<~>patient(X))))&
((?[X]:((quiet(X)|~calm(X))))=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((humble(X)<~>~strong(X))=>(~funny(X)|quiet(X))))&
((?[X]:((~tall(X)<~>old(X))))=>(?[X]:((~calm(X)|~humble(X)))))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|wise(X))))&
(![X]:((generous(X)<~>wise(X))=>(happy(X)<~>strong(X))))&
(![X]:((quiet(X)|kind(X))=>generous(X)))&
(![X]:((~wise(X)|~calm(X))=>~quiet(X)))&
((humble(paul)&~curious(paul)))&
((~rich(fred)<~>humble(fred)))&
(?[X]:((wise(X)&~rich(X))))&
((patient(fred)<~>quiet(fred))) | ~happy(john) | [] | null | 0 |
If alice is either old or not tall then someone is both patient and not happy. If someone is not wise or calm then john is either rich or not happy and vice versa. Everyone who is not rich or not old is both generous and patient. Everyone who is generous or strong is curious or not humble and vice versa. If someone is creative or not strong then mary is either not wise or not generous and vice versa. Everyone who is both patient and brave is not strong or calm. Everyone who is not strong or rich is creative. Everyone who is old or not happy is brave or not calm and vice versa. If someone is happy or not calm then mary is tall or strong and vice versa. If someone is funny or not kind then someone is either wise or rich. If someone is both not funny and funny then someone is either not old or not creative. Everyone who is tall is both not wise and not patient. If lucy is not generous or not funny then someone is either humble or brave and vice versa. Everyone who is not tall is curious or not old. Everyone who is not calm is both not rich and not curious. If someone is both not old and curious then someone is either not funny or generous. Alice is both not wise and not brave. Someone is old or brave. Mary is either humble or not humble. Someone is funny. Someone is tall. Someone is wise or not funny. Someone is quiet. Susan is either not tall or creative. | Alice is generous. | entailment | (((old(alice)<~>~tall(alice)))=>(?[X]:((patient(X)&~happy(X)))))&
((?[X]:((~wise(X)|calm(X))))<=>((rich(john)<~>~happy(john))))&
(![X]:((~rich(X)|~old(X))=>(generous(X)&patient(X))))&
(![X]:((generous(X)|strong(X))<=>(curious(X)|~humble(X))))&
((?[X]:((creative(X)|~strong(X))))<=>((~wise(mary)<~>~generous(mary))))&
(![X]:((patient(X)&brave(X))=>(~strong(X)|calm(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
(![X]:((old(X)|~happy(X))<=>(brave(X)|~calm(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((tall(mary)|strong(mary))))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:(tall(X)=>(~wise(X)&~patient(X))))&
(((~generous(lucy)|~funny(lucy)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(![X]:(~calm(X)=>(~rich(X)&~curious(X))))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((~funny(X)<~>generous(X)))))&
((~wise(alice)&~brave(alice)))&
(?[X]:((old(X)|brave(X))))&
((humble(mary)<~>~humble(mary)))&
(?[X]:(funny(X)))&
(?[X]:(tall(X)))&
(?[X]:((wise(X)|~funny(X))))&
(?[X]:(quiet(X)))&
((~tall(susan)<~>creative(susan))) | generous(alice) | [
"p2",
"p7",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5154161146274054390140377
% SZS output start Proof for 5154161146274054390140377
3. ! [X0] : ((~old(X0) | ~rich(X0)) => (patient(X0) & generous(X0))) [input p2]
8. ! [X0] : ((~happy(X0) | old(X0)) <=> (~calm(X0) | brave(X0))) [input p7]
15. ! [X0] : (~calm(X0) => (~curious(X0) & ~rich(X0))) [input p14]
17. ~brave(alice) & ~wise(alice) [input p16]
25. ~generous(alice) [input hypothesis]
32. ! [X0] : ((patient(X0) & generous(X0)) | (old(X0) & rich(X0))) [ennf transformation 3]
41. ! [X0] : ((~curious(X0) & ~rich(X0)) | calm(X0)) [ennf transformation 15]
56. ! [X0] : (((~happy(X0) | old(X0)) | (calm(X0) & ~brave(X0))) & ((~calm(X0) | brave(X0)) | (happy(X0) & ~old(X0)))) [nnf transformation 8]
57. ! [X0] : ((~happy(X0) | old(X0) | (calm(X0) & ~brave(X0))) & (~calm(X0) | brave(X0) | (happy(X0) & ~old(X0)))) [flattening 56]
100. generous(X0) | rich(X0) [cnf transformation 32]
101. generous(X0) | old(X0) [cnf transformation 32]
117. ~calm(X0) | brave(X0) | ~old(X0) [cnf transformation 57]
138. ~rich(X0) | calm(X0) [cnf transformation 41]
143. ~brave(alice) [cnf transformation 17]
152. ~generous(alice) [cnf transformation 25]
158. 2 <=> old(alice) [avatar definition]
339. rich(alice) [resolution 100,152]
341. old(alice) [resolution 101,152]
353. calm(alice) [resolution 138,339]
362. brave(alice) | ~old(alice) [resolution 117,353]
364. ~old(alice) [subsumption resolution 362,143]
368. ~2 [avatar split clause 364,158]
369. 2 [avatar split clause 341,158]
370. $false [avatar sat refutation 368,369]
% SZS output end Proof for 5154161146274054390140377
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not kind is both not humble and not happy and vice versa.
Everyone who is both brave and not old is either calm or not curious and vice versa.
If someone is either not creative or tall then mary is generous.
Everyone who is either generous or not generous is humble or not kind.
Everyone who is not happy is not strong and vice versa.
Everyone who is calm is both calm and not strong.
Everyone who is either kind or tall is not quiet or not old.
If mary is curious or not kind then john is not quiet or wise and vice versa.
Everyone who is not kind or not tall is both not generous and happy and vice versa.
If someone is either not curious or not brave then someone is not quiet or not happy and vice versa.
Everyone who is rich is not humble or not calm and vice versa.
Everyone who is strong is not curious or kind and vice versa.
Everyone who is both not happy and not humble is not tall and vice versa.
If john is not brave or generous then someone is either tall or creative.
Paul is either creative or strong.
Alice is not patient or creative.
Someone is either not tall or not curious. | Paul is not calm. | entailment | (![X]:((curious(X)|~kind(X))<=>(~humble(X)&~happy(X))))&
(![X]:((brave(X)&~old(X))<=>(calm(X)<~>~curious(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>(generous(mary)))&
(![X]:((generous(X)<~>~generous(X))=>(humble(X)|~kind(X))))&
(![X]:(~happy(X)<=>~strong(X)))&
(![X]:(calm(X)=>(calm(X)&~strong(X))))&
(![X]:((kind(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(((curious(mary)|~kind(mary)))<=>((~quiet(john)|wise(john))))&
(![X]:((~kind(X)|~tall(X))<=>(~generous(X)&happy(X))))&
((?[X]:((~curious(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)|~happy(X)))))&
(![X]:(rich(X)<=>(~humble(X)|~calm(X))))&
(![X]:(strong(X)<=>(~curious(X)|kind(X))))&
(![X]:((~happy(X)&~humble(X))<=>~tall(X)))&
(((~brave(john)|generous(john)))=>(?[X]:((tall(X)<~>creative(X)))))&
((creative(paul)<~>strong(paul)))&
((~patient(alice)|creative(alice)))&
(?[X]:((~tall(X)<~>~curious(X)))) | ~calm(paul) | [
"p0",
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6473433345957136911782469
% SZS output start Proof for 6473433345957136911782469
1. ! [X0] : ((~kind(X0) | curious(X0)) <=> (~happy(X0) & ~humble(X0))) [input p0]
6. ! [X0] : (calm(X0) => (~strong(X0) & calm(X0))) [input p5]
9. ! [X0] : ((~tall(X0) | ~kind(X0)) <=> (happy(X0) & ~generous(X0))) [input p8]
12. ! [X0] : (strong(X0) <=> (kind(X0) | ~curious(X0))) [input p11]
18. calm(paul) [input hypothesis]
24. ! [X0] : ((~strong(X0) & calm(X0)) | ~calm(X0)) [ennf transformation 6]
28. ! [X0] : (((~kind(X0) | curious(X0)) | (happy(X0) | humble(X0))) & ((~happy(X0) & ~humble(X0)) | (kind(X0) & ~curious(X0)))) [nnf transformation 1]
29. ! [X0] : ((~kind(X0) | curious(X0) | happy(X0) | humble(X0)) & ((~happy(X0) & ~humble(X0)) | (kind(X0) & ~curious(X0)))) [flattening 28]
38. ! [X0] : (((~tall(X0) | ~kind(X0)) | (~happy(X0) | generous(X0))) & ((happy(X0) & ~generous(X0)) | (tall(X0) & kind(X0)))) [nnf transformation 9]
39. ! [X0] : ((~tall(X0) | ~kind(X0) | ~happy(X0) | generous(X0)) & ((happy(X0) & ~generous(X0)) | (tall(X0) & kind(X0)))) [flattening 38]
45. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & ((kind(X0) | ~curious(X0)) | ~strong(X0))) [nnf transformation 12]
46. ! [X0] : ((strong(X0) | (~kind(X0) & curious(X0))) & (kind(X0) | ~curious(X0) | ~strong(X0))) [flattening 45]
59. ~happy(X0) | kind(X0) [cnf transformation 29]
74. ~strong(X0) | ~calm(X0) [cnf transformation 24]
83. happy(X0) | kind(X0) [cnf transformation 39]
94. strong(X0) | ~kind(X0) [cnf transformation 46]
106. calm(paul) [cnf transformation 18]
143. kind(X0) [subsumption resolution 83,59]
178. strong(X0) [subsumption resolution 94,143]
210. ~calm(X0) [resolution 74,178]
212. $false [resolution 210,106]
% SZS output end Proof for 6473433345957136911782469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or not strong is curious and vice versa. Everyone who is not rich is funny. Everyone who is either not old or calm is humble. Everyone who is either not brave or kind is both wise and not wise. Everyone who is patient or creative is not happy and vice versa. Everyone who is both happy and rich is not wise or not tall and vice versa. Everyone who is not strong or not brave is both not kind and tall and vice versa. Everyone who is rich or not brave is tall and vice versa. Everyone who is not wise is either not tall or old and vice versa. Everyone who is either not kind or happy is not happy or not calm. If john is both tall and curious then someone is both rich and wise. If someone is creative then someone is happy and vice versa. Everyone who is not old or creative is wise. If mary is patient or not generous then paul is both not happy and creative and vice versa. If someone is kind or not humble then fred is either not kind or old and vice versa. If someone is both not wise and not humble then someone is patient or calm and vice versa. Mary is strong or tall. Alice is creative or not generous. Susan is not rich or not creative. John is not generous. Susan is strong or not patient. Someone is happy or wise. Alice is both generous and funny. | Susan is old. | entailment | (![X]:((calm(X)|~strong(X))<=>curious(X)))&
(![X]:(~rich(X)=>funny(X)))&
(![X]:((~old(X)<~>calm(X))=>humble(X)))&
(![X]:((~brave(X)<~>kind(X))=>(wise(X)&~wise(X))))&
(![X]:((patient(X)|creative(X))<=>~happy(X)))&
(![X]:((happy(X)&rich(X))<=>(~wise(X)|~tall(X))))&
(![X]:((~strong(X)|~brave(X))<=>(~kind(X)&tall(X))))&
(![X]:((rich(X)|~brave(X))<=>tall(X)))&
(![X]:(~wise(X)<=>(~tall(X)<~>old(X))))&
(![X]:((~kind(X)<~>happy(X))=>(~happy(X)|~calm(X))))&
(((tall(john)&curious(john)))=>(?[X]:((rich(X)&wise(X)))))&
((?[X]:(creative(X)))<=>(?[X]:(happy(X))))&
(![X]:((~old(X)|creative(X))=>wise(X)))&
(((patient(mary)|~generous(mary)))<=>((~happy(paul)&creative(paul))))&
((?[X]:((kind(X)|~humble(X))))<=>((~kind(fred)<~>old(fred))))&
((?[X]:((~wise(X)&~humble(X))))<=>(?[X]:((patient(X)|calm(X)))))&
((strong(mary)|tall(mary)))&
((creative(alice)|~generous(alice)))&
((~rich(susan)|~creative(susan)))&
(~generous(john))&
((strong(susan)|~patient(susan)))&
(?[X]:((happy(X)|wise(X))))&
((generous(alice)&funny(alice))) | old(susan) | [
"p3",
"p4",
"p5",
"p6",
"p7",
"p8",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5669515563416034543202060
% SZS output start Proof for 5669515563416034543202060
4. ! [X0] : ((~brave(X0) <~> kind(X0)) => (~wise(X0) & wise(X0))) [input p3]
5. ! [X0] : ((creative(X0) | patient(X0)) <=> ~happy(X0)) [input p4]
6. ! [X0] : ((rich(X0) & happy(X0)) <=> (~tall(X0) | ~wise(X0))) [input p5]
7. ! [X0] : ((~brave(X0) | ~strong(X0)) <=> (tall(X0) & ~kind(X0))) [input p6]
8. ! [X0] : ((~brave(X0) | rich(X0)) <=> tall(X0)) [input p7]
9. ! [X0] : (~wise(X0) <=> (~tall(X0) <~> old(X0))) [input p8]
19. ~creative(susan) | ~rich(susan) [input p18]
21. ~patient(susan) | strong(susan) [input p20]
24. ~old(susan) [input hypothesis]
32. ! [X0] : ((~wise(X0) & wise(X0)) | (~brave(X0) <=> kind(X0))) [ennf transformation 4]
39. ! [X0] : ((~wise(X0) & wise(X0)) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0)))) [nnf transformation 32]
40. ! [X0] : (((creative(X0) | patient(X0)) | happy(X0)) & (~happy(X0) | (~creative(X0) & ~patient(X0)))) [nnf transformation 5]
41. ! [X0] : ((creative(X0) | patient(X0) | happy(X0)) & (~happy(X0) | (~creative(X0) & ~patient(X0)))) [flattening 40]
42. ! [X0] : (((rich(X0) & happy(X0)) | (tall(X0) & wise(X0))) & ((~tall(X0) | ~wise(X0)) | (~rich(X0) | ~happy(X0)))) [nnf transformation 6]
43. ! [X0] : (((rich(X0) & happy(X0)) | (tall(X0) & wise(X0))) & (~tall(X0) | ~wise(X0) | ~rich(X0) | ~happy(X0))) [flattening 42]
44. ! [X0] : (((~brave(X0) | ~strong(X0)) | (~tall(X0) | kind(X0))) & ((tall(X0) & ~kind(X0)) | (brave(X0) & strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((~brave(X0) | ~strong(X0) | ~tall(X0) | kind(X0)) & ((tall(X0) & ~kind(X0)) | (brave(X0) & strong(X0)))) [flattening 44]
46. ! [X0] : (((~brave(X0) | rich(X0)) | ~tall(X0)) & (tall(X0) | (brave(X0) & ~rich(X0)))) [nnf transformation 8]
47. ! [X0] : ((~brave(X0) | rich(X0) | ~tall(X0)) & (tall(X0) | (brave(X0) & ~rich(X0)))) [flattening 46]
48. ! [X0] : ((~wise(X0) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0)))) & (((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | wise(X0))) [nnf transformation 9]
74. wise(X0) | kind(X0) | brave(X0) [cnf transformation 39]
75. wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 39]
76. ~wise(X0) | kind(X0) | brave(X0) [cnf transformation 39]
77. ~wise(X0) | ~brave(X0) | ~kind(X0) [cnf transformation 39]
80. happy(X0) | patient(X0) | creative(X0) [cnf transformation 41]
81. ~tall(X0) | ~wise(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 43]
85. tall(X0) | rich(X0) [cnf transformation 43]
87. ~kind(X0) | brave(X0) [cnf transformation 45]
88. tall(X0) | strong(X0) [cnf transformation 45]
90. ~brave(X0) | ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 45]
91. tall(X0) | ~rich(X0) [cnf transformation 47]
93. ~brave(X0) | rich(X0) | ~tall(X0) [cnf transformation 47]
94. old(X0) | ~tall(X0) | wise(X0) [cnf transformation 48]
124. ~creative(susan) | ~rich(susan) [cnf transformation 19]
126. ~patient(susan) | strong(susan) [cnf transformation 21]
129. ~old(susan) [cnf transformation 24]
131. ~kind(X0) | ~brave(X0) [subsumption resolution 75,77]
132. kind(X0) | brave(X0) [subsumption resolution 74,76]
133. ~tall(X0) | ~strong(X0) | kind(X0) [subsumption resolution 90,132]
134. ~kind(X0) [subsumption resolution 87,131]
135. ~brave(X0) | rich(X0) [subsumption resolution 93,85]
136. tall(X0) [subsumption resolution 91,85]
138. wise(X0) | old(X0) [subsumption resolution 94,136]
249. 24 <=> rich(susan) [avatar definition]
251. ~rich(susan) <- (~24) [avatar component clause 249]
253. 25 <=> creative(susan) [avatar definition]
255. ~creative(susan) <- (~25) [avatar component clause 253]
256. ~24 | ~25 [avatar split clause 124,253,249]
258. 26 <=> strong(susan) [avatar definition]
260. strong(susan) <- (26) [avatar component clause 258]
262. 27 <=> patient(susan) [avatar definition]
264. ~patient(susan) <- (~27) [avatar component clause 262]
265. 26 | ~27 [avatar split clause 126,262,258]
282. brave(X1) [resolution 132,134]
283. rich(X0) [resolution 135,282]
324. ~strong(X4) | kind(X4) [resolution 133,136]
326. ~strong(X4) [subsumption resolution 324,134]
333. ~wise(X1) | ~rich(X1) | ~happy(X1) | strong(X1) [resolution 81,88]
337. ~wise(X1) | ~happy(X1) | strong(X1) [subsumption resolution 333,283]
338. ~happy(X1) | ~wise(X1) [subsumption resolution 337,326]
340. ~wise(X0) | patient(X0) | creative(X0) [resolution 338,80]
371. creative(X0) | patient(X0) | old(X0) [resolution 340,138]
388. patient(susan) | old(susan) <- (~25) [resolution 371,255]
391. old(susan) <- (~25, ~27) [subsumption resolution 388,264]
392. $false <- (~25, ~27) [subsumption resolution 391,129]
393. 25 | 27 [avatar contradiction clause 392]
394. $false <- (~24) [subsumption resolution 251,283]
395. 24 [avatar contradiction clause 394]
396. $false <- (26) [subsumption resolution 260,326]
397. ~26 [avatar contradiction clause 396]
398. $false [avatar sat refutation 256,265,393,395,397]
% SZS output end Proof for 5669515563416034543202060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is humble or patient and vice versa.
Everyone who is not old is brave or not generous and vice versa.
If lucy is both rich and kind then someone is both not brave and generous.
Everyone who is either curious or not quiet is strong or not quiet and vice versa.
Everyone who is both creative and strong is humble.
Everyone who is creative or not kind is both not quiet and generous and vice versa.
Everyone who is both not old and strong is not strong or not happy and vice versa.
If someone is either creative or humble then paul is both not tall and not quiet and vice versa.
If paul is not quiet then someone is not creative and vice versa.
Everyone who is both not curious and not happy is not happy or tall.
Everyone who is calm is not patient and vice versa.
Everyone who is both wise and not humble is both humble and generous.
If someone is not curious or kind then someone is either not happy or not strong and vice versa.
Everyone who is both not humble and humble is quiet.
If someone is not calm then fred is generous and vice versa.
If susan is both funny and not creative then lucy is not brave and vice versa.
Lucy is either not wise or creative.
Someone is not brave.
Someone is not brave or brave.
Someone is not funny or not tall.
Someone is both quiet and patient.
Someone is not humble or not kind.
Paul is not kind or not generous.
Paul is not calm or quiet. | Paul is brave. | entailment | (![X]:(brave(X)<=>(humble(X)|patient(X))))&
(![X]:(~old(X)<=>(brave(X)|~generous(X))))&
(((rich(lucy)&kind(lucy)))=>(?[X]:((~brave(X)&generous(X)))))&
(![X]:((curious(X)<~>~quiet(X))<=>(strong(X)|~quiet(X))))&
(![X]:((creative(X)&strong(X))=>humble(X)))&
(![X]:((creative(X)|~kind(X))<=>(~quiet(X)&generous(X))))&
(![X]:((~old(X)&strong(X))<=>(~strong(X)|~happy(X))))&
((?[X]:((creative(X)<~>humble(X))))<=>((~tall(paul)&~quiet(paul))))&
((~quiet(paul))<=>(?[X]:(~creative(X))))&
(![X]:((~curious(X)&~happy(X))=>(~happy(X)|tall(X))))&
(![X]:(calm(X)<=>~patient(X)))&
(![X]:((wise(X)&~humble(X))=>(humble(X)&generous(X))))&
((?[X]:((~curious(X)|kind(X))))<=>(?[X]:((~happy(X)<~>~strong(X)))))&
(![X]:((~humble(X)&humble(X))=>quiet(X)))&
((?[X]:(~calm(X)))<=>(generous(fred)))&
(((funny(susan)&~creative(susan)))<=>(~brave(lucy)))&
((~wise(lucy)<~>creative(lucy)))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|brave(X))))&
(?[X]:((~funny(X)|~tall(X))))&
(?[X]:((quiet(X)&patient(X))))&
(?[X]:((~humble(X)|~kind(X))))&
((~kind(paul)|~generous(paul)))&
((~calm(paul)|quiet(paul))) | brave(paul) | [
"p0",
"p5",
"p8",
"p10",
"p22",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 2258935789634960106785031
% SZS output start Proof for 2258935789634960106785031
1. ! [X0] : (brave(X0) <=> (patient(X0) | humble(X0))) [input p0]
6. ! [X0] : ((~kind(X0) | creative(X0)) <=> (generous(X0) & ~quiet(X0))) [input p5]
9. ~quiet(paul) <=> ? [X0] : ~creative(X0) [input p8]
11. ! [X0] : (calm(X0) <=> ~patient(X0)) [input p10]
23. ~generous(paul) | ~kind(paul) [input p22]
24. quiet(paul) | ~calm(paul) [input p23]
25. ~brave(paul) [input hypothesis]
36. ! [X0] : ((brave(X0) | (~patient(X0) & ~humble(X0))) & ((patient(X0) | humble(X0)) | ~brave(X0))) [nnf transformation 1]
37. ! [X0] : ((brave(X0) | (~patient(X0) & ~humble(X0))) & (patient(X0) | humble(X0) | ~brave(X0))) [flattening 36]
42. ! [X0] : (((~kind(X0) | creative(X0)) | (~generous(X0) | quiet(X0))) & ((generous(X0) & ~quiet(X0)) | (kind(X0) & ~creative(X0)))) [nnf transformation 6]
43. ! [X0] : ((~kind(X0) | creative(X0) | ~generous(X0) | quiet(X0)) & ((generous(X0) & ~quiet(X0)) | (kind(X0) & ~creative(X0)))) [flattening 42]
51. (~quiet(paul) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | quiet(paul)) [nnf transformation 9]
52. (~quiet(paul) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | quiet(paul)) [rectify 51]
53. ? [X1] : ~creative(X1) => ~creative(sK1) [choice axiom]
54. (~quiet(paul) | ! [X0] : creative(X0)) & (~creative(sK1) | quiet(paul)) [skolemisation 52,53]
55. ! [X0] : ((calm(X0) | patient(X0)) & (~patient(X0) | ~calm(X0))) [nnf transformation 11]
80. ~patient(X0) | brave(X0) [cnf transformation 37]
92. ~quiet(X0) | kind(X0) [cnf transformation 43]
93. ~creative(X0) | generous(X0) [cnf transformation 43]
108. ~quiet(paul) | creative(X0) [cnf transformation 54]
111. calm(X0) | patient(X0) [cnf transformation 55]
134. ~generous(paul) | ~kind(paul) [cnf transformation 23]
135. quiet(paul) | ~calm(paul) [cnf transformation 24]
136. ~brave(paul) [cnf transformation 25]
149. 2 <=> quiet(paul) [avatar definition]
151. quiet(paul) <- (2) [avatar component clause 149]
173. 7 <=> ! [X0] : creative(X0) [avatar definition]
174. creative(X0) <- (7) [avatar component clause 173]
175. 7 | ~2 [avatar split clause 108,149,173]
265. 27 <=> kind(paul) [avatar definition]
269. 28 <=> generous(paul) [avatar definition]
271. ~generous(paul) <- (~28) [avatar component clause 269]
272. ~27 | ~28 [avatar split clause 134,269,265]
274. 29 <=> calm(paul) [avatar definition]
276. ~calm(paul) <- (~29) [avatar component clause 274]
277. ~29 | 2 [avatar split clause 135,149,274]
285. patient(paul) <- (~29) [resolution 111,276]
288. brave(paul) <- (~29) [resolution 285,80]
289. $false <- (~29) [subsumption resolution 288,136]
290. 29 [avatar contradiction clause 289]
292. kind(paul) <- (2) [resolution 151,92]
293. 27 | ~2 [avatar split clause 292,149,265]
296. generous(X0) <- (7) [resolution 174,93]
305. $false <- (7, ~28) [resolution 296,271]
306. ~7 | 28 [avatar contradiction clause 305]
307. $false [avatar sat refutation 175,272,277,290,293,306]
% SZS output end Proof for 2258935789634960106785031
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both humble and funny is old.
Everyone who is either quiet or rich is happy and vice versa.
Everyone who is not happy or not wise is not strong or not quiet and vice versa.
Everyone who is both patient and creative is patient or happy and vice versa.
Everyone who is either wise or not wise is old.
Everyone who is both not patient and happy is not brave or not old and vice versa.
If someone is brave then someone is happy.
If lucy is not strong then john is both patient and not wise.
If someone is not calm or not happy then mary is not strong or creative and vice versa.
Everyone who is both not strong and not wise is not wise.
Everyone who is quiet is either happy or not creative and vice versa.
Everyone who is both not humble and strong is not kind.
Everyone who is both not old and tall is either wise or generous and vice versa.
Everyone who is old is both tall and not kind.
Everyone who is funny is not creative or quiet.
If alice is both kind and not kind then alice is kind.
Fred is funny or old.
Susan is both funny and patient.
Someone is patient or not old.
Someone is not happy.
Someone is both humble and not patient.
Lucy is either tall or not creative. | Alice is not brave. | contradiction | (![X]:((humble(X)&funny(X))=>old(X)))&
(![X]:((quiet(X)<~>rich(X))<=>happy(X)))&
(![X]:((~happy(X)|~wise(X))<=>(~strong(X)|~quiet(X))))&
(![X]:((patient(X)&creative(X))<=>(patient(X)|happy(X))))&
(![X]:((wise(X)<~>~wise(X))=>old(X)))&
(![X]:((~patient(X)&happy(X))<=>(~brave(X)|~old(X))))&
((?[X]:(brave(X)))=>(?[X]:(happy(X))))&
((~strong(lucy))=>((patient(john)&~wise(john))))&
((?[X]:((~calm(X)|~happy(X))))<=>((~strong(mary)|creative(mary))))&
(![X]:((~strong(X)&~wise(X))=>~wise(X)))&
(![X]:(quiet(X)<=>(happy(X)<~>~creative(X))))&
(![X]:((~humble(X)&strong(X))=>~kind(X)))&
(![X]:((~old(X)&tall(X))<=>(wise(X)<~>generous(X))))&
(![X]:(old(X)=>(tall(X)&~kind(X))))&
(![X]:(funny(X)=>(~creative(X)|quiet(X))))&
(((kind(alice)&~kind(alice)))=>(kind(alice)))&
((funny(fred)|old(fred)))&
((funny(susan)&patient(susan)))&
(?[X]:((patient(X)|~old(X))))&
(?[X]:(~happy(X)))&
(?[X]:((humble(X)&~patient(X))))&
((tall(lucy)<~>~creative(lucy))) | ~brave(alice) | [
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 9018136343699668790525735
% SZS output start Proof for 9018136343699668790525735
4. ! [X0] : ((creative(X0) & patient(X0)) <=> (happy(X0) | patient(X0))) [input p3]
6. ! [X0] : ((happy(X0) & ~patient(X0)) <=> (~old(X0) | ~brave(X0))) [input p5]
23. ~brave(alice) [input hypothesis]
42. ! [X0] : (((creative(X0) & patient(X0)) | (~happy(X0) & ~patient(X0))) & ((happy(X0) | patient(X0)) | (~creative(X0) | ~patient(X0)))) [nnf transformation 4]
43. ! [X0] : (((creative(X0) & patient(X0)) | (~happy(X0) & ~patient(X0))) & (happy(X0) | patient(X0) | ~creative(X0) | ~patient(X0))) [flattening 42]
45. ! [X0] : (((happy(X0) & ~patient(X0)) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | (~happy(X0) | patient(X0)))) [nnf transformation 6]
46. ! [X0] : (((happy(X0) & ~patient(X0)) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | ~happy(X0) | patient(X0))) [flattening 45]
76. ~happy(X0) | patient(X0) [cnf transformation 43]
82. ~patient(X0) | brave(X0) [cnf transformation 46]
84. brave(X0) | happy(X0) [cnf transformation 46]
118. ~brave(alice) [cnf transformation 23]
188. happy(alice) [resolution 84,118]
190. patient(alice) [resolution 188,76]
196. brave(alice) [resolution 190,82]
198. $false [subsumption resolution 196,118]
% SZS output end Proof for 9018136343699668790525735
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not happy or not patient then someone is either kind or quiet. If someone is either not humble or not wise then someone is old and vice versa. Everyone who is not creative or happy is either strong or kind. Everyone who is creative or not old is both wise and calm. If someone is quiet or not kind then someone is kind. If lucy is not tall then someone is not old or funny and vice versa. If fred is not funny or generous then someone is both not old and not rich and vice versa. Everyone who is calm is brave and vice versa. If paul is either not funny or not strong then paul is either not calm or kind. Everyone who is patient or not strong is both not creative and not brave and vice versa. If fred is not generous or patient then someone is not generous. Everyone who is both not humble and not brave is kind or old. If paul is either not creative or happy then someone is not strong or not calm and vice versa. If someone is either creative or rich then mary is either not calm or quiet and vice versa. Everyone who is both not rich and creative is either calm or not rich. Everyone who is not old is curious and vice versa. Someone is not generous. Mary is both quiet and patient. Someone is not kind or quiet. Someone is either not rich or not quiet. Paul is both humble and old. Mary is either patient or not patient. Someone is either not generous or quiet. | Mary is brave. | contradiction | ((?[X]:((~happy(X)|~patient(X))))=>(?[X]:((kind(X)<~>quiet(X)))))&
((?[X]:((~humble(X)<~>~wise(X))))<=>(?[X]:(old(X))))&
(![X]:((~creative(X)|happy(X))=>(strong(X)<~>kind(X))))&
(![X]:((creative(X)|~old(X))=>(wise(X)&calm(X))))&
((?[X]:((quiet(X)|~kind(X))))=>(?[X]:(kind(X))))&
((~tall(lucy))<=>(?[X]:((~old(X)|funny(X)))))&
(((~funny(fred)|generous(fred)))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:(calm(X)<=>brave(X)))&
(((~funny(paul)<~>~strong(paul)))=>((~calm(paul)<~>kind(paul))))&
(![X]:((patient(X)|~strong(X))<=>(~creative(X)&~brave(X))))&
(((~generous(fred)|patient(fred)))=>(?[X]:(~generous(X))))&
(![X]:((~humble(X)&~brave(X))=>(kind(X)|old(X))))&
(((~creative(paul)<~>happy(paul)))<=>(?[X]:((~strong(X)|~calm(X)))))&
((?[X]:((creative(X)<~>rich(X))))<=>((~calm(mary)<~>quiet(mary))))&
(![X]:((~rich(X)&creative(X))=>(calm(X)<~>~rich(X))))&
(![X]:(~old(X)<=>curious(X)))&
(?[X]:(~generous(X)))&
((quiet(mary)&patient(mary)))&
(?[X]:((~kind(X)|quiet(X))))&
(?[X]:((~rich(X)<~>~quiet(X))))&
((humble(paul)&old(paul)))&
((patient(mary)<~>~patient(mary)))&
(?[X]:((~generous(X)<~>quiet(X)))) | brave(mary) | [
"p9",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 59470791810292462788164
% SZS output start Proof for 59470791810292462788164
10. ! [X0] : ((~strong(X0) | patient(X0)) <=> (~brave(X0) & ~creative(X0))) [input p9]
18. patient(mary) & quiet(mary) [input p17]
24. brave(mary) [input hypothesis]
62. ! [X0] : (((~strong(X0) | patient(X0)) | (brave(X0) | creative(X0))) & ((~brave(X0) & ~creative(X0)) | (strong(X0) & ~patient(X0)))) [nnf transformation 10]
63. ! [X0] : ((~strong(X0) | patient(X0) | brave(X0) | creative(X0)) & ((~brave(X0) & ~creative(X0)) | (strong(X0) & ~patient(X0)))) [flattening 62]
121. ~brave(X0) | ~patient(X0) [cnf transformation 63]
147. patient(mary) [cnf transformation 18]
157. brave(mary) [cnf transformation 24]
394. ~patient(mary) [resolution 121,157]
396. $false [subsumption resolution 394,147]
% SZS output end Proof for 59470791810292462788164
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and not rich is either quiet or not funny and vice versa.
Everyone who is humble is not wise.
Everyone who is quiet or wise is wise and vice versa.
Everyone who is either quiet or old is not tall.
Everyone who is happy is old and vice versa.
Everyone who is both creative and tall is not generous and vice versa.
If someone is either curious or not kind then alice is not patient.
If someone is funny or not wise then someone is both funny and not curious and vice versa.
If john is both not strong and not creative then mary is calm or not creative.
If lucy is both not kind and not brave then fred is not rich or quiet.
If someone is wise then someone is not strong or not humble.
Everyone who is both brave and strong is either curious or tall and vice versa.
Everyone who is not rich or happy is not quiet.
If someone is both not generous and happy then someone is not strong.
Everyone who is not wise or brave is either quiet or not strong.
Everyone who is not happy is not strong and vice versa.
Someone is not creative or not calm.
Someone is not curious.
Mary is either generous or not creative.
Someone is not generous.
Someone is both brave and patient.
Alice is humble or not tall. | Mary is curious. | contradiction | (![X]:((creative(X)&~rich(X))<=>(quiet(X)<~>~funny(X))))&
(![X]:(humble(X)=>~wise(X)))&
(![X]:((quiet(X)|wise(X))<=>wise(X)))&
(![X]:((quiet(X)<~>old(X))=>~tall(X)))&
(![X]:(happy(X)<=>old(X)))&
(![X]:((creative(X)&tall(X))<=>~generous(X)))&
((?[X]:((curious(X)<~>~kind(X))))=>(~patient(alice)))&
((?[X]:((funny(X)|~wise(X))))<=>(?[X]:((funny(X)&~curious(X)))))&
(((~strong(john)&~creative(john)))=>((calm(mary)|~creative(mary))))&
(((~kind(lucy)&~brave(lucy)))=>((~rich(fred)|quiet(fred))))&
((?[X]:(wise(X)))=>(?[X]:((~strong(X)|~humble(X)))))&
(![X]:((brave(X)&strong(X))<=>(curious(X)<~>tall(X))))&
(![X]:((~rich(X)|happy(X))=>~quiet(X)))&
((?[X]:((~generous(X)&happy(X))))=>(?[X]:(~strong(X))))&
(![X]:((~wise(X)|brave(X))=>(quiet(X)<~>~strong(X))))&
(![X]:(~happy(X)<=>~strong(X)))&
(?[X]:((~creative(X)|~calm(X))))&
(?[X]:(~curious(X)))&
((generous(mary)<~>~creative(mary)))&
(?[X]:(~generous(X)))&
(?[X]:((brave(X)&patient(X))))&
((humble(alice)|~tall(alice))) | curious(mary) | [
"p5",
"p11",
"p12",
"p14",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8110040030742422721102398
% SZS output start Proof for 8110040030742422721102398
6. ! [X0] : ((tall(X0) & creative(X0)) <=> ~generous(X0)) [input p5]
12. ! [X0] : ((strong(X0) & brave(X0)) <=> (curious(X0) <~> tall(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~rich(X0)) => ~quiet(X0)) [input p12]
15. ! [X0] : ((brave(X0) | ~wise(X0)) => (quiet(X0) <~> ~strong(X0))) [input p14]
16. ! [X0] : (~happy(X0) <=> ~strong(X0)) [input p15]
19. generous(mary) <~> ~creative(mary) [input p18]
23. curious(mary) [input hypothesis]
35. ! [X0] : (~quiet(X0) | (~happy(X0) & rich(X0))) [ennf transformation 13]
37. ! [X0] : ((quiet(X0) <~> ~strong(X0)) | (~brave(X0) & wise(X0))) [ennf transformation 15]
44. ! [X0] : (((tall(X0) & creative(X0)) | generous(X0)) & (~generous(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 6]
45. ! [X0] : (((tall(X0) & creative(X0)) | generous(X0)) & (~generous(X0) | ~tall(X0) | ~creative(X0))) [flattening 44]
55. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) & (((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | (~strong(X0) | ~brave(X0)))) [nnf transformation 12]
56. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0)))) & (((~tall(X0) | ~curious(X0)) & (tall(X0) | curious(X0))) | ~strong(X0) | ~brave(X0))) [flattening 55]
60. ! [X0] : (((strong(X0) | ~quiet(X0)) & (~strong(X0) | quiet(X0))) | (~brave(X0) & wise(X0))) [nnf transformation 37]
61. ! [X0] : ((~happy(X0) | strong(X0)) & (~strong(X0) | happy(X0))) [nnf transformation 16]
66. (creative(mary) | ~generous(mary)) & (~creative(mary) | generous(mary)) [nnf transformation 19]
85. ~generous(X0) | ~tall(X0) | ~creative(X0) [cnf transformation 45]
86. generous(X0) | creative(X0) [cnf transformation 45]
100. ~curious(X0) | tall(X0) | brave(X0) [cnf transformation 56]
102. ~curious(X0) | tall(X0) | strong(X0) [cnf transformation 56]
105. ~happy(X0) | ~quiet(X0) [cnf transformation 35]
108. ~brave(X0) | quiet(X0) | ~strong(X0) [cnf transformation 60]
111. ~strong(X0) | happy(X0) [cnf transformation 61]
115. ~creative(mary) | generous(mary) [cnf transformation 66]
116. creative(mary) | ~generous(mary) [cnf transformation 66]
121. curious(mary) [cnf transformation 23]
177. 14 <=> creative(mary) [avatar definition]
178. creative(mary) <- (14) [avatar component clause 177]
228. creative(mary) [subsumption resolution 116,86]
229. 14 [avatar split clause 228,177]
230. generous(mary) [subsumption resolution 115,86]
299. ~tall(mary) | ~creative(mary) [resolution 85,230]
302. ~tall(mary) <- (14) [subsumption resolution 299,178]
303. tall(mary) | brave(mary) [resolution 100,121]
305. brave(mary) <- (14) [subsumption resolution 303,302]
329. tall(mary) | strong(mary) [resolution 102,121]
331. strong(mary) <- (14) [subsumption resolution 329,302]
333. happy(mary) <- (14) [resolution 331,111]
337. quiet(mary) | ~strong(mary) <- (14) [resolution 108,305]
347. quiet(mary) <- (14) [subsumption resolution 337,331]
363. ~quiet(mary) <- (14) [resolution 333,105]
365. $false <- (14) [subsumption resolution 363,347]
366. ~14 [avatar contradiction clause 365]
367. $false [avatar sat refutation 229,366]
% SZS output end Proof for 8110040030742422721102398
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both happy and not patient then john is either not strong or calm.
If someone is funny then fred is either wise or not strong.
Everyone who is brave is either old or not funny and vice versa.
Everyone who is not humble or generous is both quiet and not curious.
If mary is strong then fred is patient or brave.
If someone is not wise or rich then someone is both strong and generous and vice versa.
If mary is both rich and brave then mary is both creative and patient.
Everyone who is either not wise or not curious is not funny.
If someone is either not creative or kind then alice is either not generous or wise and vice versa.
If someone is not brave then susan is calm and vice versa.
If someone is both not wise and wise then someone is rich and vice versa.
If susan is both not funny and calm then someone is both quiet and funny and vice versa.
If fred is not funny or kind then someone is either not strong or brave.
If someone is wise or not brave then someone is rich.
Everyone who is kind or not quiet is generous or brave and vice versa.
If paul is both patient and not tall then paul is not generous and vice versa.
Susan is both not old and not quiet.
Someone is either funny or not old.
Lucy is not kind.
Mary is wise or not calm.
Mary is not wise or humble.
Someone is patient or not creative. | Susan is generous. | contradiction | ((?[X]:((happy(X)&~patient(X))))=>((~strong(john)<~>calm(john))))&
((?[X]:(funny(X)))=>((wise(fred)<~>~strong(fred))))&
(![X]:(brave(X)<=>(old(X)<~>~funny(X))))&
(![X]:((~humble(X)|generous(X))=>(quiet(X)&~curious(X))))&
((strong(mary))=>((patient(fred)|brave(fred))))&
((?[X]:((~wise(X)|rich(X))))<=>(?[X]:((strong(X)&generous(X)))))&
(((rich(mary)&brave(mary)))=>((creative(mary)&patient(mary))))&
(![X]:((~wise(X)<~>~curious(X))=>~funny(X)))&
((?[X]:((~creative(X)<~>kind(X))))<=>((~generous(alice)<~>wise(alice))))&
((?[X]:(~brave(X)))<=>(calm(susan)))&
((?[X]:((~wise(X)&wise(X))))<=>(?[X]:(rich(X))))&
(((~funny(susan)&calm(susan)))<=>(?[X]:((quiet(X)&funny(X)))))&
(((~funny(fred)|kind(fred)))=>(?[X]:((~strong(X)<~>brave(X)))))&
((?[X]:((wise(X)|~brave(X))))=>(?[X]:(rich(X))))&
(![X]:((kind(X)|~quiet(X))<=>(generous(X)|brave(X))))&
(((patient(paul)&~tall(paul)))<=>(~generous(paul)))&
((~old(susan)&~quiet(susan)))&
(?[X]:((funny(X)<~>~old(X))))&
(~kind(lucy))&
((wise(mary)|~calm(mary)))&
((~wise(mary)|humble(mary)))&
(?[X]:((patient(X)|~creative(X)))) | generous(susan) | [
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3007232231803868811706667
% SZS output start Proof for 3007232231803868811706667
4. ! [X0] : ((generous(X0) | ~humble(X0)) => (~curious(X0) & quiet(X0))) [input p3]
17. ~quiet(susan) & ~old(susan) [input p16]
23. generous(susan) [input hypothesis]
28. ! [X0] : (generous(X0) => (~curious(X0) & quiet(X0))) [pure predicate removal 4]
31. ! [X0] : ((~curious(X0) & quiet(X0)) | ~generous(X0)) [ennf transformation 28]
86. ~generous(X0) | quiet(X0) [cnf transformation 31]
129. ~quiet(susan) [cnf transformation 17]
135. generous(susan) [cnf transformation 23]
364. quiet(susan) [resolution 86,135]
367. $false [subsumption resolution 364,129]
% SZS output end Proof for 3007232231803868811706667
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient is both not tall and happy and vice versa. Everyone who is tall is generous or strong and vice versa. Everyone who is not creative is both not humble and old. Everyone who is happy is quiet and vice versa. If someone is curious then someone is not wise or not patient. Everyone who is not funny or creative is not calm. If someone is not old or happy then someone is either not tall or not generous. Everyone who is strong or rich is both not old and generous and vice versa. If susan is happy then susan is happy or humble and vice versa. Everyone who is both tall and not humble is either curious or not strong and vice versa. Everyone who is both creative and not calm is not calm. If mary is brave then paul is wise. If someone is not generous or not strong then john is both not brave and funny. Everyone who is either curious or not tall is both not creative and not quiet. Someone is either generous or not wise. Someone is rich or old. Someone is not curious. Mary is funny. | John is old. | entailment | (![X]:(patient(X)<=>(~tall(X)&happy(X))))&
(![X]:(tall(X)<=>(generous(X)|strong(X))))&
(![X]:(~creative(X)=>(~humble(X)&old(X))))&
(![X]:(happy(X)<=>quiet(X)))&
((?[X]:(curious(X)))=>(?[X]:((~wise(X)|~patient(X)))))&
(![X]:((~funny(X)|creative(X))=>~calm(X)))&
((?[X]:((~old(X)|happy(X))))=>(?[X]:((~tall(X)<~>~generous(X)))))&
(![X]:((strong(X)|rich(X))<=>(~old(X)&generous(X))))&
((happy(susan))<=>((happy(susan)|humble(susan))))&
(![X]:((tall(X)&~humble(X))<=>(curious(X)<~>~strong(X))))&
(![X]:((creative(X)&~calm(X))=>~calm(X)))&
((brave(mary))=>(wise(paul)))&
((?[X]:((~generous(X)|~strong(X))))=>((~brave(john)&funny(john))))&
(![X]:((curious(X)<~>~tall(X))=>(~creative(X)&~quiet(X))))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:((rich(X)|old(X))))&
(?[X]:(~curious(X)))&
(funny(mary)) | old(john) | [
"p1",
"p6",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 5562367344365459500453584
% SZS output start Proof for 5562367344365459500453584
2. ! [X0] : (tall(X0) <=> (strong(X0) | generous(X0))) [input p1]
7. ? [X0] : (happy(X0) | ~old(X0)) => ? [X0] : (~tall(X0) <~> ~generous(X0)) [input p6]
8. ! [X0] : ((rich(X0) | strong(X0)) <=> (generous(X0) & ~old(X0))) [input p7]
19. ~old(john) [input hypothesis]
21. ? [X0] : (happy(X0) | ~old(X0)) => ? [X1] : (~tall(X1) <~> ~generous(X1)) [rectify 7]
33. ? [X1] : (~tall(X1) <~> ~generous(X1)) | ! [X0] : (~happy(X0) & old(X0)) [ennf transformation 21]
37. ! [X0] : ((tall(X0) | (~strong(X0) & ~generous(X0))) & ((strong(X0) | generous(X0)) | ~tall(X0))) [nnf transformation 2]
38. ! [X0] : ((tall(X0) | (~strong(X0) & ~generous(X0))) & (strong(X0) | generous(X0) | ~tall(X0))) [flattening 37]
43. ? [X1] : ((generous(X1) | tall(X1)) & (~generous(X1) | ~tall(X1))) | ! [X0] : (~happy(X0) & old(X0)) [nnf transformation 33]
44. ? [X0] : ((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) | ! [X1] : (~happy(X1) & old(X1)) [rectify 43]
45. ? [X0] : ((generous(X0) | tall(X0)) & (~generous(X0) | ~tall(X0))) => ((generous(sK1) | tall(sK1)) & (~generous(sK1) | ~tall(sK1))) [choice axiom]
46. ((generous(sK1) | tall(sK1)) & (~generous(sK1) | ~tall(sK1))) | ! [X1] : (~happy(X1) & old(X1)) [skolemisation 44,45]
47. ! [X0] : (((rich(X0) | strong(X0)) | (~generous(X0) | old(X0))) & ((generous(X0) & ~old(X0)) | (~rich(X0) & ~strong(X0)))) [nnf transformation 8]
48. ! [X0] : ((rich(X0) | strong(X0) | ~generous(X0) | old(X0)) & ((generous(X0) & ~old(X0)) | (~rich(X0) & ~strong(X0)))) [flattening 47]
62. ~tall(X0) | generous(X0) | strong(X0) [cnf transformation 38]
63. ~generous(X0) | tall(X0) [cnf transformation 38]
71. ~generous(sK1) | ~tall(sK1) | old(X1) [cnf transformation 46]
73. generous(sK1) | tall(sK1) | old(X1) [cnf transformation 46]
77. ~strong(X0) | generous(X0) [cnf transformation 48]
98. ~old(john) [cnf transformation 19]
116. 5 <=> tall(sK1) [avatar definition]
118. tall(sK1) <- (5) [avatar component clause 116]
120. tall(sK1) | old(X1) [subsumption resolution 73,63]
122. 6 <=> ! [X1] : old(X1) [avatar definition]
123. old(X1) <- (6) [avatar component clause 122]
124. 6 | 5 [avatar split clause 120,116,122]
127. 7 <=> generous(sK1) [avatar definition]
129. ~generous(sK1) <- (~7) [avatar component clause 127]
131. ~generous(sK1) | old(X1) [subsumption resolution 71,63]
132. 6 | ~7 [avatar split clause 131,127,122]
171. generous(sK1) | strong(sK1) <- (5) [resolution 62,118]
173. strong(sK1) <- (5, ~7) [subsumption resolution 171,129]
175. generous(sK1) <- (5, ~7) [resolution 173,77]
177. $false <- (5, ~7) [subsumption resolution 175,129]
178. ~5 | 7 [avatar contradiction clause 177]
179. $false <- (6) [resolution 123,98]
183. ~6 [avatar contradiction clause 179]
184. $false [avatar sat refutation 124,132,178,183]
% SZS output end Proof for 5562367344365459500453584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both curious and brave then someone is either tall or calm. If paul is either strong or not happy then someone is not wise. Everyone who is not tall or not creative is not curious or creative. If fred is both tall and kind then someone is either strong or generous and vice versa. If someone is both strong and brave then alice is either patient or happy. If fred is either not wise or not funny then john is creative. If paul is tall or not patient then someone is tall or not humble. Everyone who is both humble and not wise is either creative or humble and vice versa. If someone is not funny or funny then susan is either brave or creative. If paul is either not quiet or quiet then susan is strong. Everyone who is either not quiet or calm is generous. Everyone who is both brave and not quiet is funny or wise and vice versa. Everyone who is not wise is not quiet and vice versa. If someone is calm then someone is both strong and wise. Everyone who is either funny or tall is either generous or not kind. If someone is both happy and not curious then paul is humble. Someone is not tall or quiet. John is either tall or old. Someone is not funny. Someone is not brave or not tall. Lucy is either not calm or patient. Lucy is generous. | Fred is curious. | contradiction | ((?[X]:((curious(X)&brave(X))))=>(?[X]:((tall(X)<~>calm(X)))))&
(((strong(paul)<~>~happy(paul)))=>(?[X]:(~wise(X))))&
(![X]:((~tall(X)|~creative(X))=>(~curious(X)|creative(X))))&
(((tall(fred)&kind(fred)))<=>(?[X]:((strong(X)<~>generous(X)))))&
((?[X]:((strong(X)&brave(X))))=>((patient(alice)<~>happy(alice))))&
(((~wise(fred)<~>~funny(fred)))=>(creative(john)))&
(((tall(paul)|~patient(paul)))=>(?[X]:((tall(X)|~humble(X)))))&
(![X]:((humble(X)&~wise(X))<=>(creative(X)<~>humble(X))))&
((?[X]:((~funny(X)|funny(X))))=>((brave(susan)<~>creative(susan))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
(![X]:(~wise(X)<=>~quiet(X)))&
((?[X]:(calm(X)))=>(?[X]:((strong(X)&wise(X)))))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((?[X]:((happy(X)&~curious(X))))=>(humble(paul)))&
(?[X]:((~tall(X)|quiet(X))))&
((tall(john)<~>old(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~brave(X)|~tall(X))))&
((~calm(lucy)<~>patient(lucy)))&
(generous(lucy)) | curious(fred) | [
"p2",
"p7",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4531121646539283029292469
% SZS output start Proof for 4531121646539283029292469
3. ! [X0] : ((~creative(X0) | ~tall(X0)) => (creative(X0) | ~curious(X0))) [input p2]
8. ! [X0] : ((~wise(X0) & humble(X0)) <=> (creative(X0) <~> humble(X0))) [input p7]
12. ! [X0] : ((~quiet(X0) & brave(X0)) <=> (wise(X0) | funny(X0))) [input p11]
13. ! [X0] : (~wise(X0) <=> ~quiet(X0)) [input p12]
23. curious(fred) [input hypothesis]
28. ! [X0] : ((creative(X0) | ~curious(X0)) | (creative(X0) & tall(X0))) [ennf transformation 3]
29. ! [X0] : (creative(X0) | ~curious(X0) | (creative(X0) & tall(X0))) [flattening 28]
55. ! [X0] : (((~wise(X0) & humble(X0)) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0)))) & (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | (wise(X0) | ~humble(X0)))) [nnf transformation 8]
56. ! [X0] : (((~wise(X0) & humble(X0)) | ((creative(X0) | ~humble(X0)) & (humble(X0) | ~creative(X0)))) & (((~humble(X0) | ~creative(X0)) & (humble(X0) | creative(X0))) | wise(X0) | ~humble(X0))) [flattening 55]
60. ! [X0] : (((~quiet(X0) & brave(X0)) | (~wise(X0) & ~funny(X0))) & ((wise(X0) | funny(X0)) | (quiet(X0) | ~brave(X0)))) [nnf transformation 12]
61. ! [X0] : (((~quiet(X0) & brave(X0)) | (~wise(X0) & ~funny(X0))) & (wise(X0) | funny(X0) | quiet(X0) | ~brave(X0))) [flattening 60]
62. ! [X0] : ((~wise(X0) | quiet(X0)) & (~quiet(X0) | wise(X0))) [nnf transformation 13]
80. creative(X0) | ~curious(X0) | creative(X0) [cnf transformation 29]
94. ~humble(X0) | ~creative(X0) | wise(X0) | ~humble(X0) [cnf transformation 56]
95. humble(X0) | humble(X0) | ~creative(X0) [cnf transformation 56]
111. ~quiet(X0) | ~wise(X0) [cnf transformation 61]
113. ~wise(X0) | quiet(X0) [cnf transformation 62]
129. curious(fred) [cnf transformation 23]
132. ~humble(X0) | ~creative(X0) | wise(X0) [duplicate literal removal 94]
133. ~creative(X0) | humble(X0) [duplicate literal removal 95]
134. ~curious(X0) | creative(X0) [duplicate literal removal 80]
235. ~creative(X0) | wise(X0) [subsumption resolution 132,133]
264. ~wise(X0) [subsumption resolution 113,111]
296. creative(fred) [resolution 134,129]
302. wise(fred) [resolution 235,296]
303. $false [subsumption resolution 302,264]
% SZS output end Proof for 4531121646539283029292469
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or brave is not old or strong. If someone is not quiet then someone is both not old and generous. If lucy is either not generous or not humble then mary is rich or not brave and vice versa. If someone is curious then fred is not wise and vice versa. If someone is either not tall or not creative then lucy is either patient or not happy and vice versa. If paul is either not old or not creative then someone is not tall or kind. Everyone who is either not generous or kind is humble and vice versa. Everyone who is not rich or not happy is either generous or curious. If someone is either not humble or happy then someone is either not curious or kind and vice versa. If someone is not kind then someone is not tall or not generous. Everyone who is not creative or patient is not generous or happy. If someone is not generous or not tall then someone is generous or brave. Everyone who is not funny is not rich. Everyone who is rich is tall. Everyone who is not happy is both rich and strong. If paul is not quiet then fred is either funny or curious. Paul is not old or not calm. Alice is not generous or not creative. Lucy is kind. Paul is either rich or tall. Someone is not rich. Someone is old. Someone is creative or not old. Someone is not strong or not happy. | Fred is curious. | neutral | (![X]:((kind(X)<~>brave(X))=>(~old(X)|strong(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((~old(X)&generous(X)))))&
(((~generous(lucy)<~>~humble(lucy)))<=>((rich(mary)|~brave(mary))))&
((?[X]:(curious(X)))<=>(~wise(fred)))&
((?[X]:((~tall(X)<~>~creative(X))))<=>((patient(lucy)<~>~happy(lucy))))&
(((~old(paul)<~>~creative(paul)))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~generous(X)<~>kind(X))<=>humble(X)))&
(![X]:((~rich(X)|~happy(X))=>(generous(X)<~>curious(X))))&
((?[X]:((~humble(X)<~>happy(X))))<=>(?[X]:((~curious(X)<~>kind(X)))))&
((?[X]:(~kind(X)))=>(?[X]:((~tall(X)|~generous(X)))))&
(![X]:((~creative(X)|patient(X))=>(~generous(X)|happy(X))))&
((?[X]:((~generous(X)|~tall(X))))=>(?[X]:((generous(X)|brave(X)))))&
(![X]:(~funny(X)=>~rich(X)))&
(![X]:(rich(X)=>tall(X)))&
(![X]:(~happy(X)=>(rich(X)&strong(X))))&
((~quiet(paul))=>((funny(fred)<~>curious(fred))))&
((~old(paul)|~calm(paul)))&
((~generous(alice)|~creative(alice)))&
(kind(lucy))&
((rich(paul)<~>tall(paul)))&
(?[X]:(~rich(X)))&
(?[X]:(old(X)))&
(?[X]:((creative(X)|~old(X))))&
(?[X]:((~strong(X)|~happy(X)))) | curious(fred) | [] | null | 0 |
If someone is either strong or old then alice is curious and vice versa.
Everyone who is not curious or rich is kind or old and vice versa.
If paul is both not creative and strong then someone is either happy or not kind and vice versa.
If someone is both funny and not strong then someone is both humble and not strong.
If someone is calm then someone is not calm or not wise and vice versa.
If lucy is either generous or strong then someone is quiet or patient and vice versa.
If lucy is both not rich and generous then lucy is both not quiet and old and vice versa.
If fred is not quiet or not strong then mary is not calm and vice versa.
If mary is either not curious or not quiet then someone is both not kind and curious and vice versa.
Everyone who is either old or brave is not tall and vice versa.
If someone is old then alice is both not happy and brave and vice versa.
Everyone who is humble or not generous is either quiet or tall and vice versa.
If someone is either not calm or not rich then paul is both not humble and rich.
Everyone who is generous or not tall is both not happy and not brave.
Everyone who is not quiet or rich is both quiet and not humble and vice versa.
Everyone who is brave or patient is either not funny or not creative.
Alice is tall or calm.
Someone is not strong or curious.
Lucy is rich or not strong.
Someone is not creative.
Someone is wise. | Lucy is not generous. | contradiction | ((?[X]:((strong(X)<~>old(X))))<=>(curious(alice)))&
(![X]:((~curious(X)|rich(X))<=>(kind(X)|old(X))))&
(((~creative(paul)&strong(paul)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
((?[X]:((funny(X)&~strong(X))))=>(?[X]:((humble(X)&~strong(X)))))&
((?[X]:(calm(X)))<=>(?[X]:((~calm(X)|~wise(X)))))&
(((generous(lucy)<~>strong(lucy)))<=>(?[X]:((quiet(X)|patient(X)))))&
(((~rich(lucy)&generous(lucy)))<=>((~quiet(lucy)&old(lucy))))&
(((~quiet(fred)|~strong(fred)))<=>(~calm(mary)))&
(((~curious(mary)<~>~quiet(mary)))<=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:((old(X)<~>brave(X))<=>~tall(X)))&
((?[X]:(old(X)))<=>((~happy(alice)&brave(alice))))&
(![X]:((humble(X)|~generous(X))<=>(quiet(X)<~>tall(X))))&
((?[X]:((~calm(X)<~>~rich(X))))=>((~humble(paul)&rich(paul))))&
(![X]:((generous(X)|~tall(X))=>(~happy(X)&~brave(X))))&
(![X]:((~quiet(X)|rich(X))<=>(quiet(X)&~humble(X))))&
(![X]:((brave(X)|patient(X))=>(~funny(X)<~>~creative(X))))&
((tall(alice)|calm(alice)))&
(?[X]:((~strong(X)|curious(X))))&
((rich(lucy)|~strong(lucy)))&
(?[X]:(~creative(X)))&
(?[X]:(wise(X))) | ~generous(lucy) | [
"p9",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7128083964937761278363803
% SZS output start Proof for 7128083964937761278363803
10. ! [X0] : ((old(X0) <~> brave(X0)) <=> ~tall(X0)) [input p9]
11. ? [X0] : old(X0) <=> (brave(alice) & ~happy(alice)) [input p10]
12. ! [X0] : ((~generous(X0) | humble(X0)) <=> (quiet(X0) <~> tall(X0))) [input p11]
14. ! [X0] : ((~tall(X0) | generous(X0)) => (~brave(X0) & ~happy(X0))) [input p13]
15. ! [X0] : ((rich(X0) | ~quiet(X0)) <=> (~humble(X0) & quiet(X0))) [input p14]
22. ~generous(lucy) [input hypothesis]
27. ! [X0] : ((~brave(X0) & ~happy(X0)) | (tall(X0) & ~generous(X0))) [ennf transformation 14]
60. ! [X0] : ((((~brave(X0) | ~old(X0)) & (brave(X0) | old(X0))) | tall(X0)) & (~tall(X0) | ((old(X0) | ~brave(X0)) & (brave(X0) | ~old(X0))))) [nnf transformation 10]
61. (? [X0] : old(X0) | (~brave(alice) | happy(alice))) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [nnf transformation 11]
62. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X0] : ~old(X0)) [flattening 61]
63. (? [X0] : old(X0) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [rectify 62]
64. ? [X0] : old(X0) => old(sK7) [choice axiom]
65. (old(sK7) | ~brave(alice) | happy(alice)) & ((brave(alice) & ~happy(alice)) | ! [X1] : ~old(X1)) [skolemisation 63,64]
66. ! [X0] : (((~generous(X0) | humble(X0)) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [nnf transformation 12]
67. ! [X0] : ((~generous(X0) | humble(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | (generous(X0) & ~humble(X0)))) [flattening 66]
69. ! [X0] : (((rich(X0) | ~quiet(X0)) | (humble(X0) | ~quiet(X0))) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [nnf transformation 15]
70. ! [X0] : ((rich(X0) | ~quiet(X0) | humble(X0) | ~quiet(X0)) & ((~humble(X0) & quiet(X0)) | (~rich(X0) & quiet(X0)))) [flattening 69]
118. tall(X0) | old(X0) | brave(X0) [cnf transformation 60]
121. brave(alice) | ~old(X1) [cnf transformation 65]
126. ~tall(X0) | ~quiet(X0) | generous(X0) [cnf transformation 67]
135. ~brave(X0) | ~generous(X0) [cnf transformation 27]
136. ~brave(X0) | tall(X0) [cnf transformation 27]
137. quiet(X0) | quiet(X0) [cnf transformation 70]
151. ~generous(lucy) [cnf transformation 22]
152. quiet(X0) [duplicate literal removal 137]
245. 22 <=> generous(lucy) [avatar definition]
247. ~generous(lucy) <- (~22) [avatar component clause 245]
330. 39 <=> brave(alice) [avatar definition]
331. brave(alice) <- (39) [avatar component clause 330]
339. 41 <=> ! [X1] : ~old(X1) [avatar definition]
340. ~old(X1) <- (41) [avatar component clause 339]
341. 41 | 39 [avatar split clause 121,330,339]
362. 46 <=> tall(alice) [avatar definition]
363. ~tall(alice) <- (~46) [avatar component clause 362]
364. tall(alice) <- (46) [avatar component clause 362]
380. ~22 [avatar split clause 151,245]
385. ~generous(alice) <- (39) [resolution 135,331]
491. ~quiet(alice) | generous(alice) <- (46) [resolution 126,364]
493. ~quiet(X1) | generous(X1) | old(X1) | brave(X1) [resolution 126,118]
496. generous(alice) <- (46) [subsumption resolution 491,152]
497. $false <- (39, 46) [subsumption resolution 496,385]
498. ~39 | ~46 [avatar contradiction clause 497]
499. brave(X1) | old(X1) | generous(X1) [subsumption resolution 493,152]
546. old(X3) | generous(X3) | tall(X3) [resolution 499,136]
551. tall(X3) | generous(X3) <- (41) [subsumption resolution 546,340]
561. generous(X1) | ~quiet(X1) | generous(X1) <- (41) [resolution 551,126]
565. generous(X1) | ~quiet(X1) <- (41) [duplicate literal removal 561]
566. generous(X1) <- (41) [subsumption resolution 565,152]
567. $false <- (~22, 41) [resolution 566,247]
570. 22 | ~41 [avatar contradiction clause 567]
574. tall(alice) <- (39) [resolution 331,136]
586. $false <- (39, ~46) [subsumption resolution 574,363]
587. ~39 | 46 [avatar contradiction clause 586]
588. $false [avatar sat refutation 341,380,498,570,587]
% SZS output end Proof for 7128083964937761278363803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or creative is both wise and happy.
Everyone who is either creative or generous is either not brave or tall.
If susan is not tall or not generous then fred is either not patient or not old and vice versa.
If someone is both not tall and quiet then someone is either not quiet or kind and vice versa.
If alice is not tall or tall then susan is kind or calm.
Everyone who is both not curious and not happy is either not happy or happy and vice versa.
Everyone who is either not happy or not humble is not quiet and vice versa.
Everyone who is both humble and creative is creative and vice versa.
If someone is either patient or not patient then someone is not generous or not funny.
If someone is not strong then someone is both old and not funny and vice versa.
Everyone who is either brave or patient is quiet or not curious.
Everyone who is both tall and not brave is both old and generous and vice versa.
If alice is not old or generous then someone is both old and wise.
If paul is happy then fred is either generous or brave and vice versa.
Susan is either old or generous.
Mary is both wise and brave.
Fred is tall or creative.
Someone is both not rich and not strong.
Someone is both not happy and wise. | Alice is not old. | neutral | (![X]:((~happy(X)<~>creative(X))=>(wise(X)&happy(X))))&
(![X]:((creative(X)<~>generous(X))=>(~brave(X)<~>tall(X))))&
(((~tall(susan)|~generous(susan)))<=>((~patient(fred)<~>~old(fred))))&
((?[X]:((~tall(X)&quiet(X))))<=>(?[X]:((~quiet(X)<~>kind(X)))))&
(((~tall(alice)|tall(alice)))=>((kind(susan)|calm(susan))))&
(![X]:((~curious(X)&~happy(X))<=>(~happy(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~humble(X))<=>~quiet(X)))&
(![X]:((humble(X)&creative(X))<=>creative(X)))&
((?[X]:((patient(X)<~>~patient(X))))=>(?[X]:((~generous(X)|~funny(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((old(X)&~funny(X)))))&
(![X]:((brave(X)<~>patient(X))=>(quiet(X)|~curious(X))))&
(![X]:((tall(X)&~brave(X))<=>(old(X)&generous(X))))&
(((~old(alice)|generous(alice)))=>(?[X]:((old(X)&wise(X)))))&
((happy(paul))<=>((generous(fred)<~>brave(fred))))&
((old(susan)<~>generous(susan)))&
((wise(mary)&brave(mary)))&
((tall(fred)|creative(fred)))&
(?[X]:((~rich(X)&~strong(X))))&
(?[X]:((~happy(X)&wise(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is either not strong or not kind is not rich.
Everyone who is humble is brave.
If paul is not funny or not creative then fred is not patient.
Everyone who is curious or funny is both not funny and not happy.
Everyone who is both not creative and calm is both not rich and kind and vice versa.
Everyone who is either creative or not brave is either not happy or not rich and vice versa.
If john is not tall or not quiet then alice is creative or tall.
Everyone who is either curious or not rich is either not creative or not humble.
Everyone who is patient or not humble is both kind and funny.
Everyone who is either quiet or not happy is tall.
If someone is kind or not creative then mary is both funny and happy and vice versa.
If someone is tall or creative then lucy is creative and vice versa.
If someone is either humble or not strong then someone is patient and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
Someone is both not patient and brave.
Fred is not funny.
Susan is not humble or not strong.
Someone is not kind.
John is both not quiet and brave.
Mary is not generous or strong.
Paul is not patient. | Alice is not humble. | contradiction | (![X]:((~strong(X)<~>~kind(X))=>~rich(X)))&
(![X]:(humble(X)=>brave(X)))&
(((~funny(paul)|~creative(paul)))=>(~patient(fred)))&
(![X]:((curious(X)|funny(X))=>(~funny(X)&~happy(X))))&
(![X]:((~creative(X)&calm(X))<=>(~rich(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(~happy(X)<~>~rich(X))))&
(((~tall(john)|~quiet(john)))=>((creative(alice)|tall(alice))))&
(![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(?[X]:((~patient(X)&brave(X))))&
(~funny(fred))&
((~humble(susan)|~strong(susan)))&
(?[X]:(~kind(X)))&
((~quiet(john)&brave(john)))&
((~generous(mary)|strong(mary)))&
(~patient(paul)) | ~humble(alice) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 7555556984762366773724781
% SZS output start Proof for 7555556984762366773724781
4. ! [X0] : ((funny(X0) | curious(X0)) => (~happy(X0) & ~funny(X0))) [input p3]
9. ! [X0] : ((~humble(X0) | patient(X0)) => (funny(X0) & kind(X0))) [input p8]
24. ~humble(alice) [input hypothesis]
30. ! [X0] : ((~happy(X0) & ~funny(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 4]
34. ! [X0] : ((funny(X0) & kind(X0)) | (humble(X0) & ~patient(X0))) [ennf transformation 9]
70. ~funny(X0) | ~funny(X0) [cnf transformation 30]
94. funny(X0) | humble(X0) [cnf transformation 34]
128. ~humble(alice) [cnf transformation 24]
129. ~funny(X0) [duplicate literal removal 70]
162. humble(X0) [subsumption resolution 94,129]
218. $false [subsumption resolution 128,162]
% SZS output end Proof for 7555556984762366773724781
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not happy or not old then someone is either not brave or not generous and vice versa. If someone is happy or not creative then alice is not old. If someone is not tall or not generous then someone is both kind and curious. Everyone who is not happy or brave is not creative and vice versa. Everyone who is either not creative or funny is both kind and patient. If someone is not patient then someone is not calm. If mary is not kind or not patient then someone is old or patient and vice versa. If someone is both quiet and not funny then someone is both wise and not wise. Everyone who is not kind or old is both not quiet and not wise. If someone is both not calm and calm then someone is either not quiet or patient and vice versa. Everyone who is both humble and quiet is either not rich or humble. Everyone who is wise is either brave or rich. Everyone who is both not tall and old is either happy or not rich. If mary is both not curious and tall then fred is not old and vice versa. If someone is funny then someone is both rich and not generous. Everyone who is kind is both brave and creative. Someone is either not wise or kind. Susan is either old or not strong. Alice is either not brave or not happy. Someone is either not kind or not humble. Lucy is not calm or kind. Someone is not rich. | Lucy is not quiet. | entailment | (((~happy(fred)|~old(fred)))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((?[X]:((happy(X)|~creative(X))))=>(~old(alice)))&
((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((kind(X)&curious(X)))))&
(![X]:((~happy(X)|brave(X))<=>~creative(X)))&
(![X]:((~creative(X)<~>funny(X))=>(kind(X)&patient(X))))&
((?[X]:(~patient(X)))=>(?[X]:(~calm(X))))&
(((~kind(mary)|~patient(mary)))<=>(?[X]:((old(X)|patient(X)))))&
((?[X]:((quiet(X)&~funny(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~kind(X)|old(X))=>(~quiet(X)&~wise(X))))&
((?[X]:((~calm(X)&calm(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:((humble(X)&quiet(X))=>(~rich(X)<~>humble(X))))&
(![X]:(wise(X)=>(brave(X)<~>rich(X))))&
(![X]:((~tall(X)&old(X))=>(happy(X)<~>~rich(X))))&
(((~curious(mary)&tall(mary)))<=>(~old(fred)))&
((?[X]:(funny(X)))=>(?[X]:((rich(X)&~generous(X)))))&
(![X]:(kind(X)=>(brave(X)&creative(X))))&
(?[X]:((~wise(X)<~>kind(X))))&
((old(susan)<~>~strong(susan)))&
((~brave(alice)<~>~happy(alice)))&
(?[X]:((~kind(X)<~>~humble(X))))&
((~calm(lucy)|kind(lucy)))&
(?[X]:(~rich(X))) | ~quiet(lucy) | [
"p3",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6192370692871140266448099
% SZS output start Proof for 6192370692871140266448099
4. ! [X0] : ((brave(X0) | ~happy(X0)) <=> ~creative(X0)) [input p3]
9. ! [X0] : ((old(X0) | ~kind(X0)) => (~wise(X0) & ~quiet(X0))) [input p8]
16. ! [X0] : (kind(X0) => (creative(X0) & brave(X0))) [input p15]
23. quiet(lucy) [input hypothesis]
34. ! [X0] : ((~wise(X0) & ~quiet(X0)) | (~old(X0) & kind(X0))) [ennf transformation 9]
41. ! [X0] : ((creative(X0) & brave(X0)) | ~kind(X0)) [ennf transformation 16]
50. ! [X0] : (((brave(X0) | ~happy(X0)) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [nnf transformation 4]
51. ! [X0] : ((brave(X0) | ~happy(X0) | creative(X0)) & (~creative(X0) | (~brave(X0) & happy(X0)))) [flattening 50]
100. ~creative(X0) | ~brave(X0) [cnf transformation 51]
113. ~quiet(X0) | kind(X0) [cnf transformation 34]
134. ~kind(X0) | brave(X0) [cnf transformation 41]
135. ~kind(X0) | creative(X0) [cnf transformation 41]
146. quiet(lucy) [cnf transformation 23]
331. 41 <=> kind(lucy) [avatar definition]
333. kind(lucy) <- (41) [avatar component clause 331]
340. kind(lucy) [resolution 113,146]
341. 41 [avatar split clause 340,331]
344. brave(lucy) <- (41) [resolution 134,333]
348. creative(lucy) <- (41) [resolution 135,333]
362. ~brave(lucy) <- (41) [resolution 348,100]
364. $false <- (41) [subsumption resolution 362,344]
365. ~41 [avatar contradiction clause 364]
366. $false [avatar sat refutation 341,365]
% SZS output end Proof for 6192370692871140266448099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both curious and not old is happy. Everyone who is not tall is not patient. If lucy is not strong then mary is funny and vice versa. Everyone who is kind or not quiet is not brave or happy and vice versa. Everyone who is either not curious or happy is either humble or not happy. If someone is tall or curious then alice is either not quiet or calm. Everyone who is both patient and not happy is either kind or humble and vice versa. Everyone who is both not funny and not strong is not kind and vice versa. Everyone who is both not old and not kind is generous or not wise and vice versa. If someone is not calm or not kind then paul is both humble and generous. If someone is either funny or not tall then paul is strong. If someone is old then alice is either not funny or wise and vice versa. Everyone who is both not curious and not brave is calm or not quiet. If someone is calm then susan is happy or tall and vice versa. Everyone who is curious is both not strong and tall. Everyone who is rich is both wise and strong and vice versa. Someone is strong or not wise. John is either not humble or happy. Someone is quiet. Fred is not humble or not generous. Someone is not generous. Someone is not old. Someone is either generous or tall. | Susan is kind. | entailment | (![X]:((curious(X)&~old(X))=>happy(X)))&
(![X]:(~tall(X)=>~patient(X)))&
((~strong(lucy))<=>(funny(mary)))&
(![X]:((kind(X)|~quiet(X))<=>(~brave(X)|happy(X))))&
(![X]:((~curious(X)<~>happy(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((tall(X)|curious(X))))=>((~quiet(alice)<~>calm(alice))))&
(![X]:((patient(X)&~happy(X))<=>(kind(X)<~>humble(X))))&
(![X]:((~funny(X)&~strong(X))<=>~kind(X)))&
(![X]:((~old(X)&~kind(X))<=>(generous(X)|~wise(X))))&
((?[X]:((~calm(X)|~kind(X))))=>((humble(paul)&generous(paul))))&
((?[X]:((funny(X)<~>~tall(X))))=>(strong(paul)))&
((?[X]:(old(X)))<=>((~funny(alice)<~>wise(alice))))&
(![X]:((~curious(X)&~brave(X))=>(calm(X)|~quiet(X))))&
((?[X]:(calm(X)))<=>((happy(susan)|tall(susan))))&
(![X]:(curious(X)=>(~strong(X)&tall(X))))&
(![X]:(rich(X)<=>(wise(X)&strong(X))))&
(?[X]:((strong(X)|~wise(X))))&
((~humble(john)<~>happy(john)))&
(?[X]:(quiet(X)))&
((~humble(fred)|~generous(fred)))&
(?[X]:(~generous(X)))&
(?[X]:(~old(X)))&
(?[X]:((generous(X)<~>tall(X)))) | kind(susan) | [
"p0",
"p4",
"p6",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 6304271989167059167101331
% SZS output start Proof for 6304271989167059167101331
1. ! [X0] : ((~old(X0) & curious(X0)) => happy(X0)) [input p0]
5. ! [X0] : ((~curious(X0) <~> happy(X0)) => (humble(X0) <~> ~happy(X0))) [input p4]
7. ! [X0] : ((~happy(X0) & patient(X0)) <=> (kind(X0) <~> humble(X0))) [input p6]
9. ! [X0] : ((~kind(X0) & ~old(X0)) <=> (~wise(X0) | generous(X0))) [input p8]
10. ? [X0] : (~kind(X0) | ~calm(X0)) => (generous(paul) & humble(paul)) [input p9]
24. ~kind(susan) [input hypothesis]
25. ! [X0] : (happy(X0) | (old(X0) | ~curious(X0))) [ennf transformation 1]
26. ! [X0] : (happy(X0) | old(X0) | ~curious(X0)) [flattening 25]
28. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 5]
30. (generous(paul) & humble(paul)) | ! [X0] : (kind(X0) & calm(X0)) [ennf transformation 10]
38. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 28]
40. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | (happy(X0) | ~patient(X0)))) [nnf transformation 7]
41. ! [X0] : (((~happy(X0) & patient(X0)) | ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0)))) & (((~humble(X0) | ~kind(X0)) & (humble(X0) | kind(X0))) | happy(X0) | ~patient(X0))) [flattening 40]
44. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & ((~wise(X0) | generous(X0)) | (kind(X0) | old(X0)))) [nnf transformation 9]
45. ! [X0] : (((~kind(X0) & ~old(X0)) | (wise(X0) & ~generous(X0))) & (~wise(X0) | generous(X0) | kind(X0) | old(X0))) [flattening 44]
68. ~curious(X0) | old(X0) | happy(X0) [cnf transformation 26]
78. happy(X0) | ~humble(X0) | happy(X0) | curious(X0) [cnf transformation 38]
89. ~humble(X0) | kind(X0) | ~happy(X0) [cnf transformation 41]
94. ~generous(X0) | ~old(X0) [cnf transformation 45]
96. ~generous(X0) | ~kind(X0) [cnf transformation 45]
99. humble(paul) | kind(X0) [cnf transformation 30]
101. generous(paul) | kind(X0) [cnf transformation 30]
123. ~kind(susan) [cnf transformation 24]
125. ~humble(X0) | happy(X0) | curious(X0) [duplicate literal removal 78]
155. 7 <=> ! [X0] : kind(X0) [avatar definition]
156. kind(X0) <- (7) [avatar component clause 155]
158. 8 <=> generous(paul) [avatar definition]
160. generous(paul) <- (8) [avatar component clause 158]
161. 7 | 8 [avatar split clause 101,158,155]
167. 10 <=> humble(paul) [avatar definition]
169. humble(paul) <- (10) [avatar component clause 167]
170. 7 | 10 [avatar split clause 99,167,155]
261. $false <- (7) [resolution 156,123]
262. ~7 [avatar contradiction clause 261]
265. ~old(paul) <- (8) [resolution 94,160]
268. ~kind(paul) <- (8) [resolution 96,160]
335. kind(paul) | ~happy(paul) <- (10) [resolution 89,169]
336. ~happy(paul) <- (8, 10) [subsumption resolution 335,268]
350. happy(paul) | curious(paul) <- (10) [resolution 125,169]
352. curious(paul) <- (8, 10) [subsumption resolution 350,336]
354. old(paul) | happy(paul) <- (8, 10) [resolution 352,68]
356. happy(paul) <- (8, 10) [subsumption resolution 354,265]
357. $false <- (8, 10) [subsumption resolution 356,336]
358. ~8 | ~10 [avatar contradiction clause 357]
359. $false [avatar sat refutation 161,170,262,358]
% SZS output end Proof for 6304271989167059167101331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old or not generous then someone is not creative or kind and vice versa.
Everyone who is either funny or not humble is patient or not generous and vice versa.
Everyone who is humble or kind is both calm and tall and vice versa.
Everyone who is both generous and not brave is either creative or not creative and vice versa.
If someone is either calm or wise then fred is both rich and not curious.
Everyone who is both not rich and not quiet is strong or not creative and vice versa.
If mary is not tall or funny then susan is both not happy and kind and vice versa.
Everyone who is humble is both rich and patient.
If someone is both not tall and not patient then someone is both curious and not rich and vice versa.
Everyone who is old or not calm is both not calm and humble.
Everyone who is both old and not curious is happy or not rich and vice versa.
If fred is both old and kind then someone is both tall and not brave.
Everyone who is either not old or rich is not kind or not rich and vice versa.
If susan is not wise then lucy is either calm or not curious and vice versa.
Everyone who is either not creative or not curious is patient.
Everyone who is rich is creative or not happy.
Lucy is not curious or rich.
Susan is both not old and calm.
Someone is both not funny and not brave.
John is either happy or not humble.
Paul is not tall or kind.
Someone is either calm or happy. | Mary is not generous. | contradiction | ((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(patient(X)|~generous(X))))&
(![X]:((humble(X)|kind(X))<=>(calm(X)&tall(X))))&
(![X]:((generous(X)&~brave(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:((calm(X)<~>wise(X))))=>((rich(fred)&~curious(fred))))&
(![X]:((~rich(X)&~quiet(X))<=>(strong(X)|~creative(X))))&
(((~tall(mary)|funny(mary)))<=>((~happy(susan)&kind(susan))))&
(![X]:(humble(X)=>(rich(X)&patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((old(X)|~calm(X))=>(~calm(X)&humble(X))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)|~rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(~kind(X)|~rich(X))))&
((~wise(susan))<=>((calm(lucy)<~>~curious(lucy))))&
(![X]:((~creative(X)<~>~curious(X))=>patient(X)))&
(![X]:(rich(X)=>(creative(X)|~happy(X))))&
((~curious(lucy)|rich(lucy)))&
((~old(susan)&calm(susan)))&
(?[X]:((~funny(X)&~brave(X))))&
((happy(john)<~>~humble(john)))&
((~tall(paul)|kind(paul)))&
(?[X]:((calm(X)<~>happy(X)))) | ~generous(mary) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 711161503571672789825443
% SZS output start Proof for 711161503571672789825443
4. ! [X0] : ((~brave(X0) & generous(X0)) <=> (creative(X0) <~> ~creative(X0))) [input p3]
23. ~generous(mary) [input hypothesis]
43. ! [X0] : (((~brave(X0) & generous(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | (brave(X0) | ~generous(X0)))) [nnf transformation 4]
44. ! [X0] : (((~brave(X0) & generous(X0)) | ((creative(X0) | creative(X0)) & (~creative(X0) | ~creative(X0)))) & (((creative(X0) | ~creative(X0)) & (~creative(X0) | creative(X0))) | brave(X0) | ~generous(X0))) [flattening 43]
86. generous(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 44]
87. generous(X0) | creative(X0) | creative(X0) [cnf transformation 44]
144. ~generous(mary) [cnf transformation 23]
147. generous(X0) | ~creative(X0) [duplicate literal removal 86]
148. generous(X0) | creative(X0) [duplicate literal removal 87]
168. 5 <=> ! [X3] : generous(X3) [avatar definition]
169. generous(X3) <- (5) [avatar component clause 168]
184. generous(X0) [subsumption resolution 147,148]
185. 5 [avatar split clause 184,168]
272. $false <- (5) [resolution 169,144]
273. ~5 [avatar contradiction clause 272]
274. $false [avatar sat refutation 185,273]
% SZS output end Proof for 711161503571672789825443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not curious is kind and vice versa.
Everyone who is not strong is wise and vice versa.
If someone is not happy or not patient then someone is not creative.
If someone is brave then lucy is either happy or not kind.
If someone is both creative and not brave then someone is old or strong.
Everyone who is either funny or curious is both happy and rich and vice versa.
Everyone who is either not funny or not old is either strong or not strong and vice versa.
Everyone who is rich is both kind and funny and vice versa.
If mary is creative then mary is quiet or curious.
Everyone who is calm is not creative or wise.
Everyone who is both not kind and funny is not brave or not old and vice versa.
Everyone who is either calm or not humble is both not quiet and strong and vice versa.
If someone is not strong or calm then fred is both not happy and funny.
Everyone who is not calm or wise is both happy and not wise and vice versa.
If alice is both funny and tall then someone is either happy or not strong.
Someone is not happy or creative.
Someone is either generous or not patient.
Susan is brave or not funny.
John is not creative.
Someone is tall.
John is humble.
Someone is either happy or not generous. | Lucy is curious. | contradiction | (![X]:((strong(X)|~curious(X))<=>kind(X)))&
(![X]:(~strong(X)<=>wise(X)))&
((?[X]:((~happy(X)|~patient(X))))=>(?[X]:(~creative(X))))&
((?[X]:(brave(X)))=>((happy(lucy)<~>~kind(lucy))))&
((?[X]:((creative(X)&~brave(X))))=>(?[X]:((old(X)|strong(X)))))&
(![X]:((funny(X)<~>curious(X))<=>(happy(X)&rich(X))))&
(![X]:((~funny(X)<~>~old(X))<=>(strong(X)<~>~strong(X))))&
(![X]:(rich(X)<=>(kind(X)&funny(X))))&
((creative(mary))=>((quiet(mary)|curious(mary))))&
(![X]:(calm(X)=>(~creative(X)|wise(X))))&
(![X]:((~kind(X)&funny(X))<=>(~brave(X)|~old(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(~quiet(X)&strong(X))))&
((?[X]:((~strong(X)|calm(X))))=>((~happy(fred)&funny(fred))))&
(![X]:((~calm(X)|wise(X))<=>(happy(X)&~wise(X))))&
(((funny(alice)&tall(alice)))=>(?[X]:((happy(X)<~>~strong(X)))))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((generous(X)<~>~patient(X))))&
((brave(susan)|~funny(susan)))&
(~creative(john))&
(?[X]:(tall(X)))&
(humble(john))&
(?[X]:((happy(X)<~>~generous(X)))) | curious(lucy) | [
"p0",
"p1",
"p5",
"p6",
"p7",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3954563173510733925333236
% SZS output start Proof for 3954563173510733925333236
1. ! [X0] : ((~curious(X0) | strong(X0)) <=> kind(X0)) [input p0]
2. ! [X0] : (~strong(X0) <=> wise(X0)) [input p1]
6. ! [X0] : ((funny(X0) <~> curious(X0)) <=> (rich(X0) & happy(X0))) [input p5]
7. ! [X0] : ((~funny(X0) <~> ~old(X0)) <=> (strong(X0) <~> ~strong(X0))) [input p6]
8. ! [X0] : (rich(X0) <=> (funny(X0) & kind(X0))) [input p7]
11. ! [X0] : ((funny(X0) & ~kind(X0)) <=> (~old(X0) | ~brave(X0))) [input p10]
14. ! [X0] : ((wise(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p13]
23. curious(lucy) [input hypothesis]
36. ! [X0] : (((~curious(X0) | strong(X0)) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [nnf transformation 1]
37. ! [X0] : ((~curious(X0) | strong(X0) | ~kind(X0)) & (kind(X0) | (curious(X0) & ~strong(X0)))) [flattening 36]
38. ! [X0] : ((~strong(X0) | ~wise(X0)) & (wise(X0) | strong(X0))) [nnf transformation 2]
46. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | (~rich(X0) | ~happy(X0))) & ((rich(X0) & happy(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [nnf transformation 6]
47. ! [X0] : ((((~curious(X0) | ~funny(X0)) & (curious(X0) | funny(X0))) | ~rich(X0) | ~happy(X0)) & ((rich(X0) & happy(X0)) | ((funny(X0) | ~curious(X0)) & (curious(X0) | ~funny(X0))))) [flattening 46]
48. ! [X0] : ((((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | ((strong(X0) | strong(X0)) & (~strong(X0) | ~strong(X0)))) & (((strong(X0) | ~strong(X0)) & (~strong(X0) | strong(X0))) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0))))) [nnf transformation 7]
49. ! [X0] : ((rich(X0) | (~funny(X0) | ~kind(X0))) & ((funny(X0) & kind(X0)) | ~rich(X0))) [nnf transformation 8]
50. ! [X0] : ((rich(X0) | ~funny(X0) | ~kind(X0)) & ((funny(X0) & kind(X0)) | ~rich(X0))) [flattening 49]
51. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & ((~old(X0) | ~brave(X0)) | (~funny(X0) | kind(X0)))) [nnf transformation 11]
52. ! [X0] : (((funny(X0) & ~kind(X0)) | (old(X0) & brave(X0))) & (~old(X0) | ~brave(X0) | ~funny(X0) | kind(X0))) [flattening 51]
55. ! [X0] : (((wise(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [nnf transformation 14]
56. ! [X0] : ((wise(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (~wise(X0) & calm(X0)))) [flattening 55]
70. ~strong(X0) | kind(X0) [cnf transformation 37]
73. wise(X0) | strong(X0) [cnf transformation 38]
83. ~curious(X0) | funny(X0) | rich(X0) [cnf transformation 47]
90. ~old(X0) | ~funny(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 48]
91. ~old(X0) | ~funny(X0) | strong(X0) | strong(X0) [cnf transformation 48]
95. ~rich(X0) | funny(X0) [cnf transformation 50]
101. ~kind(X0) | old(X0) [cnf transformation 52]
117. ~wise(X0) | ~wise(X0) [cnf transformation 56]
130. curious(lucy) [cnf transformation 23]
131. ~wise(X0) [duplicate literal removal 117]
133. ~old(X0) | ~funny(X0) | ~strong(X0) [duplicate literal removal 90]
134. ~old(X0) | ~funny(X0) | strong(X0) [duplicate literal removal 91]
175. ~funny(X0) | ~old(X0) [subsumption resolution 133,134]
198. 15 <=> ! [X0] : strong(X0) [avatar definition]
199. strong(X0) <- (15) [avatar component clause 198]
256. strong(X0) [resolution 73,131]
257. 15 [avatar split clause 256,198]
258. kind(X0) <- (15) [resolution 199,70]
266. old(X0) <- (15) [resolution 101,258]
293. funny(lucy) | rich(lucy) [resolution 83,130]
294. funny(lucy) [subsumption resolution 293,95]
300. ~old(lucy) [resolution 294,175]
302. $false <- (15) [subsumption resolution 300,266]
303. ~15 [avatar contradiction clause 302]
304. $false [avatar sat refutation 257,303]
% SZS output end Proof for 3954563173510733925333236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
If someone is not tall then someone is either generous or quiet and vice versa.
Everyone who is wise is funny or not tall.
Everyone who is tall is both rich and funny and vice versa.
Everyone who is either creative or strong is both not calm and not brave and vice versa.
Everyone who is not tall or rich is both tall and calm.
Everyone who is generous or patient is quiet or not quiet and vice versa.
Everyone who is both tall and humble is creative or kind and vice versa.
Everyone who is both not happy and quiet is calm or patient and vice versa.
Everyone who is strong is either kind or not humble and vice versa.
If lucy is funny or not rich then paul is either not brave or not happy and vice versa.
If someone is both happy and not humble then fred is both not funny and not brave and vice versa.
Everyone who is either creative or calm is happy.
Everyone who is not old or not brave is both not quiet and humble.
Everyone who is not tall is either not rich or patient and vice versa.
Someone is either generous or not calm.
Paul is not tall or wise.
Someone is tall or not strong.
Someone is not curious.
Someone is either not old or brave. | Lucy is kind. | entailment | ((?[X]:(~tall(X)))<=>(?[X]:((generous(X)<~>quiet(X)))))&
(![X]:(wise(X)=>(funny(X)|~tall(X))))&
(![X]:(tall(X)<=>(rich(X)&funny(X))))&
(![X]:((creative(X)<~>strong(X))<=>(~calm(X)&~brave(X))))&
(![X]:((~tall(X)|rich(X))=>(tall(X)&calm(X))))&
(![X]:((generous(X)|patient(X))<=>(quiet(X)|~quiet(X))))&
(![X]:((tall(X)&humble(X))<=>(creative(X)|kind(X))))&
(![X]:((~happy(X)&quiet(X))<=>(calm(X)|patient(X))))&
(![X]:(strong(X)<=>(kind(X)<~>~humble(X))))&
(((funny(lucy)|~rich(lucy)))<=>((~brave(paul)<~>~happy(paul))))&
((?[X]:((happy(X)&~humble(X))))<=>((~funny(fred)&~brave(fred))))&
(![X]:((creative(X)<~>calm(X))=>happy(X)))&
(![X]:((~old(X)|~brave(X))=>(~quiet(X)&humble(X))))&
(![X]:(~tall(X)<=>(~rich(X)<~>patient(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
((~tall(paul)|wise(paul)))&
(?[X]:((tall(X)|~strong(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~old(X)<~>brave(X)))) | kind(lucy) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5196990411432899023191563
% SZS output start Proof for 5196990411432899023191563
3. ! [X0] : (tall(X0) <=> (funny(X0) & rich(X0))) [input p2]
4. ! [X0] : ((creative(X0) <~> strong(X0)) <=> (~brave(X0) & ~calm(X0))) [input p3]
5. ! [X0] : ((rich(X0) | ~tall(X0)) => (calm(X0) & tall(X0))) [input p4]
7. ! [X0] : ((humble(X0) & tall(X0)) <=> (kind(X0) | creative(X0))) [input p6]
8. ! [X0] : ((quiet(X0) & ~happy(X0)) <=> (patient(X0) | calm(X0))) [input p7]
9. ! [X0] : (strong(X0) <=> (kind(X0) <~> ~humble(X0))) [input p8]
12. ! [X0] : ((creative(X0) <~> calm(X0)) => happy(X0)) [input p11]
20. ~kind(lucy) [input hypothesis]
25. ! [X0] : ((calm(X0) & tall(X0)) | (~rich(X0) & tall(X0))) [ennf transformation 5]
26. ! [X0] : (happy(X0) | (creative(X0) <=> calm(X0))) [ennf transformation 12]
33. ! [X0] : ((tall(X0) | (~funny(X0) | ~rich(X0))) & ((funny(X0) & rich(X0)) | ~tall(X0))) [nnf transformation 3]
34. ! [X0] : ((tall(X0) | ~funny(X0) | ~rich(X0)) & ((funny(X0) & rich(X0)) | ~tall(X0))) [flattening 33]
35. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | (brave(X0) | calm(X0))) & ((~brave(X0) & ~calm(X0)) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [nnf transformation 4]
36. ! [X0] : ((((~strong(X0) | ~creative(X0)) & (strong(X0) | creative(X0))) | brave(X0) | calm(X0)) & ((~brave(X0) & ~calm(X0)) | ((creative(X0) | ~strong(X0)) & (strong(X0) | ~creative(X0))))) [flattening 35]
39. ! [X0] : (((humble(X0) & tall(X0)) | (~kind(X0) & ~creative(X0))) & ((kind(X0) | creative(X0)) | (~humble(X0) | ~tall(X0)))) [nnf transformation 7]
40. ! [X0] : (((humble(X0) & tall(X0)) | (~kind(X0) & ~creative(X0))) & (kind(X0) | creative(X0) | ~humble(X0) | ~tall(X0))) [flattening 39]
41. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~patient(X0) & ~calm(X0))) & ((patient(X0) | calm(X0)) | (~quiet(X0) | happy(X0)))) [nnf transformation 8]
42. ! [X0] : (((quiet(X0) & ~happy(X0)) | (~patient(X0) & ~calm(X0))) & (patient(X0) | calm(X0) | ~quiet(X0) | happy(X0))) [flattening 41]
43. ! [X0] : ((strong(X0) | ((kind(X0) | humble(X0)) & (~humble(X0) | ~kind(X0)))) & (((humble(X0) | ~kind(X0)) & (~humble(X0) | kind(X0))) | ~strong(X0))) [nnf transformation 9]
51. ! [X0] : (happy(X0) | ((creative(X0) | ~calm(X0)) & (calm(X0) | ~creative(X0)))) [nnf transformation 26]
66. ~tall(X0) | rich(X0) [cnf transformation 34]
69. ~calm(X0) | strong(X0) | ~creative(X0) [cnf transformation 36]
75. tall(X0) | tall(X0) [cnf transformation 25]
78. ~rich(X0) | calm(X0) [cnf transformation 25]
86. ~creative(X0) | humble(X0) [cnf transformation 40]
89. ~happy(X0) | ~calm(X0) [cnf transformation 42]
93. ~humble(X0) | kind(X0) | ~strong(X0) [cnf transformation 43]
108. happy(X0) | creative(X0) | ~calm(X0) [cnf transformation 51]
123. ~kind(lucy) [cnf transformation 20]
124. tall(X0) [duplicate literal removal 75]
138. 4 <=> ! [X3] : tall(X3) [avatar definition]
139. tall(X3) <- (4) [avatar component clause 138]
150. 4 [avatar split clause 124,138]
199. ~calm(X0) | creative(X0) [subsumption resolution 108,89]
245. rich(X0) <- (4) [resolution 66,139]
255. calm(X0) <- (4) [resolution 78,245]
276. creative(X0) <- (4) [resolution 199,255]
279. humble(X0) <- (4) [resolution 276,86]
285. strong(X0) | ~creative(X0) <- (4) [resolution 69,255]
287. strong(X0) <- (4) [subsumption resolution 285,276]
302. kind(X0) | ~strong(X0) <- (4) [resolution 93,279]
305. kind(X0) <- (4) [subsumption resolution 302,287]
307. $false <- (4) [resolution 305,123]
311. ~4 [avatar contradiction clause 307]
312. $false [avatar sat refutation 150,311]
% SZS output end Proof for 5196990411432899023191563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both generous and not creative then someone is happy and vice versa. Everyone who is both not calm and quiet is either quiet or rich. If fred is either not curious or strong then someone is old or not curious. If someone is curious then mary is both not old and generous and vice versa. Everyone who is not curious is both not generous and not old and vice versa. Everyone who is not kind or wise is funny. Everyone who is either brave or rich is tall. Everyone who is not old is both not generous and not calm. If susan is either old or not strong then fred is strong or funny. If paul is not generous then john is not kind and vice versa. If someone is either not brave or wise then mary is both not old and generous. If alice is humble or patient then paul is not generous and vice versa. If someone is either rich or tall then someone is not quiet or humble. Everyone who is both generous and happy is either brave or tall and vice versa. Someone is either humble or not wise. Paul is not kind or patient. Someone is quiet. Someone is generous or not happy. Fred is either generous or strong. | Fred is generous. | contradiction | (((generous(fred)&~creative(fred)))<=>(?[X]:(happy(X))))&
(![X]:((~calm(X)&quiet(X))=>(quiet(X)<~>rich(X))))&
(((~curious(fred)<~>strong(fred)))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:(curious(X)))<=>((~old(mary)&generous(mary))))&
(![X]:(~curious(X)<=>(~generous(X)&~old(X))))&
(![X]:((~kind(X)|wise(X))=>funny(X)))&
(![X]:((brave(X)<~>rich(X))=>tall(X)))&
(![X]:(~old(X)=>(~generous(X)&~calm(X))))&
(((old(susan)<~>~strong(susan)))=>((strong(fred)|funny(fred))))&
((~generous(paul))<=>(~kind(john)))&
((?[X]:((~brave(X)<~>wise(X))))=>((~old(mary)&generous(mary))))&
(((humble(alice)|patient(alice)))<=>(~generous(paul)))&
((?[X]:((rich(X)<~>tall(X))))=>(?[X]:((~quiet(X)|humble(X)))))&
(![X]:((generous(X)&happy(X))<=>(brave(X)<~>tall(X))))&
(?[X]:((humble(X)<~>~wise(X))))&
((~kind(paul)|patient(paul)))&
(?[X]:(quiet(X)))&
(?[X]:((generous(X)|~happy(X))))&
((generous(fred)<~>strong(fred))) | generous(fred) | [
"p3",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 584876659797828583586443
% SZS output start Proof for 584876659797828583586443
4. ? [X0] : curious(X0) <=> (generous(mary) & ~old(mary)) [input p3]
5. ! [X0] : (~curious(X0) <=> (~old(X0) & ~generous(X0))) [input p4]
8. ! [X0] : (~old(X0) => (~calm(X0) & ~generous(X0))) [input p7]
20. generous(fred) [input hypothesis]
28. ! [X0] : ((~calm(X0) & ~generous(X0)) | old(X0)) [ennf transformation 8]
40. (? [X0] : curious(X0) | (~generous(mary) | old(mary))) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [nnf transformation 4]
41. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X0] : ~curious(X0)) [flattening 40]
42. (? [X0] : curious(X0) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [rectify 41]
43. ? [X0] : curious(X0) => curious(sK2) [choice axiom]
44. (curious(sK2) | ~generous(mary) | old(mary)) & ((generous(mary) & ~old(mary)) | ! [X1] : ~curious(X1)) [skolemisation 42,43]
45. ! [X0] : ((~curious(X0) | (old(X0) | generous(X0))) & ((~old(X0) & ~generous(X0)) | curious(X0))) [nnf transformation 5]
46. ! [X0] : ((~curious(X0) | old(X0) | generous(X0)) & ((~old(X0) & ~generous(X0)) | curious(X0))) [flattening 45]
73. ~old(mary) | ~curious(X1) [cnf transformation 44]
74. generous(mary) | ~curious(X1) [cnf transformation 44]
76. ~generous(X0) | curious(X0) [cnf transformation 46]
81. ~generous(X0) | old(X0) [cnf transformation 28]
107. generous(fred) [cnf transformation 20]
118. 3 <=> generous(fred) [avatar definition]
120. generous(fred) <- (3) [avatar component clause 118]
132. 6 <=> curious(fred) [avatar definition]
133. curious(fred) <- (6) [avatar component clause 132]
146. 9 <=> old(mary) [avatar definition]
147. ~old(mary) <- (~9) [avatar component clause 146]
150. 10 <=> generous(mary) [avatar definition]
151. generous(mary) <- (10) [avatar component clause 150]
159. 12 <=> ! [X1] : ~curious(X1) [avatar definition]
160. ~curious(X1) <- (12) [avatar component clause 159]
161. 12 | 10 [avatar split clause 74,150,159]
162. 12 | ~9 [avatar split clause 73,146,159]
240. 3 [avatar split clause 107,118]
241. curious(fred) <- (3) [resolution 76,120]
244. 6 | ~3 [avatar split clause 241,118,132]
246. old(mary) <- (10) [resolution 81,151]
248. $false <- (~9, 10) [subsumption resolution 246,147]
249. 9 | ~10 [avatar contradiction clause 248]
250. $false <- (6, 12) [resolution 160,133]
255. ~6 | ~12 [avatar contradiction clause 250]
256. $false [avatar sat refutation 161,162,240,244,249,255]
% SZS output end Proof for 584876659797828583586443
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not happy then alice is strong and vice versa.
If someone is both not generous and patient then someone is either funny or generous and vice versa.
Everyone who is both generous and not rich is not happy or not brave and vice versa.
If mary is both humble and not strong then paul is either not generous or rich and vice versa.
Everyone who is patient or curious is either calm or not funny.
If someone is rich or curious then alice is both old and not rich.
If someone is not quiet then someone is wise.
If john is not wise then someone is tall or old.
Everyone who is both not curious and creative is not strong and vice versa.
Everyone who is either not rich or quiet is either strong or not creative and vice versa.
If lucy is humble then fred is not quiet.
Everyone who is generous or funny is not patient and vice versa.
Everyone who is both curious and not strong is rich or old and vice versa.
If someone is both not happy and strong then fred is either strong or not happy.
If someone is old or not wise then john is either not strong or funny and vice versa.
If alice is either not rich or not generous then someone is patient or happy.
Paul is not happy or creative.
Someone is either not curious or brave.
Someone is either not wise or wise.
Lucy is strong.
Fred is not wise. | Mary is calm. | neutral | ((?[X]:((calm(X)|~happy(X))))<=>(strong(alice)))&
((?[X]:((~generous(X)&patient(X))))<=>(?[X]:((funny(X)<~>generous(X)))))&
(![X]:((generous(X)&~rich(X))<=>(~happy(X)|~brave(X))))&
(((humble(mary)&~strong(mary)))<=>((~generous(paul)<~>rich(paul))))&
(![X]:((patient(X)|curious(X))=>(calm(X)<~>~funny(X))))&
((?[X]:((rich(X)|curious(X))))=>((old(alice)&~rich(alice))))&
((?[X]:(~quiet(X)))=>(?[X]:(wise(X))))&
((~wise(john))=>(?[X]:((tall(X)|old(X)))))&
(![X]:((~curious(X)&creative(X))<=>~strong(X)))&
(![X]:((~rich(X)<~>quiet(X))<=>(strong(X)<~>~creative(X))))&
((humble(lucy))=>(~quiet(fred)))&
(![X]:((generous(X)|funny(X))<=>~patient(X)))&
(![X]:((curious(X)&~strong(X))<=>(rich(X)|old(X))))&
((?[X]:((~happy(X)&strong(X))))=>((strong(fred)<~>~happy(fred))))&
((?[X]:((old(X)|~wise(X))))<=>((~strong(john)<~>funny(john))))&
(((~rich(alice)<~>~generous(alice)))=>(?[X]:((patient(X)|happy(X)))))&
((~happy(paul)|creative(paul)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~wise(X)<~>wise(X))))&
(strong(lucy))&
(~wise(fred)) | calm(mary) | [] | null | 0 |
If someone is both funny and calm then paul is tall. If lucy is creative or not rich then mary is not quiet or calm. If lucy is not tall then someone is both strong and creative and vice versa. If someone is both funny and curious then susan is either creative or generous and vice versa. If fred is strong then john is kind or wise and vice versa. If someone is happy or not brave then alice is either brave or patient and vice versa. If someone is not happy then someone is both curious and brave. Everyone who is both calm and generous is both rich and kind. If john is both not old and humble then someone is humble and vice versa. Everyone who is brave or creative is both humble and strong and vice versa. If someone is not kind then someone is not wise. Everyone who is both calm and not brave is patient or strong and vice versa. If someone is either calm or curious then lucy is either not strong or creative and vice versa. If alice is either not calm or not tall then alice is rich or humble and vice versa. If alice is kind then someone is not calm. If someone is either funny or not kind then paul is both not creative and kind. Susan is tall. Someone is both kind and curious. Someone is either not patient or not curious. Fred is both not wise and not tall. Someone is not curious or strong. Paul is quiet or not patient. Alice is funny or generous. | Susan is not generous. | neutral | ((?[X]:((funny(X)&calm(X))))=>(tall(paul)))&
(((creative(lucy)|~rich(lucy)))=>((~quiet(mary)|calm(mary))))&
((~tall(lucy))<=>(?[X]:((strong(X)&creative(X)))))&
((?[X]:((funny(X)&curious(X))))<=>((creative(susan)<~>generous(susan))))&
((strong(fred))<=>((kind(john)|wise(john))))&
((?[X]:((happy(X)|~brave(X))))<=>((brave(alice)<~>patient(alice))))&
((?[X]:(~happy(X)))=>(?[X]:((curious(X)&brave(X)))))&
(![X]:((calm(X)&generous(X))=>(rich(X)&kind(X))))&
(((~old(john)&humble(john)))<=>(?[X]:(humble(X))))&
(![X]:((brave(X)|creative(X))<=>(humble(X)&strong(X))))&
((?[X]:(~kind(X)))=>(?[X]:(~wise(X))))&
(![X]:((calm(X)&~brave(X))<=>(patient(X)|strong(X))))&
((?[X]:((calm(X)<~>curious(X))))<=>((~strong(lucy)<~>creative(lucy))))&
(((~calm(alice)<~>~tall(alice)))<=>((rich(alice)|humble(alice))))&
((kind(alice))=>(?[X]:(~calm(X))))&
((?[X]:((funny(X)<~>~kind(X))))=>((~creative(paul)&kind(paul))))&
(tall(susan))&
(?[X]:((kind(X)&curious(X))))&
(?[X]:((~patient(X)<~>~curious(X))))&
((~wise(fred)&~tall(fred)))&
(?[X]:((~curious(X)|strong(X))))&
((quiet(paul)|~patient(paul)))&
((funny(alice)|generous(alice))) | ~generous(susan) | [] | null | 0 |
Everyone who is either not happy or brave is calm and vice versa.
Everyone who is rich is both quiet and strong and vice versa.
If someone is not patient or old then lucy is both not quiet and patient and vice versa.
Everyone who is either not wise or not curious is patient and vice versa.
Everyone who is either not quiet or not happy is tall and vice versa.
If fred is both not creative and rich then someone is not humble or not kind and vice versa.
If someone is either happy or curious then someone is both happy and not patient.
Everyone who is either wise or brave is either not old or not rich and vice versa.
Everyone who is not strong or not curious is both calm and not funny and vice versa.
If someone is either humble or kind then susan is both not happy and kind.
Everyone who is either generous or happy is not generous and vice versa.
If lucy is not brave or not quiet then paul is both humble and not generous and vice versa.
If lucy is funny then someone is kind or not happy and vice versa.
Everyone who is either rich or not calm is old.
If john is either not humble or brave then someone is either not calm or not patient and vice versa.
If someone is both quiet and not patient then mary is both not curious and not rich.
Fred is both tall and not quiet.
Susan is both not quiet and not generous.
Someone is not old.
Alice is rich or not curious.
Susan is calm.
Alice is both not generous and calm. | Lucy is kind. | entailment | (![X]:((~happy(X)<~>brave(X))<=>calm(X)))&
(![X]:(rich(X)<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|old(X))))<=>((~quiet(lucy)&patient(lucy))))&
(![X]:((~wise(X)<~>~curious(X))<=>patient(X)))&
(![X]:((~quiet(X)<~>~happy(X))<=>tall(X)))&
(((~creative(fred)&rich(fred)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((happy(X)&~patient(X)))))&
(![X]:((wise(X)<~>brave(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((~strong(X)|~curious(X))<=>(calm(X)&~funny(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((~happy(susan)&kind(susan))))&
(![X]:((generous(X)<~>happy(X))<=>~generous(X)))&
(((~brave(lucy)|~quiet(lucy)))<=>((humble(paul)&~generous(paul))))&
((funny(lucy))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((rich(X)<~>~calm(X))=>old(X)))&
(((~humble(john)<~>brave(john)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))=>((~curious(mary)&~rich(mary))))&
((tall(fred)&~quiet(fred)))&
((~quiet(susan)&~generous(susan)))&
(?[X]:(~old(X)))&
((rich(alice)|~curious(alice)))&
(calm(susan))&
((~generous(alice)&calm(alice))) | kind(lucy) | [
"p1",
"p5",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 392570341344592016724142
% SZS output start Proof for 392570341344592016724142
2. ! [X0] : (rich(X0) <=> (strong(X0) & quiet(X0))) [input p1]
6. (rich(fred) & ~creative(fred)) <=> ? [X0] : (~kind(X0) | ~humble(X0)) [input p5]
17. ~quiet(fred) & tall(fred) [input p16]
23. ~kind(lucy) [input hypothesis]
32. ! [X0] : ((rich(X0) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | ~rich(X0))) [nnf transformation 2]
33. ! [X0] : ((rich(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | ~rich(X0))) [flattening 32]
41. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X0] : (~kind(X0) | ~humble(X0)) | (~rich(fred) | creative(fred))) [nnf transformation 6]
42. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X0] : (~kind(X0) | ~humble(X0)) | ~rich(fred) | creative(fred)) [flattening 41]
43. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X1] : (~kind(X1) | ~humble(X1)) | ~rich(fred) | creative(fred)) [rectify 42]
44. ? [X1] : (~kind(X1) | ~humble(X1)) => (~kind(sK1) | ~humble(sK1)) [choice axiom]
45. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & ((~kind(sK1) | ~humble(sK1)) | ~rich(fred) | creative(fred)) [skolemisation 43,44]
72. ~rich(X0) | quiet(X0) [cnf transformation 33]
90. rich(fred) | kind(X0) [cnf transformation 45]
137. ~quiet(fred) [cnf transformation 17]
145. ~kind(lucy) [cnf transformation 23]
176. 7 <=> ! [X0] : kind(X0) [avatar definition]
177. kind(X0) <- (7) [avatar component clause 176]
179. 8 <=> rich(fred) [avatar definition]
181. rich(fred) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 90,179,176]
336. quiet(fred) <- (8) [resolution 72,181]
337. $false <- (8) [subsumption resolution 336,137]
338. ~8 [avatar contradiction clause 337]
339. $false <- (7) [resolution 177,145]
344. ~7 [avatar contradiction clause 339]
345. $false [avatar sat refutation 182,338,344]
% SZS output end Proof for 392570341344592016724142
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both rich and not kind then someone is either not patient or calm and vice versa.
Everyone who is not happy is both not creative and not curious.
If someone is both not rich and not strong then someone is either not creative or not calm.
If someone is both not quiet and generous then someone is not generous.
Everyone who is kind is strong.
If someone is both not kind and not patient then someone is both not funny and humble.
If paul is calm then alice is both not generous and curious and vice versa.
Everyone who is kind or quiet is either creative or old.
Everyone who is either quiet or not curious is funny and vice versa.
If susan is not creative then someone is not brave.
Everyone who is calm or not humble is wise.
If someone is kind then alice is either quiet or not kind.
Everyone who is not old is not brave.
Everyone who is humble or not brave is both not happy and happy.
Everyone who is not brave or happy is not patient or strong and vice versa.
Everyone who is both old and calm is either kind or not patient and vice versa.
Someone is either quiet or curious.
Someone is patient or tall.
Someone is not funny.
Lucy is not quiet or old.
Someone is either not tall or not quiet. | Lucy is rich. | neutral | ((?[X]:((rich(X)&~kind(X))))<=>(?[X]:((~patient(X)<~>calm(X)))))&
(![X]:(~happy(X)=>(~creative(X)&~curious(X))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((~creative(X)<~>~calm(X)))))&
((?[X]:((~quiet(X)&generous(X))))=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>strong(X)))&
((?[X]:((~kind(X)&~patient(X))))=>(?[X]:((~funny(X)&humble(X)))))&
((calm(paul))<=>((~generous(alice)&curious(alice))))&
(![X]:((kind(X)|quiet(X))=>(creative(X)<~>old(X))))&
(![X]:((quiet(X)<~>~curious(X))<=>funny(X)))&
((~creative(susan))=>(?[X]:(~brave(X))))&
(![X]:((calm(X)|~humble(X))=>wise(X)))&
((?[X]:(kind(X)))=>((quiet(alice)<~>~kind(alice))))&
(![X]:(~old(X)=>~brave(X)))&
(![X]:((humble(X)|~brave(X))=>(~happy(X)&happy(X))))&
(![X]:((~brave(X)|happy(X))<=>(~patient(X)|strong(X))))&
(![X]:((old(X)&calm(X))<=>(kind(X)<~>~patient(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
(?[X]:((patient(X)|tall(X))))&
(?[X]:(~funny(X)))&
((~quiet(lucy)|old(lucy)))&
(?[X]:((~tall(X)<~>~quiet(X)))) | rich(lucy) | [] | 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. | Fred is funny. | 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))) | funny(fred) | [] | null | 0 |
Everyone who is brave is not funny and vice versa.
If someone is both not rich and not creative then someone is both curious and old and vice versa.
Everyone who is either not rich or funny is calm or not curious.
If someone is both not curious and not generous then someone is not generous or old.
If someone is either wise or not old then mary is either not humble or patient and vice versa.
Everyone who is curious is either quiet or not calm and vice versa.
If someone is either not curious or tall then someone is curious.
Everyone who is both happy and calm is humble or tall and vice versa.
Everyone who is rich is both quiet and wise and vice versa.
Everyone who is humble is not generous or not creative and vice versa.
If fred is both humble and not brave then someone is not curious or not patient and vice versa.
Everyone who is not funny is both not generous and not strong and vice versa.
If someone is both brave and creative then someone is patient or not patient.
Everyone who is both quiet and humble is not kind and vice versa.
If lucy is both not curious and not strong then paul is not quiet and vice versa.
If someone is not generous then someone is not generous or creative and vice versa.
Someone is calm.
Someone is not happy or not humble.
Mary is either not patient or not curious.
Susan is humble.
Alice is humble.
Someone is not creative or not strong.
Someone is patient. | Alice is not patient. | neutral | (![X]:(brave(X)<=>~funny(X)))&
((?[X]:((~rich(X)&~creative(X))))<=>(?[X]:((curious(X)&old(X)))))&
(![X]:((~rich(X)<~>funny(X))=>(calm(X)|~curious(X))))&
((?[X]:((~curious(X)&~generous(X))))=>(?[X]:((~generous(X)|old(X)))))&
((?[X]:((wise(X)<~>~old(X))))<=>((~humble(mary)<~>patient(mary))))&
(![X]:(curious(X)<=>(quiet(X)<~>~calm(X))))&
((?[X]:((~curious(X)<~>tall(X))))=>(?[X]:(curious(X))))&
(![X]:((happy(X)&calm(X))<=>(humble(X)|tall(X))))&
(![X]:(rich(X)<=>(quiet(X)&wise(X))))&
(![X]:(humble(X)<=>(~generous(X)|~creative(X))))&
(((humble(fred)&~brave(fred)))<=>(?[X]:((~curious(X)|~patient(X)))))&
(![X]:(~funny(X)<=>(~generous(X)&~strong(X))))&
((?[X]:((brave(X)&creative(X))))=>(?[X]:((patient(X)|~patient(X)))))&
(![X]:((quiet(X)&humble(X))<=>~kind(X)))&
(((~curious(lucy)&~strong(lucy)))<=>(~quiet(paul)))&
((?[X]:(~generous(X)))<=>(?[X]:((~generous(X)|creative(X)))))&
(?[X]:(calm(X)))&
(?[X]:((~happy(X)|~humble(X))))&
((~patient(mary)<~>~curious(mary)))&
(humble(susan))&
(humble(alice))&
(?[X]:((~creative(X)|~strong(X))))&
(?[X]:(patient(X))) | ~patient(alice) | [] | null | 0 |
If someone is tall then someone is both not creative and not brave. Everyone who is happy is both not calm and not happy. If lucy is rich then someone is not strong. Everyone who is both not old and not generous is not curious. If someone is both strong and not calm then someone is not quiet or not humble and vice versa. Everyone who is either not quiet or not curious is either not funny or old and vice versa. Everyone who is not curious or funny is either curious or strong. If alice is wise or strong then someone is not creative or curious and vice versa. If lucy is both not wise and not quiet then someone is both strong and not quiet and vice versa. Everyone who is either strong or rich is either not strong or tall. If someone is calm then lucy is curious and vice versa. If mary is either old or not generous then someone is either not kind or generous and vice versa. Everyone who is not strong or tall is tall and vice versa. If paul is either patient or rich then someone is either not funny or not happy and vice versa. If fred is either not wise or humble then someone is not generous or quiet. If lucy is rich then someone is either strong or not curious. Someone is either brave or not curious. Someone is old. John is not happy. Alice is not quiet or patient. John is both brave and not quiet. Fred is both wise and not calm. John is both rich and not funny. Someone is either funny or not wise. | John is funny. | contradiction | ((?[X]:(tall(X)))=>(?[X]:((~creative(X)&~brave(X)))))&
(![X]:(happy(X)=>(~calm(X)&~happy(X))))&
((rich(lucy))=>(?[X]:(~strong(X))))&
(![X]:((~old(X)&~generous(X))=>~curious(X)))&
((?[X]:((strong(X)&~calm(X))))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((~quiet(X)<~>~curious(X))<=>(~funny(X)<~>old(X))))&
(![X]:((~curious(X)|funny(X))=>(curious(X)<~>strong(X))))&
(((wise(alice)|strong(alice)))<=>(?[X]:((~creative(X)|curious(X)))))&
(((~wise(lucy)&~quiet(lucy)))<=>(?[X]:((strong(X)&~quiet(X)))))&
(![X]:((strong(X)<~>rich(X))=>(~strong(X)<~>tall(X))))&
((?[X]:(calm(X)))<=>(curious(lucy)))&
(((old(mary)<~>~generous(mary)))<=>(?[X]:((~kind(X)<~>generous(X)))))&
(![X]:((~strong(X)|tall(X))<=>tall(X)))&
(((patient(paul)<~>rich(paul)))<=>(?[X]:((~funny(X)<~>~happy(X)))))&
(((~wise(fred)<~>humble(fred)))=>(?[X]:((~generous(X)|quiet(X)))))&
((rich(lucy))=>(?[X]:((strong(X)<~>~curious(X)))))&
(?[X]:((brave(X)<~>~curious(X))))&
(?[X]:(old(X)))&
(~happy(john))&
((~quiet(alice)|patient(alice)))&
((brave(john)&~quiet(john)))&
((wise(fred)&~calm(fred)))&
((rich(john)&~funny(john)))&
(?[X]:((funny(X)<~>~wise(X)))) | funny(john) | [
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 767838600574472750829266
% SZS output start Proof for 767838600574472750829266
23. ~funny(john) & rich(john) [input p22]
25. funny(john) [input hypothesis]
158. ~funny(john) [cnf transformation 23]
161. funny(john) [cnf transformation 25]
393. $false [subsumption resolution 161,158]
% SZS output end Proof for 767838600574472750829266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is both not wise and not rich and vice versa.
If john is not calm then lucy is both quiet and humble and vice versa.
Everyone who is either creative or wise is calm or not brave and vice versa.
Everyone who is not brave is either not curious or tall.
Everyone who is either quiet or funny is patient or tall.
Everyone who is both not patient and not happy is either funny or not tall.
Everyone who is not brave is rich and vice versa.
If susan is rich then someone is either wise or not creative and vice versa.
If susan is humble or patient then someone is both happy and not curious.
If someone is not calm then mary is either curious or not patient.
Everyone who is creative or not patient is either brave or creative.
Everyone who is generous or humble is tall.
Everyone who is not rich or not old is patient and vice versa.
If someone is not tall or brave then someone is either quiet or not calm.
If paul is both not curious and not creative then alice is both not funny and wise.
Someone is either not creative or generous.
John is either not old or not calm.
Someone is either tall or patient.
Someone is curious.
Fred is not kind.
Susan is generous.
Susan is not calm or not quiet.
Fred is both not calm and not humble. | Paul is not patient. | contradiction | (![X]:(creative(X)<=>(~wise(X)&~rich(X))))&
((~calm(john))<=>((quiet(lucy)&humble(lucy))))&
(![X]:((creative(X)<~>wise(X))<=>(calm(X)|~brave(X))))&
(![X]:(~brave(X)=>(~curious(X)<~>tall(X))))&
(![X]:((quiet(X)<~>funny(X))=>(patient(X)|tall(X))))&
(![X]:((~patient(X)&~happy(X))=>(funny(X)<~>~tall(X))))&
(![X]:(~brave(X)<=>rich(X)))&
((rich(susan))<=>(?[X]:((wise(X)<~>~creative(X)))))&
(((humble(susan)|patient(susan)))=>(?[X]:((happy(X)&~curious(X)))))&
((?[X]:(~calm(X)))=>((curious(mary)<~>~patient(mary))))&
(![X]:((creative(X)|~patient(X))=>(brave(X)<~>creative(X))))&
(![X]:((generous(X)|humble(X))=>tall(X)))&
(![X]:((~rich(X)|~old(X))<=>patient(X)))&
((?[X]:((~tall(X)|brave(X))))=>(?[X]:((quiet(X)<~>~calm(X)))))&
(((~curious(paul)&~creative(paul)))=>((~funny(alice)&wise(alice))))&
(?[X]:((~creative(X)<~>generous(X))))&
((~old(john)<~>~calm(john)))&
(?[X]:((tall(X)<~>patient(X))))&
(?[X]:(curious(X)))&
(~kind(fred))&
(generous(susan))&
((~calm(susan)|~quiet(susan)))&
((~calm(fred)&~humble(fred))) | ~patient(paul) | [
"p0",
"p6",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5507900058155359283624366
% SZS output start Proof for 5507900058155359283624366
1. ! [X0] : (creative(X0) <=> (~rich(X0) & ~wise(X0))) [input p0]
7. ! [X0] : (~brave(X0) <=> rich(X0)) [input p6]
11. ! [X0] : ((~patient(X0) | creative(X0)) => (brave(X0) <~> creative(X0))) [input p10]
13. ! [X0] : ((~old(X0) | ~rich(X0)) <=> patient(X0)) [input p12]
24. ~patient(paul) [input hypothesis]
34. ! [X0] : ((brave(X0) <~> creative(X0)) | (patient(X0) & ~creative(X0))) [ennf transformation 11]
39. ! [X0] : ((creative(X0) | (rich(X0) | wise(X0))) & ((~rich(X0) & ~wise(X0)) | ~creative(X0))) [nnf transformation 1]
40. ! [X0] : ((creative(X0) | rich(X0) | wise(X0)) & ((~rich(X0) & ~wise(X0)) | ~creative(X0))) [flattening 39]
47. ! [X0] : ((~brave(X0) | ~rich(X0)) & (rich(X0) | brave(X0))) [nnf transformation 7]
55. ! [X0] : (((~creative(X0) | ~brave(X0)) & (creative(X0) | brave(X0))) | (patient(X0) & ~creative(X0))) [nnf transformation 34]
56. ! [X0] : (((~old(X0) | ~rich(X0)) | ~patient(X0)) & (patient(X0) | (old(X0) & rich(X0)))) [nnf transformation 13]
57. ! [X0] : ((~old(X0) | ~rich(X0) | ~patient(X0)) & (patient(X0) | (old(X0) & rich(X0)))) [flattening 56]
72. ~rich(X0) | ~creative(X0) [cnf transformation 40]
88. ~brave(X0) | ~rich(X0) [cnf transformation 47]
98. patient(X0) | brave(X0) | creative(X0) [cnf transformation 55]
103. patient(X0) | rich(X0) [cnf transformation 57]
123. ~patient(paul) [cnf transformation 24]
212. 19 <=> creative(paul) [avatar definition]
213. ~creative(paul) <- (~19) [avatar component clause 212]
262. rich(paul) [resolution 103,123]
265. ~creative(paul) [resolution 262,72]
266. ~19 [avatar split clause 265,212]
290. 31 <=> brave(paul) [avatar definition]
292. brave(paul) <- (31) [avatar component clause 290]
322. brave(paul) | creative(paul) [resolution 98,123]
324. brave(paul) <- (~19) [subsumption resolution 322,213]
325. 31 | 19 [avatar split clause 324,212,290]
328. ~rich(paul) <- (31) [resolution 292,88]
329. $false <- (31) [subsumption resolution 328,262]
330. ~31 [avatar contradiction clause 329]
331. $false [avatar sat refutation 266,325,330]
% SZS output end Proof for 5507900058155359283624366
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is tall and vice versa.
If someone is both not calm and curious then john is both tall and not tall.
If someone is either calm or not wise then mary is both patient and not wise and vice versa.
Everyone who is both not humble and funny is calm or not tall and vice versa.
Everyone who is either wise or tall is wise and vice versa.
Everyone who is both kind and not brave is both not curious and not rich and vice versa.
Everyone who is both not old and not patient is not wise.
If susan is both quiet and patient then someone is both tall and quiet.
If someone is both calm and funny then someone is either curious or not creative.
Everyone who is both tall and brave is either strong or brave.
Everyone who is kind is strong or not strong and vice versa.
If fred is not patient then john is both not wise and not old.
Everyone who is both curious and not brave is not kind and vice versa.
Everyone who is either not humble or not brave is either not creative or not brave and vice versa.
If someone is either happy or not funny then lucy is not calm or not patient and vice versa.
Everyone who is both not funny and quiet is not creative.
John is not old or curious.
Lucy is either quiet or happy.
Someone is patient or not brave.
Someone is calm.
Someone is not calm.
Fred is either humble or kind.
Susan is funny. | Lucy is not creative. | entailment | (![X]:(~old(X)<=>tall(X)))&
((?[X]:((~calm(X)&curious(X))))=>((tall(john)&~tall(john))))&
((?[X]:((calm(X)<~>~wise(X))))<=>((patient(mary)&~wise(mary))))&
(![X]:((~humble(X)&funny(X))<=>(calm(X)|~tall(X))))&
(![X]:((wise(X)<~>tall(X))<=>wise(X)))&
(![X]:((kind(X)&~brave(X))<=>(~curious(X)&~rich(X))))&
(![X]:((~old(X)&~patient(X))=>~wise(X)))&
(((quiet(susan)&patient(susan)))=>(?[X]:((tall(X)&quiet(X)))))&
((?[X]:((calm(X)&funny(X))))=>(?[X]:((curious(X)<~>~creative(X)))))&
(![X]:((tall(X)&brave(X))=>(strong(X)<~>brave(X))))&
(![X]:(kind(X)<=>(strong(X)|~strong(X))))&
((~patient(fred))=>((~wise(john)&~old(john))))&
(![X]:((curious(X)&~brave(X))<=>~kind(X)))&
(![X]:((~humble(X)<~>~brave(X))<=>(~creative(X)<~>~brave(X))))&
((?[X]:((happy(X)<~>~funny(X))))<=>((~calm(lucy)|~patient(lucy))))&
(![X]:((~funny(X)&quiet(X))=>~creative(X)))&
((~old(john)|curious(john)))&
((quiet(lucy)<~>happy(lucy)))&
(?[X]:((patient(X)|~brave(X))))&
(?[X]:(calm(X)))&
(?[X]:(~calm(X)))&
((humble(fred)<~>kind(fred)))&
(funny(susan)) | ~creative(lucy) | [
"p3",
"p4",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4759300896396469190744582
% SZS output start Proof for 4759300896396469190744582
4. ! [X0] : ((funny(X0) & ~humble(X0)) <=> (~tall(X0) | calm(X0))) [input p3]
5. ! [X0] : ((wise(X0) <~> tall(X0)) <=> wise(X0)) [input p4]
14. ! [X0] : ((~humble(X0) <~> ~brave(X0)) <=> (~creative(X0) <~> ~brave(X0))) [input p13]
24. creative(lucy) [input hypothesis]
43. ! [X0] : (((funny(X0) & ~humble(X0)) | (tall(X0) & ~calm(X0))) & ((~tall(X0) | calm(X0)) | (~funny(X0) | humble(X0)))) [nnf transformation 4]
44. ! [X0] : (((funny(X0) & ~humble(X0)) | (tall(X0) & ~calm(X0))) & (~tall(X0) | calm(X0) | ~funny(X0) | humble(X0))) [flattening 43]
45. ! [X0] : ((((~tall(X0) | ~wise(X0)) & (tall(X0) | wise(X0))) | ~wise(X0)) & (wise(X0) | ((wise(X0) | ~tall(X0)) & (tall(X0) | ~wise(X0))))) [nnf transformation 5]
59. ! [X0] : ((((brave(X0) | humble(X0)) & (~brave(X0) | ~humble(X0))) | ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0)))) & (((brave(X0) | creative(X0)) & (~brave(X0) | ~creative(X0))) | ((~humble(X0) | brave(X0)) & (~brave(X0) | humble(X0))))) [nnf transformation 14]
85. ~humble(X0) | tall(X0) [cnf transformation 44]
89. wise(X0) | wise(X0) | ~tall(X0) [cnf transformation 45]
91. ~tall(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 45]
111. ~brave(X0) | ~creative(X0) | ~brave(X0) | humble(X0) [cnf transformation 59]
118. brave(X0) | humble(X0) | ~creative(X0) | brave(X0) [cnf transformation 59]
135. creative(lucy) [cnf transformation 24]
136. ~brave(X0) | ~creative(X0) | humble(X0) [duplicate literal removal 111]
139. brave(X0) | humble(X0) | ~creative(X0) [duplicate literal removal 118]
141. wise(X0) | ~tall(X0) [duplicate literal removal 89]
142. ~wise(X0) | ~tall(X0) [duplicate literal removal 91]
180. ~tall(X0) [subsumption resolution 141,142]
227. ~creative(X0) | humble(X0) [subsumption resolution 136,139]
291. humble(lucy) [resolution 227,135]
293. tall(lucy) [resolution 291,85]
295. $false [subsumption resolution 293,180]
% SZS output end Proof for 4759300896396469190744582
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or wise then mary is either old or calm and vice versa.
If someone is tall or not brave then someone is not tall or not rich and vice versa.
Everyone who is either not wise or not calm is either not brave or wise and vice versa.
If someone is tall or not creative then john is both curious and not creative and vice versa.
Everyone who is not old or funny is not wise.
Everyone who is either not humble or rich is either wise or generous and vice versa.
If paul is both not patient and not humble then susan is either happy or not humble and vice versa.
Everyone who is humble is patient.
Everyone who is either happy or not humble is quiet.
If someone is either old or not humble then john is either not patient or not tall.
If someone is creative or not curious then paul is patient or not patient.
If alice is either not brave or creative then john is funny and vice versa.
If susan is both not creative and strong then someone is either calm or not kind and vice versa.
If someone is either not generous or not humble then john is not rich and vice versa.
If lucy is either not curious or not humble then fred is not curious or not happy and vice versa.
If someone is rich or strong then alice is both generous and not patient and vice versa.
John is both wise and not happy.
Someone is not funny or not curious.
Someone is either not quiet or not rich.
Susan is not creative.
Someone is humble.
Mary is quiet.
Someone is strong or not quiet. | John is not happy. | entailment | ((?[X]:((humble(X)<~>wise(X))))<=>((old(mary)<~>calm(mary))))&
((?[X]:((tall(X)|~brave(X))))<=>(?[X]:((~tall(X)|~rich(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(~brave(X)<~>wise(X))))&
((?[X]:((tall(X)|~creative(X))))<=>((curious(john)&~creative(john))))&
(![X]:((~old(X)|funny(X))=>~wise(X)))&
(![X]:((~humble(X)<~>rich(X))<=>(wise(X)<~>generous(X))))&
(((~patient(paul)&~humble(paul)))<=>((happy(susan)<~>~humble(susan))))&
(![X]:(humble(X)=>patient(X)))&
(![X]:((happy(X)<~>~humble(X))=>quiet(X)))&
((?[X]:((old(X)<~>~humble(X))))=>((~patient(john)<~>~tall(john))))&
((?[X]:((creative(X)|~curious(X))))=>((patient(paul)|~patient(paul))))&
(((~brave(alice)<~>creative(alice)))<=>(funny(john)))&
(((~creative(susan)&strong(susan)))<=>(?[X]:((calm(X)<~>~kind(X)))))&
((?[X]:((~generous(X)<~>~humble(X))))<=>(~rich(john)))&
(((~curious(lucy)<~>~humble(lucy)))<=>((~curious(fred)|~happy(fred))))&
((?[X]:((rich(X)|strong(X))))<=>((generous(alice)&~patient(alice))))&
((wise(john)&~happy(john)))&
(?[X]:((~funny(X)|~curious(X))))&
(?[X]:((~quiet(X)<~>~rich(X))))&
(~creative(susan))&
(?[X]:(humble(X)))&
(quiet(mary))&
(?[X]:((strong(X)|~quiet(X)))) | ~happy(john) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4536968830261425646516962
% SZS output start Proof for 4536968830261425646516962
17. ~happy(john) & wise(john) [input p16]
24. happy(john) [input hypothesis]
154. ~happy(john) [cnf transformation 17]
162. happy(john) [cnf transformation 24]
439. $false [subsumption resolution 162,154]
% SZS output end Proof for 4536968830261425646516962
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is curious or not wise then someone is not generous and vice versa.
If susan is not tall then alice is brave.
If someone is either not humble or humble then susan is not tall.
If someone is both brave and patient then john is patient and vice versa.
Everyone who is either not wise or quiet is old or not kind and vice versa.
If someone is either tall or patient then someone is both not strong and happy.
If someone is happy or not curious then susan is both kind and not humble and vice versa.
Everyone who is both not happy and not funny is either not generous or not happy.
Everyone who is both quiet and kind is not brave or funny and vice versa.
If alice is curious or creative then someone is both creative and quiet.
Everyone who is not curious or tall is both not old and funny and vice versa.
If someone is not rich or not strong then someone is both not calm and not old.
If alice is either wise or funny then someone is strong and vice versa.
Everyone who is both not calm and not quiet is either not patient or not creative and vice versa.
If someone is either not tall or not funny then someone is either strong or not calm and vice versa.
Everyone who is wise or happy is not kind.
Mary is both wise and happy.
Fred is not humble or quiet.
Susan is either not generous or old.
Lucy is tall or not strong.
Someone is either not generous or not curious.
John is either wise or not kind.
John is old or happy.
Someone is funny. | Mary is not brave. | contradiction | (((curious(lucy)|~wise(lucy)))<=>(?[X]:(~generous(X))))&
((~tall(susan))=>(brave(alice)))&
((?[X]:((~humble(X)<~>humble(X))))=>(~tall(susan)))&
((?[X]:((brave(X)&patient(X))))<=>(patient(john)))&
(![X]:((~wise(X)<~>quiet(X))<=>(old(X)|~kind(X))))&
((?[X]:((tall(X)<~>patient(X))))=>(?[X]:((~strong(X)&happy(X)))))&
((?[X]:((happy(X)|~curious(X))))<=>((kind(susan)&~humble(susan))))&
(![X]:((~happy(X)&~funny(X))=>(~generous(X)<~>~happy(X))))&
(![X]:((quiet(X)&kind(X))<=>(~brave(X)|funny(X))))&
(((curious(alice)|creative(alice)))=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:((~curious(X)|tall(X))<=>(~old(X)&funny(X))))&
((?[X]:((~rich(X)|~strong(X))))=>(?[X]:((~calm(X)&~old(X)))))&
(((wise(alice)<~>funny(alice)))<=>(?[X]:(strong(X))))&
(![X]:((~calm(X)&~quiet(X))<=>(~patient(X)<~>~creative(X))))&
((?[X]:((~tall(X)<~>~funny(X))))<=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((wise(X)|happy(X))=>~kind(X)))&
((wise(mary)&happy(mary)))&
((~humble(fred)|quiet(fred)))&
((~generous(susan)<~>old(susan)))&
((tall(lucy)|~strong(lucy)))&
(?[X]:((~generous(X)<~>~curious(X))))&
((wise(john)<~>~kind(john)))&
((old(john)|happy(john)))&
(?[X]:(funny(X))) | ~brave(mary) | [
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2934533019000980586397702
% SZS output start Proof for 2934533019000980586397702
9. ! [X0] : ((kind(X0) & quiet(X0)) <=> (funny(X0) | ~brave(X0))) [input p8]
16. ! [X0] : ((happy(X0) | wise(X0)) => ~kind(X0)) [input p15]
17. happy(mary) & wise(mary) [input p16]
25. ~brave(mary) [input hypothesis]
37. ! [X0] : (~kind(X0) | (~happy(X0) & ~wise(X0))) [ennf transformation 16]
60. ! [X0] : (((kind(X0) & quiet(X0)) | (~funny(X0) & brave(X0))) & ((funny(X0) | ~brave(X0)) | (~kind(X0) | ~quiet(X0)))) [nnf transformation 9]
61. ! [X0] : (((kind(X0) & quiet(X0)) | (~funny(X0) & brave(X0))) & (funny(X0) | ~brave(X0) | ~kind(X0) | ~quiet(X0))) [flattening 60]
116. kind(X0) | brave(X0) [cnf transformation 61]
148. ~happy(X0) | ~kind(X0) [cnf transformation 37]
150. happy(mary) [cnf transformation 17]
161. ~brave(mary) [cnf transformation 25]
416. ~kind(mary) [resolution 148,150]
421. brave(mary) [resolution 416,116]
422. $false [subsumption resolution 421,161]
% SZS output end Proof for 2934533019000980586397702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise or not tall is both not brave and not calm and vice versa.
If someone is both not funny and not curious then someone is either not kind or not brave.
Everyone who is not humble is both generous and not brave and vice versa.
Everyone who is both calm and not tall is not old.
Everyone who is rich is not tall.
Everyone who is both quiet and not curious is either not old or tall and vice versa.
Everyone who is not happy is not patient.
If someone is both strong and old then someone is not patient or strong.
If john is generous or not tall then susan is humble.
Everyone who is not strong or not funny is rich.
If someone is brave or happy then susan is both rich and happy.
Everyone who is either not quiet or not brave is both not funny and not brave.
If someone is both patient and not wise then someone is either not brave or quiet and vice versa.
Everyone who is humble is both not quiet and not rich.
Everyone who is both brave and generous is humble or strong.
If someone is tall then someone is either not curious or humble.
Someone is strong or not humble.
Someone is either creative or not wise.
Alice is old.
Someone is humble or not patient.
Someone is not funny or quiet.
Mary is both quiet and curious. | Susan is not humble. | entailment | (![X]:((~wise(X)|~tall(X))<=>(~brave(X)&~calm(X))))&
((?[X]:((~funny(X)&~curious(X))))=>(?[X]:((~kind(X)<~>~brave(X)))))&
(![X]:(~humble(X)<=>(generous(X)&~brave(X))))&
(![X]:((calm(X)&~tall(X))=>~old(X)))&
(![X]:(rich(X)=>~tall(X)))&
(![X]:((quiet(X)&~curious(X))<=>(~old(X)<~>tall(X))))&
(![X]:(~happy(X)=>~patient(X)))&
((?[X]:((strong(X)&old(X))))=>(?[X]:((~patient(X)|strong(X)))))&
(((generous(john)|~tall(john)))=>(humble(susan)))&
(![X]:((~strong(X)|~funny(X))=>rich(X)))&
((?[X]:((brave(X)|happy(X))))=>((rich(susan)&happy(susan))))&
(![X]:((~quiet(X)<~>~brave(X))=>(~funny(X)&~brave(X))))&
((?[X]:((patient(X)&~wise(X))))<=>(?[X]:((~brave(X)<~>quiet(X)))))&
(![X]:(humble(X)=>(~quiet(X)&~rich(X))))&
(![X]:((brave(X)&generous(X))=>(humble(X)|strong(X))))&
((?[X]:(tall(X)))=>(?[X]:((~curious(X)<~>humble(X)))))&
(?[X]:((strong(X)|~humble(X))))&
(?[X]:((creative(X)<~>~wise(X))))&
(old(alice))&
(?[X]:((humble(X)|~patient(X))))&
(?[X]:((~funny(X)|quiet(X))))&
((quiet(mary)&curious(mary))) | ~humble(susan) | [
"p6",
"p10",
"p11",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 888731542214928086652810
% SZS output start Proof for 888731542214928086652810
7. ! [X0] : (~happy(X0) => ~patient(X0)) [input p6]
11. ? [X0] : (happy(X0) | brave(X0)) => (happy(susan) & rich(susan)) [input p10]
12. ! [X0] : ((~quiet(X0) <~> ~brave(X0)) => (~brave(X0) & ~funny(X0))) [input p11]
13. ? [X0] : (~wise(X0) & patient(X0)) <=> ? [X0] : (~brave(X0) <~> quiet(X0)) [input p12]
14. ! [X0] : (humble(X0) => (~rich(X0) & ~quiet(X0))) [input p13]
23. humble(susan) [input hypothesis]
26. ? [X0] : (~wise(X0) & patient(X0)) <=> ? [X1] : (~brave(X1) <~> quiet(X1)) [rectify 13]
32. ! [X0] : (~patient(X0) | happy(X0)) [ennf transformation 7]
36. (happy(susan) & rich(susan)) | ! [X0] : (~happy(X0) & ~brave(X0)) [ennf transformation 11]
37. ! [X0] : ((~brave(X0) & ~funny(X0)) | (~quiet(X0) <=> ~brave(X0))) [ennf transformation 12]
38. ! [X0] : ((~rich(X0) & ~quiet(X0)) | ~humble(X0)) [ennf transformation 14]
55. ! [X0] : ((~brave(X0) & ~funny(X0)) | ((~quiet(X0) | brave(X0)) & (~brave(X0) | quiet(X0)))) [nnf transformation 37]
56. (? [X0] : (~wise(X0) & patient(X0)) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (? [X1] : ((~quiet(X1) | brave(X1)) & (quiet(X1) | ~brave(X1))) | ! [X0] : (wise(X0) | ~patient(X0))) [nnf transformation 26]
57. (? [X0] : (~wise(X0) & patient(X0)) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (? [X2] : ((~quiet(X2) | brave(X2)) & (quiet(X2) | ~brave(X2))) | ! [X3] : (wise(X3) | ~patient(X3))) [rectify 56]
58. ? [X0] : (~wise(X0) & patient(X0)) => (~wise(sK2) & patient(sK2)) [choice axiom]
59. ? [X2] : ((~quiet(X2) | brave(X2)) & (quiet(X2) | ~brave(X2))) => ((~quiet(sK3) | brave(sK3)) & (quiet(sK3) | ~brave(sK3))) [choice axiom]
60. ((~wise(sK2) & patient(sK2)) | ! [X1] : ((~brave(X1) | ~quiet(X1)) & (quiet(X1) | brave(X1)))) & (((~quiet(sK3) | brave(sK3)) & (quiet(sK3) | ~brave(sK3))) | ! [X3] : (wise(X3) | ~patient(X3))) [skolemisation 57,59,58]
92. ~patient(X0) | happy(X0) [cnf transformation 32]
99. rich(susan) | ~happy(X0) [cnf transformation 36]
104. ~brave(X0) | ~brave(X0) | quiet(X0) [cnf transformation 55]
108. patient(sK2) | quiet(X1) | brave(X1) [cnf transformation 60]
112. ~quiet(X0) | ~humble(X0) [cnf transformation 38]
113. ~rich(X0) | ~humble(X0) [cnf transformation 38]
125. humble(susan) [cnf transformation 23]
126. ~brave(X0) | quiet(X0) [duplicate literal removal 104]
157. 8 <=> humble(susan) [avatar definition]
159. humble(susan) <- (8) [avatar component clause 157]
167. 10 <=> ! [X0] : ~happy(X0) [avatar definition]
168. ~happy(X0) <- (10) [avatar component clause 167]
179. 13 <=> rich(susan) [avatar definition]
181. rich(susan) <- (13) [avatar component clause 179]
182. 10 | 13 [avatar split clause 99,179,167]
192. 15 <=> ! [X1] : quiet(X1) [avatar definition]
193. quiet(X1) <- (15) [avatar component clause 192]
197. 16 <=> patient(sK2) [avatar definition]
199. patient(sK2) <- (16) [avatar component clause 197]
201. patient(sK2) | quiet(X1) [subsumption resolution 108,126]
202. 15 | 16 [avatar split clause 201,197,192]
265. 8 [avatar split clause 125,157]
268. happy(sK2) <- (16) [resolution 92,199]
269. $false <- (10, 16) [subsumption resolution 268,168]
270. ~10 | ~16 [avatar contradiction clause 269]
274. ~humble(susan) <- (13) [resolution 113,181]
276. $false <- (8, 13) [subsumption resolution 274,159]
277. ~8 | ~13 [avatar contradiction clause 276]
281. ~humble(X0) <- (15) [resolution 193,112]
283. $false <- (8, 15) [resolution 281,159]
284. ~8 | ~15 [avatar contradiction clause 283]
285. $false [avatar sat refutation 182,202,265,270,277,284]
% SZS output end Proof for 888731542214928086652810
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both calm and patient is both brave and quiet.
If someone is both not kind and strong then mary is not patient and vice versa.
If paul is not kind or generous then someone is not quiet or not humble and vice versa.
If john is not wise or not rich then lucy is not quiet and vice versa.
Everyone who is both happy and brave is both strong and quiet.
If someone is old then someone is both not funny and humble and vice versa.
Everyone who is either not tall or quiet is both not tall and not patient and vice versa.
Everyone who is both not tall and creative is funny or curious and vice versa.
Everyone who is strong is humble.
If someone is not old or not patient then paul is both creative and strong.
Everyone who is either humble or brave is both happy and quiet.
If fred is either not brave or not humble then someone is both rich and not rich and vice versa.
If someone is either not rich or not patient then someone is both not wise and not generous and vice versa.
Everyone who is old or brave is both rich and not strong.
Everyone who is not kind is both not creative and wise and vice versa.
If mary is funny then someone is rich and vice versa.
Someone is either patient or not rich.
Someone is both not happy and humble.
Someone is not quiet or old.
Someone is both not patient and creative.
Mary is both creative and old.
Fred is old.
Lucy is either tall or calm. | Mary is tall. | contradiction | (![X]:((calm(X)&patient(X))=>(brave(X)&quiet(X))))&
((?[X]:((~kind(X)&strong(X))))<=>(~patient(mary)))&
(((~kind(paul)|generous(paul)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(((~wise(john)|~rich(john)))<=>(~quiet(lucy)))&
(![X]:((happy(X)&brave(X))=>(strong(X)&quiet(X))))&
((?[X]:(old(X)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((~tall(X)<~>quiet(X))<=>(~tall(X)&~patient(X))))&
(![X]:((~tall(X)&creative(X))<=>(funny(X)|curious(X))))&
(![X]:(strong(X)=>humble(X)))&
((?[X]:((~old(X)|~patient(X))))=>((creative(paul)&strong(paul))))&
(![X]:((humble(X)<~>brave(X))=>(happy(X)&quiet(X))))&
(((~brave(fred)<~>~humble(fred)))<=>(?[X]:((rich(X)&~rich(X)))))&
((?[X]:((~rich(X)<~>~patient(X))))<=>(?[X]:((~wise(X)&~generous(X)))))&
(![X]:((old(X)|brave(X))=>(rich(X)&~strong(X))))&
(![X]:(~kind(X)<=>(~creative(X)&wise(X))))&
((funny(mary))<=>(?[X]:(rich(X))))&
(?[X]:((patient(X)<~>~rich(X))))&
(?[X]:((~happy(X)&humble(X))))&
(?[X]:((~quiet(X)|old(X))))&
(?[X]:((~patient(X)&creative(X))))&
((creative(mary)&old(mary)))&
(old(fred))&
((tall(lucy)<~>calm(lucy))) | tall(mary) | [
"p7",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 5360287713292840291433543
% SZS output start Proof for 5360287713292840291433543
8. ! [X0] : ((creative(X0) & ~tall(X0)) <=> (curious(X0) | funny(X0))) [input p7]
14. ! [X0] : ((brave(X0) | old(X0)) => (~strong(X0) & rich(X0))) [input p13]
16. funny(mary) <=> ? [X0] : rich(X0) [input p15]
22. old(fred) [input p21]
24. tall(mary) [input hypothesis]
34. ! [X0] : ((~strong(X0) & rich(X0)) | (~brave(X0) & ~old(X0))) [ennf transformation 14]
53. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & ((curious(X0) | funny(X0)) | (~creative(X0) | tall(X0)))) [nnf transformation 8]
54. ! [X0] : (((creative(X0) & ~tall(X0)) | (~curious(X0) & ~funny(X0))) & (curious(X0) | funny(X0) | ~creative(X0) | tall(X0))) [flattening 53]
67. (funny(mary) | ! [X0] : ~rich(X0)) & (? [X0] : rich(X0) | ~funny(mary)) [nnf transformation 16]
68. (funny(mary) | ! [X0] : ~rich(X0)) & (? [X1] : rich(X1) | ~funny(mary)) [rectify 67]
69. ? [X1] : rich(X1) => rich(sK7) [choice axiom]
70. (funny(mary) | ! [X0] : ~rich(X0)) & (rich(sK7) | ~funny(mary)) [skolemisation 68,69]
105. ~tall(X0) | ~funny(X0) [cnf transformation 54]
130. ~old(X0) | rich(X0) [cnf transformation 34]
138. funny(mary) | ~rich(X0) [cnf transformation 70]
148. old(fred) [cnf transformation 22]
151. tall(mary) [cnf transformation 24]
300. 33 <=> ! [X0] : ~rich(X0) [avatar definition]
301. ~rich(X0) <- (33) [avatar component clause 300]
303. 34 <=> funny(mary) [avatar definition]
306. 33 | 34 [avatar split clause 138,303,300]
345. ~funny(mary) [resolution 105,151]
350. rich(fred) [resolution 130,148]
354. $false <- (33) [subsumption resolution 350,301]
355. ~33 [avatar contradiction clause 354]
358. ~34 [avatar split clause 345,303]
359. $false [avatar sat refutation 306,355,358]
% SZS output end Proof for 5360287713292840291433543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not happy is generous. Everyone who is either patient or tall is not wise or generous. If someone is either patient or not calm then paul is both brave and not quiet and vice versa. If john is creative or not rich then fred is either not quiet or quiet and vice versa. If someone is both not creative and happy then fred is either generous or not curious and vice versa. Everyone who is either patient or not old is either not kind or not brave and vice versa. If someone is generous then mary is funny and vice versa. If someone is not kind then someone is both not brave and calm and vice versa. If someone is both not brave and not happy then mary is either not rich or not curious and vice versa. Everyone who is not tall or happy is both tall and not quiet and vice versa. Everyone who is either wise or not tall is both not patient and strong and vice versa. Everyone who is funny or patient is both not rich and rich. Everyone who is either curious or not strong is not humble or generous. If someone is not happy or not creative then alice is not tall or quiet and vice versa. Everyone who is both patient and brave is either kind or not brave and vice versa. If paul is both not tall and calm then john is both curious and not kind and vice versa. Someone is either happy or curious. Paul is either tall or funny. Someone is not happy or quiet. Someone is either not happy or happy. Alice is not quiet or not rich. Someone is humble. | Fred is calm. | neutral | (![X]:((curious(X)<~>~happy(X))=>generous(X)))&
(![X]:((patient(X)<~>tall(X))=>(~wise(X)|generous(X))))&
((?[X]:((patient(X)<~>~calm(X))))<=>((brave(paul)&~quiet(paul))))&
(((creative(john)|~rich(john)))<=>((~quiet(fred)<~>quiet(fred))))&
((?[X]:((~creative(X)&happy(X))))<=>((generous(fred)<~>~curious(fred))))&
(![X]:((patient(X)<~>~old(X))<=>(~kind(X)<~>~brave(X))))&
((?[X]:(generous(X)))<=>(funny(mary)))&
((?[X]:(~kind(X)))<=>(?[X]:((~brave(X)&calm(X)))))&
((?[X]:((~brave(X)&~happy(X))))<=>((~rich(mary)<~>~curious(mary))))&
(![X]:((~tall(X)|happy(X))<=>(tall(X)&~quiet(X))))&
(![X]:((wise(X)<~>~tall(X))<=>(~patient(X)&strong(X))))&
(![X]:((funny(X)|patient(X))=>(~rich(X)&rich(X))))&
(![X]:((curious(X)<~>~strong(X))=>(~humble(X)|generous(X))))&
((?[X]:((~happy(X)|~creative(X))))<=>((~tall(alice)|quiet(alice))))&
(![X]:((patient(X)&brave(X))<=>(kind(X)<~>~brave(X))))&
(((~tall(paul)&calm(paul)))<=>((curious(john)&~kind(john))))&
(?[X]:((happy(X)<~>curious(X))))&
((tall(paul)<~>funny(paul)))&
(?[X]:((~happy(X)|quiet(X))))&
(?[X]:((~happy(X)<~>happy(X))))&
((~quiet(alice)|~rich(alice)))&
(?[X]:(humble(X))) | calm(fred) | [] | null | 0 |
If someone is both patient and not patient then someone is quiet or not wise and vice versa. Everyone who is quiet is either funny or strong. Everyone who is either not funny or not old is both not humble and not kind. Everyone who is quiet or wise is not strong or not funny and vice versa. If someone is both not patient and not brave then someone is wise or brave and vice versa. Everyone who is humble is creative and vice versa. If someone is either not patient or creative then someone is both strong and not wise. If susan is brave or curious then someone is either not brave or not quiet. Everyone who is either generous or not tall is either not brave or funny. Everyone who is both funny and strong is both not tall and humble. Everyone who is both not humble and humble is not happy or generous and vice versa. Everyone who is both not creative and not wise is both not quiet and not curious. If john is either not tall or not old then susan is both rich and happy. If someone is both funny and quiet then john is humble and vice versa. Everyone who is patient or not funny is either humble or not kind. Someone is humble or not strong. Susan is not generous or not wise. Someone is not creative or strong. Someone is humble. Lucy is not creative or rich. Someone is both not patient and creative. Someone is both tall and happy. Fred is generous or not old. | Lucy is creative. | neutral | ((?[X]:((patient(X)&~patient(X))))<=>(?[X]:((quiet(X)|~wise(X)))))&
(![X]:(quiet(X)=>(funny(X)<~>strong(X))))&
(![X]:((~funny(X)<~>~old(X))=>(~humble(X)&~kind(X))))&
(![X]:((quiet(X)|wise(X))<=>(~strong(X)|~funny(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((wise(X)|brave(X)))))&
(![X]:(humble(X)<=>creative(X)))&
((?[X]:((~patient(X)<~>creative(X))))=>(?[X]:((strong(X)&~wise(X)))))&
(((brave(susan)|curious(susan)))=>(?[X]:((~brave(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~brave(X)<~>funny(X))))&
(![X]:((funny(X)&strong(X))=>(~tall(X)&humble(X))))&
(![X]:((~humble(X)&humble(X))<=>(~happy(X)|generous(X))))&
(![X]:((~creative(X)&~wise(X))=>(~quiet(X)&~curious(X))))&
(((~tall(john)<~>~old(john)))=>((rich(susan)&happy(susan))))&
((?[X]:((funny(X)&quiet(X))))<=>(humble(john)))&
(![X]:((patient(X)|~funny(X))=>(humble(X)<~>~kind(X))))&
(?[X]:((humble(X)|~strong(X))))&
((~generous(susan)|~wise(susan)))&
(?[X]:((~creative(X)|strong(X))))&
(?[X]:(humble(X)))&
((~creative(lucy)|rich(lucy)))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((tall(X)&happy(X))))&
((generous(fred)|~old(fred))) | creative(lucy) | [] | null | 0 |
Everyone who is either not curious or patient is not happy and vice versa.
Everyone who is both not strong and not old is both curious and strong.
Everyone who is both generous and rich is both not strong and rich.
Everyone who is both not kind and not generous is not patient and vice versa.
Everyone who is wise or not quiet is patient or wise and vice versa.
Everyone who is brave or happy is both not generous and happy and vice versa.
If fred is humble or not curious then someone is both not generous and tall and vice versa.
If susan is curious or happy then john is either not generous or funny.
If fred is either not quiet or kind then someone is not patient or not generous.
Everyone who is not humble is both not humble and not old and vice versa.
If fred is not funny or not creative then alice is both not curious and not tall.
Everyone who is either not strong or generous is either not happy or not brave and vice versa.
If someone is both not rich and not old then someone is wise or patient.
If someone is patient or not kind then someone is generous or rich.
If john is curious or not kind then fred is both not creative and humble and vice versa.
Everyone who is rich is wise or not funny.
Fred is both not calm and not humble.
Fred is not humble.
Someone is both quiet and not brave.
Mary is either not creative or not rich.
Someone is either not happy or calm.
John is not generous or curious. | Susan is happy. | neutral | (![X]:((~curious(X)<~>patient(X))<=>~happy(X)))&
(![X]:((~strong(X)&~old(X))=>(curious(X)&strong(X))))&
(![X]:((generous(X)&rich(X))=>(~strong(X)&rich(X))))&
(![X]:((~kind(X)&~generous(X))<=>~patient(X)))&
(![X]:((wise(X)|~quiet(X))<=>(patient(X)|wise(X))))&
(![X]:((brave(X)|happy(X))<=>(~generous(X)&happy(X))))&
(((humble(fred)|~curious(fred)))<=>(?[X]:((~generous(X)&tall(X)))))&
(((curious(susan)|happy(susan)))=>((~generous(john)<~>funny(john))))&
(((~quiet(fred)<~>kind(fred)))=>(?[X]:((~patient(X)|~generous(X)))))&
(![X]:(~humble(X)<=>(~humble(X)&~old(X))))&
(((~funny(fred)|~creative(fred)))=>((~curious(alice)&~tall(alice))))&
(![X]:((~strong(X)<~>generous(X))<=>(~happy(X)<~>~brave(X))))&
((?[X]:((~rich(X)&~old(X))))=>(?[X]:((wise(X)|patient(X)))))&
((?[X]:((patient(X)|~kind(X))))=>(?[X]:((generous(X)|rich(X)))))&
(((curious(john)|~kind(john)))<=>((~creative(fred)&humble(fred))))&
(![X]:(rich(X)=>(wise(X)|~funny(X))))&
((~calm(fred)&~humble(fred)))&
(~humble(fred))&
(?[X]:((quiet(X)&~brave(X))))&
((~creative(mary)<~>~rich(mary)))&
(?[X]:((~happy(X)<~>calm(X))))&
((~generous(john)|curious(john))) | happy(susan) | [] | null | 0 |
If someone is not brave then fred is either not happy or not quiet and vice versa.
If susan is either quiet or not funny then paul is patient or kind.
If someone is rich then susan is not humble and vice versa.
Everyone who is not wise or humble is not humble and vice versa.
Everyone who is not calm or not happy is both generous and tall and vice versa.
Everyone who is either not old or funny is old and vice versa.
Everyone who is kind is generous or brave and vice versa.
If mary is not calm or not wise then someone is creative or rich.
If susan is funny or not quiet then lucy is not patient or not tall and vice versa.
If john is not wise then someone is either not wise or quiet.
Everyone who is either tall or not wise is humble and vice versa.
If someone is quiet then someone is both not curious and not wise.
Everyone who is not humble is not happy or not funny and vice versa.
Everyone who is both tall and kind is both not patient and strong.
Everyone who is both not creative and generous is both not humble and generous.
Someone is either curious or not strong.
Fred is both strong and calm.
Someone is creative or not brave.
Mary is either not tall or creative.
Someone is not old or not quiet.
Someone is either quiet or not quiet.
Paul is either not generous or calm. | Mary is not strong. | contradiction | ((?[X]:(~brave(X)))<=>((~happy(fred)<~>~quiet(fred))))&
(((quiet(susan)<~>~funny(susan)))=>((patient(paul)|kind(paul))))&
((?[X]:(rich(X)))<=>(~humble(susan)))&
(![X]:((~wise(X)|humble(X))<=>~humble(X)))&
(![X]:((~calm(X)|~happy(X))<=>(generous(X)&tall(X))))&
(![X]:((~old(X)<~>funny(X))<=>old(X)))&
(![X]:(kind(X)<=>(generous(X)|brave(X))))&
(((~calm(mary)|~wise(mary)))=>(?[X]:((creative(X)|rich(X)))))&
(((funny(susan)|~quiet(susan)))<=>((~patient(lucy)|~tall(lucy))))&
((~wise(john))=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((tall(X)<~>~wise(X))<=>humble(X)))&
((?[X]:(quiet(X)))=>(?[X]:((~curious(X)&~wise(X)))))&
(![X]:(~humble(X)<=>(~happy(X)|~funny(X))))&
(![X]:((tall(X)&kind(X))=>(~patient(X)&strong(X))))&
(![X]:((~creative(X)&generous(X))=>(~humble(X)&generous(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
((strong(fred)&calm(fred)))&
(?[X]:((creative(X)|~brave(X))))&
((~tall(mary)<~>creative(mary)))&
(?[X]:((~old(X)|~quiet(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
((~generous(paul)<~>calm(paul))) | ~strong(mary) | [
"p3",
"p4",
"p5",
"p6",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 73103191057486282006623
% SZS output start Proof for 73103191057486282006623
4. ! [X0] : ((humble(X0) | ~wise(X0)) <=> ~humble(X0)) [input p3]
5. ! [X0] : ((~happy(X0) | ~calm(X0)) <=> (tall(X0) & generous(X0))) [input p4]
6. ! [X0] : ((~old(X0) <~> funny(X0)) <=> old(X0)) [input p5]
7. ! [X0] : (kind(X0) <=> (brave(X0) | generous(X0))) [input p6]
13. ! [X0] : (~humble(X0) <=> (~funny(X0) | ~happy(X0))) [input p12]
14. ! [X0] : ((kind(X0) & tall(X0)) => (strong(X0) & ~patient(X0))) [input p13]
23. ~strong(mary) [input hypothesis]
30. ! [X0] : ((strong(X0) & ~patient(X0)) | (~kind(X0) | ~tall(X0))) [ennf transformation 14]
31. ! [X0] : ((strong(X0) & ~patient(X0)) | ~kind(X0) | ~tall(X0)) [flattening 30]
43. ! [X0] : (((humble(X0) | ~wise(X0)) | humble(X0)) & (~humble(X0) | (~humble(X0) & wise(X0)))) [nnf transformation 4]
44. ! [X0] : ((humble(X0) | ~wise(X0) | humble(X0)) & (~humble(X0) | (~humble(X0) & wise(X0)))) [flattening 43]
45. ! [X0] : (((~happy(X0) | ~calm(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (happy(X0) & calm(X0)))) [nnf transformation 5]
46. ! [X0] : ((~happy(X0) | ~calm(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (happy(X0) & calm(X0)))) [flattening 45]
47. ! [X0] : ((((~funny(X0) | old(X0)) & (funny(X0) | ~old(X0))) | ~old(X0)) & (old(X0) | ((~old(X0) | ~funny(X0)) & (funny(X0) | old(X0))))) [nnf transformation 6]
48. ! [X0] : ((kind(X0) | (~brave(X0) & ~generous(X0))) & ((brave(X0) | generous(X0)) | ~kind(X0))) [nnf transformation 7]
49. ! [X0] : ((kind(X0) | (~brave(X0) & ~generous(X0))) & (brave(X0) | generous(X0) | ~kind(X0))) [flattening 48]
61. ! [X0] : ((~humble(X0) | (funny(X0) & happy(X0))) & ((~funny(X0) | ~happy(X0)) | humble(X0))) [nnf transformation 13]
62. ! [X0] : ((~humble(X0) | (funny(X0) & happy(X0))) & (~funny(X0) | ~happy(X0) | humble(X0))) [flattening 61]
84. ~humble(X0) | ~humble(X0) [cnf transformation 44]
87. generous(X0) | happy(X0) [cnf transformation 46]
89. tall(X0) | happy(X0) [cnf transformation 46]
91. old(X0) | funny(X0) | old(X0) [cnf transformation 47]
93. funny(X0) | ~old(X0) | ~old(X0) [cnf transformation 47]
96. ~generous(X0) | kind(X0) [cnf transformation 49]
112. ~funny(X0) | ~happy(X0) | humble(X0) [cnf transformation 62]
116. ~tall(X0) | ~kind(X0) | strong(X0) [cnf transformation 31]
131. ~strong(mary) [cnf transformation 23]
132. old(X0) | funny(X0) [duplicate literal removal 91]
133. ~old(X0) | funny(X0) [duplicate literal removal 93]
134. ~humble(X0) [duplicate literal removal 84]
186. funny(X0) [subsumption resolution 132,133]
244. ~happy(X0) | humble(X0) [subsumption resolution 112,186]
245. ~happy(X0) [subsumption resolution 244,134]
298. kind(X0) | happy(X0) [resolution 96,87]
301. kind(X0) [subsumption resolution 298,245]
312. ~kind(X1) | strong(X1) | happy(X1) [resolution 116,89]
316. strong(X1) | happy(X1) [subsumption resolution 312,301]
317. strong(X1) [subsumption resolution 316,245]
322. $false [resolution 317,131]
% SZS output end Proof for 73103191057486282006623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not brave or not tall then mary is wise and vice versa.
If someone is happy or tall then someone is tall.
Everyone who is not curious is both not wise and wise.
If susan is creative or happy then mary is not creative and vice versa.
Everyone who is either patient or tall is both wise and not brave.
If alice is both funny and rich then alice is both not funny and kind.
Everyone who is not calm or humble is both strong and quiet.
If fred is not tall then susan is both not creative and brave and vice versa.
If john is either old or not humble then someone is either patient or not wise.
Everyone who is not quiet is both funny and calm and vice versa.
If fred is not creative or not happy then someone is not strong or tall and vice versa.
If alice is not happy then john is rich and vice versa.
If john is brave then someone is both happy and strong and vice versa.
Everyone who is old or not strong is not curious and vice versa.
Everyone who is either not creative or wise is either not quiet or patient and vice versa.
If someone is humble or not brave then lucy is not funny and vice versa.
Susan is both calm and not creative.
Someone is not creative.
Someone is either brave or patient.
Paul is not calm or wise.
Susan is either not brave or strong.
Someone is not old.
Someone is wise.
Someone is not quiet. | Susan is not brave. | contradiction | (((~brave(fred)|~tall(fred)))<=>(wise(mary)))&
((?[X]:((happy(X)|tall(X))))=>(?[X]:(tall(X))))&
(![X]:(~curious(X)=>(~wise(X)&wise(X))))&
(((creative(susan)|happy(susan)))<=>(~creative(mary)))&
(![X]:((patient(X)<~>tall(X))=>(wise(X)&~brave(X))))&
(((funny(alice)&rich(alice)))=>((~funny(alice)&kind(alice))))&
(![X]:((~calm(X)|humble(X))=>(strong(X)&quiet(X))))&
((~tall(fred))<=>((~creative(susan)&brave(susan))))&
(((old(john)<~>~humble(john)))=>(?[X]:((patient(X)<~>~wise(X)))))&
(![X]:(~quiet(X)<=>(funny(X)&calm(X))))&
(((~creative(fred)|~happy(fred)))<=>(?[X]:((~strong(X)|tall(X)))))&
((~happy(alice))<=>(rich(john)))&
((brave(john))<=>(?[X]:((happy(X)&strong(X)))))&
(![X]:((old(X)|~strong(X))<=>~curious(X)))&
(![X]:((~creative(X)<~>wise(X))<=>(~quiet(X)<~>patient(X))))&
((?[X]:((humble(X)|~brave(X))))<=>(~funny(lucy)))&
((calm(susan)&~creative(susan)))&
(?[X]:(~creative(X)))&
(?[X]:((brave(X)<~>patient(X))))&
((~calm(paul)|wise(paul)))&
((~brave(susan)<~>strong(susan)))&
(?[X]:(~old(X)))&
(?[X]:(wise(X)))&
(?[X]:(~quiet(X))) | ~brave(susan) | [
"p2",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7105892124749619341471353
% SZS output start Proof for 7105892124749619341471353
3. ! [X0] : (~curious(X0) => (wise(X0) & ~wise(X0))) [input p2]
14. ! [X0] : ((~strong(X0) | old(X0)) <=> ~curious(X0)) [input p13]
21. ~brave(susan) <~> strong(susan) [input p20]
25. ~brave(susan) [input hypothesis]
27. ! [X0] : ((~strong(X0) | old(X0)) => ~curious(X0)) [unused predicate definition removal 14]
30. ! [X0] : ((wise(X0) & ~wise(X0)) | curious(X0)) [ennf transformation 3]
36. ! [X0] : (~curious(X0) | (strong(X0) & ~old(X0))) [ennf transformation 27]
72. (~strong(susan) | brave(susan)) & (strong(susan) | ~brave(susan)) [nnf transformation 21]
84. ~wise(X0) | curious(X0) [cnf transformation 30]
85. wise(X0) | curious(X0) [cnf transformation 30]
118. ~curious(X0) | strong(X0) [cnf transformation 36]
137. ~strong(susan) | brave(susan) [cnf transformation 72]
141. ~brave(susan) [cnf transformation 25]
170. curious(X0) [subsumption resolution 84,85]
196. 12 <=> brave(susan) [avatar definition]
232. 19 <=> ! [X0] : strong(X0) [avatar definition]
233. strong(X0) <- (19) [avatar component clause 232]
273. strong(X0) [subsumption resolution 118,170]
274. 19 [avatar split clause 273,232]
318. 37 <=> strong(susan) [avatar definition]
320. ~strong(susan) <- (~37) [avatar component clause 318]
321. 12 | ~37 [avatar split clause 137,318,196]
323. ~12 [avatar split clause 141,196]
326. $false <- (19, ~37) [resolution 320,233]
327. ~19 | 37 [avatar contradiction clause 326]
328. $false [avatar sat refutation 274,321,323,327]
% SZS output end Proof for 7105892124749619341471353
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or humble is humble and vice versa. Everyone who is not tall is not calm or not tall. Everyone who is both not funny and not curious is not generous or generous. Everyone who is not calm is either funny or quiet. Everyone who is either old or not tall is funny or old and vice versa. If lucy is both not humble and not creative then mary is not rich or patient. If paul is both not creative and funny then someone is humble or calm. Everyone who is not calm is rich and vice versa. Everyone who is either quiet or not generous is both not curious and not wise. If fred is both quiet and happy then john is either generous or not wise. Everyone who is tall is not kind or patient. Everyone who is not tall or calm is calm. Everyone who is not kind is both not calm and calm and vice versa. If paul is not calm then someone is either creative or not calm. Everyone who is either quiet or not rich is both rich and generous and vice versa. Everyone who is generous or not rich is either tall or not patient and vice versa. Paul is either not kind or patient. John is both not rich and not funny. Paul is both rich and patient. Someone is not calm. Someone is both tall and not strong. Susan is not creative or not funny. | John is patient. | entailment | (![X]:((funny(X)|humble(X))<=>humble(X)))&
(![X]:(~tall(X)=>(~calm(X)|~tall(X))))&
(![X]:((~funny(X)&~curious(X))=>(~generous(X)|generous(X))))&
(![X]:(~calm(X)=>(funny(X)<~>quiet(X))))&
(![X]:((old(X)<~>~tall(X))<=>(funny(X)|old(X))))&
(((~humble(lucy)&~creative(lucy)))=>((~rich(mary)|patient(mary))))&
(((~creative(paul)&funny(paul)))=>(?[X]:((humble(X)|calm(X)))))&
(![X]:(~calm(X)<=>rich(X)))&
(![X]:((quiet(X)<~>~generous(X))=>(~curious(X)&~wise(X))))&
(((quiet(fred)&happy(fred)))=>((generous(john)<~>~wise(john))))&
(![X]:(tall(X)=>(~kind(X)|patient(X))))&
(![X]:((~tall(X)|calm(X))=>calm(X)))&
(![X]:(~kind(X)<=>(~calm(X)&calm(X))))&
((~calm(paul))=>(?[X]:((creative(X)<~>~calm(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(rich(X)&generous(X))))&
(![X]:((generous(X)|~rich(X))<=>(tall(X)<~>~patient(X))))&
((~kind(paul)<~>patient(paul)))&
((~rich(john)&~funny(john)))&
((rich(paul)&patient(paul)))&
(?[X]:(~calm(X)))&
(?[X]:((tall(X)&~strong(X))))&
((~creative(susan)|~funny(susan))) | patient(john) | [
"p4",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5422327738501542088937172
% SZS output start Proof for 5422327738501542088937172
5. ! [X0] : ((old(X0) <~> ~tall(X0)) <=> (old(X0) | funny(X0))) [input p4]
16. ! [X0] : ((~rich(X0) | generous(X0)) <=> (tall(X0) <~> ~patient(X0))) [input p15]
18. ~funny(john) & ~rich(john) [input p17]
23. ~patient(john) [input hypothesis]
44. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [nnf transformation 5]
45. ! [X0] : ((((tall(X0) | ~old(X0)) & (~tall(X0) | old(X0))) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ((old(X0) | tall(X0)) & (~tall(X0) | ~old(X0))))) [flattening 44]
57. ! [X0] : (((~rich(X0) | generous(X0)) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | (rich(X0) & ~generous(X0)))) [nnf transformation 16]
58. ! [X0] : ((~rich(X0) | generous(X0) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0)))) & (((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | (rich(X0) & ~generous(X0)))) [flattening 57]
72. old(X0) | funny(X0) | old(X0) | tall(X0) [cnf transformation 45]
76. tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 45]
100. ~tall(X0) | patient(X0) | rich(X0) [cnf transformation 58]
105. ~rich(john) [cnf transformation 18]
106. ~funny(john) [cnf transformation 18]
112. ~patient(john) [cnf transformation 23]
115. old(X0) | funny(X0) | tall(X0) [duplicate literal removal 72]
116. ~old(X0) | tall(X0) [duplicate literal removal 76]
117. tall(X0) | funny(X0) [subsumption resolution 115,116]
282. patient(X0) | rich(X0) | funny(X0) [resolution 100,117]
435. rich(john) | funny(john) [resolution 282,112]
440. funny(john) [subsumption resolution 435,105]
441. $false [subsumption resolution 440,106]
% SZS output end Proof for 5422327738501542088937172
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is not calm or old and vice versa.
If someone is both kind and not creative then lucy is either rich or kind and vice versa.
Everyone who is either funny or not old is either not happy or kind.
Everyone who is either not tall or not creative is either not brave or not happy and vice versa.
If fred is both wise and generous then someone is not generous and vice versa.
If someone is wise then someone is both not rich and not kind and vice versa.
Everyone who is both not curious and funny is either wise or strong and vice versa.
Everyone who is both rich and tall is either strong or not old and vice versa.
Everyone who is either calm or quiet is not tall and vice versa.
Everyone who is tall or rich is not tall or not curious.
If someone is not tall or not funny then paul is not humble or not old.
Everyone who is not calm or rich is both not calm and not curious.
If susan is either not old or tall then fred is curious.
Everyone who is both not wise and happy is curious or strong and vice versa.
If mary is both brave and not wise then someone is quiet and vice versa.
If susan is not creative then paul is both old and not generous.
Someone is tall or curious.
Mary is either curious or generous.
Someone is generous.
Susan is either wise or not old.
Susan is both not happy and not brave.
Fred is not quiet.
Someone is funny or not quiet.
Someone is not funny or not brave. | Paul is not old. | neutral | ((?[X]:(~generous(X)))<=>(?[X]:((~calm(X)|old(X)))))&
((?[X]:((kind(X)&~creative(X))))<=>((rich(lucy)<~>kind(lucy))))&
(![X]:((funny(X)<~>~old(X))=>(~happy(X)<~>kind(X))))&
(![X]:((~tall(X)<~>~creative(X))<=>(~brave(X)<~>~happy(X))))&
(((wise(fred)&generous(fred)))<=>(?[X]:(~generous(X))))&
((?[X]:(wise(X)))<=>(?[X]:((~rich(X)&~kind(X)))))&
(![X]:((~curious(X)&funny(X))<=>(wise(X)<~>strong(X))))&
(![X]:((rich(X)&tall(X))<=>(strong(X)<~>~old(X))))&
(![X]:((calm(X)<~>quiet(X))<=>~tall(X)))&
(![X]:((tall(X)|rich(X))=>(~tall(X)|~curious(X))))&
((?[X]:((~tall(X)|~funny(X))))=>((~humble(paul)|~old(paul))))&
(![X]:((~calm(X)|rich(X))=>(~calm(X)&~curious(X))))&
(((~old(susan)<~>tall(susan)))=>(curious(fred)))&
(![X]:((~wise(X)&happy(X))<=>(curious(X)|strong(X))))&
(((brave(mary)&~wise(mary)))<=>(?[X]:(quiet(X))))&
((~creative(susan))=>((old(paul)&~generous(paul))))&
(?[X]:((tall(X)|curious(X))))&
((curious(mary)<~>generous(mary)))&
(?[X]:(generous(X)))&
((wise(susan)<~>~old(susan)))&
((~happy(susan)&~brave(susan)))&
(~quiet(fred))&
(?[X]:((funny(X)|~quiet(X))))&
(?[X]:((~funny(X)|~brave(X)))) | ~old(paul) | [] | null | 0 |
Everyone who is either wise or not happy is both not patient and kind.
Everyone who is not quiet is both not creative and calm and vice versa.
If someone is either not patient or not old then someone is either patient or calm and vice versa.
Everyone who is happy or not wise is both brave and not brave and vice versa.
Everyone who is either funny or not kind is kind and vice versa.
Everyone who is not generous or quiet is both strong and not tall.
Everyone who is not rich or not tall is quiet or patient and vice versa.
If john is not generous then paul is both quiet and old and vice versa.
Everyone who is not happy or not humble is brave and vice versa.
If someone is both funny and not humble then alice is both not quiet and tall and vice versa.
If someone is not brave or not calm then mary is happy.
If susan is both happy and brave then someone is either calm or happy.
If alice is either creative or not creative then someone is humble.
If john is calm then alice is curious or not tall and vice versa.
Everyone who is both old and not curious is brave and vice versa.
If someone is both not brave and not humble then paul is both not funny and strong and vice versa.
Susan is either not kind or quiet.
Alice is both old and creative.
Susan is both not quiet and tall.
Someone is wise.
Someone is not kind.
Someone is wise or not kind.
Someone is creative or happy. | Alice is brave. | entailment | (![X]:((wise(X)<~>~happy(X))=>(~patient(X)&kind(X))))&
(![X]:(~quiet(X)<=>(~creative(X)&calm(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:((patient(X)<~>calm(X)))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
(![X]:((~happy(X)|~humble(X))<=>brave(X)))&
((?[X]:((funny(X)&~humble(X))))<=>((~quiet(alice)&tall(alice))))&
((?[X]:((~brave(X)|~calm(X))))=>(happy(mary)))&
(((happy(susan)&brave(susan)))=>(?[X]:((calm(X)<~>happy(X)))))&
(((creative(alice)<~>~creative(alice)))=>(?[X]:(humble(X))))&
((calm(john))<=>((curious(alice)|~tall(alice))))&
(![X]:((old(X)&~curious(X))<=>brave(X)))&
((?[X]:((~brave(X)&~humble(X))))<=>((~funny(paul)&strong(paul))))&
((~kind(susan)<~>quiet(susan)))&
((old(alice)&creative(alice)))&
((~quiet(susan)&tall(susan)))&
(?[X]:(wise(X)))&
(?[X]:(~kind(X)))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:((creative(X)|happy(X)))) | brave(alice) | [
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 1434764794702330725563301
% SZS output start Proof for 1434764794702330725563301
4. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p3]
9. ! [X0] : ((~humble(X0) | ~happy(X0)) <=> brave(X0)) [input p8]
24. ~brave(alice) [input hypothesis]
40. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 4]
41. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 40]
47. ! [X0] : (((~humble(X0) | ~happy(X0)) | ~brave(X0)) & (brave(X0) | (humble(X0) & happy(X0)))) [nnf transformation 9]
48. ! [X0] : ((~humble(X0) | ~happy(X0) | ~brave(X0)) & (brave(X0) | (humble(X0) & happy(X0)))) [flattening 47]
93. brave(X0) | ~happy(X0) [cnf transformation 41]
95. ~brave(X0) | ~happy(X0) [cnf transformation 41]
113. brave(X0) | happy(X0) [cnf transformation 48]
146. ~brave(alice) [cnf transformation 24]
188. ~happy(X0) [subsumption resolution 93,95]
205. brave(X0) [subsumption resolution 113,188]
259. $false [subsumption resolution 146,205]
% SZS output end Proof for 1434764794702330725563301
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not creative then paul is not curious or not creative and vice versa. Everyone who is humble is strong and vice versa. If someone is patient or calm then alice is both rich and not brave. If alice is both brave and not humble then lucy is not patient or wise and vice versa. Everyone who is both curious and kind is both not curious and not tall. If mary is both calm and not rich then alice is strong or funny. If john is both not old and not curious then someone is either not creative or not generous and vice versa. If lucy is not patient then lucy is generous or funny. Everyone who is not strong or not quiet is both kind and not curious. Everyone who is both not old and funny is both quiet and wise. Everyone who is both not creative and strong is not strong. If paul is not curious or quiet then alice is either strong or brave. If someone is either curious or not generous then susan is both not calm and happy. Everyone who is both not strong and not happy is both kind and not calm and vice versa. Everyone who is brave or not generous is both kind and creative. If someone is not strong then fred is both not rich and not humble. Someone is not happy or tall. Mary is strong or patient. Someone is both not quiet and creative. Fred is generous or wise. Lucy is both not quiet and old. John is either quiet or happy. John is both not old and not strong. | Fred is rich. | contradiction | ((?[X]:((calm(X)|~creative(X))))<=>((~curious(paul)|~creative(paul))))&
(![X]:(humble(X)<=>strong(X)))&
((?[X]:((patient(X)|calm(X))))=>((rich(alice)&~brave(alice))))&
(((brave(alice)&~humble(alice)))<=>((~patient(lucy)|wise(lucy))))&
(![X]:((curious(X)&kind(X))=>(~curious(X)&~tall(X))))&
(((calm(mary)&~rich(mary)))=>((strong(alice)|funny(alice))))&
(((~old(john)&~curious(john)))<=>(?[X]:((~creative(X)<~>~generous(X)))))&
((~patient(lucy))=>((generous(lucy)|funny(lucy))))&
(![X]:((~strong(X)|~quiet(X))=>(kind(X)&~curious(X))))&
(![X]:((~old(X)&funny(X))=>(quiet(X)&wise(X))))&
(![X]:((~creative(X)&strong(X))=>~strong(X)))&
(((~curious(paul)|quiet(paul)))=>((strong(alice)<~>brave(alice))))&
((?[X]:((curious(X)<~>~generous(X))))=>((~calm(susan)&happy(susan))))&
(![X]:((~strong(X)&~happy(X))<=>(kind(X)&~calm(X))))&
(![X]:((brave(X)|~generous(X))=>(kind(X)&creative(X))))&
((?[X]:(~strong(X)))=>((~rich(fred)&~humble(fred))))&
(?[X]:((~happy(X)|tall(X))))&
((strong(mary)|patient(mary)))&
(?[X]:((~quiet(X)&creative(X))))&
((generous(fred)|wise(fred)))&
((~quiet(lucy)&old(lucy)))&
((quiet(john)<~>happy(john)))&
((~old(john)&~strong(john))) | rich(fred) | [
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 388244303222616960111304
% SZS output start Proof for 388244303222616960111304
16. ? [X0] : ~strong(X0) => (~humble(fred) & ~rich(fred)) [input p15]
23. ~strong(john) & ~old(john) [input p22]
24. rich(fred) [input hypothesis]
40. (~humble(fred) & ~rich(fred)) | ! [X0] : strong(X0) [ennf transformation 16]
111. ~rich(fred) | strong(X0) [cnf transformation 40]
123. ~strong(john) [cnf transformation 23]
124. rich(fred) [cnf transformation 24]
266. 30 <=> ! [X0] : strong(X0) [avatar definition]
267. strong(X0) <- (30) [avatar component clause 266]
274. 32 <=> rich(fred) [avatar definition]
277. 30 | ~32 [avatar split clause 111,274,266]
316. 32 [avatar split clause 124,274]
328. $false <- (30) [resolution 267,123]
329. ~30 [avatar contradiction clause 328]
330. $false [avatar sat refutation 277,316,329]
% SZS output end Proof for 388244303222616960111304
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both brave and calm is not curious or tall. Everyone who is not old is either not generous or old. Everyone who is curious is brave. Everyone who is not happy or not creative is old or generous and vice versa. Everyone who is both not curious and not creative is quiet or kind. If someone is tall or generous then someone is both not patient and humble and vice versa. Everyone who is both not quiet and not kind is happy. Everyone who is either not brave or not quiet is both old and wise. Everyone who is both not brave and quiet is not old. Everyone who is both not rich and creative is both funny and not curious. Everyone who is either not brave or not generous is funny or rich. Everyone who is both patient and curious is either wise or brave and vice versa. If someone is curious then lucy is both creative and not humble. Everyone who is either generous or calm is not brave or patient. If mary is either funny or wise then someone is both curious and not kind. Everyone who is both not tall and rich is calm or not curious and vice versa. Mary is both not brave and patient. Susan is either not humble or not generous. Someone is either rich or not quiet. Someone is not rich. Mary is not curious or kind. Susan is either funny or not curious. Susan is both curious and not old. | Susan is tall. | entailment | (![X]:((brave(X)&calm(X))=>(~curious(X)|tall(X))))&
(![X]:(~old(X)=>(~generous(X)<~>old(X))))&
(![X]:(curious(X)=>brave(X)))&
(![X]:((~happy(X)|~creative(X))<=>(old(X)|generous(X))))&
(![X]:((~curious(X)&~creative(X))=>(quiet(X)|kind(X))))&
((?[X]:((tall(X)|generous(X))))<=>(?[X]:((~patient(X)&humble(X)))))&
(![X]:((~quiet(X)&~kind(X))=>happy(X)))&
(![X]:((~brave(X)<~>~quiet(X))=>(old(X)&wise(X))))&
(![X]:((~brave(X)&quiet(X))=>~old(X)))&
(![X]:((~rich(X)&creative(X))=>(funny(X)&~curious(X))))&
(![X]:((~brave(X)<~>~generous(X))=>(funny(X)|rich(X))))&
(![X]:((patient(X)&curious(X))<=>(wise(X)<~>brave(X))))&
((?[X]:(curious(X)))=>((creative(lucy)&~humble(lucy))))&
(![X]:((generous(X)<~>calm(X))=>(~brave(X)|patient(X))))&
(((funny(mary)<~>wise(mary)))=>(?[X]:((curious(X)&~kind(X)))))&
(![X]:((~tall(X)&rich(X))<=>(calm(X)|~curious(X))))&
((~brave(mary)&patient(mary)))&
((~humble(susan)<~>~generous(susan)))&
(?[X]:((rich(X)<~>~quiet(X))))&
(?[X]:(~rich(X)))&
((~curious(mary)|kind(mary)))&
((funny(susan)<~>~curious(susan)))&
((curious(susan)&~old(susan))) | tall(susan) | [
"p0",
"p1",
"p2",
"p3",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 3907089635777947805795899
% SZS output start Proof for 3907089635777947805795899
1. ! [X0] : ((calm(X0) & brave(X0)) => (tall(X0) | ~curious(X0))) [input p0]
2. ! [X0] : (~old(X0) => (~generous(X0) <~> old(X0))) [input p1]
3. ! [X0] : (curious(X0) => brave(X0)) [input p2]
4. ! [X0] : ((~creative(X0) | ~happy(X0)) <=> (generous(X0) | old(X0))) [input p3]
10. ! [X0] : ((creative(X0) & ~rich(X0)) => (~curious(X0) & funny(X0))) [input p9]
16. ! [X0] : ((rich(X0) & ~tall(X0)) <=> (~curious(X0) | calm(X0))) [input p15]
23. ~old(susan) & curious(susan) [input p22]
24. ~tall(susan) [input hypothesis]
26. ! [X0] : ((tall(X0) | ~curious(X0)) | (~calm(X0) | ~brave(X0))) [ennf transformation 1]
27. ! [X0] : (tall(X0) | ~curious(X0) | ~calm(X0) | ~brave(X0)) [flattening 26]
28. ! [X0] : ((~generous(X0) <~> old(X0)) | old(X0)) [ennf transformation 2]
29. ! [X0] : (brave(X0) | ~curious(X0)) [ennf transformation 3]
37. ! [X0] : ((~curious(X0) & funny(X0)) | (~creative(X0) | rich(X0))) [ennf transformation 10]
38. ! [X0] : ((~curious(X0) & funny(X0)) | ~creative(X0) | rich(X0)) [flattening 37]
45. ! [X0] : (((~old(X0) | generous(X0)) & (old(X0) | ~generous(X0))) | old(X0)) [nnf transformation 28]
46. ! [X0] : (((~creative(X0) | ~happy(X0)) | (~generous(X0) & ~old(X0))) & ((generous(X0) | old(X0)) | (creative(X0) & happy(X0)))) [nnf transformation 4]
47. ! [X0] : ((~creative(X0) | ~happy(X0) | (~generous(X0) & ~old(X0))) & (generous(X0) | old(X0) | (creative(X0) & happy(X0)))) [flattening 46]
61. ! [X0] : (((rich(X0) & ~tall(X0)) | (curious(X0) & ~calm(X0))) & ((~curious(X0) | calm(X0)) | (~rich(X0) | tall(X0)))) [nnf transformation 16]
62. ! [X0] : (((rich(X0) & ~tall(X0)) | (curious(X0) & ~calm(X0))) & (~curious(X0) | calm(X0) | ~rich(X0) | tall(X0))) [flattening 61]
70. ~curious(X0) | tall(X0) | ~calm(X0) | ~brave(X0) [cnf transformation 27]
71. old(X0) | ~generous(X0) | old(X0) [cnf transformation 45]
73. ~curious(X0) | brave(X0) [cnf transformation 29]
75. generous(X0) | old(X0) | creative(X0) [cnf transformation 47]
91. ~creative(X0) | ~curious(X0) | rich(X0) [cnf transformation 38]
108. ~rich(X0) | calm(X0) | ~curious(X0) | tall(X0) [cnf transformation 62]
112. rich(X0) | curious(X0) [cnf transformation 62]
123. curious(susan) [cnf transformation 23]
124. ~old(susan) [cnf transformation 23]
125. ~tall(susan) [cnf transformation 24]
126. ~generous(X0) | old(X0) [duplicate literal removal 71]
127. creative(X0) | old(X0) [subsumption resolution 75,126]
229. 22 <=> curious(susan) [avatar definition]
231. curious(susan) <- (22) [avatar component clause 229]
234. 22 [avatar split clause 123,229]
237. brave(susan) <- (22) [resolution 73,231]
330. ~curious(X0) | rich(X0) | old(X0) [resolution 91,127]
331. rich(X0) | old(X0) [subsumption resolution 330,112]
357. tall(susan) | ~calm(susan) | ~brave(susan) <- (22) [resolution 70,231]
360. ~calm(susan) | ~brave(susan) <- (22) [subsumption resolution 357,125]
361. ~calm(susan) <- (22) [subsumption resolution 360,237]
373. ~curious(X0) | calm(X0) | tall(X0) | old(X0) [resolution 108,331]
495. calm(susan) | tall(susan) | old(susan) <- (22) [resolution 373,231]
497. tall(susan) | old(susan) <- (22) [subsumption resolution 495,361]
498. old(susan) <- (22) [subsumption resolution 497,125]
499. $false <- (22) [subsumption resolution 498,124]
500. ~22 [avatar contradiction clause 499]
501. $false [avatar sat refutation 234,500]
% SZS output end Proof for 3907089635777947805795899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or not brave is both rich and quiet. If someone is not patient or not generous then lucy is calm and vice versa. If mary is not generous then john is either funny or not curious. Everyone who is not kind or not humble is not brave or not funny. Everyone who is both brave and funny is not curious or not strong. If someone is funny then lucy is creative. If john is kind or not strong then someone is humble and vice versa. If alice is both rich and kind then john is both humble and not generous. If john is not wise or not brave then john is both not patient and kind. Everyone who is either calm or strong is not strong and vice versa. If someone is either brave or not brave then john is either generous or not old. Everyone who is either generous or not generous is not wise. If someone is not calm or not tall then someone is creative or not calm and vice versa. If mary is both not brave and rich then someone is either funny or tall and vice versa. Everyone who is calm is either not brave or creative and vice versa. Everyone who is brave or not quiet is either not tall or not humble. Someone is calm. Fred is both generous and humble. Susan is calm. Paul is not quiet or not wise. John is happy. Someone is either not happy or brave. | Alice is wise. | contradiction | (![X]:((~creative(X)|~brave(X))=>(rich(X)&quiet(X))))&
((?[X]:((~patient(X)|~generous(X))))<=>(calm(lucy)))&
((~generous(mary))=>((funny(john)<~>~curious(john))))&
(![X]:((~kind(X)|~humble(X))=>(~brave(X)|~funny(X))))&
(![X]:((brave(X)&funny(X))=>(~curious(X)|~strong(X))))&
((?[X]:(funny(X)))=>(creative(lucy)))&
(((kind(john)|~strong(john)))<=>(?[X]:(humble(X))))&
(((rich(alice)&kind(alice)))=>((humble(john)&~generous(john))))&
(((~wise(john)|~brave(john)))=>((~patient(john)&kind(john))))&
(![X]:((calm(X)<~>strong(X))<=>~strong(X)))&
((?[X]:((brave(X)<~>~brave(X))))=>((generous(john)<~>~old(john))))&
(![X]:((generous(X)<~>~generous(X))=>~wise(X)))&
((?[X]:((~calm(X)|~tall(X))))<=>(?[X]:((creative(X)|~calm(X)))))&
(((~brave(mary)&rich(mary)))<=>(?[X]:((funny(X)<~>tall(X)))))&
(![X]:(calm(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((brave(X)|~quiet(X))=>(~tall(X)<~>~humble(X))))&
(?[X]:(calm(X)))&
((generous(fred)&humble(fred)))&
(calm(susan))&
((~quiet(paul)|~wise(paul)))&
(happy(john))&
(?[X]:((~happy(X)<~>brave(X)))) | wise(alice) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8229941323052186202279585
% SZS output start Proof for 8229941323052186202279585
12. ! [X0] : ((generous(X0) <~> ~generous(X0)) => ~wise(X0)) [input p11]
23. wise(alice) [input hypothesis]
36. ! [X0] : (~wise(X0) | (generous(X0) <=> ~generous(X0))) [ennf transformation 12]
50. ! [X0] : (~wise(X0) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) [nnf transformation 36]
98. ~wise(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
99. ~wise(X0) | generous(X0) | generous(X0) [cnf transformation 50]
126. wise(alice) [cnf transformation 23]
127. ~wise(X0) | ~generous(X0) [duplicate literal removal 98]
128. ~wise(X0) | generous(X0) [duplicate literal removal 99]
245. ~wise(X0) [subsumption resolution 127,128]
306. $false [subsumption resolution 126,245]
% SZS output end Proof for 8229941323052186202279585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both humble and not brave then mary is both kind and not humble and vice versa. Everyone who is not happy or rich is both not calm and not rich and vice versa. If lucy is either kind or not quiet then lucy is either generous or not calm. Everyone who is either strong or not quiet is either not calm or not curious. Everyone who is not humble is not happy or curious and vice versa. If someone is not calm then someone is kind or generous. Everyone who is either not curious or not generous is not patient. Everyone who is not generous is calm or generous and vice versa. Everyone who is not kind is brave or not tall and vice versa. If john is both not strong and not tall then alice is not old. Everyone who is both old and generous is both not quiet and not brave and vice versa. Everyone who is not patient is both kind and not funny and vice versa. Everyone who is not brave or not strong is old. Everyone who is both quiet and not wise is not strong or quiet and vice versa. Everyone who is either old or not generous is either patient or generous and vice versa. Susan is both calm and not strong. Someone is not calm or tall. Fred is either not strong or not curious. Susan is quiet or calm. Someone is either not rich or not curious. Mary is either tall or not wise. | Mary is not patient. | contradiction | ((?[X]:((humble(X)&~brave(X))))<=>((kind(mary)&~humble(mary))))&
(![X]:((~happy(X)|rich(X))<=>(~calm(X)&~rich(X))))&
(((kind(lucy)<~>~quiet(lucy)))=>((generous(lucy)<~>~calm(lucy))))&
(![X]:((strong(X)<~>~quiet(X))=>(~calm(X)<~>~curious(X))))&
(![X]:(~humble(X)<=>(~happy(X)|curious(X))))&
((?[X]:(~calm(X)))=>(?[X]:((kind(X)|generous(X)))))&
(![X]:((~curious(X)<~>~generous(X))=>~patient(X)))&
(![X]:(~generous(X)<=>(calm(X)|generous(X))))&
(![X]:(~kind(X)<=>(brave(X)|~tall(X))))&
(((~strong(john)&~tall(john)))=>(~old(alice)))&
(![X]:((old(X)&generous(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(~patient(X)<=>(kind(X)&~funny(X))))&
(![X]:((~brave(X)|~strong(X))=>old(X)))&
(![X]:((quiet(X)&~wise(X))<=>(~strong(X)|quiet(X))))&
(![X]:((old(X)<~>~generous(X))<=>(patient(X)<~>generous(X))))&
((calm(susan)&~strong(susan)))&
(?[X]:((~calm(X)|tall(X))))&
((~strong(fred)<~>~curious(fred)))&
((quiet(susan)|calm(susan)))&
(?[X]:((~rich(X)<~>~curious(X))))&
((tall(mary)<~>~wise(mary))) | ~patient(mary) | [
"p7",
"p8",
"p10",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5139886671227556773124868
% SZS output start Proof for 5139886671227556773124868
8. ! [X0] : (~generous(X0) <=> (generous(X0) | calm(X0))) [input p7]
9. ! [X0] : (~kind(X0) <=> (~tall(X0) | brave(X0))) [input p8]
11. ! [X0] : ((generous(X0) & old(X0)) <=> (~brave(X0) & ~quiet(X0))) [input p10]
12. ! [X0] : (~patient(X0) <=> (~funny(X0) & kind(X0))) [input p11]
14. ! [X0] : ((~wise(X0) & quiet(X0)) <=> (quiet(X0) | ~strong(X0))) [input p13]
21. tall(mary) <~> ~wise(mary) [input p20]
22. ~patient(mary) [input hypothesis]
46. ! [X0] : ((~generous(X0) | (~generous(X0) & ~calm(X0))) & ((generous(X0) | calm(X0)) | generous(X0))) [nnf transformation 8]
47. ! [X0] : ((~generous(X0) | (~generous(X0) & ~calm(X0))) & (generous(X0) | calm(X0) | generous(X0))) [flattening 46]
48. ! [X0] : ((~kind(X0) | (tall(X0) & ~brave(X0))) & ((~tall(X0) | brave(X0)) | kind(X0))) [nnf transformation 9]
49. ! [X0] : ((~kind(X0) | (tall(X0) & ~brave(X0))) & (~tall(X0) | brave(X0) | kind(X0))) [flattening 48]
50. ! [X0] : (((generous(X0) & old(X0)) | (brave(X0) | quiet(X0))) & ((~brave(X0) & ~quiet(X0)) | (~generous(X0) | ~old(X0)))) [nnf transformation 11]
51. ! [X0] : (((generous(X0) & old(X0)) | brave(X0) | quiet(X0)) & ((~brave(X0) & ~quiet(X0)) | ~generous(X0) | ~old(X0))) [flattening 50]
52. ! [X0] : ((~patient(X0) | (funny(X0) | ~kind(X0))) & ((~funny(X0) & kind(X0)) | patient(X0))) [nnf transformation 12]
53. ! [X0] : ((~patient(X0) | funny(X0) | ~kind(X0)) & ((~funny(X0) & kind(X0)) | patient(X0))) [flattening 52]
54. ! [X0] : (((~wise(X0) & quiet(X0)) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | (wise(X0) | ~quiet(X0)))) [nnf transformation 14]
55. ! [X0] : (((~wise(X0) & quiet(X0)) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | wise(X0) | ~quiet(X0))) [flattening 54]
63. (wise(mary) | ~tall(mary)) & (~wise(mary) | tall(mary)) [nnf transformation 21]
89. ~generous(X0) | ~generous(X0) [cnf transformation 47]
91. ~kind(X0) | ~brave(X0) [cnf transformation 49]
92. ~kind(X0) | tall(X0) [cnf transformation 49]
97. generous(X0) | brave(X0) | quiet(X0) [cnf transformation 51]
98. patient(X0) | kind(X0) [cnf transformation 53]
107. ~wise(X0) | ~quiet(X0) [cnf transformation 55]
125. wise(mary) | ~tall(mary) [cnf transformation 63]
126. ~patient(mary) [cnf transformation 22]
132. ~generous(X0) [duplicate literal removal 89]
136. 1 <=> kind(mary) [avatar definition]
137. kind(mary) <- (1) [avatar component clause 136]
205. quiet(X0) | brave(X0) [subsumption resolution 97,132]
229. 20 <=> tall(mary) [avatar definition]
233. 21 <=> wise(mary) [avatar definition]
235. wise(mary) <- (21) [avatar component clause 233]
236. ~20 | 21 [avatar split clause 125,233,229]
245. kind(mary) [resolution 98,126]
248. 1 [avatar split clause 245,136]
249. tall(mary) <- (1) [resolution 137,92]
250. ~brave(mary) <- (1) [resolution 137,91]
253. 20 | ~1 [avatar split clause 249,136,229]
259. ~quiet(mary) <- (21) [resolution 107,235]
268. brave(mary) <- (21) [resolution 205,259]
269. $false <- (1, 21) [subsumption resolution 268,250]
270. ~1 | ~21 [avatar contradiction clause 269]
271. $false [avatar sat refutation 236,248,253,270]
% SZS output end Proof for 5139886671227556773124868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is funny then alice is not rich.
Everyone who is generous is both curious and funny.
Everyone who is generous is both not tall and quiet and vice versa.
If someone is both funny and not wise then someone is funny.
Everyone who is kind is not creative or happy and vice versa.
If someone is both curious and not creative then john is either wise or not generous.
If someone is not funny then someone is kind.
Everyone who is not humble or tall is patient or not patient and vice versa.
If someone is not funny then someone is wise or creative.
Everyone who is either wise or humble is both not calm and not curious and vice versa.
If john is not kind then someone is both wise and patient.
Everyone who is both creative and not happy is not kind or not curious and vice versa.
Everyone who is rich is both not humble and patient.
If paul is not happy or curious then someone is either quiet or curious.
If someone is both creative and happy then someone is patient and vice versa.
Everyone who is not brave or kind is both not creative and not patient.
Someone is not brave or not curious.
Someone is either not curious or not funny.
Alice is not kind or rich.
Lucy is not humble or not funny.
Someone is humble.
Someone is both happy and not funny.
Fred is wise. | Lucy is patient. | contradiction | ((funny(alice))=>(~rich(alice)))&
(![X]:(generous(X)=>(curious(X)&funny(X))))&
(![X]:(generous(X)<=>(~tall(X)&quiet(X))))&
((?[X]:((funny(X)&~wise(X))))=>(?[X]:(funny(X))))&
(![X]:(kind(X)<=>(~creative(X)|happy(X))))&
((?[X]:((curious(X)&~creative(X))))=>((wise(john)<~>~generous(john))))&
((?[X]:(~funny(X)))=>(?[X]:(kind(X))))&
(![X]:((~humble(X)|tall(X))<=>(patient(X)|~patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)|creative(X)))))&
(![X]:((wise(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
((~kind(john))=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((creative(X)&~happy(X))<=>(~kind(X)|~curious(X))))&
(![X]:(rich(X)=>(~humble(X)&patient(X))))&
(((~happy(paul)|curious(paul)))=>(?[X]:((quiet(X)<~>curious(X)))))&
((?[X]:((creative(X)&happy(X))))<=>(?[X]:(patient(X))))&
(![X]:((~brave(X)|kind(X))=>(~creative(X)&~patient(X))))&
(?[X]:((~brave(X)|~curious(X))))&
(?[X]:((~curious(X)<~>~funny(X))))&
((~kind(alice)|rich(alice)))&
((~humble(lucy)|~funny(lucy)))&
(?[X]:(humble(X)))&
(?[X]:((happy(X)&~funny(X))))&
(wise(fred)) | patient(lucy) | [
"p4",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4249018594952375897362898
% SZS output start Proof for 4249018594952375897362898
5. ! [X0] : (kind(X0) <=> (happy(X0) | ~creative(X0))) [input p4]
15. ? [X0] : (happy(X0) & creative(X0)) <=> ? [X0] : patient(X0) [input p14]
16. ! [X0] : ((kind(X0) | ~brave(X0)) => (~patient(X0) & ~creative(X0))) [input p15]
24. patient(lucy) [input hypothesis]
28. ? [X0] : (happy(X0) & creative(X0)) <=> ? [X1] : patient(X1) [rectify 15]
38. ! [X0] : ((~patient(X0) & ~creative(X0)) | (~kind(X0) & brave(X0))) [ennf transformation 16]
44. ! [X0] : ((kind(X0) | (~happy(X0) & creative(X0))) & ((happy(X0) | ~creative(X0)) | ~kind(X0))) [nnf transformation 5]
45. ! [X0] : ((kind(X0) | (~happy(X0) & creative(X0))) & (happy(X0) | ~creative(X0) | ~kind(X0))) [flattening 44]
64. (? [X0] : (happy(X0) & creative(X0)) | ! [X1] : ~patient(X1)) & (? [X1] : patient(X1) | ! [X0] : (~happy(X0) | ~creative(X0))) [nnf transformation 28]
65. (? [X0] : (happy(X0) & creative(X0)) | ! [X1] : ~patient(X1)) & (? [X2] : patient(X2) | ! [X3] : (~happy(X3) | ~creative(X3))) [rectify 64]
66. ? [X0] : (happy(X0) & creative(X0)) => (happy(sK5) & creative(sK5)) [choice axiom]
67. ? [X2] : patient(X2) => patient(sK6) [choice axiom]
68. ((happy(sK5) & creative(sK5)) | ! [X1] : ~patient(X1)) & (patient(sK6) | ! [X3] : (~happy(X3) | ~creative(X3))) [skolemisation 65,67,66]
87. ~happy(X0) | kind(X0) [cnf transformation 45]
116. creative(sK5) | ~patient(X1) [cnf transformation 68]
117. happy(sK5) | ~patient(X1) [cnf transformation 68]
119. ~creative(X0) | ~kind(X0) [cnf transformation 38]
131. patient(lucy) [cnf transformation 24]
215. 19 <=> ! [X1] : ~patient(X1) [avatar definition]
216. ~patient(X1) <- (19) [avatar component clause 215]
218. 20 <=> happy(sK5) [avatar definition]
220. happy(sK5) <- (20) [avatar component clause 218]
221. 19 | 20 [avatar split clause 117,218,215]
223. 21 <=> creative(sK5) [avatar definition]
225. creative(sK5) <- (21) [avatar component clause 223]
226. 19 | 21 [avatar split clause 116,223,215]
271. $false <- (19) [resolution 216,131]
272. ~19 [avatar contradiction clause 271]
274. kind(sK5) <- (20) [resolution 87,220]
281. ~kind(sK5) <- (21) [resolution 119,225]
284. $false <- (20, 21) [subsumption resolution 281,274]
285. ~20 | ~21 [avatar contradiction clause 284]
286. $false [avatar sat refutation 221,226,272,285]
% SZS output end Proof for 4249018594952375897362898
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not strong or generous then paul is not calm and vice versa. If susan is either happy or not wise then paul is either not humble or not rich. If fred is either kind or wise then lucy is either not brave or old and vice versa. Everyone who is either funny or not rich is both not wise and not calm. Everyone who is creative or old is both not creative and not brave. Everyone who is both patient and kind is either strong or wise. Everyone who is rich is both not rich and not brave. Everyone who is both kind and curious is tall or not wise. If mary is not generous then someone is either kind or not rich. If fred is both kind and not patient then someone is curious and vice versa. Everyone who is tall or not curious is not strong. Everyone who is both rich and creative is both wise and kind and vice versa. Everyone who is both not humble and not wise is both not curious and happy. Everyone who is either not wise or not generous is either not patient or not old and vice versa. Everyone who is either funny or not generous is both not creative and rich and vice versa. Everyone who is not rich is generous and vice versa. Someone is quiet. Someone is strong. Someone is not calm. Susan is either kind or not kind. Lucy is curious. Susan is old or generous. | Susan is not funny. | entailment | (((~strong(mary)<~>generous(mary)))<=>(~calm(paul)))&
(((happy(susan)<~>~wise(susan)))=>((~humble(paul)<~>~rich(paul))))&
(((kind(fred)<~>wise(fred)))<=>((~brave(lucy)<~>old(lucy))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~calm(X))))&
(![X]:((creative(X)|old(X))=>(~creative(X)&~brave(X))))&
(![X]:((patient(X)&kind(X))=>(strong(X)<~>wise(X))))&
(![X]:(rich(X)=>(~rich(X)&~brave(X))))&
(![X]:((kind(X)&curious(X))=>(tall(X)|~wise(X))))&
((~generous(mary))=>(?[X]:((kind(X)<~>~rich(X)))))&
(((kind(fred)&~patient(fred)))<=>(?[X]:(curious(X))))&
(![X]:((tall(X)|~curious(X))=>~strong(X)))&
(![X]:((rich(X)&creative(X))<=>(wise(X)&kind(X))))&
(![X]:((~humble(X)&~wise(X))=>(~curious(X)&happy(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~creative(X)&rich(X))))&
(![X]:(~rich(X)<=>generous(X)))&
(?[X]:(quiet(X)))&
(?[X]:(strong(X)))&
(?[X]:(~calm(X)))&
((kind(susan)<~>~kind(susan)))&
(curious(lucy))&
((old(susan)|generous(susan))) | ~funny(susan) | [
"p6",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4253584798387306775114470
% SZS output start Proof for 4253584798387306775114470
7. ! [X0] : (rich(X0) => (~brave(X0) & ~rich(X0))) [input p6]
15. ! [X0] : ((funny(X0) <~> ~generous(X0)) <=> (rich(X0) & ~creative(X0))) [input p14]
16. ! [X0] : (~rich(X0) <=> generous(X0)) [input p15]
23. funny(susan) [input hypothesis]
30. ! [X0] : ((~brave(X0) & ~rich(X0)) | ~rich(X0)) [ennf transformation 7]
53. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | (~rich(X0) | creative(X0))) & ((rich(X0) & ~creative(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [nnf transformation 15]
54. ! [X0] : ((((generous(X0) | ~funny(X0)) & (~generous(X0) | funny(X0))) | ~rich(X0) | creative(X0)) & ((rich(X0) & ~creative(X0)) | ((funny(X0) | generous(X0)) & (~generous(X0) | ~funny(X0))))) [flattening 53]
55. ! [X0] : ((~rich(X0) | ~generous(X0)) & (generous(X0) | rich(X0))) [nnf transformation 16]
87. ~rich(X0) | ~rich(X0) [cnf transformation 30]
113. rich(X0) | ~generous(X0) | ~funny(X0) [cnf transformation 54]
117. generous(X0) | rich(X0) [cnf transformation 55]
125. funny(susan) [cnf transformation 23]
126. ~rich(X0) [duplicate literal removal 87]
210. ~funny(X0) | ~generous(X0) [subsumption resolution 113,126]
211. generous(X0) [subsumption resolution 117,126]
218. ~generous(susan) [resolution 210,125]
220. $false [subsumption resolution 218,211]
% SZS output end Proof for 4253584798387306775114470
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either rich or not creative then fred is not tall or not happy and vice versa. If someone is brave then someone is calm and vice versa. If alice is both not wise and not quiet then someone is both calm and not old and vice versa. Everyone who is wise or not patient is either not happy or rich and vice versa. Everyone who is not kind is either wise or creative. Everyone who is calm is not old and vice versa. Everyone who is both wise and not humble is not quiet or not kind. Everyone who is quiet or humble is not funny or not old. If paul is not strong then someone is either not happy or old. If susan is not brave or wise then someone is not calm and vice versa. Everyone who is both rich and not humble is not funny. If susan is either kind or wise then someone is not curious. Everyone who is not rich is not old or curious and vice versa. Everyone who is not wise or creative is both not curious and quiet. If lucy is kind or not kind then mary is not funny and vice versa. Everyone who is both kind and funny is both funny and not happy. Someone is both not quiet and not happy. John is not calm. Lucy is either creative or not tall. Someone is not calm. Someone is not rich or not funny. John is both not tall and not creative. Someone is either wise or funny. | Mary is old. | entailment | ((?[X]:((rich(X)<~>~creative(X))))<=>((~tall(fred)|~happy(fred))))&
((?[X]:(brave(X)))<=>(?[X]:(calm(X))))&
(((~wise(alice)&~quiet(alice)))<=>(?[X]:((calm(X)&~old(X)))))&
(![X]:((wise(X)|~patient(X))<=>(~happy(X)<~>rich(X))))&
(![X]:(~kind(X)=>(wise(X)<~>creative(X))))&
(![X]:(calm(X)<=>~old(X)))&
(![X]:((wise(X)&~humble(X))=>(~quiet(X)|~kind(X))))&
(![X]:((quiet(X)|humble(X))=>(~funny(X)|~old(X))))&
((~strong(paul))=>(?[X]:((~happy(X)<~>old(X)))))&
(((~brave(susan)|wise(susan)))<=>(?[X]:(~calm(X))))&
(![X]:((rich(X)&~humble(X))=>~funny(X)))&
(((kind(susan)<~>wise(susan)))=>(?[X]:(~curious(X))))&
(![X]:(~rich(X)<=>(~old(X)|curious(X))))&
(![X]:((~wise(X)|creative(X))=>(~curious(X)&quiet(X))))&
(((kind(lucy)|~kind(lucy)))<=>(~funny(mary)))&
(![X]:((kind(X)&funny(X))=>(funny(X)&~happy(X))))&
(?[X]:((~quiet(X)&~happy(X))))&
(~calm(john))&
((creative(lucy)<~>~tall(lucy)))&
(?[X]:(~calm(X)))&
(?[X]:((~rich(X)|~funny(X))))&
((~tall(john)&~creative(john)))&
(?[X]:((wise(X)<~>funny(X)))) | old(mary) | [
"p2",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3721624961291146682637502
% SZS output start Proof for 3721624961291146682637502
3. (~quiet(alice) & ~wise(alice)) <=> ? [X0] : (~old(X0) & calm(X0)) [input p2]
6. ! [X0] : (calm(X0) <=> ~old(X0)) [input p5]
14. ! [X0] : ((creative(X0) | ~wise(X0)) => (quiet(X0) & ~curious(X0))) [input p13]
24. ~old(mary) [input hypothesis]
35. ! [X0] : ((quiet(X0) & ~curious(X0)) | (~creative(X0) & wise(X0))) [ennf transformation 14]
48. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X0] : (~old(X0) & calm(X0)) | (quiet(alice) | wise(alice))) [nnf transformation 3]
49. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X0] : (~old(X0) & calm(X0)) | quiet(alice) | wise(alice)) [flattening 48]
50. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & (? [X1] : (~old(X1) & calm(X1)) | quiet(alice) | wise(alice)) [rectify 49]
51. ? [X1] : (~old(X1) & calm(X1)) => (~old(sK3) & calm(sK3)) [choice axiom]
52. ((~quiet(alice) & ~wise(alice)) | ! [X0] : (old(X0) | ~calm(X0))) & ((~old(sK3) & calm(sK3)) | quiet(alice) | wise(alice)) [skolemisation 50,51]
56. ! [X0] : ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0))) [nnf transformation 6]
89. ~wise(alice) | old(X0) | ~calm(X0) [cnf transformation 52]
90. ~quiet(alice) | old(X0) | ~calm(X0) [cnf transformation 52]
99. ~old(X0) | ~calm(X0) [cnf transformation 56]
100. old(X0) | calm(X0) [cnf transformation 56]
115. quiet(X0) | wise(X0) [cnf transformation 35]
133. ~old(mary) [cnf transformation 24]
163. 7 <=> ! [X1] : ~calm(X1) [avatar definition]
164. ~calm(X1) <- (7) [avatar component clause 163]
179. 11 <=> ! [X0] : (old(X0) | ~calm(X0)) [avatar definition]
180. old(X0) | ~calm(X0) <- (11) [avatar component clause 179]
182. 12 <=> quiet(alice) [avatar definition]
184. ~quiet(alice) <- (~12) [avatar component clause 182]
185. 11 | ~12 [avatar split clause 90,182,179]
187. 13 <=> wise(alice) [avatar definition]
189. ~wise(alice) <- (~13) [avatar component clause 187]
190. 11 | ~13 [avatar split clause 89,187,179]
268. ~calm(X0) <- (11) [subsumption resolution 180,99]
269. 7 | ~11 [avatar split clause 268,179,163]
270. calm(mary) [resolution 100,133]
272. $false <- (7) [subsumption resolution 270,164]
273. ~7 [avatar contradiction clause 272]
278. wise(alice) <- (~12) [resolution 115,184]
279. $false <- (~12, ~13) [subsumption resolution 278,189]
280. 12 | 13 [avatar contradiction clause 279]
281. $false [avatar sat refutation 185,190,269,273,280]
% SZS output end Proof for 3721624961291146682637502
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not patient or generous then mary is not quiet or not humble. Everyone who is both wise and not happy is either old or not creative and vice versa. Everyone who is not quiet or not happy is both calm and creative. Everyone who is both patient and not generous is both quiet and not generous and vice versa. Everyone who is curious or not wise is not wise or not rich and vice versa. Everyone who is either not quiet or not happy is either not happy or brave. If lucy is both not rich and not patient then fred is both not tall and not old and vice versa. Everyone who is both creative and not rich is both not happy and rich and vice versa. Everyone who is not generous is generous. Everyone who is not wise or funny is not happy. Everyone who is either not patient or wise is either not brave or not strong. If someone is either rich or not curious then lucy is both happy and tall and vice versa. Everyone who is tall is both happy and not calm. Everyone who is either not patient or not humble is either strong or happy and vice versa. Everyone who is both curious and generous is either not happy or brave. Everyone who is either not generous or not strong is funny or not generous. Lucy is either tall or not quiet. Someone is brave. Someone is not old. Someone is either kind or calm. John is either not tall or old. Someone is calm or not curious. | Lucy is not creative. | contradiction | ((?[X]:((~patient(X)|generous(X))))=>((~quiet(mary)|~humble(mary))))&
(![X]:((wise(X)&~happy(X))<=>(old(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~happy(X))=>(calm(X)&creative(X))))&
(![X]:((patient(X)&~generous(X))<=>(quiet(X)&~generous(X))))&
(![X]:((curious(X)|~wise(X))<=>(~wise(X)|~rich(X))))&
(![X]:((~quiet(X)<~>~happy(X))=>(~happy(X)<~>brave(X))))&
(((~rich(lucy)&~patient(lucy)))<=>((~tall(fred)&~old(fred))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&rich(X))))&
(![X]:(~generous(X)=>generous(X)))&
(![X]:((~wise(X)|funny(X))=>~happy(X)))&
(![X]:((~patient(X)<~>wise(X))=>(~brave(X)<~>~strong(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((happy(lucy)&tall(lucy))))&
(![X]:(tall(X)=>(happy(X)&~calm(X))))&
(![X]:((~patient(X)<~>~humble(X))<=>(strong(X)<~>happy(X))))&
(![X]:((curious(X)&generous(X))=>(~happy(X)<~>brave(X))))&
(![X]:((~generous(X)<~>~strong(X))=>(funny(X)|~generous(X))))&
((tall(lucy)<~>~quiet(lucy)))&
(?[X]:(brave(X)))&
(?[X]:(~old(X)))&
(?[X]:((kind(X)<~>calm(X))))&
((~tall(john)<~>old(john)))&
(?[X]:((calm(X)|~curious(X)))) | ~creative(lucy) | [
"p2",
"p4",
"p7",
"p9",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9216288350696774432759736
% SZS output start Proof for 9216288350696774432759736
3. ! [X0] : ((~happy(X0) | ~quiet(X0)) => (creative(X0) & calm(X0))) [input p2]
5. ! [X0] : ((~wise(X0) | curious(X0)) <=> (~rich(X0) | ~wise(X0))) [input p4]
8. ! [X0] : ((~rich(X0) & creative(X0)) <=> (rich(X0) & ~happy(X0))) [input p7]
10. ! [X0] : ((funny(X0) | ~wise(X0)) => ~happy(X0)) [input p9]
12. ? [X0] : (rich(X0) <~> ~curious(X0)) <=> (tall(lucy) & happy(lucy)) [input p11]
17. tall(lucy) <~> ~quiet(lucy) [input p16]
23. ~creative(lucy) [input hypothesis]
26. ! [X0] : ((creative(X0) & calm(X0)) | (happy(X0) & quiet(X0))) [ennf transformation 3]
29. ! [X0] : (~happy(X0) | (~funny(X0) & wise(X0))) [ennf transformation 10]
40. ! [X0] : (((~wise(X0) | curious(X0)) | (rich(X0) & wise(X0))) & ((~rich(X0) | ~wise(X0)) | (wise(X0) & ~curious(X0)))) [nnf transformation 5]
41. ! [X0] : ((~wise(X0) | curious(X0) | (rich(X0) & wise(X0))) & (~rich(X0) | ~wise(X0) | (wise(X0) & ~curious(X0)))) [flattening 40]
45. ! [X0] : (((~rich(X0) & creative(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 8]
46. ! [X0] : (((~rich(X0) & creative(X0)) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | rich(X0) | ~creative(X0))) [flattening 45]
48. (? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | (~tall(lucy) | ~happy(lucy))) & ((tall(lucy) & happy(lucy)) | ! [X0] : ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) [nnf transformation 12]
49. (? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~tall(lucy) | ~happy(lucy)) & ((tall(lucy) & happy(lucy)) | ! [X0] : ((rich(X0) | curious(X0)) & (~curious(X0) | ~rich(X0)))) [flattening 48]
50. (? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) | ~tall(lucy) | ~happy(lucy)) & ((tall(lucy) & happy(lucy)) | ! [X1] : ((rich(X1) | curious(X1)) & (~curious(X1) | ~rich(X1)))) [rectify 49]
51. ? [X0] : ((curious(X0) | ~rich(X0)) & (~curious(X0) | rich(X0))) => ((curious(sK0) | ~rich(sK0)) & (~curious(sK0) | rich(sK0))) [choice axiom]
52. (((curious(sK0) | ~rich(sK0)) & (~curious(sK0) | rich(sK0))) | ~tall(lucy) | ~happy(lucy)) & ((tall(lucy) & happy(lucy)) | ! [X1] : ((rich(X1) | curious(X1)) & (~curious(X1) | ~rich(X1)))) [skolemisation 50,51]
56. (quiet(lucy) | ~tall(lucy)) & (~quiet(lucy) | tall(lucy)) [nnf transformation 17]
77. creative(X0) | quiet(X0) [cnf transformation 26]
78. creative(X0) | happy(X0) [cnf transformation 26]
83. ~rich(X0) | ~wise(X0) | ~curious(X0) [cnf transformation 41]
86. ~wise(X0) | curious(X0) | rich(X0) [cnf transformation 41]
96. rich(X0) | rich(X0) | ~creative(X0) [cnf transformation 46]
98. ~rich(X0) | ~rich(X0) | happy(X0) [cnf transformation 46]
100. ~happy(X0) | wise(X0) [cnf transformation 29]
110. ~curious(sK0) | rich(sK0) | ~tall(lucy) | ~happy(lucy) [cnf transformation 52]
111. curious(sK0) | ~rich(sK0) | ~tall(lucy) | ~happy(lucy) [cnf transformation 52]
126. ~quiet(lucy) | tall(lucy) [cnf transformation 56]
135. ~creative(lucy) [cnf transformation 23]
138. ~creative(X0) | rich(X0) [duplicate literal removal 96]
139. ~rich(X0) | happy(X0) [duplicate literal removal 98]
179. 9 <=> happy(lucy) [avatar definition]
183. 10 <=> tall(lucy) [avatar definition]
187. 11 <=> rich(sK0) [avatar definition]
188. rich(sK0) <- (11) [avatar component clause 187]
189. ~rich(sK0) <- (~11) [avatar component clause 187]
191. 12 <=> curious(sK0) [avatar definition]
192. ~curious(sK0) <- (~12) [avatar component clause 191]
193. curious(sK0) <- (12) [avatar component clause 191]
194. ~9 | ~10 | ~11 | 12 [avatar split clause 111,191,187,183,179]
195. ~9 | ~10 | 11 | ~12 [avatar split clause 110,191,187,183,179]
197. 13 <=> ! [X1] : (rich(X1) | curious(X1)) [avatar definition]
198. rich(X1) | curious(X1) <- (13) [avatar component clause 197]
210. 15 <=> quiet(lucy) [avatar definition]
214. 10 | ~15 [avatar split clause 126,210,183]
246. quiet(lucy) [resolution 77,135]
249. 15 [avatar split clause 246,210]
250. happy(lucy) [resolution 78,135]
253. 9 [avatar split clause 250,179]
260. rich(X0) | happy(X0) [resolution 138,78]
262. happy(X0) [subsumption resolution 260,139]
263. wise(X0) [resolution 262,100]
265. curious(sK0) <- (~11, 13) [resolution 198,189]
267. $false <- (~11, ~12, 13) [subsumption resolution 265,192]
268. 11 | 12 | ~13 [avatar contradiction clause 267]
308. ~wise(sK0) | ~curious(sK0) <- (11) [resolution 83,188]
310. ~curious(sK0) <- (11) [subsumption resolution 308,263]
311. $false <- (11, 12) [subsumption resolution 310,193]
312. ~11 | ~12 [avatar contradiction clause 311]
317. curious(X0) | rich(X0) [resolution 86,263]
319. 13 [avatar split clause 317,197]
320. $false [avatar sat refutation 194,195,214,249,253,268,312,319]
% SZS output end Proof for 9216288350696774432759736
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is tall then alice is both not funny and not strong and vice versa. Everyone who is not rich or calm is both not calm and not creative. If susan is not happy then someone is either patient or not creative. If alice is both not creative and not kind then paul is happy. Everyone who is not patient is both wise and not brave. If mary is not quiet then john is both not quiet and not kind and vice versa. Everyone who is kind is brave and vice versa. If someone is both not humble and not kind then john is both brave and not happy. Everyone who is tall or not creative is either tall or not kind and vice versa. If someone is not curious or wise then lucy is both not creative and not kind. Everyone who is brave or not patient is brave or not happy. Everyone who is not quiet is not tall or not wise. Everyone who is generous or brave is both kind and not old and vice versa. Everyone who is either not humble or happy is strong. If susan is humble then fred is not generous. Everyone who is kind or not humble is both not calm and not patient. Fred is both not generous and not creative. Paul is not rich or strong. Someone is humble. John is humble or patient. Someone is not happy or kind. Mary is either happy or not generous. | Mary is tall. | contradiction | ((?[X]:(tall(X)))<=>((~funny(alice)&~strong(alice))))&
(![X]:((~rich(X)|calm(X))=>(~calm(X)&~creative(X))))&
((~happy(susan))=>(?[X]:((patient(X)<~>~creative(X)))))&
(((~creative(alice)&~kind(alice)))=>(happy(paul)))&
(![X]:(~patient(X)=>(wise(X)&~brave(X))))&
((~quiet(mary))<=>((~quiet(john)&~kind(john))))&
(![X]:(kind(X)<=>brave(X)))&
((?[X]:((~humble(X)&~kind(X))))=>((brave(john)&~happy(john))))&
(![X]:((tall(X)|~creative(X))<=>(tall(X)<~>~kind(X))))&
((?[X]:((~curious(X)|wise(X))))=>((~creative(lucy)&~kind(lucy))))&
(![X]:((brave(X)|~patient(X))=>(brave(X)|~happy(X))))&
(![X]:(~quiet(X)=>(~tall(X)|~wise(X))))&
(![X]:((generous(X)|brave(X))<=>(kind(X)&~old(X))))&
(![X]:((~humble(X)<~>happy(X))=>strong(X)))&
((humble(susan))=>(~generous(fred)))&
(![X]:((kind(X)|~humble(X))=>(~calm(X)&~patient(X))))&
((~generous(fred)&~creative(fred)))&
((~rich(paul)|strong(paul)))&
(?[X]:(humble(X)))&
((humble(john)|patient(john)))&
(?[X]:((~happy(X)|kind(X))))&
((happy(mary)<~>~generous(mary))) | tall(mary) | [
"p4",
"p6",
"p8",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5728984222343658827861194
% SZS output start Proof for 5728984222343658827861194
5. ! [X0] : (~patient(X0) => (~brave(X0) & wise(X0))) [input p4]
7. ! [X0] : (kind(X0) <=> brave(X0)) [input p6]
9. ! [X0] : ((~creative(X0) | tall(X0)) <=> (tall(X0) <~> ~kind(X0))) [input p8]
16. ! [X0] : ((~humble(X0) | kind(X0)) => (~patient(X0) & ~calm(X0))) [input p15]
23. tall(mary) [input hypothesis]
26. ! [X0] : ((~humble(X0) | kind(X0)) => ~patient(X0)) [pure predicate removal 16]
31. ! [X0] : ((~brave(X0) & wise(X0)) | patient(X0)) [ennf transformation 5]
40. ! [X0] : (~patient(X0) | (humble(X0) & ~kind(X0))) [ennf transformation 26]
51. ! [X0] : ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0))) [nnf transformation 7]
52. ! [X0] : (((~creative(X0) | tall(X0)) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0)))) & (((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | (creative(X0) & ~tall(X0)))) [nnf transformation 9]
53. ! [X0] : ((~creative(X0) | tall(X0) | ((tall(X0) | kind(X0)) & (~kind(X0) | ~tall(X0)))) & (((kind(X0) | ~tall(X0)) & (~kind(X0) | tall(X0))) | (creative(X0) & ~tall(X0)))) [flattening 52]
70. ~brave(X0) | patient(X0) [cnf transformation 31]
74. ~kind(X0) | brave(X0) [cnf transformation 51]
80. kind(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 53]
97. ~kind(X0) | ~patient(X0) [cnf transformation 40]
107. tall(mary) [cnf transformation 23]
108. ~tall(X0) | kind(X0) [duplicate literal removal 80]
237. kind(mary) [resolution 108,107]
239. ~patient(mary) [resolution 237,97]
240. brave(mary) [resolution 237,74]
246. patient(mary) [resolution 240,70]
247. $false [subsumption resolution 246,239]
% SZS output end Proof for 5728984222343658827861194
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Subsets and Splits