premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
Everyone who is not calm is not funny and vice versa. If fred is both not curious and kind then alice is both not kind and not happy. If someone is funny then lucy is brave and vice versa. Everyone who is rich is both not rich and not creative and vice versa. If someone is old or not kind then someone is not strong and vice versa. Everyone who is both wise and not happy is both rich and kind. Everyone who is either not creative or quiet is calm and vice versa. If mary is not wise then mary is both not strong and not quiet. Everyone who is either not funny or not brave is funny. If someone is creative then someone is not strong or wise and vice versa. If someone is not humble or not rich then someone is not wise and vice versa. If fred is both not funny and not calm then alice is kind or old. If mary is not curious or not happy then susan is not patient or not happy and vice versa. If mary is both quiet and tall then someone is not generous and vice versa. Everyone who is both not rich and not kind is old and vice versa. Everyone who is both creative and old is both kind and tall and vice versa. Someone is either not happy or patient. Susan is both not rich and not curious. Someone is not humble. Paul is either not wise or happy. Alice is not humble or not quiet. Someone is not quiet or curious. Susan is funny or rich. | Lucy is creative. | entailment | (![X]:(~calm(X)<=>~funny(X)))&
(((~curious(fred)&kind(fred)))=>((~kind(alice)&~happy(alice))))&
((?[X]:(funny(X)))<=>(brave(lucy)))&
(![X]:(rich(X)<=>(~rich(X)&~creative(X))))&
((?[X]:((old(X)|~kind(X))))<=>(?[X]:(~strong(X))))&
(![X]:((wise(X)&~happy(X))=>(rich(X)&kind(X))))&
(![X]:((~creative(X)<~>quiet(X))<=>calm(X)))&
((~wise(mary))=>((~strong(mary)&~quiet(mary))))&
(![X]:((~funny(X)<~>~brave(X))=>funny(X)))&
((?[X]:(creative(X)))<=>(?[X]:((~strong(X)|wise(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(?[X]:(~wise(X))))&
(((~funny(fred)&~calm(fred)))=>((kind(alice)|old(alice))))&
(((~curious(mary)|~happy(mary)))<=>((~patient(susan)|~happy(susan))))&
(((quiet(mary)&tall(mary)))<=>(?[X]:(~generous(X))))&
(![X]:((~rich(X)&~kind(X))<=>old(X)))&
(![X]:((creative(X)&old(X))<=>(kind(X)&tall(X))))&
(?[X]:((~happy(X)<~>patient(X))))&
((~rich(susan)&~curious(susan)))&
(?[X]:(~humble(X)))&
((~wise(paul)<~>happy(paul)))&
((~humble(alice)|~quiet(alice)))&
(?[X]:((~quiet(X)|curious(X))))&
((funny(susan)|rich(susan))) | creative(lucy) | [
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 6951268413902403418584055
% SZS output start Proof for 6951268413902403418584055
4. ! [X0] : (rich(X0) <=> (~creative(X0) & ~rich(X0))) [input p3]
24. ~creative(lucy) [input hypothesis]
41. ! [X0] : ((rich(X0) | (creative(X0) | rich(X0))) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [nnf transformation 4]
42. ! [X0] : ((rich(X0) | creative(X0) | rich(X0)) & ((~creative(X0) & ~rich(X0)) | ~rich(X0))) [flattening 41]
85. ~rich(X0) | ~rich(X0) [cnf transformation 42]
87. rich(X0) | creative(X0) | rich(X0) [cnf transformation 42]
132. ~creative(lucy) [cnf transformation 24]
134. ~rich(X0) [duplicate literal removal 85]
135. creative(X0) | rich(X0) [duplicate literal removal 87]
324. rich(lucy) [resolution 135,132]
326. $false [subsumption resolution 324,134]
% SZS output end Proof for 6951268413902403418584055
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or humble is both wise and strong and vice versa.
Everyone who is either not humble or not kind is both kind and generous and vice versa.
If someone is not patient or kind then someone is either patient or not kind.
If susan is both quiet and not tall then someone is not curious and vice versa.
Everyone who is not patient or not funny is both not old and happy and vice versa.
Everyone who is not generous or not kind is both rich and generous and vice versa.
Everyone who is both not brave and not patient is kind or creative and vice versa.
If someone is not calm or not creative then paul is both kind and quiet and vice versa.
If someone is either not quiet or not happy then fred is happy and vice versa.
Everyone who is either not strong or tall is not rich or calm.
If john is curious then someone is calm.
If someone is brave then susan is either not wise or not tall.
Everyone who is either quiet or not creative is either old or humble and vice versa.
If someone is generous then mary is brave.
Everyone who is not humble or humble is both strong and calm.
If someone is either happy or not calm then mary is not curious.
Someone is curious or not happy.
John is quiet or not old.
Someone is either not wise or funny.
Alice is calm or curious.
Someone is either creative or funny.
Lucy is either happy or kind. | Alice is humble. | contradiction | (![X]:((generous(X)|humble(X))<=>(wise(X)&strong(X))))&
(![X]:((~humble(X)<~>~kind(X))<=>(kind(X)&generous(X))))&
((?[X]:((~patient(X)|kind(X))))=>(?[X]:((patient(X)<~>~kind(X)))))&
(((quiet(susan)&~tall(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((~patient(X)|~funny(X))<=>(~old(X)&happy(X))))&
(![X]:((~generous(X)|~kind(X))<=>(rich(X)&generous(X))))&
(![X]:((~brave(X)&~patient(X))<=>(kind(X)|creative(X))))&
((?[X]:((~calm(X)|~creative(X))))<=>((kind(paul)&quiet(paul))))&
((?[X]:((~quiet(X)<~>~happy(X))))<=>(happy(fred)))&
(![X]:((~strong(X)<~>tall(X))=>(~rich(X)|calm(X))))&
((curious(john))=>(?[X]:(calm(X))))&
((?[X]:(brave(X)))=>((~wise(susan)<~>~tall(susan))))&
(![X]:((quiet(X)<~>~creative(X))<=>(old(X)<~>humble(X))))&
((?[X]:(generous(X)))=>(brave(mary)))&
(![X]:((~humble(X)|humble(X))=>(strong(X)&calm(X))))&
((?[X]:((happy(X)<~>~calm(X))))=>(~curious(mary)))&
(?[X]:((curious(X)|~happy(X))))&
((quiet(john)|~old(john)))&
(?[X]:((~wise(X)<~>funny(X))))&
((calm(alice)|curious(alice)))&
(?[X]:((creative(X)<~>funny(X))))&
((happy(lucy)<~>kind(lucy))) | humble(alice) | [
"p1",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4510375809961806895217238
% SZS output start Proof for 4510375809961806895217238
2. ! [X0] : ((~humble(X0) <~> ~kind(X0)) <=> (generous(X0) & kind(X0))) [input p1]
6. ! [X0] : ((~kind(X0) | ~generous(X0)) <=> (generous(X0) & rich(X0))) [input p5]
23. humble(alice) [input hypothesis]
35. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | (~generous(X0) | ~kind(X0))) & ((generous(X0) & kind(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [nnf transformation 2]
36. ! [X0] : ((((kind(X0) | humble(X0)) & (~kind(X0) | ~humble(X0))) | ~generous(X0) | ~kind(X0)) & ((generous(X0) & kind(X0)) | ((~humble(X0) | kind(X0)) & (~kind(X0) | humble(X0))))) [flattening 35]
48. ! [X0] : (((~kind(X0) | ~generous(X0)) | (~generous(X0) | ~rich(X0))) & ((generous(X0) & rich(X0)) | (kind(X0) & generous(X0)))) [nnf transformation 6]
49. ! [X0] : ((~kind(X0) | ~generous(X0) | ~generous(X0) | ~rich(X0)) & ((generous(X0) & rich(X0)) | (kind(X0) & generous(X0)))) [flattening 48]
82. kind(X0) | ~humble(X0) | kind(X0) [cnf transformation 36]
85. ~kind(X0) | ~humble(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 36]
101. generous(X0) | generous(X0) [cnf transformation 49]
147. humble(alice) [cnf transformation 23]
148. generous(X0) [duplicate literal removal 101]
150. ~humble(X0) | kind(X0) [duplicate literal removal 82]
151. ~kind(X0) | ~humble(X0) | ~generous(X0) [duplicate literal removal 85]
355. kind(alice) [resolution 150,147]
364. ~humble(alice) | ~generous(alice) [resolution 151,355]
366. ~generous(alice) [subsumption resolution 364,147]
367. $false [subsumption resolution 366,148]
% SZS output end Proof for 4510375809961806895217238
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or generous then someone is both not wise and funny and vice versa.
Everyone who is not wise or not happy is either tall or not curious.
Everyone who is either quiet or rich is both kind and tall.
Everyone who is not strong is both strong and not quiet.
If susan is not rich then john is either not tall or calm.
Everyone who is generous is not brave.
Everyone who is not happy is either not patient or brave.
Everyone who is both strong and not kind is not patient and vice versa.
If john is curious then someone is either strong or not generous.
Everyone who is not strong is not tall and vice versa.
Everyone who is both humble and quiet is rich and vice versa.
Everyone who is humble or not rich is not calm and vice versa.
Everyone who is either not funny or not happy is either not quiet or not generous and vice versa.
If someone is happy then fred is both not strong and brave and vice versa.
If john is not old or rich then someone is generous or kind and vice versa.
If someone is not brave then someone is both not wise and not calm and vice versa.
Alice is both brave and patient.
Someone is not rich or curious.
Someone is either not happy or not funny.
Mary is not rich.
Mary is either curious or old.
Someone is not rich or happy.
Fred is both generous and not wise.
Someone is curious. | John is not curious. | contradiction | ((?[X]:((brave(X)|generous(X))))<=>(?[X]:((~wise(X)&funny(X)))))&
(![X]:((~wise(X)|~happy(X))=>(tall(X)<~>~curious(X))))&
(![X]:((quiet(X)<~>rich(X))=>(kind(X)&tall(X))))&
(![X]:(~strong(X)=>(strong(X)&~quiet(X))))&
((~rich(susan))=>((~tall(john)<~>calm(john))))&
(![X]:(generous(X)=>~brave(X)))&
(![X]:(~happy(X)=>(~patient(X)<~>brave(X))))&
(![X]:((strong(X)&~kind(X))<=>~patient(X)))&
((curious(john))=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:(~strong(X)<=>~tall(X)))&
(![X]:((humble(X)&quiet(X))<=>rich(X)))&
(![X]:((humble(X)|~rich(X))<=>~calm(X)))&
(![X]:((~funny(X)<~>~happy(X))<=>(~quiet(X)<~>~generous(X))))&
((?[X]:(happy(X)))<=>((~strong(fred)&brave(fred))))&
(((~old(john)|rich(john)))<=>(?[X]:((generous(X)|kind(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((~wise(X)&~calm(X)))))&
((brave(alice)&patient(alice)))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:((~happy(X)<~>~funny(X))))&
(~rich(mary))&
((curious(mary)<~>old(mary)))&
(?[X]:((~rich(X)|happy(X))))&
((generous(fred)&~wise(fred)))&
(?[X]:(curious(X))) | ~curious(john) | [
"p1",
"p3",
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8787852362604119192731868
% SZS output start Proof for 8787852362604119192731868
2. ! [X0] : ((~happy(X0) | ~wise(X0)) => (tall(X0) <~> ~curious(X0))) [input p1]
4. ! [X0] : (~strong(X0) => (~quiet(X0) & strong(X0))) [input p3]
10. ! [X0] : (~strong(X0) <=> ~tall(X0)) [input p9]
14. ? [X0] : happy(X0) <=> (brave(fred) & ~strong(fred)) [input p13]
25. ~curious(john) [input hypothesis]
28. ! [X0] : ((tall(X0) <~> ~curious(X0)) | (happy(X0) & wise(X0))) [ennf transformation 2]
30. ! [X0] : ((~quiet(X0) & strong(X0)) | strong(X0)) [ennf transformation 4]
40. ! [X0] : (((curious(X0) | ~tall(X0)) & (~curious(X0) | tall(X0))) | (happy(X0) & wise(X0))) [nnf transformation 28]
49. ! [X0] : ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))) [nnf transformation 10]
55. (? [X0] : happy(X0) | (~brave(fred) | strong(fred))) & ((brave(fred) & ~strong(fred)) | ! [X0] : ~happy(X0)) [nnf transformation 14]
56. (? [X0] : happy(X0) | ~brave(fred) | strong(fred)) & ((brave(fred) & ~strong(fred)) | ! [X0] : ~happy(X0)) [flattening 55]
57. (? [X0] : happy(X0) | ~brave(fred) | strong(fred)) & ((brave(fred) & ~strong(fred)) | ! [X1] : ~happy(X1)) [rectify 56]
58. ? [X0] : happy(X0) => happy(sK3) [choice axiom]
59. (happy(sK3) | ~brave(fred) | strong(fred)) & ((brave(fred) & ~strong(fred)) | ! [X1] : ~happy(X1)) [skolemisation 57,58]
88. ~tall(X0) | curious(X0) | happy(X0) [cnf transformation 40]
93. strong(X0) | strong(X0) [cnf transformation 30]
106. ~strong(X0) | tall(X0) [cnf transformation 49]
121. ~strong(fred) | ~happy(X1) [cnf transformation 59]
143. ~curious(john) [cnf transformation 25]
144. strong(X0) [duplicate literal removal 93]
192. 11 <=> curious(john) [avatar definition]
194. ~curious(john) <- (~11) [avatar component clause 192]
200. tall(X0) [subsumption resolution 106,144]
202. 13 <=> ! [X1] : ~happy(X1) [avatar definition]
203. ~happy(X1) <- (13) [avatar component clause 202]
209. ~happy(X1) [subsumption resolution 121,144]
210. 13 [avatar split clause 209,202]
293. ~11 [avatar split clause 143,192]
324. curious(X0) | happy(X0) [resolution 88,200]
325. curious(X0) <- (13) [subsumption resolution 324,203]
326. $false <- (~11, 13) [resolution 325,194]
329. 11 | ~13 [avatar contradiction clause 326]
330. $false [avatar sat refutation 210,293,329]
% SZS output end Proof for 8787852362604119192731868
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not creative and rich is humble or rich and vice versa.
If someone is either not brave or quiet then paul is both not old and calm and vice versa.
Everyone who is either not wise or not curious is both kind and wise and vice versa.
Everyone who is curious is tall and vice versa.
Everyone who is both funny and not rich is either not rich or funny and vice versa.
If someone is calm or not generous then someone is creative.
If someone is tall or not patient then paul is not happy and vice versa.
Everyone who is both not happy and creative is either strong or not kind and vice versa.
Everyone who is not tall is both not humble and not strong and vice versa.
Everyone who is both tall and not curious is not tall and vice versa.
Everyone who is not creative or not tall is not strong or not old.
Everyone who is not patient is calm or funny.
If alice is not happy then paul is not creative or not funny.
If paul is not old then mary is either old or not creative.
Someone is either not curious or wise.
Someone is not creative.
Someone is tall or old.
Someone is both humble and not creative. | Mary is not old. | entailment | (![X]:((~creative(X)&rich(X))<=>(humble(X)|rich(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((~old(paul)&calm(paul))))&
(![X]:((~wise(X)<~>~curious(X))<=>(kind(X)&wise(X))))&
(![X]:(curious(X)<=>tall(X)))&
(![X]:((funny(X)&~rich(X))<=>(~rich(X)<~>funny(X))))&
((?[X]:((calm(X)|~generous(X))))=>(?[X]:(creative(X))))&
((?[X]:((tall(X)|~patient(X))))<=>(~happy(paul)))&
(![X]:((~happy(X)&creative(X))<=>(strong(X)<~>~kind(X))))&
(![X]:(~tall(X)<=>(~humble(X)&~strong(X))))&
(![X]:((tall(X)&~curious(X))<=>~tall(X)))&
(![X]:((~creative(X)|~tall(X))=>(~strong(X)|~old(X))))&
(![X]:(~patient(X)=>(calm(X)|funny(X))))&
((~happy(alice))=>((~creative(paul)|~funny(paul))))&
((~old(paul))=>((old(mary)<~>~creative(mary))))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:(~creative(X)))&
(?[X]:((tall(X)|old(X))))&
(?[X]:((humble(X)&~creative(X)))) | ~old(mary) | [
"p0",
"p2",
"p3",
"p4",
"p7",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 6030599787730524286529293
% SZS output start Proof for 6030599787730524286529293
1. ! [X0] : ((rich(X0) & ~creative(X0)) <=> (rich(X0) | humble(X0))) [input p0]
3. ! [X0] : ((~wise(X0) <~> ~curious(X0)) <=> (wise(X0) & kind(X0))) [input p2]
4. ! [X0] : (curious(X0) <=> tall(X0)) [input p3]
5. ! [X0] : ((~rich(X0) & funny(X0)) <=> (~rich(X0) <~> funny(X0))) [input p4]
8. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (strong(X0) <~> ~kind(X0))) [input p7]
10. ! [X0] : ((~curious(X0) & tall(X0)) <=> ~tall(X0)) [input p9]
11. ! [X0] : ((~tall(X0) | ~creative(X0)) => (~old(X0) | ~strong(X0))) [input p10]
19. old(mary) [input hypothesis]
23. ! [X0] : ((~old(X0) | ~strong(X0)) | (tall(X0) & creative(X0))) [ennf transformation 11]
24. ! [X0] : (~old(X0) | ~strong(X0) | (tall(X0) & creative(X0))) [flattening 23]
30. ! [X0] : (((rich(X0) & ~creative(X0)) | (~rich(X0) & ~humble(X0))) & ((rich(X0) | humble(X0)) | (~rich(X0) | creative(X0)))) [nnf transformation 1]
31. ! [X0] : (((rich(X0) & ~creative(X0)) | (~rich(X0) & ~humble(X0))) & (rich(X0) | humble(X0) | ~rich(X0) | creative(X0))) [flattening 30]
37. ! [X0] : ((((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (~wise(X0) | ~kind(X0))) & ((wise(X0) & kind(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0))))) [nnf transformation 3]
38. ! [X0] : ((((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | ~wise(X0) | ~kind(X0)) & ((wise(X0) & kind(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0))))) [flattening 37]
39. ! [X0] : ((curious(X0) | ~tall(X0)) & (tall(X0) | ~curious(X0))) [nnf transformation 4]
40. ! [X0] : (((~rich(X0) & funny(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (rich(X0) | ~funny(X0)))) [nnf transformation 5]
41. ! [X0] : (((~rich(X0) & funny(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0)))) & (((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | rich(X0) | ~funny(X0))) [flattening 40]
49. ! [X0] : (((creative(X0) & ~happy(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | (~creative(X0) | happy(X0)))) [nnf transformation 8]
50. ! [X0] : (((creative(X0) & ~happy(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) & (((kind(X0) | ~strong(X0)) & (~kind(X0) | strong(X0))) | ~creative(X0) | happy(X0))) [flattening 49]
53. ! [X0] : (((~curious(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (curious(X0) | ~tall(X0)))) [nnf transformation 10]
54. ! [X0] : (((~curious(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | curious(X0) | ~tall(X0))) [flattening 53]
67. ~rich(X0) | ~creative(X0) [cnf transformation 31]
78. wise(X0) | ~curious(X0) | wise(X0) [cnf transformation 38]
80. ~curious(X0) | ~wise(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 38]
83. ~tall(X0) | curious(X0) [cnf transformation 39]
85. ~funny(X0) | rich(X0) | rich(X0) | ~funny(X0) [cnf transformation 41]
86. funny(X0) | funny(X0) | rich(X0) [cnf transformation 41]
89. ~rich(X0) | ~rich(X0) | ~funny(X0) [cnf transformation 41]
99. strong(X0) | creative(X0) | kind(X0) [cnf transformation 50]
104. tall(X0) | tall(X0) [cnf transformation 54]
106. ~strong(X0) | ~old(X0) | creative(X0) [cnf transformation 24]
118. old(mary) [cnf transformation 19]
120. tall(X0) [duplicate literal removal 104]
121. ~funny(X0) | rich(X0) [duplicate literal removal 85]
122. funny(X0) | rich(X0) [duplicate literal removal 86]
123. ~funny(X0) | ~rich(X0) [duplicate literal removal 89]
124. ~curious(X0) | wise(X0) [duplicate literal removal 78]
125. ~kind(X0) | ~wise(X0) | ~curious(X0) [duplicate literal removal 80]
154. ~funny(X0) [subsumption resolution 121,123]
186. 14 <=> old(mary) [avatar definition]
187. old(mary) <- (14) [avatar component clause 186]
204. 14 [avatar split clause 118,186]
210. curious(X0) [resolution 83,120]
213. rich(X0) [resolution 122,154]
214. ~creative(X0) [resolution 213,67]
218. wise(X0) [resolution 124,210]
235. ~old(X0) | creative(X0) | creative(X0) | kind(X0) [resolution 106,99]
236. ~old(X0) | creative(X0) | kind(X0) [duplicate literal removal 235]
237. ~old(X0) | kind(X0) [subsumption resolution 236,214]
244. kind(mary) <- (14) [resolution 237,187]
247. ~wise(mary) | ~curious(mary) <- (14) [resolution 244,125]
248. ~curious(mary) <- (14) [subsumption resolution 247,218]
249. $false <- (14) [subsumption resolution 248,210]
250. ~14 [avatar contradiction clause 249]
251. $false [avatar sat refutation 204,250]
% SZS output end Proof for 6030599787730524286529293
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then someone is quiet. If someone is either not curious or not patient then fred is both old and not generous. If someone is brave then alice is both not quiet and humble. Everyone who is both not funny and not old is both tall and not kind and vice versa. If someone is either not generous or tall then john is both generous and kind and vice versa. Everyone who is happy or tall is tall and vice versa. If paul is both not happy and strong then someone is not old. Everyone who is brave is either not funny or brave. Everyone who is either wise or rich is both not humble and calm and vice versa. Everyone who is both not humble and not tall is kind. If someone is not kind or happy then alice is patient. Everyone who is either not humble or humble is both not calm and not curious and vice versa. Everyone who is not happy is brave or not strong and vice versa. Everyone who is both humble and calm is either not humble or calm and vice versa. If john is either creative or curious then someone is rich or not wise and vice versa. Everyone who is creative or not brave is not wise or not patient and vice versa. Fred is either old or kind. Someone is both not generous and wise. Someone is not patient or tall. Fred is patient. Someone is either strong or old. Alice is happy. Paul is brave. Paul is patient or kind. | Fred is happy. | contradiction | ((?[X]:(curious(X)))=>(?[X]:(quiet(X))))&
((?[X]:((~curious(X)<~>~patient(X))))=>((old(fred)&~generous(fred))))&
((?[X]:(brave(X)))=>((~quiet(alice)&humble(alice))))&
(![X]:((~funny(X)&~old(X))<=>(tall(X)&~kind(X))))&
((?[X]:((~generous(X)<~>tall(X))))<=>((generous(john)&kind(john))))&
(![X]:((happy(X)|tall(X))<=>tall(X)))&
(((~happy(paul)&strong(paul)))=>(?[X]:(~old(X))))&
(![X]:(brave(X)=>(~funny(X)<~>brave(X))))&
(![X]:((wise(X)<~>rich(X))<=>(~humble(X)&calm(X))))&
(![X]:((~humble(X)&~tall(X))=>kind(X)))&
((?[X]:((~kind(X)|happy(X))))=>(patient(alice)))&
(![X]:((~humble(X)<~>humble(X))<=>(~calm(X)&~curious(X))))&
(![X]:(~happy(X)<=>(brave(X)|~strong(X))))&
(![X]:((humble(X)&calm(X))<=>(~humble(X)<~>calm(X))))&
(((creative(john)<~>curious(john)))<=>(?[X]:((rich(X)|~wise(X)))))&
(![X]:((creative(X)|~brave(X))<=>(~wise(X)|~patient(X))))&
((old(fred)<~>kind(fred)))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((~patient(X)|tall(X))))&
(patient(fred))&
(?[X]:((strong(X)<~>old(X))))&
(happy(alice))&
(brave(paul))&
((patient(paul)|kind(paul))) | happy(fred) | [
"p1",
"p3",
"p5",
"p11",
"p16",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 352769840231748179693400
% SZS output start Proof for 352769840231748179693400
2. ? [X0] : (~curious(X0) <~> ~patient(X0)) => (~generous(fred) & old(fred)) [input p1]
4. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (~kind(X0) & tall(X0))) [input p3]
6. ! [X0] : ((tall(X0) | happy(X0)) <=> tall(X0)) [input p5]
12. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~curious(X0) & ~calm(X0))) [input p11]
17. old(fred) <~> kind(fred) [input p16]
20. patient(fred) [input p19]
25. happy(fred) [input hypothesis]
28. (~generous(fred) & old(fred)) | ! [X0] : (~curious(X0) <=> ~patient(X0)) [ennf transformation 2]
39. (~generous(fred) & old(fred)) | ! [X0] : ((~curious(X0) | patient(X0)) & (~patient(X0) | curious(X0))) [nnf transformation 28]
40. ! [X0] : (((~old(X0) & ~funny(X0)) | (kind(X0) | ~tall(X0))) & ((~kind(X0) & tall(X0)) | (old(X0) | funny(X0)))) [nnf transformation 4]
41. ! [X0] : (((~old(X0) & ~funny(X0)) | kind(X0) | ~tall(X0)) & ((~kind(X0) & tall(X0)) | old(X0) | funny(X0))) [flattening 40]
47. ! [X0] : (((tall(X0) | happy(X0)) | ~tall(X0)) & (tall(X0) | (~tall(X0) & ~happy(X0)))) [nnf transformation 6]
48. ! [X0] : ((tall(X0) | happy(X0) | ~tall(X0)) & (tall(X0) | (~tall(X0) & ~happy(X0)))) [flattening 47]
54. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | (curious(X0) | calm(X0))) & ((~curious(X0) & ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 12]
55. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | curious(X0) | calm(X0)) & ((~curious(X0) & ~calm(X0)) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [flattening 54]
66. (~kind(fred) | ~old(fred)) & (kind(fred) | old(fred)) [nnf transformation 17]
75. old(fred) | ~patient(X0) | curious(X0) [cnf transformation 39]
84. ~tall(X0) | kind(X0) | ~old(X0) [cnf transformation 41]
91. ~happy(X0) | tall(X0) [cnf transformation 48]
108. ~curious(X0) | humble(X0) | humble(X0) [cnf transformation 55]
109. ~curious(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 55]
132. ~kind(fred) | ~old(fred) [cnf transformation 66]
136. patient(fred) [cnf transformation 20]
142. happy(fred) [cnf transformation 25]
149. ~curious(X0) | humble(X0) [duplicate literal removal 108]
150. ~humble(X0) | ~curious(X0) [duplicate literal removal 109]
153. 1 <=> ! [X1] : ~curious(X1) [avatar definition]
154. ~curious(X1) <- (1) [avatar component clause 153]
169. 5 <=> ! [X0] : (~patient(X0) | curious(X0)) [avatar definition]
170. ~patient(X0) | curious(X0) <- (5) [avatar component clause 169]
173. 6 <=> old(fred) [avatar definition]
177. 5 | 6 [avatar split clause 75,173,169]
244. ~curious(X0) [subsumption resolution 149,150]
245. 1 [avatar split clause 244,153]
277. 28 <=> kind(fred) [avatar definition]
280. ~6 | ~28 [avatar split clause 132,277,173]
313. tall(fred) [resolution 91,142]
370. kind(fred) | ~old(fred) [resolution 84,313]
382. ~6 | 28 [avatar split clause 370,277,173]
388. ~patient(X0) <- (1, 5) [subsumption resolution 170,154]
392. $false <- (1, 5) [resolution 388,136]
397. ~1 | ~5 [avatar contradiction clause 392]
398. $false [avatar sat refutation 177,245,280,382,397]
% SZS output end Proof for 352769840231748179693400
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and strong is quiet or not creative and vice versa.
Everyone who is happy is not creative or patient and vice versa.
Everyone who is either old or not brave is not kind and vice versa.
Everyone who is both not happy and not kind is both funny and happy.
Everyone who is happy is both not old and wise.
Everyone who is not quiet is not kind.
Everyone who is either generous or wise is both not happy and calm and vice versa.
If mary is both patient and not humble then someone is either not calm or creative.
Everyone who is both not tall and wise is either not patient or not calm and vice versa.
Everyone who is either not calm or funny is either not old or not wise and vice versa.
If susan is both generous and not wise then someone is old and vice versa.
If alice is curious or not quiet then someone is both not tall and quiet and vice versa.
Everyone who is not tall or generous is either rich or calm and vice versa.
If someone is not rich or tall then someone is both not generous and not funny.
Everyone who is either rich or not kind is either not brave or calm.
Everyone who is quiet is wise and vice versa.
Someone is quiet.
Alice is either funny or rich.
Mary is rich.
Lucy is either not humble or old.
Someone is not kind. | Mary is not patient. | contradiction | (![X]:((rich(X)&strong(X))<=>(quiet(X)|~creative(X))))&
(![X]:(happy(X)<=>(~creative(X)|patient(X))))&
(![X]:((old(X)<~>~brave(X))<=>~kind(X)))&
(![X]:((~happy(X)&~kind(X))=>(funny(X)&happy(X))))&
(![X]:(happy(X)=>(~old(X)&wise(X))))&
(![X]:(~quiet(X)=>~kind(X)))&
(![X]:((generous(X)<~>wise(X))<=>(~happy(X)&calm(X))))&
(((patient(mary)&~humble(mary)))=>(?[X]:((~calm(X)<~>creative(X)))))&
(![X]:((~tall(X)&wise(X))<=>(~patient(X)<~>~calm(X))))&
(![X]:((~calm(X)<~>funny(X))<=>(~old(X)<~>~wise(X))))&
(((generous(susan)&~wise(susan)))<=>(?[X]:(old(X))))&
(((curious(alice)|~quiet(alice)))<=>(?[X]:((~tall(X)&quiet(X)))))&
(![X]:((~tall(X)|generous(X))<=>(rich(X)<~>calm(X))))&
((?[X]:((~rich(X)|tall(X))))=>(?[X]:((~generous(X)&~funny(X)))))&
(![X]:((rich(X)<~>~kind(X))=>(~brave(X)<~>calm(X))))&
(![X]:(quiet(X)<=>wise(X)))&
(?[X]:(quiet(X)))&
((funny(alice)<~>rich(alice)))&
(rich(mary))&
((~humble(lucy)<~>old(lucy)))&
(?[X]:(~kind(X))) | ~patient(mary) | [
"p0",
"p2",
"p3",
"p4",
"p5",
"p6",
"p8",
"p9",
"p10",
"p12",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7017128498022013157146774
% SZS output start Proof for 7017128498022013157146774
1. ! [X0] : ((strong(X0) & rich(X0)) <=> (~creative(X0) | quiet(X0))) [input p0]
3. ! [X0] : ((old(X0) <~> ~brave(X0)) <=> ~kind(X0)) [input p2]
4. ! [X0] : ((~kind(X0) & ~happy(X0)) => (happy(X0) & funny(X0))) [input p3]
5. ! [X0] : (happy(X0) => (wise(X0) & ~old(X0))) [input p4]
6. ! [X0] : (~quiet(X0) => ~kind(X0)) [input p5]
7. ! [X0] : ((generous(X0) <~> wise(X0)) <=> (calm(X0) & ~happy(X0))) [input p6]
9. ! [X0] : ((wise(X0) & ~tall(X0)) <=> (~patient(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((~calm(X0) <~> funny(X0)) <=> (~old(X0) <~> ~wise(X0))) [input p9]
11. (~wise(susan) & generous(susan)) <=> ? [X0] : old(X0) [input p10]
13. ! [X0] : ((generous(X0) | ~tall(X0)) <=> (rich(X0) <~> calm(X0))) [input p12]
14. ? [X0] : (tall(X0) | ~rich(X0)) => ? [X0] : (~funny(X0) & ~generous(X0)) [input p13]
15. ! [X0] : ((rich(X0) <~> ~kind(X0)) => (~brave(X0) <~> calm(X0))) [input p14]
16. ! [X0] : (quiet(X0) <=> wise(X0)) [input p15]
22. ~patient(mary) [input hypothesis]
23. ? [X0] : (tall(X0) | ~rich(X0)) => ? [X1] : (~funny(X1) & ~generous(X1)) [rectify 14]
24. ! [X0] : ((happy(X0) & funny(X0)) | (kind(X0) | happy(X0))) [ennf transformation 4]
25. ! [X0] : ((happy(X0) & funny(X0)) | kind(X0) | happy(X0)) [flattening 24]
26. ! [X0] : ((wise(X0) & ~old(X0)) | ~happy(X0)) [ennf transformation 5]
27. ! [X0] : (~kind(X0) | quiet(X0)) [ennf transformation 6]
30. ? [X1] : (~funny(X1) & ~generous(X1)) | ! [X0] : (~tall(X0) & rich(X0)) [ennf transformation 23]
31. ! [X0] : ((~brave(X0) <~> calm(X0)) | (rich(X0) <=> ~kind(X0))) [ennf transformation 15]
32. ! [X0] : (((strong(X0) & rich(X0)) | (creative(X0) & ~quiet(X0))) & ((~creative(X0) | quiet(X0)) | (~strong(X0) | ~rich(X0)))) [nnf transformation 1]
33. ! [X0] : (((strong(X0) & rich(X0)) | (creative(X0) & ~quiet(X0))) & (~creative(X0) | quiet(X0) | ~strong(X0) | ~rich(X0))) [flattening 32]
36. ! [X0] : ((((brave(X0) | ~old(X0)) & (~brave(X0) | old(X0))) | kind(X0)) & (~kind(X0) | ((old(X0) | brave(X0)) & (~brave(X0) | ~old(X0))))) [nnf transformation 3]
37. ! [X0] : ((((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | (~calm(X0) | happy(X0))) & ((calm(X0) & ~happy(X0)) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0))))) [nnf transformation 7]
38. ! [X0] : ((((~wise(X0) | ~generous(X0)) & (wise(X0) | generous(X0))) | ~calm(X0) | happy(X0)) & ((calm(X0) & ~happy(X0)) | ((generous(X0) | ~wise(X0)) & (wise(X0) | ~generous(X0))))) [flattening 37]
42. ! [X0] : (((wise(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | (~wise(X0) | tall(X0)))) [nnf transformation 9]
43. ! [X0] : (((wise(X0) & ~tall(X0)) | ((~patient(X0) | calm(X0)) & (~calm(X0) | patient(X0)))) & (((calm(X0) | patient(X0)) & (~calm(X0) | ~patient(X0))) | ~wise(X0) | tall(X0))) [flattening 42]
44. ! [X0] : ((((~funny(X0) | calm(X0)) & (funny(X0) | ~calm(X0))) | ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0)))) & (((wise(X0) | old(X0)) & (~wise(X0) | ~old(X0))) | ((~calm(X0) | ~funny(X0)) & (funny(X0) | calm(X0))))) [nnf transformation 10]
45. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | (wise(susan) | ~generous(susan))) [nnf transformation 11]
46. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (? [X0] : old(X0) | wise(susan) | ~generous(susan)) [flattening 45]
47. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (? [X1] : old(X1) | wise(susan) | ~generous(susan)) [rectify 46]
48. ? [X1] : old(X1) => old(sK1) [choice axiom]
49. ((~wise(susan) & generous(susan)) | ! [X0] : ~old(X0)) & (old(sK1) | wise(susan) | ~generous(susan)) [skolemisation 47,48]
55. ! [X0] : (((generous(X0) | ~tall(X0)) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (~generous(X0) & tall(X0)))) [nnf transformation 13]
56. ! [X0] : ((generous(X0) | ~tall(X0) | ((rich(X0) | ~calm(X0)) & (calm(X0) | ~rich(X0)))) & (((~calm(X0) | ~rich(X0)) & (calm(X0) | rich(X0))) | (~generous(X0) & tall(X0)))) [flattening 55]
57. ? [X0] : (~funny(X0) & ~generous(X0)) | ! [X1] : (~tall(X1) & rich(X1)) [rectify 30]
58. ? [X0] : (~funny(X0) & ~generous(X0)) => (~funny(sK3) & ~generous(sK3)) [choice axiom]
59. (~funny(sK3) & ~generous(sK3)) | ! [X1] : (~tall(X1) & rich(X1)) [skolemisation 57,58]
60. ! [X0] : (((~calm(X0) | brave(X0)) & (calm(X0) | ~brave(X0))) | ((rich(X0) | kind(X0)) & (~kind(X0) | ~rich(X0)))) [nnf transformation 31]
61. ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))) [nnf transformation 16]
69. ~quiet(X0) | rich(X0) [cnf transformation 33]
77. ~kind(X0) | old(X0) | brave(X0) [cnf transformation 36]
81. happy(X0) | kind(X0) | happy(X0) [cnf transformation 25]
83. ~happy(X0) | wise(X0) [cnf transformation 26]
84. ~kind(X0) | quiet(X0) [cnf transformation 27]
86. ~happy(X0) | generous(X0) | ~wise(X0) [cnf transformation 38]
94. ~wise(X0) | patient(X0) | calm(X0) | tall(X0) [cnf transformation 43]
103. ~calm(X0) | funny(X0) | ~wise(X0) | old(X0) [cnf transformation 44]
109. ~wise(susan) | ~old(X0) [cnf transformation 49]
117. ~calm(X0) | ~rich(X0) | tall(X0) [cnf transformation 56]
122. ~generous(sK3) | ~tall(X1) [cnf transformation 59]
124. ~funny(sK3) | ~tall(X1) [cnf transformation 59]
125. ~kind(X0) | ~brave(X0) | calm(X0) | ~rich(X0) [cnf transformation 60]
129. ~quiet(X0) | wise(X0) [cnf transformation 61]
130. ~wise(X0) | quiet(X0) [cnf transformation 61]
138. ~patient(mary) [cnf transformation 22]
139. kind(X0) | happy(X0) [duplicate literal removal 81]
141. ~happy(X0) | generous(X0) [subsumption resolution 86,83]
143. 1 <=> patient(mary) [avatar definition]
145. ~patient(mary) <- (~1) [avatar component clause 143]
161. 5 <=> ! [X0] : ~old(X0) [avatar definition]
162. ~old(X0) <- (5) [avatar component clause 161]
164. 6 <=> wise(susan) [avatar definition]
166. ~wise(susan) <- (~6) [avatar component clause 164]
167. 5 | ~6 [avatar split clause 109,164,161]
203. 14 <=> ! [X1] : ~tall(X1) [avatar definition]
204. ~tall(X1) <- (14) [avatar component clause 203]
206. 15 <=> funny(sK3) [avatar definition]
208. ~funny(sK3) <- (~15) [avatar component clause 206]
209. 14 | ~15 [avatar split clause 124,206,203]
211. 16 <=> ! [X1] : rich(X1) [avatar definition]
212. rich(X1) <- (16) [avatar component clause 211]
215. 17 <=> generous(sK3) [avatar definition]
218. 14 | ~17 [avatar split clause 122,215,203]
240. ~1 [avatar split clause 138,143]
253. happy(X0) | quiet(X0) [resolution 139,84]
277. brave(X0) | old(X0) | happy(X0) [resolution 77,139]
334. quiet(X2) | wise(X2) [resolution 253,83]
336. wise(X2) [subsumption resolution 334,129]
353. quiet(X1) [resolution 336,130]
361. rich(X2) [resolution 353,69]
364. 16 [avatar split clause 361,211]
365. tall(X0) | calm(X0) | patient(X0) [resolution 94,336]
451. ~brave(X0) | calm(X0) | ~rich(X0) | happy(X0) [resolution 125,139]
452. ~brave(X0) | calm(X0) | happy(X0) <- (16) [subsumption resolution 451,212]
517. $false <- (~6) [subsumption resolution 166,336]
518. 6 [avatar contradiction clause 517]
567. calm(X0) | happy(X0) | old(X0) | happy(X0) <- (16) [resolution 452,277]
568. calm(X0) | happy(X0) | old(X0) <- (16) [duplicate literal removal 567]
569. calm(X0) | happy(X0) <- (5, 16) [subsumption resolution 568,162]
596. happy(X5) | funny(X5) | ~wise(X5) | old(X5) <- (5, 16) [resolution 569,103]
608. happy(X5) | funny(X5) | old(X5) <- (5, 16) [subsumption resolution 596,336]
609. funny(X5) | happy(X5) <- (5, 16) [subsumption resolution 608,162]
675. happy(sK3) <- (5, ~15, 16) [resolution 609,208]
706. generous(sK3) <- (5, ~15, 16) [resolution 675,141]
711. 17 | ~5 | 15 | ~16 [avatar split clause 706,211,206,161,215]
729. calm(X0) | patient(X0) <- (14) [resolution 365,204]
774. patient(X7) | ~rich(X7) | tall(X7) <- (14) [resolution 729,117]
785. patient(X7) | tall(X7) <- (14, 16) [subsumption resolution 774,212]
786. patient(X7) <- (14, 16) [subsumption resolution 785,204]
792. $false <- (~1, 14, 16) [resolution 786,145]
799. 1 | ~14 | ~16 [avatar contradiction clause 792]
800. $false [avatar sat refutation 167,209,218,240,364,518,711,799]
% SZS output end Proof for 7017128498022013157146774
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not funny and not humble then alice is both curious and strong.
Everyone who is calm is wise and vice versa.
If fred is both not old and wise then someone is calm or rich.
If mary is old then mary is brave and vice versa.
If susan is both not tall and kind then susan is not kind or kind.
Everyone who is both calm and rich is not kind.
Everyone who is either patient or kind is not wise and vice versa.
Everyone who is not old or rich is happy or rich and vice versa.
If someone is either not patient or kind then someone is funny and vice versa.
If someone is both not rich and happy then someone is either tall or not funny and vice versa.
Everyone who is both not generous and brave is either calm or patient and vice versa.
If mary is both tall and not brave then someone is patient and vice versa.
If someone is both patient and wise then lucy is brave.
If someone is creative then john is both not creative and calm and vice versa.
If fred is either old or not kind then mary is not brave and vice versa.
Everyone who is both generous and not creative is both tall and not curious.
Fred is both not humble and not strong.
John is either not wise or tall.
Fred is not curious or kind.
Lucy is tall or not brave.
John is old.
Someone is humble or rich.
Alice is both not generous and strong.
Someone is strong or happy. | John is creative. | contradiction | ((?[X]:((~funny(X)&~humble(X))))=>((curious(alice)&strong(alice))))&
(![X]:(calm(X)<=>wise(X)))&
(((~old(fred)&wise(fred)))=>(?[X]:((calm(X)|rich(X)))))&
((old(mary))<=>(brave(mary)))&
(((~tall(susan)&kind(susan)))=>((~kind(susan)|kind(susan))))&
(![X]:((calm(X)&rich(X))=>~kind(X)))&
(![X]:((patient(X)<~>kind(X))<=>~wise(X)))&
(![X]:((~old(X)|rich(X))<=>(happy(X)|rich(X))))&
((?[X]:((~patient(X)<~>kind(X))))<=>(?[X]:(funny(X))))&
((?[X]:((~rich(X)&happy(X))))<=>(?[X]:((tall(X)<~>~funny(X)))))&
(![X]:((~generous(X)&brave(X))<=>(calm(X)<~>patient(X))))&
(((tall(mary)&~brave(mary)))<=>(?[X]:(patient(X))))&
((?[X]:((patient(X)&wise(X))))=>(brave(lucy)))&
((?[X]:(creative(X)))<=>((~creative(john)&calm(john))))&
(((old(fred)<~>~kind(fred)))<=>(~brave(mary)))&
(![X]:((generous(X)&~creative(X))=>(tall(X)&~curious(X))))&
((~humble(fred)&~strong(fred)))&
((~wise(john)<~>tall(john)))&
((~curious(fred)|kind(fred)))&
((tall(lucy)|~brave(lucy)))&
(old(john))&
(?[X]:((humble(X)|rich(X))))&
((~generous(alice)&strong(alice)))&
(?[X]:((strong(X)|happy(X)))) | creative(john) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7616048736953630231235376
% SZS output start Proof for 7616048736953630231235376
14. ? [X0] : creative(X0) <=> (calm(john) & ~creative(john)) [input p13]
25. creative(john) [input hypothesis]
62. (? [X0] : creative(X0) | (~calm(john) | creative(john))) & ((calm(john) & ~creative(john)) | ! [X0] : ~creative(X0)) [nnf transformation 14]
63. (? [X0] : creative(X0) | ~calm(john) | creative(john)) & ((calm(john) & ~creative(john)) | ! [X0] : ~creative(X0)) [flattening 62]
64. (? [X0] : creative(X0) | ~calm(john) | creative(john)) & ((calm(john) & ~creative(john)) | ! [X1] : ~creative(X1)) [rectify 63]
65. ? [X0] : creative(X0) => creative(sK6) [choice axiom]
66. (creative(sK6) | ~calm(john) | creative(john)) & ((calm(john) & ~creative(john)) | ! [X1] : ~creative(X1)) [skolemisation 64,65]
110. ~creative(john) | ~creative(X1) [cnf transformation 66]
130. creative(john) [cnf transformation 25]
251. 28 <=> creative(john) [avatar definition]
253. creative(john) <- (28) [avatar component clause 251]
264. 31 <=> ! [X1] : ~creative(X1) [avatar definition]
265. ~creative(X1) <- (31) [avatar component clause 264]
267. 31 | ~28 [avatar split clause 110,251,264]
315. 28 [avatar split clause 130,251]
316. $false <- (28, 31) [subsumption resolution 253,265]
317. ~28 | ~31 [avatar contradiction clause 316]
318. $false [avatar sat refutation 267,315,317]
% SZS output end Proof for 7616048736953630231235376
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is curious. Everyone who is not quiet or not generous is not creative or curious and vice versa. If paul is not calm or wise then fred is not rich. Everyone who is either not humble or not generous is not kind or funny. If fred is not strong or not generous then someone is calm or wise. If someone is happy then someone is tall or not curious. If paul is both humble and brave then lucy is either not rich or not curious. If lucy is tall then someone is not wise. Everyone who is not patient or not funny is either generous or not old. If susan is both strong and not calm then paul is both not tall and not calm. Everyone who is both not humble and not creative is both old and not kind. Everyone who is not patient is not calm or humble and vice versa. Everyone who is either curious or not generous is either funny or not wise and vice versa. If paul is not patient then john is either creative or not humble and vice versa. Everyone who is not happy is either tall or not tall and vice versa. Everyone who is not funny is generous and vice versa. John is both curious and rich. Someone is either not humble or not curious. Fred is strong or kind. Lucy is strong. Mary is rich. Paul is not creative or wise. Someone is both not tall and not funny. Lucy is either strong or quiet. | Paul is patient. | neutral | (![X]:(~humble(X)=>curious(X)))&
(![X]:((~quiet(X)|~generous(X))<=>(~creative(X)|curious(X))))&
(((~calm(paul)|wise(paul)))=>(~rich(fred)))&
(![X]:((~humble(X)<~>~generous(X))=>(~kind(X)|funny(X))))&
(((~strong(fred)|~generous(fred)))=>(?[X]:((calm(X)|wise(X)))))&
((?[X]:(happy(X)))=>(?[X]:((tall(X)|~curious(X)))))&
(((humble(paul)&brave(paul)))=>((~rich(lucy)<~>~curious(lucy))))&
((tall(lucy))=>(?[X]:(~wise(X))))&
(![X]:((~patient(X)|~funny(X))=>(generous(X)<~>~old(X))))&
(((strong(susan)&~calm(susan)))=>((~tall(paul)&~calm(paul))))&
(![X]:((~humble(X)&~creative(X))=>(old(X)&~kind(X))))&
(![X]:(~patient(X)<=>(~calm(X)|humble(X))))&
(![X]:((curious(X)<~>~generous(X))<=>(funny(X)<~>~wise(X))))&
((~patient(paul))<=>((creative(john)<~>~humble(john))))&
(![X]:(~happy(X)<=>(tall(X)<~>~tall(X))))&
(![X]:(~funny(X)<=>generous(X)))&
((curious(john)&rich(john)))&
(?[X]:((~humble(X)<~>~curious(X))))&
((strong(fred)|kind(fred)))&
(strong(lucy))&
(rich(mary))&
((~creative(paul)|wise(paul)))&
(?[X]:((~tall(X)&~funny(X))))&
((strong(lucy)<~>quiet(lucy))) | patient(paul) | [] | null | 0 |
If someone is both funny and tall then fred is calm or strong.
Everyone who is not rich or not funny is both not happy and not patient.
If lucy is not patient then someone is not wise and vice versa.
If someone is not tall or generous then someone is both not generous and kind and vice versa.
Everyone who is both not quiet and not calm is either not strong or generous.
Everyone who is either quiet or funny is not tall.
If someone is either generous or curious then lucy is curious and vice versa.
If someone is either old or not funny then someone is either not curious or not kind and vice versa.
Everyone who is either generous or not funny is old or not curious and vice versa.
Everyone who is either tall or not curious is both not old and funny.
Everyone who is patient or not happy is brave and vice versa.
Everyone who is both not generous and not patient is both not patient and rich and vice versa.
Everyone who is calm or not creative is tall and vice versa.
Everyone who is patient or creative is not brave.
If susan is either not kind or old then lucy is rich or kind and vice versa.
If someone is not patient then someone is both curious and not patient.
Someone is either not wise or happy.
Someone is curious or not brave.
Mary is tall.
Mary is either patient or not quiet.
Someone is not wise.
Someone is either kind or generous.
Someone is not kind or not humble. | Fred is not patient. | entailment | ((?[X]:((funny(X)&tall(X))))=>((calm(fred)|strong(fred))))&
(![X]:((~rich(X)|~funny(X))=>(~happy(X)&~patient(X))))&
((~patient(lucy))<=>(?[X]:(~wise(X))))&
((?[X]:((~tall(X)|generous(X))))<=>(?[X]:((~generous(X)&kind(X)))))&
(![X]:((~quiet(X)&~calm(X))=>(~strong(X)<~>generous(X))))&
(![X]:((quiet(X)<~>funny(X))=>~tall(X)))&
((?[X]:((generous(X)<~>curious(X))))<=>(curious(lucy)))&
((?[X]:((old(X)<~>~funny(X))))<=>(?[X]:((~curious(X)<~>~kind(X)))))&
(![X]:((generous(X)<~>~funny(X))<=>(old(X)|~curious(X))))&
(![X]:((tall(X)<~>~curious(X))=>(~old(X)&funny(X))))&
(![X]:((patient(X)|~happy(X))<=>brave(X)))&
(![X]:((~generous(X)&~patient(X))<=>(~patient(X)&rich(X))))&
(![X]:((calm(X)|~creative(X))<=>tall(X)))&
(![X]:((patient(X)|creative(X))=>~brave(X)))&
(((~kind(susan)<~>old(susan)))<=>((rich(lucy)|kind(lucy))))&
((?[X]:(~patient(X)))=>(?[X]:((curious(X)&~patient(X)))))&
(?[X]:((~wise(X)<~>happy(X))))&
(?[X]:((curious(X)|~brave(X))))&
(tall(mary))&
((patient(mary)<~>~quiet(mary)))&
(?[X]:(~wise(X)))&
(?[X]:((kind(X)<~>generous(X))))&
(?[X]:((~kind(X)|~humble(X)))) | ~patient(fred) | [
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8675984456455796668392224
% SZS output start Proof for 8675984456455796668392224
11. ! [X0] : ((~happy(X0) | patient(X0)) <=> brave(X0)) [input p10]
14. ! [X0] : ((creative(X0) | patient(X0)) => ~brave(X0)) [input p13]
24. patient(fred) [input hypothesis]
28. ! [X0] : ((~happy(X0) | patient(X0)) => brave(X0)) [unused predicate definition removal 11]
37. ! [X0] : (brave(X0) | (happy(X0) & ~patient(X0))) [ennf transformation 28]
38. ! [X0] : (~brave(X0) | (~creative(X0) & ~patient(X0))) [ennf transformation 14]
121. brave(X0) | ~patient(X0) [cnf transformation 37]
130. ~brave(X0) | ~patient(X0) [cnf transformation 38]
149. patient(fred) [cnf transformation 24]
264. ~patient(X0) [subsumption resolution 130,121]
318. $false [subsumption resolution 149,264]
% SZS output end Proof for 8675984456455796668392224
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not brave is funny or old and vice versa.
If someone is happy or not wise then someone is patient or generous and vice versa.
Everyone who is not old is strong.
If someone is not curious then mary is both tall and not wise and vice versa.
If someone is not patient or not old then john is either not patient or not creative.
If someone is either humble or rich then lucy is either not quiet or not brave and vice versa.
If fred is both patient and funny then alice is both tall and not humble.
Everyone who is both not quiet and not calm is both generous and rich and vice versa.
Everyone who is not curious or not humble is both not calm and creative and vice versa.
Everyone who is either not old or not kind is not funny or not wise and vice versa.
If someone is generous then john is tall or not creative and vice versa.
If someone is both not happy and not wise then someone is either not humble or tall.
If lucy is humble then someone is either not patient or not wise and vice versa.
Everyone who is both brave and happy is strong and vice versa.
If someone is not rich then alice is old or generous.
Everyone who is either not strong or brave is patient or calm and vice versa.
Someone is either not happy or not wise.
Someone is not tall.
Someone is both funny and patient.
Mary is not funny.
Paul is happy.
Alice is not humble or not happy.
Someone is both patient and creative.
Paul is both calm and not wise. | Alice is calm. | contradiction | (![X]:((humble(X)<~>~brave(X))<=>(funny(X)|old(X))))&
((?[X]:((happy(X)|~wise(X))))<=>(?[X]:((patient(X)|generous(X)))))&
(![X]:(~old(X)=>strong(X)))&
((?[X]:(~curious(X)))<=>((tall(mary)&~wise(mary))))&
((?[X]:((~patient(X)|~old(X))))=>((~patient(john)<~>~creative(john))))&
((?[X]:((humble(X)<~>rich(X))))<=>((~quiet(lucy)<~>~brave(lucy))))&
(((patient(fred)&funny(fred)))=>((tall(alice)&~humble(alice))))&
(![X]:((~quiet(X)&~calm(X))<=>(generous(X)&rich(X))))&
(![X]:((~curious(X)|~humble(X))<=>(~calm(X)&creative(X))))&
(![X]:((~old(X)<~>~kind(X))<=>(~funny(X)|~wise(X))))&
((?[X]:(generous(X)))<=>((tall(john)|~creative(john))))&
((?[X]:((~happy(X)&~wise(X))))=>(?[X]:((~humble(X)<~>tall(X)))))&
((humble(lucy))<=>(?[X]:((~patient(X)<~>~wise(X)))))&
(![X]:((brave(X)&happy(X))<=>strong(X)))&
((?[X]:(~rich(X)))=>((old(alice)|generous(alice))))&
(![X]:((~strong(X)<~>brave(X))<=>(patient(X)|calm(X))))&
(?[X]:((~happy(X)<~>~wise(X))))&
(?[X]:(~tall(X)))&
(?[X]:((funny(X)&patient(X))))&
(~funny(mary))&
(happy(paul))&
((~humble(alice)|~happy(alice)))&
(?[X]:((patient(X)&creative(X))))&
((calm(paul)&~wise(paul))) | calm(alice) | [
"p0",
"p2",
"p8",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4661367093604520620931195
% SZS output start Proof for 4661367093604520620931195
1. ! [X0] : ((humble(X0) <~> ~brave(X0)) <=> (old(X0) | funny(X0))) [input p0]
3. ! [X0] : (~old(X0) => strong(X0)) [input p2]
9. ! [X0] : ((~humble(X0) | ~curious(X0)) <=> (creative(X0) & ~calm(X0))) [input p8]
14. ! [X0] : ((happy(X0) & brave(X0)) <=> strong(X0)) [input p13]
16. ! [X0] : ((~strong(X0) <~> brave(X0)) <=> (calm(X0) | patient(X0))) [input p15]
22. ~happy(alice) | ~humble(alice) [input p21]
25. calm(alice) [input hypothesis]
28. ! [X0] : (strong(X0) | old(X0)) [ennf transformation 3]
35. ! [X0] : ((((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | (~old(X0) & ~funny(X0))) & ((old(X0) | funny(X0)) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0))))) [nnf transformation 1]
36. ! [X0] : ((((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | (~old(X0) & ~funny(X0))) & (old(X0) | funny(X0) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0))))) [flattening 35]
54. ! [X0] : (((~humble(X0) | ~curious(X0)) | (~creative(X0) | calm(X0))) & ((creative(X0) & ~calm(X0)) | (humble(X0) & curious(X0)))) [nnf transformation 9]
55. ! [X0] : ((~humble(X0) | ~curious(X0) | ~creative(X0) | calm(X0)) & ((creative(X0) & ~calm(X0)) | (humble(X0) & curious(X0)))) [flattening 54]
71. ! [X0] : (((happy(X0) & brave(X0)) | ~strong(X0)) & (strong(X0) | (~happy(X0) | ~brave(X0)))) [nnf transformation 14]
72. ! [X0] : (((happy(X0) & brave(X0)) | ~strong(X0)) & (strong(X0) | ~happy(X0) | ~brave(X0))) [flattening 71]
73. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~calm(X0) & ~patient(X0))) & ((calm(X0) | patient(X0)) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [nnf transformation 16]
74. ! [X0] : ((((~brave(X0) | strong(X0)) & (brave(X0) | ~strong(X0))) | (~calm(X0) & ~patient(X0))) & (calm(X0) | patient(X0) | ((~strong(X0) | ~brave(X0)) & (brave(X0) | strong(X0))))) [flattening 73]
89. ~old(X0) | ~humble(X0) | brave(X0) [cnf transformation 36]
94. strong(X0) | old(X0) [cnf transformation 28]
117. ~calm(X0) | humble(X0) [cnf transformation 55]
138. ~strong(X0) | happy(X0) [cnf transformation 72]
145. ~calm(X0) | strong(X0) | ~brave(X0) [cnf transformation 74]
153. ~happy(alice) | ~humble(alice) [cnf transformation 22]
158. calm(alice) [cnf transformation 25]
266. 25 <=> humble(alice) [avatar definition]
267. humble(alice) <- (25) [avatar component clause 266]
325. 38 <=> old(alice) [avatar definition]
327. old(alice) <- (38) [avatar component clause 325]
346. 42 <=> happy(alice) [avatar definition]
348. ~happy(alice) <- (~42) [avatar component clause 346]
349. ~25 | ~42 [avatar split clause 153,346,266]
359. humble(alice) [resolution 117,158]
360. 25 [avatar split clause 359,266]
364. happy(X0) | old(X0) [resolution 138,94]
387. ~humble(alice) | brave(alice) <- (38) [resolution 89,327]
388. brave(alice) <- (25, 38) [subsumption resolution 387,267]
414. old(alice) <- (~42) [resolution 364,348]
464. strong(alice) | ~brave(alice) [resolution 145,158]
467. strong(alice) <- (25, 38) [subsumption resolution 464,388]
492. happy(alice) <- (25, 38) [resolution 467,138]
494. $false <- (25, 38, ~42) [subsumption resolution 492,348]
495. ~25 | ~38 | 42 [avatar contradiction clause 494]
506. 38 | 42 [avatar split clause 414,346,325]
507. $false [avatar sat refutation 349,360,495,506]
% SZS output end Proof for 4661367093604520620931195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either strong or rich then john is humble.
Everyone who is old is both not wise and patient and vice versa.
Everyone who is not patient or not tall is calm and vice versa.
Everyone who is not quiet or not rich is both not quiet and strong and vice versa.
Everyone who is both not humble and quiet is not happy or kind and vice versa.
Everyone who is not creative or not calm is strong or not brave and vice versa.
Everyone who is either curious or not wise is not strong and vice versa.
Everyone who is either not rich or wise is either brave or not wise.
Everyone who is both strong and curious is quiet or not curious.
Everyone who is wise is not funny or generous.
Everyone who is wise is both patient and not wise.
Everyone who is either not tall or not strong is either not rich or calm.
Everyone who is both not humble and old is not generous or happy and vice versa.
Everyone who is both not kind and not generous is both happy and generous.
If someone is both not calm and happy then fred is both humble and not creative.
Everyone who is not generous is not wise or not patient.
Mary is both not wise and not calm.
Someone is brave or not happy.
Fred is either tall or strong.
Susan is generous.
Someone is quiet.
Susan is either old or rich.
Someone is both not tall and curious. | John is rich. | entailment | (((strong(mary)<~>rich(mary)))=>(humble(john)))&
(![X]:(old(X)<=>(~wise(X)&patient(X))))&
(![X]:((~patient(X)|~tall(X))<=>calm(X)))&
(![X]:((~quiet(X)|~rich(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~humble(X)&quiet(X))<=>(~happy(X)|kind(X))))&
(![X]:((~creative(X)|~calm(X))<=>(strong(X)|~brave(X))))&
(![X]:((curious(X)<~>~wise(X))<=>~strong(X)))&
(![X]:((~rich(X)<~>wise(X))=>(brave(X)<~>~wise(X))))&
(![X]:((strong(X)&curious(X))=>(quiet(X)|~curious(X))))&
(![X]:(wise(X)=>(~funny(X)|generous(X))))&
(![X]:(wise(X)=>(patient(X)&~wise(X))))&
(![X]:((~tall(X)<~>~strong(X))=>(~rich(X)<~>calm(X))))&
(![X]:((~humble(X)&old(X))<=>(~generous(X)|happy(X))))&
(![X]:((~kind(X)&~generous(X))=>(happy(X)&generous(X))))&
((?[X]:((~calm(X)&happy(X))))=>((humble(fred)&~creative(fred))))&
(![X]:(~generous(X)=>(~wise(X)|~patient(X))))&
((~wise(mary)&~calm(mary)))&
(?[X]:((brave(X)|~happy(X))))&
((tall(fred)<~>strong(fred)))&
(generous(susan))&
(?[X]:(quiet(X)))&
((old(susan)<~>rich(susan)))&
(?[X]:((~tall(X)&curious(X)))) | rich(john) | [
"p1",
"p2",
"p3",
"p4",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7044026190574053496655593
% SZS output start Proof for 7044026190574053496655593
2. ! [X0] : (old(X0) <=> (patient(X0) & ~wise(X0))) [input p1]
3. ! [X0] : ((~tall(X0) | ~patient(X0)) <=> calm(X0)) [input p2]
4. ! [X0] : ((~rich(X0) | ~quiet(X0)) <=> (strong(X0) & ~quiet(X0))) [input p3]
5. ! [X0] : ((quiet(X0) & ~humble(X0)) <=> (kind(X0) | ~happy(X0))) [input p4]
12. ! [X0] : ((~tall(X0) <~> ~strong(X0)) => (~rich(X0) <~> calm(X0))) [input p11]
13. ! [X0] : ((old(X0) & ~humble(X0)) <=> (happy(X0) | ~generous(X0))) [input p12]
15. ? [X0] : (happy(X0) & ~calm(X0)) => (~creative(fred) & humble(fred)) [input p14]
24. ~rich(john) [input hypothesis]
31. ! [X0] : ((~rich(X0) <~> calm(X0)) | (~tall(X0) <=> ~strong(X0))) [ennf transformation 12]
34. (~creative(fred) & humble(fred)) | ! [X0] : (~happy(X0) | calm(X0)) [ennf transformation 15]
38. ! [X0] : ((old(X0) | (~patient(X0) | wise(X0))) & ((patient(X0) & ~wise(X0)) | ~old(X0))) [nnf transformation 2]
39. ! [X0] : ((old(X0) | ~patient(X0) | wise(X0)) & ((patient(X0) & ~wise(X0)) | ~old(X0))) [flattening 38]
40. ! [X0] : (((~tall(X0) | ~patient(X0)) | ~calm(X0)) & (calm(X0) | (tall(X0) & patient(X0)))) [nnf transformation 3]
41. ! [X0] : ((~tall(X0) | ~patient(X0) | ~calm(X0)) & (calm(X0) | (tall(X0) & patient(X0)))) [flattening 40]
42. ! [X0] : (((~rich(X0) | ~quiet(X0)) | (~strong(X0) | quiet(X0))) & ((strong(X0) & ~quiet(X0)) | (rich(X0) & quiet(X0)))) [nnf transformation 4]
43. ! [X0] : ((~rich(X0) | ~quiet(X0) | ~strong(X0) | quiet(X0)) & ((strong(X0) & ~quiet(X0)) | (rich(X0) & quiet(X0)))) [flattening 42]
44. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~kind(X0) & happy(X0))) & ((kind(X0) | ~happy(X0)) | (~quiet(X0) | humble(X0)))) [nnf transformation 5]
45. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~kind(X0) & happy(X0))) & (kind(X0) | ~happy(X0) | ~quiet(X0) | humble(X0))) [flattening 44]
50. ! [X0] : (((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | ((~tall(X0) | strong(X0)) & (~strong(X0) | tall(X0)))) [nnf transformation 31]
51. ! [X0] : (((old(X0) & ~humble(X0)) | (~happy(X0) & generous(X0))) & ((happy(X0) | ~generous(X0)) | (~old(X0) | humble(X0)))) [nnf transformation 13]
52. ! [X0] : (((old(X0) & ~humble(X0)) | (~happy(X0) & generous(X0))) & (happy(X0) | ~generous(X0) | ~old(X0) | humble(X0))) [flattening 51]
64. ~old(X0) | patient(X0) [cnf transformation 39]
67. calm(X0) | tall(X0) [cnf transformation 41]
68. ~calm(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 41]
70. ~quiet(X0) | rich(X0) [cnf transformation 43]
72. rich(X0) | strong(X0) [cnf transformation 43]
75. ~humble(X0) | happy(X0) [cnf transformation 45]
77. happy(X0) | quiet(X0) [cnf transformation 45]
96. ~calm(X0) | rich(X0) | ~strong(X0) | tall(X0) [cnf transformation 50]
100. ~humble(X0) | ~happy(X0) [cnf transformation 52]
102. ~happy(X0) | old(X0) [cnf transformation 52]
105. humble(fred) | ~happy(X0) | calm(X0) [cnf transformation 34]
119. ~rich(john) [cnf transformation 24]
140. rich(X0) | ~strong(X0) | tall(X0) [subsumption resolution 96,67]
141. tall(X0) | rich(X0) [subsumption resolution 140,72]
144. ~humble(X0) [subsumption resolution 100,75]
147. 4 <=> ! [X0] : (~happy(X0) | calm(X0)) [avatar definition]
148. ~happy(X0) | calm(X0) <- (4) [avatar component clause 147]
154. ~happy(X0) | calm(X0) [subsumption resolution 105,144]
155. 4 [avatar split clause 154,147]
199. quiet(X0) | old(X0) [resolution 102,77]
204. quiet(X0) | calm(X0) <- (4) [resolution 148,77]
212. old(X0) | rich(X0) [resolution 199,70]
213. calm(X0) | rich(X0) <- (4) [resolution 204,70]
214. rich(X0) | patient(X0) [resolution 212,64]
216. rich(X0) | ~patient(X0) | ~tall(X0) <- (4) [resolution 213,68]
217. rich(X0) | ~patient(X0) <- (4) [subsumption resolution 216,141]
218. rich(X0) <- (4) [subsumption resolution 217,214]
219. $false <- (4) [resolution 218,119]
222. ~4 [avatar contradiction clause 219]
223. $false [avatar sat refutation 155,222]
% SZS output end Proof for 7044026190574053496655593
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not funny then paul is tall or not patient. Everyone who is either not brave or wise is both generous and not quiet and vice versa. If someone is either happy or creative then paul is both calm and not tall. If someone is not rich then john is both not quiet and not strong. Everyone who is not curious or brave is not kind or not brave. Everyone who is either humble or wise is old and vice versa. Everyone who is either rich or not happy is both not brave and quiet and vice versa. If paul is both not generous and not wise then someone is not quiet and vice versa. Everyone who is brave is funny. Everyone who is brave is both not tall and generous and vice versa. Everyone who is both strong and not generous is both not kind and not quiet. If someone is not quiet or funny then someone is calm or not quiet. Everyone who is not kind is rich and vice versa. If someone is calm or not humble then someone is either not calm or not patient and vice versa. Everyone who is either not patient or not rich is happy. If someone is either not quiet or not generous then someone is both not curious and not calm. Someone is not patient or funny. Someone is both tall and generous. Someone is both curious and not humble. John is either not calm or creative. Susan is wise. Someone is either not humble or not curious. | Mary is not rich. | contradiction | ((~funny(mary))=>((tall(paul)|~patient(paul))))&
(![X]:((~brave(X)<~>wise(X))<=>(generous(X)&~quiet(X))))&
((?[X]:((happy(X)<~>creative(X))))=>((calm(paul)&~tall(paul))))&
((?[X]:(~rich(X)))=>((~quiet(john)&~strong(john))))&
(![X]:((~curious(X)|brave(X))=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)<~>wise(X))<=>old(X)))&
(![X]:((rich(X)<~>~happy(X))<=>(~brave(X)&quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:(~quiet(X))))&
(![X]:(brave(X)=>funny(X)))&
(![X]:(brave(X)<=>(~tall(X)&generous(X))))&
(![X]:((strong(X)&~generous(X))=>(~kind(X)&~quiet(X))))&
((?[X]:((~quiet(X)|funny(X))))=>(?[X]:((calm(X)|~quiet(X)))))&
(![X]:(~kind(X)<=>rich(X)))&
((?[X]:((calm(X)|~humble(X))))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
(![X]:((~patient(X)<~>~rich(X))=>happy(X)))&
((?[X]:((~quiet(X)<~>~generous(X))))=>(?[X]:((~curious(X)&~calm(X)))))&
(?[X]:((~patient(X)|funny(X))))&
(?[X]:((tall(X)&generous(X))))&
(?[X]:((curious(X)&~humble(X))))&
((~calm(john)<~>creative(john)))&
(wise(susan))&
(?[X]:((~humble(X)<~>~curious(X)))) | ~rich(mary) | [
"p1",
"p3",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 5722669410361308178581232
% SZS output start Proof for 5722669410361308178581232
2. ! [X0] : ((~brave(X0) <~> wise(X0)) <=> (~quiet(X0) & generous(X0))) [input p1]
4. ? [X0] : ~rich(X0) => (~strong(john) & ~quiet(john)) [input p3]
8. (~wise(paul) & ~generous(paul)) <=> ? [X0] : ~quiet(X0) [input p7]
10. ! [X0] : (brave(X0) <=> (generous(X0) & ~tall(X0))) [input p9]
23. ~rich(mary) [input hypothesis]
29. ? [X0] : ~rich(X0) => ~quiet(john) [pure predicate removal 4]
33. ~quiet(john) | ! [X0] : rich(X0) [ennf transformation 29]
41. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | (quiet(X0) | ~generous(X0))) & ((~quiet(X0) & generous(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~wise(X0) | brave(X0)) & (wise(X0) | ~brave(X0))) | quiet(X0) | ~generous(X0)) & ((~quiet(X0) & generous(X0)) | ((~brave(X0) | ~wise(X0)) & (wise(X0) | brave(X0))))) [flattening 41]
46. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | (wise(paul) | generous(paul))) [nnf transformation 8]
47. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (? [X0] : ~quiet(X0) | wise(paul) | generous(paul)) [flattening 46]
48. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (? [X1] : ~quiet(X1) | wise(paul) | generous(paul)) [rectify 47]
49. ? [X1] : ~quiet(X1) => ~quiet(sK0) [choice axiom]
50. ((~wise(paul) & ~generous(paul)) | ! [X0] : quiet(X0)) & (~quiet(sK0) | wise(paul) | generous(paul)) [skolemisation 48,49]
51. ! [X0] : ((brave(X0) | (~generous(X0) | tall(X0))) & ((generous(X0) & ~tall(X0)) | ~brave(X0))) [nnf transformation 10]
52. ! [X0] : ((brave(X0) | ~generous(X0) | tall(X0)) & ((generous(X0) & ~tall(X0)) | ~brave(X0))) [flattening 51]
77. generous(X0) | wise(X0) | brave(X0) [cnf transformation 42]
87. ~quiet(john) | rich(X0) [cnf transformation 33]
97. ~generous(paul) | quiet(X0) [cnf transformation 50]
98. ~wise(paul) | quiet(X0) [cnf transformation 50]
101. ~brave(X0) | generous(X0) [cnf transformation 52]
128. ~rich(mary) [cnf transformation 23]
158. 7 <=> ! [X0] : rich(X0) [avatar definition]
159. rich(X0) <- (7) [avatar component clause 158]
161. 8 <=> quiet(john) [avatar definition]
163. ~quiet(john) <- (~8) [avatar component clause 161]
164. 7 | ~8 [avatar split clause 87,161,158]
166. 9 <=> ! [X0] : quiet(X0) [avatar definition]
167. quiet(X0) <- (9) [avatar component clause 166]
169. 10 <=> wise(paul) [avatar definition]
171. ~wise(paul) <- (~10) [avatar component clause 169]
172. 9 | ~10 [avatar split clause 98,169,166]
174. 11 <=> generous(paul) [avatar definition]
176. ~generous(paul) <- (~11) [avatar component clause 174]
177. 9 | ~11 [avatar split clause 97,174,166]
278. wise(paul) | brave(paul) <- (~11) [resolution 77,176]
279. brave(paul) <- (~10, ~11) [subsumption resolution 278,171]
281. generous(paul) <- (~10, ~11) [resolution 279,101]
284. $false <- (~10, ~11) [subsumption resolution 281,176]
285. 10 | 11 [avatar contradiction clause 284]
291. $false <- (~8, 9) [resolution 167,163]
296. 8 | ~9 [avatar contradiction clause 291]
297. $false <- (7) [resolution 159,128]
298. ~7 [avatar contradiction clause 297]
299. $false [avatar sat refutation 164,172,177,285,296,298]
% SZS output end Proof for 5722669410361308178581232
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not tall and tall then someone is either strong or not quiet and vice versa. If someone is both not strong and not calm then paul is both rich and not wise and vice versa. Everyone who is both not tall and quiet is both brave and generous. If john is either not strong or not generous then someone is wise or not wise. If someone is both not creative and not calm then someone is not generous. If someone is not kind then susan is old and vice versa. Everyone who is both not creative and not old is either not humble or rich and vice versa. If someone is not kind or old then someone is brave or calm and vice versa. If someone is not kind or not humble then mary is both happy and wise. Everyone who is either not strong or tall is not funny and vice versa. If someone is generous or not patient then someone is both strong and not creative. If someone is not generous then alice is both not rich and not tall. If john is either calm or curious then susan is not happy or rich and vice versa. Everyone who is not funny is either generous or not funny. Everyone who is either kind or not creative is not generous and vice versa. Everyone who is both old and not funny is both happy and patient and vice versa. Lucy is both not generous and patient. John is not old or not rich. Someone is either not wise or not curious. Someone is quiet or not rich. Alice is either wise or not kind. Susan is both not creative and funny. Someone is generous or happy. Someone is generous or brave. | Alice is not funny. | contradiction | (((~tall(mary)&tall(mary)))<=>(?[X]:((strong(X)<~>~quiet(X)))))&
((?[X]:((~strong(X)&~calm(X))))<=>((rich(paul)&~wise(paul))))&
(![X]:((~tall(X)&quiet(X))=>(brave(X)&generous(X))))&
(((~strong(john)<~>~generous(john)))=>(?[X]:((wise(X)|~wise(X)))))&
((?[X]:((~creative(X)&~calm(X))))=>(?[X]:(~generous(X))))&
((?[X]:(~kind(X)))<=>(old(susan)))&
(![X]:((~creative(X)&~old(X))<=>(~humble(X)<~>rich(X))))&
((?[X]:((~kind(X)|old(X))))<=>(?[X]:((brave(X)|calm(X)))))&
((?[X]:((~kind(X)|~humble(X))))=>((happy(mary)&wise(mary))))&
(![X]:((~strong(X)<~>tall(X))<=>~funny(X)))&
((?[X]:((generous(X)|~patient(X))))=>(?[X]:((strong(X)&~creative(X)))))&
((?[X]:(~generous(X)))=>((~rich(alice)&~tall(alice))))&
(((calm(john)<~>curious(john)))<=>((~happy(susan)|rich(susan))))&
(![X]:(~funny(X)=>(generous(X)<~>~funny(X))))&
(![X]:((kind(X)<~>~creative(X))<=>~generous(X)))&
(![X]:((old(X)&~funny(X))<=>(happy(X)&patient(X))))&
((~generous(lucy)&patient(lucy)))&
((~old(john)|~rich(john)))&
(?[X]:((~wise(X)<~>~curious(X))))&
(?[X]:((quiet(X)|~rich(X))))&
((wise(alice)<~>~kind(alice)))&
((~creative(susan)&funny(susan)))&
(?[X]:((generous(X)|happy(X))))&
(?[X]:((generous(X)|brave(X)))) | ~funny(alice) | [
"p0",
"p2",
"p9",
"p11",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 521300236087021888141071
% SZS output start Proof for 521300236087021888141071
1. (tall(mary) & ~tall(mary)) <=> ? [X0] : (strong(X0) <~> ~quiet(X0)) [input p0]
3. ! [X0] : ((quiet(X0) & ~tall(X0)) => (generous(X0) & brave(X0))) [input p2]
10. ! [X0] : ((~strong(X0) <~> tall(X0)) <=> ~funny(X0)) [input p9]
12. ? [X0] : ~generous(X0) => (~tall(alice) & ~rich(alice)) [input p11]
14. ! [X0] : (~funny(X0) => (generous(X0) <~> ~funny(X0))) [input p13]
17. patient(lucy) & ~generous(lucy) [input p16]
25. ~funny(alice) [input hypothesis]
29. ! [X0] : ((generous(X0) & brave(X0)) | (~quiet(X0) | tall(X0))) [ennf transformation 3]
30. ! [X0] : ((generous(X0) & brave(X0)) | ~quiet(X0) | tall(X0)) [flattening 29]
35. (~tall(alice) & ~rich(alice)) | ! [X0] : generous(X0) [ennf transformation 12]
36. ! [X0] : ((generous(X0) <~> ~funny(X0)) | funny(X0)) [ennf transformation 14]
37. ((tall(mary) & ~tall(mary)) | ! [X0] : ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (? [X0] : ((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | (~tall(mary) | tall(mary))) [nnf transformation 1]
38. ((tall(mary) & ~tall(mary)) | ! [X0] : ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (? [X0] : ((quiet(X0) | ~strong(X0)) & (~quiet(X0) | strong(X0))) | ~tall(mary) | tall(mary)) [flattening 37]
39. ((tall(mary) & ~tall(mary)) | ! [X0] : ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (? [X1] : ((quiet(X1) | ~strong(X1)) & (~quiet(X1) | strong(X1))) | ~tall(mary) | tall(mary)) [rectify 38]
40. ? [X1] : ((quiet(X1) | ~strong(X1)) & (~quiet(X1) | strong(X1))) => ((quiet(sK0) | ~strong(sK0)) & (~quiet(sK0) | strong(sK0))) [choice axiom]
41. ((tall(mary) & ~tall(mary)) | ! [X0] : ((strong(X0) | quiet(X0)) & (~quiet(X0) | ~strong(X0)))) & (((quiet(sK0) | ~strong(sK0)) & (~quiet(sK0) | strong(sK0))) | ~tall(mary) | tall(mary)) [skolemisation 39,40]
64. ! [X0] : ((((~tall(X0) | strong(X0)) & (tall(X0) | ~strong(X0))) | funny(X0)) & (~funny(X0) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0))))) [nnf transformation 10]
70. ! [X0] : (((funny(X0) | ~generous(X0)) & (~funny(X0) | generous(X0))) | funny(X0)) [nnf transformation 36]
87. ~tall(mary) | strong(X0) | quiet(X0) [cnf transformation 41]
89. tall(mary) | strong(X0) | quiet(X0) [cnf transformation 41]
95. ~quiet(X0) | generous(X0) | tall(X0) [cnf transformation 30]
117. ~strong(X0) | tall(X0) | funny(X0) [cnf transformation 64]
118. ~tall(X0) | strong(X0) | funny(X0) [cnf transformation 64]
124. ~tall(alice) | generous(X0) [cnf transformation 35]
132. funny(X0) | ~generous(X0) | funny(X0) [cnf transformation 70]
141. ~generous(lucy) [cnf transformation 17]
153. ~funny(alice) [cnf transformation 25]
154. ~generous(X0) | funny(X0) [duplicate literal removal 132]
156. 1 <=> ! [X0] : (strong(X0) | quiet(X0)) [avatar definition]
157. quiet(X0) | strong(X0) <- (1) [avatar component clause 156]
159. 2 <=> tall(mary) [avatar definition]
162. 1 | 2 [avatar split clause 89,159,156]
167. 1 | ~2 [avatar split clause 87,159,156]
276. 28 <=> ! [X0] : generous(X0) [avatar definition]
277. generous(X0) <- (28) [avatar component clause 276]
279. 29 <=> tall(alice) [avatar definition]
282. 28 | ~29 [avatar split clause 124,279,276]
384. generous(X0) | tall(X0) | strong(X0) <- (1) [resolution 95,157]
515. tall(X1) | strong(X1) | funny(X1) <- (1) [resolution 384,154]
520. funny(X1) | strong(X1) <- (1) [subsumption resolution 515,118]
670. strong(alice) <- (1) [resolution 520,153]
717. tall(alice) | funny(alice) <- (1) [resolution 670,117]
721. tall(alice) <- (1) [subsumption resolution 717,153]
722. 29 | ~1 [avatar split clause 721,156,279]
726. $false <- (28) [resolution 277,141]
731. ~28 [avatar contradiction clause 726]
732. $false [avatar sat refutation 162,167,282,722,731]
% SZS output end Proof for 521300236087021888141071
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is both not humble and strong. Everyone who is not funny is both creative and not kind and vice versa. Everyone who is both wise and not old is both old and not funny. If someone is not brave or brave then someone is either not patient or rich. Everyone who is either quiet or not patient is either not calm or not happy. If someone is either tall or patient then lucy is both creative and not curious. If someone is both not quiet and not wise then someone is brave or strong. Everyone who is both tall and brave is wise or creative and vice versa. Everyone who is both patient and tall is both brave and not quiet and vice versa. Everyone who is both wise and not happy is not brave. If susan is both wise and rich then mary is not funny and vice versa. Everyone who is both patient and not happy is either not curious or quiet. If someone is either patient or funny then susan is not generous or old and vice versa. If someone is generous then lucy is not rich and vice versa. Everyone who is not humble is either wise or calm and vice versa. If someone is brave or calm then lucy is both happy and rich and vice versa. Lucy is either not curious or humble. Someone is either funny or not kind. John is not generous. Mary is either not brave or quiet. Mary is either not humble or calm. Someone is patient or not brave. Mary is curious or funny. Someone is both not brave and not strong. | Lucy is creative. | entailment | (![X]:(~funny(X)=>(~humble(X)&strong(X))))&
(![X]:(~funny(X)<=>(creative(X)&~kind(X))))&
(![X]:((wise(X)&~old(X))=>(old(X)&~funny(X))))&
((?[X]:((~brave(X)|brave(X))))=>(?[X]:((~patient(X)<~>rich(X)))))&
(![X]:((quiet(X)<~>~patient(X))=>(~calm(X)<~>~happy(X))))&
((?[X]:((tall(X)<~>patient(X))))=>((creative(lucy)&~curious(lucy))))&
((?[X]:((~quiet(X)&~wise(X))))=>(?[X]:((brave(X)|strong(X)))))&
(![X]:((tall(X)&brave(X))<=>(wise(X)|creative(X))))&
(![X]:((patient(X)&tall(X))<=>(brave(X)&~quiet(X))))&
(![X]:((wise(X)&~happy(X))=>~brave(X)))&
(((wise(susan)&rich(susan)))<=>(~funny(mary)))&
(![X]:((patient(X)&~happy(X))=>(~curious(X)<~>quiet(X))))&
((?[X]:((patient(X)<~>funny(X))))<=>((~generous(susan)|old(susan))))&
((?[X]:(generous(X)))<=>(~rich(lucy)))&
(![X]:(~humble(X)<=>(wise(X)<~>calm(X))))&
((?[X]:((brave(X)|calm(X))))<=>((happy(lucy)&rich(lucy))))&
((~curious(lucy)<~>humble(lucy)))&
(?[X]:((funny(X)<~>~kind(X))))&
(~generous(john))&
((~brave(mary)<~>quiet(mary)))&
((~humble(mary)<~>calm(mary)))&
(?[X]:((patient(X)|~brave(X))))&
((curious(mary)|funny(mary)))&
(?[X]:((~brave(X)&~strong(X)))) | creative(lucy) | [
"p4",
"p5",
"p7",
"p8",
"p9",
"p14",
"p19",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4624521546574764648951970
% SZS output start Proof for 4624521546574764648951970
5. ! [X0] : ((quiet(X0) <~> ~patient(X0)) => (~calm(X0) <~> ~happy(X0))) [input p4]
6. ? [X0] : (tall(X0) <~> patient(X0)) => (~curious(lucy) & creative(lucy)) [input p5]
8. ! [X0] : ((brave(X0) & tall(X0)) <=> (creative(X0) | wise(X0))) [input p7]
9. ! [X0] : ((tall(X0) & patient(X0)) <=> (~quiet(X0) & brave(X0))) [input p8]
10. ! [X0] : ((~happy(X0) & wise(X0)) => ~brave(X0)) [input p9]
15. ! [X0] : (~humble(X0) <=> (wise(X0) <~> calm(X0))) [input p14]
20. ~brave(mary) <~> quiet(mary) [input p19]
21. ~humble(mary) <~> calm(mary) [input p20]
25. ~creative(lucy) [input hypothesis]
32. ! [X0] : ((~calm(X0) <~> ~happy(X0)) | (quiet(X0) <=> ~patient(X0))) [ennf transformation 5]
33. (~curious(lucy) & creative(lucy)) | ! [X0] : (tall(X0) <=> patient(X0)) [ennf transformation 6]
35. ! [X0] : (~brave(X0) | (happy(X0) | ~wise(X0))) [ennf transformation 10]
36. ! [X0] : (~brave(X0) | happy(X0) | ~wise(X0)) [flattening 35]
45. ! [X0] : (((happy(X0) | calm(X0)) & (~happy(X0) | ~calm(X0))) | ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) [nnf transformation 32]
46. (~curious(lucy) & creative(lucy)) | ! [X0] : ((tall(X0) | ~patient(X0)) & (patient(X0) | ~tall(X0))) [nnf transformation 33]
50. ! [X0] : (((brave(X0) & tall(X0)) | (~creative(X0) & ~wise(X0))) & ((creative(X0) | wise(X0)) | (~brave(X0) | ~tall(X0)))) [nnf transformation 8]
51. ! [X0] : (((brave(X0) & tall(X0)) | (~creative(X0) & ~wise(X0))) & (creative(X0) | wise(X0) | ~brave(X0) | ~tall(X0))) [flattening 50]
52. ! [X0] : (((tall(X0) & patient(X0)) | (quiet(X0) | ~brave(X0))) & ((~quiet(X0) & brave(X0)) | (~tall(X0) | ~patient(X0)))) [nnf transformation 9]
53. ! [X0] : (((tall(X0) & patient(X0)) | quiet(X0) | ~brave(X0)) & ((~quiet(X0) & brave(X0)) | ~tall(X0) | ~patient(X0))) [flattening 52]
66. ! [X0] : ((~humble(X0) | ((wise(X0) | ~calm(X0)) & (calm(X0) | ~wise(X0)))) & (((~calm(X0) | ~wise(X0)) & (calm(X0) | wise(X0))) | humble(X0))) [nnf transformation 15]
76. (~quiet(mary) | brave(mary)) & (quiet(mary) | ~brave(mary)) [nnf transformation 20]
77. (~calm(mary) | humble(mary)) & (calm(mary) | ~humble(mary)) [nnf transformation 21]
93. ~happy(X0) | ~calm(X0) | ~patient(X0) | ~quiet(X0) [cnf transformation 45]
97. creative(lucy) | patient(X0) | ~tall(X0) [cnf transformation 46]
103. ~wise(X0) | tall(X0) [cnf transformation 51]
105. ~wise(X0) | brave(X0) [cnf transformation 51]
108. ~tall(X0) | ~quiet(X0) | ~patient(X0) [cnf transformation 53]
111. ~brave(X0) | happy(X0) | ~wise(X0) [cnf transformation 36]
125. calm(X0) | wise(X0) | humble(X0) [cnf transformation 66]
128. ~calm(X0) | wise(X0) | ~humble(X0) [cnf transformation 66]
139. quiet(mary) | ~brave(mary) [cnf transformation 76]
141. calm(mary) | ~humble(mary) [cnf transformation 77]
142. ~calm(mary) | humble(mary) [cnf transformation 77]
147. ~creative(lucy) [cnf transformation 25]
176. 7 <=> ! [X0] : (patient(X0) | ~tall(X0)) [avatar definition]
177. ~tall(X0) | patient(X0) <- (7) [avatar component clause 176]
180. 8 <=> creative(lucy) [avatar definition]
184. 7 | 8 [avatar split clause 97,180,176]
197. ~wise(X0) | happy(X0) [subsumption resolution 111,105]
290. 31 <=> brave(mary) [avatar definition]
294. 32 <=> quiet(mary) [avatar definition]
295. quiet(mary) <- (32) [avatar component clause 294]
298. ~31 | 32 [avatar split clause 139,294,290]
300. 33 <=> humble(mary) [avatar definition]
301. ~humble(mary) <- (~33) [avatar component clause 300]
302. humble(mary) <- (33) [avatar component clause 300]
304. 34 <=> calm(mary) [avatar definition]
305. calm(mary) <- (34) [avatar component clause 304]
306. ~calm(mary) <- (~34) [avatar component clause 304]
307. 33 | ~34 [avatar split clause 142,304,300]
308. ~33 | 34 [avatar split clause 141,304,300]
323. ~8 [avatar split clause 147,180]
374. wise(mary) | humble(mary) <- (~34) [resolution 125,306]
375. wise(mary) <- (~33, ~34) [subsumption resolution 374,301]
379. brave(mary) <- (~33, ~34) [resolution 375,105]
380. tall(mary) <- (~33, ~34) [resolution 375,103]
384. 31 | 33 | 34 [avatar split clause 379,304,300,290]
430. ~quiet(mary) | ~patient(mary) <- (~33, ~34) [resolution 380,108]
432. patient(mary) <- (7, ~33, ~34) [resolution 380,177]
433. ~patient(mary) <- (32, ~33, ~34) [subsumption resolution 430,295]
434. $false <- (7, 32, ~33, ~34) [subsumption resolution 432,433]
435. ~7 | ~32 | 33 | 34 [avatar contradiction clause 434]
437. 47 <=> happy(mary) [avatar definition]
439. happy(mary) <- (47) [avatar component clause 437]
441. 48 <=> patient(mary) [avatar definition]
446. wise(mary) | ~humble(mary) <- (34) [resolution 305,128]
448. wise(mary) <- (33, 34) [subsumption resolution 446,302]
463. happy(mary) <- (33, 34) [resolution 448,197]
465. brave(mary) <- (33, 34) [resolution 448,105]
466. tall(mary) <- (33, 34) [resolution 448,103]
468. 47 | ~33 | ~34 [avatar split clause 463,304,300,437]
470. ~calm(mary) | ~patient(mary) | ~quiet(mary) <- (47) [resolution 439,93]
471. ~patient(mary) | ~quiet(mary) <- (34, 47) [subsumption resolution 470,305]
500. patient(mary) <- (7, 33, 34) [resolution 466,177]
504. 31 | ~33 | ~34 [avatar split clause 465,304,300,290]
505. ~32 | ~48 | ~34 | ~47 [avatar split clause 471,437,304,441,294]
508. 48 | ~7 | ~33 | ~34 [avatar split clause 500,304,300,176,441]
510. $false [avatar sat refutation 184,298,307,308,323,384,435,468,504,505,508]
% SZS output end Proof for 4624521546574764648951970
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If paul is humble then someone is kind or generous. If alice is either tall or curious then alice is curious or humble and vice versa. If someone is either not generous or humble then someone is patient. If paul is either not creative or old then lucy is either brave or not humble and vice versa. If lucy is either creative or not strong then mary is kind and vice versa. Everyone who is either not calm or patient is old or rich and vice versa. If susan is not creative then someone is old or not creative and vice versa. Everyone who is not strong or not funny is both not humble and generous and vice versa. If someone is not tall or not curious then someone is either brave or not wise and vice versa. If fred is both old and not tall then lucy is humble and vice versa. Everyone who is either not strong or not creative is not creative and vice versa. If paul is not strong then someone is quiet. Everyone who is not curious is not strong and vice versa. Everyone who is strong is both creative and not quiet and vice versa. Everyone who is both not curious and strong is either strong or rich. Everyone who is both quiet and not calm is both curious and not strong. Someone is either not rich or not tall. Someone is both strong and not brave. Alice is not rich. Alice is patient. Someone is either happy or not wise. | Fred is funny. | neutral | ((humble(paul))=>(?[X]:((kind(X)|generous(X)))))&
(((tall(alice)<~>curious(alice)))<=>((curious(alice)|humble(alice))))&
((?[X]:((~generous(X)<~>humble(X))))=>(?[X]:(patient(X))))&
(((~creative(paul)<~>old(paul)))<=>((brave(lucy)<~>~humble(lucy))))&
(((creative(lucy)<~>~strong(lucy)))<=>(kind(mary)))&
(![X]:((~calm(X)<~>patient(X))<=>(old(X)|rich(X))))&
((~creative(susan))<=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~strong(X)|~funny(X))<=>(~humble(X)&generous(X))))&
((?[X]:((~tall(X)|~curious(X))))<=>(?[X]:((brave(X)<~>~wise(X)))))&
(((old(fred)&~tall(fred)))<=>(humble(lucy)))&
(![X]:((~strong(X)<~>~creative(X))<=>~creative(X)))&
((~strong(paul))=>(?[X]:(quiet(X))))&
(![X]:(~curious(X)<=>~strong(X)))&
(![X]:(strong(X)<=>(creative(X)&~quiet(X))))&
(![X]:((~curious(X)&strong(X))=>(strong(X)<~>rich(X))))&
(![X]:((quiet(X)&~calm(X))=>(curious(X)&~strong(X))))&
(?[X]:((~rich(X)<~>~tall(X))))&
(?[X]:((strong(X)&~brave(X))))&
(~rich(alice))&
(patient(alice))&
(?[X]:((happy(X)<~>~wise(X)))) | funny(fred) | [] | null | 0 |
If lucy is wise then paul is not tall and vice versa.
Everyone who is not kind is old.
If mary is both calm and strong then alice is either not calm or old and vice versa.
Everyone who is not generous or tall is not wise or curious.
If someone is both not kind and wise then someone is wise or not generous and vice versa.
Everyone who is not kind is both not generous and strong.
If fred is both funny and not brave then someone is either not happy or creative.
Everyone who is both quiet and not curious is either humble or calm and vice versa.
If mary is not curious then alice is old or quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Alice is happy.
Someone is either not curious or brave.
Someone is either not generous or not calm.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient. | Alice is happy. | entailment | ((wise(lucy))<=>(~tall(paul)))&
(![X]:(~kind(X)=>old(X)))&
(((calm(mary)&strong(mary)))<=>((~calm(alice)<~>old(alice))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | happy(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2806898977944238364312929
% SZS output start Proof for 2806898977944238364312929
16. happy(alice) [input p15]
22. ~happy(alice) [input hypothesis]
129. happy(alice) [cnf transformation 16]
137. ~happy(alice) [cnf transformation 22]
321. $false [subsumption resolution 137,129]
% SZS output end Proof for 2806898977944238364312929
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is rich then someone is not wise and vice versa.
Everyone who is rich or not quiet is either brave or not quiet and vice versa.
Everyone who is both happy and not kind is either not happy or brave and vice versa.
If john is either not quiet or not humble then someone is not strong and vice versa.
Everyone who is not humble or kind is both not humble and brave and vice versa.
If susan is either not funny or calm then someone is happy or not rich and vice versa.
Everyone who is both not quiet and not wise is funny and vice versa.
Everyone who is not quiet is both tall and not happy and vice versa.
If fred is wise or humble then someone is both not humble and patient.
If someone is not funny or happy then someone is not happy and vice versa.
Everyone who is either creative or not happy is not old or not humble.
If susan is both not funny and old then paul is not generous and vice versa.
If lucy is happy then mary is both kind and not calm.
If someone is generous or not tall then someone is both wise and quiet.
Everyone who is not rich or not brave is not humble.
John is not generous.
Someone is either generous or creative.
Someone is humble.
Alice is not calm or not quiet.
Someone is either calm or not old.
Someone is happy or tall.
Alice is brave or rich. | Susan is not calm. | entailment | ((rich(fred))<=>(?[X]:(~wise(X))))&
(![X]:((rich(X)|~quiet(X))<=>(brave(X)<~>~quiet(X))))&
(![X]:((happy(X)&~kind(X))<=>(~happy(X)<~>brave(X))))&
(((~quiet(john)<~>~humble(john)))<=>(?[X]:(~strong(X))))&
(![X]:((~humble(X)|kind(X))<=>(~humble(X)&brave(X))))&
(((~funny(susan)<~>calm(susan)))<=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~quiet(X)&~wise(X))<=>funny(X)))&
(![X]:(~quiet(X)<=>(tall(X)&~happy(X))))&
(((wise(fred)|humble(fred)))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((~funny(X)|happy(X))))<=>(?[X]:(~happy(X))))&
(![X]:((creative(X)<~>~happy(X))=>(~old(X)|~humble(X))))&
(((~funny(susan)&old(susan)))<=>(~generous(paul)))&
((happy(lucy))=>((kind(mary)&~calm(mary))))&
((?[X]:((generous(X)|~tall(X))))=>(?[X]:((wise(X)&quiet(X)))))&
(![X]:((~rich(X)|~brave(X))=>~humble(X)))&
(~generous(john))&
(?[X]:((generous(X)<~>creative(X))))&
(?[X]:(humble(X)))&
((~calm(alice)|~quiet(alice)))&
(?[X]:((calm(X)<~>~old(X))))&
(?[X]:((happy(X)|tall(X))))&
((brave(alice)|rich(alice))) | ~calm(susan) | [
"p1",
"p2",
"p4",
"p5",
"p6",
"p7",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 335986113569724271413347
% SZS output start Proof for 335986113569724271413347
2. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (brave(X0) <~> ~quiet(X0))) [input p1]
3. ! [X0] : ((~kind(X0) & happy(X0)) <=> (~happy(X0) <~> brave(X0))) [input p2]
5. ! [X0] : ((kind(X0) | ~humble(X0)) <=> (brave(X0) & ~humble(X0))) [input p4]
6. (~funny(susan) <~> calm(susan)) <=> ? [X0] : (~rich(X0) | happy(X0)) [input p5]
7. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> funny(X0)) [input p6]
8. ! [X0] : (~quiet(X0) <=> (~happy(X0) & tall(X0))) [input p7]
21. ? [X0] : (tall(X0) | happy(X0)) [input p20]
23. calm(susan) [input hypothesis]
37. ! [X0] : (((~quiet(X0) | rich(X0)) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) & (((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | (quiet(X0) & ~rich(X0)))) [nnf transformation 2]
38. ! [X0] : ((~quiet(X0) | rich(X0) | ((brave(X0) | quiet(X0)) & (~quiet(X0) | ~brave(X0)))) & (((quiet(X0) | ~brave(X0)) & (~quiet(X0) | brave(X0))) | (quiet(X0) & ~rich(X0)))) [flattening 37]
39. ! [X0] : (((~kind(X0) & happy(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | (kind(X0) | ~happy(X0)))) [nnf transformation 3]
40. ! [X0] : (((~kind(X0) & happy(X0)) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0)))) & (((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | kind(X0) | ~happy(X0))) [flattening 39]
45. ! [X0] : (((kind(X0) | ~humble(X0)) | (~brave(X0) | humble(X0))) & ((brave(X0) & ~humble(X0)) | (~kind(X0) & humble(X0)))) [nnf transformation 5]
46. ! [X0] : ((kind(X0) | ~humble(X0) | ~brave(X0) | humble(X0)) & ((brave(X0) & ~humble(X0)) | (~kind(X0) & humble(X0)))) [flattening 45]
47. (((~calm(susan) | funny(susan)) & (calm(susan) | ~funny(susan))) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X0] : (~rich(X0) | happy(X0)) | ((~funny(susan) | ~calm(susan)) & (calm(susan) | funny(susan)))) [nnf transformation 6]
48. (((~calm(susan) | funny(susan)) & (calm(susan) | ~funny(susan))) | ! [X0] : (rich(X0) & ~happy(X0))) & (? [X1] : (~rich(X1) | happy(X1)) | ((~funny(susan) | ~calm(susan)) & (calm(susan) | funny(susan)))) [rectify 47]
49. ? [X1] : (~rich(X1) | happy(X1)) => (~rich(sK2) | happy(sK2)) [choice axiom]
50. (((~calm(susan) | funny(susan)) & (calm(susan) | ~funny(susan))) | ! [X0] : (rich(X0) & ~happy(X0))) & ((~rich(sK2) | happy(sK2)) | ((~funny(susan) | ~calm(susan)) & (calm(susan) | funny(susan)))) [skolemisation 48,49]
51. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) | quiet(X0)))) [nnf transformation 7]
52. ! [X0] : (((~wise(X0) & ~quiet(X0)) | ~funny(X0)) & (funny(X0) | wise(X0) | quiet(X0))) [flattening 51]
53. ! [X0] : ((~quiet(X0) | (happy(X0) | ~tall(X0))) & ((~happy(X0) & tall(X0)) | quiet(X0))) [nnf transformation 8]
54. ! [X0] : ((~quiet(X0) | happy(X0) | ~tall(X0)) & ((~happy(X0) & tall(X0)) | quiet(X0))) [flattening 53]
76. ? [X0] : (tall(X0) | happy(X0)) => (tall(sK10) | happy(sK10)) [choice axiom]
77. tall(sK10) | happy(sK10) [skolemisation 21,76]
83. quiet(X0) | ~brave(X0) | quiet(X0) [cnf transformation 38]
86. brave(X0) | ~happy(X0) | kind(X0) | ~happy(X0) [cnf transformation 40]
88. happy(X0) | brave(X0) | happy(X0) [cnf transformation 40]
99. brave(X0) | ~kind(X0) [cnf transformation 46]
105. ~calm(susan) | funny(susan) | ~happy(X0) [cnf transformation 50]
108. ~funny(X0) | ~quiet(X0) [cnf transformation 52]
112. ~tall(X0) | happy(X0) | ~quiet(X0) [cnf transformation 54]
138. tall(sK10) | happy(sK10) [cnf transformation 77]
140. calm(susan) [cnf transformation 23]
141. brave(X0) | ~happy(X0) | kind(X0) [duplicate literal removal 86]
142. happy(X0) | brave(X0) [duplicate literal removal 88]
143. ~brave(X0) | quiet(X0) [duplicate literal removal 83]
158. kind(X0) | brave(X0) [subsumption resolution 141,142]
178. brave(X0) [subsumption resolution 99,158]
183. 9 <=> funny(susan) [avatar definition]
185. funny(susan) <- (9) [avatar component clause 183]
187. 10 <=> calm(susan) [avatar definition]
192. 11 <=> ! [X0] : ~happy(X0) [avatar definition]
193. ~happy(X0) <- (11) [avatar component clause 192]
194. 11 | 9 | ~10 [avatar split clause 105,187,183,192]
315. 37 <=> happy(sK10) [avatar definition]
316. ~happy(sK10) <- (~37) [avatar component clause 315]
317. happy(sK10) <- (37) [avatar component clause 315]
319. 38 <=> tall(sK10) [avatar definition]
321. tall(sK10) <- (38) [avatar component clause 319]
322. 37 | 38 [avatar split clause 138,319,315]
323. 10 [avatar split clause 140,187]
330. $false <- (11, 37) [resolution 317,193]
331. ~11 | ~37 [avatar contradiction clause 330]
333. ~quiet(susan) <- (9) [resolution 108,185]
341. quiet(X0) [resolution 143,178]
344. $false <- (9) [resolution 341,333]
345. ~9 [avatar contradiction clause 344]
370. happy(sK10) | ~quiet(sK10) <- (38) [resolution 321,112]
371. ~quiet(sK10) <- (~37, 38) [subsumption resolution 370,316]
372. $false <- (~37, 38) [subsumption resolution 371,341]
373. 37 | ~38 [avatar contradiction clause 372]
374. $false [avatar sat refutation 194,322,323,331,345,373]
% SZS output end Proof for 335986113569724271413347
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet then lucy is either not strong or not rich.
If someone is either not patient or not quiet then someone is curious.
Everyone who is patient is both not tall and happy.
Everyone who is not rich is not brave or not creative and vice versa.
If someone is either tall or patient then someone is either happy or curious and vice versa.
Everyone who is creative or not creative is kind or not quiet and vice versa.
If paul is not calm or creative then someone is both wise and rich and vice versa.
If alice is not funny then john is humble and vice versa.
If someone is not strong then someone is either not kind or not old.
If fred is curious then someone is both not strong and not brave and vice versa.
Everyone who is kind or not calm is not old.
Everyone who is not old is both not creative and not strong and vice versa.
Everyone who is brave is either humble or not funny and vice versa.
Everyone who is rich is creative and vice versa.
If mary is happy or creative then someone is not funny and vice versa.
Everyone who is either not old or not kind is kind.
Someone is either generous or kind.
Mary is rich or calm.
Lucy is not calm or brave.
Someone is both not wise and curious.
Someone is not quiet.
Someone is either not generous or not patient.
Susan is not patient. | John is not rich. | entailment | ((?[X]:(quiet(X)))=>((~strong(lucy)<~>~rich(lucy))))&
((?[X]:((~patient(X)<~>~quiet(X))))=>(?[X]:(curious(X))))&
(![X]:(patient(X)=>(~tall(X)&happy(X))))&
(![X]:(~rich(X)<=>(~brave(X)|~creative(X))))&
((?[X]:((tall(X)<~>patient(X))))<=>(?[X]:((happy(X)<~>curious(X)))))&
(![X]:((creative(X)|~creative(X))<=>(kind(X)|~quiet(X))))&
(((~calm(paul)|creative(paul)))<=>(?[X]:((wise(X)&rich(X)))))&
((~funny(alice))<=>(humble(john)))&
((?[X]:(~strong(X)))=>(?[X]:((~kind(X)<~>~old(X)))))&
((curious(fred))<=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((kind(X)|~calm(X))=>~old(X)))&
(![X]:(~old(X)<=>(~creative(X)&~strong(X))))&
(![X]:(brave(X)<=>(humble(X)<~>~funny(X))))&
(![X]:(rich(X)<=>creative(X)))&
(((happy(mary)|creative(mary)))<=>(?[X]:(~funny(X))))&
(![X]:((~old(X)<~>~kind(X))=>kind(X)))&
(?[X]:((generous(X)<~>kind(X))))&
((rich(mary)|calm(mary)))&
((~calm(lucy)|brave(lucy)))&
(?[X]:((~wise(X)&curious(X))))&
(?[X]:(~quiet(X)))&
(?[X]:((~generous(X)<~>~patient(X))))&
(~patient(susan)) | ~rich(john) | [
"p3",
"p10",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6611699421957444855401588
% SZS output start Proof for 6611699421957444855401588
4. ! [X0] : (~rich(X0) <=> (~creative(X0) | ~brave(X0))) [input p3]
11. ! [X0] : ((~calm(X0) | kind(X0)) => ~old(X0)) [input p10]
12. ! [X0] : (~old(X0) <=> (~strong(X0) & ~creative(X0))) [input p11]
16. ! [X0] : ((~old(X0) <~> ~kind(X0)) => kind(X0)) [input p15]
24. rich(john) [input hypothesis]
32. ! [X0] : (~old(X0) | (calm(X0) & ~kind(X0))) [ennf transformation 11]
33. ! [X0] : (kind(X0) | (~old(X0) <=> ~kind(X0))) [ennf transformation 16]
39. ! [X0] : ((~rich(X0) | (creative(X0) & brave(X0))) & ((~creative(X0) | ~brave(X0)) | rich(X0))) [nnf transformation 4]
40. ! [X0] : ((~rich(X0) | (creative(X0) & brave(X0))) & (~creative(X0) | ~brave(X0) | rich(X0))) [flattening 39]
62. ! [X0] : ((~old(X0) | (strong(X0) | creative(X0))) & ((~strong(X0) & ~creative(X0)) | old(X0))) [nnf transformation 12]
63. ! [X0] : ((~old(X0) | strong(X0) | creative(X0)) & ((~strong(X0) & ~creative(X0)) | old(X0))) [flattening 62]
71. ! [X0] : (kind(X0) | ((~old(X0) | kind(X0)) & (~kind(X0) | old(X0)))) [nnf transformation 33]
90. ~rich(X0) | creative(X0) [cnf transformation 40]
115. ~old(X0) | ~kind(X0) [cnf transformation 32]
117. ~creative(X0) | old(X0) [cnf transformation 63]
130. kind(X0) | ~old(X0) | kind(X0) [cnf transformation 71]
141. rich(john) [cnf transformation 24]
142. kind(X0) | ~old(X0) [duplicate literal removal 130]
290. ~old(X0) [subsumption resolution 142,115]
337. creative(john) [resolution 90,141]
341. old(john) [resolution 117,337]
344. $false [subsumption resolution 341,290]
% SZS output end Proof for 6611699421957444855401588
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or not generous is not generous and vice versa.
Everyone who is not old is both generous and calm.
If someone is not curious or not humble then paul is either patient or not quiet.
Everyone who is both not humble and not generous is either not rich or not old and vice versa.
If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa.
If someone is generous or tall then alice is strong and vice versa.
Everyone who is not happy is brave or humble.
Everyone who is not happy or not funny is both creative and quiet.
If someone is not creative or quiet then someone is both wise and not wise.
Everyone who is not patient is both not kind and happy and vice versa.
If someone is either brave or wise then susan is both brave and not strong and vice versa.
If someone is either kind or happy then someone is both not kind and not creative and vice versa.
Everyone who is not wise or humble is creative or not strong and vice versa.
Everyone who is both funny and strong is either funny or curious and vice versa.
Everyone who is either strong or not strong is humble.
Mary is either quiet or happy.
John is either not tall or wise.
Alice is not kind or rich. | John is not curious. | contradiction | (![X]:((~creative(X)<~>~generous(X))<=>~generous(X)))&
(![X]:(~old(X)=>(generous(X)&calm(X))))&
((?[X]:((~curious(X)|~humble(X))))=>((patient(paul)<~>~quiet(paul))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
((?[X]:((~creative(X)|quiet(X))))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
((?[X]:((brave(X)<~>wise(X))))<=>((brave(susan)&~strong(susan))))&
((?[X]:((kind(X)<~>happy(X))))<=>(?[X]:((~kind(X)&~creative(X)))))&
(![X]:((~wise(X)|humble(X))<=>(creative(X)|~strong(X))))&
(![X]:((funny(X)&strong(X))<=>(funny(X)<~>curious(X))))&
(![X]:((strong(X)<~>~strong(X))=>humble(X)))&
((quiet(mary)<~>happy(mary)))&
((~tall(john)<~>wise(john)))&
((~kind(alice)|rich(alice))) | ~curious(john) | [
"p0",
"p2",
"p8",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4576736474066864657561017
% SZS output start Proof for 4576736474066864657561017
1. ! [X0] : ((~creative(X0) <~> ~generous(X0)) <=> ~generous(X0)) [input p0]
3. ? [X0] : (~humble(X0) | ~curious(X0)) => (patient(paul) <~> ~quiet(paul)) [input p2]
9. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X0] : (~wise(X0) & wise(X0)) [input p8]
10. ! [X0] : (~patient(X0) <=> (happy(X0) & ~kind(X0))) [input p9]
12. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X0] : (~creative(X0) & ~kind(X0)) [input p11]
19. ~curious(john) [input hypothesis]
21. ? [X0] : (quiet(X0) | ~creative(X0)) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 9]
22. ? [X0] : (kind(X0) <~> happy(X0)) <=> ? [X1] : (~creative(X1) & ~kind(X1)) [rectify 12]
25. (patient(paul) <~> ~quiet(paul)) | ! [X0] : (humble(X0) & curious(X0)) [ennf transformation 3]
29. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (~quiet(X0) & creative(X0)) [ennf transformation 21]
31. ! [X0] : ((((generous(X0) | creative(X0)) & (~generous(X0) | ~creative(X0))) | generous(X0)) & (~generous(X0) | ((~creative(X0) | generous(X0)) & (~generous(X0) | creative(X0))))) [nnf transformation 1]
32. ((quiet(paul) | ~patient(paul)) & (~quiet(paul) | patient(paul))) | ! [X0] : (humble(X0) & curious(X0)) [nnf transformation 25]
44. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : (~quiet(X1) & creative(X1)) [rectify 29]
45. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK3) & wise(sK3)) [choice axiom]
46. (~wise(sK3) & wise(sK3)) | ! [X1] : (~quiet(X1) & creative(X1)) [skolemisation 44,45]
47. ! [X0] : ((~patient(X0) | (~happy(X0) | kind(X0))) & ((happy(X0) & ~kind(X0)) | patient(X0))) [nnf transformation 10]
48. ! [X0] : ((~patient(X0) | ~happy(X0) | kind(X0)) & ((happy(X0) & ~kind(X0)) | patient(X0))) [flattening 47]
54. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X1] : (~creative(X1) & ~kind(X1)) | ! [X0] : ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0)))) [nnf transformation 22]
55. (? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | ! [X1] : (creative(X1) | kind(X1))) & (? [X2] : (~creative(X2) & ~kind(X2)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [rectify 54]
56. ? [X0] : ((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) => ((~happy(sK5) | ~kind(sK5)) & (happy(sK5) | kind(sK5))) [choice axiom]
57. ? [X2] : (~creative(X2) & ~kind(X2)) => (~creative(sK6) & ~kind(sK6)) [choice axiom]
58. (((~happy(sK5) | ~kind(sK5)) & (happy(sK5) | kind(sK5))) | ! [X1] : (creative(X1) | kind(X1))) & ((~creative(sK6) & ~kind(sK6)) | ! [X3] : ((kind(X3) | ~happy(X3)) & (happy(X3) | ~kind(X3)))) [skolemisation 55,57,56]
66. ~generous(X0) | ~generous(X0) | creative(X0) [cnf transformation 31]
69. generous(X0) | creative(X0) | generous(X0) [cnf transformation 31]
73. quiet(paul) | ~patient(paul) | curious(X0) [cnf transformation 32]
94. wise(sK3) | ~quiet(X1) [cnf transformation 46]
96. ~wise(sK3) | ~quiet(X1) [cnf transformation 46]
97. ~kind(X0) | patient(X0) [cnf transformation 48]
98. happy(X0) | patient(X0) [cnf transformation 48]
109. ~creative(sK6) | kind(X3) | ~happy(X3) [cnf transformation 58]
129. ~curious(john) [cnf transformation 19]
134. ~generous(X0) | creative(X0) [duplicate literal removal 66]
135. generous(X0) | creative(X0) [duplicate literal removal 69]
136. creative(X0) [subsumption resolution 134,135]
141. 2 <=> patient(paul) [avatar definition]
143. ~patient(paul) <- (~2) [avatar component clause 141]
145. 3 <=> quiet(paul) [avatar definition]
147. quiet(paul) <- (3) [avatar component clause 145]
150. 4 <=> ! [X0] : curious(X0) [avatar definition]
151. curious(X0) <- (4) [avatar component clause 150]
152. 4 | ~2 | 3 [avatar split clause 73,145,141,150]
205. 16 <=> ! [X1] : ~quiet(X1) [avatar definition]
206. ~quiet(X1) <- (16) [avatar component clause 205]
208. 17 <=> wise(sK3) [avatar definition]
211. 16 | ~17 [avatar split clause 96,208,205]
212. 16 | 17 [avatar split clause 94,208,205]
241. ~happy(X3) | kind(X3) [subsumption resolution 109,136]
279. kind(X0) | patient(X0) [resolution 241,98]
282. patient(X0) [subsumption resolution 279,97]
284. $false <- (~2) [resolution 282,143]
285. 2 [avatar contradiction clause 284]
286. $false <- (4) [resolution 151,129]
288. ~4 [avatar contradiction clause 286]
289. $false <- (3, 16) [subsumption resolution 147,206]
290. ~3 | ~16 [avatar contradiction clause 289]
291. $false [avatar sat refutation 152,211,212,285,288,290]
% SZS output end Proof for 4576736474066864657561017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave is both brave and not calm and vice versa.
Everyone who is either not funny or not humble is both humble and not patient.
If fred is either not old or old then susan is either quiet or calm.
Everyone who is tall is funny.
If john is not kind then john is either tall or not quiet and vice versa.
Everyone who is patient or not quiet is not tall or funny.
If someone is not strong then someone is not humble or patient.
Everyone who is funny or not kind is not humble and vice versa.
If mary is creative or not quiet then someone is either not old or not rich.
Everyone who is both rich and not old is not calm or strong.
If someone is quiet or not funny then fred is quiet or calm and vice versa.
Everyone who is both happy and not strong is either old or not quiet and vice versa.
Everyone who is curious is either curious or patient and vice versa.
If someone is brave or not creative then fred is old.
If someone is both not rich and not kind then someone is old.
Everyone who is strong or not generous is either not brave or not generous and vice versa.
Someone is either not humble or quiet.
Paul is not happy.
Paul is both not rich and not curious.
Someone is either patient or curious.
Someone is brave.
Fred is not humble or not happy.
Someone is creative or quiet.
Someone is kind or not patient. | Mary is humble. | neutral | (![X]:(brave(X)<=>(brave(X)&~calm(X))))&
(![X]:((~funny(X)<~>~humble(X))=>(humble(X)&~patient(X))))&
(((~old(fred)<~>old(fred)))=>((quiet(susan)<~>calm(susan))))&
(![X]:(tall(X)=>funny(X)))&
((~kind(john))<=>((tall(john)<~>~quiet(john))))&
(![X]:((patient(X)|~quiet(X))=>(~tall(X)|funny(X))))&
((?[X]:(~strong(X)))=>(?[X]:((~humble(X)|patient(X)))))&
(![X]:((funny(X)|~kind(X))<=>~humble(X)))&
(((creative(mary)|~quiet(mary)))=>(?[X]:((~old(X)<~>~rich(X)))))&
(![X]:((rich(X)&~old(X))=>(~calm(X)|strong(X))))&
((?[X]:((quiet(X)|~funny(X))))<=>((quiet(fred)|calm(fred))))&
(![X]:((happy(X)&~strong(X))<=>(old(X)<~>~quiet(X))))&
(![X]:(curious(X)<=>(curious(X)<~>patient(X))))&
((?[X]:((brave(X)|~creative(X))))=>(old(fred)))&
((?[X]:((~rich(X)&~kind(X))))=>(?[X]:(old(X))))&
(![X]:((strong(X)|~generous(X))<=>(~brave(X)<~>~generous(X))))&
(?[X]:((~humble(X)<~>quiet(X))))&
(~happy(paul))&
((~rich(paul)&~curious(paul)))&
(?[X]:((patient(X)<~>curious(X))))&
(?[X]:(brave(X)))&
((~humble(fred)|~happy(fred)))&
(?[X]:((creative(X)|quiet(X))))&
(?[X]:((kind(X)|~patient(X)))) | humble(mary) | [] | null | 0 |
If alice is quiet then susan is tall and vice versa.
If fred is generous or not brave then susan is both funny and not kind.
If john is either rich or kind then someone is either not old or old and vice versa.
Everyone who is both generous and not wise is both not wise and kind.
If someone is not old then someone is not rich and vice versa.
If susan is both tall and strong then someone is old.
Everyone who is either not strong or not humble is generous or curious and vice versa.
If someone is not old or old then someone is quiet or not creative.
If someone is wise or not quiet then john is either tall or wise.
Everyone who is both strong and not rich is both not creative and not quiet and vice versa.
Everyone who is either funny or not creative is both happy and old and vice versa.
If john is both patient and not happy then lucy is not brave or not humble and vice versa.
Everyone who is not curious is either funny or creative and vice versa.
If someone is funny or not funny then mary is not funny.
If john is not funny or not patient then someone is either not curious or not patient and vice versa.
Everyone who is both not curious and tall is both strong and not funny.
Mary is not patient or not kind.
Someone is not rich or quiet.
Lucy is either funny or happy.
Someone is happy.
Susan is not curious.
Fred is either calm or not wise.
John is humble or not curious.
Fred is curious. | Fred is happy. | entailment | ((quiet(alice))<=>(tall(susan)))&
(((generous(fred)|~brave(fred)))=>((funny(susan)&~kind(susan))))&
(((rich(john)<~>kind(john)))<=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((generous(X)&~wise(X))=>(~wise(X)&kind(X))))&
((?[X]:(~old(X)))<=>(?[X]:(~rich(X))))&
(((tall(susan)&strong(susan)))=>(?[X]:(old(X))))&
(![X]:((~strong(X)<~>~humble(X))<=>(generous(X)|curious(X))))&
((?[X]:((~old(X)|old(X))))=>(?[X]:((quiet(X)|~creative(X)))))&
((?[X]:((wise(X)|~quiet(X))))=>((tall(john)<~>wise(john))))&
(![X]:((strong(X)&~rich(X))<=>(~creative(X)&~quiet(X))))&
(![X]:((funny(X)<~>~creative(X))<=>(happy(X)&old(X))))&
(((patient(john)&~happy(john)))<=>((~brave(lucy)|~humble(lucy))))&
(![X]:(~curious(X)<=>(funny(X)<~>creative(X))))&
((?[X]:((funny(X)|~funny(X))))=>(~funny(mary)))&
(((~funny(john)|~patient(john)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((~curious(X)&tall(X))=>(strong(X)&~funny(X))))&
((~patient(mary)|~kind(mary)))&
(?[X]:((~rich(X)|quiet(X))))&
((funny(lucy)<~>happy(lucy)))&
(?[X]:(happy(X)))&
(~curious(susan))&
((calm(fred)<~>~wise(fred)))&
((humble(john)|~curious(john)))&
(curious(fred)) | happy(fred) | [
"p10",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 8182671681578397532655378
% SZS output start Proof for 8182671681578397532655378
11. ! [X0] : ((funny(X0) <~> ~creative(X0)) <=> (old(X0) & happy(X0))) [input p10]
13. ! [X0] : (~curious(X0) <=> (funny(X0) <~> creative(X0))) [input p12]
24. curious(fred) [input p23]
25. ~happy(fred) [input hypothesis]
58. ! [X0] : ((((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | (~old(X0) | ~happy(X0))) & ((old(X0) & happy(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))))) [nnf transformation 11]
59. ! [X0] : ((((creative(X0) | ~funny(X0)) & (~creative(X0) | funny(X0))) | ~old(X0) | ~happy(X0)) & ((old(X0) & happy(X0)) | ((funny(X0) | creative(X0)) & (~creative(X0) | ~funny(X0))))) [flattening 58]
62. ! [X0] : ((~curious(X0) | ((funny(X0) | ~creative(X0)) & (creative(X0) | ~funny(X0)))) & (((~creative(X0) | ~funny(X0)) & (creative(X0) | funny(X0))) | curious(X0))) [nnf transformation 13]
109. ~creative(X0) | happy(X0) | ~funny(X0) [cnf transformation 59]
110. happy(X0) | funny(X0) | creative(X0) [cnf transformation 59]
122. ~curious(X0) | creative(X0) | ~funny(X0) [cnf transformation 62]
123. ~creative(X0) | funny(X0) | ~curious(X0) [cnf transformation 62]
143. curious(fred) [cnf transformation 24]
144. ~happy(fred) [cnf transformation 25]
438. funny(fred) | creative(fred) [resolution 110,144]
441. 56 <=> creative(fred) [avatar definition]
443. creative(fred) <- (56) [avatar component clause 441]
445. 57 <=> funny(fred) [avatar definition]
447. funny(fred) <- (57) [avatar component clause 445]
448. 56 | 57 [avatar split clause 438,445,441]
489. creative(fred) | ~funny(fred) [resolution 122,143]
492. creative(fred) <- (57) [subsumption resolution 489,447]
493. 56 | ~57 [avatar split clause 492,445,441]
510. funny(fred) | ~curious(fred) <- (56) [resolution 443,123]
513. happy(fred) | ~funny(fred) <- (56) [resolution 443,109]
516. ~funny(fred) <- (56) [subsumption resolution 513,144]
519. ~57 | ~56 [avatar split clause 516,441,445]
525. funny(fred) <- (56) [subsumption resolution 510,143]
526. 57 | ~56 [avatar split clause 525,441,445]
527. $false [avatar sat refutation 448,493,519,526]
% SZS output end Proof for 8182671681578397532655378
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or not rich is either humble or calm and vice versa.
If someone is funny or tall then alice is kind and vice versa.
If mary is creative then mary is both wise and not humble and vice versa.
If someone is not tall or generous then susan is not tall and vice versa.
Everyone who is happy is not happy or old.
Everyone who is not creative is tall and vice versa.
Everyone who is either not patient or not brave is either not kind or quiet.
Everyone who is either generous or not quiet is not rich or kind.
Everyone who is not strong is generous or not brave.
If john is either humble or not quiet then lucy is both not wise and not funny and vice versa.
Everyone who is brave is not old or not creative.
If fred is either old or strong then someone is either not patient or strong and vice versa.
Everyone who is not creative or happy is both quiet and humble and vice versa.
Everyone who is both quiet and generous is not funny.
If lucy is either strong or humble then someone is either not patient or not calm and vice versa.
If someone is both creative and generous then someone is both strong and curious.
Alice is both brave and curious.
Alice is not funny.
Alice is both curious and brave.
John is brave or humble.
Fred is kind or not curious.
Someone is either not kind or tall.
Paul is not creative or not patient.
Someone is not curious. | Mary is tall. | neutral | (![X]:((creative(X)|~rich(X))<=>(humble(X)<~>calm(X))))&
((?[X]:((funny(X)|tall(X))))<=>(kind(alice)))&
((creative(mary))<=>((wise(mary)&~humble(mary))))&
((?[X]:((~tall(X)|generous(X))))<=>(~tall(susan)))&
(![X]:(happy(X)=>(~happy(X)|old(X))))&
(![X]:(~creative(X)<=>tall(X)))&
(![X]:((~patient(X)<~>~brave(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((generous(X)<~>~quiet(X))=>(~rich(X)|kind(X))))&
(![X]:(~strong(X)=>(generous(X)|~brave(X))))&
(((humble(john)<~>~quiet(john)))<=>((~wise(lucy)&~funny(lucy))))&
(![X]:(brave(X)=>(~old(X)|~creative(X))))&
(((old(fred)<~>strong(fred)))<=>(?[X]:((~patient(X)<~>strong(X)))))&
(![X]:((~creative(X)|happy(X))<=>(quiet(X)&humble(X))))&
(![X]:((quiet(X)&generous(X))=>~funny(X)))&
(((strong(lucy)<~>humble(lucy)))<=>(?[X]:((~patient(X)<~>~calm(X)))))&
((?[X]:((creative(X)&generous(X))))=>(?[X]:((strong(X)&curious(X)))))&
((brave(alice)&curious(alice)))&
(~funny(alice))&
((curious(alice)&brave(alice)))&
((brave(john)|humble(john)))&
((kind(fred)|~curious(fred)))&
(?[X]:((~kind(X)<~>tall(X))))&
((~creative(paul)|~patient(paul)))&
(?[X]:(~curious(X))) | tall(mary) | [] | null | 0 |
Everyone who is quiet or not kind is old or tall. Everyone who is creative is either patient or wise and vice versa. Everyone who is both not quiet and not old is creative or not happy and vice versa. Everyone who is not happy is not brave and vice versa. If someone is both not old and kind then someone is not brave or not wise. If someone is both not kind and brave then someone is both calm and not rich. If someone is both humble and not calm then fred is both not quiet and not calm. If someone is not humble or brave then someone is both wise and strong and vice versa. Everyone who is not curious is both humble and calm and vice versa. Everyone who is either old or creative is both not kind and not curious and vice versa. Everyone who is strong is humble and vice versa. Everyone who is both curious and tall is curious and vice versa. Everyone who is either strong or quiet is either patient or not brave. If someone is both not quiet and not kind then susan is funny or not patient. If lucy is either patient or not happy then paul is either brave or not brave and vice versa. Everyone who is both brave and not old is kind and vice versa. Someone is either not generous or strong. Fred is not calm or old. Someone is both quiet and not humble. Someone is old or not creative. Lucy is not tall. Alice is either rich or not patient. Someone is both not wise and not kind. Someone is not wise or not generous. | Alice is not wise. | neutral | (![X]:((quiet(X)|~kind(X))=>(old(X)|tall(X))))&
(![X]:(creative(X)<=>(patient(X)<~>wise(X))))&
(![X]:((~quiet(X)&~old(X))<=>(creative(X)|~happy(X))))&
(![X]:(~happy(X)<=>~brave(X)))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((~brave(X)|~wise(X)))))&
((?[X]:((~kind(X)&brave(X))))=>(?[X]:((calm(X)&~rich(X)))))&
((?[X]:((humble(X)&~calm(X))))=>((~quiet(fred)&~calm(fred))))&
((?[X]:((~humble(X)|brave(X))))<=>(?[X]:((wise(X)&strong(X)))))&
(![X]:(~curious(X)<=>(humble(X)&calm(X))))&
(![X]:((old(X)<~>creative(X))<=>(~kind(X)&~curious(X))))&
(![X]:(strong(X)<=>humble(X)))&
(![X]:((curious(X)&tall(X))<=>curious(X)))&
(![X]:((strong(X)<~>quiet(X))=>(patient(X)<~>~brave(X))))&
((?[X]:((~quiet(X)&~kind(X))))=>((funny(susan)|~patient(susan))))&
(((patient(lucy)<~>~happy(lucy)))<=>((brave(paul)<~>~brave(paul))))&
(![X]:((brave(X)&~old(X))<=>kind(X)))&
(?[X]:((~generous(X)<~>strong(X))))&
((~calm(fred)|old(fred)))&
(?[X]:((quiet(X)&~humble(X))))&
(?[X]:((old(X)|~creative(X))))&
(~tall(lucy))&
((rich(alice)<~>~patient(alice)))&
(?[X]:((~wise(X)&~kind(X))))&
(?[X]:((~wise(X)|~generous(X)))) | ~wise(alice) | [] | null | 0 |
Everyone who is creative is both not quiet and not strong and vice versa.
Everyone who is not strong or tall is either not rich or not calm and vice versa.
If john is not generous then mary is either creative or not quiet and vice versa.
Everyone who is either not kind or old is either rich or not kind.
Everyone who is not strong or not happy is not funny or calm and vice versa.
If fred is rich or wise then mary is both not tall and not calm and vice versa.
Everyone who is not generous is calm or brave and vice versa.
If fred is not creative then lucy is quiet and vice versa.
Everyone who is either not quiet or not calm is tall or not patient and vice versa.
If someone is both brave and not tall then someone is both curious and strong and vice versa.
If mary is either happy or not kind then lucy is either funny or brave and vice versa.
If someone is kind or not generous then someone is quiet.
If fred is both not funny and tall then lucy is funny.
If lucy is curious then someone is both not quiet and kind.
If someone is creative or kind then someone is not humble and vice versa.
Everyone who is calm or not happy is either not humble or not old.
Someone is either old or not brave.
Someone is not curious or not strong.
Mary is not old.
John is either patient or quiet.
Mary is either rich or not wise.
Mary is not curious.
Someone is either rich or calm.
John is not tall or not strong. | Mary is not kind. | neutral | (![X]:(creative(X)<=>(~quiet(X)&~strong(X))))&
(![X]:((~strong(X)|tall(X))<=>(~rich(X)<~>~calm(X))))&
((~generous(john))<=>((creative(mary)<~>~quiet(mary))))&
(![X]:((~kind(X)<~>old(X))=>(rich(X)<~>~kind(X))))&
(![X]:((~strong(X)|~happy(X))<=>(~funny(X)|calm(X))))&
(((rich(fred)|wise(fred)))<=>((~tall(mary)&~calm(mary))))&
(![X]:(~generous(X)<=>(calm(X)|brave(X))))&
((~creative(fred))<=>(quiet(lucy)))&
(![X]:((~quiet(X)<~>~calm(X))<=>(tall(X)|~patient(X))))&
((?[X]:((brave(X)&~tall(X))))<=>(?[X]:((curious(X)&strong(X)))))&
(((happy(mary)<~>~kind(mary)))<=>((funny(lucy)<~>brave(lucy))))&
((?[X]:((kind(X)|~generous(X))))=>(?[X]:(quiet(X))))&
(((~funny(fred)&tall(fred)))=>(funny(lucy)))&
((curious(lucy))=>(?[X]:((~quiet(X)&kind(X)))))&
((?[X]:((creative(X)|kind(X))))<=>(?[X]:(~humble(X))))&
(![X]:((calm(X)|~happy(X))=>(~humble(X)<~>~old(X))))&
(?[X]:((old(X)<~>~brave(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(~old(mary))&
((patient(john)<~>quiet(john)))&
((rich(mary)<~>~wise(mary)))&
(~curious(mary))&
(?[X]:((rich(X)<~>calm(X))))&
((~tall(john)|~strong(john))) | ~kind(mary) | [] | null | 0 |
If alice is tall or creative then someone is either not generous or not curious and vice versa. If john is both not patient and strong then paul is not funny or humble. Everyone who is funny or quiet is either not humble or not rich. If lucy is either funny or not humble then alice is either humble or not kind. If mary is both wise and not humble then someone is not rich and vice versa. If someone is not old then paul is strong. Everyone who is either rich or generous is either not tall or wise. If someone is not rich then someone is not creative or happy and vice versa. If susan is not wise then paul is rich and vice versa. If alice is both calm and not wise then someone is not wise or not humble. Everyone who is patient or creative is brave. Everyone who is not curious is both tall and wise. Everyone who is either not quiet or tall is not quiet or not old. Everyone who is both creative and wise is either creative or not generous and vice versa. Everyone who is generous or curious is both humble and not tall. Everyone who is not tall or humble is funny or humble and vice versa. Paul is not funny or not strong. Someone is not patient. John is rich or creative. John is quiet or old. Someone is either not rich or not calm. | Alice is not quiet. | entailment | (((tall(alice)|creative(alice)))<=>(?[X]:((~generous(X)<~>~curious(X)))))&
(((~patient(john)&strong(john)))=>((~funny(paul)|humble(paul))))&
(![X]:((funny(X)|quiet(X))=>(~humble(X)<~>~rich(X))))&
(((funny(lucy)<~>~humble(lucy)))=>((humble(alice)<~>~kind(alice))))&
(((wise(mary)&~humble(mary)))<=>(?[X]:(~rich(X))))&
((?[X]:(~old(X)))=>(strong(paul)))&
(![X]:((rich(X)<~>generous(X))=>(~tall(X)<~>wise(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)|happy(X)))))&
((~wise(susan))<=>(rich(paul)))&
(((calm(alice)&~wise(alice)))=>(?[X]:((~wise(X)|~humble(X)))))&
(![X]:((patient(X)|creative(X))=>brave(X)))&
(![X]:(~curious(X)=>(tall(X)&wise(X))))&
(![X]:((~quiet(X)<~>tall(X))=>(~quiet(X)|~old(X))))&
(![X]:((creative(X)&wise(X))<=>(creative(X)<~>~generous(X))))&
(![X]:((generous(X)|curious(X))=>(humble(X)&~tall(X))))&
(![X]:((~tall(X)|humble(X))<=>(funny(X)|humble(X))))&
((~funny(paul)|~strong(paul)))&
(?[X]:(~patient(X)))&
((rich(john)|creative(john)))&
((quiet(john)|old(john)))&
(?[X]:((~rich(X)<~>~calm(X)))) | ~quiet(alice) | [
"p2",
"p4",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 878164802449103582434835
% SZS output start Proof for 878164802449103582434835
3. ! [X0] : ((quiet(X0) | funny(X0)) => (~humble(X0) <~> ~rich(X0))) [input p2]
5. (~humble(mary) & wise(mary)) <=> ? [X0] : ~rich(X0) [input p4]
12. ! [X0] : (~curious(X0) => (wise(X0) & tall(X0))) [input p11]
14. ! [X0] : ((wise(X0) & creative(X0)) <=> (creative(X0) <~> ~generous(X0))) [input p13]
15. ! [X0] : ((curious(X0) | generous(X0)) => (~tall(X0) & humble(X0))) [input p14]
22. quiet(alice) [input hypothesis]
27. ! [X0] : ((~humble(X0) <~> ~rich(X0)) | (~quiet(X0) & ~funny(X0))) [ennf transformation 3]
33. ! [X0] : ((wise(X0) & tall(X0)) | curious(X0)) [ennf transformation 12]
36. ! [X0] : ((~tall(X0) & humble(X0)) | (~curious(X0) & ~generous(X0))) [ennf transformation 15]
42. ! [X0] : (((rich(X0) | humble(X0)) & (~rich(X0) | ~humble(X0))) | (~quiet(X0) & ~funny(X0))) [nnf transformation 27]
44. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | (humble(mary) | ~wise(mary))) [nnf transformation 5]
45. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (? [X0] : ~rich(X0) | humble(mary) | ~wise(mary)) [flattening 44]
46. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (? [X1] : ~rich(X1) | humble(mary) | ~wise(mary)) [rectify 45]
47. ? [X1] : ~rich(X1) => ~rich(sK1) [choice axiom]
48. ((~humble(mary) & wise(mary)) | ! [X0] : rich(X0)) & (~rich(sK1) | humble(mary) | ~wise(mary)) [skolemisation 46,47]
59. ! [X0] : (((wise(X0) & creative(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | (~wise(X0) | ~creative(X0)))) [nnf transformation 14]
60. ! [X0] : (((wise(X0) & creative(X0)) | ((creative(X0) | generous(X0)) & (~generous(X0) | ~creative(X0)))) & (((generous(X0) | ~creative(X0)) & (~generous(X0) | creative(X0))) | ~wise(X0) | ~creative(X0))) [flattening 59]
76. ~rich(X0) | ~humble(X0) | ~quiet(X0) [cnf transformation 42]
84. wise(mary) | rich(X0) [cnf transformation 48]
85. ~humble(mary) | rich(X0) [cnf transformation 48]
97. curious(X0) | tall(X0) [cnf transformation 33]
98. wise(X0) | curious(X0) [cnf transformation 33]
102. generous(X0) | ~creative(X0) | ~wise(X0) | ~creative(X0) [cnf transformation 60]
104. creative(X0) | creative(X0) | generous(X0) [cnf transformation 60]
107. ~generous(X0) | humble(X0) [cnf transformation 36]
108. ~curious(X0) | humble(X0) [cnf transformation 36]
109. ~generous(X0) | ~tall(X0) [cnf transformation 36]
110. ~curious(X0) | ~tall(X0) [cnf transformation 36]
121. quiet(alice) [cnf transformation 22]
122. generous(X0) | ~creative(X0) | ~wise(X0) [duplicate literal removal 102]
123. generous(X0) | creative(X0) [duplicate literal removal 104]
129. 2 <=> tall(alice) [avatar definition]
131. tall(alice) <- (2) [avatar component clause 129]
179. 13 <=> humble(alice) [avatar definition]
181. ~humble(alice) <- (~13) [avatar component clause 179]
191. 15 <=> ! [X0] : rich(X0) [avatar definition]
192. rich(X0) <- (15) [avatar component clause 191]
194. 16 <=> humble(mary) [avatar definition]
197. 15 | ~16 [avatar split clause 85,194,191]
199. 17 <=> wise(mary) [avatar definition]
201. wise(mary) <- (17) [avatar component clause 199]
202. 15 | 17 [avatar split clause 84,199,191]
264. ~wise(X0) | generous(X0) [subsumption resolution 122,123]
300. humble(X0) | tall(X0) [resolution 108,97]
318. generous(mary) <- (17) [resolution 264,201]
319. curious(X0) | generous(X0) [resolution 264,98]
324. humble(mary) <- (17) [resolution 318,107]
327. 16 | ~17 [avatar split clause 324,199,194]
341. ~quiet(X0) | ~humble(X0) <- (15) [resolution 76,192]
395. ~humble(alice) <- (15) [resolution 341,121]
401. ~13 | ~15 [avatar split clause 395,191,179]
445. tall(alice) <- (~13) [resolution 181,300]
452. 2 | 13 [avatar split clause 445,179,129]
454. generous(X0) | ~tall(X0) [resolution 319,110]
456. ~tall(X0) [subsumption resolution 454,109]
485. $false <- (2) [resolution 456,131]
486. ~2 [avatar contradiction clause 485]
487. $false [avatar sat refutation 197,202,327,401,452,486]
% SZS output end Proof for 878164802449103582434835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either not rich or curious then paul is not old or wise and vice versa. If john is both not brave and patient then lucy is both funny and not old and vice versa. Everyone who is wise is either tall or calm and vice versa. If someone is either curious or kind then someone is both not generous and not funny and vice versa. If john is not tall or not happy then paul is either not generous or funny and vice versa. Everyone who is not old or happy is funny or not strong and vice versa. If susan is quiet or not strong then susan is both not happy and tall and vice versa. Everyone who is not curious is either kind or brave. Everyone who is both not quiet and not tall is both not creative and humble and vice versa. Everyone who is creative is kind. Everyone who is both not wise and rich is both strong and kind and vice versa. Everyone who is humble or old is not curious. Everyone who is either not rich or calm is rich and vice versa. If someone is wise then lucy is tall. Everyone who is rich is either funny or not calm. If someone is calm then john is not curious. Someone is either not generous or quiet. Lucy is either not curious or funny. Someone is not wise. Someone is wise or old. Someone is not funny or calm. Mary is not patient or not kind. Someone is both not wise and not creative. John is old or not kind. | Lucy is not rich. | neutral | (((~rich(lucy)<~>curious(lucy)))<=>((~old(paul)|wise(paul))))&
(((~brave(john)&patient(john)))<=>((funny(lucy)&~old(lucy))))&
(![X]:(wise(X)<=>(tall(X)<~>calm(X))))&
((?[X]:((curious(X)<~>kind(X))))<=>(?[X]:((~generous(X)&~funny(X)))))&
(((~tall(john)|~happy(john)))<=>((~generous(paul)<~>funny(paul))))&
(![X]:((~old(X)|happy(X))<=>(funny(X)|~strong(X))))&
(((quiet(susan)|~strong(susan)))<=>((~happy(susan)&tall(susan))))&
(![X]:(~curious(X)=>(kind(X)<~>brave(X))))&
(![X]:((~quiet(X)&~tall(X))<=>(~creative(X)&humble(X))))&
(![X]:(creative(X)=>kind(X)))&
(![X]:((~wise(X)&rich(X))<=>(strong(X)&kind(X))))&
(![X]:((humble(X)|old(X))=>~curious(X)))&
(![X]:((~rich(X)<~>calm(X))<=>rich(X)))&
((?[X]:(wise(X)))=>(tall(lucy)))&
(![X]:(rich(X)=>(funny(X)<~>~calm(X))))&
((?[X]:(calm(X)))=>(~curious(john)))&
(?[X]:((~generous(X)<~>quiet(X))))&
((~curious(lucy)<~>funny(lucy)))&
(?[X]:(~wise(X)))&
(?[X]:((wise(X)|old(X))))&
(?[X]:((~funny(X)|calm(X))))&
((~patient(mary)|~kind(mary)))&
(?[X]:((~wise(X)&~creative(X))))&
((old(john)|~kind(john))) | ~rich(lucy) | [] | null | 0 |
Everyone who is old is either strong or not wise and vice versa.
Everyone who is either not kind or strong is not humble or strong and vice versa.
Everyone who is either funny or patient is not generous.
If paul is either calm or wise then someone is funny.
Everyone who is calm is both creative and wise.
Everyone who is either not wise or calm is either humble or not creative and vice versa.
Everyone who is both not old and wise is either not quiet or not patient and vice versa.
If someone is not happy or wise then paul is either not funny or kind.
Everyone who is not kind is not rich or not happy and vice versa.
Everyone who is both not tall and creative is not brave and vice versa.
Everyone who is tall is not old or creative and vice versa.
Everyone who is old is not strong.
If john is both rich and not calm then mary is not old and vice versa.
If someone is either kind or old then someone is either rich or not creative and vice versa.
Everyone who is humble or kind is generous or tall and vice versa.
Someone is happy or creative.
Someone is curious.
Someone is both not strong and kind.
Someone is both not humble and curious.
Someone is not patient or rich. | John is curious. | neutral | (![X]:(old(X)<=>(strong(X)<~>~wise(X))))&
(![X]:((~kind(X)<~>strong(X))<=>(~humble(X)|strong(X))))&
(![X]:((funny(X)<~>patient(X))=>~generous(X)))&
(((calm(paul)<~>wise(paul)))=>(?[X]:(funny(X))))&
(![X]:(calm(X)=>(creative(X)&wise(X))))&
(![X]:((~wise(X)<~>calm(X))<=>(humble(X)<~>~creative(X))))&
(![X]:((~old(X)&wise(X))<=>(~quiet(X)<~>~patient(X))))&
((?[X]:((~happy(X)|wise(X))))=>((~funny(paul)<~>kind(paul))))&
(![X]:(~kind(X)<=>(~rich(X)|~happy(X))))&
(![X]:((~tall(X)&creative(X))<=>~brave(X)))&
(![X]:(tall(X)<=>(~old(X)|creative(X))))&
(![X]:(old(X)=>~strong(X)))&
(((rich(john)&~calm(john)))<=>(~old(mary)))&
((?[X]:((kind(X)<~>old(X))))<=>(?[X]:((rich(X)<~>~creative(X)))))&
(![X]:((humble(X)|kind(X))<=>(generous(X)|tall(X))))&
(?[X]:((happy(X)|creative(X))))&
(?[X]:(curious(X)))&
(?[X]:((~strong(X)&kind(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((~patient(X)|rich(X)))) | curious(john) | [] | null | 0 |
If someone is kind or quiet then someone is happy.
Everyone who is both not tall and not generous is either curious or not curious and vice versa.
If susan is tall then someone is humble.
Everyone who is not strong is tall or not strong.
Everyone who is not patient is funny or quiet.
Everyone who is old or not happy is creative or calm.
If someone is either not brave or quiet then mary is both curious and humble and vice versa.
Everyone who is either calm or kind is not generous or not kind and vice versa.
Everyone who is not calm or happy is either strong or quiet and vice versa.
Everyone who is either tall or strong is strong or not brave and vice versa.
Everyone who is patient is either not brave or not strong and vice versa.
Everyone who is both not calm and calm is funny and vice versa.
Everyone who is old is both not funny and patient and vice versa.
If fred is both not creative and calm then mary is kind and vice versa.
If someone is not old or not strong then lucy is old.
Everyone who is both not creative and generous is strong.
Someone is both brave and calm.
Someone is either not kind or curious.
Alice is either brave or not tall.
Fred is not rich or not strong.
John is both creative and happy.
Someone is both not kind and not curious.
Someone is creative. | John is not brave. | neutral | ((?[X]:((kind(X)|quiet(X))))=>(?[X]:(happy(X))))&
(![X]:((~tall(X)&~generous(X))<=>(curious(X)<~>~curious(X))))&
((tall(susan))=>(?[X]:(humble(X))))&
(![X]:(~strong(X)=>(tall(X)|~strong(X))))&
(![X]:(~patient(X)=>(funny(X)|quiet(X))))&
(![X]:((old(X)|~happy(X))=>(creative(X)|calm(X))))&
((?[X]:((~brave(X)<~>quiet(X))))<=>((curious(mary)&humble(mary))))&
(![X]:((calm(X)<~>kind(X))<=>(~generous(X)|~kind(X))))&
(![X]:((~calm(X)|happy(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((tall(X)<~>strong(X))<=>(strong(X)|~brave(X))))&
(![X]:(patient(X)<=>(~brave(X)<~>~strong(X))))&
(![X]:((~calm(X)&calm(X))<=>funny(X)))&
(![X]:(old(X)<=>(~funny(X)&patient(X))))&
(((~creative(fred)&calm(fred)))<=>(kind(mary)))&
((?[X]:((~old(X)|~strong(X))))=>(old(lucy)))&
(![X]:((~creative(X)&generous(X))=>strong(X)))&
(?[X]:((brave(X)&calm(X))))&
(?[X]:((~kind(X)<~>curious(X))))&
((brave(alice)<~>~tall(alice)))&
((~rich(fred)|~strong(fred)))&
((creative(john)&happy(john)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(creative(X))) | ~brave(john) | [] | null | 0 |
If alice is not kind or not curious then someone is tall.
If someone is either rich or wise then someone is patient and vice versa.
If mary is both not humble and curious then someone is both not strong and not rich and vice versa.
Everyone who is not curious or patient is generous or not creative and vice versa.
Everyone who is not kind is both not funny and not old.
Everyone who is not humble or wise is not brave or rich and vice versa.
Everyone who is either not calm or generous is both patient and not curious and vice versa.
Everyone who is both not rich and brave is not calm or generous.
Everyone who is either not patient or wise is either happy or not creative.
If fred is not curious then someone is both brave and not old and vice versa.
Everyone who is strong or not funny is both not humble and not quiet and vice versa.
Everyone who is both not kind and tall is both calm and not wise.
Everyone who is not patient or not funny is both patient and not rich and vice versa.
Everyone who is brave is creative or patient and vice versa.
If fred is tall then someone is not funny or not calm and vice versa.
Everyone who is either not strong or happy is not tall or calm.
Alice is patient.
Susan is not strong.
Someone is either tall or not brave.
Paul is either creative or not rich.
Fred is not curious or not happy.
Fred is tall or not old. | Mary is not tall. | neutral | (((~kind(alice)|~curious(alice)))=>(?[X]:(tall(X))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:(patient(X))))&
(((~humble(mary)&curious(mary)))<=>(?[X]:((~strong(X)&~rich(X)))))&
(![X]:((~curious(X)|patient(X))<=>(generous(X)|~creative(X))))&
(![X]:(~kind(X)=>(~funny(X)&~old(X))))&
(![X]:((~humble(X)|wise(X))<=>(~brave(X)|rich(X))))&
(![X]:((~calm(X)<~>generous(X))<=>(patient(X)&~curious(X))))&
(![X]:((~rich(X)&brave(X))=>(~calm(X)|generous(X))))&
(![X]:((~patient(X)<~>wise(X))=>(happy(X)<~>~creative(X))))&
((~curious(fred))<=>(?[X]:((brave(X)&~old(X)))))&
(![X]:((strong(X)|~funny(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((~kind(X)&tall(X))=>(calm(X)&~wise(X))))&
(![X]:((~patient(X)|~funny(X))<=>(patient(X)&~rich(X))))&
(![X]:(brave(X)<=>(creative(X)|patient(X))))&
((tall(fred))<=>(?[X]:((~funny(X)|~calm(X)))))&
(![X]:((~strong(X)<~>happy(X))=>(~tall(X)|calm(X))))&
(patient(alice))&
(~strong(susan))&
(?[X]:((tall(X)<~>~brave(X))))&
((creative(paul)<~>~rich(paul)))&
((~curious(fred)|~happy(fred)))&
((tall(fred)|~old(fred))) | ~tall(mary) | [] | null | 0 |
Everyone who is either brave or not rich is either kind or not quiet and vice versa.
If paul is not kind or old then john is rich and vice versa.
Everyone who is quiet is either not happy or generous and vice versa.
Everyone who is both not old and not tall is either not calm or curious and vice versa.
If someone is either not quiet or funny then mary is not brave.
Everyone who is both old and not strong is not wise or old and vice versa.
If paul is either wise or not rich then someone is either not tall or kind.
If someone is wise then someone is not generous.
Everyone who is not calm or kind is generous or brave.
If someone is either not brave or not wise then lucy is not curious or not generous.
Everyone who is both not generous and not quiet is not rich or old and vice versa.
Everyone who is not rich or kind is both not calm and not tall.
If lucy is either not brave or wise then someone is patient or not calm and vice versa.
Everyone who is humble or patient is funny or not happy and vice versa.
Everyone who is not strong or generous is wise or calm and vice versa.
If someone is both funny and quiet then someone is brave or not generous and vice versa.
Someone is either not humble or generous.
Someone is both happy and not funny.
Paul is happy or creative.
Someone is both not brave and not quiet.
John is either wise or not curious.
Susan is either funny or not funny.
Someone is humble or quiet.
Someone is quiet or tall. | Mary is not wise. | contradiction | (![X]:((brave(X)<~>~rich(X))<=>(kind(X)<~>~quiet(X))))&
(((~kind(paul)|old(paul)))<=>(rich(john)))&
(![X]:(quiet(X)<=>(~happy(X)<~>generous(X))))&
(![X]:((~old(X)&~tall(X))<=>(~calm(X)<~>curious(X))))&
((?[X]:((~quiet(X)<~>funny(X))))=>(~brave(mary)))&
(![X]:((old(X)&~strong(X))<=>(~wise(X)|old(X))))&
(((wise(paul)<~>~rich(paul)))=>(?[X]:((~tall(X)<~>kind(X)))))&
((?[X]:(wise(X)))=>(?[X]:(~generous(X))))&
(![X]:((~calm(X)|kind(X))=>(generous(X)|brave(X))))&
((?[X]:((~brave(X)<~>~wise(X))))=>((~curious(lucy)|~generous(lucy))))&
(![X]:((~generous(X)&~quiet(X))<=>(~rich(X)|old(X))))&
(![X]:((~rich(X)|kind(X))=>(~calm(X)&~tall(X))))&
(((~brave(lucy)<~>wise(lucy)))<=>(?[X]:((patient(X)|~calm(X)))))&
(![X]:((humble(X)|patient(X))<=>(funny(X)|~happy(X))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)|calm(X))))&
((?[X]:((funny(X)&quiet(X))))<=>(?[X]:((brave(X)|~generous(X)))))&
(?[X]:((~humble(X)<~>generous(X))))&
(?[X]:((happy(X)&~funny(X))))&
((happy(paul)|creative(paul)))&
(?[X]:((~brave(X)&~quiet(X))))&
((wise(john)<~>~curious(john)))&
((funny(susan)<~>~funny(susan)))&
(?[X]:((humble(X)|quiet(X))))&
(?[X]:((quiet(X)|tall(X)))) | ~wise(mary) | [
"p0",
"p4",
"p5",
"p7",
"p10",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7525593290773376534506994
% SZS output start Proof for 7525593290773376534506994
1. ! [X0] : ((brave(X0) <~> ~rich(X0)) <=> (kind(X0) <~> ~quiet(X0))) [input p0]
5. ? [X0] : (~quiet(X0) <~> funny(X0)) => ~brave(mary) [input p4]
6. ! [X0] : ((~strong(X0) & old(X0)) <=> (old(X0) | ~wise(X0))) [input p5]
8. ? [X0] : wise(X0) => ? [X0] : ~generous(X0) [input p7]
11. ! [X0] : ((~quiet(X0) & ~generous(X0)) <=> (old(X0) | ~rich(X0))) [input p10]
12. ! [X0] : ((kind(X0) | ~rich(X0)) => (~tall(X0) & ~calm(X0))) [input p11]
15. ! [X0] : ((generous(X0) | ~strong(X0)) <=> (calm(X0) | wise(X0))) [input p14]
16. ? [X0] : (quiet(X0) & funny(X0)) <=> ? [X0] : (~generous(X0) | brave(X0)) [input p15]
25. ~wise(mary) [input hypothesis]
26. ? [X0] : wise(X0) => ? [X1] : ~generous(X1) [rectify 8]
27. ? [X0] : (quiet(X0) & funny(X0)) <=> ? [X1] : (~generous(X1) | brave(X1)) [rectify 16]
29. ~brave(mary) | ! [X0] : (~quiet(X0) <=> funny(X0)) [ennf transformation 5]
31. ? [X1] : ~generous(X1) | ! [X0] : ~wise(X0) [ennf transformation 26]
36. ! [X0] : ((~tall(X0) & ~calm(X0)) | (~kind(X0) & rich(X0))) [ennf transformation 12]
37. ! [X0] : ((((rich(X0) | ~brave(X0)) & (~rich(X0) | brave(X0))) | ((kind(X0) | quiet(X0)) & (~quiet(X0) | ~kind(X0)))) & (((quiet(X0) | ~kind(X0)) & (~quiet(X0) | kind(X0))) | ((brave(X0) | rich(X0)) & (~rich(X0) | ~brave(X0))))) [nnf transformation 1]
43. ~brave(mary) | ! [X0] : ((~quiet(X0) | ~funny(X0)) & (funny(X0) | quiet(X0))) [nnf transformation 29]
44. ! [X0] : (((~strong(X0) & old(X0)) | (~old(X0) & wise(X0))) & ((old(X0) | ~wise(X0)) | (strong(X0) | ~old(X0)))) [nnf transformation 6]
45. ! [X0] : (((~strong(X0) & old(X0)) | (~old(X0) & wise(X0))) & (old(X0) | ~wise(X0) | strong(X0) | ~old(X0))) [flattening 44]
49. ? [X0] : ~generous(X0) | ! [X1] : ~wise(X1) [rectify 31]
50. ? [X0] : ~generous(X0) => ~generous(sK1) [choice axiom]
51. ~generous(sK1) | ! [X1] : ~wise(X1) [skolemisation 49,50]
53. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (quiet(X0) | generous(X0)))) [nnf transformation 11]
54. ! [X0] : (((~quiet(X0) & ~generous(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | quiet(X0) | generous(X0))) [flattening 53]
61. ! [X0] : (((generous(X0) | ~strong(X0)) | (~calm(X0) & ~wise(X0))) & ((calm(X0) | wise(X0)) | (~generous(X0) & strong(X0)))) [nnf transformation 15]
62. ! [X0] : ((generous(X0) | ~strong(X0) | (~calm(X0) & ~wise(X0))) & (calm(X0) | wise(X0) | (~generous(X0) & strong(X0)))) [flattening 61]
63. (? [X0] : (quiet(X0) & funny(X0)) | ! [X1] : (generous(X1) & ~brave(X1))) & (? [X1] : (~generous(X1) | brave(X1)) | ! [X0] : (~quiet(X0) | ~funny(X0))) [nnf transformation 27]
64. (? [X0] : (quiet(X0) & funny(X0)) | ! [X1] : (generous(X1) & ~brave(X1))) & (? [X2] : (~generous(X2) | brave(X2)) | ! [X3] : (~quiet(X3) | ~funny(X3))) [rectify 63]
65. ? [X0] : (quiet(X0) & funny(X0)) => (quiet(sK3) & funny(sK3)) [choice axiom]
66. ? [X2] : (~generous(X2) | brave(X2)) => (~generous(sK4) | brave(sK4)) [choice axiom]
67. ((quiet(sK3) & funny(sK3)) | ! [X1] : (generous(X1) & ~brave(X1))) & ((~generous(sK4) | brave(sK4)) | ! [X3] : (~quiet(X3) | ~funny(X3))) [skolemisation 64,66,65]
86. ~rich(X0) | brave(X0) | kind(X0) | quiet(X0) [cnf transformation 37]
103. ~brave(mary) | ~quiet(X0) | ~funny(X0) [cnf transformation 43]
105. wise(X0) | old(X0) [cnf transformation 45]
107. ~strong(X0) | wise(X0) [cnf transformation 45]
113. ~generous(sK1) | ~wise(X1) [cnf transformation 51]
120. ~generous(X0) | ~old(X0) [cnf transformation 54]
122. ~old(X0) | ~quiet(X0) [cnf transformation 54]
123. ~calm(X0) | rich(X0) [cnf transformation 36]
124. ~calm(X0) | ~kind(X0) [cnf transformation 36]
137. calm(X0) | wise(X0) | strong(X0) [cnf transformation 62]
143. funny(sK3) | generous(X1) [cnf transformation 67]
145. quiet(sK3) | generous(X1) [cnf transformation 67]
158. ~wise(mary) [cnf transformation 25]
175. 4 <=> ! [X0] : (~quiet(X0) | ~funny(X0)) [avatar definition]
176. ~funny(X0) | ~quiet(X0) <- (4) [avatar component clause 175]
178. 5 <=> brave(mary) [avatar definition]
180. ~brave(mary) <- (~5) [avatar component clause 178]
181. 4 | ~5 [avatar split clause 103,178,175]
207. 11 <=> ! [X1] : ~wise(X1) [avatar definition]
208. ~wise(X1) <- (11) [avatar component clause 207]
210. 12 <=> generous(sK1) [avatar definition]
212. ~generous(sK1) <- (~12) [avatar component clause 210]
213. 11 | ~12 [avatar split clause 113,210,207]
259. wise(X0) | calm(X0) [subsumption resolution 137,107]
261. 23 <=> ! [X1] : generous(X1) [avatar definition]
262. generous(X1) <- (23) [avatar component clause 261]
264. 24 <=> quiet(sK3) [avatar definition]
266. quiet(sK3) <- (24) [avatar component clause 264]
267. 23 | 24 [avatar split clause 145,264,261]
273. 26 <=> funny(sK3) [avatar definition]
275. funny(sK3) <- (26) [avatar component clause 273]
276. 23 | 26 [avatar split clause 143,273,261]
283. 28 <=> generous(sK4) [avatar definition]
284. generous(sK4) <- (28) [avatar component clause 283]
285. ~generous(sK4) <- (~28) [avatar component clause 283]
325. $false <- (~12, 23) [subsumption resolution 212,262]
326. 12 | ~23 [avatar contradiction clause 325]
327. $false <- (23, ~28) [resolution 285,262]
328. ~23 | 28 [avatar contradiction clause 327]
331. old(mary) [resolution 105,158]
338. ~quiet(mary) [resolution 122,331]
341. calm(mary) [resolution 259,158]
357. ~kind(mary) [resolution 341,124]
358. rich(mary) [resolution 341,123]
399. old(X1) <- (11) [resolution 208,105]
415. ~old(sK4) <- (28) [resolution 284,120]
418. $false <- (11, 28) [subsumption resolution 415,399]
419. ~11 | ~28 [avatar contradiction clause 418]
492. brave(mary) | kind(mary) | quiet(mary) [resolution 358,86]
499. kind(mary) | quiet(mary) <- (~5) [subsumption resolution 492,180]
500. quiet(mary) <- (~5) [subsumption resolution 499,357]
501. $false <- (~5) [subsumption resolution 500,338]
502. 5 [avatar contradiction clause 501]
515. ~quiet(sK3) <- (4, 26) [resolution 176,275]
516. $false <- (4, 24, 26) [subsumption resolution 515,266]
517. ~4 | ~24 | ~26 [avatar contradiction clause 516]
518. $false [avatar sat refutation 181,213,267,276,326,328,419,502,517]
% SZS output end Proof for 7525593290773376534506994
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then mary is both wise and not calm. If john is both not calm and quiet then someone is not creative and vice versa. If john is humble or not creative then someone is both not quiet and funny and vice versa. Everyone who is tall or funny is both kind and happy. Everyone who is rich is either not funny or not happy and vice versa. If someone is tall or not curious then someone is either funny or tall and vice versa. Everyone who is not rich is either not funny or kind. If lucy is either not humble or funny then someone is brave or calm and vice versa. Everyone who is calm or not old is old and vice versa. Everyone who is not brave or not happy is curious or funny. If someone is either not old or not brave then fred is both not wise and not calm and vice versa. Everyone who is either generous or not humble is either wise or not tall and vice versa. Everyone who is either humble or rich is happy or not old and vice versa. Everyone who is not brave or curious is either not creative or not strong. If paul is not curious or strong then someone is generous and vice versa. Everyone who is creative or not happy is tall or not strong. Someone is quiet or patient. Someone is not funny. Someone is wise or creative. Alice is either not humble or wise. Alice is not patient or strong. Someone is either not rich or not wise. John is either not patient or patient. | Lucy is generous. | contradiction | ((?[X]:(kind(X)))=>((wise(mary)&~calm(mary))))&
(((~calm(john)&quiet(john)))<=>(?[X]:(~creative(X))))&
(((humble(john)|~creative(john)))<=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:((tall(X)|funny(X))=>(kind(X)&happy(X))))&
(![X]:(rich(X)<=>(~funny(X)<~>~happy(X))))&
((?[X]:((tall(X)|~curious(X))))<=>(?[X]:((funny(X)<~>tall(X)))))&
(![X]:(~rich(X)=>(~funny(X)<~>kind(X))))&
(((~humble(lucy)<~>funny(lucy)))<=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((calm(X)|~old(X))<=>old(X)))&
(![X]:((~brave(X)|~happy(X))=>(curious(X)|funny(X))))&
((?[X]:((~old(X)<~>~brave(X))))<=>((~wise(fred)&~calm(fred))))&
(![X]:((generous(X)<~>~humble(X))<=>(wise(X)<~>~tall(X))))&
(![X]:((humble(X)<~>rich(X))<=>(happy(X)|~old(X))))&
(![X]:((~brave(X)|curious(X))=>(~creative(X)<~>~strong(X))))&
(((~curious(paul)|strong(paul)))<=>(?[X]:(generous(X))))&
(![X]:((creative(X)|~happy(X))=>(tall(X)|~strong(X))))&
(?[X]:((quiet(X)|patient(X))))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)|creative(X))))&
((~humble(alice)<~>wise(alice)))&
((~patient(alice)|strong(alice)))&
(?[X]:((~rich(X)<~>~wise(X))))&
((~patient(john)<~>patient(john))) | generous(lucy) | [
"p0",
"p1",
"p3",
"p5",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6269620151972421989198418
% SZS output start Proof for 6269620151972421989198418
1. ? [X0] : kind(X0) => (~calm(mary) & wise(mary)) [input p0]
2. (quiet(john) & ~calm(john)) <=> ? [X0] : ~creative(X0) [input p1]
4. ! [X0] : ((funny(X0) | tall(X0)) => (happy(X0) & kind(X0))) [input p3]
6. ? [X0] : (~curious(X0) | tall(X0)) <=> ? [X0] : (funny(X0) <~> tall(X0)) [input p5]
9. ! [X0] : ((~old(X0) | calm(X0)) <=> old(X0)) [input p8]
14. ! [X0] : ((curious(X0) | ~brave(X0)) => (~creative(X0) <~> ~strong(X0))) [input p13]
15. (strong(paul) | ~curious(paul)) <=> ? [X0] : generous(X0) [input p14]
24. generous(lucy) [input hypothesis]
25. ? [X0] : (~curious(X0) | tall(X0)) <=> ? [X1] : (funny(X1) <~> tall(X1)) [rectify 6]
26. (~calm(mary) & wise(mary)) | ! [X0] : ~kind(X0) [ennf transformation 1]
27. ! [X0] : ((happy(X0) & kind(X0)) | (~funny(X0) & ~tall(X0))) [ennf transformation 4]
31. ! [X0] : ((~creative(X0) <~> ~strong(X0)) | (~curious(X0) & brave(X0))) [ennf transformation 14]
34. ((quiet(john) & ~calm(john)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | (~quiet(john) | calm(john))) [nnf transformation 2]
35. ((quiet(john) & ~calm(john)) | ! [X0] : creative(X0)) & (? [X0] : ~creative(X0) | ~quiet(john) | calm(john)) [flattening 34]
36. ((quiet(john) & ~calm(john)) | ! [X0] : creative(X0)) & (? [X1] : ~creative(X1) | ~quiet(john) | calm(john)) [rectify 35]
37. ? [X1] : ~creative(X1) => ~creative(sK0) [choice axiom]
38. ((quiet(john) & ~calm(john)) | ! [X0] : creative(X0)) & (~creative(sK0) | ~quiet(john) | calm(john)) [skolemisation 36,37]
45. (? [X0] : (~curious(X0) | tall(X0)) | ! [X1] : ((funny(X1) | ~tall(X1)) & (tall(X1) | ~funny(X1)))) & (? [X1] : ((~tall(X1) | ~funny(X1)) & (tall(X1) | funny(X1))) | ! [X0] : (curious(X0) & ~tall(X0))) [nnf transformation 25]
46. (? [X0] : (~curious(X0) | tall(X0)) | ! [X1] : ((funny(X1) | ~tall(X1)) & (tall(X1) | ~funny(X1)))) & (? [X2] : ((~tall(X2) | ~funny(X2)) & (tall(X2) | funny(X2))) | ! [X3] : (curious(X3) & ~tall(X3))) [rectify 45]
47. ? [X0] : (~curious(X0) | tall(X0)) => (~curious(sK2) | tall(sK2)) [choice axiom]
48. ? [X2] : ((~tall(X2) | ~funny(X2)) & (tall(X2) | funny(X2))) => ((~tall(sK3) | ~funny(sK3)) & (tall(sK3) | funny(sK3))) [choice axiom]
49. ((~curious(sK2) | tall(sK2)) | ! [X1] : ((funny(X1) | ~tall(X1)) & (tall(X1) | ~funny(X1)))) & (((~tall(sK3) | ~funny(sK3)) & (tall(sK3) | funny(sK3))) | ! [X3] : (curious(X3) & ~tall(X3))) [skolemisation 46,48,47]
55. ! [X0] : (((~old(X0) | calm(X0)) | ~old(X0)) & (old(X0) | (old(X0) & ~calm(X0)))) [nnf transformation 9]
56. ! [X0] : ((~old(X0) | calm(X0) | ~old(X0)) & (old(X0) | (old(X0) & ~calm(X0)))) [flattening 55]
65. ! [X0] : (((strong(X0) | creative(X0)) & (~strong(X0) | ~creative(X0))) | (~curious(X0) & brave(X0))) [nnf transformation 31]
66. ((strong(paul) | ~curious(paul)) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (~strong(paul) & curious(paul))) [nnf transformation 15]
67. (strong(paul) | ~curious(paul) | ! [X0] : ~generous(X0)) & (? [X0] : generous(X0) | (~strong(paul) & curious(paul))) [flattening 66]
68. (strong(paul) | ~curious(paul) | ! [X0] : ~generous(X0)) & (? [X1] : generous(X1) | (~strong(paul) & curious(paul))) [rectify 67]
69. ? [X1] : generous(X1) => generous(sK6) [choice axiom]
70. (strong(paul) | ~curious(paul) | ! [X0] : ~generous(X0)) & (generous(sK6) | (~strong(paul) & curious(paul))) [skolemisation 68,69]
83. ~calm(mary) | ~kind(X0) [cnf transformation 26]
85. ~calm(john) | creative(X0) [cnf transformation 38]
92. ~tall(X0) | kind(X0) [cnf transformation 27]
93. ~funny(X0) | kind(X0) [cnf transformation 27]
101. tall(sK3) | funny(sK3) | curious(X3) [cnf transformation 49]
115. old(X0) | old(X0) [cnf transformation 56]
116. ~old(X0) | calm(X0) | ~old(X0) [cnf transformation 56]
140. ~strong(X0) | ~creative(X0) | ~curious(X0) [cnf transformation 65]
145. strong(paul) | ~curious(paul) | ~generous(X0) [cnf transformation 70]
158. generous(lucy) [cnf transformation 24]
159. old(X0) [duplicate literal removal 115]
160. ~old(X0) | calm(X0) [duplicate literal removal 116]
162. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
163. ~kind(X0) <- (1) [avatar component clause 162]
165. 2 <=> calm(mary) [avatar definition]
167. ~calm(mary) <- (~2) [avatar component clause 165]
168. 1 | ~2 [avatar split clause 83,165,162]
175. 4 <=> ! [X0] : creative(X0) [avatar definition]
176. creative(X0) <- (4) [avatar component clause 175]
183. 6 <=> calm(john) [avatar definition]
185. ~calm(john) <- (~6) [avatar component clause 183]
186. 4 | ~6 [avatar split clause 85,183,175]
235. 17 <=> ! [X3] : curious(X3) [avatar definition]
236. curious(X3) <- (17) [avatar component clause 235]
238. 18 <=> funny(sK3) [avatar definition]
239. funny(sK3) <- (18) [avatar component clause 238]
242. 19 <=> tall(sK3) [avatar definition]
243. tall(sK3) <- (19) [avatar component clause 242]
250. 17 | 18 | 19 [avatar split clause 101,242,238,235]
306. 31 <=> ! [X0] : ~generous(X0) [avatar definition]
307. ~generous(X0) <- (31) [avatar component clause 306]
309. 32 <=> curious(paul) [avatar definition]
310. curious(paul) <- (32) [avatar component clause 309]
311. ~curious(paul) <- (~32) [avatar component clause 309]
313. 33 <=> strong(paul) [avatar definition]
315. strong(paul) <- (33) [avatar component clause 313]
316. 31 | ~32 | 33 [avatar split clause 145,313,309,306]
373. $false <- (31) [resolution 307,158]
374. ~31 [avatar contradiction clause 373]
376. kind(sK3) <- (18) [resolution 93,239]
379. calm(X0) [resolution 160,159]
382. $false <- (~2) [subsumption resolution 167,379]
383. 2 [avatar contradiction clause 382]
385. $false <- (1, 18) [resolution 163,376]
386. ~1 | ~18 [avatar contradiction clause 385]
389. kind(sK3) <- (19) [resolution 243,92]
390. $false <- (1, 19) [subsumption resolution 389,163]
391. ~1 | ~19 [avatar contradiction clause 390]
420. ~creative(paul) | ~curious(paul) <- (33) [resolution 140,315]
421. ~curious(paul) <- (4, 33) [subsumption resolution 420,176]
422. $false <- (4, 32, 33) [subsumption resolution 421,310]
423. ~4 | ~32 | ~33 [avatar contradiction clause 422]
425. $false <- (~6) [subsumption resolution 185,379]
426. 6 [avatar contradiction clause 425]
428. $false <- (17, ~32) [subsumption resolution 311,236]
429. ~17 | 32 [avatar contradiction clause 428]
430. $false [avatar sat refutation 168,186,250,316,374,383,386,391,423,426,429]
% SZS output end Proof for 6269620151972421989198418
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both old and not old then someone is quiet or not humble and vice versa. If lucy is not creative or not patient then someone is both generous and tall and vice versa. Everyone who is either not brave or humble is not curious and vice versa. Everyone who is either funny or not funny is calm. Everyone who is both not creative and not tall is not strong or curious. If someone is wise then alice is either quiet or not funny and vice versa. Everyone who is either generous or humble is not quiet. Everyone who is not wise is calm or not quiet and vice versa. Everyone who is both calm and happy is both not quiet and not calm. If someone is kind then someone is both strong and not wise. If paul is humble or generous then susan is not happy. Everyone who is both not strong and not creative is either quiet or not humble. If someone is strong or generous then john is both not curious and kind and vice versa. Everyone who is old or not strong is either brave or not tall. Everyone who is both patient and creative is either not wise or not curious. If someone is not humble then alice is either humble or calm and vice versa. Lucy is generous. Susan is kind or old. John is both not old and not generous. Fred is either not rich or not patient. Susan is both curious and strong. Susan is quiet or not kind. | John is strong. | neutral | ((?[X]:((old(X)&~old(X))))<=>(?[X]:((quiet(X)|~humble(X)))))&
(((~creative(lucy)|~patient(lucy)))<=>(?[X]:((generous(X)&tall(X)))))&
(![X]:((~brave(X)<~>humble(X))<=>~curious(X)))&
(![X]:((funny(X)<~>~funny(X))=>calm(X)))&
(![X]:((~creative(X)&~tall(X))=>(~strong(X)|curious(X))))&
((?[X]:(wise(X)))<=>((quiet(alice)<~>~funny(alice))))&
(![X]:((generous(X)<~>humble(X))=>~quiet(X)))&
(![X]:(~wise(X)<=>(calm(X)|~quiet(X))))&
(![X]:((calm(X)&happy(X))=>(~quiet(X)&~calm(X))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)&~wise(X)))))&
(((humble(paul)|generous(paul)))=>(~happy(susan)))&
(![X]:((~strong(X)&~creative(X))=>(quiet(X)<~>~humble(X))))&
((?[X]:((strong(X)|generous(X))))<=>((~curious(john)&kind(john))))&
(![X]:((old(X)|~strong(X))=>(brave(X)<~>~tall(X))))&
(![X]:((patient(X)&creative(X))=>(~wise(X)<~>~curious(X))))&
((?[X]:(~humble(X)))<=>((humble(alice)<~>calm(alice))))&
(generous(lucy))&
((kind(susan)|old(susan)))&
((~old(john)&~generous(john)))&
((~rich(fred)<~>~patient(fred)))&
((curious(susan)&strong(susan)))&
((quiet(susan)|~kind(susan))) | strong(john) | [] | null | 0 |
If someone is generous or funny then someone is both quiet and creative. Everyone who is happy is either patient or wise. If susan is not rich or curious then someone is both not brave and rich and vice versa. Everyone who is not humble or not happy is brave and vice versa. Everyone who is not creative or humble is both not tall and tall. If someone is either old or not happy then alice is humble or not creative. If paul is either patient or not humble then someone is either not brave or not generous. Everyone who is kind is generous or not tall and vice versa. If someone is either strong or not patient then someone is not humble or kind. If mary is strong then someone is not tall or not quiet and vice versa. Everyone who is both tall and patient is both not generous and creative. Everyone who is not kind is both not rich and curious. Everyone who is not humble is not funny or creative. If someone is curious or tall then someone is either not strong or not quiet and vice versa. Everyone who is not kind is either not generous or quiet. Mary is either wise or not happy. Someone is either quiet or funny. Fred is not calm or tall. Paul is both creative and brave. Mary is wise or happy. Someone is rich. Lucy is either generous or not wise. | Susan is not happy. | neutral | ((?[X]:((generous(X)|funny(X))))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:(happy(X)=>(patient(X)<~>wise(X))))&
(((~rich(susan)|curious(susan)))<=>(?[X]:((~brave(X)&rich(X)))))&
(![X]:((~humble(X)|~happy(X))<=>brave(X)))&
(![X]:((~creative(X)|humble(X))=>(~tall(X)&tall(X))))&
((?[X]:((old(X)<~>~happy(X))))=>((humble(alice)|~creative(alice))))&
(((patient(paul)<~>~humble(paul)))=>(?[X]:((~brave(X)<~>~generous(X)))))&
(![X]:(kind(X)<=>(generous(X)|~tall(X))))&
((?[X]:((strong(X)<~>~patient(X))))=>(?[X]:((~humble(X)|kind(X)))))&
((strong(mary))<=>(?[X]:((~tall(X)|~quiet(X)))))&
(![X]:((tall(X)&patient(X))=>(~generous(X)&creative(X))))&
(![X]:(~kind(X)=>(~rich(X)&curious(X))))&
(![X]:(~humble(X)=>(~funny(X)|creative(X))))&
((?[X]:((curious(X)|tall(X))))<=>(?[X]:((~strong(X)<~>~quiet(X)))))&
(![X]:(~kind(X)=>(~generous(X)<~>quiet(X))))&
((wise(mary)<~>~happy(mary)))&
(?[X]:((quiet(X)<~>funny(X))))&
((~calm(fred)|tall(fred)))&
((creative(paul)&brave(paul)))&
((wise(mary)|happy(mary)))&
(?[X]:(rich(X)))&
((generous(lucy)<~>~wise(lucy))) | ~happy(susan) | [] | null | 0 |
If someone is not old then alice is either not humble or not quiet and vice versa.
If someone is both curious and not quiet then someone is both not wise and not generous.
If john is strong then someone is not tall or kind.
Everyone who is both not patient and not wise is both not humble and not patient.
Everyone who is strong or not tall is both not calm and rich.
Everyone who is not quiet or not humble is either old or quiet.
Everyone who is not generous is funny.
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.
If someone is either not happy or quiet then someone is curious or funny.
Everyone who is both not curious and funny is both wise and not patient.
Someone is either generous or old.
Alice is brave or not patient.
Someone is either kind or not rich.
Someone is not humble.
Susan is both not happy and not strong.
Someone is both not rich and not patient. | Susan is patient. | entailment | ((?[X]:(~old(X)))<=>((~humble(alice)<~>~quiet(alice))))&
((?[X]:((curious(X)&~quiet(X))))=>(?[X]:((~wise(X)&~generous(X)))))&
((strong(john))=>(?[X]:((~tall(X)|kind(X)))))&
(![X]:((~patient(X)&~wise(X))=>(~humble(X)&~patient(X))))&
(![X]:((strong(X)|~tall(X))=>(~calm(X)&rich(X))))&
(![X]:((~quiet(X)|~humble(X))=>(old(X)<~>quiet(X))))&
(![X]:(~generous(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]:((~happy(X)<~>quiet(X))))=>(?[X]:((curious(X)|funny(X)))))&
(![X]:((~curious(X)&funny(X))=>(wise(X)&~patient(X))))&
(?[X]:((generous(X)<~>old(X))))&
((brave(alice)|~patient(alice)))&
(?[X]:((kind(X)<~>~rich(X))))&
(?[X]:(~humble(X)))&
((~happy(susan)&~strong(susan)))&
(?[X]:((~rich(X)&~patient(X)))) | patient(susan) | [
"p11",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4098451425395207609739462
% SZS output start Proof for 4098451425395207609739462
12. ! [X0] : ((~brave(X0) | humble(X0)) => (happy(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((happy(X0) | ~brave(X0)) <=> (strong(X0) | ~patient(X0))) [input p12]
21. ~strong(susan) & ~happy(susan) [input p20]
23. ~patient(susan) [input hypothesis]
37. ! [X0] : ((happy(X0) & ~happy(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 12]
52. ! [X0] : (((happy(X0) | ~brave(X0)) | (~strong(X0) & patient(X0))) & ((strong(X0) | ~patient(X0)) | (~happy(X0) & brave(X0)))) [nnf transformation 13]
53. ! [X0] : ((happy(X0) | ~brave(X0) | (~strong(X0) & patient(X0))) & (strong(X0) | ~patient(X0) | (~happy(X0) & brave(X0)))) [flattening 52]
94. ~happy(X0) | brave(X0) [cnf transformation 37]
96. happy(X0) | brave(X0) [cnf transformation 37]
99. happy(X0) | ~brave(X0) | patient(X0) [cnf transformation 53]
117. ~happy(susan) [cnf transformation 21]
121. ~patient(susan) [cnf transformation 23]
177. brave(X0) [subsumption resolution 94,96]
180. happy(X0) | patient(X0) [subsumption resolution 99,177]
232. patient(susan) [resolution 180,117]
233. $false [subsumption resolution 232,121]
% SZS output end Proof for 4098451425395207609739462
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or quiet is both not kind and not brave and vice versa.
If someone is both not quiet and not patient then someone is happy and vice versa.
If someone is patient then mary is either patient or creative.
If someone is both not humble and generous then someone is humble or strong and vice versa.
Everyone who is calm is either not calm or not old.
Everyone who is humble or patient is both wise and tall and vice versa.
If alice is either curious or not funny then someone is either old or not humble and vice versa.
Everyone who is funny is not strong.
Everyone who is either strong or not happy is patient or quiet.
Everyone who is tall is either kind or happy.
Everyone who is happy or tall is not brave.
If someone is humble then someone is patient or not wise and vice versa.
If mary is both not happy and creative then someone is tall or not funny.
Everyone who is not happy or creative is both happy and generous and vice versa.
If john is both not brave and not calm then someone is either curious or funny.
Everyone who is not funny or tall is not humble or strong and vice versa.
John is happy or not happy.
John is not patient.
Someone is either old or brave.
Susan is patient.
Someone is tall or happy.
Paul is not creative or not old.
Alice is either not wise or strong. | Mary is not funny. | neutral | (![X]:((~happy(X)|quiet(X))<=>(~kind(X)&~brave(X))))&
((?[X]:((~quiet(X)&~patient(X))))<=>(?[X]:(happy(X))))&
((?[X]:(patient(X)))=>((patient(mary)<~>creative(mary))))&
((?[X]:((~humble(X)&generous(X))))<=>(?[X]:((humble(X)|strong(X)))))&
(![X]:(calm(X)=>(~calm(X)<~>~old(X))))&
(![X]:((humble(X)|patient(X))<=>(wise(X)&tall(X))))&
(((curious(alice)<~>~funny(alice)))<=>(?[X]:((old(X)<~>~humble(X)))))&
(![X]:(funny(X)=>~strong(X)))&
(![X]:((strong(X)<~>~happy(X))=>(patient(X)|quiet(X))))&
(![X]:(tall(X)=>(kind(X)<~>happy(X))))&
(![X]:((happy(X)|tall(X))=>~brave(X)))&
((?[X]:(humble(X)))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~happy(mary)&creative(mary)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((~happy(X)|creative(X))<=>(happy(X)&generous(X))))&
(((~brave(john)&~calm(john)))=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~humble(X)|strong(X))))&
((happy(john)|~happy(john)))&
(~patient(john))&
(?[X]:((old(X)<~>brave(X))))&
(patient(susan))&
(?[X]:((tall(X)|happy(X))))&
((~creative(paul)|~old(paul)))&
((~wise(alice)<~>strong(alice))) | ~funny(mary) | [] | null | 0 |
If someone is happy then someone is kind or rich and vice versa. Everyone who is both brave and curious is both brave and not old and vice versa. Everyone who is not brave or brave is both not old and strong. Everyone who is strong is both not creative and not brave and vice versa. If lucy is either rich or calm then paul is not brave. Everyone who is not old is either wise or creative. Everyone who is both patient and humble is both humble and old. Everyone who is either tall or not patient is either not kind or wise and vice versa. Everyone who is creative is not curious or calm and vice versa. If fred is generous or not curious then susan is not humble and vice versa. If someone is either patient or not old then someone is both not humble and creative. If someone is both wise and not curious then someone is both not rich and not old. Everyone who is both tall and funny is not tall and vice versa. Everyone who is both not generous and not kind is either not generous or not curious and vice versa. Lucy is either not generous or kind. Someone is not creative or not tall. Someone is wise or not wise. Someone is brave or not rich. | Lucy is generous. | entailment | ((?[X]:(happy(X)))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((brave(X)&curious(X))<=>(brave(X)&~old(X))))&
(![X]:((~brave(X)|brave(X))=>(~old(X)&strong(X))))&
(![X]:(strong(X)<=>(~creative(X)&~brave(X))))&
(((rich(lucy)<~>calm(lucy)))=>(~brave(paul)))&
(![X]:(~old(X)=>(wise(X)<~>creative(X))))&
(![X]:((patient(X)&humble(X))=>(humble(X)&old(X))))&
(![X]:((tall(X)<~>~patient(X))<=>(~kind(X)<~>wise(X))))&
(![X]:(creative(X)<=>(~curious(X)|calm(X))))&
(((generous(fred)|~curious(fred)))<=>(~humble(susan)))&
((?[X]:((patient(X)<~>~old(X))))=>(?[X]:((~humble(X)&creative(X)))))&
((?[X]:((wise(X)&~curious(X))))=>(?[X]:((~rich(X)&~old(X)))))&
(![X]:((tall(X)&funny(X))<=>~tall(X)))&
(![X]:((~generous(X)&~kind(X))<=>(~generous(X)<~>~curious(X))))&
((~generous(lucy)<~>kind(lucy)))&
(?[X]:((~creative(X)|~tall(X))))&
(?[X]:((wise(X)|~wise(X))))&
(?[X]:((brave(X)|~rich(X)))) | generous(lucy) | [
"p2",
"p3",
"p5",
"p7",
"p8",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2941165259737042456472625
% SZS output start Proof for 2941165259737042456472625
3. ! [X0] : ((brave(X0) | ~brave(X0)) => (strong(X0) & ~old(X0))) [input p2]
4. ! [X0] : (strong(X0) <=> (~brave(X0) & ~creative(X0))) [input p3]
6. ! [X0] : (~old(X0) => (wise(X0) <~> creative(X0))) [input p5]
8. ! [X0] : ((tall(X0) <~> ~patient(X0)) <=> (~kind(X0) <~> wise(X0))) [input p7]
9. ! [X0] : (creative(X0) <=> (calm(X0) | ~curious(X0))) [input p8]
11. ? [X0] : (patient(X0) <~> ~old(X0)) => ? [X0] : (creative(X0) & ~humble(X0)) [input p10]
13. ! [X0] : ((funny(X0) & tall(X0)) <=> ~tall(X0)) [input p12]
14. ! [X0] : ((~kind(X0) & ~generous(X0)) <=> (~generous(X0) <~> ~curious(X0))) [input p13]
19. ~generous(lucy) [input hypothesis]
21. ? [X0] : (patient(X0) <~> ~old(X0)) => ? [X1] : (creative(X1) & ~humble(X1)) [rectify 11]
23. ! [X0] : (strong(X0) => (~brave(X0) & ~creative(X0))) [unused predicate definition removal 4]
24. ! [X0] : ((strong(X0) & ~old(X0)) | (~brave(X0) & brave(X0))) [ennf transformation 3]
25. ! [X0] : ((~brave(X0) & ~creative(X0)) | ~strong(X0)) [ennf transformation 23]
27. ! [X0] : ((wise(X0) <~> creative(X0)) | old(X0)) [ennf transformation 6]
30. ? [X1] : (creative(X1) & ~humble(X1)) | ! [X0] : (patient(X0) <=> ~old(X0)) [ennf transformation 21]
40. ! [X0] : (((~creative(X0) | ~wise(X0)) & (creative(X0) | wise(X0))) | old(X0)) [nnf transformation 27]
41. ! [X0] : ((((patient(X0) | ~tall(X0)) & (~patient(X0) | tall(X0))) | ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0)))) & (((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | ((tall(X0) | patient(X0)) & (~patient(X0) | ~tall(X0))))) [nnf transformation 8]
42. ! [X0] : ((creative(X0) | (~calm(X0) & curious(X0))) & ((calm(X0) | ~curious(X0)) | ~creative(X0))) [nnf transformation 9]
43. ! [X0] : ((creative(X0) | (~calm(X0) & curious(X0))) & (calm(X0) | ~curious(X0) | ~creative(X0))) [flattening 42]
46. ? [X1] : (creative(X1) & ~humble(X1)) | ! [X0] : ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0))) [nnf transformation 30]
47. ? [X0] : (creative(X0) & ~humble(X0)) | ! [X1] : ((patient(X1) | old(X1)) & (~old(X1) | ~patient(X1))) [rectify 46]
48. ? [X0] : (creative(X0) & ~humble(X0)) => (creative(sK2) & ~humble(sK2)) [choice axiom]
49. (creative(sK2) & ~humble(sK2)) | ! [X1] : ((patient(X1) | old(X1)) & (~old(X1) | ~patient(X1))) [skolemisation 47,48]
53. ! [X0] : (((funny(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) | ~tall(X0)))) [nnf transformation 13]
54. ! [X0] : (((funny(X0) & tall(X0)) | tall(X0)) & (~tall(X0) | ~funny(X0) | ~tall(X0))) [flattening 53]
55. ! [X0] : (((~kind(X0) & ~generous(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | (kind(X0) | generous(X0)))) [nnf transformation 14]
56. ! [X0] : (((~kind(X0) & ~generous(X0)) | ((~generous(X0) | curious(X0)) & (~curious(X0) | generous(X0)))) & (((curious(X0) | generous(X0)) & (~curious(X0) | ~generous(X0))) | kind(X0) | generous(X0))) [flattening 55]
71. ~old(X0) | brave(X0) [cnf transformation 24]
72. ~old(X0) | ~brave(X0) [cnf transformation 24]
73. strong(X0) | brave(X0) [cnf transformation 24]
74. ~brave(X0) | strong(X0) [cnf transformation 24]
75. ~creative(X0) | ~strong(X0) [cnf transformation 25]
79. creative(X0) | wise(X0) | old(X0) [cnf transformation 40]
85. ~wise(X0) | kind(X0) | ~patient(X0) | ~tall(X0) [cnf transformation 41]
92. creative(X0) | curious(X0) [cnf transformation 43]
100. creative(sK2) | patient(X1) | old(X1) [cnf transformation 49]
104. tall(X0) | tall(X0) [cnf transformation 54]
110. ~kind(X0) | ~curious(X0) | generous(X0) [cnf transformation 56]
117. ~generous(lucy) [cnf transformation 19]
121. tall(X0) [duplicate literal removal 104]
146. strong(X0) [subsumption resolution 73,74]
147. ~old(X0) [subsumption resolution 71,72]
149. ~creative(X0) [subsumption resolution 75,146]
150. wise(X0) | old(X0) [subsumption resolution 79,149]
151. wise(X0) [subsumption resolution 150,147]
156. ~tall(X0) | ~patient(X0) | kind(X0) [subsumption resolution 85,151]
158. curious(X0) [subsumption resolution 92,149]
170. patient(X1) | old(X1) [subsumption resolution 100,149]
171. patient(X1) [subsumption resolution 170,147]
173. ~kind(X0) | generous(X0) [subsumption resolution 110,158]
175. 9 <=> generous(lucy) [avatar definition]
177. ~generous(lucy) <- (~9) [avatar component clause 175]
184. ~9 [avatar split clause 117,175]
197. ~patient(X1) | kind(X1) [resolution 156,121]
199. kind(X1) [subsumption resolution 197,171]
200. generous(X0) [resolution 199,173]
201. $false <- (~9) [resolution 200,177]
202. 9 [avatar contradiction clause 201]
203. $false [avatar sat refutation 184,202]
% SZS output end Proof for 2941165259737042456472625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 is either not strong or humble and vice versa.
Everyone who is not curious or quiet is either happy or not rich.
If mary is both kind and not old then john is either generous or kind and vice versa.
Everyone who is brave or kind is both wise and not tall.
Everyone who is either generous or humble is either happy or not calm and vice versa.
Everyone who is either rich or not quiet is not creative.
Everyone who is not quiet is quiet or strong.
If mary is both calm and patient then someone is either not happy or strong and vice versa.
If someone is not patient or happy then alice is both not humble and tall.
If someone is kind then paul is old and vice versa.
Everyone who is not quiet is not creative or not quiet and vice versa.
Everyone who is either not strong or not generous is either creative or not quiet.
Everyone who is curious is either wise or generous.
Everyone who is old or strong is both quiet and not calm.
Everyone who is both curious and not creative is both humble and old.
Someone is either not curious or strong.
Someone is either not generous or not happy.
Someone is either funny or old.
Someone is either not curious or not creative.
Fred is both not wise and not tall.
Someone is both not brave and not tall.
Someone is both generous and not patient. | Mary is happy. | contradiction | (![X]:(old(X)<=>(~strong(X)<~>humble(X))))&
(![X]:((~curious(X)|quiet(X))=>(happy(X)<~>~rich(X))))&
(((kind(mary)&~old(mary)))<=>((generous(john)<~>kind(john))))&
(![X]:((brave(X)|kind(X))=>(wise(X)&~tall(X))))&
(![X]:((generous(X)<~>humble(X))<=>(happy(X)<~>~calm(X))))&
(![X]:((rich(X)<~>~quiet(X))=>~creative(X)))&
(![X]:(~quiet(X)=>(quiet(X)|strong(X))))&
(((calm(mary)&patient(mary)))<=>(?[X]:((~happy(X)<~>strong(X)))))&
((?[X]:((~patient(X)|happy(X))))=>((~humble(alice)&tall(alice))))&
((?[X]:(kind(X)))<=>(old(paul)))&
(![X]:(~quiet(X)<=>(~creative(X)|~quiet(X))))&
(![X]:((~strong(X)<~>~generous(X))=>(creative(X)<~>~quiet(X))))&
(![X]:(curious(X)=>(wise(X)<~>generous(X))))&
(![X]:((old(X)|strong(X))=>(quiet(X)&~calm(X))))&
(![X]:((curious(X)&~creative(X))=>(humble(X)&old(X))))&
(?[X]:((~curious(X)<~>strong(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((funny(X)<~>old(X))))&
(?[X]:((~curious(X)<~>~creative(X))))&
((~wise(fred)&~tall(fred)))&
(?[X]:((~brave(X)&~tall(X))))&
(?[X]:((generous(X)&~patient(X)))) | happy(mary) | [
"p1",
"p5",
"p6",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4930992155047927768248584
% SZS output start Proof for 4930992155047927768248584
2. ! [X0] : ((quiet(X0) | ~curious(X0)) => (happy(X0) <~> ~rich(X0))) [input p1]
6. ! [X0] : ((rich(X0) <~> ~quiet(X0)) => ~creative(X0)) [input p5]
7. ! [X0] : (~quiet(X0) => (strong(X0) | quiet(X0))) [input p6]
11. ! [X0] : (~quiet(X0) <=> (~quiet(X0) | ~creative(X0))) [input p10]
14. ! [X0] : ((strong(X0) | old(X0)) => (~calm(X0) & quiet(X0))) [input p13]
23. happy(mary) [input hypothesis]
26. ! [X0] : ((happy(X0) <~> ~rich(X0)) | (~quiet(X0) & curious(X0))) [ennf transformation 2]
28. ! [X0] : (~creative(X0) | (rich(X0) <=> ~quiet(X0))) [ennf transformation 6]
29. ! [X0] : ((strong(X0) | quiet(X0)) | quiet(X0)) [ennf transformation 7]
30. ! [X0] : (strong(X0) | quiet(X0) | quiet(X0)) [flattening 29]
34. ! [X0] : ((~calm(X0) & quiet(X0)) | (~strong(X0) & ~old(X0))) [ennf transformation 14]
38. ! [X0] : (((rich(X0) | ~happy(X0)) & (~rich(X0) | happy(X0))) | (~quiet(X0) & curious(X0))) [nnf transformation 26]
42. ! [X0] : (~creative(X0) | ((rich(X0) | quiet(X0)) & (~quiet(X0) | ~rich(X0)))) [nnf transformation 28]
52. ! [X0] : ((~quiet(X0) | (quiet(X0) & creative(X0))) & ((~quiet(X0) | ~creative(X0)) | quiet(X0))) [nnf transformation 11]
53. ! [X0] : ((~quiet(X0) | (quiet(X0) & creative(X0))) & (~quiet(X0) | ~creative(X0) | quiet(X0))) [flattening 52]
79. ~happy(X0) | rich(X0) | ~quiet(X0) [cnf transformation 38]
96. ~creative(X0) | ~quiet(X0) | ~rich(X0) [cnf transformation 42]
98. strong(X0) | quiet(X0) | quiet(X0) [cnf transformation 30]
112. ~quiet(X0) | creative(X0) [cnf transformation 53]
121. quiet(X0) | ~strong(X0) [cnf transformation 34]
139. happy(mary) [cnf transformation 23]
140. quiet(X0) | strong(X0) [duplicate literal removal 98]
223. quiet(X0) [subsumption resolution 121,140]
266. creative(X0) [resolution 112,223]
313. 31 <=> rich(mary) [avatar definition]
315. rich(mary) <- (31) [avatar component clause 313]
317. rich(mary) | ~quiet(mary) [resolution 79,139]
319. rich(mary) [subsumption resolution 317,223]
320. 31 [avatar split clause 319,313]
324. ~quiet(X0) | ~rich(X0) [resolution 96,266]
325. ~rich(X0) [subsumption resolution 324,223]
326. $false <- (31) [resolution 325,315]
327. ~31 [avatar contradiction clause 326]
328. $false [avatar sat refutation 320,327]
% SZS output end Proof for 4930992155047927768248584
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both kind and not creative then someone is either not brave or creative and vice versa. If someone is both not creative and not rich then someone is either humble or not patient and vice versa. If someone is old then alice is both tall and generous and vice versa. Everyone who is not patient or humble is either not strong or not creative. Everyone who is either not creative or not kind is not calm or not generous and vice versa. Everyone who is either patient or not humble is both humble and rich. If someone is tall then someone is not rich or generous. Everyone who is both not creative and curious is both not humble and tall and vice versa. Everyone who is either calm or not old is not wise or not rich. Everyone who is either quiet or humble is old or not wise and vice versa. If someone is either creative or not tall then someone is either not curious or not old and vice versa. Everyone who is either curious or not humble is either not happy or not rich and vice versa. Everyone who is both brave and happy is both humble and old and vice versa. Everyone who is either old or calm is not wise and vice versa. Everyone who is wise or not kind is both quiet and brave. Everyone who is either not creative or not patient is quiet and vice versa. Susan is either not kind or funny. Someone is not funny. Someone is either not rich or brave. Lucy is not happy. Susan is both kind and wise. John is either not wise or not rich. Someone is both not happy and not curious. Someone is both not quiet and strong. | Susan is old. | entailment | ((?[X]:((kind(X)&~creative(X))))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((?[X]:((~creative(X)&~rich(X))))<=>(?[X]:((humble(X)<~>~patient(X)))))&
((?[X]:(old(X)))<=>((tall(alice)&generous(alice))))&
(![X]:((~patient(X)|humble(X))=>(~strong(X)<~>~creative(X))))&
(![X]:((~creative(X)<~>~kind(X))<=>(~calm(X)|~generous(X))))&
(![X]:((patient(X)<~>~humble(X))=>(humble(X)&rich(X))))&
((?[X]:(tall(X)))=>(?[X]:((~rich(X)|generous(X)))))&
(![X]:((~creative(X)&curious(X))<=>(~humble(X)&tall(X))))&
(![X]:((calm(X)<~>~old(X))=>(~wise(X)|~rich(X))))&
(![X]:((quiet(X)<~>humble(X))<=>(old(X)|~wise(X))))&
((?[X]:((creative(X)<~>~tall(X))))<=>(?[X]:((~curious(X)<~>~old(X)))))&
(![X]:((curious(X)<~>~humble(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((brave(X)&happy(X))<=>(humble(X)&old(X))))&
(![X]:((old(X)<~>calm(X))<=>~wise(X)))&
(![X]:((wise(X)|~kind(X))=>(quiet(X)&brave(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>quiet(X)))&
((~kind(susan)<~>funny(susan)))&
(?[X]:(~funny(X)))&
(?[X]:((~rich(X)<~>brave(X))))&
(~happy(lucy))&
((kind(susan)&wise(susan)))&
((~wise(john)<~>~rich(john)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~quiet(X)&strong(X)))) | old(susan) | [
"p4",
"p5",
"p8",
"p9",
"p13",
"p14",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5836459780193784892672632
% SZS output start Proof for 5836459780193784892672632
5. ! [X0] : ((~creative(X0) <~> ~kind(X0)) <=> (~generous(X0) | ~calm(X0))) [input p4]
6. ! [X0] : ((patient(X0) <~> ~humble(X0)) => (rich(X0) & humble(X0))) [input p5]
9. ! [X0] : ((calm(X0) <~> ~old(X0)) => (~rich(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((quiet(X0) <~> humble(X0)) <=> (~wise(X0) | old(X0))) [input p9]
14. ! [X0] : ((old(X0) <~> calm(X0)) <=> ~wise(X0)) [input p13]
15. ! [X0] : ((~kind(X0) | wise(X0)) => (brave(X0) & quiet(X0))) [input p14]
16. ! [X0] : ((~creative(X0) <~> ~patient(X0)) <=> quiet(X0)) [input p15]
21. wise(susan) & kind(susan) [input p20]
25. ~old(susan) [input hypothesis]
31. ! [X0] : ((rich(X0) & humble(X0)) | (patient(X0) <=> ~humble(X0))) [ennf transformation 6]
33. ! [X0] : ((~rich(X0) | ~wise(X0)) | (calm(X0) <=> ~old(X0))) [ennf transformation 9]
34. ! [X0] : (~rich(X0) | ~wise(X0) | (calm(X0) <=> ~old(X0))) [flattening 33]
35. ! [X0] : ((brave(X0) & quiet(X0)) | (kind(X0) & ~wise(X0))) [ennf transformation 15]
52. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (generous(X0) & calm(X0))) & ((~generous(X0) | ~calm(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [nnf transformation 5]
53. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (generous(X0) & calm(X0))) & (~generous(X0) | ~calm(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [flattening 52]
54. ! [X0] : ((rich(X0) & humble(X0)) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) [nnf transformation 31]
60. ! [X0] : (~rich(X0) | ~wise(X0) | ((calm(X0) | old(X0)) & (~old(X0) | ~calm(X0)))) [nnf transformation 34]
61. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | (wise(X0) & ~old(X0))) & ((~wise(X0) | old(X0)) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [nnf transformation 10]
62. ! [X0] : ((((~humble(X0) | ~quiet(X0)) & (humble(X0) | quiet(X0))) | (wise(X0) & ~old(X0))) & (~wise(X0) | old(X0) | ((quiet(X0) | ~humble(X0)) & (humble(X0) | ~quiet(X0))))) [flattening 61]
71. ! [X0] : ((((~calm(X0) | ~old(X0)) & (calm(X0) | old(X0))) | wise(X0)) & (~wise(X0) | ((old(X0) | ~calm(X0)) & (calm(X0) | ~old(X0))))) [nnf transformation 14]
72. ! [X0] : ((((patient(X0) | creative(X0)) & (~patient(X0) | ~creative(X0))) | ~quiet(X0)) & (quiet(X0) | ((~creative(X0) | patient(X0)) & (~patient(X0) | creative(X0))))) [nnf transformation 16]
105. ~creative(X0) | ~kind(X0) | calm(X0) [cnf transformation 53]
111. ~patient(X0) | ~humble(X0) | rich(X0) [cnf transformation 54]
119. ~wise(X0) | ~rich(X0) | calm(X0) | old(X0) [cnf transformation 60]
120. ~quiet(X0) | old(X0) | humble(X0) | ~wise(X0) [cnf transformation 62]
147. ~wise(X0) | old(X0) | ~calm(X0) [cnf transformation 71]
150. ~wise(X0) | quiet(X0) [cnf transformation 35]
157. ~quiet(X0) | creative(X0) | patient(X0) [cnf transformation 72]
164. kind(susan) [cnf transformation 21]
165. wise(susan) [cnf transformation 21]
172. ~old(susan) [cnf transformation 25]
304. 30 <=> kind(susan) [avatar definition]
306. kind(susan) <- (30) [avatar component clause 304]
323. 30 [avatar split clause 164,304]
334. quiet(susan) [resolution 150,165]
544. old(susan) | ~calm(susan) [resolution 147,165]
546. ~calm(susan) [subsumption resolution 544,172]
627. 71 <=> patient(susan) [avatar definition]
628. patient(susan) <- (71) [avatar component clause 627]
631. 72 <=> creative(susan) [avatar definition]
632. creative(susan) <- (72) [avatar component clause 631]
640. creative(susan) | patient(susan) [resolution 157,334]
681. ~rich(susan) | calm(susan) | old(susan) [resolution 119,165]
685. ~rich(susan) | old(susan) [subsumption resolution 681,546]
686. ~rich(susan) [subsumption resolution 685,172]
692. 71 | 72 [avatar split clause 640,631,627]
695. old(susan) | humble(susan) | ~wise(susan) [resolution 120,334]
702. humble(susan) | ~wise(susan) [subsumption resolution 695,172]
703. humble(susan) [subsumption resolution 702,165]
737. ~kind(susan) | calm(susan) <- (72) [resolution 632,105]
739. calm(susan) <- (30, 72) [subsumption resolution 737,306]
740. $false <- (30, 72) [subsumption resolution 739,546]
741. ~30 | ~72 [avatar contradiction clause 740]
894. ~humble(susan) | rich(susan) <- (71) [resolution 628,111]
895. rich(susan) <- (71) [subsumption resolution 894,703]
896. $false <- (71) [subsumption resolution 895,686]
897. ~71 [avatar contradiction clause 896]
898. $false [avatar sat refutation 323,692,741,897]
% SZS output end Proof for 5836459780193784892672632
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5500
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not strong or not kind is not rich.
Everyone who is humble is brave.
If paul is curious or funny then someone 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.
If susan is both not calm and not creative then alice is both happy and wise and vice versa.
John is both not quiet and brave.
Mary is not generous or strong.
Someone is funny.
Paul is not patient.
Alice is both not happy and not calm.
Alice is not creative or not generous.
Paul is quiet. | Alice is not happy. | entailment | (![X]:((~strong(X)<~>~kind(X))=>~rich(X)))&
(![X]:(humble(X)=>brave(X)))&
(((curious(paul)|funny(paul)))=>(?[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)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
((~quiet(john)&brave(john)))&
((~generous(mary)|strong(mary)))&
(?[X]:(funny(X)))&
(~patient(paul))&
((~happy(alice)&~calm(alice)))&
((~creative(alice)|~generous(alice)))&
(quiet(paul)) | ~happy(alice) | [
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 2701363664734748397403998
% SZS output start Proof for 2701363664734748397403998
21. ~calm(alice) & ~happy(alice) [input p20]
24. happy(alice) [input hypothesis]
128. ~happy(alice) [cnf transformation 21]
131. happy(alice) [cnf transformation 24]
260. 29 <=> happy(alice) [avatar definition]
281. ~29 [avatar split clause 128,260]
282. 29 [avatar split clause 131,260]
283. $false [avatar sat refutation 281,282]
% SZS output end Proof for 2701363664734748397403998
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not creative then lucy is rich and vice versa.
If fred is not brave then someone is not generous or curious and vice versa.
Everyone who is both not humble and not calm is happy or brave.
Everyone who is either old or not wise is either generous or not kind and vice versa.
Everyone who is tall or not humble is both not wise and funny and vice versa.
Everyone who is rich or not calm is not patient or not rich and vice versa.
If mary is not rich then mary is both not funny and not patient and vice versa.
Everyone who is either kind or not rich is not calm and vice versa.
If susan is not funny or not patient then someone is both patient and happy.
If someone is either humble or curious then susan is not calm or not generous and vice versa.
Everyone who is strong or tall is calm and vice versa.
Everyone who is either funny or not creative is both old and not rich.
Everyone who is not generous or not happy is funny.
If someone is both not tall and not humble then someone is either not creative or creative.
Everyone who is not happy is either not kind or creative and vice versa.
Everyone who is either happy or curious is both not wise and not humble and vice versa.
Paul is both not kind and strong.
Mary is tall or not brave.
Someone is both not strong and not funny.
Someone is either creative or brave.
Someone is either wise or not calm.
Paul is calm.
Susan is either not happy or not old.
Someone is old or kind. | Paul is not funny. | neutral | ((?[X]:((calm(X)|~creative(X))))<=>(rich(lucy)))&
((~brave(fred))<=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~humble(X)&~calm(X))=>(happy(X)|brave(X))))&
(![X]:((old(X)<~>~wise(X))<=>(generous(X)<~>~kind(X))))&
(![X]:((tall(X)|~humble(X))<=>(~wise(X)&funny(X))))&
(![X]:((rich(X)|~calm(X))<=>(~patient(X)|~rich(X))))&
((~rich(mary))<=>((~funny(mary)&~patient(mary))))&
(![X]:((kind(X)<~>~rich(X))<=>~calm(X)))&
(((~funny(susan)|~patient(susan)))=>(?[X]:((patient(X)&happy(X)))))&
((?[X]:((humble(X)<~>curious(X))))<=>((~calm(susan)|~generous(susan))))&
(![X]:((strong(X)|tall(X))<=>calm(X)))&
(![X]:((funny(X)<~>~creative(X))=>(old(X)&~rich(X))))&
(![X]:((~generous(X)|~happy(X))=>funny(X)))&
((?[X]:((~tall(X)&~humble(X))))=>(?[X]:((~creative(X)<~>creative(X)))))&
(![X]:(~happy(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((happy(X)<~>curious(X))<=>(~wise(X)&~humble(X))))&
((~kind(paul)&strong(paul)))&
((tall(mary)|~brave(mary)))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:((creative(X)<~>brave(X))))&
(?[X]:((wise(X)<~>~calm(X))))&
(calm(paul))&
((~happy(susan)<~>~old(susan)))&
(?[X]:((old(X)|kind(X)))) | ~funny(paul) | [] | null | 0 |
Everyone who is both not patient and happy is not tall and vice versa. If someone is tall or rich then susan is not old or not curious. Everyone who is not calm or not brave is both happy and not wise and vice versa. Everyone who is either happy or not creative is either not calm or not curious and vice versa. If fred is not funny or not kind then someone is funny. Everyone who is not kind or not quiet is both not humble and happy and vice versa. Everyone who is both happy and not kind is not old. If someone is either not rich or creative then alice is creative and vice versa. Everyone who is creative or curious is not kind or not creative. Everyone who is not brave is not curious or not humble and vice versa. If someone is either happy or not rich then someone is either not humble or not rich and vice versa. If john is both funny and tall then susan is either not humble or funny. Everyone who is not calm or not curious is kind. If someone is both not quiet and patient then fred is patient and vice versa. If john is both quiet and old then susan is not humble and vice versa. Everyone who is not generous is not brave and vice versa. Lucy is either not kind or not rich. Someone is generous. Someone is not old. Someone is not wise. Someone is both tall and strong. | John is not rich. | contradiction | (![X]:((~patient(X)&happy(X))<=>~tall(X)))&
((?[X]:((tall(X)|rich(X))))=>((~old(susan)|~curious(susan))))&
(![X]:((~calm(X)|~brave(X))<=>(happy(X)&~wise(X))))&
(![X]:((happy(X)<~>~creative(X))<=>(~calm(X)<~>~curious(X))))&
(((~funny(fred)|~kind(fred)))=>(?[X]:(funny(X))))&
(![X]:((~kind(X)|~quiet(X))<=>(~humble(X)&happy(X))))&
(![X]:((happy(X)&~kind(X))=>~old(X)))&
((?[X]:((~rich(X)<~>creative(X))))<=>(creative(alice)))&
(![X]:((creative(X)|curious(X))=>(~kind(X)|~creative(X))))&
(![X]:(~brave(X)<=>(~curious(X)|~humble(X))))&
((?[X]:((happy(X)<~>~rich(X))))<=>(?[X]:((~humble(X)<~>~rich(X)))))&
(((funny(john)&tall(john)))=>((~humble(susan)<~>funny(susan))))&
(![X]:((~calm(X)|~curious(X))=>kind(X)))&
((?[X]:((~quiet(X)&patient(X))))<=>(patient(fred)))&
(((quiet(john)&old(john)))<=>(~humble(susan)))&
(![X]:(~generous(X)<=>~brave(X)))&
((~kind(lucy)<~>~rich(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~old(X)))&
(?[X]:(~wise(X)))&
(?[X]:((tall(X)&strong(X)))) | ~rich(john) | [
"p2",
"p3",
"p5",
"p7",
"p8",
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 7803634495775281146277633
% SZS output start Proof for 7803634495775281146277633
3. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (~wise(X0) & happy(X0))) [input p2]
4. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> (~calm(X0) <~> ~curious(X0))) [input p3]
6. ! [X0] : ((~quiet(X0) | ~kind(X0)) <=> (happy(X0) & ~humble(X0))) [input p5]
8. ? [X0] : (~rich(X0) <~> creative(X0)) <=> creative(alice) [input p7]
9. ! [X0] : ((curious(X0) | creative(X0)) => (~creative(X0) | ~kind(X0))) [input p8]
10. ! [X0] : (~brave(X0) <=> (~humble(X0) | ~curious(X0))) [input p9]
13. ! [X0] : ((~curious(X0) | ~calm(X0)) => kind(X0)) [input p12]
22. ~rich(john) [input hypothesis]
31. ! [X0] : ((~creative(X0) | ~kind(X0)) | (~curious(X0) & ~creative(X0))) [ennf transformation 9]
32. ! [X0] : (~creative(X0) | ~kind(X0) | (~curious(X0) & ~creative(X0))) [flattening 31]
35. ! [X0] : (kind(X0) | (curious(X0) & calm(X0))) [ennf transformation 13]
39. ! [X0] : (((~brave(X0) | ~calm(X0)) | (wise(X0) | ~happy(X0))) & ((~wise(X0) & happy(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 3]
40. ! [X0] : ((~brave(X0) | ~calm(X0) | wise(X0) | ~happy(X0)) & ((~wise(X0) & happy(X0)) | (brave(X0) & calm(X0)))) [flattening 39]
41. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0)))) & (((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 4]
44. ! [X0] : (((~quiet(X0) | ~kind(X0)) | (~happy(X0) | humble(X0))) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [nnf transformation 6]
45. ! [X0] : ((~quiet(X0) | ~kind(X0) | ~happy(X0) | humble(X0)) & ((happy(X0) & ~humble(X0)) | (quiet(X0) & kind(X0)))) [flattening 44]
46. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~creative(alice)) & (creative(alice) | ! [X0] : ((~rich(X0) | ~creative(X0)) & (creative(X0) | rich(X0)))) [nnf transformation 8]
47. (? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) | ~creative(alice)) & (creative(alice) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [rectify 46]
48. ? [X0] : ((~creative(X0) | rich(X0)) & (creative(X0) | ~rich(X0))) => ((~creative(sK1) | rich(sK1)) & (creative(sK1) | ~rich(sK1))) [choice axiom]
49. (((~creative(sK1) | rich(sK1)) & (creative(sK1) | ~rich(sK1))) | ~creative(alice)) & (creative(alice) | ! [X1] : ((~rich(X1) | ~creative(X1)) & (creative(X1) | rich(X1)))) [skolemisation 47,48]
50. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & ((~humble(X0) | ~curious(X0)) | brave(X0))) [nnf transformation 10]
51. ! [X0] : ((~brave(X0) | (humble(X0) & curious(X0))) & (~humble(X0) | ~curious(X0) | brave(X0))) [flattening 50]
78. calm(X0) | happy(X0) [cnf transformation 40]
79. brave(X0) | happy(X0) [cnf transformation 40]
83. ~creative(X0) | ~calm(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 41]
84. ~curious(X0) | ~calm(X0) | happy(X0) | creative(X0) [cnf transformation 41]
89. creative(X0) | ~happy(X0) | ~curious(X0) | calm(X0) [cnf transformation 41]
95. kind(X0) | happy(X0) [cnf transformation 45]
99. creative(alice) | creative(X1) | rich(X1) [cnf transformation 49]
103. ~creative(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 32]
106. ~brave(X0) | curious(X0) [cnf transformation 51]
118. kind(X0) | calm(X0) [cnf transformation 35]
119. kind(X0) | curious(X0) [cnf transformation 35]
133. ~rich(john) [cnf transformation 22]
134. ~kind(X0) | ~creative(X0) [duplicate literal removal 103]
151. ~curious(X0) | creative(X0) | calm(X0) [subsumption resolution 89,78]
154. ~curious(X0) | happy(X0) | creative(X0) [subsumption resolution 84,151]
171. 8 <=> creative(alice) [avatar definition]
172. creative(alice) <- (8) [avatar component clause 171]
189. 12 <=> ! [X1] : (creative(X1) | rich(X1)) [avatar definition]
190. creative(X1) | rich(X1) <- (12) [avatar component clause 189]
191. 12 | 8 [avatar split clause 99,171,189]
293. curious(X0) | happy(X0) [resolution 106,79]
296. ~creative(X0) | curious(X0) [resolution 134,119]
297. ~creative(X1) | calm(X1) [resolution 134,118]
298. ~creative(X2) | happy(X2) [resolution 134,95]
340. 37 <=> curious(alice) [avatar definition]
342. curious(alice) <- (37) [avatar component clause 340]
344. 38 <=> calm(alice) [avatar definition]
400. ~calm(X0) | ~curious(X0) | ~happy(X0) | rich(X0) <- (12) [resolution 83,190]
413. happy(X0) | happy(X0) | creative(X0) [resolution 293,154]
415. happy(X0) | creative(X0) [duplicate literal removal 413]
416. happy(X0) [subsumption resolution 415,298]
422. curious(X0) | rich(X0) <- (12) [resolution 296,190]
426. calm(X0) | rich(X0) <- (12) [resolution 297,190]
446. ~calm(X0) | ~curious(X0) | rich(X0) <- (12) [subsumption resolution 400,416]
447. ~curious(X0) | rich(X0) <- (12) [subsumption resolution 446,426]
448. rich(X0) <- (12) [subsumption resolution 447,422]
449. $false <- (12) [resolution 448,133]
450. ~12 [avatar contradiction clause 449]
451. ~calm(alice) | ~curious(alice) | ~happy(alice) <- (8) [resolution 172,83]
455. curious(alice) <- (8) [resolution 172,296]
456. calm(alice) <- (8) [resolution 172,297]
458. ~calm(alice) | ~happy(alice) <- (8, 37) [subsumption resolution 451,342]
459. ~calm(alice) <- (8, 37) [subsumption resolution 458,416]
460. ~38 | ~8 | ~37 [avatar split clause 459,340,171,344]
461. 38 | ~8 [avatar split clause 456,171,344]
462. 37 | ~8 [avatar split clause 455,171,340]
466. $false [avatar sat refutation 191,450,460,461,462]
% SZS output end Proof for 7803634495775281146277633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not quiet or not kind then someone is either happy or not creative and vice versa.
Everyone who is both not strong and creative is both not rich and not curious.
If susan is either not tall or creative then someone is either old or not rich and vice versa.
If john is generous or not quiet then fred is not funny and vice versa.
If john is both not kind and not creative then john is kind.
If paul is either rich or brave then someone is not generous and vice versa.
If john is happy then susan is both happy and patient.
Everyone who is both not calm and old is strong and vice versa.
Everyone who is either patient or rich is both quiet and not kind.
Everyone who is both brave and quiet is both generous and humble.
If someone is either not rich or not creative then lucy is patient or old and vice versa.
If someone is not brave or not funny then someone is either wise or not rich and vice versa.
Everyone who is either not quiet or rich is both rich and humble.
If paul is both not kind and not curious then susan is either not brave or not funny.
Everyone who is either not rich or not creative is not calm.
Everyone who is not tall is both wise and generous and vice versa.
John is either generous or not quiet.
Lucy is humble or happy.
Lucy is either not wise or not happy.
Mary is either brave or creative.
Someone is not quiet.
Fred is both not strong and rich.
Someone is either patient or not wise.
Someone is either not creative or creative. | Fred is creative. | contradiction | (((~quiet(lucy)|~kind(lucy)))<=>(?[X]:((happy(X)<~>~creative(X)))))&
(![X]:((~strong(X)&creative(X))=>(~rich(X)&~curious(X))))&
(((~tall(susan)<~>creative(susan)))<=>(?[X]:((old(X)<~>~rich(X)))))&
(((generous(john)|~quiet(john)))<=>(~funny(fred)))&
(((~kind(john)&~creative(john)))=>(kind(john)))&
(((rich(paul)<~>brave(paul)))<=>(?[X]:(~generous(X))))&
((happy(john))=>((happy(susan)&patient(susan))))&
(![X]:((~calm(X)&old(X))<=>strong(X)))&
(![X]:((patient(X)<~>rich(X))=>(quiet(X)&~kind(X))))&
(![X]:((brave(X)&quiet(X))=>(generous(X)&humble(X))))&
((?[X]:((~rich(X)<~>~creative(X))))<=>((patient(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~funny(X))))<=>(?[X]:((wise(X)<~>~rich(X)))))&
(![X]:((~quiet(X)<~>rich(X))=>(rich(X)&humble(X))))&
(((~kind(paul)&~curious(paul)))=>((~brave(susan)<~>~funny(susan))))&
(![X]:((~rich(X)<~>~creative(X))=>~calm(X)))&
(![X]:(~tall(X)<=>(wise(X)&generous(X))))&
((generous(john)<~>~quiet(john)))&
((humble(lucy)|happy(lucy)))&
((~wise(lucy)<~>~happy(lucy)))&
((brave(mary)<~>creative(mary)))&
(?[X]:(~quiet(X)))&
((~strong(fred)&rich(fred)))&
(?[X]:((patient(X)<~>~wise(X))))&
(?[X]:((~creative(X)<~>creative(X)))) | creative(fred) | [
"p1",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 1391079053993389910417909
% SZS output start Proof for 1391079053993389910417909
2. ! [X0] : ((creative(X0) & ~strong(X0)) => (~curious(X0) & ~rich(X0))) [input p1]
22. rich(fred) & ~strong(fred) [input p21]
25. creative(fred) [input hypothesis]
30. ! [X0] : ((~curious(X0) & ~rich(X0)) | (~creative(X0) | strong(X0))) [ennf transformation 2]
31. ! [X0] : ((~curious(X0) & ~rich(X0)) | ~creative(X0) | strong(X0)) [flattening 30]
92. ~rich(X0) | ~creative(X0) | strong(X0) [cnf transformation 31]
148. ~strong(fred) [cnf transformation 22]
149. rich(fred) [cnf transformation 22]
154. creative(fred) [cnf transformation 25]
394. ~creative(fred) | strong(fred) [resolution 92,149]
397. strong(fred) [subsumption resolution 394,154]
398. $false [subsumption resolution 397,148]
% SZS output end Proof for 1391079053993389910417909
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm or not patient then paul is both not curious and funny.
Everyone who is happy is either not brave or tall and vice versa.
If someone is not humble then someone is quiet or wise and vice versa.
If someone is either not kind or not strong then someone is either funny or old and vice versa.
If someone is humble then alice is not generous or not strong and vice versa.
Everyone who is both wise and not strong is not generous or not creative.
If paul is not rich then john is both strong and not humble and vice versa.
Everyone who is tall is strong or curious and vice versa.
Everyone who is kind is either happy or not tall and vice versa.
Everyone who is not happy is generous.
Everyone who is not generous is not old.
Everyone who is not tall is either not rich or creative.
Everyone who is both old and kind is both calm and curious and vice versa.
Everyone who is either not funny or not happy is tall.
If someone is not wise or not curious then someone is brave and vice versa.
If someone is both not humble and old then someone is either not wise or humble and vice versa.
Someone is creative.
Fred is wise.
John is both not patient and not brave.
Paul is old or not kind.
Someone is either not strong or not tall.
John is curious.
Someone is either not strong or old.
Lucy is either not humble or not wise. | John is not kind. | entailment | ((?[X]:((calm(X)|~patient(X))))=>((~curious(paul)&funny(paul))))&
(![X]:(happy(X)<=>(~brave(X)<~>tall(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((quiet(X)|wise(X)))))&
((?[X]:((~kind(X)<~>~strong(X))))<=>(?[X]:((funny(X)<~>old(X)))))&
((?[X]:(humble(X)))<=>((~generous(alice)|~strong(alice))))&
(![X]:((wise(X)&~strong(X))=>(~generous(X)|~creative(X))))&
((~rich(paul))<=>((strong(john)&~humble(john))))&
(![X]:(tall(X)<=>(strong(X)|curious(X))))&
(![X]:(kind(X)<=>(happy(X)<~>~tall(X))))&
(![X]:(~happy(X)=>generous(X)))&
(![X]:(~generous(X)=>~old(X)))&
(![X]:(~tall(X)=>(~rich(X)<~>creative(X))))&
(![X]:((old(X)&kind(X))<=>(calm(X)&curious(X))))&
(![X]:((~funny(X)<~>~happy(X))=>tall(X)))&
((?[X]:((~wise(X)|~curious(X))))<=>(?[X]:(brave(X))))&
((?[X]:((~humble(X)&old(X))))<=>(?[X]:((~wise(X)<~>humble(X)))))&
(?[X]:(creative(X)))&
(wise(fred))&
((~patient(john)&~brave(john)))&
((old(paul)|~kind(paul)))&
(?[X]:((~strong(X)<~>~tall(X))))&
(curious(john))&
(?[X]:((~strong(X)<~>old(X))))&
((~humble(lucy)<~>~wise(lucy))) | ~kind(john) | [
"p1",
"p7",
"p8",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3323021503412810632780099
% SZS output start Proof for 3323021503412810632780099
2. ! [X0] : (happy(X0) <=> (~brave(X0) <~> tall(X0))) [input p1]
8. ! [X0] : (tall(X0) <=> (curious(X0) | strong(X0))) [input p7]
9. ! [X0] : (kind(X0) <=> (happy(X0) <~> ~tall(X0))) [input p8]
19. ~brave(john) & ~patient(john) [input p18]
22. curious(john) [input p21]
25. kind(john) [input hypothesis]
37. ! [X0] : ((happy(X0) | ((~brave(X0) | ~tall(X0)) & (tall(X0) | brave(X0)))) & (((~tall(X0) | brave(X0)) & (tall(X0) | ~brave(X0))) | ~happy(X0))) [nnf transformation 2]
55. ! [X0] : ((tall(X0) | (~curious(X0) & ~strong(X0))) & ((curious(X0) | strong(X0)) | ~tall(X0))) [nnf transformation 8]
56. ! [X0] : ((tall(X0) | (~curious(X0) & ~strong(X0))) & (curious(X0) | strong(X0) | ~tall(X0))) [flattening 55]
57. ! [X0] : ((kind(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | ~kind(X0))) [nnf transformation 9]
86. ~tall(X0) | brave(X0) | ~happy(X0) [cnf transformation 37]
109. ~curious(X0) | tall(X0) [cnf transformation 56]
110. ~kind(X0) | happy(X0) | ~tall(X0) [cnf transformation 57]
136. ~brave(john) [cnf transformation 19]
140. curious(john) [cnf transformation 22]
145. kind(john) [cnf transformation 25]
350. tall(john) [resolution 109,140]
388. happy(john) | ~tall(john) [resolution 110,145]
403. 51 <=> tall(john) [avatar definition]
404. tall(john) <- (51) [avatar component clause 403]
407. 52 <=> happy(john) [avatar definition]
409. happy(john) <- (52) [avatar component clause 407]
410. ~51 | 52 [avatar split clause 388,407,403]
411. 51 [avatar split clause 350,403]
451. brave(john) | ~happy(john) <- (51) [resolution 404,86]
452. ~happy(john) <- (51) [subsumption resolution 451,136]
453. $false <- (51, 52) [subsumption resolution 452,409]
454. ~51 | ~52 [avatar contradiction clause 453]
455. $false [avatar sat refutation 410,411,454]
% SZS output end Proof for 3323021503412810632780099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny and quiet is not humble. Everyone who is not kind is both old and funny and vice versa. If susan is not tall or tall then someone is funny or kind. If someone is rich or not wise then john is not funny or not humble and vice versa. Everyone who is both calm and not creative is either not funny or not strong and vice versa. If john is either rich or not funny then someone is not old or not humble and vice versa. Everyone who is not patient is both calm and generous and vice versa. Everyone who is both not curious and funny is either not humble or happy and vice versa. Everyone who is both not patient and not strong is either not tall or funny. If john is both not rich and curious then someone is both kind and not strong. Everyone who is brave or humble is not old and vice versa. If someone is wise then someone is both creative and old and vice versa. Everyone who is both rich and tall is either patient or not curious. If alice is either creative or generous then paul is calm or not calm and vice versa. Everyone who is calm is not humble or not brave and vice versa. Everyone who is funny or not calm is not patient. Someone is kind or not brave. Someone is generous or quiet. Someone is both not funny and old. Susan is calm or wise. Someone is both patient and not funny. Someone is not strong. | Paul is not calm. | contradiction | (![X]:((funny(X)&quiet(X))=>~humble(X)))&
(![X]:(~kind(X)<=>(old(X)&funny(X))))&
(((~tall(susan)|tall(susan)))=>(?[X]:((funny(X)|kind(X)))))&
((?[X]:((rich(X)|~wise(X))))<=>((~funny(john)|~humble(john))))&
(![X]:((calm(X)&~creative(X))<=>(~funny(X)<~>~strong(X))))&
(((rich(john)<~>~funny(john)))<=>(?[X]:((~old(X)|~humble(X)))))&
(![X]:(~patient(X)<=>(calm(X)&generous(X))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(![X]:((funny(X)|~calm(X))=>~patient(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
(?[X]:((~funny(X)&old(X))))&
((calm(susan)|wise(susan)))&
(?[X]:((patient(X)&~funny(X))))&
(?[X]:(~strong(X))) | ~calm(paul) | [
"p6",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5522152514203907325429210
% SZS output start Proof for 5522152514203907325429210
7. ! [X0] : (~patient(X0) <=> (generous(X0) & calm(X0))) [input p6]
16. ! [X0] : ((~calm(X0) | funny(X0)) => ~patient(X0)) [input p15]
23. ~calm(paul) [input hypothesis]
37. ! [X0] : (~patient(X0) | (calm(X0) & ~funny(X0))) [ennf transformation 16]
51. ! [X0] : ((~patient(X0) | (~generous(X0) | ~calm(X0))) & ((generous(X0) & calm(X0)) | patient(X0))) [nnf transformation 7]
52. ! [X0] : ((~patient(X0) | ~generous(X0) | ~calm(X0)) & ((generous(X0) & calm(X0)) | patient(X0))) [flattening 51]
100. calm(X0) | patient(X0) [cnf transformation 52]
131. ~patient(X0) | calm(X0) [cnf transformation 37]
140. ~calm(paul) [cnf transformation 23]
256. calm(X0) [subsumption resolution 131,100]
275. $false [subsumption resolution 140,256]
% SZS output end Proof for 5522152514203907325429210
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is both not generous and wise.
If someone is not patient or not rich then john is not happy or patient.
If someone is both old and not brave then someone is kind or not creative and vice versa.
If someone is both wise and not rich then alice is not tall and vice versa.
If lucy is either wise or not brave then someone is not quiet.
If someone is either not wise or not funny then someone is both tall and quiet.
If mary is not kind or not patient then someone is humble or not generous.
If someone is either kind or not curious then susan is happy or not generous.
If someone is both not tall and not wise then someone is both creative and quiet and vice versa.
If john is either humble or not patient then someone is not generous or not rich.
If someone is wise or not curious then someone is patient or not wise and vice versa.
If paul is either not strong or quiet then mary is not old.
If john is patient then paul is either not happy or not creative.
If someone is either kind or not brave then someone is not quiet or kind and vice versa.
Everyone who is either not curious or rich is either not funny or creative and vice versa.
If paul is quiet or not wise then lucy is either old or not old.
Someone is both not calm and not humble.
Fred is either not creative or not old.
John is either not creative or strong.
Someone is both not happy and not funny.
Someone is old.
Someone is kind.
Someone is both creative and kind.
Alice is either not rich or strong. | Mary is patient. | neutral | (![X]:(generous(X)=>(~generous(X)&wise(X))))&
((?[X]:((~patient(X)|~rich(X))))=>((~happy(john)|patient(john))))&
((?[X]:((old(X)&~brave(X))))<=>(?[X]:((kind(X)|~creative(X)))))&
((?[X]:((wise(X)&~rich(X))))<=>(~tall(alice)))&
(((wise(lucy)<~>~brave(lucy)))=>(?[X]:(~quiet(X))))&
((?[X]:((~wise(X)<~>~funny(X))))=>(?[X]:((tall(X)&quiet(X)))))&
(((~kind(mary)|~patient(mary)))=>(?[X]:((humble(X)|~generous(X)))))&
((?[X]:((kind(X)<~>~curious(X))))=>((happy(susan)|~generous(susan))))&
((?[X]:((~tall(X)&~wise(X))))<=>(?[X]:((creative(X)&quiet(X)))))&
(((humble(john)<~>~patient(john)))=>(?[X]:((~generous(X)|~rich(X)))))&
((?[X]:((wise(X)|~curious(X))))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~strong(paul)<~>quiet(paul)))=>(~old(mary)))&
((patient(john))=>((~happy(paul)<~>~creative(paul))))&
((?[X]:((kind(X)<~>~brave(X))))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~curious(X)<~>rich(X))<=>(~funny(X)<~>creative(X))))&
(((quiet(paul)|~wise(paul)))=>((old(lucy)<~>~old(lucy))))&
(?[X]:((~calm(X)&~humble(X))))&
((~creative(fred)<~>~old(fred)))&
((~creative(john)<~>strong(john)))&
(?[X]:((~happy(X)&~funny(X))))&
(?[X]:(old(X)))&
(?[X]:(kind(X)))&
(?[X]:((creative(X)&kind(X))))&
((~rich(alice)<~>strong(alice))) | patient(mary) | [] | null | 0 |
Everyone who is both not brave and not strong is not creative.
Everyone who is generous or wise is both creative and calm.
If someone is kind or not strong then john is either kind or not old and vice versa.
If someone is both funny and not funny then someone is patient and vice versa.
Everyone who is generous or quiet is tall or not happy.
Everyone who is not calm is either rich or not quiet and vice versa.
Everyone who is creative is either rich or creative and vice versa.
If someone is both not generous and not kind then someone is either not funny or not generous.
If mary is old then someone is strong or humble.
Everyone who is either not old or quiet is not creative.
Everyone who is either not strong or old is not wise or calm.
Everyone who is old or not strong is not happy or not funny and vice versa.
If someone is both strong and not brave then lucy is both old and not curious.
If someone is patient then someone is generous.
Everyone who is not strong is not tall and vice versa.
If alice is both not calm and funny then someone is brave or humble.
Lucy is funny.
Someone is both not generous and curious.
Someone is both not calm and not brave.
Alice is strong or not creative.
Someone is not happy or not wise.
John is generous.
Someone is quiet.
Mary is both strong and not funny. | Mary is not calm. | neutral | (![X]:((~brave(X)&~strong(X))=>~creative(X)))&
(![X]:((generous(X)|wise(X))=>(creative(X)&calm(X))))&
((?[X]:((kind(X)|~strong(X))))<=>((kind(john)<~>~old(john))))&
((?[X]:((funny(X)&~funny(X))))<=>(?[X]:(patient(X))))&
(![X]:((generous(X)|quiet(X))=>(tall(X)|~happy(X))))&
(![X]:(~calm(X)<=>(rich(X)<~>~quiet(X))))&
(![X]:(creative(X)<=>(rich(X)<~>creative(X))))&
((?[X]:((~generous(X)&~kind(X))))=>(?[X]:((~funny(X)<~>~generous(X)))))&
((old(mary))=>(?[X]:((strong(X)|humble(X)))))&
(![X]:((~old(X)<~>quiet(X))=>~creative(X)))&
(![X]:((~strong(X)<~>old(X))=>(~wise(X)|calm(X))))&
(![X]:((old(X)|~strong(X))<=>(~happy(X)|~funny(X))))&
((?[X]:((strong(X)&~brave(X))))=>((old(lucy)&~curious(lucy))))&
((?[X]:(patient(X)))=>(?[X]:(generous(X))))&
(![X]:(~strong(X)<=>~tall(X)))&
(((~calm(alice)&funny(alice)))=>(?[X]:((brave(X)|humble(X)))))&
(funny(lucy))&
(?[X]:((~generous(X)&curious(X))))&
(?[X]:((~calm(X)&~brave(X))))&
((strong(alice)|~creative(alice)))&
(?[X]:((~happy(X)|~wise(X))))&
(generous(john))&
(?[X]:(quiet(X)))&
((strong(mary)&~funny(mary))) | ~calm(mary) | [] | null | 0 |
Everyone who is either not old or not patient is not brave or not patient. Everyone who is humble or creative is not curious or patient. Everyone who is both brave and strong is either curious or creative and vice versa. Everyone who is both kind and brave is either not generous or quiet and vice versa. Everyone who is rich is tall or generous and vice versa. If someone is not kind or not tall then someone is either generous or curious. If lucy is both curious and old then someone is not creative and vice versa. Everyone who is not happy is not old. If someone is either quiet or calm then someone is not generous or not kind and vice versa. Everyone who is creative is not quiet and vice versa. Everyone who is not patient or generous is not kind. If someone is either not rich or funny then someone is both not old and not quiet and vice versa. If mary is either not calm or happy then paul is calm. Everyone who is either not wise or not old is both patient and rich and vice versa. Everyone who is generous or not creative is either not curious or not brave and vice versa. Everyone who is wise is not calm or funny and vice versa. Lucy is both kind and not wise. Mary is kind or quiet. Someone is either not curious or rich. Mary is not funny or not wise. Mary is either not humble or humble. Someone is either rich or humble. Someone is both not brave and patient. John is not kind or not rich. | Mary is not strong. | entailment | (![X]:((~old(X)<~>~patient(X))=>(~brave(X)|~patient(X))))&
(![X]:((humble(X)|creative(X))=>(~curious(X)|patient(X))))&
(![X]:((brave(X)&strong(X))<=>(curious(X)<~>creative(X))))&
(![X]:((kind(X)&brave(X))<=>(~generous(X)<~>quiet(X))))&
(![X]:(rich(X)<=>(tall(X)|generous(X))))&
((?[X]:((~kind(X)|~tall(X))))=>(?[X]:((generous(X)<~>curious(X)))))&
(((curious(lucy)&old(lucy)))<=>(?[X]:(~creative(X))))&
(![X]:(~happy(X)=>~old(X)))&
((?[X]:((quiet(X)<~>calm(X))))<=>(?[X]:((~generous(X)|~kind(X)))))&
(![X]:(creative(X)<=>~quiet(X)))&
(![X]:((~patient(X)|generous(X))=>~kind(X)))&
((?[X]:((~rich(X)<~>funny(X))))<=>(?[X]:((~old(X)&~quiet(X)))))&
(((~calm(mary)<~>happy(mary)))=>(calm(paul)))&
(![X]:((~wise(X)<~>~old(X))<=>(patient(X)&rich(X))))&
(![X]:((generous(X)|~creative(X))<=>(~curious(X)<~>~brave(X))))&
(![X]:(wise(X)<=>(~calm(X)|funny(X))))&
((kind(lucy)&~wise(lucy)))&
((kind(mary)|quiet(mary)))&
(?[X]:((~curious(X)<~>rich(X))))&
((~funny(mary)|~wise(mary)))&
((~humble(mary)<~>humble(mary)))&
(?[X]:((rich(X)<~>humble(X))))&
(?[X]:((~brave(X)&patient(X))))&
((~kind(john)|~rich(john))) | ~strong(mary) | [
"p2",
"p3",
"p9",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7891004581440599615188568
% SZS output start Proof for 7891004581440599615188568
3. ! [X0] : ((strong(X0) & brave(X0)) <=> (curious(X0) <~> creative(X0))) [input p2]
4. ! [X0] : ((brave(X0) & kind(X0)) <=> (~generous(X0) <~> quiet(X0))) [input p3]
10. ! [X0] : (creative(X0) <=> ~quiet(X0)) [input p9]
11. ! [X0] : ((generous(X0) | ~patient(X0)) => ~kind(X0)) [input p10]
15. ! [X0] : ((~creative(X0) | generous(X0)) <=> (~curious(X0) <~> ~brave(X0))) [input p14]
18. quiet(mary) | kind(mary) [input p17]
25. strong(mary) [input hypothesis]
35. ! [X0] : (~kind(X0) | (~generous(X0) & patient(X0))) [ennf transformation 11]
38. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (~strong(X0) | ~brave(X0)))) [nnf transformation 3]
39. ! [X0] : (((strong(X0) & brave(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | ~strong(X0) | ~brave(X0))) [flattening 38]
40. ! [X0] : (((brave(X0) & kind(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0)))) & (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | (~brave(X0) | ~kind(X0)))) [nnf transformation 4]
41. ! [X0] : (((brave(X0) & kind(X0)) | ((~generous(X0) | ~quiet(X0)) & (quiet(X0) | generous(X0)))) & (((~quiet(X0) | generous(X0)) & (quiet(X0) | ~generous(X0))) | ~brave(X0) | ~kind(X0))) [flattening 40]
58. ! [X0] : ((creative(X0) | quiet(X0)) & (~quiet(X0) | ~creative(X0))) [nnf transformation 10]
67. ! [X0] : (((~creative(X0) | generous(X0)) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (creative(X0) & ~generous(X0)))) [nnf transformation 15]
68. ! [X0] : ((~creative(X0) | generous(X0) | ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0)))) & (((brave(X0) | curious(X0)) & (~brave(X0) | ~curious(X0))) | (creative(X0) & ~generous(X0)))) [flattening 67]
84. ~strong(X0) | curious(X0) | creative(X0) | ~brave(X0) [cnf transformation 39]
85. ~strong(X0) | ~curious(X0) | ~creative(X0) | ~brave(X0) [cnf transformation 39]
86. ~curious(X0) | creative(X0) | brave(X0) [cnf transformation 39]
87. ~creative(X0) | curious(X0) | brave(X0) [cnf transformation 39]
94. quiet(X0) | brave(X0) | generous(X0) [cnf transformation 41]
95. ~quiet(X0) | ~generous(X0) | brave(X0) [cnf transformation 41]
113. ~quiet(X0) | ~creative(X0) [cnf transformation 58]
116. ~generous(X0) | ~kind(X0) [cnf transformation 35]
132. ~brave(X0) | ~curious(X0) | creative(X0) [cnf transformation 68]
134. brave(X0) | curious(X0) | creative(X0) [cnf transformation 68]
135. ~creative(X0) | generous(X0) | ~brave(X0) | curious(X0) [cnf transformation 68]
142. quiet(mary) | kind(mary) [cnf transformation 18]
153. strong(mary) [cnf transformation 25]
268. ~creative(X0) | generous(X0) | curious(X0) [subsumption resolution 135,87]
269. creative(X0) | brave(X0) [subsumption resolution 134,86]
270. ~curious(X0) | creative(X0) [subsumption resolution 132,269]
272. 26 <=> kind(mary) [avatar definition]
276. 27 <=> quiet(mary) [avatar definition]
278. quiet(mary) <- (27) [avatar component clause 276]
279. 26 | 27 [avatar split clause 142,276,272]
375. brave(X1) | generous(X1) | ~creative(X1) [resolution 94,113]
376. generous(X1) | brave(X1) [subsumption resolution 375,269]
390. 36 <=> generous(mary) [avatar definition]
391. ~generous(mary) <- (~36) [avatar component clause 390]
392. generous(mary) <- (36) [avatar component clause 390]
444. ~kind(mary) <- (36) [resolution 392,116]
448. ~26 | ~36 [avatar split clause 444,390,272]
449. ~generous(mary) | brave(mary) <- (27) [resolution 278,95]
451. ~creative(mary) <- (27) [resolution 278,113]
458. brave(mary) <- (27) [subsumption resolution 449,376]
541. curious(mary) | creative(mary) | ~brave(mary) [resolution 84,153]
542. curious(mary) | ~brave(mary) <- (27) [subsumption resolution 541,451]
543. curious(mary) <- (27) [subsumption resolution 542,458]
549. creative(mary) <- (27) [resolution 543,270]
551. $false <- (27) [subsumption resolution 549,451]
552. ~27 [avatar contradiction clause 551]
553. curious(mary) | creative(mary) [subsumption resolution 541,269]
554. creative(mary) [subsumption resolution 553,270]
578. ~curious(mary) | ~creative(mary) | ~brave(mary) [resolution 85,153]
579. ~curious(mary) | ~brave(mary) [subsumption resolution 578,554]
581. 60 <=> brave(mary) [avatar definition]
583. ~brave(mary) <- (~60) [avatar component clause 581]
585. 61 <=> curious(mary) [avatar definition]
588. ~60 | ~61 [avatar split clause 579,585,581]
605. generous(mary) | curious(mary) [resolution 554,268]
608. curious(mary) <- (~36) [subsumption resolution 605,391]
609. 61 | 36 [avatar split clause 608,390,585]
686. brave(mary) <- (~36) [resolution 376,391]
690. $false <- (~36, ~60) [subsumption resolution 686,583]
691. 36 | 60 [avatar contradiction clause 690]
692. $false [avatar sat refutation 279,448,552,588,609,691]
% SZS output end Proof for 7891004581440599615188568
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not humble is either not brave or kind. Everyone who is both not kind and humble is both curious and not humble. Everyone who is not tall or not creative is both not strong and generous and vice versa. Everyone who is either quiet or not quiet is rich or not quiet. Everyone who is both kind and not old is both not kind and not rich. If lucy is both quiet and wise then someone is either not funny or not creative. Everyone who is both not strong and funny is both not curious and not calm and vice versa. Everyone who is either not calm or strong is patient or rich and vice versa. If john is not patient then john is tall or not patient. Everyone who is not quiet or humble is both not funny and patient. Everyone who is both not creative and not quiet is either generous or humble and vice versa. Everyone who is either strong or not patient is patient. Everyone who is either not strong or not brave is either not kind or not rich and vice versa. Everyone who is both curious and kind is either not funny or not wise. Everyone who is not kind or wise is either not humble or not curious and vice versa. Everyone who is not old or kind is generous or tall and vice versa. Someone is either old or not kind. Someone is tall. Susan is calm. John is both curious and tall. John is both quiet and brave. Fred is strong or patient. | Susan is not tall. | contradiction | (![X]:((kind(X)&~humble(X))=>(~brave(X)<~>kind(X))))&
(![X]:((~kind(X)&humble(X))=>(curious(X)&~humble(X))))&
(![X]:((~tall(X)|~creative(X))<=>(~strong(X)&generous(X))))&
(![X]:((quiet(X)<~>~quiet(X))=>(rich(X)|~quiet(X))))&
(![X]:((kind(X)&~old(X))=>(~kind(X)&~rich(X))))&
(((quiet(lucy)&wise(lucy)))=>(?[X]:((~funny(X)<~>~creative(X)))))&
(![X]:((~strong(X)&funny(X))<=>(~curious(X)&~calm(X))))&
(![X]:((~calm(X)<~>strong(X))<=>(patient(X)|rich(X))))&
((~patient(john))=>((tall(john)|~patient(john))))&
(![X]:((~quiet(X)|humble(X))=>(~funny(X)&patient(X))))&
(![X]:((~creative(X)&~quiet(X))<=>(generous(X)<~>humble(X))))&
(![X]:((strong(X)<~>~patient(X))=>patient(X)))&
(![X]:((~strong(X)<~>~brave(X))<=>(~kind(X)<~>~rich(X))))&
(![X]:((curious(X)&kind(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~humble(X)<~>~curious(X))))&
(![X]:((~old(X)|kind(X))<=>(generous(X)|tall(X))))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:(tall(X)))&
(calm(susan))&
((curious(john)&tall(john)))&
((quiet(john)&brave(john)))&
((strong(fred)|patient(fred))) | ~tall(susan) | [
"p2",
"p7",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7554721974083588557571684
% SZS output start Proof for 7554721974083588557571684
3. ! [X0] : ((~creative(X0) | ~tall(X0)) <=> (generous(X0) & ~strong(X0))) [input p2]
8. ! [X0] : ((~calm(X0) <~> strong(X0)) <=> (rich(X0) | patient(X0))) [input p7]
12. ! [X0] : ((strong(X0) <~> ~patient(X0)) => patient(X0)) [input p11]
19. calm(susan) [input p18]
23. ~tall(susan) [input hypothesis]
37. ! [X0] : (patient(X0) | (strong(X0) <=> ~patient(X0))) [ennf transformation 12]
41. ! [X0] : (((~creative(X0) | ~tall(X0)) | (~generous(X0) | strong(X0))) & ((generous(X0) & ~strong(X0)) | (creative(X0) & tall(X0)))) [nnf transformation 3]
42. ! [X0] : ((~creative(X0) | ~tall(X0) | ~generous(X0) | strong(X0)) & ((generous(X0) & ~strong(X0)) | (creative(X0) & tall(X0)))) [flattening 41]
49. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~rich(X0) & ~patient(X0))) & ((rich(X0) | patient(X0)) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [nnf transformation 8]
50. ! [X0] : ((((~strong(X0) | calm(X0)) & (strong(X0) | ~calm(X0))) | (~rich(X0) & ~patient(X0))) & (rich(X0) | patient(X0) | ((~calm(X0) | ~strong(X0)) & (strong(X0) | calm(X0))))) [flattening 49]
53. ! [X0] : (patient(X0) | ((strong(X0) | patient(X0)) & (~patient(X0) | ~strong(X0)))) [nnf transformation 37]
69. ~strong(X0) | tall(X0) [cnf transformation 42]
86. ~patient(X0) | ~calm(X0) | strong(X0) [cnf transformation 50]
102. patient(X0) | strong(X0) | patient(X0) [cnf transformation 53]
126. calm(susan) [cnf transformation 19]
132. ~tall(susan) [cnf transformation 23]
133. patient(X0) | strong(X0) [duplicate literal removal 102]
174. 7 <=> strong(susan) [avatar definition]
176. strong(susan) <- (7) [avatar component clause 174]
183. ~calm(X0) | strong(X0) | strong(X0) [resolution 86,133]
185. ~calm(X0) | strong(X0) [duplicate literal removal 183]
195. strong(susan) [resolution 185,126]
197. 7 [avatar split clause 195,174]
210. tall(susan) <- (7) [resolution 176,69]
211. $false <- (7) [subsumption resolution 210,132]
212. ~7 [avatar contradiction clause 211]
213. $false [avatar sat refutation 197,212]
% SZS output end Proof for 7554721974083588557571684
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not brave then lucy is generous or not strong.
If someone is funny or not old then susan is either not creative or not curious and vice versa.
Everyone who is both not brave and creative is not brave and vice versa.
Everyone who is both quiet and happy is not happy and vice versa.
Everyone who is both kind and creative is either not generous or funny and vice versa.
If susan is not strong then someone is not humble and vice versa.
Everyone who is both brave and not calm is both not happy and not kind and vice versa.
Everyone who is either kind or strong is both not calm and not creative.
Everyone who is both not strong and old is either not funny or not quiet and vice versa.
If john is either not rich or not kind then mary is either not wise or tall and vice versa.
Everyone who is either not rich or wise is either rich or not creative and vice versa.
Everyone who is both happy and strong is both not calm and not old and vice versa.
Everyone who is both calm and patient is quiet or curious.
Everyone who is not rich or not strong is not humble.
If someone is both creative and strong then someone is funny and vice versa.
Everyone who is rich or not creative is not strong and vice versa.
Fred is either quiet or not tall.
Someone is either not humble or not brave.
Alice is either not brave or not quiet.
John is creative or not happy.
Paul is both creative and funny.
Mary is either creative or not happy.
Alice is funny or not kind. | Alice is strong. | contradiction | ((~brave(susan))=>((generous(lucy)|~strong(lucy))))&
((?[X]:((funny(X)|~old(X))))<=>((~creative(susan)<~>~curious(susan))))&
(![X]:((~brave(X)&creative(X))<=>~brave(X)))&
(![X]:((quiet(X)&happy(X))<=>~happy(X)))&
(![X]:((kind(X)&creative(X))<=>(~generous(X)<~>funny(X))))&
((~strong(susan))<=>(?[X]:(~humble(X))))&
(![X]:((brave(X)&~calm(X))<=>(~happy(X)&~kind(X))))&
(![X]:((kind(X)<~>strong(X))=>(~calm(X)&~creative(X))))&
(![X]:((~strong(X)&old(X))<=>(~funny(X)<~>~quiet(X))))&
(((~rich(john)<~>~kind(john)))<=>((~wise(mary)<~>tall(mary))))&
(![X]:((~rich(X)<~>wise(X))<=>(rich(X)<~>~creative(X))))&
(![X]:((happy(X)&strong(X))<=>(~calm(X)&~old(X))))&
(![X]:((calm(X)&patient(X))=>(quiet(X)|curious(X))))&
(![X]:((~rich(X)|~strong(X))=>~humble(X)))&
((?[X]:((creative(X)&strong(X))))<=>(?[X]:(funny(X))))&
(![X]:((rich(X)|~creative(X))<=>~strong(X)))&
((quiet(fred)<~>~tall(fred)))&
(?[X]:((~humble(X)<~>~brave(X))))&
((~brave(alice)<~>~quiet(alice)))&
((creative(john)|~happy(john)))&
((creative(paul)&funny(paul)))&
((creative(mary)<~>~happy(mary)))&
((funny(alice)|~kind(alice))) | strong(alice) | [
"p3",
"p6",
"p11",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 7827952115937877573802803
% SZS output start Proof for 7827952115937877573802803
4. ! [X0] : ((happy(X0) & quiet(X0)) <=> ~happy(X0)) [input p3]
7. ! [X0] : ((~calm(X0) & brave(X0)) <=> (~kind(X0) & ~happy(X0))) [input p6]
12. ! [X0] : ((strong(X0) & happy(X0)) <=> (~old(X0) & ~calm(X0))) [input p11]
19. ~brave(alice) <~> ~quiet(alice) [input p18]
24. strong(alice) [input hypothesis]
37. ! [X0] : (((happy(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | (~happy(X0) | ~quiet(X0)))) [nnf transformation 4]
38. ! [X0] : (((happy(X0) & quiet(X0)) | happy(X0)) & (~happy(X0) | ~happy(X0) | ~quiet(X0))) [flattening 37]
45. ! [X0] : (((~calm(X0) & brave(X0)) | (kind(X0) | happy(X0))) & ((~kind(X0) & ~happy(X0)) | (calm(X0) | ~brave(X0)))) [nnf transformation 7]
46. ! [X0] : (((~calm(X0) & brave(X0)) | kind(X0) | happy(X0)) & ((~kind(X0) & ~happy(X0)) | calm(X0) | ~brave(X0))) [flattening 45]
52. ! [X0] : (((strong(X0) & happy(X0)) | (old(X0) | calm(X0))) & ((~old(X0) & ~calm(X0)) | (~strong(X0) | ~happy(X0)))) [nnf transformation 12]
53. ! [X0] : (((strong(X0) & happy(X0)) | old(X0) | calm(X0)) & ((~old(X0) & ~calm(X0)) | ~strong(X0) | ~happy(X0))) [flattening 52]
65. (quiet(alice) | brave(alice)) & (~quiet(alice) | ~brave(alice)) [nnf transformation 19]
77. ~happy(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 38]
79. happy(X0) | happy(X0) [cnf transformation 38]
88. ~happy(X0) | calm(X0) | ~brave(X0) [cnf transformation 46]
118. ~calm(X0) | ~strong(X0) | ~happy(X0) [cnf transformation 53]
135. quiet(alice) | brave(alice) [cnf transformation 65]
142. strong(alice) [cnf transformation 24]
147. ~happy(X0) | ~quiet(X0) [duplicate literal removal 77]
148. happy(X0) [duplicate literal removal 79]
190. ~quiet(X0) [subsumption resolution 147,148]
204. ~brave(X0) | calm(X0) [subsumption resolution 88,148]
235. ~calm(X0) | ~strong(X0) [subsumption resolution 118,148]
265. brave(alice) [subsumption resolution 135,190]
291. calm(alice) [resolution 204,265]
310. ~strong(alice) [resolution 235,291]
313. $false [subsumption resolution 310,142]
% SZS output end Proof for 7827952115937877573802803
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either tall or humble. Everyone who is either old or not rich is rich or strong. If someone is either rich or not quiet then someone is quiet or creative and vice versa. Everyone who is not rich is both tall and not quiet and vice versa. Everyone who is either not funny or not rich is both not generous and not quiet and vice versa. Everyone who is curious or patient is either tall or not tall and vice versa. Everyone who is not funny or not tall is either tall or brave. If paul is rich then paul is either not generous or patient. Everyone who is either happy or not creative is not happy and vice versa. If someone is either humble or strong then someone is tall or not creative. Everyone who is either not quiet or quiet is both quiet and not kind and vice versa. Everyone who is both creative and not kind is either not wise or calm and vice versa. Everyone who is tall is either not funny or not creative. If mary is quiet then fred is either rich or not curious and vice versa. If someone is both quiet and not strong then someone is not happy and vice versa. Everyone who is not creative or creative is either not kind or not generous. Someone is either not patient or strong. Someone is both old and rich. Susan is either not wise or old. Alice is both not creative and not wise. Susan is quiet or creative. Susan is not strong. Alice is strong or wise. | Fred is not creative. | entailment | (![X]:(~brave(X)=>(tall(X)<~>humble(X))))&
(![X]:((old(X)<~>~rich(X))=>(rich(X)|strong(X))))&
((?[X]:((rich(X)<~>~quiet(X))))<=>(?[X]:((quiet(X)|creative(X)))))&
(![X]:(~rich(X)<=>(tall(X)&~quiet(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>(~generous(X)&~quiet(X))))&
(![X]:((curious(X)|patient(X))<=>(tall(X)<~>~tall(X))))&
(![X]:((~funny(X)|~tall(X))=>(tall(X)<~>brave(X))))&
((rich(paul))=>((~generous(paul)<~>patient(paul))))&
(![X]:((happy(X)<~>~creative(X))<=>~happy(X)))&
((?[X]:((humble(X)<~>strong(X))))=>(?[X]:((tall(X)|~creative(X)))))&
(![X]:((~quiet(X)<~>quiet(X))<=>(quiet(X)&~kind(X))))&
(![X]:((creative(X)&~kind(X))<=>(~wise(X)<~>calm(X))))&
(![X]:(tall(X)=>(~funny(X)<~>~creative(X))))&
((quiet(mary))<=>((rich(fred)<~>~curious(fred))))&
((?[X]:((quiet(X)&~strong(X))))<=>(?[X]:(~happy(X))))&
(![X]:((~creative(X)|creative(X))=>(~kind(X)<~>~generous(X))))&
(?[X]:((~patient(X)<~>strong(X))))&
(?[X]:((old(X)&rich(X))))&
((~wise(susan)<~>old(susan)))&
((~creative(alice)&~wise(alice)))&
((quiet(susan)|creative(susan)))&
(~strong(susan))&
((strong(alice)|wise(alice))) | ~creative(fred) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 5902273006144026405576252
% SZS output start Proof for 5902273006144026405576252
9. ! [X0] : ((happy(X0) <~> ~creative(X0)) <=> ~happy(X0)) [input p8]
24. creative(fred) [input hypothesis]
51. ! [X0] : ((((creative(X0) | ~happy(X0)) & (~creative(X0) | happy(X0))) | happy(X0)) & (~happy(X0) | ((happy(X0) | creative(X0)) & (~creative(X0) | ~happy(X0))))) [nnf transformation 9]
105. ~happy(X0) | ~creative(X0) | ~happy(X0) [cnf transformation 51]
107. ~creative(X0) | happy(X0) | happy(X0) [cnf transformation 51]
147. creative(fred) [cnf transformation 24]
154. ~happy(X0) | ~creative(X0) [duplicate literal removal 105]
155. ~creative(X0) | happy(X0) [duplicate literal removal 107]
161. 1 <=> ! [X1] : ~creative(X1) [avatar definition]
162. ~creative(X1) <- (1) [avatar component clause 161]
211. ~creative(X0) [subsumption resolution 154,155]
212. 1 [avatar split clause 211,161]
289. $false <- (1) [resolution 162,147]
290. ~1 [avatar contradiction clause 289]
291. $false [avatar sat refutation 212,290]
% SZS output end Proof for 5902273006144026405576252
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not quiet or not creative then someone is either brave or not kind.
Everyone who is not tall or not creative is both wise and not patient.
If someone is not humble or curious then alice is not patient and vice versa.
Everyone who is both rich and not patient is brave or creative.
Everyone who is either strong or not funny is not strong.
Everyone who is both calm and not calm is both not funny and creative and vice versa.
Everyone who is not old or not calm is old or tall and vice versa.
If someone is old or curious then someone is tall and vice versa.
If mary is both patient and not kind then someone is both not quiet and humble.
If alice is either not quiet or not happy then someone is both patient and not calm and vice versa.
If someone is not humble or not rich then paul is tall and vice versa.
Everyone who is both not rich and not creative is not calm or happy.
Everyone who is both humble and not humble is humble or not strong and vice versa.
If mary is curious then someone is both curious and not curious.
If someone is both generous and not brave then someone is not happy.
Lucy is either strong or not generous.
Susan is both not happy and not quiet.
Someone is brave.
Lucy is either not happy or not wise.
Someone is quiet.
Lucy is not humble or not tall. | Mary is funny. | contradiction | ((?[X]:((~quiet(X)<~>~creative(X))))=>(?[X]:((brave(X)<~>~kind(X)))))&
(![X]:((~tall(X)|~creative(X))=>(wise(X)&~patient(X))))&
((?[X]:((~humble(X)|curious(X))))<=>(~patient(alice)))&
(![X]:((rich(X)&~patient(X))=>(brave(X)|creative(X))))&
(![X]:((strong(X)<~>~funny(X))=>~strong(X)))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)&creative(X))))&
(![X]:((~old(X)|~calm(X))<=>(old(X)|tall(X))))&
((?[X]:((old(X)|curious(X))))<=>(?[X]:(tall(X))))&
(((patient(mary)&~kind(mary)))=>(?[X]:((~quiet(X)&humble(X)))))&
(((~quiet(alice)<~>~happy(alice)))<=>(?[X]:((patient(X)&~calm(X)))))&
((?[X]:((~humble(X)|~rich(X))))<=>(tall(paul)))&
(![X]:((~rich(X)&~creative(X))=>(~calm(X)|happy(X))))&
(![X]:((humble(X)&~humble(X))<=>(humble(X)|~strong(X))))&
((curious(mary))=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:((generous(X)&~brave(X))))=>(?[X]:(~happy(X))))&
((strong(lucy)<~>~generous(lucy)))&
((~happy(susan)&~quiet(susan)))&
(?[X]:(brave(X)))&
((~happy(lucy)<~>~wise(lucy)))&
(?[X]:(quiet(X)))&
((~humble(lucy)|~tall(lucy))) | funny(mary) | [
"p4",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4084087297849766817200006
% SZS output start Proof for 4084087297849766817200006
5. ! [X0] : ((strong(X0) <~> ~funny(X0)) => ~strong(X0)) [input p4]
13. ! [X0] : ((~humble(X0) & humble(X0)) <=> (~strong(X0) | humble(X0))) [input p12]
22. funny(mary) [input hypothesis]
30. ! [X0] : (~strong(X0) | (strong(X0) <=> ~funny(X0))) [ennf transformation 5]
45. ! [X0] : (~strong(X0) | ((strong(X0) | funny(X0)) & (~funny(X0) | ~strong(X0)))) [nnf transformation 30]
65. ! [X0] : (((~humble(X0) & humble(X0)) | (strong(X0) & ~humble(X0))) & ((~strong(X0) | humble(X0)) | (humble(X0) | ~humble(X0)))) [nnf transformation 13]
66. ! [X0] : (((~humble(X0) & humble(X0)) | (strong(X0) & ~humble(X0))) & (~strong(X0) | humble(X0) | humble(X0) | ~humble(X0))) [flattening 65]
90. ~strong(X0) | ~funny(X0) | ~strong(X0) [cnf transformation 45]
117. humble(X0) | strong(X0) [cnf transformation 66]
118. ~humble(X0) | ~humble(X0) [cnf transformation 66]
132. funny(mary) [cnf transformation 22]
134. ~humble(X0) [duplicate literal removal 118]
137. ~funny(X0) | ~strong(X0) [duplicate literal removal 90]
261. strong(X0) [subsumption resolution 117,134]
297. ~strong(mary) [resolution 137,132]
298. $false [subsumption resolution 297,261]
% SZS output end Proof for 4084087297849766817200006
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and not tall then alice is not creative or funny and vice versa. Everyone who is creative or not strong is both calm and not rich. Everyone who is patient or not rich is strong or not tall. If mary is both quiet and not brave then john is both strong and brave and vice versa. Everyone who is both happy and funny is happy and vice versa. Everyone who is both not humble and not curious is not strong or tall and vice versa. Everyone who is not strong or funny is calm. If lucy is either tall or not generous then fred is either tall or not strong. If someone is both not calm and not happy then fred is old or not generous and vice versa. Everyone who is either not calm or rich is both creative and curious. If mary is curious then fred is either not calm or not happy. If fred is either not calm or not humble then paul is either not generous or curious and vice versa. If someone is kind or not calm then john is both not quiet and not brave. If susan is quiet or not tall then john is both strong and calm and vice versa. Everyone who is curious is either curious or humble. Everyone who is both old and not brave is not calm or not strong and vice versa. Paul is both not creative and quiet. Mary is either not brave or patient. Fred is not rich. John is not curious. Someone is either not creative or not happy. Susan is both not calm and quiet. Someone is both not wise and humble. | Alice is not rich. | neutral | ((?[X]:((~rich(X)&~tall(X))))<=>((~creative(alice)|funny(alice))))&
(![X]:((creative(X)|~strong(X))=>(calm(X)&~rich(X))))&
(![X]:((patient(X)|~rich(X))=>(strong(X)|~tall(X))))&
(((quiet(mary)&~brave(mary)))<=>((strong(john)&brave(john))))&
(![X]:((happy(X)&funny(X))<=>happy(X)))&
(![X]:((~humble(X)&~curious(X))<=>(~strong(X)|tall(X))))&
(![X]:((~strong(X)|funny(X))=>calm(X)))&
(((tall(lucy)<~>~generous(lucy)))=>((tall(fred)<~>~strong(fred))))&
((?[X]:((~calm(X)&~happy(X))))<=>((old(fred)|~generous(fred))))&
(![X]:((~calm(X)<~>rich(X))=>(creative(X)&curious(X))))&
((curious(mary))=>((~calm(fred)<~>~happy(fred))))&
(((~calm(fred)<~>~humble(fred)))<=>((~generous(paul)<~>curious(paul))))&
((?[X]:((kind(X)|~calm(X))))=>((~quiet(john)&~brave(john))))&
(((quiet(susan)|~tall(susan)))<=>((strong(john)&calm(john))))&
(![X]:(curious(X)=>(curious(X)<~>humble(X))))&
(![X]:((old(X)&~brave(X))<=>(~calm(X)|~strong(X))))&
((~creative(paul)&quiet(paul)))&
((~brave(mary)<~>patient(mary)))&
(~rich(fred))&
(~curious(john))&
(?[X]:((~creative(X)<~>~happy(X))))&
((~calm(susan)&quiet(susan)))&
(?[X]:((~wise(X)&humble(X)))) | ~rich(alice) | [] | null | 0 |
Everyone who is both wise and curious is calm and vice versa.
If susan is happy or not old then alice is both not curious and not quiet.
If someone is both humble and not humble then mary is either not wise or humble and vice versa.
If mary is not quiet or not funny then someone is funny.
If fred is not wise or not generous then mary is either strong or not brave.
If someone is both not calm and not strong then someone is both humble and not rich.
Everyone who is happy or calm is not creative and vice versa.
If john is either not generous or kind then someone is either happy or not kind and vice versa.
Everyone who is either not humble or strong is either not strong or not curious.
If lucy is both not curious and not strong then someone is either not brave or not patient and vice versa.
Everyone who is either not tall or quiet is brave or not calm.
Everyone who is either not kind or not rich is either not quiet or generous.
Everyone who is tall or not funny is not wise or wise and vice versa.
Everyone who is either funny or rich is both not wise and not rich and vice versa.
Everyone who is both not generous and not creative is either humble or not generous.
Everyone who is either creative or calm is strong or not old and vice versa.
Someone is not patient or not creative.
Susan is both not patient and not old.
Someone is happy.
Lucy is either not wise or wise.
Someone is tall.
Someone is both not strong and curious.
Susan is quiet. | Alice is rich. | neutral | (![X]:((wise(X)&curious(X))<=>calm(X)))&
(((happy(susan)|~old(susan)))=>((~curious(alice)&~quiet(alice))))&
((?[X]:((humble(X)&~humble(X))))<=>((~wise(mary)<~>humble(mary))))&
(((~quiet(mary)|~funny(mary)))=>(?[X]:(funny(X))))&
(((~wise(fred)|~generous(fred)))=>((strong(mary)<~>~brave(mary))))&
((?[X]:((~calm(X)&~strong(X))))=>(?[X]:((humble(X)&~rich(X)))))&
(![X]:((happy(X)|calm(X))<=>~creative(X)))&
(((~generous(john)<~>kind(john)))<=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((~humble(X)<~>strong(X))=>(~strong(X)<~>~curious(X))))&
(((~curious(lucy)&~strong(lucy)))<=>(?[X]:((~brave(X)<~>~patient(X)))))&
(![X]:((~tall(X)<~>quiet(X))=>(brave(X)|~calm(X))))&
(![X]:((~kind(X)<~>~rich(X))=>(~quiet(X)<~>generous(X))))&
(![X]:((tall(X)|~funny(X))<=>(~wise(X)|wise(X))))&
(![X]:((funny(X)<~>rich(X))<=>(~wise(X)&~rich(X))))&
(![X]:((~generous(X)&~creative(X))=>(humble(X)<~>~generous(X))))&
(![X]:((creative(X)<~>calm(X))<=>(strong(X)|~old(X))))&
(?[X]:((~patient(X)|~creative(X))))&
((~patient(susan)&~old(susan)))&
(?[X]:(happy(X)))&
((~wise(lucy)<~>wise(lucy)))&
(?[X]:(tall(X)))&
(?[X]:((~strong(X)&curious(X))))&
(quiet(susan)) | rich(alice) | [] | null | 0 |
If john is patient or generous then someone is both not quiet and kind.
If lucy is humble or not brave then lucy is not calm or not humble and vice versa.
Everyone who is both creative and not old is not brave or curious and vice versa.
If someone is not curious or kind then someone is both quiet and patient and vice versa.
If paul is not tall or generous then fred is either humble or not generous and vice versa.
If someone is both not old and kind then someone is old or not brave.
Everyone who is happy or not strong is not calm and vice versa.
Everyone who is old is wise and vice versa.
Everyone who is both wise and not curious is either patient or not happy and vice versa.
If someone is not tall or not wise then someone is both patient and not wise.
Everyone who is either humble or not old is both brave and funny and vice versa.
Everyone who is funny is both not kind and humble.
If someone is either not wise or not brave then paul is not humble and vice versa.
Everyone who is not quiet is either not tall or not quiet and vice versa.
If susan is either old or strong then susan is happy.
Everyone who is either creative or not generous is not generous or not wise.
Lucy is curious or old.
Paul is not curious.
Someone is either quiet or funny.
Someone is not humble.
Alice is funny or not kind.
Someone is both not calm and creative.
Someone is either brave or not happy. | Fred is not generous. | neutral | (((patient(john)|generous(john)))=>(?[X]:((~quiet(X)&kind(X)))))&
(((humble(lucy)|~brave(lucy)))<=>((~calm(lucy)|~humble(lucy))))&
(![X]:((creative(X)&~old(X))<=>(~brave(X)|curious(X))))&
((?[X]:((~curious(X)|kind(X))))<=>(?[X]:((quiet(X)&patient(X)))))&
(((~tall(paul)|generous(paul)))<=>((humble(fred)<~>~generous(fred))))&
((?[X]:((~old(X)&kind(X))))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:((happy(X)|~strong(X))<=>~calm(X)))&
(![X]:(old(X)<=>wise(X)))&
(![X]:((wise(X)&~curious(X))<=>(patient(X)<~>~happy(X))))&
((?[X]:((~tall(X)|~wise(X))))=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((humble(X)<~>~old(X))<=>(brave(X)&funny(X))))&
(![X]:(funny(X)=>(~kind(X)&humble(X))))&
((?[X]:((~wise(X)<~>~brave(X))))<=>(~humble(paul)))&
(![X]:(~quiet(X)<=>(~tall(X)<~>~quiet(X))))&
(((old(susan)<~>strong(susan)))=>(happy(susan)))&
(![X]:((creative(X)<~>~generous(X))=>(~generous(X)|~wise(X))))&
((curious(lucy)|old(lucy)))&
(~curious(paul))&
(?[X]:((quiet(X)<~>funny(X))))&
(?[X]:(~humble(X)))&
((funny(alice)|~kind(alice)))&
(?[X]:((~calm(X)&creative(X))))&
(?[X]:((brave(X)<~>~happy(X)))) | ~generous(fred) | [] | null | 0 |
If paul is both curious and 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 calm.
Mary is not kind.
Paul is not patient.
Someone is both quiet and generous.
Someone is creative or quiet.
Lucy is not old.
Paul is calm or not humble. | Alice is creative. | contradiction | (((curious(paul)&~rich(paul)))=>(?[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)|calm(X))))&
(~kind(mary))&
(~patient(paul))&
(?[X]:((quiet(X)&generous(X))))&
(?[X]:((creative(X)|quiet(X))))&
(~old(lucy))&
((calm(paul)|~humble(paul))) | creative(alice) | [
"p6",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7018866680998536594198419
% SZS output start Proof for 7018866680998536594198419
7. ! [X0] : ((~calm(X0) & ~creative(X0)) <=> (kind(X0) | strong(X0))) [input p6]
15. ! [X0] : ((~creative(X0) <~> ~kind(X0)) <=> kind(X0)) [input p14]
25. creative(alice) [input hypothesis]
53. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~kind(X0) & ~strong(X0))) & ((kind(X0) | strong(X0)) | (calm(X0) | creative(X0)))) [nnf transformation 7]
54. ! [X0] : (((~calm(X0) & ~creative(X0)) | (~kind(X0) & ~strong(X0))) & (kind(X0) | strong(X0) | calm(X0) | creative(X0))) [flattening 53]
68. ! [X0] : ((((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0))))) [nnf transformation 15]
84. ~creative(X0) | ~kind(X0) [cnf transformation 54]
112. kind(X0) | ~creative(X0) | kind(X0) [cnf transformation 68]
121. creative(alice) [cnf transformation 25]
122. kind(X0) | ~creative(X0) [duplicate literal removal 112]
140. 4 <=> ! [X1] : ~creative(X1) [avatar definition]
141. ~creative(X1) <- (4) [avatar component clause 140]
226. ~creative(X0) [subsumption resolution 122,84]
227. 4 [avatar split clause 226,140]
243. $false <- (4) [resolution 141,121]
244. ~4 [avatar contradiction clause 243]
245. $false [avatar sat refutation 227,244]
% SZS output end Proof for 7018866680998536594198419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative and calm is old. If someone is both not quiet and not calm then fred is not old or calm and vice versa. Everyone who is both not creative and kind is not calm or rich and vice versa. If alice is both old and not calm then someone is quiet or happy and vice versa. Everyone who is kind is both quiet and generous. If someone is both not kind and not calm then someone is both not curious and not tall and vice versa. If someone is not humble or not calm then lucy is strong or not patient. Everyone who is both not rich and happy is curious and vice versa. Everyone who is strong is both funny and strong and vice versa. If fred is either not tall or not creative then fred is not rich or not funny. Everyone who is not brave or funny is not tall and vice versa. If someone is either not kind or curious then paul is both not quiet and not generous. Everyone who is happy or not calm is not brave. Everyone who is either not wise or not curious is not patient and vice versa. Everyone who is both not brave and not old is both not calm and tall. If lucy is both curious and not brave then alice is both rich and patient and vice versa. Lucy is humble. Susan is brave. Someone is either strong or not calm. Alice is quiet or creative. Someone is generous or not old. Susan is both patient and calm. | Paul is kind. | contradiction | (![X]:((creative(X)&calm(X))=>old(X)))&
((?[X]:((~quiet(X)&~calm(X))))<=>((~old(fred)|calm(fred))))&
(![X]:((~creative(X)&kind(X))<=>(~calm(X)|rich(X))))&
(((old(alice)&~calm(alice)))<=>(?[X]:((quiet(X)|happy(X)))))&
(![X]:(kind(X)=>(quiet(X)&generous(X))))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
((?[X]:((~humble(X)|~calm(X))))=>((strong(lucy)|~patient(lucy))))&
(![X]:((~rich(X)&happy(X))<=>curious(X)))&
(![X]:(strong(X)<=>(funny(X)&strong(X))))&
(((~tall(fred)<~>~creative(fred)))=>((~rich(fred)|~funny(fred))))&
(![X]:((~brave(X)|funny(X))<=>~tall(X)))&
((?[X]:((~kind(X)<~>curious(X))))=>((~quiet(paul)&~generous(paul))))&
(![X]:((happy(X)|~calm(X))=>~brave(X)))&
(![X]:((~wise(X)<~>~curious(X))<=>~patient(X)))&
(![X]:((~brave(X)&~old(X))=>(~calm(X)&tall(X))))&
(((curious(lucy)&~brave(lucy)))<=>((rich(alice)&patient(alice))))&
(humble(lucy))&
(brave(susan))&
(?[X]:((strong(X)<~>~calm(X))))&
((quiet(alice)|creative(alice)))&
(?[X]:((generous(X)|~old(X))))&
((patient(susan)&calm(susan))) | kind(paul) | [
"p1",
"p2",
"p4",
"p5",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 212731064695894696620266
% SZS output start Proof for 212731064695894696620266
2. ? [X0] : (~calm(X0) & ~quiet(X0)) <=> (calm(fred) | ~old(fred)) [input p1]
3. ! [X0] : ((kind(X0) & ~creative(X0)) <=> (rich(X0) | ~calm(X0))) [input p2]
5. ! [X0] : (kind(X0) => (generous(X0) & quiet(X0))) [input p4]
6. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X0] : (~tall(X0) & ~curious(X0)) [input p5]
11. ! [X0] : ((funny(X0) | ~brave(X0)) <=> ~tall(X0)) [input p10]
12. ? [X0] : (~kind(X0) <~> curious(X0)) => (~generous(paul) & ~quiet(paul)) [input p11]
13. ! [X0] : ((~calm(X0) | happy(X0)) => ~brave(X0)) [input p12]
23. kind(paul) [input hypothesis]
24. ? [X0] : (~calm(X0) & ~kind(X0)) <=> ? [X1] : (~tall(X1) & ~curious(X1)) [rectify 6]
29. ! [X0] : ((generous(X0) & quiet(X0)) | ~kind(X0)) [ennf transformation 5]
34. (~generous(paul) & ~quiet(paul)) | ! [X0] : (~kind(X0) <=> curious(X0)) [ennf transformation 12]
35. ! [X0] : (~brave(X0) | (calm(X0) & ~happy(X0))) [ennf transformation 13]
38. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & ((calm(fred) | ~old(fred)) | ! [X0] : (calm(X0) | quiet(X0))) [nnf transformation 2]
39. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X0] : (calm(X0) | quiet(X0))) [flattening 38]
40. (? [X0] : (~calm(X0) & ~quiet(X0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X1] : (calm(X1) | quiet(X1))) [rectify 39]
41. ? [X0] : (~calm(X0) & ~quiet(X0)) => (~calm(sK0) & ~quiet(sK0)) [choice axiom]
42. ((~calm(sK0) & ~quiet(sK0)) | (~calm(fred) & old(fred))) & (calm(fred) | ~old(fred) | ! [X1] : (calm(X1) | quiet(X1))) [skolemisation 40,41]
43. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & ((rich(X0) | ~calm(X0)) | (~kind(X0) | creative(X0)))) [nnf transformation 3]
44. ! [X0] : (((kind(X0) & ~creative(X0)) | (~rich(X0) & calm(X0))) & (rich(X0) | ~calm(X0) | ~kind(X0) | creative(X0))) [flattening 43]
50. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : (tall(X1) | curious(X1))) & (? [X1] : (~tall(X1) & ~curious(X1)) | ! [X0] : (calm(X0) | kind(X0))) [nnf transformation 24]
51. (? [X0] : (~calm(X0) & ~kind(X0)) | ! [X1] : (tall(X1) | curious(X1))) & (? [X2] : (~tall(X2) & ~curious(X2)) | ! [X3] : (calm(X3) | kind(X3))) [rectify 50]
52. ? [X0] : (~calm(X0) & ~kind(X0)) => (~calm(sK2) & ~kind(sK2)) [choice axiom]
53. ? [X2] : (~tall(X2) & ~curious(X2)) => (~tall(sK3) & ~curious(sK3)) [choice axiom]
54. ((~calm(sK2) & ~kind(sK2)) | ! [X1] : (tall(X1) | curious(X1))) & ((~tall(sK3) & ~curious(sK3)) | ! [X3] : (calm(X3) | kind(X3))) [skolemisation 51,53,52]
60. ! [X0] : (((funny(X0) | ~brave(X0)) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [nnf transformation 11]
61. ! [X0] : ((funny(X0) | ~brave(X0) | tall(X0)) & (~tall(X0) | (~funny(X0) & brave(X0)))) [flattening 60]
62. (~generous(paul) & ~quiet(paul)) | ! [X0] : ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0))) [nnf transformation 34]
76. ~calm(sK0) | ~calm(fred) [cnf transformation 42]
80. kind(X0) | calm(X0) [cnf transformation 44]
87. ~kind(X0) | quiet(X0) [cnf transformation 29]
91. ~kind(sK2) | tall(X1) | curious(X1) [cnf transformation 54]
92. ~calm(sK2) | tall(X1) | curious(X1) [cnf transformation 54]
102. ~tall(X0) | brave(X0) [cnf transformation 61]
106. ~quiet(paul) | ~kind(X0) | ~curious(X0) [cnf transformation 62]
110. ~brave(X0) | calm(X0) [cnf transformation 35]
128. kind(paul) [cnf transformation 23]
130. 1 <=> calm(fred) [avatar definition]
132. ~calm(fred) <- (~1) [avatar component clause 130]
134. 2 <=> calm(sK0) [avatar definition]
136. ~calm(sK0) <- (~2) [avatar component clause 134]
137. ~1 | ~2 [avatar split clause 76,134,130]
181. 12 <=> ! [X1] : (tall(X1) | curious(X1)) [avatar definition]
182. tall(X1) | curious(X1) <- (12) [avatar component clause 181]
184. 13 <=> calm(sK2) [avatar definition]
187. 12 | ~13 [avatar split clause 92,184,181]
189. 14 <=> kind(sK2) [avatar definition]
191. ~kind(sK2) <- (~14) [avatar component clause 189]
192. 12 | ~14 [avatar split clause 91,189,181]
194. 15 <=> ! [X0] : calm(X0) [avatar definition]
195. calm(X0) <- (15) [avatar component clause 194]
220. 21 <=> ! [X0] : (~kind(X0) | ~curious(X0)) [avatar definition]
221. ~curious(X0) | ~kind(X0) <- (21) [avatar component clause 220]
232. 24 <=> quiet(paul) [avatar definition]
235. 21 | ~24 [avatar split clause 106,232,220]
288. calm(sK2) <- (~14) [resolution 80,191]
291. 13 | 14 [avatar split clause 288,189,184]
292. quiet(paul) [resolution 87,128]
297. 24 [avatar split clause 292,232]
308. brave(X0) | curious(X0) <- (12) [resolution 182,102]
424. curious(X1) | calm(X1) <- (12) [resolution 308,110]
440. calm(X0) | ~kind(X0) <- (12, 21) [resolution 424,221]
446. calm(X0) <- (12, 21) [subsumption resolution 440,80]
447. 15 | ~12 | ~21 [avatar split clause 446,220,181,194]
449. $false <- (~1, 15) [resolution 195,132]
453. $false <- (~2, 15) [resolution 195,136]
458. 2 | ~15 [avatar contradiction clause 453]
462. 1 | ~15 [avatar contradiction clause 449]
463. $false [avatar sat refutation 137,187,192,235,291,297,447,458,462]
% SZS output end Proof for 212731064695894696620266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not wise is either not happy or wise.
Everyone who is not rich or not humble is both not kind and rich.
Everyone who is happy or not brave is either quiet or old and vice versa.
Everyone who is wise or not curious is not strong and vice versa.
Everyone who is not patient is patient.
If susan is brave then someone is tall.
Everyone who is not old or happy is both old and not wise and vice versa.
If someone is either funny or kind then someone is strong.
Everyone who is both not strong and not wise is either not generous or old.
If someone is not brave then john is not calm or funny.
If someone is either not kind or generous then lucy is both not brave and not creative.
If alice is both funny and not old then someone is not old or brave and vice versa.
If someone is either not old or creative then someone is tall.
If paul is either funny or strong then alice is both humble and not rich.
Everyone who is both not creative and not calm is either not tall or happy.
Someone is either happy or calm.
Susan is brave or not strong.
Someone is either funny or not generous.
Someone is not creative.
Someone is not funny or not kind. | John is not rich. | contradiction | (![X]:(~wise(X)=>(~happy(X)<~>wise(X))))&
(![X]:((~rich(X)|~humble(X))=>(~kind(X)&rich(X))))&
(![X]:((happy(X)|~brave(X))<=>(quiet(X)<~>old(X))))&
(![X]:((wise(X)|~curious(X))<=>~strong(X)))&
(![X]:(~patient(X)=>patient(X)))&
((brave(susan))=>(?[X]:(tall(X))))&
(![X]:((~old(X)|happy(X))<=>(old(X)&~wise(X))))&
((?[X]:((funny(X)<~>kind(X))))=>(?[X]:(strong(X))))&
(![X]:((~strong(X)&~wise(X))=>(~generous(X)<~>old(X))))&
((?[X]:(~brave(X)))=>((~calm(john)|funny(john))))&
((?[X]:((~kind(X)<~>generous(X))))=>((~brave(lucy)&~creative(lucy))))&
(((funny(alice)&~old(alice)))<=>(?[X]:((~old(X)|brave(X)))))&
((?[X]:((~old(X)<~>creative(X))))=>(?[X]:(tall(X))))&
(((funny(paul)<~>strong(paul)))=>((humble(alice)&~rich(alice))))&
(![X]:((~creative(X)&~calm(X))=>(~tall(X)<~>happy(X))))&
(?[X]:((happy(X)<~>calm(X))))&
((brave(susan)|~strong(susan)))&
(?[X]:((funny(X)<~>~generous(X))))&
(?[X]:(~creative(X)))&
(?[X]:((~funny(X)|~kind(X)))) | ~rich(john) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 2334733151768855983114011
% SZS output start Proof for 2334733151768855983114011
2. ! [X0] : ((~humble(X0) | ~rich(X0)) => (rich(X0) & ~kind(X0))) [input p1]
21. ~rich(john) [input hypothesis]
25. ! [X0] : (~rich(X0) => (rich(X0) & ~kind(X0))) [pure predicate removal 2]
28. ! [X0] : ((rich(X0) & ~kind(X0)) | rich(X0)) [ennf transformation 25]
79. rich(X0) | rich(X0) [cnf transformation 28]
122. ~rich(john) [cnf transformation 21]
125. rich(X0) [duplicate literal removal 79]
224. $false [subsumption resolution 122,125]
% SZS output end Proof for 2334733151768855983114011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not old or old is not kind and vice versa. If someone is either not generous or not brave then someone is either not generous or strong and vice versa. Everyone who is creative is either patient or wise. If someone is either strong or not calm then lucy is either not old or not quiet. If someone is not curious then alice is strong. Everyone who is not rich or brave is not quiet. Everyone who is both not funny and generous is curious or happy. If someone is happy or not patient then someone is old or not rich and vice versa. Everyone who is not creative is not wise. Everyone who is both brave and creative is not strong. If someone is either not funny or not happy then fred is both wise and not tall. If someone is creative then john is quiet. If someone is generous or not rich then someone is either not generous or wise. Everyone who is both generous and quiet is strong. If someone is either not funny or tall then john is both generous and kind. Paul is both happy and tall. Someone is not creative. Someone is not old. Lucy is not old or curious. Someone is either not creative or not wise. Someone is not funny or not patient. Someone is not patient. | John is kind. | contradiction | (![X]:((~old(X)<~>old(X))<=>~kind(X)))&
((?[X]:((~generous(X)<~>~brave(X))))<=>(?[X]:((~generous(X)<~>strong(X)))))&
(![X]:(creative(X)=>(patient(X)<~>wise(X))))&
((?[X]:((strong(X)<~>~calm(X))))=>((~old(lucy)<~>~quiet(lucy))))&
((?[X]:(~curious(X)))=>(strong(alice)))&
(![X]:((~rich(X)|brave(X))=>~quiet(X)))&
(![X]:((~funny(X)&generous(X))=>(curious(X)|happy(X))))&
((?[X]:((happy(X)|~patient(X))))<=>(?[X]:((old(X)|~rich(X)))))&
(![X]:(~creative(X)=>~wise(X)))&
(![X]:((brave(X)&creative(X))=>~strong(X)))&
((?[X]:((~funny(X)<~>~happy(X))))=>((wise(fred)&~tall(fred))))&
((?[X]:(creative(X)))=>(quiet(john)))&
((?[X]:((generous(X)|~rich(X))))=>(?[X]:((~generous(X)<~>wise(X)))))&
(![X]:((generous(X)&quiet(X))=>strong(X)))&
((?[X]:((~funny(X)<~>tall(X))))=>((generous(john)&kind(john))))&
((happy(paul)&tall(paul)))&
(?[X]:(~creative(X)))&
(?[X]:(~old(X)))&
((~old(lucy)|curious(lucy)))&
(?[X]:((~creative(X)<~>~wise(X))))&
(?[X]:((~funny(X)|~patient(X))))&
(?[X]:(~patient(X))) | kind(john) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 331976927618506146435623
% SZS output start Proof for 331976927618506146435623
1. ! [X0] : ((~old(X0) <~> old(X0)) <=> ~kind(X0)) [input p0]
23. kind(john) [input hypothesis]
27. ! [X0] : ((~old(X0) <~> old(X0)) => ~kind(X0)) [unused predicate definition removal 1]
31. ! [X0] : (~kind(X0) | (~old(X0) <=> old(X0))) [ennf transformation 27]
44. ! [X0] : (~kind(X0) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 31]
74. ~kind(X0) | old(X0) | old(X0) [cnf transformation 44]
75. ~kind(X0) | ~old(X0) | ~old(X0) [cnf transformation 44]
120. kind(john) [cnf transformation 23]
121. ~kind(X0) | old(X0) [duplicate literal removal 74]
122. ~kind(X0) | ~old(X0) [duplicate literal removal 75]
123. ~kind(X0) [subsumption resolution 121,122]
264. $false [subsumption resolution 120,123]
% SZS output end Proof for 331976927618506146435623
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is tall is quiet and vice versa. If someone is not strong or not kind then someone is not wise. Everyone who is both not humble and not strong is both not calm and not strong. If someone is both wise and not humble then mary is humble. If alice is both old and rich then someone is both not funny and quiet. If paul is not calm then susan is either old or not rich. Everyone who is both funny and not patient is rich and vice versa. Everyone who is both not brave and humble is kind or not calm. If john is happy then fred is either not old or not happy and vice versa. If someone is either brave or creative then someone is not brave and vice versa. Everyone who is curious is funny. If lucy is funny then fred is not quiet and vice versa. Everyone who is calm is either funny or not rich and vice versa. If john is not kind then someone is either quiet or old. Everyone who is not strong is both generous and old and vice versa. If someone is either patient or kind then fred is both curious and not rich and vice versa. Someone is either creative or not strong. Someone is calm or not creative. Paul is not brave. Susan is not tall. Fred is not funny or not creative. Susan is happy. Someone is either not generous or strong. | Lucy is brave. | neutral | (![X]:(tall(X)<=>quiet(X)))&
((?[X]:((~strong(X)|~kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~humble(X)&~strong(X))=>(~calm(X)&~strong(X))))&
((?[X]:((wise(X)&~humble(X))))=>(humble(mary)))&
(((old(alice)&rich(alice)))=>(?[X]:((~funny(X)&quiet(X)))))&
((~calm(paul))=>((old(susan)<~>~rich(susan))))&
(![X]:((funny(X)&~patient(X))<=>rich(X)))&
(![X]:((~brave(X)&humble(X))=>(kind(X)|~calm(X))))&
((happy(john))<=>((~old(fred)<~>~happy(fred))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>funny(X)))&
((funny(lucy))<=>(~quiet(fred)))&
(![X]:(calm(X)<=>(funny(X)<~>~rich(X))))&
((~kind(john))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:(~strong(X)<=>(generous(X)&old(X))))&
((?[X]:((patient(X)<~>kind(X))))<=>((curious(fred)&~rich(fred))))&
(?[X]:((creative(X)<~>~strong(X))))&
(?[X]:((calm(X)|~creative(X))))&
(~brave(paul))&
(~tall(susan))&
((~funny(fred)|~creative(fred)))&
(happy(susan))&
(?[X]:((~generous(X)<~>strong(X)))) | brave(lucy) | [] | null | 0 |
If someone is calm then alice is both creative and tall and vice versa. Everyone who is both not patient and funny is either brave or funny. Everyone who is either tall or not generous is not calm or not happy. Everyone who is either not humble or strong is rich. Everyone who is quiet or not patient is creative. If john is not patient then someone is both wise and not kind and vice versa. If fred is not humble then someone is curious. If alice is not patient then fred is either not strong or not quiet and vice versa. Everyone who is strong or not rich is both creative and not patient. Everyone who is both not happy and quiet is either not old or not happy and vice versa. Everyone who is both funny and not creative is not quiet or not wise and vice versa. If someone is quiet or not wise then someone is both not old and not rich and vice versa. Everyone who is either strong or old is not kind or humble. Everyone who is quiet is old or not funny and vice versa. If someone is either not curious or kind then paul is both not calm and not creative and vice versa. Mary is not calm or not funny. Fred is either not old or humble. Someone is not happy. Someone is not creative or not patient. Fred is patient. | Alice is not curious. | neutral | ((?[X]:(calm(X)))<=>((creative(alice)&tall(alice))))&
(![X]:((~patient(X)&funny(X))=>(brave(X)<~>funny(X))))&
(![X]:((tall(X)<~>~generous(X))=>(~calm(X)|~happy(X))))&
(![X]:((~humble(X)<~>strong(X))=>rich(X)))&
(![X]:((quiet(X)|~patient(X))=>creative(X)))&
((~patient(john))<=>(?[X]:((wise(X)&~kind(X)))))&
((~humble(fred))=>(?[X]:(curious(X))))&
((~patient(alice))<=>((~strong(fred)<~>~quiet(fred))))&
(![X]:((strong(X)|~rich(X))=>(creative(X)&~patient(X))))&
(![X]:((~happy(X)&quiet(X))<=>(~old(X)<~>~happy(X))))&
(![X]:((funny(X)&~creative(X))<=>(~quiet(X)|~wise(X))))&
((?[X]:((quiet(X)|~wise(X))))<=>(?[X]:((~old(X)&~rich(X)))))&
(![X]:((strong(X)<~>old(X))=>(~kind(X)|humble(X))))&
(![X]:(quiet(X)<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>kind(X))))<=>((~calm(paul)&~creative(paul))))&
((~calm(mary)|~funny(mary)))&
((~old(fred)<~>humble(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~creative(X)|~patient(X))))&
(patient(fred)) | ~curious(alice) | [] | null | 0 |
Everyone who is quiet is both not quiet and creative and vice versa.
If alice is either brave or not patient then someone is not kind.
Everyone who is both patient and not quiet is either tall or not strong.
If someone is not funny then someone is either not funny or brave.
Everyone who is kind or old is either wise or not old and vice versa.
If paul is either patient or not patient then susan is humble or not old.
If paul is creative or calm then john is either brave or tall and vice versa.
Everyone who is either kind or old is happy or not creative.
Everyone who is not patient is both happy and creative.
Everyone who is creative or old is not humble.
If fred is both not strong and not brave then lucy is both not rich and humble and vice versa.
If someone is brave or not tall then mary is either not brave or not kind and vice versa.
Everyone who is either not patient or not brave is both not wise and not calm and vice versa.
Everyone who is strong or creative is not wise and vice versa.
If someone is strong then alice is either old or not patient.
Everyone who is not tall or strong is not tall or not wise and vice versa.
John is not strong.
Fred is either not creative or not kind.
Someone is curious or tall.
Paul is both generous and not tall.
John is not curious or not quiet.
Someone is either not generous or calm.
Someone is both not quiet and calm. | Fred is creative. | contradiction | (![X]:(quiet(X)<=>(~quiet(X)&creative(X))))&
(((brave(alice)<~>~patient(alice)))=>(?[X]:(~kind(X))))&
(![X]:((patient(X)&~quiet(X))=>(tall(X)<~>~strong(X))))&
((?[X]:(~funny(X)))=>(?[X]:((~funny(X)<~>brave(X)))))&
(![X]:((kind(X)|old(X))<=>(wise(X)<~>~old(X))))&
(((patient(paul)<~>~patient(paul)))=>((humble(susan)|~old(susan))))&
(((creative(paul)|calm(paul)))<=>((brave(john)<~>tall(john))))&
(![X]:((kind(X)<~>old(X))=>(happy(X)|~creative(X))))&
(![X]:(~patient(X)=>(happy(X)&creative(X))))&
(![X]:((creative(X)|old(X))=>~humble(X)))&
(((~strong(fred)&~brave(fred)))<=>((~rich(lucy)&humble(lucy))))&
((?[X]:((brave(X)|~tall(X))))<=>((~brave(mary)<~>~kind(mary))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~wise(X)&~calm(X))))&
(![X]:((strong(X)|creative(X))<=>~wise(X)))&
((?[X]:(strong(X)))=>((old(alice)<~>~patient(alice))))&
(![X]:((~tall(X)|strong(X))<=>(~tall(X)|~wise(X))))&
(~strong(john))&
((~creative(fred)<~>~kind(fred)))&
(?[X]:((curious(X)|tall(X))))&
((generous(paul)&~tall(paul)))&
((~curious(john)|~quiet(john)))&
(?[X]:((~generous(X)<~>calm(X))))&
(?[X]:((~quiet(X)&calm(X)))) | creative(fred) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 466395091248797925316867
% SZS output start Proof for 466395091248797925316867
1. ! [X0] : (quiet(X0) <=> (creative(X0) & ~quiet(X0))) [input p0]
24. creative(fred) [input hypothesis]
37. ! [X0] : ((quiet(X0) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | ~quiet(X0))) [nnf transformation 1]
38. ! [X0] : ((quiet(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | ~quiet(X0))) [flattening 37]
73. ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
75. quiet(X0) | ~creative(X0) | quiet(X0) [cnf transformation 38]
135. creative(fred) [cnf transformation 24]
140. ~quiet(X0) [duplicate literal removal 73]
141. ~creative(X0) | quiet(X0) [duplicate literal removal 75]
265. 26 <=> creative(fred) [avatar definition]
267. creative(fred) <- (26) [avatar component clause 265]
293. 26 [avatar split clause 135,265]
297. quiet(fred) <- (26) [resolution 141,267]
299. $false <- (26) [subsumption resolution 297,140]
300. ~26 [avatar contradiction clause 299]
303. $false [avatar sat refutation 293,300]
% SZS output end Proof for 466395091248797925316867
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not kind then susan is either brave or patient.
Everyone who is either creative or not humble is not creative.
If lucy is curious or not wise then mary is both not kind and wise.
Everyone who is rich or humble is both curious and tall and vice versa.
Everyone who is both kind and patient is both not happy and funny and vice versa.
Everyone who is not brave or old is both brave and not strong and vice versa.
If john is both not creative and not tall then someone is either strong or quiet.
Everyone who is not humble is kind or curious.
Everyone who is patient or rich is not generous and vice versa.
Everyone who is not calm is both not happy and not old and vice versa.
If someone is both not strong and not creative then mary is either not curious or not quiet and vice versa.
Everyone who is either tall or old is not kind.
Everyone who is happy or not funny is either rich or quiet and vice versa.
Everyone who is humble is wise and vice versa.
If someone is curious or strong then someone is either humble or not humble and vice versa.
Everyone who is both strong and not generous is either tall or not patient.
Susan is either not curious or curious.
Fred is not happy or kind.
Lucy is either not brave or kind.
Mary is not patient.
John is wise or strong.
Someone is tall or not rich. | Lucy is humble. | neutral | ((~kind(susan))=>((brave(susan)<~>patient(susan))))&
(![X]:((creative(X)<~>~humble(X))=>~creative(X)))&
(((curious(lucy)|~wise(lucy)))=>((~kind(mary)&wise(mary))))&
(![X]:((rich(X)|humble(X))<=>(curious(X)&tall(X))))&
(![X]:((kind(X)&patient(X))<=>(~happy(X)&funny(X))))&
(![X]:((~brave(X)|old(X))<=>(brave(X)&~strong(X))))&
(((~creative(john)&~tall(john)))=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:(~humble(X)=>(kind(X)|curious(X))))&
(![X]:((patient(X)|rich(X))<=>~generous(X)))&
(![X]:(~calm(X)<=>(~happy(X)&~old(X))))&
((?[X]:((~strong(X)&~creative(X))))<=>((~curious(mary)<~>~quiet(mary))))&
(![X]:((tall(X)<~>old(X))=>~kind(X)))&
(![X]:((happy(X)|~funny(X))<=>(rich(X)<~>quiet(X))))&
(![X]:(humble(X)<=>wise(X)))&
((?[X]:((curious(X)|strong(X))))<=>(?[X]:((humble(X)<~>~humble(X)))))&
(![X]:((strong(X)&~generous(X))=>(tall(X)<~>~patient(X))))&
((~curious(susan)<~>curious(susan)))&
((~happy(fred)|kind(fred)))&
((~brave(lucy)<~>kind(lucy)))&
(~patient(mary))&
((wise(john)|strong(john)))&
(?[X]:((tall(X)|~rich(X)))) | humble(lucy) | [] | null | 0 |
If paul is either not patient or humble then fred is kind or humble and vice versa. If alice is not strong or not curious then lucy is either wise or not rich. If someone is either generous or not generous then lucy is not happy. Everyone who is both funny and wise is strong or not rich and vice versa. Everyone who is brave is either creative or not rich and vice versa. Everyone who is either not rich or funny is not strong or creative and vice versa. Everyone who is not calm or rich is either not strong or tall and vice versa. If someone is either not happy or humble then someone is both not patient and quiet. Everyone who is either kind or not patient is both rich and brave and vice versa. Everyone who is both kind and not generous is not curious and vice versa. If alice is not patient or not calm then someone is not kind and vice versa. Everyone who is happy is both not creative and not brave. If mary is old then susan is either not funny or old and vice versa. If john is either not tall or curious then someone is both humble and wise. Everyone who is generous or funny is not kind. Someone is both quiet and funny. Someone is both not humble and not strong. John is both not calm and brave. Someone is both not old and generous. Someone is not kind. John is either creative or not rich. Lucy is either not curious or not tall. | Susan is curious. | entailment | (((~patient(paul)<~>humble(paul)))<=>((kind(fred)|humble(fred))))&
(((~strong(alice)|~curious(alice)))=>((wise(lucy)<~>~rich(lucy))))&
((?[X]:((generous(X)<~>~generous(X))))=>(~happy(lucy)))&
(![X]:((funny(X)&wise(X))<=>(strong(X)|~rich(X))))&
(![X]:(brave(X)<=>(creative(X)<~>~rich(X))))&
(![X]:((~rich(X)<~>funny(X))<=>(~strong(X)|creative(X))))&
(![X]:((~calm(X)|rich(X))<=>(~strong(X)<~>tall(X))))&
((?[X]:((~happy(X)<~>humble(X))))=>(?[X]:((~patient(X)&quiet(X)))))&
(![X]:((kind(X)<~>~patient(X))<=>(rich(X)&brave(X))))&
(![X]:((kind(X)&~generous(X))<=>~curious(X)))&
(((~patient(alice)|~calm(alice)))<=>(?[X]:(~kind(X))))&
(![X]:(happy(X)=>(~creative(X)&~brave(X))))&
((old(mary))<=>((~funny(susan)<~>old(susan))))&
(((~tall(john)<~>curious(john)))=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((generous(X)|funny(X))=>~kind(X)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:((~humble(X)&~strong(X))))&
((~calm(john)&brave(john)))&
(?[X]:((~old(X)&generous(X))))&
(?[X]:(~kind(X)))&
((creative(john)<~>~rich(john)))&
((~curious(lucy)<~>~tall(lucy))) | curious(susan) | [
"p3",
"p5",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6035546599788090244607723
% SZS output start Proof for 6035546599788090244607723
4. ! [X0] : ((wise(X0) & funny(X0)) <=> (~rich(X0) | strong(X0))) [input p3]
6. ! [X0] : ((~rich(X0) <~> funny(X0)) <=> (creative(X0) | ~strong(X0))) [input p5]
10. ! [X0] : ((~generous(X0) & kind(X0)) <=> ~curious(X0)) [input p9]
15. ! [X0] : ((funny(X0) | generous(X0)) => ~kind(X0)) [input p14]
23. ~curious(susan) [input hypothesis]
32. ! [X0] : (~kind(X0) | (~funny(X0) & ~generous(X0))) [ennf transformation 15]
37. ! [X0] : (((wise(X0) & funny(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (~wise(X0) | ~funny(X0)))) [nnf transformation 4]
38. ! [X0] : (((wise(X0) & funny(X0)) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | ~wise(X0) | ~funny(X0))) [flattening 37]
40. ! [X0] : ((((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0))))) [nnf transformation 6]
41. ! [X0] : ((((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0))))) [flattening 40]
50. ! [X0] : (((~generous(X0) & kind(X0)) | curious(X0)) & (~curious(X0) | (generous(X0) | ~kind(X0)))) [nnf transformation 10]
51. ! [X0] : (((~generous(X0) & kind(X0)) | curious(X0)) & (~curious(X0) | generous(X0) | ~kind(X0))) [flattening 50]
84. ~strong(X0) | funny(X0) [cnf transformation 38]
85. funny(X0) | rich(X0) [cnf transformation 38]
94. funny(X0) | ~rich(X0) | strong(X0) [cnf transformation 41]
96. ~funny(X0) | rich(X0) | strong(X0) [cnf transformation 41]
113. curious(X0) | kind(X0) [cnf transformation 51]
129. ~kind(X0) | ~funny(X0) [cnf transformation 32]
142. ~curious(susan) [cnf transformation 23]
200. rich(X0) | strong(X0) [subsumption resolution 96,85]
202. funny(X0) | strong(X0) [subsumption resolution 94,200]
203. funny(X0) [subsumption resolution 202,84]
269. ~kind(X0) [subsumption resolution 129,203]
293. kind(susan) [resolution 113,142]
294. $false [subsumption resolution 293,269]
% SZS output end Proof for 6035546599788090244607723
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either old or rich is either not calm or not generous and vice versa. If someone is not old or not generous then someone is either not curious or tall and vice versa. If someone is not creative then susan is rich and vice versa. Everyone who is either not brave or brave is not kind. Everyone who is brave or not curious is either happy or not patient and vice versa. Everyone who is either rich or not calm is not strong or calm. Everyone who is both not old and strong is not strong. If someone is not funny then someone is both not old and not wise and vice versa. Everyone who is both humble and creative is both happy and humble. Everyone who is not old is both not creative and humble and vice versa. Everyone who is both not kind and curious is not humble. If someone is both not creative and calm then someone is not calm or strong. If someone is either calm or not happy then john is not rich. Everyone who is either calm or creative is not old. If paul is kind or not humble then someone is happy or rich and vice versa. Everyone who is old is either not strong or humble and vice versa. Alice is both brave and quiet. Lucy is old or not rich. Someone is either not patient or not wise. Someone is not happy or creative. Someone is either not generous or not creative. Someone is both not patient and not rich. Paul is not humble or not happy. Someone is either quiet or creative. | Paul is not old. | contradiction | (![X]:((old(X)<~>rich(X))<=>(~calm(X)<~>~generous(X))))&
((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~curious(X)<~>tall(X)))))&
((?[X]:(~creative(X)))<=>(rich(susan)))&
(![X]:((~brave(X)<~>brave(X))=>~kind(X)))&
(![X]:((brave(X)|~curious(X))<=>(happy(X)<~>~patient(X))))&
(![X]:((rich(X)<~>~calm(X))=>(~strong(X)|calm(X))))&
(![X]:((~old(X)&strong(X))=>~strong(X)))&
((?[X]:(~funny(X)))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((humble(X)&creative(X))=>(happy(X)&humble(X))))&
(![X]:(~old(X)<=>(~creative(X)&humble(X))))&
(![X]:((~kind(X)&curious(X))=>~humble(X)))&
((?[X]:((~creative(X)&calm(X))))=>(?[X]:((~calm(X)|strong(X)))))&
((?[X]:((calm(X)<~>~happy(X))))=>(~rich(john)))&
(![X]:((calm(X)<~>creative(X))=>~old(X)))&
(((kind(paul)|~humble(paul)))<=>(?[X]:((happy(X)|rich(X)))))&
(![X]:(old(X)<=>(~strong(X)<~>humble(X))))&
((brave(alice)&quiet(alice)))&
((old(lucy)|~rich(lucy)))&
(?[X]:((~patient(X)<~>~wise(X))))&
(?[X]:((~happy(X)|creative(X))))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:((~patient(X)&~rich(X))))&
((~humble(paul)|~happy(paul)))&
(?[X]:((quiet(X)<~>creative(X)))) | ~old(paul) | [
"p2",
"p3",
"p9",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 3411423008269683308889487
% SZS output start Proof for 3411423008269683308889487
3. ? [X0] : ~creative(X0) <=> rich(susan) [input p2]
4. ! [X0] : ((~brave(X0) <~> brave(X0)) => ~kind(X0)) [input p3]
10. ! [X0] : (~old(X0) <=> (humble(X0) & ~creative(X0))) [input p9]
15. (~humble(paul) | kind(paul)) <=> ? [X0] : (rich(X0) | happy(X0)) [input p14]
25. ~old(paul) [input hypothesis]
29. ! [X0] : (~kind(X0) | (~brave(X0) <=> brave(X0))) [ennf transformation 4]
47. (? [X0] : ~creative(X0) | ~rich(susan)) & (rich(susan) | ! [X0] : creative(X0)) [nnf transformation 3]
48. (? [X0] : ~creative(X0) | ~rich(susan)) & (rich(susan) | ! [X1] : creative(X1)) [rectify 47]
49. ? [X0] : ~creative(X0) => ~creative(sK2) [choice axiom]
50. (~creative(sK2) | ~rich(susan)) & (rich(susan) | ! [X1] : creative(X1)) [skolemisation 48,49]
51. ! [X0] : (~kind(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) [nnf transformation 29]
60. ! [X0] : ((~old(X0) | (~humble(X0) | creative(X0))) & ((humble(X0) & ~creative(X0)) | old(X0))) [nnf transformation 10]
61. ! [X0] : ((~old(X0) | ~humble(X0) | creative(X0)) & ((humble(X0) & ~creative(X0)) | old(X0))) [flattening 60]
67. ((~humble(paul) | kind(paul)) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | (humble(paul) & ~kind(paul))) [nnf transformation 15]
68. (~humble(paul) | kind(paul) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X0] : (rich(X0) | happy(X0)) | (humble(paul) & ~kind(paul))) [flattening 67]
69. (~humble(paul) | kind(paul) | ! [X0] : (~rich(X0) & ~happy(X0))) & (? [X1] : (rich(X1) | happy(X1)) | (humble(paul) & ~kind(paul))) [rectify 68]
70. ? [X1] : (rich(X1) | happy(X1)) => (rich(sK6) | happy(sK6)) [choice axiom]
71. (~humble(paul) | kind(paul) | ! [X0] : (~rich(X0) & ~happy(X0))) & ((rich(sK6) | happy(sK6)) | (humble(paul) & ~kind(paul))) [skolemisation 69,70]
100. rich(susan) | creative(X1) [cnf transformation 50]
102. ~kind(X0) | brave(X0) | brave(X0) [cnf transformation 51]
103. ~kind(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 51]
118. ~creative(X0) | old(X0) [cnf transformation 61]
119. humble(X0) | old(X0) [cnf transformation 61]
130. ~humble(paul) | kind(paul) | ~rich(X0) [cnf transformation 71]
148. ~old(paul) [cnf transformation 25]
151. ~kind(X0) | brave(X0) [duplicate literal removal 102]
152. ~kind(X0) | ~brave(X0) [duplicate literal removal 103]
182. 8 <=> ! [X3] : old(X3) [avatar definition]
183. old(X3) <- (8) [avatar component clause 182]
188. 9 <=> rich(susan) [avatar definition]
189. rich(susan) <- (9) [avatar component clause 188]
197. 11 <=> ! [X1] : creative(X1) [avatar definition]
198. creative(X1) <- (11) [avatar component clause 197]
199. 11 | 9 [avatar split clause 100,188,197]
200. ~kind(X0) [subsumption resolution 151,152]
248. ~humble(paul) | ~rich(X0) [subsumption resolution 130,200]
250. 23 <=> ! [X0] : ~rich(X0) [avatar definition]
251. ~rich(X0) <- (23) [avatar component clause 250]
253. 24 <=> humble(paul) [avatar definition]
255. ~humble(paul) <- (~24) [avatar component clause 253]
256. 23 | ~24 [avatar split clause 248,253,250]
325. $false <- (9, 23) [subsumption resolution 189,251]
326. ~9 | ~23 [avatar contradiction clause 325]
333. old(paul) <- (~24) [resolution 119,255]
334. $false <- (~24) [subsumption resolution 333,148]
335. 24 [avatar contradiction clause 334]
336. old(X0) <- (11) [resolution 198,118]
339. 8 | ~11 [avatar split clause 336,197,182]
340. $false <- (8) [resolution 183,148]
345. ~8 [avatar contradiction clause 340]
346. $false [avatar sat refutation 199,256,326,335,339,345]
% SZS output end Proof for 3411423008269683308889487
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or happy then lucy is both not happy and not patient.
Everyone who is quiet or curious is funny and vice versa.
If someone is not creative or not happy then someone is not rich.
If mary is creative or humble then someone is both not creative and not old.
If someone is both not creative and generous then someone is not funny or brave and vice versa.
Everyone who is not kind is curious or not quiet.
If paul is strong or creative then john is wise.
If mary is tall or not patient then someone is calm and vice versa.
Everyone who is not tall or not rich is old.
Everyone who is old is not strong and vice versa.
Everyone who is both not kind and not calm is both not calm and not generous and vice versa.
Everyone who is funny or generous is either patient or calm.
Everyone who is not strong is either not generous or patient.
Everyone who is calm or not rich is both not strong and quiet and vice versa.
Everyone who is funny or wise is quiet or calm.
Everyone who is not calm or tall is both wise and old.
Someone is either not kind or not generous.
Alice is both tall and humble.
Someone is either not calm or not curious.
Someone is both not creative and not brave.
Fred is either not brave or strong. | Mary is curious. | neutral | ((?[X]:((rich(X)<~>happy(X))))=>((~happy(lucy)&~patient(lucy))))&
(![X]:((quiet(X)|curious(X))<=>funny(X)))&
((?[X]:((~creative(X)|~happy(X))))=>(?[X]:(~rich(X))))&
(((creative(mary)|humble(mary)))=>(?[X]:((~creative(X)&~old(X)))))&
((?[X]:((~creative(X)&generous(X))))<=>(?[X]:((~funny(X)|brave(X)))))&
(![X]:(~kind(X)=>(curious(X)|~quiet(X))))&
(((strong(paul)|creative(paul)))=>(wise(john)))&
(((tall(mary)|~patient(mary)))<=>(?[X]:(calm(X))))&
(![X]:((~tall(X)|~rich(X))=>old(X)))&
(![X]:(old(X)<=>~strong(X)))&
(![X]:((~kind(X)&~calm(X))<=>(~calm(X)&~generous(X))))&
(![X]:((funny(X)|generous(X))=>(patient(X)<~>calm(X))))&
(![X]:(~strong(X)=>(~generous(X)<~>patient(X))))&
(![X]:((calm(X)|~rich(X))<=>(~strong(X)&quiet(X))))&
(![X]:((funny(X)|wise(X))=>(quiet(X)|calm(X))))&
(![X]:((~calm(X)|tall(X))=>(wise(X)&old(X))))&
(?[X]:((~kind(X)<~>~generous(X))))&
((tall(alice)&humble(alice)))&
(?[X]:((~calm(X)<~>~curious(X))))&
(?[X]:((~creative(X)&~brave(X))))&
((~brave(fred)<~>strong(fred))) | curious(mary) | [] | null | 0 |
If someone is both calm and not strong then someone is either old or not strong.
Everyone who is either wise or not humble is both not calm and generous and vice versa.
Everyone who is old is not funny or creative and vice versa.
Everyone who is kind is not old and vice versa.
Everyone who is strong or rich is either strong or not rich and vice versa.
Everyone who is strong is both creative and not generous.
Everyone who is both tall and creative is not curious or creative.
If lucy is generous then john is either humble or not old and vice versa.
If fred is both not strong and not quiet then someone is either curious or quiet.
If someone is both calm and happy then someone is both not tall and brave and vice versa.
Everyone who is both not old and wise is both not generous and not tall and vice versa.
Everyone who is patient is both old and not brave and vice versa.
If someone is both not rich and not happy then susan is not brave or rich.
If someone is either happy or not tall then lucy is calm or old.
If someone is both brave and wise then paul is curious and vice versa.
Fred is not rich or wise.
Someone is not curious or rich.
Lucy is old.
Someone is both not kind and strong.
Paul is brave. | Fred is strong. | entailment | ((?[X]:((calm(X)&~strong(X))))=>(?[X]:((old(X)<~>~strong(X)))))&
(![X]:((wise(X)<~>~humble(X))<=>(~calm(X)&generous(X))))&
(![X]:(old(X)<=>(~funny(X)|creative(X))))&
(![X]:(kind(X)<=>~old(X)))&
(![X]:((strong(X)|rich(X))<=>(strong(X)<~>~rich(X))))&
(![X]:(strong(X)=>(creative(X)&~generous(X))))&
(![X]:((tall(X)&creative(X))=>(~curious(X)|creative(X))))&
((generous(lucy))<=>((humble(john)<~>~old(john))))&
(((~strong(fred)&~quiet(fred)))=>(?[X]:((curious(X)<~>quiet(X)))))&
((?[X]:((calm(X)&happy(X))))<=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:((~old(X)&wise(X))<=>(~generous(X)&~tall(X))))&
(![X]:(patient(X)<=>(old(X)&~brave(X))))&
((?[X]:((~rich(X)&~happy(X))))=>((~brave(susan)|rich(susan))))&
((?[X]:((happy(X)<~>~tall(X))))=>((calm(lucy)|old(lucy))))&
((?[X]:((brave(X)&wise(X))))<=>(curious(paul)))&
((~rich(fred)|wise(fred)))&
(?[X]:((~curious(X)|rich(X))))&
(old(lucy))&
(?[X]:((~kind(X)&strong(X))))&
(brave(paul)) | strong(fred) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 393044343643749032862910
% SZS output start Proof for 393044343643749032862910
5. ! [X0] : ((rich(X0) | strong(X0)) <=> (strong(X0) <~> ~rich(X0))) [input p4]
21. ~strong(fred) [input hypothesis]
44. ! [X0] : (((rich(X0) | strong(X0)) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0)))) & (((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | (~rich(X0) & ~strong(X0)))) [nnf transformation 5]
45. ! [X0] : ((rich(X0) | strong(X0) | ((strong(X0) | rich(X0)) & (~rich(X0) | ~strong(X0)))) & (((rich(X0) | ~strong(X0)) & (~rich(X0) | strong(X0))) | (~rich(X0) & ~strong(X0)))) [flattening 44]
79. ~rich(X0) | strong(X0) | ~rich(X0) [cnf transformation 45]
80. rich(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 45]
83. rich(X0) | strong(X0) | strong(X0) | rich(X0) [cnf transformation 45]
113. ~strong(fred) [cnf transformation 21]
114. ~rich(X0) | strong(X0) [duplicate literal removal 79]
115. rich(X0) | ~strong(X0) [duplicate literal removal 80]
116. rich(X0) | strong(X0) [duplicate literal removal 83]
130. rich(X0) [subsumption resolution 115,116]
131. strong(X0) [subsumption resolution 114,130]
210. $false [subsumption resolution 113,131]
% SZS output end Proof for 393044343643749032862910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either rich or creative and vice versa.
Everyone who is not wise or strong is both patient and not creative and vice versa.
If someone is either not tall or not old then susan is strong and vice versa.
If someone is strong or patient then mary is both generous and not calm.
If alice is tall or creative then fred is not kind or not humble and vice versa.
Everyone who is not creative or quiet is both tall and not strong.
If john is not happy or not kind then john is not quiet and vice versa.
If someone is not curious then lucy is happy.
Everyone who is not kind or not rich is either kind or not humble.
If john is both not happy and strong then someone is happy or kind.
Everyone who is not brave is tall or not funny and vice versa.
Everyone who is generous is not kind or quiet and vice versa.
Everyone who is both not generous and creative is both patient and tall.
If someone is curious then fred is funny and vice versa.
Everyone who is not rich is both not humble and not curious and vice versa.
Mary is both tall and quiet.
Lucy is tall or happy.
Someone is generous.
Someone is not happy.
Someone is wise.
Mary is not strong. | John is not curious. | entailment | (![X]:(creative(X)<=>(rich(X)<~>creative(X))))&
(![X]:((~wise(X)|strong(X))<=>(patient(X)&~creative(X))))&
((?[X]:((~tall(X)<~>~old(X))))<=>(strong(susan)))&
((?[X]:((strong(X)|patient(X))))=>((generous(mary)&~calm(mary))))&
(((tall(alice)|creative(alice)))<=>((~kind(fred)|~humble(fred))))&
(![X]:((~creative(X)|quiet(X))=>(tall(X)&~strong(X))))&
(((~happy(john)|~kind(john)))<=>(~quiet(john)))&
((?[X]:(~curious(X)))=>(happy(lucy)))&
(![X]:((~kind(X)|~rich(X))=>(kind(X)<~>~humble(X))))&
(((~happy(john)&strong(john)))=>(?[X]:((happy(X)|kind(X)))))&
(![X]:(~brave(X)<=>(tall(X)|~funny(X))))&
(![X]:(generous(X)<=>(~kind(X)|quiet(X))))&
(![X]:((~generous(X)&creative(X))=>(patient(X)&tall(X))))&
((?[X]:(curious(X)))<=>(funny(fred)))&
(![X]:(~rich(X)<=>(~humble(X)&~curious(X))))&
((tall(mary)&quiet(mary)))&
((tall(lucy)|happy(lucy)))&
(?[X]:(generous(X)))&
(?[X]:(~happy(X)))&
(?[X]:(wise(X)))&
(~strong(mary)) | ~curious(john) | [
"p0",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6143588358013568514714709
% SZS output start Proof for 6143588358013568514714709
1. ! [X0] : (creative(X0) <=> (rich(X0) <~> creative(X0))) [input p0]
15. ! [X0] : (~rich(X0) <=> (~curious(X0) & ~humble(X0))) [input p14]
22. curious(john) [input hypothesis]
35. ! [X0] : ((creative(X0) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | ~creative(X0))) [nnf transformation 1]
53. ! [X0] : ((~rich(X0) | (curious(X0) | humble(X0))) & ((~curious(X0) & ~humble(X0)) | rich(X0))) [nnf transformation 15]
54. ! [X0] : ((~rich(X0) | curious(X0) | humble(X0)) & ((~curious(X0) & ~humble(X0)) | rich(X0))) [flattening 53]
62. ~creative(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 35]
63. creative(X0) | creative(X0) | ~rich(X0) [cnf transformation 35]
99. ~curious(X0) | rich(X0) [cnf transformation 54]
108. curious(john) [cnf transformation 22]
110. ~creative(X0) | ~rich(X0) [duplicate literal removal 62]
111. creative(X0) | ~rich(X0) [duplicate literal removal 63]
112. ~rich(X0) [subsumption resolution 110,111]
218. 23 <=> ! [X1] : ~curious(X1) [avatar definition]
219. ~curious(X1) <- (23) [avatar component clause 218]
221. ~curious(X0) [subsumption resolution 99,112]
222. 23 [avatar split clause 221,218]
229. $false <- (23) [resolution 219,108]
230. ~23 [avatar contradiction clause 229]
231. $false [avatar sat refutation 222,230]
% SZS output end Proof for 6143588358013568514714709
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous or not patient is both not curious and not quiet. If alice is both strong and not humble then someone is not calm or kind and vice versa. Everyone who is patient or tall is either brave or quiet and vice versa. Everyone who is either not happy or calm is not creative and vice versa. If john is generous or brave then someone is either not humble or happy. Everyone who is both quiet and humble is not patient or curious. Everyone who is both not strong and not quiet is generous and vice versa. Everyone who is kind is not happy and vice versa. If someone is not humble or not wise then paul is either funny or not rich and vice versa. Everyone who is either wise or generous is both kind and tall. Everyone who is kind or funny is not brave and vice versa. If susan is patient then lucy is not patient or funny. If alice is not creative then someone is either humble or not funny and vice versa. Everyone who is both not kind and rich is both not patient and generous. If someone is curious then someone is not strong or not wise. If someone is not kind then susan is not tall and vice versa. John is happy or not funny. Someone is not quiet. Fred is both not tall and not patient. Someone is either quiet or not happy. Lucy is rich or strong. John is both not creative and brave. Someone is strong. | Alice is curious. | contradiction | (![X]:((~generous(X)|~patient(X))=>(~curious(X)&~quiet(X))))&
(((strong(alice)&~humble(alice)))<=>(?[X]:((~calm(X)|kind(X)))))&
(![X]:((patient(X)|tall(X))<=>(brave(X)<~>quiet(X))))&
(![X]:((~happy(X)<~>calm(X))<=>~creative(X)))&
(((generous(john)|brave(john)))=>(?[X]:((~humble(X)<~>happy(X)))))&
(![X]:((quiet(X)&humble(X))=>(~patient(X)|curious(X))))&
(![X]:((~strong(X)&~quiet(X))<=>generous(X)))&
(![X]:(kind(X)<=>~happy(X)))&
((?[X]:((~humble(X)|~wise(X))))<=>((funny(paul)<~>~rich(paul))))&
(![X]:((wise(X)<~>generous(X))=>(kind(X)&tall(X))))&
(![X]:((kind(X)|funny(X))<=>~brave(X)))&
((patient(susan))=>((~patient(lucy)|funny(lucy))))&
((~creative(alice))<=>(?[X]:((humble(X)<~>~funny(X)))))&
(![X]:((~kind(X)&rich(X))=>(~patient(X)&generous(X))))&
((?[X]:(curious(X)))=>(?[X]:((~strong(X)|~wise(X)))))&
((?[X]:(~kind(X)))<=>(~tall(susan)))&
((happy(john)|~funny(john)))&
(?[X]:(~quiet(X)))&
((~tall(fred)&~patient(fred)))&
(?[X]:((quiet(X)<~>~happy(X))))&
((rich(lucy)|strong(lucy)))&
((~creative(john)&brave(john)))&
(?[X]:(strong(X))) | curious(alice) | [
"p0",
"p1",
"p6",
"p7",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6330845787413395612565005
% SZS output start Proof for 6330845787413395612565005
1. ! [X0] : ((~patient(X0) | ~generous(X0)) => (~quiet(X0) & ~curious(X0))) [input p0]
2. (~humble(alice) & strong(alice)) <=> ? [X0] : (kind(X0) | ~calm(X0)) [input p1]
7. ! [X0] : ((~quiet(X0) & ~strong(X0)) <=> generous(X0)) [input p6]
8. ! [X0] : (kind(X0) <=> ~happy(X0)) [input p7]
20. ? [X0] : (quiet(X0) <~> ~happy(X0)) [input p19]
24. curious(alice) [input hypothesis]
26. ! [X0] : ((~quiet(X0) & ~curious(X0)) | (patient(X0) & generous(X0))) [ennf transformation 1]
36. ((~humble(alice) & strong(alice)) | ! [X0] : (~kind(X0) & calm(X0))) & (? [X0] : (kind(X0) | ~calm(X0)) | (humble(alice) | ~strong(alice))) [nnf transformation 2]
37. ((~humble(alice) & strong(alice)) | ! [X0] : (~kind(X0) & calm(X0))) & (? [X0] : (kind(X0) | ~calm(X0)) | humble(alice) | ~strong(alice)) [flattening 36]
38. ((~humble(alice) & strong(alice)) | ! [X0] : (~kind(X0) & calm(X0))) & (? [X1] : (kind(X1) | ~calm(X1)) | humble(alice) | ~strong(alice)) [rectify 37]
39. ? [X1] : (kind(X1) | ~calm(X1)) => (kind(sK0) | ~calm(sK0)) [choice axiom]
40. ((~humble(alice) & strong(alice)) | ! [X0] : (~kind(X0) & calm(X0))) & ((kind(sK0) | ~calm(sK0)) | humble(alice) | ~strong(alice)) [skolemisation 38,39]
47. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | (quiet(X0) | strong(X0)))) [nnf transformation 7]
48. ! [X0] : (((~quiet(X0) & ~strong(X0)) | ~generous(X0)) & (generous(X0) | quiet(X0) | strong(X0))) [flattening 47]
49. ! [X0] : ((kind(X0) | happy(X0)) & (~happy(X0) | ~kind(X0))) [nnf transformation 8]
70. ? [X0] : ((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) [nnf transformation 20]
71. ? [X0] : ((happy(X0) | ~quiet(X0)) & (~happy(X0) | quiet(X0))) => ((happy(sK7) | ~quiet(sK7)) & (~happy(sK7) | quiet(sK7))) [choice axiom]
72. (happy(sK7) | ~quiet(sK7)) & (~happy(sK7) | quiet(sK7)) [skolemisation 70,71]
75. ~curious(X0) | generous(X0) [cnf transformation 26]
77. ~quiet(X0) | generous(X0) [cnf transformation 26]
81. strong(alice) | ~kind(X0) [cnf transformation 40]
100. ~strong(X0) | ~generous(X0) [cnf transformation 48]
101. ~quiet(X0) | ~generous(X0) [cnf transformation 48]
103. happy(X0) | kind(X0) [cnf transformation 49]
131. ~happy(sK7) | quiet(sK7) [cnf transformation 72]
137. curious(alice) [cnf transformation 24]
139. 1 <=> ! [X0] : ~kind(X0) [avatar definition]
140. ~kind(X0) <- (1) [avatar component clause 139]
151. 4 <=> strong(alice) [avatar definition]
153. strong(alice) <- (4) [avatar component clause 151]
154. 1 | 4 [avatar split clause 81,151,139]
188. ~quiet(X0) [subsumption resolution 101,77]
287. ~happy(sK7) [subsumption resolution 131,188]
298. generous(alice) [resolution 75,137]
301. ~generous(alice) <- (4) [resolution 100,153]
302. $false <- (4) [subsumption resolution 301,298]
303. ~4 [avatar contradiction clause 302]
307. kind(sK7) [resolution 103,287]
311. $false <- (1) [subsumption resolution 307,140]
312. ~1 [avatar contradiction clause 311]
313. $false [avatar sat refutation 154,303,312]
% SZS output end Proof for 6330845787413395612565005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
Everyone who is both humble and quiet is both not generous and patient and vice versa. If fred is either old or not curious then someone is kind and vice versa. If fred is either funny or not calm then alice is either brave or old. Everyone who is not strong is not generous. If someone is not humble then someone is not creative or tall. Everyone who is both quiet and patient is not generous. Everyone who is either not strong or strong is both generous and creative. If someone is both funny and not quiet then someone is both generous and kind. If lucy is either not wise or calm then john is patient. If john is not wise then lucy is brave. Everyone who is generous or strong is brave and vice versa. Everyone who is not humble is both quiet and not humble. Everyone who is either quiet or wise is both rich and not wise and vice versa. If someone is both creative and rich then someone is both tall and not funny. Everyone who is not old is either not happy or generous. If someone is not creative then mary is funny or tall. Someone is not humble. Fred is both rich and not old. Paul is not rich or calm. John is either not patient or not kind. Alice is either not brave or not wise. Someone is rich. Someone is creative. Someone is both funny and brave. | Fred is not brave. | contradiction | (![X]:((humble(X)&quiet(X))<=>(~generous(X)&patient(X))))&
(((old(fred)<~>~curious(fred)))<=>(?[X]:(kind(X))))&
(((funny(fred)<~>~calm(fred)))=>((brave(alice)<~>old(alice))))&
(![X]:(~strong(X)=>~generous(X)))&
((?[X]:(~humble(X)))=>(?[X]:((~creative(X)|tall(X)))))&
(![X]:((quiet(X)&patient(X))=>~generous(X)))&
(![X]:((~strong(X)<~>strong(X))=>(generous(X)&creative(X))))&
((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((generous(X)&kind(X)))))&
(((~wise(lucy)<~>calm(lucy)))=>(patient(john)))&
((~wise(john))=>(brave(lucy)))&
(![X]:((generous(X)|strong(X))<=>brave(X)))&
(![X]:(~humble(X)=>(quiet(X)&~humble(X))))&
(![X]:((quiet(X)<~>wise(X))<=>(rich(X)&~wise(X))))&
((?[X]:((creative(X)&rich(X))))=>(?[X]:((tall(X)&~funny(X)))))&
(![X]:(~old(X)=>(~happy(X)<~>generous(X))))&
((?[X]:(~creative(X)))=>((funny(mary)|tall(mary))))&
(?[X]:(~humble(X)))&
((rich(fred)&~old(fred)))&
((~rich(paul)|calm(paul)))&
((~patient(john)<~>~kind(john)))&
((~brave(alice)<~>~wise(alice)))&
(?[X]:(rich(X)))&
(?[X]:(creative(X)))&
(?[X]:((funny(X)&brave(X)))) | ~brave(fred) | [
"p3",
"p6",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 5850964722059087587122051
% SZS output start Proof for 5850964722059087587122051
4. ! [X0] : (~strong(X0) => ~generous(X0)) [input p3]
7. ! [X0] : ((~strong(X0) <~> strong(X0)) => (creative(X0) & generous(X0))) [input p6]
11. ! [X0] : ((strong(X0) | generous(X0)) <=> brave(X0)) [input p10]
25. ~brave(fred) [input hypothesis]
33. ! [X0] : (~generous(X0) | strong(X0)) [ennf transformation 4]
36. ! [X0] : ((creative(X0) & generous(X0)) | (~strong(X0) <=> strong(X0))) [ennf transformation 7]
50. ! [X0] : ((creative(X0) & generous(X0)) | ((~strong(X0) | ~strong(X0)) & (strong(X0) | strong(X0)))) [nnf transformation 36]
55. ! [X0] : (((strong(X0) | generous(X0)) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [nnf transformation 11]
56. ! [X0] : ((strong(X0) | generous(X0) | ~brave(X0)) & (brave(X0) | (~strong(X0) & ~generous(X0)))) [flattening 55]
85. ~generous(X0) | strong(X0) [cnf transformation 33]
87. generous(X0) | strong(X0) | strong(X0) [cnf transformation 50]
97. brave(X0) | ~strong(X0) [cnf transformation 56]
122. ~brave(fred) [cnf transformation 25]
125. generous(X0) | strong(X0) [duplicate literal removal 87]
169. strong(X0) [subsumption resolution 125,85]
206. brave(X0) [subsumption resolution 97,169]
233. $false [subsumption resolution 122,206]
% SZS output end Proof for 5850964722059087587122051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.016 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not happy and humble then lucy is either not patient or not wise and vice versa. Everyone who is not calm is either old or not humble and vice versa. If john is not quiet or not creative then someone is not old or not patient. Everyone who is not generous or not curious is brave or not old and vice versa. Everyone who is not happy is generous and vice versa. If someone is not strong or not brave then someone is both curious and not calm and vice versa. Everyone who is either not brave or kind is either wise or old and vice versa. If someone is calm then lucy is both quiet and creative. Everyone who is either not old or humble is both quiet and curious. Everyone who is curious is wise or not happy. Everyone who is quiet or not patient is both old and strong. Everyone who is rich is either tall or not curious and vice versa. Everyone who is not humble is kind. Everyone who is creative or rich is quiet and vice versa. Everyone who is both old and not brave is not wise or brave and vice versa. If someone is either funny or strong then john is either not rich or not kind and vice versa. Fred is either patient or not tall. Someone is funny or not generous. Someone is calm. John is either not old or not strong. Someone is either kind or happy. Someone is either not patient or quiet. Someone is both strong and not happy. | Lucy is not patient. | contradiction | ((?[X]:((~happy(X)&humble(X))))<=>((~patient(lucy)<~>~wise(lucy))))&
(![X]:(~calm(X)<=>(old(X)<~>~humble(X))))&
(((~quiet(john)|~creative(john)))=>(?[X]:((~old(X)|~patient(X)))))&
(![X]:((~generous(X)|~curious(X))<=>(brave(X)|~old(X))))&
(![X]:(~happy(X)<=>generous(X)))&
((?[X]:((~strong(X)|~brave(X))))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~brave(X)<~>kind(X))<=>(wise(X)<~>old(X))))&
((?[X]:(calm(X)))=>((quiet(lucy)&creative(lucy))))&
(![X]:((~old(X)<~>humble(X))=>(quiet(X)&curious(X))))&
(![X]:(curious(X)=>(wise(X)|~happy(X))))&
(![X]:((quiet(X)|~patient(X))=>(old(X)&strong(X))))&
(![X]:(rich(X)<=>(tall(X)<~>~curious(X))))&
(![X]:(~humble(X)=>kind(X)))&
(![X]:((creative(X)|rich(X))<=>quiet(X)))&
(![X]:((old(X)&~brave(X))<=>(~wise(X)|brave(X))))&
((?[X]:((funny(X)<~>strong(X))))<=>((~rich(john)<~>~kind(john))))&
((patient(fred)<~>~tall(fred)))&
(?[X]:((funny(X)|~generous(X))))&
(?[X]:(calm(X)))&
((~old(john)<~>~strong(john)))&
(?[X]:((kind(X)<~>happy(X))))&
(?[X]:((~patient(X)<~>quiet(X))))&
(?[X]:((strong(X)&~happy(X)))) | ~patient(lucy) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p8",
"p10",
"p12",
"p14",
"p18",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 7634463242361107966304101
% SZS output start Proof for 7634463242361107966304101
1. ? [X0] : (humble(X0) & ~happy(X0)) <=> (~patient(lucy) <~> ~wise(lucy)) [input p0]
4. ! [X0] : ((~curious(X0) | ~generous(X0)) <=> (~old(X0) | brave(X0))) [input p3]
5. ! [X0] : (~happy(X0) <=> generous(X0)) [input p4]
7. ! [X0] : ((~brave(X0) <~> kind(X0)) <=> (wise(X0) <~> old(X0))) [input p6]
8. ? [X0] : calm(X0) => (creative(lucy) & quiet(lucy)) [input p7]
9. ! [X0] : ((~old(X0) <~> humble(X0)) => (curious(X0) & quiet(X0))) [input p8]
11. ! [X0] : ((~patient(X0) | quiet(X0)) => (strong(X0) & old(X0))) [input p10]
13. ! [X0] : (~humble(X0) => kind(X0)) [input p12]
15. ! [X0] : ((~brave(X0) & old(X0)) <=> (brave(X0) | ~wise(X0))) [input p14]
19. ? [X0] : calm(X0) [input p18]
22. ? [X0] : (~patient(X0) <~> quiet(X0)) [input p21]
24. ~patient(lucy) [input hypothesis]
27. (creative(lucy) & quiet(lucy)) | ! [X0] : ~calm(X0) [ennf transformation 8]
28. ! [X0] : ((curious(X0) & quiet(X0)) | (~old(X0) <=> humble(X0))) [ennf transformation 9]
31. ! [X0] : ((strong(X0) & old(X0)) | (patient(X0) & ~quiet(X0))) [ennf transformation 11]
32. ! [X0] : (kind(X0) | humble(X0)) [ennf transformation 13]
33. (? [X0] : (humble(X0) & ~happy(X0)) | ((~patient(lucy) | wise(lucy)) & (~wise(lucy) | patient(lucy)))) & (((wise(lucy) | patient(lucy)) & (~wise(lucy) | ~patient(lucy))) | ! [X0] : (~humble(X0) | happy(X0))) [nnf transformation 1]
34. (? [X0] : (humble(X0) & ~happy(X0)) | ((~patient(lucy) | wise(lucy)) & (~wise(lucy) | patient(lucy)))) & (((wise(lucy) | patient(lucy)) & (~wise(lucy) | ~patient(lucy))) | ! [X1] : (~humble(X1) | happy(X1))) [rectify 33]
35. ? [X0] : (humble(X0) & ~happy(X0)) => (humble(sK0) & ~happy(sK0)) [choice axiom]
36. ((humble(sK0) & ~happy(sK0)) | ((~patient(lucy) | wise(lucy)) & (~wise(lucy) | patient(lucy)))) & (((wise(lucy) | patient(lucy)) & (~wise(lucy) | ~patient(lucy))) | ! [X1] : (~humble(X1) | happy(X1))) [skolemisation 34,35]
40. ! [X0] : (((~curious(X0) | ~generous(X0)) | (old(X0) & ~brave(X0))) & ((~old(X0) | brave(X0)) | (curious(X0) & generous(X0)))) [nnf transformation 4]
41. ! [X0] : ((~curious(X0) | ~generous(X0) | (old(X0) & ~brave(X0))) & (~old(X0) | brave(X0) | (curious(X0) & generous(X0)))) [flattening 40]
42. ! [X0] : ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))) [nnf transformation 5]
48. ! [X0] : ((((~kind(X0) | brave(X0)) & (kind(X0) | ~brave(X0))) | ((wise(X0) | ~old(X0)) & (old(X0) | ~wise(X0)))) & (((~old(X0) | ~wise(X0)) & (old(X0) | wise(X0))) | ((~brave(X0) | ~kind(X0)) & (kind(X0) | brave(X0))))) [nnf transformation 7]
49. ! [X0] : ((curious(X0) & quiet(X0)) | ((~old(X0) | ~humble(X0)) & (humble(X0) | old(X0)))) [nnf transformation 28]
53. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & ((brave(X0) | ~wise(X0)) | (brave(X0) | ~old(X0)))) [nnf transformation 15]
54. ! [X0] : (((~brave(X0) & old(X0)) | (~brave(X0) & wise(X0))) & (brave(X0) | ~wise(X0) | brave(X0) | ~old(X0))) [flattening 53]
62. ? [X0] : calm(X0) => calm(sK6) [choice axiom]
63. calm(sK6) [skolemisation 19,62]
68. ? [X0] : ((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) [nnf transformation 22]
69. ? [X0] : ((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) => ((~quiet(sK8) | patient(sK8)) & (quiet(sK8) | ~patient(sK8))) [choice axiom]
70. (~quiet(sK8) | patient(sK8)) & (quiet(sK8) | ~patient(sK8)) [skolemisation 68,69]
74. wise(lucy) | patient(lucy) | ~humble(X1) | happy(X1) [cnf transformation 36]
85. ~old(X0) | brave(X0) | generous(X0) [cnf transformation 41]
90. ~generous(X0) | ~happy(X0) [cnf transformation 42]
103. ~kind(X0) | brave(X0) | wise(X0) | ~old(X0) [cnf transformation 48]
104. quiet(lucy) | ~calm(X0) [cnf transformation 27]
106. quiet(X0) | humble(X0) | old(X0) [cnf transformation 49]
111. ~quiet(X0) | old(X0) [cnf transformation 31]
112. old(X0) | patient(X0) [cnf transformation 31]
119. kind(X0) | humble(X0) [cnf transformation 32]
123. brave(X0) | ~wise(X0) | brave(X0) | ~old(X0) [cnf transformation 54]
124. old(X0) | wise(X0) [cnf transformation 54]
127. ~brave(X0) | ~brave(X0) [cnf transformation 54]
139. calm(sK6) [cnf transformation 63]
144. quiet(sK8) | ~patient(sK8) [cnf transformation 70]
148. ~patient(lucy) [cnf transformation 24]
149. brave(X0) | ~wise(X0) | ~old(X0) [duplicate literal removal 123]
150. ~brave(X0) [duplicate literal removal 127]
152. 1 <=> wise(lucy) [avatar definition]
156. 2 <=> patient(lucy) [avatar definition]
172. 5 <=> ! [X1] : (~humble(X1) | happy(X1)) [avatar definition]
173. ~humble(X1) | happy(X1) <- (5) [avatar component clause 172]
174. 5 | 2 | 1 [avatar split clause 74,152,156,172]
225. 17 <=> ! [X0] : ~calm(X0) [avatar definition]
226. ~calm(X0) <- (17) [avatar component clause 225]
233. 19 <=> quiet(lucy) [avatar definition]
235. quiet(lucy) <- (19) [avatar component clause 233]
236. 17 | 19 [avatar split clause 104,233,225]
237. ~old(X0) | ~wise(X0) [subsumption resolution 149,150]
308. 34 <=> patient(sK8) [avatar definition]
312. 35 <=> quiet(sK8) [avatar definition]
313. quiet(sK8) <- (35) [avatar component clause 312]
316. ~34 | 35 [avatar split clause 144,312,308]
317. ~2 [avatar split clause 148,156]
320. $false <- (17) [resolution 226,139]
321. ~17 [avatar contradiction clause 320]
326. old(lucy) <- (19) [resolution 111,235]
335. ~wise(lucy) <- (19) [resolution 237,326]
428. humble(X1) | old(X1) | old(X1) [resolution 106,111]
429. old(X1) | humble(X1) [duplicate literal removal 428]
431. 46 <=> old(sK8) [avatar definition]
432. ~old(sK8) <- (~46) [avatar component clause 431]
433. old(sK8) <- (46) [avatar component clause 431]
527. brave(X1) | wise(X1) | ~old(X1) | humble(X1) [resolution 103,119]
535. wise(X1) | ~old(X1) | humble(X1) [subsumption resolution 527,150]
536. wise(X1) | humble(X1) [subsumption resolution 535,124]
669. humble(X7) | ~wise(X7) [resolution 429,237]
674. humble(X7) [subsumption resolution 669,536]
766. happy(X3) <- (5) [resolution 674,173]
786. patient(sK8) <- (~46) [resolution 432,112]
789. 34 | 46 [avatar split clause 786,431,308]
792. old(sK8) <- (35) [resolution 313,111]
804. 46 | ~35 [avatar split clause 792,312,431]
807. brave(sK8) | generous(sK8) <- (46) [resolution 433,85]
813. generous(sK8) <- (46) [subsumption resolution 807,150]
847. ~happy(sK8) <- (46) [resolution 813,90]
848. $false <- (5, 46) [subsumption resolution 847,766]
849. ~5 | ~46 [avatar contradiction clause 848]
856. ~1 | ~19 [avatar split clause 335,233,152]
857. $false [avatar sat refutation 174,236,316,317,321,789,804,849,856]
% SZS output end Proof for 7634463242361107966304101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is curious or not strong then susan is not patient or not wise and vice versa.
If alice is not creative or not rich then someone is generous or tall and vice versa.
Everyone who is kind is either happy or wise and vice versa.
Everyone who is quiet or not humble is either not creative or not happy and vice versa.
Everyone who is either not strong or not happy is humble.
Everyone who is patient or not kind is not humble or not rich and vice versa.
Everyone who is both not brave and tall is not tall or not calm and vice versa.
If fred is either calm or patient then alice is not strong.
Everyone who is both not brave and humble is quiet and vice versa.
If someone is patient then alice is both tall and not funny and vice versa.
If someone is both not creative and not humble then paul is either patient or happy.
Everyone who is not funny or tall is both tall and not happy and vice versa.
If john is both curious and creative then susan is kind or creative.
Everyone who is both not patient and not generous is not creative and vice versa.
If someone is not old or not patient then someone is not generous or quiet.
Everyone who is brave or calm is not rich.
Someone is not funny or quiet.
Someone is either not wise or tall.
Fred is either not rich or not curious.
Mary is patient.
Someone is both curious and patient.
Lucy is either kind or quiet.
Someone is either not curious or tall. | Paul is not generous. | neutral | ((?[X]:((curious(X)|~strong(X))))<=>((~patient(susan)|~wise(susan))))&
(((~creative(alice)|~rich(alice)))<=>(?[X]:((generous(X)|tall(X)))))&
(![X]:(kind(X)<=>(happy(X)<~>wise(X))))&
(![X]:((quiet(X)|~humble(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:((~strong(X)<~>~happy(X))=>humble(X)))&
(![X]:((patient(X)|~kind(X))<=>(~humble(X)|~rich(X))))&
(![X]:((~brave(X)&tall(X))<=>(~tall(X)|~calm(X))))&
(((calm(fred)<~>patient(fred)))=>(~strong(alice)))&
(![X]:((~brave(X)&humble(X))<=>quiet(X)))&
((?[X]:(patient(X)))<=>((tall(alice)&~funny(alice))))&
((?[X]:((~creative(X)&~humble(X))))=>((patient(paul)<~>happy(paul))))&
(![X]:((~funny(X)|tall(X))<=>(tall(X)&~happy(X))))&
(((curious(john)&creative(john)))=>((kind(susan)|creative(susan))))&
(![X]:((~patient(X)&~generous(X))<=>~creative(X)))&
((?[X]:((~old(X)|~patient(X))))=>(?[X]:((~generous(X)|quiet(X)))))&
(![X]:((brave(X)|calm(X))=>~rich(X)))&
(?[X]:((~funny(X)|quiet(X))))&
(?[X]:((~wise(X)<~>tall(X))))&
((~rich(fred)<~>~curious(fred)))&
(patient(mary))&
(?[X]:((curious(X)&patient(X))))&
((kind(lucy)<~>quiet(lucy)))&
(?[X]:((~curious(X)<~>tall(X)))) | ~generous(paul) | [] | null | 0 |
If someone is strong then someone is either not funny or patient.
If fred is funny or not patient then someone is funny or strong.
Everyone who is either old or not kind is both generous and not curious.
Everyone who is kind or generous is either not happy or not patient.
Everyone who is both not creative and not humble is both generous and old.
If alice is not curious or not calm then someone is brave or humble and vice versa.
If someone is either not patient or not calm then susan is not creative or curious and vice versa.
If mary is both brave and not quiet then mary is either not calm or tall and vice versa.
Everyone who is not rich is either not calm or not rich and vice versa.
If john is creative or patient then someone is funny.
Everyone who is both funny and tall is humble or brave.
If susan is either not funny or kind then fred is either not kind or not brave and vice versa.
Everyone who is calm is creative.
If someone is either strong or not curious then someone is not rich.
If someone is old or tall then someone is not calm.
If fred is either not rich or kind then john is both not funny and not kind and vice versa.
Someone is tall or generous.
Someone is strong.
Someone is kind or generous.
Mary is not strong.
Susan is either not creative or not brave.
Someone is both humble and not strong.
Susan is not tall. | Mary is not calm. | contradiction | ((?[X]:(strong(X)))=>(?[X]:((~funny(X)<~>patient(X)))))&
(((funny(fred)|~patient(fred)))=>(?[X]:((funny(X)|strong(X)))))&
(![X]:((old(X)<~>~kind(X))=>(generous(X)&~curious(X))))&
(![X]:((kind(X)|generous(X))=>(~happy(X)<~>~patient(X))))&
(![X]:((~creative(X)&~humble(X))=>(generous(X)&old(X))))&
(((~curious(alice)|~calm(alice)))<=>(?[X]:((brave(X)|humble(X)))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>((~creative(susan)|curious(susan))))&
(((brave(mary)&~quiet(mary)))<=>((~calm(mary)<~>tall(mary))))&
(![X]:(~rich(X)<=>(~calm(X)<~>~rich(X))))&
(((creative(john)|patient(john)))=>(?[X]:(funny(X))))&
(![X]:((funny(X)&tall(X))=>(humble(X)|brave(X))))&
(((~funny(susan)<~>kind(susan)))<=>((~kind(fred)<~>~brave(fred))))&
(![X]:(calm(X)=>creative(X)))&
((?[X]:((strong(X)<~>~curious(X))))=>(?[X]:(~rich(X))))&
((?[X]:((old(X)|tall(X))))=>(?[X]:(~calm(X))))&
(((~rich(fred)<~>kind(fred)))<=>((~funny(john)&~kind(john))))&
(?[X]:((tall(X)|generous(X))))&
(?[X]:(strong(X)))&
(?[X]:((kind(X)|generous(X))))&
(~strong(mary))&
((~creative(susan)<~>~brave(susan)))&
(?[X]:((humble(X)&~strong(X))))&
(~tall(susan)) | ~calm(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4106560360895883422838997
% SZS output start Proof for 4106560360895883422838997
9. ! [X0] : (~rich(X0) <=> (~calm(X0) <~> ~rich(X0))) [input p8]
24. ~calm(mary) [input hypothesis]
60. ! [X0] : ((~rich(X0) | ((~calm(X0) | rich(X0)) & (~rich(X0) | calm(X0)))) & (((rich(X0) | calm(X0)) & (~rich(X0) | ~calm(X0))) | rich(X0))) [nnf transformation 9]
113. rich(X0) | calm(X0) | rich(X0) [cnf transformation 60]
114. ~rich(X0) | ~rich(X0) | calm(X0) [cnf transformation 60]
147. ~calm(mary) [cnf transformation 24]
148. rich(X0) | calm(X0) [duplicate literal removal 113]
149. ~rich(X0) | calm(X0) [duplicate literal removal 114]
257. calm(X0) [subsumption resolution 148,149]
340. $false [subsumption resolution 147,257]
% SZS output end Proof for 4106560360895883422838997
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is calm or not quiet then someone is either not funny or curious.
If mary is not strong or tall then someone is not old or not calm and vice versa.
Everyone who is curious or funny is not creative or not funny and vice versa.
If someone is either patient or wise then someone is either creative or not curious and vice versa.
Everyone who is either quiet or not quiet is not funny and vice versa.
Everyone who is both quiet and not old is either not funny or tall and vice versa.
If someone is either brave or wise then alice is both funny and not calm and vice versa.
Everyone who is not brave or not strong is not tall or not curious.
Everyone who is strong or not kind is not patient and vice versa.
If susan is both not quiet and not calm then someone is calm.
Everyone who is not wise is old.
If someone is either kind or curious then someone is not curious or generous.
If alice is both not funny and not strong then someone is either generous or not rich.
If someone is generous or rich then someone is both curious and not generous.
Everyone who is not strong is either creative or funny and vice versa.
Everyone who is not generous is both curious and not old and vice versa.
Lucy is either tall or not curious.
Paul is not wise or not humble.
Someone is not generous or calm.
Mary is curious or not strong.
Someone is not humble or funny.
Mary is not old or calm. | Paul is funny. | contradiction | ((?[X]:((calm(X)|~quiet(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(((~strong(mary)|tall(mary)))<=>(?[X]:((~old(X)|~calm(X)))))&
(![X]:((curious(X)|funny(X))<=>(~creative(X)|~funny(X))))&
((?[X]:((patient(X)<~>wise(X))))<=>(?[X]:((creative(X)<~>~curious(X)))))&
(![X]:((quiet(X)<~>~quiet(X))<=>~funny(X)))&
(![X]:((quiet(X)&~old(X))<=>(~funny(X)<~>tall(X))))&
((?[X]:((brave(X)<~>wise(X))))<=>((funny(alice)&~calm(alice))))&
(![X]:((~brave(X)|~strong(X))=>(~tall(X)|~curious(X))))&
(![X]:((strong(X)|~kind(X))<=>~patient(X)))&
(((~quiet(susan)&~calm(susan)))=>(?[X]:(calm(X))))&
(![X]:(~wise(X)=>old(X)))&
((?[X]:((kind(X)<~>curious(X))))=>(?[X]:((~curious(X)|generous(X)))))&
(((~funny(alice)&~strong(alice)))=>(?[X]:((generous(X)<~>~rich(X)))))&
((?[X]:((generous(X)|rich(X))))=>(?[X]:((curious(X)&~generous(X)))))&
(![X]:(~strong(X)<=>(creative(X)<~>funny(X))))&
(![X]:(~generous(X)<=>(curious(X)&~old(X))))&
((tall(lucy)<~>~curious(lucy)))&
((~wise(paul)|~humble(paul)))&
(?[X]:((~generous(X)|calm(X))))&
((curious(mary)|~strong(mary)))&
(?[X]:((~humble(X)|funny(X))))&
((~old(mary)|calm(mary))) | funny(paul) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 8195554364025183668596899
% SZS output start Proof for 8195554364025183668596899
5. ! [X0] : ((quiet(X0) <~> ~quiet(X0)) <=> ~funny(X0)) [input p4]
23. funny(paul) [input hypothesis]
56. ! [X0] : ((((quiet(X0) | ~quiet(X0)) & (~quiet(X0) | quiet(X0))) | funny(X0)) & (~funny(X0) | ((quiet(X0) | quiet(X0)) & (~quiet(X0) | ~quiet(X0))))) [nnf transformation 5]
104. ~funny(X0) | ~quiet(X0) | ~quiet(X0) [cnf transformation 56]
105. ~funny(X0) | quiet(X0) | quiet(X0) [cnf transformation 56]
147. funny(paul) [cnf transformation 23]
148. ~funny(X0) | ~quiet(X0) [duplicate literal removal 104]
149. ~funny(X0) | quiet(X0) [duplicate literal removal 105]
232. ~funny(X0) [subsumption resolution 148,149]
350. $false [subsumption resolution 147,232]
% SZS output end Proof for 8195554364025183668596899
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either happy or not humble then someone is either kind or not curious. Everyone who is either tall or not patient is strong or tall and vice versa. If mary is both not brave and humble then john is both funny and not old and vice versa. If lucy is both tall and wise then someone is both calm and creative and vice versa. If someone is either kind or wise then paul is either curious or not creative. If alice is either wise or strong then alice is both not generous and calm and vice versa. If someone is both wise and curious then fred is not generous. Everyone who is not happy is both not tall and not calm. Everyone who is either rich or humble is quiet or creative. Everyone who is both not quiet and not generous is either strong or not brave and vice versa. Everyone who is either not generous or not wise is both rich and calm. If john is not creative then someone is both not patient and not brave and vice versa. Everyone who is both not tall and not happy is funny or curious and vice versa. Everyone who is both not quiet and happy is either not old or old and vice versa. Everyone who is both not curious and generous is old and vice versa. Everyone who is not funny is either not quiet or not generous and vice versa. Someone is not humble. Someone is either not tall or not happy. Someone is not curious or not calm. Someone is either not happy or wise. Someone is creative or kind. | Alice is not calm. | neutral | (((happy(paul)<~>~humble(paul)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((tall(X)<~>~patient(X))<=>(strong(X)|tall(X))))&
(((~brave(mary)&humble(mary)))<=>((funny(john)&~old(john))))&
(((tall(lucy)&wise(lucy)))<=>(?[X]:((calm(X)&creative(X)))))&
((?[X]:((kind(X)<~>wise(X))))=>((curious(paul)<~>~creative(paul))))&
(((wise(alice)<~>strong(alice)))<=>((~generous(alice)&calm(alice))))&
((?[X]:((wise(X)&curious(X))))=>(~generous(fred)))&
(![X]:(~happy(X)=>(~tall(X)&~calm(X))))&
(![X]:((rich(X)<~>humble(X))=>(quiet(X)|creative(X))))&
(![X]:((~quiet(X)&~generous(X))<=>(strong(X)<~>~brave(X))))&
(![X]:((~generous(X)<~>~wise(X))=>(rich(X)&calm(X))))&
((~creative(john))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(funny(X)|curious(X))))&
(![X]:((~quiet(X)&happy(X))<=>(~old(X)<~>old(X))))&
(![X]:((~curious(X)&generous(X))<=>old(X)))&
(![X]:(~funny(X)<=>(~quiet(X)<~>~generous(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~tall(X)<~>~happy(X))))&
(?[X]:((~curious(X)|~calm(X))))&
(?[X]:((~happy(X)<~>wise(X))))&
(?[X]:((creative(X)|kind(X)))) | ~calm(alice) | [] | null | 0 |
If someone is both not strong and calm then someone is both wise and not old. Everyone who is either kind or tall is either calm or rich. If lucy is not strong then john is both not kind and tall and vice versa. Everyone who is either not generous or strong is either not humble or not wise and vice versa. Everyone who is not kind or wise is either not funny or happy and vice versa. Everyone who is both not tall and not quiet is either not creative or not kind and vice versa. Everyone who is not quiet is either not creative or kind. Everyone who is both rich and not wise is either not patient or strong and vice versa. If john is both not wise and not generous then someone is both not patient and not quiet. Everyone who is not kind or rich is either not tall or tall and vice versa. If alice is wise then someone is both funny and not wise and vice versa. If someone is rich then someone is both generous and not rich and vice versa. Everyone who is not funny or quiet is both not brave and kind. Everyone who is either calm or funny is not curious and vice versa. If paul is both not happy and not calm then someone is both not funny and happy. Everyone who is patient or not curious is both patient and quiet. Someone is both calm and not old. Fred is old. Paul is either quiet or old. Someone is both not patient and not wise. Someone is not generous or funny. Lucy is both not wise and not kind. Someone is not patient. Alice is old. | Lucy is not creative. | entailment | ((?[X]:((~strong(X)&calm(X))))=>(?[X]:((wise(X)&~old(X)))))&
(![X]:((kind(X)<~>tall(X))=>(calm(X)<~>rich(X))))&
((~strong(lucy))<=>((~kind(john)&tall(john))))&
(![X]:((~generous(X)<~>strong(X))<=>(~humble(X)<~>~wise(X))))&
(![X]:((~kind(X)|wise(X))<=>(~funny(X)<~>happy(X))))&
(![X]:((~tall(X)&~quiet(X))<=>(~creative(X)<~>~kind(X))))&
(![X]:(~quiet(X)=>(~creative(X)<~>kind(X))))&
(![X]:((rich(X)&~wise(X))<=>(~patient(X)<~>strong(X))))&
(((~wise(john)&~generous(john)))=>(?[X]:((~patient(X)&~quiet(X)))))&
(![X]:((~kind(X)|rich(X))<=>(~tall(X)<~>tall(X))))&
((wise(alice))<=>(?[X]:((funny(X)&~wise(X)))))&
((?[X]:(rich(X)))<=>(?[X]:((generous(X)&~rich(X)))))&
(![X]:((~funny(X)|quiet(X))=>(~brave(X)&kind(X))))&
(![X]:((calm(X)<~>funny(X))<=>~curious(X)))&
(((~happy(paul)&~calm(paul)))=>(?[X]:((~funny(X)&happy(X)))))&
(![X]:((patient(X)|~curious(X))=>(patient(X)&quiet(X))))&
(?[X]:((calm(X)&~old(X))))&
(old(fred))&
((quiet(paul)<~>old(paul)))&
(?[X]:((~patient(X)&~wise(X))))&
(?[X]:((~generous(X)|funny(X))))&
((~wise(lucy)&~kind(lucy)))&
(?[X]:(~patient(X)))&
(old(alice)) | ~creative(lucy) | [
"p5",
"p6",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 8303838739584704658751284
% SZS output start Proof for 8303838739584704658751284
6. ! [X0] : ((~quiet(X0) & ~tall(X0)) <=> (~creative(X0) <~> ~kind(X0))) [input p5]
7. ! [X0] : (~quiet(X0) => (~creative(X0) <~> kind(X0))) [input p6]
22. ~kind(lucy) & ~wise(lucy) [input p21]
25. creative(lucy) [input hypothesis]
32. ! [X0] : ((~creative(X0) <~> kind(X0)) | quiet(X0)) [ennf transformation 7]
49. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | (quiet(X0) | tall(X0)))) [nnf transformation 6]
50. ! [X0] : (((~quiet(X0) & ~tall(X0)) | ((~creative(X0) | kind(X0)) & (~kind(X0) | creative(X0)))) & (((kind(X0) | creative(X0)) & (~kind(X0) | ~creative(X0))) | quiet(X0) | tall(X0))) [flattening 49]
51. ! [X0] : (((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | quiet(X0)) [nnf transformation 32]
107. ~quiet(X0) | ~creative(X0) | kind(X0) [cnf transformation 50]
108. kind(X0) | ~creative(X0) | quiet(X0) [cnf transformation 51]
149. ~kind(lucy) [cnf transformation 22]
152. creative(lucy) [cnf transformation 25]
184. ~creative(X0) | kind(X0) [subsumption resolution 108,107]
283. kind(lucy) [resolution 184,152]
284. $false [subsumption resolution 283,149]
% SZS output end Proof for 8303838739584704658751284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not funny or generous then susan is both rich and not calm. If alice is either tall or creative then john is either kind or not brave and vice versa. Everyone who is both old and patient is creative or humble and vice versa. If susan is both strong and not happy then someone is both not strong and not brave. If someone is old then someone is either tall or not creative. If someone is not creative then paul is both not curious and generous. Everyone who is either old or calm is both not curious and funny and vice versa. Everyone who is both not funny and humble is not curious or wise and vice versa. Everyone who is quiet or not patient is curious. If alice is patient or not rich then someone is not curious or not calm and vice versa. If someone is both not old and not strong then susan is tall and vice versa. If alice is not humble or not tall then mary is either not kind or not humble. Everyone who is either patient or not strong is happy and vice versa. Everyone who is either not tall or not curious is brave and vice versa. John is both not tall and not strong. Susan is either not generous or not tall. Someone is not tall. Alice is either not tall or not wise. Lucy is not calm. | Susan is not calm. | entailment | ((?[X]:((~funny(X)|generous(X))))=>((rich(susan)&~calm(susan))))&
(((tall(alice)<~>creative(alice)))<=>((kind(john)<~>~brave(john))))&
(![X]:((old(X)&patient(X))<=>(creative(X)|humble(X))))&
(((strong(susan)&~happy(susan)))=>(?[X]:((~strong(X)&~brave(X)))))&
((?[X]:(old(X)))=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:(~creative(X)))=>((~curious(paul)&generous(paul))))&
(![X]:((old(X)<~>calm(X))<=>(~curious(X)&funny(X))))&
(![X]:((~funny(X)&humble(X))<=>(~curious(X)|wise(X))))&
(![X]:((quiet(X)|~patient(X))=>curious(X)))&
(((patient(alice)|~rich(alice)))<=>(?[X]:((~curious(X)|~calm(X)))))&
((?[X]:((~old(X)&~strong(X))))<=>(tall(susan)))&
(((~humble(alice)|~tall(alice)))=>((~kind(mary)<~>~humble(mary))))&
(![X]:((patient(X)<~>~strong(X))<=>happy(X)))&
(![X]:((~tall(X)<~>~curious(X))<=>brave(X)))&
((~tall(john)&~strong(john)))&
((~generous(susan)<~>~tall(susan)))&
(?[X]:(~tall(X)))&
((~tall(alice)<~>~wise(alice)))&
(~calm(lucy)) | ~calm(susan) | [
"p0",
"p2",
"p5",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 6533829182229877345582838
% SZS output start Proof for 6533829182229877345582838
1. ? [X0] : (generous(X0) | ~funny(X0)) => (~calm(susan) & rich(susan)) [input p0]
3. ! [X0] : ((patient(X0) & old(X0)) <=> (humble(X0) | creative(X0))) [input p2]
6. ? [X0] : ~creative(X0) => (generous(paul) & ~curious(paul)) [input p5]
11. ? [X0] : (~strong(X0) & ~old(X0)) <=> tall(susan) [input p10]
16. ~generous(susan) <~> ~tall(susan) [input p15]
20. calm(susan) [input hypothesis]
24. (~calm(susan) & rich(susan)) | ! [X0] : (~generous(X0) & funny(X0)) [ennf transformation 1]
28. (generous(paul) & ~curious(paul)) | ! [X0] : creative(X0) [ennf transformation 6]
33. ! [X0] : (((patient(X0) & old(X0)) | (~humble(X0) & ~creative(X0))) & ((humble(X0) | creative(X0)) | (~patient(X0) | ~old(X0)))) [nnf transformation 3]
34. ! [X0] : (((patient(X0) & old(X0)) | (~humble(X0) & ~creative(X0))) & (humble(X0) | creative(X0) | ~patient(X0) | ~old(X0))) [flattening 33]
50. (? [X0] : (~strong(X0) & ~old(X0)) | ~tall(susan)) & (tall(susan) | ! [X0] : (strong(X0) | old(X0))) [nnf transformation 11]
51. (? [X0] : (~strong(X0) & ~old(X0)) | ~tall(susan)) & (tall(susan) | ! [X1] : (strong(X1) | old(X1))) [rectify 50]
52. ? [X0] : (~strong(X0) & ~old(X0)) => (~strong(sK3) & ~old(sK3)) [choice axiom]
53. ((~strong(sK3) & ~old(sK3)) | ~tall(susan)) & (tall(susan) | ! [X1] : (strong(X1) | old(X1))) [skolemisation 51,52]
57. (tall(susan) | generous(susan)) & (~tall(susan) | ~generous(susan)) [nnf transformation 16]
64. ~calm(susan) | ~generous(X0) [cnf transformation 24]
74. ~creative(X0) | old(X0) [cnf transformation 34]
83. generous(paul) | creative(X0) [cnf transformation 28]
101. ~old(sK3) | ~tall(susan) [cnf transformation 53]
116. tall(susan) | generous(susan) [cnf transformation 57]
121. calm(susan) [cnf transformation 20]
123. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
124. ~generous(X0) <- (1) [avatar component clause 123]
126. 2 <=> calm(susan) [avatar definition]
129. 1 | ~2 [avatar split clause 64,126,123]
196. 16 <=> ! [X0] : creative(X0) [avatar definition]
197. creative(X0) <- (16) [avatar component clause 196]
199. 17 <=> generous(paul) [avatar definition]
201. generous(paul) <- (17) [avatar component clause 199]
202. 16 | 17 [avatar split clause 83,199,196]
235. 25 <=> tall(susan) [avatar definition]
244. 27 <=> old(sK3) [avatar definition]
246. ~old(sK3) <- (~27) [avatar component clause 244]
247. ~25 | ~27 [avatar split clause 101,244,235]
269. 32 <=> generous(susan) [avatar definition]
271. generous(susan) <- (32) [avatar component clause 269]
272. 32 | 25 [avatar split clause 116,235,269]
280. 2 [avatar split clause 121,126]
285. old(X0) <- (16) [resolution 74,197]
288. $false <- (16, ~27) [resolution 285,246]
289. ~16 | 27 [avatar contradiction clause 288]
290. $false <- (1, 17) [subsumption resolution 201,124]
291. ~1 | ~17 [avatar contradiction clause 290]
292. $false <- (1, 32) [subsumption resolution 271,124]
293. ~1 | ~32 [avatar contradiction clause 292]
294. $false [avatar sat refutation 129,202,247,272,280,289,291,293]
% SZS output end Proof for 6533829182229877345582838
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is both not humble and not rich and vice versa. Everyone who is either tall or not humble is both not curious and patient and vice versa. Everyone who is either creative or not rich is curious. If mary is creative or not old then someone is either tall or not old. If someone is both creative and not calm then someone is both quiet and not quiet and vice versa. If someone is either not curious or not old then mary is not brave or not curious. Everyone who is patient or quiet is both not kind and not strong and vice versa. If fred is generous then fred is not tall or creative and vice versa. Everyone who is either not calm or not strong is either kind or not rich and vice versa. If someone is both not kind and old then someone is not humble and vice versa. Everyone who is either not quiet or not calm is both not strong and quiet and vice versa. Everyone who is both patient and not humble is strong or not strong. Everyone who is not funny is not kind and vice versa. Everyone who is either not strong or strong is brave or not curious. If someone is not kind then fred is both not generous and humble. Everyone who is curious or not humble is both not brave and not quiet. Alice is generous. Mary is both not calm and funny. Someone is not wise or not quiet. Alice is patient or not funny. Mary is not humble or not creative. Someone is either not brave or brave. Susan is rich. Alice is both not tall and not kind. | Mary is not kind. | contradiction | (![X]:(~humble(X)<=>(~humble(X)&~rich(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(~curious(X)&patient(X))))&
(![X]:((creative(X)<~>~rich(X))=>curious(X)))&
(((creative(mary)|~old(mary)))=>(?[X]:((tall(X)<~>~old(X)))))&
((?[X]:((creative(X)&~calm(X))))<=>(?[X]:((quiet(X)&~quiet(X)))))&
((?[X]:((~curious(X)<~>~old(X))))=>((~brave(mary)|~curious(mary))))&
(![X]:((patient(X)|quiet(X))<=>(~kind(X)&~strong(X))))&
((generous(fred))<=>((~tall(fred)|creative(fred))))&
(![X]:((~calm(X)<~>~strong(X))<=>(kind(X)<~>~rich(X))))&
((?[X]:((~kind(X)&old(X))))<=>(?[X]:(~humble(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~strong(X)&quiet(X))))&
(![X]:((patient(X)&~humble(X))=>(strong(X)|~strong(X))))&
(![X]:(~funny(X)<=>~kind(X)))&
(![X]:((~strong(X)<~>strong(X))=>(brave(X)|~curious(X))))&
((?[X]:(~kind(X)))=>((~generous(fred)&humble(fred))))&
(![X]:((curious(X)|~humble(X))=>(~brave(X)&~quiet(X))))&
(generous(alice))&
((~calm(mary)&funny(mary)))&
(?[X]:((~wise(X)|~quiet(X))))&
((patient(alice)|~funny(alice)))&
((~humble(mary)|~creative(mary)))&
(?[X]:((~brave(X)<~>brave(X))))&
(rich(susan))&
((~tall(alice)&~kind(alice))) | ~kind(mary) | [
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3529329461616335897886114
% SZS output start Proof for 3529329461616335897886114
13. ! [X0] : (~funny(X0) <=> ~kind(X0)) [input p12]
18. funny(mary) & ~calm(mary) [input p17]
25. ~kind(mary) [input hypothesis]
65. ! [X0] : ((~funny(X0) | kind(X0)) & (~kind(X0) | funny(X0))) [nnf transformation 13]
118. ~funny(X0) | kind(X0) [cnf transformation 65]
129. funny(mary) [cnf transformation 18]
137. ~kind(mary) [cnf transformation 25]
263. kind(mary) [resolution 118,129]
265. $false [subsumption resolution 263,137]
% SZS output end Proof for 3529329461616335897886114
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not curious and kind is happy and vice versa.
If lucy is both brave and humble then someone is patient or wise.
Everyone who is creative is generous or not calm and vice versa.
If susan is both not calm and happy then someone is both rich and not old and vice versa.
If someone is not brave or not patient then fred is old and vice versa.
If lucy is not creative then fred is not wise and vice versa.
Everyone who is brave or not tall is calm or not rich and vice versa.
Everyone who is both rich and not patient is tall or curious.
Everyone who is not creative is both not quiet and happy.
If someone is brave or strong then someone is either not tall or happy and vice versa.
Everyone who is not wise or not kind is happy.
If fred is either not calm or tall then lucy is not brave or kind.
Everyone who is not curious or generous is curious and vice versa.
Everyone who is either not happy or not calm is not tall and vice versa.
Everyone who is either tall or not quiet is either wise or not funny and vice versa.
Susan is not happy.
Fred is not patient.
Mary is brave or curious.
Someone is patient.
Susan is calm or not rich.
Someone is happy or strong. | Fred is not curious. | contradiction | (![X]:((~curious(X)&kind(X))<=>happy(X)))&
(((brave(lucy)&humble(lucy)))=>(?[X]:((patient(X)|wise(X)))))&
(![X]:(creative(X)<=>(generous(X)|~calm(X))))&
(((~calm(susan)&happy(susan)))<=>(?[X]:((rich(X)&~old(X)))))&
((?[X]:((~brave(X)|~patient(X))))<=>(old(fred)))&
((~creative(lucy))<=>(~wise(fred)))&
(![X]:((brave(X)|~tall(X))<=>(calm(X)|~rich(X))))&
(![X]:((rich(X)&~patient(X))=>(tall(X)|curious(X))))&
(![X]:(~creative(X)=>(~quiet(X)&happy(X))))&
((?[X]:((brave(X)|strong(X))))<=>(?[X]:((~tall(X)<~>happy(X)))))&
(![X]:((~wise(X)|~kind(X))=>happy(X)))&
(((~calm(fred)<~>tall(fred)))=>((~brave(lucy)|kind(lucy))))&
(![X]:((~curious(X)|generous(X))<=>curious(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>~tall(X)))&
(![X]:((tall(X)<~>~quiet(X))<=>(wise(X)<~>~funny(X))))&
(~happy(susan))&
(~patient(fred))&
((brave(mary)|curious(mary)))&
(?[X]:(patient(X)))&
((calm(susan)|~rich(susan)))&
(?[X]:((happy(X)|strong(X)))) | ~curious(fred) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 52664032989985794088570
% SZS output start Proof for 52664032989985794088570
13. ! [X0] : ((generous(X0) | ~curious(X0)) <=> curious(X0)) [input p12]
22. ~curious(fred) [input hypothesis]
53. ! [X0] : (((generous(X0) | ~curious(X0)) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [nnf transformation 13]
54. ! [X0] : ((generous(X0) | ~curious(X0) | ~curious(X0)) & (curious(X0) | (~generous(X0) & curious(X0)))) [flattening 53]
93. curious(X0) | curious(X0) [cnf transformation 54]
114. ~curious(fred) [cnf transformation 22]
115. curious(X0) [duplicate literal removal 93]
221. $false [subsumption resolution 114,115]
% SZS output end Proof for 52664032989985794088570
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not brave is both not creative and old. Everyone who is either brave or not strong is both not patient and patient and vice versa. Everyone who is not tall or not wise is both happy and not creative and vice versa. If lucy is patient or not generous then alice is not old or wise. Everyone who is not funny or not creative is either old or not quiet. Everyone who is both not calm and not generous is both creative and tall and vice versa. If someone is both tall and not patient then someone is not curious or not old. If mary is both not happy and generous then someone is both curious and quiet. If susan is both not old and quiet then mary is either generous or not humble. If someone is not old then susan is kind. Everyone who is quiet is either not brave or patient. Everyone who is not happy is strong or rich and vice versa. If someone is rich or funny then someone is both not quiet and strong and vice versa. Everyone who is wise is both not quiet and rich and vice versa. Everyone who is either wise or not brave is both not tall and rich. Everyone who is both not tall and not happy is not quiet. Someone is either quiet or not strong. Paul is generous or wise. John is both calm and not tall. Someone is not curious. Someone is either not rich or not humble. Someone is either tall or not happy. | Mary is not brave. | contradiction | (![X]:((curious(X)|~brave(X))=>(~creative(X)&old(X))))&
(![X]:((brave(X)<~>~strong(X))<=>(~patient(X)&patient(X))))&
(![X]:((~tall(X)|~wise(X))<=>(happy(X)&~creative(X))))&
(((patient(lucy)|~generous(lucy)))=>((~old(alice)|wise(alice))))&
(![X]:((~funny(X)|~creative(X))=>(old(X)<~>~quiet(X))))&
(![X]:((~calm(X)&~generous(X))<=>(creative(X)&tall(X))))&
((?[X]:((tall(X)&~patient(X))))=>(?[X]:((~curious(X)|~old(X)))))&
(((~happy(mary)&generous(mary)))=>(?[X]:((curious(X)&quiet(X)))))&
(((~old(susan)&quiet(susan)))=>((generous(mary)<~>~humble(mary))))&
((?[X]:(~old(X)))=>(kind(susan)))&
(![X]:(quiet(X)=>(~brave(X)<~>patient(X))))&
(![X]:(~happy(X)<=>(strong(X)|rich(X))))&
((?[X]:((rich(X)|funny(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
(![X]:(wise(X)<=>(~quiet(X)&rich(X))))&
(![X]:((wise(X)<~>~brave(X))=>(~tall(X)&rich(X))))&
(![X]:((~tall(X)&~happy(X))=>~quiet(X)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((generous(paul)|wise(paul)))&
((calm(john)&~tall(john)))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>~humble(X))))&
(?[X]:((tall(X)<~>~happy(X)))) | ~brave(mary) | [
"p0",
"p1",
"p2",
"p4",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8252991862174025816940413
% SZS output start Proof for 8252991862174025816940413
1. ! [X0] : ((~brave(X0) | curious(X0)) => (old(X0) & ~creative(X0))) [input p0]
2. ! [X0] : ((brave(X0) <~> ~strong(X0)) <=> (patient(X0) & ~patient(X0))) [input p1]
3. ! [X0] : ((~wise(X0) | ~tall(X0)) <=> (~creative(X0) & happy(X0))) [input p2]
5. ! [X0] : ((~creative(X0) | ~funny(X0)) => (old(X0) <~> ~quiet(X0))) [input p4]
12. ! [X0] : (~happy(X0) <=> (rich(X0) | strong(X0))) [input p11]
14. ! [X0] : (wise(X0) <=> (rich(X0) & ~quiet(X0))) [input p13]
23. ~brave(mary) [input hypothesis]
27. ! [X0] : ((old(X0) & ~creative(X0)) | (brave(X0) & ~curious(X0))) [ennf transformation 1]
30. ! [X0] : ((old(X0) <~> ~quiet(X0)) | (creative(X0) & funny(X0))) [ennf transformation 5]
40. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [nnf transformation 2]
41. ! [X0] : ((((strong(X0) | ~brave(X0)) & (~strong(X0) | brave(X0))) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | ((brave(X0) | strong(X0)) & (~strong(X0) | ~brave(X0))))) [flattening 40]
42. ! [X0] : (((~wise(X0) | ~tall(X0)) | (creative(X0) | ~happy(X0))) & ((~creative(X0) & happy(X0)) | (wise(X0) & tall(X0)))) [nnf transformation 3]
43. ! [X0] : ((~wise(X0) | ~tall(X0) | creative(X0) | ~happy(X0)) & ((~creative(X0) & happy(X0)) | (wise(X0) & tall(X0)))) [flattening 42]
44. ! [X0] : (((quiet(X0) | ~old(X0)) & (~quiet(X0) | old(X0))) | (creative(X0) & funny(X0))) [nnf transformation 30]
54. ! [X0] : ((~happy(X0) | (~rich(X0) & ~strong(X0))) & ((rich(X0) | strong(X0)) | happy(X0))) [nnf transformation 12]
55. ! [X0] : ((~happy(X0) | (~rich(X0) & ~strong(X0))) & (rich(X0) | strong(X0) | happy(X0))) [flattening 54]
61. ! [X0] : ((wise(X0) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | ~wise(X0))) [nnf transformation 14]
62. ! [X0] : ((wise(X0) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | ~wise(X0))) [flattening 61]
76. ~creative(X0) | brave(X0) [cnf transformation 27]
78. old(X0) | brave(X0) [cnf transformation 27]
80. ~patient(X0) | brave(X0) | strong(X0) [cnf transformation 41]
82. patient(X0) | brave(X0) | strong(X0) [cnf transformation 41]
86. happy(X0) | wise(X0) [cnf transformation 43]
95. ~old(X0) | quiet(X0) | creative(X0) [cnf transformation 44]
108. ~happy(X0) | ~strong(X0) [cnf transformation 55]
115. ~quiet(X0) | ~wise(X0) [cnf transformation 62]
133. ~brave(mary) [cnf transformation 23]
134. strong(X0) | brave(X0) [subsumption resolution 80,82]
261. ~strong(X0) | wise(X0) [resolution 108,86]
286. wise(X0) | brave(X0) [resolution 261,134]
287. quiet(X0) | creative(X0) | brave(X0) [resolution 95,78]
288. quiet(X0) | brave(X0) [subsumption resolution 287,76]
312. brave(X4) | ~wise(X4) [resolution 288,115]
316. brave(X4) [subsumption resolution 312,286]
345. $false [resolution 316,133]
% SZS output end Proof for 8252991862174025816940413
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich or curious then john is kind or tall and vice versa.
Everyone who is wise or kind is not tall or not kind and vice versa.
If fred is both not wise and not funny then mary is either not funny or not quiet and vice versa.
Everyone who is both rich and wise is either not rich or tall and vice versa.
Everyone who is both not quiet and not patient is not old.
Everyone who is not rich is both curious and not kind and vice versa.
Everyone who is either not strong or not quiet is either old or brave.
If someone is kind then susan is not quiet and vice versa.
If someone is patient then someone is either old or not humble and vice versa.
Everyone who is not funny or not patient is either strong or tall and vice versa.
If someone is not funny or not kind then someone is not patient or calm and vice versa.
If alice is either not rich or not tall then fred is both kind and not calm.
Everyone who is not patient or calm is both rich and not old.
Everyone who is happy is humble or not patient and vice versa.
Everyone who is not rich or not funny is not quiet or rich and vice versa.
Everyone who is either kind or wise is not strong or old.
Someone is kind.
Mary is either not quiet or not humble.
Alice is not quiet or creative.
Someone is either not humble or not funny.
Paul is both not curious and kind.
Someone is calm or patient.
Someone is not kind or strong. | Mary is rich. | neutral | (((~rich(mary)|curious(mary)))<=>((kind(john)|tall(john))))&
(![X]:((wise(X)|kind(X))<=>(~tall(X)|~kind(X))))&
(((~wise(fred)&~funny(fred)))<=>((~funny(mary)<~>~quiet(mary))))&
(![X]:((rich(X)&wise(X))<=>(~rich(X)<~>tall(X))))&
(![X]:((~quiet(X)&~patient(X))=>~old(X)))&
(![X]:(~rich(X)<=>(curious(X)&~kind(X))))&
(![X]:((~strong(X)<~>~quiet(X))=>(old(X)<~>brave(X))))&
((?[X]:(kind(X)))<=>(~quiet(susan)))&
((?[X]:(patient(X)))<=>(?[X]:((old(X)<~>~humble(X)))))&
(![X]:((~funny(X)|~patient(X))<=>(strong(X)<~>tall(X))))&
((?[X]:((~funny(X)|~kind(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
(((~rich(alice)<~>~tall(alice)))=>((kind(fred)&~calm(fred))))&
(![X]:((~patient(X)|calm(X))=>(rich(X)&~old(X))))&
(![X]:(happy(X)<=>(humble(X)|~patient(X))))&
(![X]:((~rich(X)|~funny(X))<=>(~quiet(X)|rich(X))))&
(![X]:((kind(X)<~>wise(X))=>(~strong(X)|old(X))))&
(?[X]:(kind(X)))&
((~quiet(mary)<~>~humble(mary)))&
((~quiet(alice)|creative(alice)))&
(?[X]:((~humble(X)<~>~funny(X))))&
((~curious(paul)&kind(paul)))&
(?[X]:((calm(X)|patient(X))))&
(?[X]:((~kind(X)|strong(X)))) | rich(mary) | [] | null | 0 |
Everyone who is tall or happy is not quiet.
If john is not tall then someone is not kind or quiet.
If someone is kind then someone is not happy.
Everyone who is either patient or old is both not tall and not old.
If paul is both brave and happy then john is either not kind or not generous and vice versa.
If paul is not creative or rich then john is wise or curious and vice versa.
Everyone who is either calm or not funny is not old.
Everyone who is both happy and not happy is not wise and vice versa.
If susan is not funny or not curious then john is calm or not curious and vice versa.
Everyone who is both patient and not curious is brave.
Everyone who is both not humble and funny is not funny.
Everyone who is both generous and not tall is either kind or creative and vice versa.
Everyone who is not patient or rich is not rich or not wise and vice versa.
If someone is either creative or not curious then fred is either not happy or not brave.
If lucy is either not patient or humble then someone is happy and vice versa.
Everyone who is tall is generous.
Paul is wise or strong.
Susan is rich or creative.
Fred is kind or strong.
Someone is both not happy and not tall.
Fred is not creative.
John is not happy or creative.
Lucy is both strong and not quiet. | John is not patient. | entailment | (![X]:((tall(X)|happy(X))=>~quiet(X)))&
((~tall(john))=>(?[X]:((~kind(X)|quiet(X)))))&
((?[X]:(kind(X)))=>(?[X]:(~happy(X))))&
(![X]:((patient(X)<~>old(X))=>(~tall(X)&~old(X))))&
(((brave(paul)&happy(paul)))<=>((~kind(john)<~>~generous(john))))&
(((~creative(paul)|rich(paul)))<=>((wise(john)|curious(john))))&
(![X]:((calm(X)<~>~funny(X))=>~old(X)))&
(![X]:((happy(X)&~happy(X))<=>~wise(X)))&
(((~funny(susan)|~curious(susan)))<=>((calm(john)|~curious(john))))&
(![X]:((patient(X)&~curious(X))=>brave(X)))&
(![X]:((~humble(X)&funny(X))=>~funny(X)))&
(![X]:((generous(X)&~tall(X))<=>(kind(X)<~>creative(X))))&
(![X]:((~patient(X)|rich(X))<=>(~rich(X)|~wise(X))))&
((?[X]:((creative(X)<~>~curious(X))))=>((~happy(fred)<~>~brave(fred))))&
(((~patient(lucy)<~>humble(lucy)))<=>(?[X]:(happy(X))))&
(![X]:(tall(X)=>generous(X)))&
((wise(paul)|strong(paul)))&
((rich(susan)|creative(susan)))&
((kind(fred)|strong(fred)))&
(?[X]:((~happy(X)&~tall(X))))&
(~creative(fred))&
((~happy(john)|creative(john)))&
((strong(lucy)&~quiet(lucy))) | ~patient(john) | [
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 341559145501077740816742
% SZS output start Proof for 341559145501077740816742
8. ! [X0] : ((~happy(X0) & happy(X0)) <=> ~wise(X0)) [input p7]
13. ! [X0] : ((rich(X0) | ~patient(X0)) <=> (~wise(X0) | ~rich(X0))) [input p12]
24. patient(john) [input hypothesis]
51. ! [X0] : (((~happy(X0) & happy(X0)) | wise(X0)) & (~wise(X0) | (happy(X0) | ~happy(X0)))) [nnf transformation 8]
52. ! [X0] : (((~happy(X0) & happy(X0)) | wise(X0)) & (~wise(X0) | happy(X0) | ~happy(X0))) [flattening 51]
57. ! [X0] : (((rich(X0) | ~patient(X0)) | (wise(X0) & rich(X0))) & ((~wise(X0) | ~rich(X0)) | (~rich(X0) & patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((rich(X0) | ~patient(X0) | (wise(X0) & rich(X0))) & (~wise(X0) | ~rich(X0) | (~rich(X0) & patient(X0)))) [flattening 57]
87. happy(X0) | wise(X0) [cnf transformation 52]
88. ~happy(X0) | wise(X0) [cnf transformation 52]
102. ~wise(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 58]
103. rich(X0) | ~patient(X0) | rich(X0) [cnf transformation 58]
120. patient(john) [cnf transformation 24]
121. ~wise(X0) | ~rich(X0) [duplicate literal removal 102]
122. ~patient(X0) | rich(X0) [duplicate literal removal 103]
188. wise(X0) [subsumption resolution 87,88]
205. ~rich(X0) [subsumption resolution 121,188]
257. rich(john) [resolution 122,120]
259. $false [subsumption resolution 257,205]
% SZS output end Proof for 341559145501077740816742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous or not happy is quiet or not strong and vice versa. Everyone who is not tall is wise or not patient. Everyone who is not brave is either wise or old. Everyone who is not funny is both not kind and not humble and vice versa. Everyone who is not rich is either not generous or not old and vice versa. If someone is not generous or funny then someone is curious. If someone is both not kind and brave then alice is not old or funny. If fred is both not tall and not humble then someone is brave or not rich and vice versa. Everyone who is both humble and funny is not funny or calm and vice versa. If someone is both calm and not funny then fred is patient or not generous and vice versa. Everyone who is either kind or not patient is either not patient or funny. Everyone who is not quiet or not calm is both humble and not creative and vice versa. Everyone who is not brave or not calm is curious and vice versa. Everyone who is both creative and not brave is either not tall or not humble. If mary is funny or not kind then someone is funny or not strong and vice versa. Everyone who is strong is either not old or not tall and vice versa. Someone is both kind and humble. Someone is not creative. Lucy is curious or not calm. Someone is curious. Someone is calm. Susan is both rich and strong. Someone is not brave. Mary is not kind or not quiet. | Mary is funny. | entailment | (![X]:((generous(X)|~happy(X))<=>(quiet(X)|~strong(X))))&
(![X]:(~tall(X)=>(wise(X)|~patient(X))))&
(![X]:(~brave(X)=>(wise(X)<~>old(X))))&
(![X]:(~funny(X)<=>(~kind(X)&~humble(X))))&
(![X]:(~rich(X)<=>(~generous(X)<~>~old(X))))&
((?[X]:((~generous(X)|funny(X))))=>(?[X]:(curious(X))))&
((?[X]:((~kind(X)&brave(X))))=>((~old(alice)|funny(alice))))&
(((~tall(fred)&~humble(fred)))<=>(?[X]:((brave(X)|~rich(X)))))&
(![X]:((humble(X)&funny(X))<=>(~funny(X)|calm(X))))&
((?[X]:((calm(X)&~funny(X))))<=>((patient(fred)|~generous(fred))))&
(![X]:((kind(X)<~>~patient(X))=>(~patient(X)<~>funny(X))))&
(![X]:((~quiet(X)|~calm(X))<=>(humble(X)&~creative(X))))&
(![X]:((~brave(X)|~calm(X))<=>curious(X)))&
(![X]:((creative(X)&~brave(X))=>(~tall(X)<~>~humble(X))))&
(((funny(mary)|~kind(mary)))<=>(?[X]:((funny(X)|~strong(X)))))&
(![X]:(strong(X)<=>(~old(X)<~>~tall(X))))&
(?[X]:((kind(X)&humble(X))))&
(?[X]:(~creative(X)))&
((curious(lucy)|~calm(lucy)))&
(?[X]:(curious(X)))&
(?[X]:(calm(X)))&
((rich(susan)&strong(susan)))&
(?[X]:(~brave(X)))&
((~kind(mary)|~quiet(mary))) | funny(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8124709879875656640901078
% SZS output start Proof for 8124709879875656640901078
9. ! [X0] : ((funny(X0) & humble(X0)) <=> (calm(X0) | ~funny(X0))) [input p8]
25. ~funny(mary) [input hypothesis]
53. ! [X0] : (((funny(X0) & humble(X0)) | (~calm(X0) & funny(X0))) & ((calm(X0) | ~funny(X0)) | (~funny(X0) | ~humble(X0)))) [nnf transformation 9]
54. ! [X0] : (((funny(X0) & humble(X0)) | (~calm(X0) & funny(X0))) & (calm(X0) | ~funny(X0) | ~funny(X0) | ~humble(X0))) [flattening 53]
105. funny(X0) | funny(X0) [cnf transformation 54]
142. ~funny(mary) [cnf transformation 25]
146. funny(X0) [duplicate literal removal 105]
215. $false [subsumption resolution 142,146]
% SZS output end Proof for 8124709879875656640901078
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave is either curious or not creative and vice versa. If someone is calm then john is not humble and vice versa. If someone is quiet or old then someone is both not tall and calm. Everyone who is not wise is either strong or not quiet and vice versa. Everyone who is both curious and generous is funny or not strong and vice versa. Everyone who is either not tall or strong is both not curious and funny. If john is not rich or not old then mary is both quiet and not calm and vice versa. Everyone who is both not creative and old is quiet or not humble and vice versa. Everyone who is kind or not wise is both wise and not strong and vice versa. If someone is kind or not creative then someone is both not happy and strong and vice versa. Everyone who is not tall is not strong or calm. If someone is both patient and curious then john is patient. Everyone who is both not strong and not funny is either not funny or brave. Everyone who is not brave is either not old or humble. Everyone who is either old or funny is either creative or wise. If someone is not humble or not generous then someone is happy and vice versa. Paul is funny. Someone is not old or not strong. Someone is either not strong or not wise. Paul is not rich or not generous. Someone is not patient or not quiet. Someone is either not generous or not patient. Paul is creative. | Paul is old. | entailment | (![X]:((creative(X)|brave(X))<=>(curious(X)<~>~creative(X))))&
((?[X]:(calm(X)))<=>(~humble(john)))&
((?[X]:((quiet(X)|old(X))))=>(?[X]:((~tall(X)&calm(X)))))&
(![X]:(~wise(X)<=>(strong(X)<~>~quiet(X))))&
(![X]:((curious(X)&generous(X))<=>(funny(X)|~strong(X))))&
(![X]:((~tall(X)<~>strong(X))=>(~curious(X)&funny(X))))&
(((~rich(john)|~old(john)))<=>((quiet(mary)&~calm(mary))))&
(![X]:((~creative(X)&old(X))<=>(quiet(X)|~humble(X))))&
(![X]:((kind(X)|~wise(X))<=>(wise(X)&~strong(X))))&
((?[X]:((kind(X)|~creative(X))))<=>(?[X]:((~happy(X)&strong(X)))))&
(![X]:(~tall(X)=>(~strong(X)|calm(X))))&
((?[X]:((patient(X)&curious(X))))=>(patient(john)))&
(![X]:((~strong(X)&~funny(X))=>(~funny(X)<~>brave(X))))&
(![X]:(~brave(X)=>(~old(X)<~>humble(X))))&
(![X]:((old(X)<~>funny(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~humble(X)|~generous(X))))<=>(?[X]:(happy(X))))&
(funny(paul))&
(?[X]:((~old(X)|~strong(X))))&
(?[X]:((~strong(X)<~>~wise(X))))&
((~rich(paul)|~generous(paul)))&
(?[X]:((~patient(X)|~quiet(X))))&
(?[X]:((~generous(X)<~>~patient(X))))&
(creative(paul)) | old(paul) | [
"p8",
"p14",
"p16",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7791356944652539114339928
% SZS output start Proof for 7791356944652539114339928
9. ! [X0] : ((~wise(X0) | kind(X0)) <=> (~strong(X0) & wise(X0))) [input p8]
15. ! [X0] : ((old(X0) <~> funny(X0)) => (creative(X0) <~> wise(X0))) [input p14]
17. funny(paul) [input p16]
23. creative(paul) [input p22]
24. ~old(paul) [input hypothesis]
36. ! [X0] : ((creative(X0) <~> wise(X0)) | (old(X0) <=> funny(X0))) [ennf transformation 15]
54. ! [X0] : (((~wise(X0) | kind(X0)) | (strong(X0) | ~wise(X0))) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [nnf transformation 9]
55. ! [X0] : ((~wise(X0) | kind(X0) | strong(X0) | ~wise(X0)) & ((~strong(X0) & wise(X0)) | (wise(X0) & ~kind(X0)))) [flattening 54]
63. ! [X0] : (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0)))) [nnf transformation 36]
115. wise(X0) | wise(X0) [cnf transformation 55]
133. ~wise(X0) | ~creative(X0) | old(X0) | ~funny(X0) [cnf transformation 63]
137. funny(paul) [cnf transformation 17]
145. creative(paul) [cnf transformation 23]
146. ~old(paul) [cnf transformation 24]
148. wise(X0) [duplicate literal removal 115]
246. ~funny(X0) | old(X0) | ~creative(X0) [subsumption resolution 133,148]
435. old(paul) | ~creative(paul) [resolution 246,137]
437. ~creative(paul) [subsumption resolution 435,146]
438. $false [subsumption resolution 437,145]
% SZS output end Proof for 7791356944652539114339928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is creative then someone is either not kind or not rich.
If someone is patient then someone is either patient or funny and vice versa.
Everyone who is not funny or not kind is either curious or strong and vice versa.
Everyone who is both quiet and funny is not tall or not rich.
Everyone who is both happy and wise is both kind and humble.
Everyone who is both happy and creative is both not rich and tall.
If someone is strong then someone is not kind or not rich.
Everyone who is generous is either not quiet or not happy and vice versa.
Everyone who is both happy and not creative is generous or calm and vice versa.
If someone is not tall or not rich then lucy is strong.
Everyone who is not curious or calm is not humble and vice versa.
Everyone who is either old or wise is both not funny and humble.
Everyone who is both not wise and creative is either not calm or brave.
Everyone who is either not curious or happy is both brave and not generous.
Everyone who is not rich is either generous or not old and vice versa.
Everyone who is calm is not brave.
John is both wise and not rich.
Someone is either funny or not humble.
Someone is not humble or not strong.
Someone is either kind or not tall.
Someone is not strong.
Alice is creative or patient.
Someone is both not strong and not creative. | John is not strong. | entailment | ((creative(lucy))=>(?[X]:((~kind(X)<~>~rich(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((patient(X)<~>funny(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(curious(X)<~>strong(X))))&
(![X]:((quiet(X)&funny(X))=>(~tall(X)|~rich(X))))&
(![X]:((happy(X)&wise(X))=>(kind(X)&humble(X))))&
(![X]:((happy(X)&creative(X))=>(~rich(X)&tall(X))))&
((?[X]:(strong(X)))=>(?[X]:((~kind(X)|~rich(X)))))&
(![X]:(generous(X)<=>(~quiet(X)<~>~happy(X))))&
(![X]:((happy(X)&~creative(X))<=>(generous(X)|calm(X))))&
((?[X]:((~tall(X)|~rich(X))))=>(strong(lucy)))&
(![X]:((~curious(X)|calm(X))<=>~humble(X)))&
(![X]:((old(X)<~>wise(X))=>(~funny(X)&humble(X))))&
(![X]:((~wise(X)&creative(X))=>(~calm(X)<~>brave(X))))&
(![X]:((~curious(X)<~>happy(X))=>(brave(X)&~generous(X))))&
(![X]:(~rich(X)<=>(generous(X)<~>~old(X))))&
(![X]:(calm(X)=>~brave(X)))&
((wise(john)&~rich(john)))&
(?[X]:((funny(X)<~>~humble(X))))&
(?[X]:((~humble(X)|~strong(X))))&
(?[X]:((kind(X)<~>~tall(X))))&
(?[X]:(~strong(X)))&
((creative(alice)|patient(alice)))&
(?[X]:((~strong(X)&~creative(X)))) | ~strong(john) | [
"p2",
"p4",
"p8",
"p10",
"p11",
"p13",
"p14",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 19993155335769952881596
% SZS output start Proof for 19993155335769952881596
3. ! [X0] : ((~kind(X0) | ~funny(X0)) <=> (curious(X0) <~> strong(X0))) [input p2]
5. ! [X0] : ((wise(X0) & happy(X0)) => (humble(X0) & kind(X0))) [input p4]
9. ! [X0] : ((~creative(X0) & happy(X0)) <=> (calm(X0) | generous(X0))) [input p8]
11. ! [X0] : ((calm(X0) | ~curious(X0)) <=> ~humble(X0)) [input p10]
12. ! [X0] : ((old(X0) <~> wise(X0)) => (humble(X0) & ~funny(X0))) [input p11]
14. ! [X0] : ((~curious(X0) <~> happy(X0)) => (~generous(X0) & brave(X0))) [input p13]
15. ! [X0] : (~rich(X0) <=> (generous(X0) <~> ~old(X0))) [input p14]
17. ~rich(john) & wise(john) [input p16]
24. strong(john) [input hypothesis]
30. ! [X0] : ((humble(X0) & kind(X0)) | (~wise(X0) | ~happy(X0))) [ennf transformation 5]
31. ! [X0] : ((humble(X0) & kind(X0)) | ~wise(X0) | ~happy(X0)) [flattening 30]
36. ! [X0] : ((humble(X0) & ~funny(X0)) | (old(X0) <=> wise(X0))) [ennf transformation 12]
39. ! [X0] : ((~generous(X0) & brave(X0)) | (~curious(X0) <=> happy(X0))) [ennf transformation 14]
49. ! [X0] : (((~kind(X0) | ~funny(X0)) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (kind(X0) & funny(X0)))) [nnf transformation 3]
50. ! [X0] : ((~kind(X0) | ~funny(X0) | ((curious(X0) | ~strong(X0)) & (strong(X0) | ~curious(X0)))) & (((~strong(X0) | ~curious(X0)) & (strong(X0) | curious(X0))) | (kind(X0) & funny(X0)))) [flattening 49]
55. ! [X0] : (((~creative(X0) & happy(X0)) | (~calm(X0) & ~generous(X0))) & ((calm(X0) | generous(X0)) | (creative(X0) | ~happy(X0)))) [nnf transformation 9]
56. ! [X0] : (((~creative(X0) & happy(X0)) | (~calm(X0) & ~generous(X0))) & (calm(X0) | generous(X0) | creative(X0) | ~happy(X0))) [flattening 55]
57. ! [X0] : (((calm(X0) | ~curious(X0)) | humble(X0)) & (~humble(X0) | (~calm(X0) & curious(X0)))) [nnf transformation 11]
58. ! [X0] : ((calm(X0) | ~curious(X0) | humble(X0)) & (~humble(X0) | (~calm(X0) & curious(X0)))) [flattening 57]
59. ! [X0] : ((humble(X0) & ~funny(X0)) | ((old(X0) | ~wise(X0)) & (wise(X0) | ~old(X0)))) [nnf transformation 36]
61. ! [X0] : ((~generous(X0) & brave(X0)) | ((~curious(X0) | ~happy(X0)) & (happy(X0) | curious(X0)))) [nnf transformation 39]
62. ! [X0] : ((~rich(X0) | ((generous(X0) | old(X0)) & (~old(X0) | ~generous(X0)))) & (((old(X0) | ~generous(X0)) & (~old(X0) | generous(X0))) | rich(X0))) [nnf transformation 15]
83. ~strong(X0) | ~curious(X0) | funny(X0) [cnf transformation 50]
89. ~wise(X0) | humble(X0) | ~happy(X0) [cnf transformation 31]
98. ~generous(X0) | happy(X0) [cnf transformation 56]
104. ~humble(X0) | curious(X0) [cnf transformation 58]
108. ~wise(X0) | old(X0) | ~funny(X0) [cnf transformation 59]
110. ~wise(X0) | old(X0) | humble(X0) [cnf transformation 59]
116. ~generous(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 61]
117. ~old(X0) | generous(X0) | rich(X0) [cnf transformation 62]
122. wise(john) [cnf transformation 17]
123. ~rich(john) [cnf transformation 17]
133. strong(john) [cnf transformation 24]
198. ~generous(X0) | ~curious(X0) [subsumption resolution 116,98]
246. ~curious(john) | funny(john) [resolution 83,133]
260. 24 <=> happy(john) [avatar definition]
261. happy(john) <- (24) [avatar component clause 260]
268. humble(john) | ~happy(john) [resolution 89,122]
299. 32 <=> curious(john) [avatar definition]
301. ~curious(john) <- (~32) [avatar component clause 299]
309. 34 <=> funny(john) [avatar definition]
312. 34 | ~32 [avatar split clause 246,299,309]
345. old(john) | ~funny(john) [resolution 108,122]
347. 41 <=> old(john) [avatar definition]
349. old(john) <- (41) [avatar component clause 347]
350. ~34 | 41 [avatar split clause 345,347,309]
351. old(john) | humble(john) [resolution 110,122]
353. 42 <=> humble(john) [avatar definition]
355. humble(john) <- (42) [avatar component clause 353]
356. 42 | 41 [avatar split clause 351,347,353]
358. curious(john) <- (42) [resolution 355,104]
359. $false <- (~32, 42) [subsumption resolution 358,301]
360. 32 | ~42 [avatar contradiction clause 359]
361. generous(john) | rich(john) <- (41) [resolution 349,117]
364. generous(john) <- (41) [subsumption resolution 361,123]
369. ~curious(john) <- (41) [resolution 364,198]
371. happy(john) <- (41) [resolution 364,98]
375. 24 | ~41 [avatar split clause 371,347,260]
384. ~32 | ~41 [avatar split clause 369,347,299]
385. humble(john) <- (24) [subsumption resolution 268,261]
386. 42 | ~24 [avatar split clause 385,260,353]
387. $false [avatar sat refutation 312,350,356,360,375,384,386]
% SZS output end Proof for 19993155335769952881596
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not rich is not kind or strong and vice versa. If susan is either rich or not patient then fred is not strong or calm. Everyone who is both generous and not generous is patient or strong. If susan is generous or not rich then someone is either strong or not wise and vice versa. If someone is not curious or tall then someone is either not wise or happy. If someone is happy or rich then someone is both not old and not brave. If someone is not generous then someone is kind or old. Everyone who is both brave and old is both not curious and rich. Everyone who is either old or humble is not curious or not patient. Everyone who is patient or rich is kind. Everyone who is old or not curious is not old. Everyone who is not patient is not strong or not funny and vice versa. If susan is curious or not patient then fred is not rich or not patient and vice versa. Everyone who is either curious or calm is both old and not calm and vice versa. Everyone who is funny or kind is not happy or not funny. Everyone who is curious is not old or strong. Fred is not patient. Susan is not brave or not strong. Susan is both strong and not brave. Someone is quiet or not old. Mary is strong or funny. Someone is both not generous and patient. Someone is kind. Mary is both patient and not wise. | Mary is generous. | neutral | (![X]:((curious(X)|~rich(X))<=>(~kind(X)|strong(X))))&
(((rich(susan)<~>~patient(susan)))=>((~strong(fred)|calm(fred))))&
(![X]:((generous(X)&~generous(X))=>(patient(X)|strong(X))))&
(((generous(susan)|~rich(susan)))<=>(?[X]:((strong(X)<~>~wise(X)))))&
((?[X]:((~curious(X)|tall(X))))=>(?[X]:((~wise(X)<~>happy(X)))))&
((?[X]:((happy(X)|rich(X))))=>(?[X]:((~old(X)&~brave(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((kind(X)|old(X)))))&
(![X]:((brave(X)&old(X))=>(~curious(X)&rich(X))))&
(![X]:((old(X)<~>humble(X))=>(~curious(X)|~patient(X))))&
(![X]:((patient(X)|rich(X))=>kind(X)))&
(![X]:((old(X)|~curious(X))=>~old(X)))&
(![X]:(~patient(X)<=>(~strong(X)|~funny(X))))&
(((curious(susan)|~patient(susan)))<=>((~rich(fred)|~patient(fred))))&
(![X]:((curious(X)<~>calm(X))<=>(old(X)&~calm(X))))&
(![X]:((funny(X)|kind(X))=>(~happy(X)|~funny(X))))&
(![X]:(curious(X)=>(~old(X)|strong(X))))&
(~patient(fred))&
((~brave(susan)|~strong(susan)))&
((strong(susan)&~brave(susan)))&
(?[X]:((quiet(X)|~old(X))))&
((strong(mary)|funny(mary)))&
(?[X]:((~generous(X)&patient(X))))&
(?[X]:(kind(X)))&
((patient(mary)&~wise(mary))) | generous(mary) | [] | null | 0 |
Everyone who is calm is both not rich and not strong.
Everyone who is happy is either tall or not creative and vice versa.
Everyone who is both not tall and kind is both not patient and tall.
If someone is not wise or funny then someone is both quiet and not rich.
Everyone who is both not humble and patient is both patient and wise.
Everyone who is not rich is either quiet or patient and vice versa.
Everyone who is not generous is both calm and not tall and vice versa.
Everyone who is not patient or wise is both not old and happy.
If someone is creative then john is not patient or brave and vice versa.
Everyone who is either not tall or wise is both rich and not curious and vice versa.
Everyone who is curious is not calm or not humble and vice versa.
If john is both not happy and patient then someone is either not strong or not wise and vice versa.
If someone is both funny and patient then mary is kind.
Everyone who is not rich or not strong is both funny and old and vice versa.
Mary is not humble.
Mary is both quiet and strong.
Someone is either not patient or not rich.
Someone is either calm or quiet.
Someone is both patient and wise.
Alice is either brave or not happy. | John is not rich. | contradiction | (![X]:(calm(X)=>(~rich(X)&~strong(X))))&
(![X]:(happy(X)<=>(tall(X)<~>~creative(X))))&
(![X]:((~tall(X)&kind(X))=>(~patient(X)&tall(X))))&
((?[X]:((~wise(X)|funny(X))))=>(?[X]:((quiet(X)&~rich(X)))))&
(![X]:((~humble(X)&patient(X))=>(patient(X)&wise(X))))&
(![X]:(~rich(X)<=>(quiet(X)<~>patient(X))))&
(![X]:(~generous(X)<=>(calm(X)&~tall(X))))&
(![X]:((~patient(X)|wise(X))=>(~old(X)&happy(X))))&
((?[X]:(creative(X)))<=>((~patient(john)|brave(john))))&
(![X]:((~tall(X)<~>wise(X))<=>(rich(X)&~curious(X))))&
(![X]:(curious(X)<=>(~calm(X)|~humble(X))))&
(((~happy(john)&patient(john)))<=>(?[X]:((~strong(X)<~>~wise(X)))))&
((?[X]:((funny(X)&patient(X))))=>(kind(mary)))&
(![X]:((~rich(X)|~strong(X))<=>(funny(X)&old(X))))&
(~humble(mary))&
((quiet(mary)&strong(mary)))&
(?[X]:((~patient(X)<~>~rich(X))))&
(?[X]:((calm(X)<~>quiet(X))))&
(?[X]:((patient(X)&wise(X))))&
((brave(alice)<~>~happy(alice))) | ~rich(john) | [
"p3",
"p5",
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5333360048856223692276651
% SZS output start Proof for 5333360048856223692276651
4. ? [X0] : (funny(X0) | ~wise(X0)) => ? [X0] : (~rich(X0) & quiet(X0)) [input p3]
6. ! [X0] : (~rich(X0) <=> (quiet(X0) <~> patient(X0))) [input p5]
8. ! [X0] : ((wise(X0) | ~patient(X0)) => (happy(X0) & ~old(X0))) [input p7]
14. ! [X0] : ((~strong(X0) | ~rich(X0)) <=> (old(X0) & funny(X0))) [input p13]
21. ~rich(john) [input hypothesis]
22. ? [X0] : (funny(X0) | ~wise(X0)) => ? [X1] : (~rich(X1) & quiet(X1)) [rectify 4]
26. ? [X1] : (~rich(X1) & quiet(X1)) | ! [X0] : (~funny(X0) & wise(X0)) [ennf transformation 22]
29. ! [X0] : ((happy(X0) & ~old(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 8]
32. ? [X0] : (~rich(X0) & quiet(X0)) | ! [X1] : (~funny(X1) & wise(X1)) [rectify 26]
33. ? [X0] : (~rich(X0) & quiet(X0)) => (~rich(sK0) & quiet(sK0)) [choice axiom]
34. (~rich(sK0) & quiet(sK0)) | ! [X1] : (~funny(X1) & wise(X1)) [skolemisation 32,33]
35. ! [X0] : ((~rich(X0) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0)))) & (((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | rich(X0))) [nnf transformation 6]
50. ! [X0] : (((~strong(X0) | ~rich(X0)) | (~old(X0) | ~funny(X0))) & ((old(X0) & funny(X0)) | (strong(X0) & rich(X0)))) [nnf transformation 14]
51. ! [X0] : ((~strong(X0) | ~rich(X0) | ~old(X0) | ~funny(X0)) & ((old(X0) & funny(X0)) | (strong(X0) & rich(X0)))) [flattening 50]
70. quiet(sK0) | ~funny(X1) [cnf transformation 34]
72. ~rich(sK0) | ~funny(X1) [cnf transformation 34]
76. ~quiet(X0) | ~patient(X0) | rich(X0) [cnf transformation 35]
77. ~quiet(X0) | patient(X0) | ~rich(X0) [cnf transformation 35]
79. ~old(X0) | patient(X0) [cnf transformation 29]
102. funny(X0) | rich(X0) [cnf transformation 51]
104. old(X0) | rich(X0) [cnf transformation 51]
118. ~rich(john) [cnf transformation 21]
121. 1 <=> ! [X1] : ~funny(X1) [avatar definition]
122. ~funny(X1) <- (1) [avatar component clause 121]
124. 2 <=> rich(sK0) [avatar definition]
127. 1 | ~2 [avatar split clause 72,124,121]
133. 4 <=> quiet(sK0) [avatar definition]
135. quiet(sK0) <- (4) [avatar component clause 133]
136. 1 | 4 [avatar split clause 70,133,121]
224. patient(X1) | rich(X1) [resolution 104,79]
310. ~patient(sK0) | rich(sK0) <- (4) [resolution 76,135]
329. patient(sK0) | ~rich(sK0) <- (4) [resolution 77,135]
455. patient(sK0) <- (4) [subsumption resolution 329,224]
456. rich(sK0) <- (4) [subsumption resolution 310,455]
457. 2 | ~4 [avatar split clause 456,133,124]
459. rich(X1) <- (1) [resolution 122,102]
484. $false <- (1) [resolution 459,118]
485. ~1 [avatar contradiction clause 484]
486. $false [avatar sat refutation 127,136,457,485]
% SZS output end Proof for 5333360048856223692276651
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and wise is not funny or not generous and vice versa. If someone is either rich or humble then john is either not wise or not strong and vice versa. Everyone who is either not creative or strong is generous. If paul is both not patient and not curious then lucy is not happy. If fred is both kind and not funny then someone is not humble and vice versa. If someone is either generous or happy then alice is both quiet and humble and vice versa. If someone is either not strong or not humble then someone is both not old and generous. If paul is not brave then someone is calm and vice versa. If someone is calm or generous then susan is either funny or not calm and vice versa. If someone is not old or not brave then someone is not generous and vice versa. Everyone who is happy is either strong or not kind and vice versa. Everyone who is wise or strong is either tall or humble. If someone is not strong or not calm then paul is either brave or not funny and vice versa. Everyone who is not patient or not humble is both not happy and rich. If susan is curious or not tall then someone is patient or not calm. Someone is either not rich or tall. Someone is either calm or patient. Someone is either not rich or not calm. Paul is either not old or happy. Someone is brave or calm. Someone is generous or not curious. | Paul is not old. | contradiction | (![X]:((generous(X)&wise(X))<=>(~funny(X)|~generous(X))))&
((?[X]:((rich(X)<~>humble(X))))<=>((~wise(john)<~>~strong(john))))&
(![X]:((~creative(X)<~>strong(X))=>generous(X)))&
(((~patient(paul)&~curious(paul)))=>(~happy(lucy)))&
(((kind(fred)&~funny(fred)))<=>(?[X]:(~humble(X))))&
((?[X]:((generous(X)<~>happy(X))))<=>((quiet(alice)&humble(alice))))&
((?[X]:((~strong(X)<~>~humble(X))))=>(?[X]:((~old(X)&generous(X)))))&
((~brave(paul))<=>(?[X]:(calm(X))))&
((?[X]:((calm(X)|generous(X))))<=>((funny(susan)<~>~calm(susan))))&
((?[X]:((~old(X)|~brave(X))))<=>(?[X]:(~generous(X))))&
(![X]:(happy(X)<=>(strong(X)<~>~kind(X))))&
(![X]:((wise(X)|strong(X))=>(tall(X)<~>humble(X))))&
((?[X]:((~strong(X)|~calm(X))))<=>((brave(paul)<~>~funny(paul))))&
(![X]:((~patient(X)|~humble(X))=>(~happy(X)&rich(X))))&
(((curious(susan)|~tall(susan)))=>(?[X]:((patient(X)|~calm(X)))))&
(?[X]:((~rich(X)<~>tall(X))))&
(?[X]:((calm(X)<~>patient(X))))&
(?[X]:((~rich(X)<~>~calm(X))))&
((~old(paul)<~>happy(paul)))&
(?[X]:((brave(X)|calm(X))))&
(?[X]:((generous(X)|~curious(X)))) | ~old(paul) | [
"p0",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 8997133636073489345750773
% SZS output start Proof for 8997133636073489345750773
1. ! [X0] : ((wise(X0) & generous(X0)) <=> (~generous(X0) | ~funny(X0))) [input p0]
10. ? [X0] : (~brave(X0) | ~old(X0)) <=> ? [X0] : ~generous(X0) [input p9]
22. ~old(paul) [input hypothesis]
24. ? [X0] : (~brave(X0) | ~old(X0)) <=> ? [X1] : ~generous(X1) [rectify 10]
32. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & funny(X0))) & ((~generous(X0) | ~funny(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 1]
33. ! [X0] : (((wise(X0) & generous(X0)) | (generous(X0) & funny(X0))) & (~generous(X0) | ~funny(X0) | ~wise(X0) | ~generous(X0))) [flattening 32]
61. (? [X0] : (~brave(X0) | ~old(X0)) | ! [X1] : generous(X1)) & (? [X1] : ~generous(X1) | ! [X0] : (brave(X0) & old(X0))) [nnf transformation 24]
62. (? [X0] : (~brave(X0) | ~old(X0)) | ! [X1] : generous(X1)) & (? [X2] : ~generous(X2) | ! [X3] : (brave(X3) & old(X3))) [rectify 61]
63. ? [X0] : (~brave(X0) | ~old(X0)) => (~brave(sK6) | ~old(sK6)) [choice axiom]
64. ? [X2] : ~generous(X2) => ~generous(sK7) [choice axiom]
65. ((~brave(sK6) | ~old(sK6)) | ! [X1] : generous(X1)) & (~generous(sK7) | ! [X3] : (brave(X3) & old(X3))) [skolemisation 62,64,63]
90. generous(X0) | generous(X0) [cnf transformation 33]
125. ~generous(sK7) | old(X3) [cnf transformation 65]
158. ~old(paul) [cnf transformation 22]
160. generous(X0) [duplicate literal removal 90]
284. old(X3) [subsumption resolution 125,160]
358. $false [subsumption resolution 158,284]
% SZS output end Proof for 8997133636073489345750773
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave is either not strong or rich and vice versa.
If someone is either happy or generous then mary is both brave and not quiet and vice versa.
Everyone who is not strong is not wise and vice versa.
Everyone who is not quiet or not happy is both creative and not funny.
If someone is both quiet and not patient then fred is not humble.
Everyone who is both creative and tall is not kind or not happy and vice versa.
Everyone who is generous or not quiet is both not patient and wise.
If lucy is funny or not creative then someone is either not curious or not brave and vice versa.
Everyone who is either creative or rich is not funny or old and vice versa.
Everyone who is either not tall or not kind is both not strong and not patient and vice versa.
If susan is both curious and generous then someone is curious and vice versa.
Everyone who is both generous and not humble is not strong and vice versa.
Everyone who is either creative or old is both tall and humble and vice versa.
Everyone who is either strong or creative is both generous and curious.
Someone is not happy or happy.
Someone is either brave or kind.
Mary is either brave or not generous.
Susan is either not quiet or not old.
Mary is either not patient or not wise.
Someone is not funny or kind. | Mary is not kind. | contradiction | (![X]:(~brave(X)<=>(~strong(X)<~>rich(X))))&
((?[X]:((happy(X)<~>generous(X))))<=>((brave(mary)&~quiet(mary))))&
(![X]:(~strong(X)<=>~wise(X)))&
(![X]:((~quiet(X)|~happy(X))=>(creative(X)&~funny(X))))&
((?[X]:((quiet(X)&~patient(X))))=>(~humble(fred)))&
(![X]:((creative(X)&tall(X))<=>(~kind(X)|~happy(X))))&
(![X]:((generous(X)|~quiet(X))=>(~patient(X)&wise(X))))&
(((funny(lucy)|~creative(lucy)))<=>(?[X]:((~curious(X)<~>~brave(X)))))&
(![X]:((creative(X)<~>rich(X))<=>(~funny(X)|old(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~strong(X)&~patient(X))))&
(((curious(susan)&generous(susan)))<=>(?[X]:(curious(X))))&
(![X]:((generous(X)&~humble(X))<=>~strong(X)))&
(![X]:((creative(X)<~>old(X))<=>(tall(X)&humble(X))))&
(![X]:((strong(X)<~>creative(X))=>(generous(X)&curious(X))))&
(?[X]:((~happy(X)|happy(X))))&
(?[X]:((brave(X)<~>kind(X))))&
((brave(mary)<~>~generous(mary)))&
((~quiet(susan)<~>~old(susan)))&
((~patient(mary)<~>~wise(mary)))&
(?[X]:((~funny(X)|kind(X)))) | ~kind(mary) | [
"p2",
"p5",
"p6",
"p9",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8813880837914661016691516
% SZS output start Proof for 8813880837914661016691516
3. ! [X0] : (~strong(X0) <=> ~wise(X0)) [input p2]
6. ! [X0] : ((tall(X0) & creative(X0)) <=> (~happy(X0) | ~kind(X0))) [input p5]
7. ! [X0] : ((~quiet(X0) | generous(X0)) => (wise(X0) & ~patient(X0))) [input p6]
10. ! [X0] : ((~tall(X0) <~> ~kind(X0)) <=> (~patient(X0) & ~strong(X0))) [input p9]
12. ! [X0] : ((~humble(X0) & generous(X0)) <=> ~strong(X0)) [input p11]
21. ~kind(mary) [input hypothesis]
24. ! [X0] : ((wise(X0) & ~patient(X0)) | (quiet(X0) & ~generous(X0))) [ennf transformation 7]
32. ! [X0] : ((~strong(X0) | wise(X0)) & (~wise(X0) | strong(X0))) [nnf transformation 3]
33. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & ((~happy(X0) | ~kind(X0)) | (~tall(X0) | ~creative(X0)))) [nnf transformation 6]
34. ! [X0] : (((tall(X0) & creative(X0)) | (happy(X0) & kind(X0))) & (~happy(X0) | ~kind(X0) | ~tall(X0) | ~creative(X0))) [flattening 33]
42. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | (patient(X0) | strong(X0))) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [nnf transformation 10]
43. ! [X0] : ((((kind(X0) | tall(X0)) & (~kind(X0) | ~tall(X0))) | patient(X0) | strong(X0)) & ((~patient(X0) & ~strong(X0)) | ((~tall(X0) | kind(X0)) & (~kind(X0) | tall(X0))))) [flattening 42]
49. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | (humble(X0) | ~generous(X0)))) [nnf transformation 12]
50. ! [X0] : (((~humble(X0) & generous(X0)) | strong(X0)) & (~strong(X0) | humble(X0) | ~generous(X0))) [flattening 49]
74. ~wise(X0) | strong(X0) [cnf transformation 32]
75. ~strong(X0) | wise(X0) [cnf transformation 32]
84. kind(X0) | tall(X0) [cnf transformation 34]
88. ~generous(X0) | wise(X0) [cnf transformation 24]
103. ~strong(X0) | ~tall(X0) | kind(X0) [cnf transformation 43]
112. generous(X0) | strong(X0) [cnf transformation 50]
134. ~kind(mary) [cnf transformation 21]
201. ~strong(X0) | kind(X0) [subsumption resolution 103,84]
289. strong(X0) | wise(X0) [resolution 112,88]
290. wise(X0) [subsumption resolution 289,75]
293. strong(X0) [resolution 290,74]
309. kind(X0) [resolution 201,293]
329. $false [resolution 309,134]
% SZS output end Proof for 8813880837914661016691516
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong then fred is both not generous and wise. Everyone who is either kind or brave is either not patient or not quiet and vice versa. Everyone who is either not patient or strong is calm or not calm and vice versa. If alice is both not strong and not generous then someone is both calm and rich and vice versa. Everyone who is both not funny and not curious is both patient and curious and vice versa. Everyone who is happy is either creative or strong. If someone is generous or patient then someone is curious or kind. If john is either rich or wise then alice is not wise or not humble and vice versa. If john is both not kind and wise then someone is creative and vice versa. Everyone who is either wise or not generous is both curious and kind and vice versa. Everyone who is not rich is not creative and vice versa. Everyone who is not funny or wise is both not calm and not tall and vice versa. If susan is not creative or patient then someone is both not rich and not quiet. Everyone who is both not creative and not funny is both not quiet and not kind. Everyone who is not kind or not tall is both brave and not strong and vice versa. Everyone who is both quiet and not quiet is either creative or tall. Someone is both humble and wise. Alice is either happy or creative. Susan is not kind. Someone is humble. Lucy is humble or not wise. Someone is both quiet and happy. Someone is tall. Someone is not generous or not calm. | Alice is not happy. | neutral | ((?[X]:(strong(X)))=>((~generous(fred)&wise(fred))))&
(![X]:((kind(X)<~>brave(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:((~patient(X)<~>strong(X))<=>(calm(X)|~calm(X))))&
(((~strong(alice)&~generous(alice)))<=>(?[X]:((calm(X)&rich(X)))))&
(![X]:((~funny(X)&~curious(X))<=>(patient(X)&curious(X))))&
(![X]:(happy(X)=>(creative(X)<~>strong(X))))&
((?[X]:((generous(X)|patient(X))))=>(?[X]:((curious(X)|kind(X)))))&
(((rich(john)<~>wise(john)))<=>((~wise(alice)|~humble(alice))))&
(((~kind(john)&wise(john)))<=>(?[X]:(creative(X))))&
(![X]:((wise(X)<~>~generous(X))<=>(curious(X)&kind(X))))&
(![X]:(~rich(X)<=>~creative(X)))&
(![X]:((~funny(X)|wise(X))<=>(~calm(X)&~tall(X))))&
(((~creative(susan)|patient(susan)))=>(?[X]:((~rich(X)&~quiet(X)))))&
(![X]:((~creative(X)&~funny(X))=>(~quiet(X)&~kind(X))))&
(![X]:((~kind(X)|~tall(X))<=>(brave(X)&~strong(X))))&
(![X]:((quiet(X)&~quiet(X))=>(creative(X)<~>tall(X))))&
(?[X]:((humble(X)&wise(X))))&
((happy(alice)<~>creative(alice)))&
(~kind(susan))&
(?[X]:(humble(X)))&
((humble(lucy)|~wise(lucy)))&
(?[X]:((quiet(X)&happy(X))))&
(?[X]:(tall(X)))&
(?[X]:((~generous(X)|~calm(X)))) | ~happy(alice) | [] | null | 0 |
Everyone who is humble is either not curious or not quiet and vice versa.
Everyone who is not calm is not quiet or tall and vice versa.
Everyone who is humble is both creative and kind and vice versa.
If someone is not happy then susan is either brave or rich and vice versa.
Everyone who is calm or not humble is not happy or not curious and vice versa.
Everyone who is not old or not quiet is not brave and vice versa.
Everyone who is old is patient and vice versa.
Everyone who is not humble is brave and vice versa.
If someone is either not calm or happy then someone is not old or not wise.
Everyone who is not kind is not humble and vice versa.
If someone is both not brave and not old then someone is both not tall and not generous and vice versa.
Everyone who is both not curious and tall is not quiet or not patient and vice versa.
If someone is curious or not quiet then alice is both old and not calm.
Everyone who is both patient and not wise is either not old or curious and vice versa.
If john is not generous or tall then susan is not kind.
Everyone who is both tall and wise is either not quiet or not calm.
Someone is not happy or not humble.
Paul is rich or not strong.
Someone is strong.
Lucy is not wise.
Someone is not generous.
Someone is either quiet or not generous. | John is not quiet. | contradiction | (![X]:(humble(X)<=>(~curious(X)<~>~quiet(X))))&
(![X]:(~calm(X)<=>(~quiet(X)|tall(X))))&
(![X]:(humble(X)<=>(creative(X)&kind(X))))&
((?[X]:(~happy(X)))<=>((brave(susan)<~>rich(susan))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~old(X)|~quiet(X))<=>~brave(X)))&
(![X]:(old(X)<=>patient(X)))&
(![X]:(~humble(X)<=>brave(X)))&
((?[X]:((~calm(X)<~>happy(X))))=>(?[X]:((~old(X)|~wise(X)))))&
(![X]:(~kind(X)<=>~humble(X)))&
((?[X]:((~brave(X)&~old(X))))<=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((~curious(X)&tall(X))<=>(~quiet(X)|~patient(X))))&
((?[X]:((curious(X)|~quiet(X))))=>((old(alice)&~calm(alice))))&
(![X]:((patient(X)&~wise(X))<=>(~old(X)<~>curious(X))))&
(((~generous(john)|tall(john)))=>(~kind(susan)))&
(![X]:((tall(X)&wise(X))=>(~quiet(X)<~>~calm(X))))&
(?[X]:((~happy(X)|~humble(X))))&
((rich(paul)|~strong(paul)))&
(?[X]:(strong(X)))&
(~wise(lucy))&
(?[X]:(~generous(X)))&
(?[X]:((quiet(X)<~>~generous(X)))) | ~quiet(john) | [
"p1",
"p6",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4208119050670774034520705
% SZS output start Proof for 4208119050670774034520705
2. ! [X0] : (~calm(X0) <=> (tall(X0) | ~quiet(X0))) [input p1]
7. ! [X0] : (old(X0) <=> patient(X0)) [input p6]
12. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~patient(X0) | ~quiet(X0))) [input p11]
14. ! [X0] : ((~wise(X0) & patient(X0)) <=> (~old(X0) <~> curious(X0))) [input p13]
16. ! [X0] : ((wise(X0) & tall(X0)) => (~quiet(X0) <~> ~calm(X0))) [input p15]
23. ~quiet(john) [input hypothesis]
29. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | (~wise(X0) | ~tall(X0))) [ennf transformation 16]
30. ! [X0] : ((~quiet(X0) <~> ~calm(X0)) | ~wise(X0) | ~tall(X0)) [flattening 29]
32. ! [X0] : ((~calm(X0) | (~tall(X0) & quiet(X0))) & ((tall(X0) | ~quiet(X0)) | calm(X0))) [nnf transformation 2]
33. ! [X0] : ((~calm(X0) | (~tall(X0) & quiet(X0))) & (tall(X0) | ~quiet(X0) | calm(X0))) [flattening 32]
44. ! [X0] : ((old(X0) | ~patient(X0)) & (patient(X0) | ~old(X0))) [nnf transformation 7]
56. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & ((~patient(X0) | ~quiet(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 12]
57. ! [X0] : (((tall(X0) & ~curious(X0)) | (patient(X0) & quiet(X0))) & (~patient(X0) | ~quiet(X0) | ~tall(X0) | curious(X0))) [flattening 56]
58. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | (wise(X0) | ~patient(X0)))) [nnf transformation 14]
59. ! [X0] : (((~wise(X0) & patient(X0)) | ((~old(X0) | ~curious(X0)) & (curious(X0) | old(X0)))) & (((~curious(X0) | old(X0)) & (curious(X0) | ~old(X0))) | wise(X0) | ~patient(X0))) [flattening 58]
60. ! [X0] : (((calm(X0) | quiet(X0)) & (~calm(X0) | ~quiet(X0))) | ~wise(X0) | ~tall(X0)) [nnf transformation 30]
76. ~tall(X0) | ~calm(X0) [cnf transformation 33]
91. ~old(X0) | patient(X0) [cnf transformation 44]
92. ~patient(X0) | old(X0) [cnf transformation 44]
104. ~curious(X0) | quiet(X0) [cnf transformation 57]
105. ~curious(X0) | patient(X0) [cnf transformation 57]
106. tall(X0) | quiet(X0) [cnf transformation 57]
112. curious(X0) | ~old(X0) | wise(X0) | ~patient(X0) [cnf transformation 59]
114. patient(X0) | curious(X0) | old(X0) [cnf transformation 59]
121. calm(X0) | quiet(X0) | ~wise(X0) | ~tall(X0) [cnf transformation 60]
129. ~quiet(john) [cnf transformation 23]
180. 12 <=> ! [X3] : old(X3) [avatar definition]
181. old(X3) <- (12) [avatar component clause 180]
194. 15 <=> ! [X0] : quiet(X0) [avatar definition]
195. quiet(X0) <- (15) [avatar component clause 194]
211. patient(X0) | curious(X0) [subsumption resolution 114,91]
212. patient(X0) [subsumption resolution 211,105]
213. ~old(X0) | curious(X0) | wise(X0) [subsumption resolution 112,212]
228. quiet(X0) | ~wise(X0) | ~tall(X0) [subsumption resolution 121,76]
229. ~wise(X0) | quiet(X0) [subsumption resolution 228,106]
258. $false <- (15) [resolution 195,129]
259. ~15 [avatar contradiction clause 258]
264. old(X0) [resolution 92,212]
265. 12 [avatar split clause 264,180]
398. wise(X0) | curious(X0) <- (12) [resolution 213,181]
460. curious(X2) | quiet(X2) <- (12) [resolution 398,229]
465. quiet(X2) <- (12) [subsumption resolution 460,104]
466. 15 | ~12 [avatar split clause 465,180,194]
467. $false [avatar sat refutation 259,265,466]
% SZS output end Proof for 4208119050670774034520705
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is creative or not strong then someone is wise. Everyone who is not humble is not strong. Everyone who is either funny or kind is both not brave and tall. Everyone who is patient is either not funny or not tall and vice versa. Everyone who is patient is both not kind and humble and vice versa. Everyone who is tall or not rich is strong. If someone is not patient then someone is either creative or not generous. Everyone who is not generous is not wise. Everyone who is both not rich and tall is not generous. Everyone who is either not funny or rich is patient. Everyone who is both kind and not generous is either not calm or rich and vice versa. Everyone who is not generous is patient and vice versa. Everyone who is creative is either rich or not quiet and vice versa. If someone is kind or not happy then someone is both not generous and not humble and vice versa. Everyone who is either generous or strong is both not wise and not brave and vice versa. Everyone who is both curious and not wise is not generous and vice versa. Someone is quiet or generous. Someone is not happy or not quiet. Alice is humble or funny. Someone is not wise or quiet. | Alice is patient. | entailment | ((?[X]:((creative(X)|~strong(X))))=>(?[X]:(wise(X))))&
(![X]:(~humble(X)=>~strong(X)))&
(![X]:((funny(X)<~>kind(X))=>(~brave(X)&tall(X))))&
(![X]:(patient(X)<=>(~funny(X)<~>~tall(X))))&
(![X]:(patient(X)<=>(~kind(X)&humble(X))))&
(![X]:((tall(X)|~rich(X))=>strong(X)))&
((?[X]:(~patient(X)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:(~generous(X)=>~wise(X)))&
(![X]:((~rich(X)&tall(X))=>~generous(X)))&
(![X]:((~funny(X)<~>rich(X))=>patient(X)))&
(![X]:((kind(X)&~generous(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~generous(X)<=>patient(X)))&
(![X]:(creative(X)<=>(rich(X)<~>~quiet(X))))&
((?[X]:((kind(X)|~happy(X))))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((generous(X)<~>strong(X))<=>(~wise(X)&~brave(X))))&
(![X]:((curious(X)&~wise(X))<=>~generous(X)))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~happy(X)|~quiet(X))))&
((humble(alice)|funny(alice)))&
(?[X]:((~wise(X)|quiet(X)))) | patient(alice) | [
"p0",
"p1",
"p4",
"p7",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4098060262706366478799423
% SZS output start Proof for 4098060262706366478799423
1. ? [X0] : (~strong(X0) | creative(X0)) => ? [X0] : wise(X0) [input p0]
2. ! [X0] : (~humble(X0) => ~strong(X0)) [input p1]
5. ! [X0] : (patient(X0) <=> (humble(X0) & ~kind(X0))) [input p4]
8. ! [X0] : (~generous(X0) => ~wise(X0)) [input p7]
12. ! [X0] : (~generous(X0) <=> patient(X0)) [input p11]
14. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X0] : (~humble(X0) & ~generous(X0)) [input p13]
15. ! [X0] : ((generous(X0) <~> strong(X0)) <=> (~brave(X0) & ~wise(X0))) [input p14]
21. ~patient(alice) [input hypothesis]
22. ? [X0] : (~strong(X0) | creative(X0)) => ? [X1] : wise(X1) [rectify 1]
24. ? [X0] : (~happy(X0) | kind(X0)) <=> ? [X1] : (~humble(X1) & ~generous(X1)) [rectify 14]
25. ? [X1] : wise(X1) | ! [X0] : (strong(X0) & ~creative(X0)) [ennf transformation 22]
26. ! [X0] : (~strong(X0) | humble(X0)) [ennf transformation 2]
30. ! [X0] : (~wise(X0) | generous(X0)) [ennf transformation 8]
34. ? [X0] : wise(X0) | ! [X1] : (strong(X1) & ~creative(X1)) [rectify 25]
35. ? [X0] : wise(X0) => wise(sK0) [choice axiom]
36. wise(sK0) | ! [X1] : (strong(X1) & ~creative(X1)) [skolemisation 34,35]
39. ! [X0] : ((patient(X0) | (~humble(X0) | kind(X0))) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [nnf transformation 5]
40. ! [X0] : ((patient(X0) | ~humble(X0) | kind(X0)) & ((humble(X0) & ~kind(X0)) | ~patient(X0))) [flattening 39]
48. ! [X0] : ((~generous(X0) | ~patient(X0)) & (patient(X0) | generous(X0))) [nnf transformation 12]
50. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X1] : (~humble(X1) & ~generous(X1)) | ! [X0] : (happy(X0) & ~kind(X0))) [nnf transformation 24]
51. (? [X0] : (~happy(X0) | kind(X0)) | ! [X1] : (humble(X1) | generous(X1))) & (? [X2] : (~humble(X2) & ~generous(X2)) | ! [X3] : (happy(X3) & ~kind(X3))) [rectify 50]
52. ? [X0] : (~happy(X0) | kind(X0)) => (~happy(sK2) | kind(sK2)) [choice axiom]
53. ? [X2] : (~humble(X2) & ~generous(X2)) => (~humble(sK3) & ~generous(sK3)) [choice axiom]
54. ((~happy(sK2) | kind(sK2)) | ! [X1] : (humble(X1) | generous(X1))) & ((~humble(sK3) & ~generous(sK3)) | ! [X3] : (happy(X3) & ~kind(X3))) [skolemisation 51,53,52]
55. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | (brave(X0) | wise(X0))) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [nnf transformation 15]
56. ! [X0] : ((((~strong(X0) | ~generous(X0)) & (strong(X0) | generous(X0))) | brave(X0) | wise(X0)) & ((~brave(X0) & ~wise(X0)) | ((generous(X0) | ~strong(X0)) & (strong(X0) | ~generous(X0))))) [flattening 55]
66. wise(sK0) | strong(X1) [cnf transformation 36]
67. ~strong(X0) | humble(X0) [cnf transformation 26]
77. ~patient(X0) | humble(X0) [cnf transformation 40]
78. ~humble(X0) | patient(X0) | kind(X0) [cnf transformation 40]
83. ~wise(X0) | generous(X0) [cnf transformation 30]
93. generous(X0) | patient(X0) [cnf transformation 48]
94. ~generous(X0) | ~patient(X0) [cnf transformation 48]
99. ~generous(sK3) | ~kind(X3) [cnf transformation 54]
101. ~humble(sK3) | ~kind(X3) [cnf transformation 54]
104. ~wise(X0) | strong(X0) | ~generous(X0) [cnf transformation 56]
117. ~patient(alice) [cnf transformation 21]
119. 1 <=> ! [X1] : strong(X1) [avatar definition]
120. strong(X1) <- (1) [avatar component clause 119]
122. 2 <=> wise(sK0) [avatar definition]
124. wise(sK0) <- (2) [avatar component clause 122]
125. 1 | 2 [avatar split clause 66,122,119]
131. 4 <=> ! [X1] : patient(X1) [avatar definition]
132. patient(X1) <- (4) [avatar component clause 131]
159. 11 <=> humble(sK3) [avatar definition]
164. 12 <=> ! [X3] : ~kind(X3) [avatar definition]
165. ~kind(X3) <- (12) [avatar component clause 164]
166. 12 | ~11 [avatar split clause 101,159,164]
168. 13 <=> generous(sK3) [avatar definition]
170. ~generous(sK3) <- (~13) [avatar component clause 168]
172. 12 | ~13 [avatar split clause 99,168,164]
174. ~wise(X0) | strong(X0) [subsumption resolution 104,83]
211. generous(sK0) <- (2) [resolution 83,124]
213. patient(sK3) <- (~13) [resolution 93,170]
215. ~patient(sK0) <- (2) [resolution 94,211]
218. humble(sK3) <- (~13) [resolution 213,77]
222. 11 | 13 [avatar split clause 218,168,159]
228. strong(sK0) <- (2) [resolution 174,124]
229. humble(sK0) <- (2) [resolution 228,67]
256. $false <- (4) [resolution 132,117]
263. ~4 [avatar contradiction clause 256]
267. patient(sK0) | kind(sK0) <- (2) [resolution 78,229]
272. kind(sK0) <- (2) [subsumption resolution 267,215]
273. $false <- (2, 12) [subsumption resolution 272,165]
274. ~2 | ~12 [avatar contradiction clause 273]
279. humble(X0) <- (1) [resolution 120,67]
295. patient(X0) | kind(X0) <- (1) [resolution 279,78]
298. patient(X0) <- (1, 12) [subsumption resolution 295,165]
299. 4 | ~1 | ~12 [avatar split clause 298,164,119,131]
300. $false [avatar sat refutation 125,166,172,222,263,274,299]
% SZS output end Proof for 4098060262706366478799423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not happy and old is strong.
If mary is either tall or calm then someone is either strong or happy.
Everyone who is humble is either wise or rich and vice versa.
If someone is calm or creative then alice is not generous or strong and vice versa.
If lucy is funny then alice is both humble and happy and vice versa.
Everyone who is not tall is calm and vice versa.
If alice is both creative and not generous then someone is both funny and kind and vice versa.
Everyone who is not strong or patient is curious or not happy and vice versa.
Everyone who is both not brave and humble is not quiet.
If lucy is either not rich or old then someone is generous.
Everyone who is not brave or not calm is both not humble and curious and vice versa.
If someone is both tall and curious then fred is both strong and not happy and vice versa.
Everyone who is both calm and not patient is happy or rich and vice versa.
If mary is not humble or humble then lucy is either rich or kind.
If lucy is both patient and old then mary is tall or not rich and vice versa.
Everyone who is both old and generous is kind.
Someone is not funny or strong.
Alice is old or not kind.
Susan is wise.
Paul is not tall or humble.
Susan is not brave.
Mary is both not generous and not brave.
Lucy is patient.
Someone is kind. | Susan is not tall. | entailment | (![X]:((~happy(X)&old(X))=>strong(X)))&
(((tall(mary)<~>calm(mary)))=>(?[X]:((strong(X)<~>happy(X)))))&
(![X]:(humble(X)<=>(wise(X)<~>rich(X))))&
((?[X]:((calm(X)|creative(X))))<=>((~generous(alice)|strong(alice))))&
((funny(lucy))<=>((humble(alice)&happy(alice))))&
(![X]:(~tall(X)<=>calm(X)))&
(((creative(alice)&~generous(alice)))<=>(?[X]:((funny(X)&kind(X)))))&
(![X]:((~strong(X)|patient(X))<=>(curious(X)|~happy(X))))&
(![X]:((~brave(X)&humble(X))=>~quiet(X)))&
(((~rich(lucy)<~>old(lucy)))=>(?[X]:(generous(X))))&
(![X]:((~brave(X)|~calm(X))<=>(~humble(X)&curious(X))))&
((?[X]:((tall(X)&curious(X))))<=>((strong(fred)&~happy(fred))))&
(![X]:((calm(X)&~patient(X))<=>(happy(X)|rich(X))))&
(((~humble(mary)|humble(mary)))=>((rich(lucy)<~>kind(lucy))))&
(((patient(lucy)&old(lucy)))<=>((tall(mary)|~rich(mary))))&
(![X]:((old(X)&generous(X))=>kind(X)))&
(?[X]:((~funny(X)|strong(X))))&
((old(alice)|~kind(alice)))&
(wise(susan))&
((~tall(paul)|humble(paul)))&
(~brave(susan))&
((~generous(mary)&~brave(mary)))&
(patient(lucy))&
(?[X]:(kind(X))) | ~tall(susan) | [
"p2",
"p5",
"p10",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 8466361812236253379136692
% SZS output start Proof for 8466361812236253379136692
3. ! [X0] : (humble(X0) <=> (wise(X0) <~> rich(X0))) [input p2]
6. ! [X0] : (~tall(X0) <=> calm(X0)) [input p5]
11. ! [X0] : ((~calm(X0) | ~brave(X0)) <=> (curious(X0) & ~humble(X0))) [input p10]
13. ! [X0] : ((~patient(X0) & calm(X0)) <=> (rich(X0) | happy(X0))) [input p12]
19. wise(susan) [input p18]
21. ~brave(susan) [input p20]
25. tall(susan) [input hypothesis]
37. ! [X0] : ((humble(X0) | ((wise(X0) | ~rich(X0)) & (rich(X0) | ~wise(X0)))) & (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ~humble(X0))) [nnf transformation 3]
45. ! [X0] : ((~tall(X0) | ~calm(X0)) & (calm(X0) | tall(X0))) [nnf transformation 6]
56. ! [X0] : (((~calm(X0) | ~brave(X0)) | (~curious(X0) | humble(X0))) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [nnf transformation 11]
57. ! [X0] : ((~calm(X0) | ~brave(X0) | ~curious(X0) | humble(X0)) & ((curious(X0) & ~humble(X0)) | (calm(X0) & brave(X0)))) [flattening 56]
63. ! [X0] : (((~patient(X0) & calm(X0)) | (~rich(X0) & ~happy(X0))) & ((rich(X0) | happy(X0)) | (patient(X0) | ~calm(X0)))) [nnf transformation 13]
64. ! [X0] : (((~patient(X0) & calm(X0)) | (~rich(X0) & ~happy(X0))) & (rich(X0) | happy(X0) | patient(X0) | ~calm(X0))) [flattening 63]
79. ~wise(X0) | rich(X0) | humble(X0) [cnf transformation 37]
89. ~calm(X0) | ~tall(X0) [cnf transformation 45]
100. ~humble(X0) | brave(X0) [cnf transformation 57]
111. ~rich(X0) | calm(X0) [cnf transformation 64]
126. wise(susan) [cnf transformation 19]
128. ~brave(susan) [cnf transformation 21]
133. tall(susan) [cnf transformation 25]
323. rich(susan) | humble(susan) [resolution 79,126]
325. 36 <=> humble(susan) [avatar definition]
327. humble(susan) <- (36) [avatar component clause 325]
329. 37 <=> rich(susan) [avatar definition]
331. rich(susan) <- (37) [avatar component clause 329]
332. 36 | 37 [avatar split clause 323,329,325]
335. brave(susan) <- (36) [resolution 327,100]
336. $false <- (36) [subsumption resolution 335,128]
337. ~36 [avatar contradiction clause 336]
341. calm(susan) <- (37) [resolution 331,111]
435. ~tall(susan) <- (37) [resolution 341,89]
436. $false <- (37) [subsumption resolution 435,133]
437. ~37 [avatar contradiction clause 436]
438. $false [avatar sat refutation 332,337,437]
% SZS output end Proof for 8466361812236253379136692
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not funny is both not patient and not generous.
Everyone who is brave or curious is both not curious and not wise.
Everyone who is not brave is not wise or old.
If someone is either tall or strong then lucy is rich.
If someone is happy or kind then lucy is not wise or not curious.
Everyone who is tall or not patient is either patient or not wise and vice versa.
If susan is not rich or not calm then john is curious or not patient.
Everyone who is kind is both not kind and funny and vice versa.
If someone is either calm or not patient then someone is funny or happy.
Everyone who is both not patient and generous is not humble or not tall and vice versa.
If mary is not calm then someone is humble and vice versa.
If susan is not kind or old then paul is both not rich and creative and vice versa.
Everyone who is either not funny or not kind is either kind or not patient.
If lucy is both not calm and not old then lucy is either not strong or not quiet.
Everyone who is generous or patient is not kind or not creative.
Paul is creative or not funny.
Someone is either generous or old.
Susan is either not calm or calm.
Lucy is not strong or tall.
Susan is not creative or not quiet. | Paul is not tall. | contradiction | (![X]:((quiet(X)|~funny(X))=>(~patient(X)&~generous(X))))&
(![X]:((brave(X)|curious(X))=>(~curious(X)&~wise(X))))&
(![X]:(~brave(X)=>(~wise(X)|old(X))))&
((?[X]:((tall(X)<~>strong(X))))=>(rich(lucy)))&
((?[X]:((happy(X)|kind(X))))=>((~wise(lucy)|~curious(lucy))))&
(![X]:((tall(X)|~patient(X))<=>(patient(X)<~>~wise(X))))&
(((~rich(susan)|~calm(susan)))=>((curious(john)|~patient(john))))&
(![X]:(kind(X)<=>(~kind(X)&funny(X))))&
((?[X]:((calm(X)<~>~patient(X))))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~patient(X)&generous(X))<=>(~humble(X)|~tall(X))))&
((~calm(mary))<=>(?[X]:(humble(X))))&
(((~kind(susan)|old(susan)))<=>((~rich(paul)&creative(paul))))&
(![X]:((~funny(X)<~>~kind(X))=>(kind(X)<~>~patient(X))))&
(((~calm(lucy)&~old(lucy)))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:((generous(X)|patient(X))=>(~kind(X)|~creative(X))))&
((creative(paul)|~funny(paul)))&
(?[X]:((generous(X)<~>old(X))))&
((~calm(susan)<~>calm(susan)))&
((~strong(lucy)|tall(lucy)))&
((~creative(susan)|~quiet(susan))) | ~tall(paul) | [
"p0",
"p7",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7140657526194636911567701
% SZS output start Proof for 7140657526194636911567701
1. ! [X0] : ((~funny(X0) | quiet(X0)) => (~generous(X0) & ~patient(X0))) [input p0]
8. ! [X0] : (kind(X0) <=> (funny(X0) & ~kind(X0))) [input p7]
10. ! [X0] : ((generous(X0) & ~patient(X0)) <=> (~tall(X0) | ~humble(X0))) [input p9]
21. ~tall(paul) [input hypothesis]
23. ! [X0] : ((~generous(X0) & ~patient(X0)) | (funny(X0) & ~quiet(X0))) [ennf transformation 1]
41. ! [X0] : ((kind(X0) | (~funny(X0) | kind(X0))) & ((funny(X0) & ~kind(X0)) | ~kind(X0))) [nnf transformation 8]
42. ! [X0] : ((kind(X0) | ~funny(X0) | kind(X0)) & ((funny(X0) & ~kind(X0)) | ~kind(X0))) [flattening 41]
47. ! [X0] : (((generous(X0) & ~patient(X0)) | (tall(X0) & humble(X0))) & ((~tall(X0) | ~humble(X0)) | (~generous(X0) | patient(X0)))) [nnf transformation 10]
48. ! [X0] : (((generous(X0) & ~patient(X0)) | (tall(X0) & humble(X0))) & (~tall(X0) | ~humble(X0) | ~generous(X0) | patient(X0))) [flattening 47]
64. ~generous(X0) | funny(X0) [cnf transformation 23]
82. ~kind(X0) | ~kind(X0) [cnf transformation 42]
84. kind(X0) | ~funny(X0) | kind(X0) [cnf transformation 42]
91. tall(X0) | generous(X0) [cnf transformation 48]
114. ~tall(paul) [cnf transformation 21]
117. ~kind(X0) [duplicate literal removal 82]
118. ~funny(X0) | kind(X0) [duplicate literal removal 84]
217. 21 <=> funny(paul) [avatar definition]
218. funny(paul) <- (21) [avatar component clause 217]
248. generous(paul) [resolution 91,114]
261. funny(paul) [resolution 248,64]
263. 21 [avatar split clause 261,217]
264. kind(paul) <- (21) [resolution 218,118]
265. $false <- (21) [subsumption resolution 264,117]
266. ~21 [avatar contradiction clause 265]
267. $false [avatar sat refutation 263,266]
% SZS output end Proof for 7140657526194636911567701
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble is calm or not old.
If fred is not creative or not old then someone is strong and vice versa.
Everyone who is creative or not brave is not kind.
Everyone who is both rich and calm is either brave or rich.
If someone is both wise and rich then susan is both not creative and quiet.
Everyone who is not rich or strong is happy and vice versa.
Everyone who is either rich or not brave is either tall or humble and vice versa.
If someone is both not wise and not humble then someone is not patient or not rich and vice versa.
Everyone who is both generous and not tall is either kind or brave and vice versa.
If fred is either not generous or not happy then mary is not wise and vice versa.
If paul is both not creative and patient then someone is brave or not curious and vice versa.
If paul is strong or brave then someone is either not wise or not generous.
Everyone who is not brave or generous is either not old or not funny and vice versa.
If mary is both tall and old then paul is not kind or creative.
Everyone who is not tall or calm is both humble and kind and vice versa.
If someone is curious then someone is either not funny or not strong and vice versa.
Alice is both not curious and quiet.
Someone is either creative or not calm.
Someone is both wise and not old.
Paul is either kind or not kind.
John is both not strong and not rich.
Someone is either generous or not rich.
Someone is not patient or not rich.
Someone is humble. | Alice is curious. | contradiction | (![X]:(~humble(X)=>(calm(X)|~old(X))))&
(((~creative(fred)|~old(fred)))<=>(?[X]:(strong(X))))&
(![X]:((creative(X)|~brave(X))=>~kind(X)))&
(![X]:((rich(X)&calm(X))=>(brave(X)<~>rich(X))))&
((?[X]:((wise(X)&rich(X))))=>((~creative(susan)&quiet(susan))))&
(![X]:((~rich(X)|strong(X))<=>happy(X)))&
(![X]:((rich(X)<~>~brave(X))<=>(tall(X)<~>humble(X))))&
((?[X]:((~wise(X)&~humble(X))))<=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((generous(X)&~tall(X))<=>(kind(X)<~>brave(X))))&
(((~generous(fred)<~>~happy(fred)))<=>(~wise(mary)))&
(((~creative(paul)&patient(paul)))<=>(?[X]:((brave(X)|~curious(X)))))&
(((strong(paul)|brave(paul)))=>(?[X]:((~wise(X)<~>~generous(X)))))&
(![X]:((~brave(X)|generous(X))<=>(~old(X)<~>~funny(X))))&
(((tall(mary)&old(mary)))=>((~kind(paul)|creative(paul))))&
(![X]:((~tall(X)|calm(X))<=>(humble(X)&kind(X))))&
((?[X]:(curious(X)))<=>(?[X]:((~funny(X)<~>~strong(X)))))&
((~curious(alice)&quiet(alice)))&
(?[X]:((creative(X)<~>~calm(X))))&
(?[X]:((wise(X)&~old(X))))&
((kind(paul)<~>~kind(paul)))&
((~strong(john)&~rich(john)))&
(?[X]:((generous(X)<~>~rich(X))))&
(?[X]:((~patient(X)|~rich(X))))&
(?[X]:(humble(X))) | curious(alice) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 7523952224866685933982580
% SZS output start Proof for 7523952224866685933982580
17. quiet(alice) & ~curious(alice) [input p16]
25. curious(alice) [input hypothesis]
28. ~curious(alice) [pure predicate removal 17]
146. ~curious(alice) [cnf transformation 28]
159. curious(alice) [cnf transformation 25]
350. $false [subsumption resolution 159,146]
% SZS output end Proof for 7523952224866685933982580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy then someone is old or humble and vice versa.
Everyone who is either not funny or not tall is either quiet or funny and vice versa.
If john is both not kind and creative then someone is not patient and vice versa.
If paul is not old or rich then paul is either old or not strong and vice versa.
Everyone who is not quiet is not generous or not strong.
Everyone who is both not funny and old is either not happy or rich.
Everyone who is either not strong or curious is rich and vice versa.
Everyone who is happy or tall is not quiet and vice versa.
If someone is not curious then alice is funny or not curious.
If someone is rich then susan is happy or not rich and vice versa.
Everyone who is not generous or funny is both not funny and not wise and vice versa.
Everyone who is not tall is either calm or not old.
If mary is both happy and not patient then someone is either not rich or not generous.
Everyone who is not calm or kind is brave and vice versa.
If someone is both not generous and not patient then paul is either quiet or funny and vice versa.
If susan is kind then susan is not quiet and vice versa.
John is either strong or not rich.
Someone is either not creative or not strong.
Someone is either not strong or not old. | Alice is not wise. | neutral | ((?[X]:(~happy(X)))<=>(?[X]:((old(X)|humble(X)))))&
(![X]:((~funny(X)<~>~tall(X))<=>(quiet(X)<~>funny(X))))&
(((~kind(john)&creative(john)))<=>(?[X]:(~patient(X))))&
(((~old(paul)|rich(paul)))<=>((old(paul)<~>~strong(paul))))&
(![X]:(~quiet(X)=>(~generous(X)|~strong(X))))&
(![X]:((~funny(X)&old(X))=>(~happy(X)<~>rich(X))))&
(![X]:((~strong(X)<~>curious(X))<=>rich(X)))&
(![X]:((happy(X)|tall(X))<=>~quiet(X)))&
((?[X]:(~curious(X)))=>((funny(alice)|~curious(alice))))&
((?[X]:(rich(X)))<=>((happy(susan)|~rich(susan))))&
(![X]:((~generous(X)|funny(X))<=>(~funny(X)&~wise(X))))&
(![X]:(~tall(X)=>(calm(X)<~>~old(X))))&
(((happy(mary)&~patient(mary)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((~calm(X)|kind(X))<=>brave(X)))&
((?[X]:((~generous(X)&~patient(X))))<=>((quiet(paul)<~>funny(paul))))&
((kind(susan))<=>(~quiet(susan)))&
((strong(john)<~>~rich(john)))&
(?[X]:((~creative(X)<~>~strong(X))))&
(?[X]:((~strong(X)<~>~old(X)))) | ~wise(alice) | [] | null | 0 |
Everyone who is both not calm and generous is not wise.
If someone is tall or not quiet then someone is either calm or humble and vice versa.
If someone is either creative or not calm then someone is not quiet and vice versa.
If someone is rich or not generous then someone is either not happy or not old and vice versa.
Everyone who is not old or patient is calm or not creative and vice versa.
If someone is humble then someone is not funny or generous.
Everyone who is not calm is either not happy or quiet and vice versa.
If someone is tall or happy then fred is both quiet and not wise and vice versa.
If someone is humble then someone is both not patient and calm.
Everyone who is either humble or quiet is not tall or humble.
If someone is both happy and not rich then paul is both not quiet and funny and vice versa.
Everyone who is either not wise or not brave is either not brave or not strong and vice versa.
Everyone who is not humble is not wise or not funny.
Everyone who is not generous is both not humble and not old and vice versa.
If mary is both not generous and not old then someone is not brave and vice versa.
If john is either not old or strong then fred is both strong and quiet.
Someone is not curious.
Paul is wise or not old.
Paul is not brave or rich.
Fred is either brave or not patient.
Paul is either not funny or humble.
Someone is not humble or not rich.
Someone is not brave.
Paul is either wise or not old. | Paul is quiet. | neutral | (![X]:((~calm(X)&generous(X))=>~wise(X)))&
((?[X]:((tall(X)|~quiet(X))))<=>(?[X]:((calm(X)<~>humble(X)))))&
((?[X]:((creative(X)<~>~calm(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((rich(X)|~generous(X))))<=>(?[X]:((~happy(X)<~>~old(X)))))&
(![X]:((~old(X)|patient(X))<=>(calm(X)|~creative(X))))&
((?[X]:(humble(X)))=>(?[X]:((~funny(X)|generous(X)))))&
(![X]:(~calm(X)<=>(~happy(X)<~>quiet(X))))&
((?[X]:((tall(X)|happy(X))))<=>((quiet(fred)&~wise(fred))))&
((?[X]:(humble(X)))=>(?[X]:((~patient(X)&calm(X)))))&
(![X]:((humble(X)<~>quiet(X))=>(~tall(X)|humble(X))))&
((?[X]:((happy(X)&~rich(X))))<=>((~quiet(paul)&funny(paul))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~brave(X)<~>~strong(X))))&
(![X]:(~humble(X)=>(~wise(X)|~funny(X))))&
(![X]:(~generous(X)<=>(~humble(X)&~old(X))))&
(((~generous(mary)&~old(mary)))<=>(?[X]:(~brave(X))))&
(((~old(john)<~>strong(john)))=>((strong(fred)&quiet(fred))))&
(?[X]:(~curious(X)))&
((wise(paul)|~old(paul)))&
((~brave(paul)|rich(paul)))&
((brave(fred)<~>~patient(fred)))&
((~funny(paul)<~>humble(paul)))&
(?[X]:((~humble(X)|~rich(X))))&
(?[X]:(~brave(X)))&
((wise(paul)<~>~old(paul))) | quiet(paul) | [] | null | 0 |
Everyone who is patient is old or not quiet. If someone is both not calm and not funny then someone is not strong or patient. If someone is not curious then fred is not curious or not generous and vice versa. If someone is creative or generous then susan is either brave or not generous and vice versa. If susan is tall or rich then someone is creative or kind. Everyone who is funny is not humble and vice versa. If alice is both generous and not old then someone is either funny or happy and vice versa. Everyone who is both funny and curious is not quiet or not brave and vice versa. Everyone who is either not calm or quiet is both not quiet and funny and vice versa. If mary is either happy or humble then john is happy and vice versa. Everyone who is both not tall and tall is not calm. If susan is brave or not wise then fred is not wise or not funny and vice versa. If someone is both patient and not humble then someone is either not quiet or kind. Everyone who is both rich and creative is both curious and not old and vice versa. If susan is not quiet or calm then someone is both old and tall and vice versa. If someone is either not generous or strong then alice is calm. Someone is either happy or not brave. Someone is quiet. Lucy is not funny or tall. Someone is wise or not funny. Paul is either not wise or quiet. Susan is not humble. Susan is kind or not humble. | Alice is calm. | contradiction | (![X]:(patient(X)=>(old(X)|~quiet(X))))&
((?[X]:((~calm(X)&~funny(X))))=>(?[X]:((~strong(X)|patient(X)))))&
((?[X]:(~curious(X)))<=>((~curious(fred)|~generous(fred))))&
((?[X]:((creative(X)|generous(X))))<=>((brave(susan)<~>~generous(susan))))&
(((tall(susan)|rich(susan)))=>(?[X]:((creative(X)|kind(X)))))&
(![X]:(funny(X)<=>~humble(X)))&
(((generous(alice)&~old(alice)))<=>(?[X]:((funny(X)<~>happy(X)))))&
(![X]:((funny(X)&curious(X))<=>(~quiet(X)|~brave(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~quiet(X)&funny(X))))&
(((happy(mary)<~>humble(mary)))<=>(happy(john)))&
(![X]:((~tall(X)&tall(X))=>~calm(X)))&
(((brave(susan)|~wise(susan)))<=>((~wise(fred)|~funny(fred))))&
((?[X]:((patient(X)&~humble(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~generous(X)<~>strong(X))))=>(calm(alice)))&
(?[X]:((happy(X)<~>~brave(X))))&
(?[X]:(quiet(X)))&
((~funny(lucy)|tall(lucy)))&
(?[X]:((wise(X)|~funny(X))))&
((~wise(paul)<~>quiet(paul)))&
(~humble(susan))&
((kind(susan)|~humble(susan))) | calm(alice) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6853943453481878087626062
% SZS output start Proof for 6853943453481878087626062
8. ! [X0] : ((curious(X0) & funny(X0)) <=> (~brave(X0) | ~quiet(X0))) [input p7]
9. ! [X0] : ((~calm(X0) <~> quiet(X0)) <=> (funny(X0) & ~quiet(X0))) [input p8]
24. calm(alice) [input hypothesis]
55. ! [X0] : (((curious(X0) & funny(X0)) | (brave(X0) & quiet(X0))) & ((~brave(X0) | ~quiet(X0)) | (~curious(X0) | ~funny(X0)))) [nnf transformation 8]
56. ! [X0] : (((curious(X0) & funny(X0)) | (brave(X0) & quiet(X0))) & (~brave(X0) | ~quiet(X0) | ~curious(X0) | ~funny(X0))) [flattening 55]
57. ! [X0] : ((((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | (~funny(X0) | quiet(X0))) & ((funny(X0) & ~quiet(X0)) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))))) [nnf transformation 9]
58. ! [X0] : ((((~quiet(X0) | calm(X0)) & (quiet(X0) | ~calm(X0))) | ~funny(X0) | quiet(X0)) & ((funny(X0) & ~quiet(X0)) | ((~calm(X0) | ~quiet(X0)) & (quiet(X0) | calm(X0))))) [flattening 57]
104. funny(X0) | quiet(X0) [cnf transformation 56]
109. ~quiet(X0) | ~calm(X0) | ~quiet(X0) [cnf transformation 58]
112. quiet(X0) | ~calm(X0) | ~funny(X0) | quiet(X0) [cnf transformation 58]
145. calm(alice) [cnf transformation 24]
146. ~quiet(X0) | ~calm(X0) [duplicate literal removal 109]
147. quiet(X0) | ~calm(X0) | ~funny(X0) [duplicate literal removal 112]
252. quiet(X0) | ~calm(X0) [subsumption resolution 147,104]
254. ~calm(X0) [subsumption resolution 146,252]
359. $false [subsumption resolution 145,254]
% SZS output end Proof for 6853943453481878087626062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not old then lucy is both not brave and not quiet.
If mary is strong or not calm then someone is not generous or not patient.
Everyone who is either not old or quiet is both not happy and not rich.
If someone is brave then someone is either happy or not wise and vice versa.
Everyone who is not creative or creative is both not quiet and tall.
If someone is either kind or patient then someone is not funny.
If paul is both rich and not happy then fred is not quiet.
If alice is not funny or old then someone is either not quiet or not curious.
If someone is not generous then someone is either happy or not curious.
If lucy is both not curious and not generous then fred is brave and vice versa.
Everyone who is both old and not generous is not tall or not curious and vice versa.
Everyone who is either patient or tall is not creative and vice versa.
Everyone who is both not strong and not calm is either not patient or not curious.
If someone is either not humble or creative then lucy is either generous or wise.
Everyone who is happy is both quiet and not tall and vice versa.
Everyone who is either wise or humble is either creative or humble and vice versa.
Susan is either old or creative.
Someone is both not generous and wise.
Paul is either not quiet or happy.
Susan is both strong and humble.
Susan is either curious or quiet.
Paul is old. | Mary is quiet. | contradiction | ((?[X]:(~old(X)))=>((~brave(lucy)&~quiet(lucy))))&
(((strong(mary)|~calm(mary)))=>(?[X]:((~generous(X)|~patient(X)))))&
(![X]:((~old(X)<~>quiet(X))=>(~happy(X)&~rich(X))))&
((?[X]:(brave(X)))<=>(?[X]:((happy(X)<~>~wise(X)))))&
(![X]:((~creative(X)|creative(X))=>(~quiet(X)&tall(X))))&
((?[X]:((kind(X)<~>patient(X))))=>(?[X]:(~funny(X))))&
(((rich(paul)&~happy(paul)))=>(~quiet(fred)))&
(((~funny(alice)|old(alice)))=>(?[X]:((~quiet(X)<~>~curious(X)))))&
((?[X]:(~generous(X)))=>(?[X]:((happy(X)<~>~curious(X)))))&
(((~curious(lucy)&~generous(lucy)))<=>(brave(fred)))&
(![X]:((old(X)&~generous(X))<=>(~tall(X)|~curious(X))))&
(![X]:((patient(X)<~>tall(X))<=>~creative(X)))&
(![X]:((~strong(X)&~calm(X))=>(~patient(X)<~>~curious(X))))&
((?[X]:((~humble(X)<~>creative(X))))=>((generous(lucy)<~>wise(lucy))))&
(![X]:(happy(X)<=>(quiet(X)&~tall(X))))&
(![X]:((wise(X)<~>humble(X))<=>(creative(X)<~>humble(X))))&
((old(susan)<~>creative(susan)))&
(?[X]:((~generous(X)&wise(X))))&
((~quiet(paul)<~>happy(paul)))&
((strong(susan)&humble(susan)))&
((curious(susan)<~>quiet(susan)))&
(old(paul)) | quiet(mary) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3789601767101702141679388
% SZS output start Proof for 3789601767101702141679388
5. ! [X0] : ((creative(X0) | ~creative(X0)) => (tall(X0) & ~quiet(X0))) [input p4]
23. quiet(mary) [input hypothesis]
34. ! [X0] : ((tall(X0) & ~quiet(X0)) | (~creative(X0) & creative(X0))) [ennf transformation 5]
81. ~quiet(X0) | creative(X0) [cnf transformation 34]
82. ~quiet(X0) | ~creative(X0) [cnf transformation 34]
131. quiet(mary) [cnf transformation 23]
188. ~quiet(X0) [subsumption resolution 81,82]
276. $false [subsumption resolution 131,188]
% SZS output end Proof for 3789601767101702141679388
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble then lucy is not funny or quiet and vice versa.
If someone is tall or not old then paul is quiet.
Everyone who is either tall or brave is either not strong or not creative and vice versa.
Everyone who is quiet or kind is either not generous or not patient and vice versa.
If mary is not quiet or happy then someone is either brave or curious.
Everyone who is not funny or not kind is either calm or not old and vice versa.
Everyone who is either creative or not calm is either not strong or patient and vice versa.
Everyone who is both not brave and strong is brave or generous and vice versa.
If alice is either not happy or not wise then someone is quiet or strong.
If someone is patient or not generous then someone is generous.
Everyone who is either strong or kind is calm and vice versa.
Everyone who is both funny and not tall is both happy and quiet.
Everyone who is not quiet is both not brave and not happy and vice versa.
Everyone who is patient or not kind is tall or not calm and vice versa.
If someone is tall or curious then someone is not brave or not rich.
If someone is both not brave and not calm then someone is either not patient or not old.
Someone is either not patient or old.
Mary is not humble or generous.
Lucy is both quiet and not creative.
Someone is funny or not funny.
Alice is not creative or creative.
Lucy is old.
Someone is rich.
Paul is either humble or not curious. | Lucy is patient. | contradiction | ((?[X]:(humble(X)))<=>((~funny(lucy)|quiet(lucy))))&
((?[X]:((tall(X)|~old(X))))=>(quiet(paul)))&
(![X]:((tall(X)<~>brave(X))<=>(~strong(X)<~>~creative(X))))&
(![X]:((quiet(X)|kind(X))<=>(~generous(X)<~>~patient(X))))&
(((~quiet(mary)|happy(mary)))=>(?[X]:((brave(X)<~>curious(X)))))&
(![X]:((~funny(X)|~kind(X))<=>(calm(X)<~>~old(X))))&
(![X]:((creative(X)<~>~calm(X))<=>(~strong(X)<~>patient(X))))&
(![X]:((~brave(X)&strong(X))<=>(brave(X)|generous(X))))&
(((~happy(alice)<~>~wise(alice)))=>(?[X]:((quiet(X)|strong(X)))))&
((?[X]:((patient(X)|~generous(X))))=>(?[X]:(generous(X))))&
(![X]:((strong(X)<~>kind(X))<=>calm(X)))&
(![X]:((funny(X)&~tall(X))=>(happy(X)&quiet(X))))&
(![X]:(~quiet(X)<=>(~brave(X)&~happy(X))))&
(![X]:((patient(X)|~kind(X))<=>(tall(X)|~calm(X))))&
((?[X]:((tall(X)|curious(X))))=>(?[X]:((~brave(X)|~rich(X)))))&
((?[X]:((~brave(X)&~calm(X))))=>(?[X]:((~patient(X)<~>~old(X)))))&
(?[X]:((~patient(X)<~>old(X))))&
((~humble(mary)|generous(mary)))&
((quiet(lucy)&~creative(lucy)))&
(?[X]:((funny(X)|~funny(X))))&
((~creative(alice)|creative(alice)))&
(old(lucy))&
(?[X]:(rich(X)))&
((humble(paul)<~>~curious(paul))) | patient(lucy) | [
"p2",
"p3",
"p6",
"p7",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 6940882103327846121674762
% SZS output start Proof for 6940882103327846121674762
3. ! [X0] : ((tall(X0) <~> brave(X0)) <=> (~strong(X0) <~> ~creative(X0))) [input p2]
4. ! [X0] : ((kind(X0) | quiet(X0)) <=> (~generous(X0) <~> ~patient(X0))) [input p3]
7. ! [X0] : ((creative(X0) <~> ~calm(X0)) <=> (~strong(X0) <~> patient(X0))) [input p6]
8. ! [X0] : ((strong(X0) & ~brave(X0)) <=> (generous(X0) | brave(X0))) [input p7]
14. ! [X0] : ((~kind(X0) | patient(X0)) <=> (~calm(X0) | tall(X0))) [input p13]
19. ~creative(lucy) & quiet(lucy) [input p18]
25. patient(lucy) [input hypothesis]
42. ! [X0] : ((((~brave(X0) | ~tall(X0)) & (brave(X0) | tall(X0))) | ((~strong(X0) | creative(X0)) & (~creative(X0) | strong(X0)))) & (((creative(X0) | strong(X0)) & (~creative(X0) | ~strong(X0))) | ((tall(X0) | ~brave(X0)) & (brave(X0) | ~tall(X0))))) [nnf transformation 3]
43. ! [X0] : (((kind(X0) | quiet(X0)) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (~kind(X0) & ~quiet(X0)))) [nnf transformation 4]
44. ! [X0] : ((kind(X0) | quiet(X0) | ((~generous(X0) | patient(X0)) & (~patient(X0) | generous(X0)))) & (((patient(X0) | generous(X0)) & (~patient(X0) | ~generous(X0))) | (~kind(X0) & ~quiet(X0)))) [flattening 43]
50. ! [X0] : ((((calm(X0) | ~creative(X0)) & (~calm(X0) | creative(X0))) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0)))) & (((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ((creative(X0) | calm(X0)) & (~calm(X0) | ~creative(X0))))) [nnf transformation 7]
51. ! [X0] : (((strong(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & ((generous(X0) | brave(X0)) | (~strong(X0) | brave(X0)))) [nnf transformation 8]
52. ! [X0] : (((strong(X0) & ~brave(X0)) | (~generous(X0) & ~brave(X0))) & (generous(X0) | brave(X0) | ~strong(X0) | brave(X0))) [flattening 51]
62. ! [X0] : (((~kind(X0) | patient(X0)) | (calm(X0) & ~tall(X0))) & ((~calm(X0) | tall(X0)) | (kind(X0) & ~patient(X0)))) [nnf transformation 14]
63. ! [X0] : ((~kind(X0) | patient(X0) | (calm(X0) & ~tall(X0))) & (~calm(X0) | tall(X0) | (kind(X0) & ~patient(X0)))) [flattening 62]
86. ~tall(X0) | strong(X0) | brave(X0) | creative(X0) [cnf transformation 42]
92. ~patient(X0) | ~generous(X0) | ~quiet(X0) [cnf transformation 44]
111. ~patient(X0) | strong(X0) | creative(X0) | calm(X0) [cnf transformation 50]
116. generous(X0) | brave(X0) | ~strong(X0) | brave(X0) [cnf transformation 52]
117. ~brave(X0) | ~brave(X0) [cnf transformation 52]
134. ~calm(X0) | tall(X0) | ~patient(X0) [cnf transformation 63]
145. quiet(lucy) [cnf transformation 19]
146. ~creative(lucy) [cnf transformation 19]
153. patient(lucy) [cnf transformation 25]
154. generous(X0) | brave(X0) | ~strong(X0) [duplicate literal removal 116]
155. ~brave(X0) [duplicate literal removal 117]
157. 1 <=> quiet(lucy) [avatar definition]
158. quiet(lucy) <- (1) [avatar component clause 157]
206. ~strong(X0) | generous(X0) [subsumption resolution 154,155]
272. 1 [avatar split clause 145,157]
291. ~generous(lucy) | ~quiet(lucy) [resolution 92,153]
292. ~generous(lucy) <- (1) [subsumption resolution 291,158]
440. 38 <=> calm(lucy) [avatar definition]
441. ~calm(lucy) <- (~38) [avatar component clause 440]
442. calm(lucy) <- (38) [avatar component clause 440]
497. tall(lucy) | ~patient(lucy) <- (38) [resolution 442,134]
518. 49 <=> strong(lucy) [avatar definition]
520. strong(lucy) <- (49) [avatar component clause 518]
523. tall(lucy) <- (38) [subsumption resolution 497,153]
547. strong(lucy) | creative(lucy) | calm(lucy) [resolution 111,153]
627. strong(lucy) | brave(lucy) | creative(lucy) <- (38) [resolution 523,86]
632. strong(lucy) | creative(lucy) <- (38) [subsumption resolution 627,155]
633. strong(lucy) <- (38) [subsumption resolution 632,146]
634. 49 | ~38 [avatar split clause 633,440,518]
649. generous(lucy) <- (49) [resolution 520,206]
652. $false <- (1, 49) [subsumption resolution 649,292]
653. ~1 | ~49 [avatar contradiction clause 652]
656. strong(lucy) | calm(lucy) [subsumption resolution 547,146]
657. strong(lucy) <- (~38) [subsumption resolution 656,441]
658. 49 | 38 [avatar split clause 657,440,518]
659. $false [avatar sat refutation 272,634,653,658]
% SZS output end Proof for 6940882103327846121674762
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or strong is not tall or not creative.
Everyone who is strong is generous or not creative and vice versa.
Everyone who is either not strong or patient is both humble and brave and vice versa.
If susan is not kind or patient then someone is both not old and funny and vice versa.
Everyone who is both humble and creative is either not quiet or not old.
Everyone who is not patient or not creative is both rich and not humble.
Everyone who is both rich and kind is quiet.
Everyone who is both kind and tall is patient and vice versa.
Everyone who is both not old and not calm is tall.
If someone is not kind then someone is not funny or generous and vice versa.
If someone is either not patient or not creative then john is not funny.
If fred is creative then john is not tall or strong.
Everyone who is either not generous or not kind is humble or not old.
Everyone who is strong is either old or creative and vice versa.
Everyone who is wise or not brave is wise or not old.
Everyone who is either not brave or not happy is funny.
Someone is not old.
Alice is both patient and calm.
Susan is quiet or strong.
Someone is both funny and not patient.
Someone is not quiet.
Someone is not wise.
Mary is either curious or kind.
Someone is both rich and not calm. | Alice is not brave. | entailment | (![X]:((rich(X)|strong(X))=>(~tall(X)|~creative(X))))&
(![X]:(strong(X)<=>(generous(X)|~creative(X))))&
(![X]:((~strong(X)<~>patient(X))<=>(humble(X)&brave(X))))&
(((~kind(susan)|patient(susan)))<=>(?[X]:((~old(X)&funny(X)))))&
(![X]:((humble(X)&creative(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((~patient(X)|~creative(X))=>(rich(X)&~humble(X))))&
(![X]:((rich(X)&kind(X))=>quiet(X)))&
(![X]:((kind(X)&tall(X))<=>patient(X)))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
((?[X]:((~patient(X)<~>~creative(X))))=>(~funny(john)))&
((creative(fred))=>((~tall(john)|strong(john))))&
(![X]:((~generous(X)<~>~kind(X))=>(humble(X)|~old(X))))&
(![X]:(strong(X)<=>(old(X)<~>creative(X))))&
(![X]:((wise(X)|~brave(X))=>(wise(X)|~old(X))))&
(![X]:((~brave(X)<~>~happy(X))=>funny(X)))&
(?[X]:(~old(X)))&
((patient(alice)&calm(alice)))&
((quiet(susan)|strong(susan)))&
(?[X]:((funny(X)&~patient(X))))&
(?[X]:(~quiet(X)))&
(?[X]:(~wise(X)))&
((curious(mary)<~>kind(mary)))&
(?[X]:((rich(X)&~calm(X)))) | ~brave(alice) | [
"p0",
"p1",
"p2",
"p5",
"p7",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 5786043772695689442456875
% SZS output start Proof for 5786043772695689442456875
1. ! [X0] : ((strong(X0) | rich(X0)) => (~creative(X0) | ~tall(X0))) [input p0]
2. ! [X0] : (strong(X0) <=> (~creative(X0) | generous(X0))) [input p1]
3. ! [X0] : ((~strong(X0) <~> patient(X0)) <=> (brave(X0) & humble(X0))) [input p2]
6. ! [X0] : ((~creative(X0) | ~patient(X0)) => (~humble(X0) & rich(X0))) [input p5]
8. ! [X0] : ((tall(X0) & kind(X0)) <=> patient(X0)) [input p7]
13. ! [X0] : ((~generous(X0) <~> ~kind(X0)) => (~old(X0) | humble(X0))) [input p12]
14. ! [X0] : (strong(X0) <=> (old(X0) <~> creative(X0))) [input p13]
18. calm(alice) & patient(alice) [input p17]
25. brave(alice) [input hypothesis]
27. ! [X0] : ((~creative(X0) | ~tall(X0)) | (~strong(X0) & ~rich(X0))) [ennf transformation 1]
28. ! [X0] : (~creative(X0) | ~tall(X0) | (~strong(X0) & ~rich(X0))) [flattening 27]
31. ! [X0] : ((~humble(X0) & rich(X0)) | (creative(X0) & patient(X0))) [ennf transformation 6]
39. ! [X0] : ((~old(X0) | humble(X0)) | (~generous(X0) <=> ~kind(X0))) [ennf transformation 13]
40. ! [X0] : (~old(X0) | humble(X0) | (~generous(X0) <=> ~kind(X0))) [flattening 39]
44. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | ~strong(X0))) [nnf transformation 2]
45. ! [X0] : ((strong(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | ~strong(X0))) [flattening 44]
46. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | (~brave(X0) | ~humble(X0))) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [nnf transformation 3]
47. ! [X0] : ((((~patient(X0) | strong(X0)) & (patient(X0) | ~strong(X0))) | ~brave(X0) | ~humble(X0)) & ((brave(X0) & humble(X0)) | ((~strong(X0) | ~patient(X0)) & (patient(X0) | strong(X0))))) [flattening 46]
54. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | (~tall(X0) | ~kind(X0)))) [nnf transformation 8]
55. ! [X0] : (((tall(X0) & kind(X0)) | ~patient(X0)) & (patient(X0) | ~tall(X0) | ~kind(X0))) [flattening 54]
62. ! [X0] : (~old(X0) | humble(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0)))) [nnf transformation 40]
63. ! [X0] : ((strong(X0) | ((old(X0) | ~creative(X0)) & (creative(X0) | ~old(X0)))) & (((~creative(X0) | ~old(X0)) & (creative(X0) | old(X0))) | ~strong(X0))) [nnf transformation 14]
77. ~creative(X0) | ~tall(X0) | ~strong(X0) [cnf transformation 28]
79. ~generous(X0) | strong(X0) [cnf transformation 45]
80. creative(X0) | strong(X0) [cnf transformation 45]
82. ~patient(X0) | ~strong(X0) | humble(X0) [cnf transformation 47]
86. ~brave(X0) | strong(X0) | ~patient(X0) | ~humble(X0) [cnf transformation 47]
97. ~humble(X0) | creative(X0) [cnf transformation 31]
100. ~patient(X0) | kind(X0) [cnf transformation 55]
101. ~patient(X0) | tall(X0) [cnf transformation 55]
109. ~old(X0) | humble(X0) | ~kind(X0) | generous(X0) [cnf transformation 62]
114. strong(X0) | old(X0) | ~creative(X0) [cnf transformation 63]
120. patient(alice) [cnf transformation 18]
131. brave(alice) [cnf transformation 25]
205. old(X0) | strong(X0) [subsumption resolution 114,80]
227. kind(alice) [resolution 100,120]
230. tall(alice) [resolution 101,120]
257. ~strong(alice) | humble(alice) [resolution 82,120]
261. 22 <=> humble(alice) [avatar definition]
263. humble(alice) <- (22) [avatar component clause 261]
265. 23 <=> strong(alice) [avatar definition]
266. strong(alice) <- (23) [avatar component clause 265]
268. 22 | ~23 [avatar split clause 257,265,261]
351. strong(alice) | ~patient(alice) | ~humble(alice) [resolution 86,131]
372. humble(X1) | ~kind(X1) | generous(X1) | strong(X1) [resolution 109,205]
375. ~kind(X1) | humble(X1) | strong(X1) [subsumption resolution 372,79]
475. 50 <=> creative(alice) [avatar definition]
477. creative(alice) <- (50) [avatar component clause 475]
518. humble(alice) | strong(alice) [resolution 375,227]
524. 23 | 22 [avatar split clause 518,261,265]
525. strong(alice) | ~humble(alice) [subsumption resolution 351,120]
526. ~22 | 23 [avatar split clause 525,265,261]
528. creative(alice) <- (22) [resolution 263,97]
669. ~tall(alice) | ~strong(alice) <- (50) [resolution 477,77]
673. ~strong(alice) <- (50) [subsumption resolution 669,230]
674. $false <- (23, 50) [subsumption resolution 673,266]
675. ~23 | ~50 [avatar contradiction clause 674]
679. 50 | ~22 [avatar split clause 528,261,475]
680. $false [avatar sat refutation 268,524,526,675,679]
% SZS output end Proof for 5786043772695689442456875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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