premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If fred is both not happy and not rich then someone is tall or not funny. Everyone who is not old is not curious. If alice is either calm or quiet then susan is not funny or not strong. Everyone who is both not rich and quiet is both not funny and old and vice versa. Everyone who is quiet is either happy or not quiet and vice versa. If mary is not brave or not funny then lucy is either creative or wise. Everyone who is brave or not kind is either happy or not tall and vice versa. Everyone who is both not tall and not old is either not wise or not brave and vice versa. Everyone who is not wise is either brave or not tall. If someone is both brave and not funny then someone is not old or not funny. Everyone who is both wise and not rich is both not strong and not generous and vice versa. If someone is not happy or happy then alice is patient or rich and vice versa. Everyone who is rich is brave or not rich and vice versa. Everyone who is either not generous or wise is wise or not brave and vice versa. Everyone who is tall or not tall is either not funny or kind. Everyone who is old is either kind or not kind and vice versa. Someone is not humble or funny. Lucy is both not quiet and funny. Fred is old. Susan is wise or not old. Susan is not creative or not generous. | Susan is kind. | entailment | (((~happy(fred)&~rich(fred)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:(~old(X)=>~curious(X)))&
(((calm(alice)<~>quiet(alice)))=>((~funny(susan)|~strong(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(~funny(X)&old(X))))&
(![X]:(quiet(X)<=>(happy(X)<~>~quiet(X))))&
(((~brave(mary)|~funny(mary)))=>((creative(lucy)<~>wise(lucy))))&
(![X]:((brave(X)|~kind(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~tall(X)&~old(X))<=>(~wise(X)<~>~brave(X))))&
(![X]:(~wise(X)=>(brave(X)<~>~tall(X))))&
((?[X]:((brave(X)&~funny(X))))=>(?[X]:((~old(X)|~funny(X)))))&
(![X]:((wise(X)&~rich(X))<=>(~strong(X)&~generous(X))))&
((?[X]:((~happy(X)|happy(X))))<=>((patient(alice)|rich(alice))))&
(![X]:(rich(X)<=>(brave(X)|~rich(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(wise(X)|~brave(X))))&
(![X]:((tall(X)|~tall(X))=>(~funny(X)<~>kind(X))))&
(![X]:(old(X)<=>(kind(X)<~>~kind(X))))&
(?[X]:((~humble(X)|funny(X))))&
((~quiet(lucy)&funny(lucy)))&
(old(fred))&
((wise(susan)|~old(susan)))&
((~creative(susan)|~generous(susan))) | kind(susan) | [
"p3",
"p4",
"p6",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 887673730117562029382501
% SZS output start Proof for 887673730117562029382501
4. ! [X0] : ((quiet(X0) & ~rich(X0)) <=> (old(X0) & ~funny(X0))) [input p3]
5. ! [X0] : (quiet(X0) <=> (happy(X0) <~> ~quiet(X0))) [input p4]
7. ! [X0] : ((~kind(X0) | brave(X0)) <=> (happy(X0) <~> ~tall(X0))) [input p6]
13. ! [X0] : (rich(X0) <=> (~rich(X0) | brave(X0))) [input p12]
15. ! [X0] : ((~tall(X0) | tall(X0)) => (~funny(X0) <~> kind(X0))) [input p14]
16. ! [X0] : (old(X0) <=> (kind(X0) <~> ~kind(X0))) [input p15]
22. ~kind(susan) [input hypothesis]
33. ! [X0] : ((~funny(X0) <~> kind(X0)) | (tall(X0) & ~tall(X0))) [ennf transformation 15]
37. ! [X0] : (((quiet(X0) & ~rich(X0)) | (~old(X0) | funny(X0))) & ((old(X0) & ~funny(X0)) | (~quiet(X0) | rich(X0)))) [nnf transformation 4]
38. ! [X0] : (((quiet(X0) & ~rich(X0)) | ~old(X0) | funny(X0)) & ((old(X0) & ~funny(X0)) | ~quiet(X0) | rich(X0))) [flattening 37]
39. ! [X0] : ((quiet(X0) | ((happy(X0) | quiet(X0)) & (~quiet(X0) | ~happy(X0)))) & (((quiet(X0) | ~happy(X0)) & (~quiet(X0) | happy(X0))) | ~quiet(X0))) [nnf transformation 5]
41. ! [X0] : (((~kind(X0) | brave(X0)) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((~kind(X0) | brave(X0) | ((happy(X0) | tall(X0)) & (~tall(X0) | ~happy(X0)))) & (((tall(X0) | ~happy(X0)) & (~tall(X0) | happy(X0))) | (kind(X0) & ~brave(X0)))) [flattening 41]
56. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & ((~rich(X0) | brave(X0)) | ~rich(X0))) [nnf transformation 13]
57. ! [X0] : ((rich(X0) | (rich(X0) & ~brave(X0))) & (~rich(X0) | brave(X0) | ~rich(X0))) [flattening 56]
60. ! [X0] : (((~kind(X0) | funny(X0)) & (kind(X0) | ~funny(X0))) | (tall(X0) & ~tall(X0))) [nnf transformation 33]
61. ! [X0] : ((old(X0) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~old(X0))) [nnf transformation 16]
67. ~old(X0) | ~rich(X0) | funny(X0) [cnf transformation 38]
69. ~quiet(X0) | happy(X0) | ~quiet(X0) [cnf transformation 39]
72. quiet(X0) | happy(X0) | quiet(X0) [cnf transformation 39]
80. tall(X0) | ~happy(X0) | kind(X0) [cnf transformation 42]
102. rich(X0) | rich(X0) [cnf transformation 57]
109. kind(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 60]
115. old(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 61]
116. old(X0) | kind(X0) | kind(X0) [cnf transformation 61]
122. ~kind(susan) [cnf transformation 22]
123. old(X0) | ~kind(X0) [duplicate literal removal 115]
124. kind(X0) | old(X0) [duplicate literal removal 116]
128. rich(X0) [duplicate literal removal 102]
129. ~quiet(X0) | happy(X0) [duplicate literal removal 69]
130. quiet(X0) | happy(X0) [duplicate literal removal 72]
166. happy(X0) [subsumption resolution 129,130]
188. kind(X0) | tall(X0) [subsumption resolution 80,166]
218. ~funny(X0) | kind(X0) [subsumption resolution 109,188]
219. old(X0) [subsumption resolution 123,124]
254. ~rich(X0) | funny(X0) [resolution 67,219]
255. funny(X0) [subsumption resolution 254,128]
256. kind(X0) [resolution 255,218]
265. $false [resolution 256,122]
% SZS output end Proof for 887673730117562029382501
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or kind is not quiet and vice versa.
Everyone who is kind or not generous is either funny or patient and vice versa.
Everyone who is not humble or not curious is not generous or brave and vice versa.
If lucy is brave then alice is both not curious and funny and vice versa.
Everyone who is not funny is both not calm and tall and vice versa.
Everyone who is not rich is either not quiet or not wise.
Everyone who is both happy and not kind is both not curious and not creative.
If someone is either strong or rich then someone is either funny or not quiet.
Everyone who is either generous or brave is not quiet.
Everyone who is not happy is either quiet or not creative.
Everyone who is both not patient and curious is not curious and vice versa.
If mary is rich then alice is either not calm or calm and vice versa.
Everyone who is not wise or generous is funny and vice versa.
Everyone who is generous is both generous and patient and vice versa.
Lucy is quiet or not quiet.
Fred is either not humble or strong.
Paul is quiet. | Mary is not funny. | entailment | (![X]:((quiet(X)<~>kind(X))<=>~quiet(X)))&
(![X]:((kind(X)|~generous(X))<=>(funny(X)<~>patient(X))))&
(![X]:((~humble(X)|~curious(X))<=>(~generous(X)|brave(X))))&
((brave(lucy))<=>((~curious(alice)&funny(alice))))&
(![X]:(~funny(X)<=>(~calm(X)&tall(X))))&
(![X]:(~rich(X)=>(~quiet(X)<~>~wise(X))))&
(![X]:((happy(X)&~kind(X))=>(~curious(X)&~creative(X))))&
((?[X]:((strong(X)<~>rich(X))))=>(?[X]:((funny(X)<~>~quiet(X)))))&
(![X]:((generous(X)<~>brave(X))=>~quiet(X)))&
(![X]:(~happy(X)=>(quiet(X)<~>~creative(X))))&
(![X]:((~patient(X)&curious(X))<=>~curious(X)))&
((rich(mary))<=>((~calm(alice)<~>calm(alice))))&
(![X]:((~wise(X)|generous(X))<=>funny(X)))&
(![X]:(generous(X)<=>(generous(X)&patient(X))))&
((quiet(lucy)|~quiet(lucy)))&
((~humble(fred)<~>strong(fred)))&
(quiet(paul)) | ~funny(mary) | [
"p0",
"p1",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1758374770192839631369509
% SZS output start Proof for 1758374770192839631369509
1. ! [X0] : ((quiet(X0) <~> kind(X0)) <=> ~quiet(X0)) [input p0]
2. ! [X0] : ((~generous(X0) | kind(X0)) <=> (funny(X0) <~> patient(X0))) [input p1]
11. ! [X0] : ((curious(X0) & ~patient(X0)) <=> ~curious(X0)) [input p10]
18. funny(mary) [input hypothesis]
26. ! [X0] : ((((~kind(X0) | ~quiet(X0)) & (kind(X0) | quiet(X0))) | quiet(X0)) & (~quiet(X0) | ((quiet(X0) | ~kind(X0)) & (kind(X0) | ~quiet(X0))))) [nnf transformation 1]
27. ! [X0] : (((~generous(X0) | kind(X0)) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (generous(X0) & ~kind(X0)))) [nnf transformation 2]
28. ! [X0] : ((~generous(X0) | kind(X0) | ((funny(X0) | ~patient(X0)) & (patient(X0) | ~funny(X0)))) & (((~patient(X0) | ~funny(X0)) & (patient(X0) | funny(X0))) | (generous(X0) & ~kind(X0)))) [flattening 27]
42. ! [X0] : (((curious(X0) & ~patient(X0)) | curious(X0)) & (~curious(X0) | (~curious(X0) | patient(X0)))) [nnf transformation 11]
43. ! [X0] : (((curious(X0) & ~patient(X0)) | curious(X0)) & (~curious(X0) | ~curious(X0) | patient(X0))) [flattening 42]
50. ~quiet(X0) | kind(X0) | ~quiet(X0) [cnf transformation 26]
52. kind(X0) | quiet(X0) | quiet(X0) [cnf transformation 26]
56. ~patient(X0) | ~funny(X0) | ~kind(X0) [cnf transformation 28]
82. ~curious(X0) | ~curious(X0) | patient(X0) [cnf transformation 43]
84. curious(X0) | curious(X0) [cnf transformation 43]
99. funny(mary) [cnf transformation 18]
102. ~curious(X0) | patient(X0) [duplicate literal removal 82]
103. curious(X0) [duplicate literal removal 84]
104. ~quiet(X0) | kind(X0) [duplicate literal removal 50]
105. kind(X0) | quiet(X0) [duplicate literal removal 52]
106. kind(X0) [subsumption resolution 104,105]
107. ~patient(X0) | ~funny(X0) [subsumption resolution 56,106]
142. patient(X0) [subsumption resolution 102,103]
163. ~funny(X0) [resolution 107,142]
164. $false [resolution 163,99]
% SZS output end Proof for 1758374770192839631369509
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.022 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is quiet or not strong is either not wise or not curious and vice versa.
Everyone who is both not strong and happy is funny or not strong and vice versa.
Everyone who is both not patient and happy is both tall and not wise.
Everyone who is strong or not rich is not funny or patient.
If someone is either happy or not tall then someone is not rich and vice versa.
Everyone who is not happy or quiet is both not brave and funny.
Everyone who is both not creative and not humble is not calm or not rich.
Everyone who is either curious or not funny is not rich or rich and vice versa.
Everyone who is not creative or wise is not creative.
Everyone who is not strong is either not quiet or rich.
Everyone who is curious or happy is not rich and vice versa.
Everyone who is not creative is either strong or not patient.
If fred is creative or funny then someone is not brave or not funny.
Everyone who is not kind or not brave is both not quiet and creative.
Everyone who is patient is both not rich and not patient.
Everyone who is not brave or not old is either not wise or tall.
Someone is either not calm or kind.
Susan is not old or not generous.
Lucy is not patient.
Paul is either happy or quiet.
Paul is creative or not happy.
Lucy is either calm or funny. | Lucy is strong. | entailment | (![X]:((quiet(X)|~strong(X))<=>(~wise(X)<~>~curious(X))))&
(![X]:((~strong(X)&happy(X))<=>(funny(X)|~strong(X))))&
(![X]:((~patient(X)&happy(X))=>(tall(X)&~wise(X))))&
(![X]:((strong(X)|~rich(X))=>(~funny(X)|patient(X))))&
((?[X]:((happy(X)<~>~tall(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~happy(X)|quiet(X))=>(~brave(X)&funny(X))))&
(![X]:((~creative(X)&~humble(X))=>(~calm(X)|~rich(X))))&
(![X]:((curious(X)<~>~funny(X))<=>(~rich(X)|rich(X))))&
(![X]:((~creative(X)|wise(X))=>~creative(X)))&
(![X]:(~strong(X)=>(~quiet(X)<~>rich(X))))&
(![X]:((curious(X)|happy(X))<=>~rich(X)))&
(![X]:(~creative(X)=>(strong(X)<~>~patient(X))))&
(((creative(fred)|funny(fred)))=>(?[X]:((~brave(X)|~funny(X)))))&
(![X]:((~kind(X)|~brave(X))=>(~quiet(X)&creative(X))))&
(![X]:(patient(X)=>(~rich(X)&~patient(X))))&
(![X]:((~brave(X)|~old(X))=>(~wise(X)<~>tall(X))))&
(?[X]:((~calm(X)<~>kind(X))))&
((~old(susan)|~generous(susan)))&
(~patient(lucy))&
((happy(paul)<~>quiet(paul)))&
((creative(paul)|~happy(paul)))&
((calm(lucy)<~>funny(lucy))) | strong(lucy) | [
"p0",
"p1",
"p2",
"p3",
"p5",
"p7",
"p10",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7204372623005634125553248
% SZS output start Proof for 7204372623005634125553248
1. ! [X0] : ((~strong(X0) | quiet(X0)) <=> (~wise(X0) <~> ~curious(X0))) [input p0]
2. ! [X0] : ((happy(X0) & ~strong(X0)) <=> (~strong(X0) | funny(X0))) [input p1]
3. ! [X0] : ((happy(X0) & ~patient(X0)) => (~wise(X0) & tall(X0))) [input p2]
4. ! [X0] : ((~rich(X0) | strong(X0)) => (patient(X0) | ~funny(X0))) [input p3]
6. ! [X0] : ((quiet(X0) | ~happy(X0)) => (funny(X0) & ~brave(X0))) [input p5]
8. ! [X0] : ((curious(X0) <~> ~funny(X0)) <=> (rich(X0) | ~rich(X0))) [input p7]
11. ! [X0] : ((happy(X0) | curious(X0)) <=> ~rich(X0)) [input p10]
15. ! [X0] : (patient(X0) => (~patient(X0) & ~rich(X0))) [input p14]
23. ~strong(lucy) [input hypothesis]
28. ! [X0] : ((~wise(X0) & tall(X0)) | (~happy(X0) | patient(X0))) [ennf transformation 3]
29. ! [X0] : ((~wise(X0) & tall(X0)) | ~happy(X0) | patient(X0)) [flattening 28]
30. ! [X0] : ((patient(X0) | ~funny(X0)) | (rich(X0) & ~strong(X0))) [ennf transformation 4]
31. ! [X0] : (patient(X0) | ~funny(X0) | (rich(X0) & ~strong(X0))) [flattening 30]
32. ! [X0] : ((funny(X0) & ~brave(X0)) | (~quiet(X0) & happy(X0))) [ennf transformation 6]
38. ! [X0] : ((~patient(X0) & ~rich(X0)) | ~patient(X0)) [ennf transformation 15]
40. ! [X0] : (((~strong(X0) | quiet(X0)) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (strong(X0) & ~quiet(X0)))) [nnf transformation 1]
41. ! [X0] : ((~strong(X0) | quiet(X0) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) & (((curious(X0) | wise(X0)) & (~curious(X0) | ~wise(X0))) | (strong(X0) & ~quiet(X0)))) [flattening 40]
42. ! [X0] : (((happy(X0) & ~strong(X0)) | (strong(X0) & ~funny(X0))) & ((~strong(X0) | funny(X0)) | (~happy(X0) | strong(X0)))) [nnf transformation 2]
43. ! [X0] : (((happy(X0) & ~strong(X0)) | (strong(X0) & ~funny(X0))) & (~strong(X0) | funny(X0) | ~happy(X0) | strong(X0))) [flattening 42]
49. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (~rich(X0) & rich(X0))) & ((rich(X0) | ~rich(X0)) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [nnf transformation 8]
50. ! [X0] : ((((funny(X0) | ~curious(X0)) & (~funny(X0) | curious(X0))) | (~rich(X0) & rich(X0))) & (rich(X0) | ~rich(X0) | ((curious(X0) | funny(X0)) & (~funny(X0) | ~curious(X0))))) [flattening 49]
52. ! [X0] : (((happy(X0) | curious(X0)) | rich(X0)) & (~rich(X0) | (~happy(X0) & ~curious(X0)))) [nnf transformation 11]
53. ! [X0] : ((happy(X0) | curious(X0) | rich(X0)) & (~rich(X0) | (~happy(X0) & ~curious(X0)))) [flattening 52]
66. curious(X0) | wise(X0) | strong(X0) [cnf transformation 41]
72. ~funny(X0) | happy(X0) [cnf transformation 43]
75. ~happy(X0) | ~wise(X0) | patient(X0) [cnf transformation 29]
77. ~funny(X0) | patient(X0) | rich(X0) [cnf transformation 31]
84. funny(X0) | happy(X0) [cnf transformation 32]
90. funny(X0) | ~curious(X0) | rich(X0) [cnf transformation 50]
91. ~rich(X0) | ~curious(X0) | funny(X0) [cnf transformation 50]
97. ~rich(X0) | ~happy(X0) [cnf transformation 53]
108. ~patient(X0) | ~patient(X0) [cnf transformation 38]
119. ~strong(lucy) [cnf transformation 23]
120. ~patient(X0) [duplicate literal removal 108]
146. happy(X0) [subsumption resolution 84,72]
147. ~curious(X0) | funny(X0) [subsumption resolution 90,91]
149. ~rich(X0) [subsumption resolution 97,146]
185. 14 <=> funny(lucy) [avatar definition]
186. funny(lucy) <- (14) [avatar component clause 185]
187. ~funny(lucy) <- (~14) [avatar component clause 185]
198. funny(X2) | strong(X2) | wise(X2) [resolution 66,147]
205. ~wise(X1) | patient(X1) [resolution 75,146]
207. ~wise(X1) [subsumption resolution 205,120]
221. strong(lucy) | wise(lucy) <- (~14) [resolution 198,187]
227. wise(lucy) <- (~14) [subsumption resolution 221,119]
228. $false <- (~14) [subsumption resolution 227,207]
229. 14 [avatar contradiction clause 228]
233. patient(lucy) | rich(lucy) <- (14) [resolution 186,77]
237. rich(lucy) <- (14) [subsumption resolution 233,120]
238. $false <- (14) [subsumption resolution 237,149]
239. ~14 [avatar contradiction clause 238]
240. $false [avatar sat refutation 229,239]
% SZS output end Proof for 7204372623005634125553248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not quiet and not tall then someone is either not happy or not wise and vice versa.
If someone is happy then someone is wise or not happy.
Everyone who is calm is not tall and vice versa.
Everyone who is happy or brave is not curious or quiet.
Everyone who is quiet is not happy or humble.
If fred is not old then alice is kind or not humble and vice versa.
Everyone who is both not generous and not humble is either brave or not rich.
If fred is both strong and not strong then someone is either old or not quiet.
Everyone who is either kind or not old is either creative or tall and vice versa.
If someone is not brave then someone is humble or not wise.
If alice is both curious and old then paul is old or not strong.
If alice is either rich or not wise then lucy is old.
If lucy is not old then someone is not creative and vice versa.
Everyone who is either not strong or old is either wise or creative.
If fred is either calm or not wise then someone is not old or not humble.
If alice is either generous or patient then susan is both not patient and not kind and vice versa.
Someone is either not happy or not strong.
Someone is old.
Someone is both tall and not humble.
Someone is either creative or not rich.
Paul is either not old or patient.
Someone is both patient and not strong.
Mary is either not wise or not rich.
Susan is not rich. | Susan is rich. | contradiction | ((?[X]:((~quiet(X)&~tall(X))))<=>(?[X]:((~happy(X)<~>~wise(X)))))&
((?[X]:(happy(X)))=>(?[X]:((wise(X)|~happy(X)))))&
(![X]:(calm(X)<=>~tall(X)))&
(![X]:((happy(X)|brave(X))=>(~curious(X)|quiet(X))))&
(![X]:(quiet(X)=>(~happy(X)|humble(X))))&
((~old(fred))<=>((kind(alice)|~humble(alice))))&
(![X]:((~generous(X)&~humble(X))=>(brave(X)<~>~rich(X))))&
(((strong(fred)&~strong(fred)))=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((kind(X)<~>~old(X))<=>(creative(X)<~>tall(X))))&
((?[X]:(~brave(X)))=>(?[X]:((humble(X)|~wise(X)))))&
(((curious(alice)&old(alice)))=>((old(paul)|~strong(paul))))&
(((rich(alice)<~>~wise(alice)))=>(old(lucy)))&
((~old(lucy))<=>(?[X]:(~creative(X))))&
(![X]:((~strong(X)<~>old(X))=>(wise(X)<~>creative(X))))&
(((calm(fred)<~>~wise(fred)))=>(?[X]:((~old(X)|~humble(X)))))&
(((generous(alice)<~>patient(alice)))<=>((~patient(susan)&~kind(susan))))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:(old(X)))&
(?[X]:((tall(X)&~humble(X))))&
(?[X]:((creative(X)<~>~rich(X))))&
((~old(paul)<~>patient(paul)))&
(?[X]:((patient(X)&~strong(X))))&
((~wise(mary)<~>~rich(mary)))&
(~rich(susan)) | rich(susan) | [
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 4455320454177593343796099
% SZS output start Proof for 4455320454177593343796099
24. ~rich(susan) [input p23]
25. rich(susan) [input hypothesis]
141. ~rich(susan) [cnf transformation 24]
142. rich(susan) [cnf transformation 25]
316. $false [subsumption resolution 142,141]
% SZS output end Proof for 4455320454177593343796099
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong is creative or not brave.
Everyone who is both rich and not curious is strong.
Everyone who is either quiet or patient is both not generous and not curious and vice versa.
Everyone who is not curious or not strong is funny.
Everyone who is wise or brave is both not wise and not humble and vice versa.
Everyone who is not generous is not strong or quiet and vice versa.
Everyone who is not tall or humble is both kind and not rich and vice versa.
If alice is both not brave and not humble then someone is either curious or brave.
Everyone who is either tall or not old is not calm.
If someone is brave then someone is not calm.
If someone is either not happy or humble then lucy is wise or quiet and vice versa.
Everyone who is not happy is both curious and humble.
Everyone who is patient or funny is both not patient and rich and vice versa.
If someone is generous or not generous then susan is not patient and vice versa.
Everyone who is both not kind and not funny is generous or not curious and vice versa.
Everyone who is brave or not funny is both not old and curious.
Alice is brave.
Someone is both brave and not generous.
Fred is not creative or calm.
Someone is not kind.
Fred is either calm or quiet.
Alice is either kind or rich.
Someone is either not humble or quiet. | Alice is tall. | entailment | (![X]:(strong(X)=>(creative(X)|~brave(X))))&
(![X]:((rich(X)&~curious(X))=>strong(X)))&
(![X]:((quiet(X)<~>patient(X))<=>(~generous(X)&~curious(X))))&
(![X]:((~curious(X)|~strong(X))=>funny(X)))&
(![X]:((wise(X)|brave(X))<=>(~wise(X)&~humble(X))))&
(![X]:(~generous(X)<=>(~strong(X)|quiet(X))))&
(![X]:((~tall(X)|humble(X))<=>(kind(X)&~rich(X))))&
(((~brave(alice)&~humble(alice)))=>(?[X]:((curious(X)<~>brave(X)))))&
(![X]:((tall(X)<~>~old(X))=>~calm(X)))&
((?[X]:(brave(X)))=>(?[X]:(~calm(X))))&
((?[X]:((~happy(X)<~>humble(X))))<=>((wise(lucy)|quiet(lucy))))&
(![X]:(~happy(X)=>(curious(X)&humble(X))))&
(![X]:((patient(X)|funny(X))<=>(~patient(X)&rich(X))))&
((?[X]:((generous(X)|~generous(X))))<=>(~patient(susan)))&
(![X]:((~kind(X)&~funny(X))<=>(generous(X)|~curious(X))))&
(![X]:((brave(X)|~funny(X))=>(~old(X)&curious(X))))&
(brave(alice))&
(?[X]:((brave(X)&~generous(X))))&
((~creative(fred)|calm(fred)))&
(?[X]:(~kind(X)))&
((calm(fred)<~>quiet(fred)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((~humble(X)<~>quiet(X)))) | tall(alice) | [
"p2",
"p3",
"p5",
"p6",
"p12",
"p14",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3083315131799889254867893
% SZS output start Proof for 3083315131799889254867893
3. ! [X0] : ((quiet(X0) <~> patient(X0)) <=> (~curious(X0) & ~generous(X0))) [input p2]
4. ! [X0] : ((~strong(X0) | ~curious(X0)) => funny(X0)) [input p3]
6. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~strong(X0))) [input p5]
7. ! [X0] : ((humble(X0) | ~tall(X0)) <=> (~rich(X0) & kind(X0))) [input p6]
13. ! [X0] : ((funny(X0) | patient(X0)) <=> (rich(X0) & ~patient(X0))) [input p12]
15. ! [X0] : ((~funny(X0) & ~kind(X0)) <=> (~curious(X0) | generous(X0))) [input p14]
22. kind(alice) <~> rich(alice) [input p21]
24. ~tall(alice) [input hypothesis]
30. ! [X0] : (funny(X0) | (strong(X0) & curious(X0))) [ennf transformation 4]
37. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | (curious(X0) | generous(X0))) & ((~curious(X0) & ~generous(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [nnf transformation 3]
38. ! [X0] : ((((~patient(X0) | ~quiet(X0)) & (patient(X0) | quiet(X0))) | curious(X0) | generous(X0)) & ((~curious(X0) & ~generous(X0)) | ((quiet(X0) | ~patient(X0)) & (patient(X0) | ~quiet(X0))))) [flattening 37]
41. ! [X0] : ((~generous(X0) | (~quiet(X0) & strong(X0))) & ((quiet(X0) | ~strong(X0)) | generous(X0))) [nnf transformation 6]
42. ! [X0] : ((~generous(X0) | (~quiet(X0) & strong(X0))) & (quiet(X0) | ~strong(X0) | generous(X0))) [flattening 41]
43. ! [X0] : (((humble(X0) | ~tall(X0)) | (rich(X0) | ~kind(X0))) & ((~rich(X0) & kind(X0)) | (~humble(X0) & tall(X0)))) [nnf transformation 7]
44. ! [X0] : ((humble(X0) | ~tall(X0) | rich(X0) | ~kind(X0)) & ((~rich(X0) & kind(X0)) | (~humble(X0) & tall(X0)))) [flattening 43]
57. ! [X0] : (((funny(X0) | patient(X0)) | (~rich(X0) | patient(X0))) & ((rich(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0)))) [nnf transformation 13]
58. ! [X0] : ((funny(X0) | patient(X0) | ~rich(X0) | patient(X0)) & ((rich(X0) & ~patient(X0)) | (~funny(X0) & ~patient(X0)))) [flattening 57]
63. ! [X0] : (((~funny(X0) & ~kind(X0)) | (curious(X0) & ~generous(X0))) & ((~curious(X0) | generous(X0)) | (funny(X0) | kind(X0)))) [nnf transformation 15]
64. ! [X0] : (((~funny(X0) & ~kind(X0)) | (curious(X0) & ~generous(X0))) & (~curious(X0) | generous(X0) | funny(X0) | kind(X0))) [flattening 63]
70. (~rich(alice) | ~kind(alice)) & (rich(alice) | kind(alice)) [nnf transformation 22]
78. ~quiet(X0) | patient(X0) | ~curious(X0) [cnf transformation 38]
82. funny(X0) | curious(X0) [cnf transformation 30]
83. funny(X0) | strong(X0) [cnf transformation 30]
89. ~strong(X0) | quiet(X0) | generous(X0) [cnf transformation 42]
92. kind(X0) | tall(X0) [cnf transformation 44]
110. ~patient(X0) | ~patient(X0) [cnf transformation 58]
113. ~funny(X0) | rich(X0) [cnf transformation 58]
119. ~kind(X0) | ~generous(X0) [cnf transformation 64]
122. ~funny(X0) | curious(X0) [cnf transformation 64]
135. ~rich(alice) | ~kind(alice) [cnf transformation 70]
138. ~tall(alice) [cnf transformation 24]
139. ~patient(X0) [duplicate literal removal 110]
194. curious(X0) [subsumption resolution 122,82]
213. 15 <=> kind(alice) [avatar definition]
214. kind(alice) <- (15) [avatar component clause 213]
215. ~kind(alice) <- (~15) [avatar component clause 213]
217. 16 <=> rich(alice) [avatar definition]
219. ~rich(alice) <- (~16) [avatar component clause 217]
220. ~15 | ~16 [avatar split clause 135,217,213]
236. rich(X0) | strong(X0) [resolution 113,83]
238. ~generous(alice) <- (15) [resolution 119,214]
261. 21 <=> strong(alice) [avatar definition]
262. strong(alice) <- (21) [avatar component clause 261]
281. strong(alice) <- (~16) [resolution 236,219]
288. 21 | 16 [avatar split clause 281,217,261]
299. quiet(alice) | generous(alice) <- (21) [resolution 262,89]
300. quiet(alice) <- (15, 21) [subsumption resolution 299,238]
358. patient(alice) | ~curious(alice) <- (15, 21) [resolution 300,78]
359. ~curious(alice) <- (15, 21) [subsumption resolution 358,139]
360. $false <- (15, 21) [subsumption resolution 359,194]
361. ~15 | ~21 [avatar contradiction clause 360]
372. tall(alice) <- (~15) [resolution 215,92]
378. $false <- (~15) [subsumption resolution 372,138]
379. 15 [avatar contradiction clause 378]
380. $false [avatar sat refutation 220,288,361,379]
% SZS output end Proof for 3083315131799889254867893
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.021 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old is not curious and vice versa.
Everyone who is rich or patient is not happy or quiet.
Everyone who is not quiet is quiet or not humble and vice versa.
Everyone who is either not tall or creative is either generous or quiet and vice versa.
If paul is both not generous and not wise then someone is both curious and creative and vice versa.
Everyone who is not creative or calm is not calm or humble and vice versa.
Everyone who is either humble or calm is not humble or kind.
If john is funny then someone is strong.
Everyone who is both strong and not quiet is old and vice versa.
Everyone who is not rich or not creative is funny or creative and vice versa.
Everyone who is both not calm and not quiet is both old and not generous.
If someone is both tall and humble then lucy is both rich and not strong.
If susan is curious then lucy is either funny or not happy and vice versa.
If alice is either not wise or curious then someone is either patient or strong and vice versa.
If someone is both not generous and not tall then someone is both not old and tall.
If someone is generous then paul is not brave.
Someone is both wise and old.
John is either old or kind.
Alice is strong or curious.
Fred is either kind or old.
Fred is not happy.
Someone is either happy or tall.
Someone is not patient. | Fred is not creative. | entailment | (![X]:(~old(X)<=>~curious(X)))&
(![X]:((rich(X)|patient(X))=>(~happy(X)|quiet(X))))&
(![X]:(~quiet(X)<=>(quiet(X)|~humble(X))))&
(![X]:((~tall(X)<~>creative(X))<=>(generous(X)<~>quiet(X))))&
(((~generous(paul)&~wise(paul)))<=>(?[X]:((curious(X)&creative(X)))))&
(![X]:((~creative(X)|calm(X))<=>(~calm(X)|humble(X))))&
(![X]:((humble(X)<~>calm(X))=>(~humble(X)|kind(X))))&
((funny(john))=>(?[X]:(strong(X))))&
(![X]:((strong(X)&~quiet(X))<=>old(X)))&
(![X]:((~rich(X)|~creative(X))<=>(funny(X)|creative(X))))&
(![X]:((~calm(X)&~quiet(X))=>(old(X)&~generous(X))))&
((?[X]:((tall(X)&humble(X))))=>((rich(lucy)&~strong(lucy))))&
((curious(susan))<=>((funny(lucy)<~>~happy(lucy))))&
(((~wise(alice)<~>curious(alice)))<=>(?[X]:((patient(X)<~>strong(X)))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~old(X)&tall(X)))))&
((?[X]:(generous(X)))=>(~brave(paul)))&
(?[X]:((wise(X)&old(X))))&
((old(john)<~>kind(john)))&
((strong(alice)|curious(alice)))&
((kind(fred)<~>old(fred)))&
(~happy(fred))&
(?[X]:((happy(X)<~>tall(X))))&
(?[X]:(~patient(X))) | ~creative(fred) | [
"p2",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 824120872368066632154658
% SZS output start Proof for 824120872368066632154658
3. ! [X0] : (~quiet(X0) <=> (~humble(X0) | quiet(X0))) [input p2]
6. ! [X0] : ((calm(X0) | ~creative(X0)) <=> (humble(X0) | ~calm(X0))) [input p5]
24. creative(fred) [input hypothesis]
37. ! [X0] : ((~quiet(X0) | (humble(X0) & ~quiet(X0))) & ((~humble(X0) | quiet(X0)) | quiet(X0))) [nnf transformation 3]
38. ! [X0] : ((~quiet(X0) | (humble(X0) & ~quiet(X0))) & (~humble(X0) | quiet(X0) | quiet(X0))) [flattening 37]
45. ! [X0] : (((calm(X0) | ~creative(X0)) | (~humble(X0) & calm(X0))) & ((humble(X0) | ~calm(X0)) | (~calm(X0) & creative(X0)))) [nnf transformation 6]
46. ! [X0] : ((calm(X0) | ~creative(X0) | (~humble(X0) & calm(X0))) & (humble(X0) | ~calm(X0) | (~calm(X0) & creative(X0)))) [flattening 45]
75. ~humble(X0) | quiet(X0) | quiet(X0) [cnf transformation 38]
76. ~quiet(X0) | ~quiet(X0) [cnf transformation 38]
91. humble(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 46]
92. calm(X0) | ~creative(X0) | calm(X0) [cnf transformation 46]
133. creative(fred) [cnf transformation 24]
137. humble(X0) | ~calm(X0) [duplicate literal removal 91]
138. ~creative(X0) | calm(X0) [duplicate literal removal 92]
139. ~humble(X0) | quiet(X0) [duplicate literal removal 75]
140. ~quiet(X0) [duplicate literal removal 76]
141. ~humble(X0) [subsumption resolution 139,140]
169. ~calm(X0) [subsumption resolution 137,141]
276. calm(fred) [resolution 138,133]
282. $false [subsumption resolution 276,169]
% SZS output end Proof for 824120872368066632154658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not quiet or patient then someone is both not wise and not happy and vice versa. Everyone who is either quiet or brave is either rich or tall and vice versa. If someone is either generous or not calm then someone is curious or brave. If someone is calm or not old then mary is quiet. Everyone who is not calm or kind is generous and vice versa. Everyone who is either not quiet or not old is either not generous or wise. If someone is either quiet or strong then someone is either brave or calm. Everyone who is either kind or not quiet is either strong or curious. Everyone who is both brave and not patient is not creative and vice versa. If someone is either not patient or wise then someone is not patient and vice versa. Everyone who is not strong or kind is either not happy or wise. Everyone who is either not kind or strong is rich. Everyone who is either humble or curious is both rich and not tall and vice versa. Everyone who is either quiet or humble is not generous and vice versa. Everyone who is either not quiet or strong is quiet. Everyone who is either rich or strong is rich or not wise. Someone is patient. Someone is not generous. Paul is strong or curious. Lucy is not humble. Someone is rich. Someone is not quiet. Susan is not creative. Fred is both creative and strong. | Alice is patient. | neutral | (((~quiet(alice)<~>patient(alice)))<=>(?[X]:((~wise(X)&~happy(X)))))&
(![X]:((quiet(X)<~>brave(X))<=>(rich(X)<~>tall(X))))&
((?[X]:((generous(X)<~>~calm(X))))=>(?[X]:((curious(X)|brave(X)))))&
((?[X]:((calm(X)|~old(X))))=>(quiet(mary)))&
(![X]:((~calm(X)|kind(X))<=>generous(X)))&
(![X]:((~quiet(X)<~>~old(X))=>(~generous(X)<~>wise(X))))&
((?[X]:((quiet(X)<~>strong(X))))=>(?[X]:((brave(X)<~>calm(X)))))&
(![X]:((kind(X)<~>~quiet(X))=>(strong(X)<~>curious(X))))&
(![X]:((brave(X)&~patient(X))<=>~creative(X)))&
((?[X]:((~patient(X)<~>wise(X))))<=>(?[X]:(~patient(X))))&
(![X]:((~strong(X)|kind(X))=>(~happy(X)<~>wise(X))))&
(![X]:((~kind(X)<~>strong(X))=>rich(X)))&
(![X]:((humble(X)<~>curious(X))<=>(rich(X)&~tall(X))))&
(![X]:((quiet(X)<~>humble(X))<=>~generous(X)))&
(![X]:((~quiet(X)<~>strong(X))=>quiet(X)))&
(![X]:((rich(X)<~>strong(X))=>(rich(X)|~wise(X))))&
(?[X]:(patient(X)))&
(?[X]:(~generous(X)))&
((strong(paul)|curious(paul)))&
(~humble(lucy))&
(?[X]:(rich(X)))&
(?[X]:(~quiet(X)))&
(~creative(susan))&
((creative(fred)&strong(fred))) | patient(alice) | [] | null | 0 |
Everyone who is both curious and strong is not strong or not creative and vice versa.
Everyone who is not happy or not funny is both funny and strong and vice versa.
If someone is either old or not funny then john is rich or not quiet.
If alice is both kind and not funny then someone is patient and vice versa.
Everyone who is both humble and rich is kind or not tall.
If someone is not funny or not creative then john is both curious and not creative and vice versa.
If someone is not strong or not generous then someone is not rich or curious.
Everyone who is quiet or strong is not calm or brave and vice versa.
Everyone who is both not happy and not strong is either curious or not patient and vice versa.
Everyone who is either tall or not humble is not rich.
If john is happy or calm then paul is not calm or not rich.
Everyone who is both not happy and not wise is not humble or generous.
If john is wise or not curious then someone is wise.
Everyone who is either not happy or quiet is not tall and vice versa.
Everyone who is curious or not curious is not brave or funny.
Susan is either not quiet or not funny.
Mary is rich.
Someone is not old.
Someone is not calm or not funny.
Someone is not kind.
Alice is not curious or not wise.
Someone is wise or quiet. | Paul is curious. | entailment | (![X]:((curious(X)&strong(X))<=>(~strong(X)|~creative(X))))&
(![X]:((~happy(X)|~funny(X))<=>(funny(X)&strong(X))))&
((?[X]:((old(X)<~>~funny(X))))=>((rich(john)|~quiet(john))))&
(((kind(alice)&~funny(alice)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&rich(X))=>(kind(X)|~tall(X))))&
((?[X]:((~funny(X)|~creative(X))))<=>((curious(john)&~creative(john))))&
((?[X]:((~strong(X)|~generous(X))))=>(?[X]:((~rich(X)|curious(X)))))&
(![X]:((quiet(X)|strong(X))<=>(~calm(X)|brave(X))))&
(![X]:((~happy(X)&~strong(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((tall(X)<~>~humble(X))=>~rich(X)))&
(((happy(john)|calm(john)))=>((~calm(paul)|~rich(paul))))&
(![X]:((~happy(X)&~wise(X))=>(~humble(X)|generous(X))))&
(((wise(john)|~curious(john)))=>(?[X]:(wise(X))))&
(![X]:((~happy(X)<~>quiet(X))<=>~tall(X)))&
(![X]:((curious(X)|~curious(X))=>(~brave(X)|funny(X))))&
((~quiet(susan)<~>~funny(susan)))&
(rich(mary))&
(?[X]:(~old(X)))&
(?[X]:((~calm(X)|~funny(X))))&
(?[X]:(~kind(X)))&
((~curious(alice)|~wise(alice)))&
(?[X]:((wise(X)|quiet(X)))) | curious(paul) | [
"p0",
"p1",
"p3",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 6566885735515021396300354
% SZS output start Proof for 6566885735515021396300354
1. ! [X0] : ((strong(X0) & curious(X0)) <=> (~creative(X0) | ~strong(X0))) [input p0]
2. ! [X0] : ((~funny(X0) | ~happy(X0)) <=> (strong(X0) & funny(X0))) [input p1]
4. (~funny(alice) & kind(alice)) <=> ? [X0] : patient(X0) [input p3]
9. ! [X0] : ((~strong(X0) & ~happy(X0)) <=> (curious(X0) <~> ~patient(X0))) [input p8]
23. ~curious(paul) [input hypothesis]
38. ! [X0] : (((strong(X0) & curious(X0)) | (creative(X0) & strong(X0))) & ((~creative(X0) | ~strong(X0)) | (~strong(X0) | ~curious(X0)))) [nnf transformation 1]
39. ! [X0] : (((strong(X0) & curious(X0)) | (creative(X0) & strong(X0))) & (~creative(X0) | ~strong(X0) | ~strong(X0) | ~curious(X0))) [flattening 38]
40. ! [X0] : (((~funny(X0) | ~happy(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (funny(X0) & happy(X0)))) [nnf transformation 2]
41. ! [X0] : ((~funny(X0) | ~happy(X0) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | (funny(X0) & happy(X0)))) [flattening 40]
43. ((~funny(alice) & kind(alice)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | (funny(alice) | ~kind(alice))) [nnf transformation 4]
44. ((~funny(alice) & kind(alice)) | ! [X0] : ~patient(X0)) & (? [X0] : patient(X0) | funny(alice) | ~kind(alice)) [flattening 43]
45. ((~funny(alice) & kind(alice)) | ! [X0] : ~patient(X0)) & (? [X1] : patient(X1) | funny(alice) | ~kind(alice)) [rectify 44]
46. ? [X1] : patient(X1) => patient(sK0) [choice axiom]
47. ((~funny(alice) & kind(alice)) | ! [X0] : ~patient(X0)) & (patient(sK0) | funny(alice) | ~kind(alice)) [skolemisation 45,46]
58. ! [X0] : (((~strong(X0) & ~happy(X0)) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0)))) & (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | (strong(X0) | happy(X0)))) [nnf transformation 9]
59. ! [X0] : (((~strong(X0) & ~happy(X0)) | ((curious(X0) | patient(X0)) & (~patient(X0) | ~curious(X0)))) & (((patient(X0) | ~curious(X0)) & (~patient(X0) | curious(X0))) | strong(X0) | happy(X0))) [flattening 58]
76. strong(X0) | strong(X0) [cnf transformation 39]
79. funny(X0) | funny(X0) [cnf transformation 41]
87. ~funny(alice) | ~patient(X0) [cnf transformation 47]
104. ~strong(X0) | curious(X0) | patient(X0) [cnf transformation 59]
125. ~curious(paul) [cnf transformation 23]
126. funny(X0) [duplicate literal removal 79]
129. strong(X0) [duplicate literal removal 76]
145. ~patient(X0) [subsumption resolution 87,126]
167. curious(X0) | patient(X0) [subsumption resolution 104,129]
168. curious(X0) [subsumption resolution 167,145]
208. $false [subsumption resolution 125,168]
% SZS output end Proof for 6566885735515021396300354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is strong then fred is brave or calm and vice versa.
Everyone who is not curious is not old.
Everyone who is tall or not generous is not humble.
Everyone who is both not creative and not rich is calm or not rich and vice versa.
Everyone who is either not tall or tall is either not rich or not curious and vice versa.
If susan is not old or quiet then fred is humble or not curious.
If someone is not generous or not creative then fred is not wise and vice versa.
Everyone who is kind or not quiet is either tall or not brave.
Everyone who is brave or kind is not patient or old and vice versa.
If someone is either not strong or funny then mary is either rich or not rich.
If john is not calm or old then mary is not quiet and vice versa.
If someone is not generous or kind then someone is either strong or not generous and vice versa.
Everyone who is both strong and happy is both kind and strong.
Everyone who is not patient is both strong and creative.
If someone is either not quiet or not patient then john is both quiet and patient and vice versa.
If john is curious then paul is patient or kind and vice versa.
Paul is either not brave or kind.
Mary is both tall and happy.
Someone is tall.
Mary is either happy or not kind.
Someone is both wise and not kind.
Someone is either old or not strong.
Someone is not old.
Mary is not curious. | John is not creative. | entailment | ((?[X]:(strong(X)))<=>((brave(fred)|calm(fred))))&
(![X]:(~curious(X)=>~old(X)))&
(![X]:((tall(X)|~generous(X))=>~humble(X)))&
(![X]:((~creative(X)&~rich(X))<=>(calm(X)|~rich(X))))&
(![X]:((~tall(X)<~>tall(X))<=>(~rich(X)<~>~curious(X))))&
(((~old(susan)|quiet(susan)))=>((humble(fred)|~curious(fred))))&
((?[X]:((~generous(X)|~creative(X))))<=>(~wise(fred)))&
(![X]:((kind(X)|~quiet(X))=>(tall(X)<~>~brave(X))))&
(![X]:((brave(X)|kind(X))<=>(~patient(X)|old(X))))&
((?[X]:((~strong(X)<~>funny(X))))=>((rich(mary)<~>~rich(mary))))&
(((~calm(john)|old(john)))<=>(~quiet(mary)))&
((?[X]:((~generous(X)|kind(X))))<=>(?[X]:((strong(X)<~>~generous(X)))))&
(![X]:((strong(X)&happy(X))=>(kind(X)&strong(X))))&
(![X]:(~patient(X)=>(strong(X)&creative(X))))&
((?[X]:((~quiet(X)<~>~patient(X))))<=>((quiet(john)&patient(john))))&
((curious(john))<=>((patient(paul)|kind(paul))))&
((~brave(paul)<~>kind(paul)))&
((tall(mary)&happy(mary)))&
(?[X]:(tall(X)))&
((happy(mary)<~>~kind(mary)))&
(?[X]:((wise(X)&~kind(X))))&
(?[X]:((old(X)<~>~strong(X))))&
(?[X]:(~old(X)))&
(~curious(mary)) | ~creative(john) | [
"p3",
"p4",
"p8",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 3588035760835334764164025
% SZS output start Proof for 3588035760835334764164025
4. ! [X0] : ((~rich(X0) & ~creative(X0)) <=> (~rich(X0) | calm(X0))) [input p3]
5. ! [X0] : ((~tall(X0) <~> tall(X0)) <=> (~rich(X0) <~> ~curious(X0))) [input p4]
9. ! [X0] : ((kind(X0) | brave(X0)) <=> (old(X0) | ~patient(X0))) [input p8]
16. curious(john) <=> (kind(paul) | patient(paul)) [input p15]
17. ~brave(paul) <~> kind(paul) [input p16]
25. creative(john) [input hypothesis]
41. ! [X0] : (((~rich(X0) & ~creative(X0)) | (rich(X0) & ~calm(X0))) & ((~rich(X0) | calm(X0)) | (rich(X0) | creative(X0)))) [nnf transformation 4]
42. ! [X0] : (((~rich(X0) & ~creative(X0)) | (rich(X0) & ~calm(X0))) & (~rich(X0) | calm(X0) | rich(X0) | creative(X0))) [flattening 41]
43. ! [X0] : ((((~tall(X0) | tall(X0)) & (tall(X0) | ~tall(X0))) | ((~rich(X0) | curious(X0)) & (~curious(X0) | rich(X0)))) & (((curious(X0) | rich(X0)) & (~curious(X0) | ~rich(X0))) | ((~tall(X0) | ~tall(X0)) & (tall(X0) | tall(X0))))) [nnf transformation 5]
49. ! [X0] : (((kind(X0) | brave(X0)) | (~old(X0) & patient(X0))) & ((old(X0) | ~patient(X0)) | (~kind(X0) & ~brave(X0)))) [nnf transformation 9]
50. ! [X0] : ((kind(X0) | brave(X0) | (~old(X0) & patient(X0))) & (old(X0) | ~patient(X0) | (~kind(X0) & ~brave(X0)))) [flattening 49]
64. (curious(john) | (~kind(paul) & ~patient(paul))) & ((kind(paul) | patient(paul)) | ~curious(john)) [nnf transformation 16]
65. (curious(john) | (~kind(paul) & ~patient(paul))) & (kind(paul) | patient(paul) | ~curious(john)) [flattening 64]
66. (~kind(paul) | brave(paul)) & (kind(paul) | ~brave(paul)) [nnf transformation 17]
85. ~creative(X0) | rich(X0) [cnf transformation 42]
88. ~curious(X0) | ~rich(X0) | tall(X0) | tall(X0) [cnf transformation 43]
89. ~curious(X0) | ~rich(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 43]
107. patient(X0) | brave(X0) | kind(X0) [cnf transformation 50]
133. curious(john) | ~patient(paul) [cnf transformation 65]
134. curious(john) | ~kind(paul) [cnf transformation 65]
135. kind(paul) | ~brave(paul) [cnf transformation 66]
148. creative(john) [cnf transformation 25]
149. ~curious(X0) | ~rich(X0) | tall(X0) [duplicate literal removal 88]
150. ~curious(X0) | ~rich(X0) | ~tall(X0) [duplicate literal removal 89]
172. ~rich(X0) | ~curious(X0) [subsumption resolution 149,150]
287. 30 <=> kind(paul) [avatar definition]
289. ~kind(paul) <- (~30) [avatar component clause 287]
291. 31 <=> curious(john) [avatar definition]
294. ~30 | 31 [avatar split clause 134,291,287]
296. 32 <=> patient(paul) [avatar definition]
298. ~patient(paul) <- (~32) [avatar component clause 296]
299. ~32 | 31 [avatar split clause 133,291,296]
302. 33 <=> brave(paul) [avatar definition]
303. ~brave(paul) <- (~33) [avatar component clause 302]
306. ~33 | 30 [avatar split clause 135,287,302]
319. rich(john) [resolution 85,148]
326. ~curious(john) [resolution 172,319]
380. brave(paul) | kind(paul) <- (~32) [resolution 107,298]
392. kind(paul) <- (~32, ~33) [subsumption resolution 380,303]
393. $false <- (~30, ~32, ~33) [subsumption resolution 392,289]
394. 30 | 32 | 33 [avatar contradiction clause 393]
395. ~31 [avatar split clause 326,291]
396. $false [avatar sat refutation 294,299,306,394,395]
% SZS output end Proof for 3588035760835334764164025
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious then paul is either rich or not old.
If lucy is not happy or creative then someone is humble and vice versa.
Everyone who is both happy and not rich is both generous and not generous and vice versa.
Everyone who is not rich or not creative is both generous and patient and vice versa.
Everyone who is either not happy or not brave is both not curious and old.
Everyone who is funny is rich and vice versa.
Everyone who is not happy is not wise.
Everyone who is not happy or not quiet is both brave and not old and vice versa.
If someone is not tall then lucy is either not generous or not rich and vice versa.
Everyone who is both not strong and not curious is both not calm and not funny and vice versa.
If alice is both quiet and strong then someone is both not strong and not funny.
If someone is both not calm and generous then someone is both not wise and brave and vice versa.
Everyone who is funny or patient is both not strong and curious.
If someone is both funny and calm then paul is not humble or calm and vice versa.
If susan is old then susan is either strong or not creative.
Everyone who is wise is both not patient and not generous.
Fred is creative.
Mary is both not strong and not wise.
Someone is either not creative or not patient.
Alice is both not strong and not quiet.
Someone is curious. | Fred is not brave. | contradiction | ((?[X]:(curious(X)))=>((rich(paul)<~>~old(paul))))&
(((~happy(lucy)|creative(lucy)))<=>(?[X]:(humble(X))))&
(![X]:((happy(X)&~rich(X))<=>(generous(X)&~generous(X))))&
(![X]:((~rich(X)|~creative(X))<=>(generous(X)&patient(X))))&
(![X]:((~happy(X)<~>~brave(X))=>(~curious(X)&old(X))))&
(![X]:(funny(X)<=>rich(X)))&
(![X]:(~happy(X)=>~wise(X)))&
(![X]:((~happy(X)|~quiet(X))<=>(brave(X)&~old(X))))&
((?[X]:(~tall(X)))<=>((~generous(lucy)<~>~rich(lucy))))&
(![X]:((~strong(X)&~curious(X))<=>(~calm(X)&~funny(X))))&
(((quiet(alice)&strong(alice)))=>(?[X]:((~strong(X)&~funny(X)))))&
((?[X]:((~calm(X)&generous(X))))<=>(?[X]:((~wise(X)&brave(X)))))&
(![X]:((funny(X)|patient(X))=>(~strong(X)&curious(X))))&
((?[X]:((funny(X)&calm(X))))<=>((~humble(paul)|calm(paul))))&
((old(susan))=>((strong(susan)<~>~creative(susan))))&
(![X]:(wise(X)=>(~patient(X)&~generous(X))))&
(creative(fred))&
((~strong(mary)&~wise(mary)))&
(?[X]:((~creative(X)<~>~patient(X))))&
((~strong(alice)&~quiet(alice)))&
(?[X]:(curious(X))) | ~brave(fred) | [
"p3",
"p4",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1318862779120339668221212
% SZS output start Proof for 1318862779120339668221212
4. ! [X0] : ((~creative(X0) | ~rich(X0)) <=> (patient(X0) & generous(X0))) [input p3]
5. ! [X0] : ((~happy(X0) <~> ~brave(X0)) => (old(X0) & ~curious(X0))) [input p4]
6. ! [X0] : (funny(X0) <=> rich(X0)) [input p5]
8. ! [X0] : ((~quiet(X0) | ~happy(X0)) <=> (~old(X0) & brave(X0))) [input p7]
13. ! [X0] : ((patient(X0) | funny(X0)) => (curious(X0) & ~strong(X0))) [input p12]
22. ~brave(fred) [input hypothesis]
25. ! [X0] : ((old(X0) & ~curious(X0)) | (~happy(X0) <=> ~brave(X0))) [ennf transformation 5]
29. ! [X0] : ((curious(X0) & ~strong(X0)) | (~patient(X0) & ~funny(X0))) [ennf transformation 13]
40. ! [X0] : (((~creative(X0) | ~rich(X0)) | (~patient(X0) | ~generous(X0))) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [nnf transformation 4]
41. ! [X0] : ((~creative(X0) | ~rich(X0) | ~patient(X0) | ~generous(X0)) & ((patient(X0) & generous(X0)) | (creative(X0) & rich(X0)))) [flattening 40]
42. ! [X0] : ((old(X0) & ~curious(X0)) | ((~happy(X0) | brave(X0)) & (~brave(X0) | happy(X0)))) [nnf transformation 25]
43. ! [X0] : ((funny(X0) | ~rich(X0)) & (rich(X0) | ~funny(X0))) [nnf transformation 6]
44. ! [X0] : (((~quiet(X0) | ~happy(X0)) | (old(X0) | ~brave(X0))) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [nnf transformation 8]
45. ! [X0] : ((~quiet(X0) | ~happy(X0) | old(X0) | ~brave(X0)) & ((~old(X0) & brave(X0)) | (quiet(X0) & happy(X0)))) [flattening 44]
81. patient(X0) | rich(X0) [cnf transformation 41]
85. ~happy(X0) | ~curious(X0) | brave(X0) [cnf transformation 42]
89. ~rich(X0) | funny(X0) [cnf transformation 43]
91. brave(X0) | happy(X0) [cnf transformation 45]
112. ~funny(X0) | curious(X0) [cnf transformation 29]
113. ~patient(X0) | curious(X0) [cnf transformation 29]
131. ~brave(fred) [cnf transformation 22]
289. happy(fred) [resolution 91,131]
294. rich(X1) | curious(X1) [resolution 113,81]
350. ~curious(fred) | brave(fred) [resolution 85,289]
352. ~curious(fred) [subsumption resolution 350,131]
409. curious(X0) | funny(X0) [resolution 294,89]
410. curious(X0) [subsumption resolution 409,112]
438. $false [resolution 410,352]
% SZS output end Proof for 1318862779120339668221212
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or calm is quiet.
If mary is tall then susan is either strong or not kind.
Everyone who is either creative or quiet is both not rich and happy.
If alice is curious or quiet then someone is both strong and not tall and vice versa.
If someone is not curious or rich then alice is both not rich and humble.
If someone is both not creative and not rich then fred is calm and vice versa.
Everyone who is quiet or not tall is generous.
If someone is not tall then john is either not kind or calm and vice versa.
Everyone who is not kind or curious is humble.
Everyone who is curious is both not rich and calm and vice versa.
Everyone who is strong or calm is not humble.
Everyone who is both happy and not wise is either tall or funny and vice versa.
Everyone who is either not kind or patient is both creative and funny and vice versa.
Everyone who is either not curious or patient is curious.
Everyone who is both calm and kind is both funny and not wise.
Everyone who is not calm is old or humble and vice versa.
Someone is strong.
Mary is not funny.
Someone is wise or calm.
John is both not brave and old.
Lucy is not rich.
John is not brave or humble.
Mary is both creative and not tall. | Susan is humble. | neutral | (![X]:((wise(X)|calm(X))=>quiet(X)))&
((tall(mary))=>((strong(susan)<~>~kind(susan))))&
(![X]:((creative(X)<~>quiet(X))=>(~rich(X)&happy(X))))&
(((curious(alice)|quiet(alice)))<=>(?[X]:((strong(X)&~tall(X)))))&
((?[X]:((~curious(X)|rich(X))))=>((~rich(alice)&humble(alice))))&
((?[X]:((~creative(X)&~rich(X))))<=>(calm(fred)))&
(![X]:((quiet(X)|~tall(X))=>generous(X)))&
((?[X]:(~tall(X)))<=>((~kind(john)<~>calm(john))))&
(![X]:((~kind(X)|curious(X))=>humble(X)))&
(![X]:(curious(X)<=>(~rich(X)&calm(X))))&
(![X]:((strong(X)|calm(X))=>~humble(X)))&
(![X]:((happy(X)&~wise(X))<=>(tall(X)<~>funny(X))))&
(![X]:((~kind(X)<~>patient(X))<=>(creative(X)&funny(X))))&
(![X]:((~curious(X)<~>patient(X))=>curious(X)))&
(![X]:((calm(X)&kind(X))=>(funny(X)&~wise(X))))&
(![X]:(~calm(X)<=>(old(X)|humble(X))))&
(?[X]:(strong(X)))&
(~funny(mary))&
(?[X]:((wise(X)|calm(X))))&
((~brave(john)&old(john)))&
(~rich(lucy))&
((~brave(john)|humble(john)))&
((creative(mary)&~tall(mary))) | humble(susan) | [] | null | 0 |
If fred is humble then susan is either not calm or not patient and vice versa. Everyone who is not old is calm. Everyone who is both old and rich is happy. If someone is rich or not wise then susan is not creative. Everyone who is curious or generous is either patient or happy and vice versa. Everyone who is either not happy or not kind is not quiet. Everyone who is either not generous or not wise is either curious or brave and vice versa. Everyone who is not quiet or not kind is both not brave and not creative. Everyone who is both funny and old is humble. If someone is both patient and not quiet then someone is either humble or not generous and vice versa. Everyone who is both not happy and tall is either humble or tall and vice versa. If susan is not calm then mary is quiet or rich and vice versa. Everyone who is patient is both brave and wise and vice versa. Everyone who is brave is curious. Everyone who is both not patient and quiet is both curious and not humble. Everyone who is creative or not funny is calm. Lucy is not patient. Lucy is either not patient or not kind. Someone is both not curious and not humble. John is generous or not happy. Someone is not generous. Someone is not happy or calm. Someone is either kind or tall. John is not patient or wise. | John is generous. | entailment | ((humble(fred))<=>((~calm(susan)<~>~patient(susan))))&
(![X]:(~old(X)=>calm(X)))&
(![X]:((old(X)&rich(X))=>happy(X)))&
((?[X]:((rich(X)|~wise(X))))=>(~creative(susan)))&
(![X]:((curious(X)|generous(X))<=>(patient(X)<~>happy(X))))&
(![X]:((~happy(X)<~>~kind(X))=>~quiet(X)))&
(![X]:((~generous(X)<~>~wise(X))<=>(curious(X)<~>brave(X))))&
(![X]:((~quiet(X)|~kind(X))=>(~brave(X)&~creative(X))))&
(![X]:((funny(X)&old(X))=>humble(X)))&
((?[X]:((patient(X)&~quiet(X))))<=>(?[X]:((humble(X)<~>~generous(X)))))&
(![X]:((~happy(X)&tall(X))<=>(humble(X)<~>tall(X))))&
((~calm(susan))<=>((quiet(mary)|rich(mary))))&
(![X]:(patient(X)<=>(brave(X)&wise(X))))&
(![X]:(brave(X)=>curious(X)))&
(![X]:((~patient(X)&quiet(X))=>(curious(X)&~humble(X))))&
(![X]:((creative(X)|~funny(X))=>calm(X)))&
(~patient(lucy))&
((~patient(lucy)<~>~kind(lucy)))&
(?[X]:((~curious(X)&~humble(X))))&
((generous(john)|~happy(john)))&
(?[X]:(~generous(X)))&
(?[X]:((~happy(X)|calm(X))))&
(?[X]:((kind(X)<~>tall(X))))&
((~patient(john)|wise(john))) | generous(john) | [
"p7",
"p9",
"p10",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 6655719545497846499237454
% SZS output start Proof for 6655719545497846499237454
8. ! [X0] : ((~kind(X0) | ~quiet(X0)) => (~creative(X0) & ~brave(X0))) [input p7]
10. ? [X0] : (~quiet(X0) & patient(X0)) <=> ? [X0] : (humble(X0) <~> ~generous(X0)) [input p9]
11. ! [X0] : ((tall(X0) & ~happy(X0)) <=> (humble(X0) <~> tall(X0))) [input p10]
13. ! [X0] : (patient(X0) <=> (wise(X0) & brave(X0))) [input p12]
20. ~happy(john) | generous(john) [input p19]
25. ~generous(john) [input hypothesis]
26. ? [X0] : (~quiet(X0) & patient(X0)) <=> ? [X1] : (humble(X1) <~> ~generous(X1)) [rectify 10]
27. ! [X0] : ((~kind(X0) | ~quiet(X0)) => ~brave(X0)) [pure predicate removal 8]
34. ! [X0] : (~brave(X0) | (kind(X0) & quiet(X0))) [ennf transformation 27]
46. (? [X0] : (~quiet(X0) & patient(X0)) | ! [X1] : ((humble(X1) | generous(X1)) & (~generous(X1) | ~humble(X1)))) & (? [X1] : ((generous(X1) | ~humble(X1)) & (~generous(X1) | humble(X1))) | ! [X0] : (quiet(X0) | ~patient(X0))) [nnf transformation 26]
47. (? [X0] : (~quiet(X0) & patient(X0)) | ! [X1] : ((humble(X1) | generous(X1)) & (~generous(X1) | ~humble(X1)))) & (? [X2] : ((generous(X2) | ~humble(X2)) & (~generous(X2) | humble(X2))) | ! [X3] : (quiet(X3) | ~patient(X3))) [rectify 46]
48. ? [X0] : (~quiet(X0) & patient(X0)) => (~quiet(sK0) & patient(sK0)) [choice axiom]
49. ? [X2] : ((generous(X2) | ~humble(X2)) & (~generous(X2) | humble(X2))) => ((generous(sK1) | ~humble(sK1)) & (~generous(sK1) | humble(sK1))) [choice axiom]
50. ((~quiet(sK0) & patient(sK0)) | ! [X1] : ((humble(X1) | generous(X1)) & (~generous(X1) | ~humble(X1)))) & (((generous(sK1) | ~humble(sK1)) & (~generous(sK1) | humble(sK1))) | ! [X3] : (quiet(X3) | ~patient(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((tall(X0) & ~happy(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~tall(X0) | happy(X0)))) [nnf transformation 11]
52. ! [X0] : (((tall(X0) & ~happy(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | ~tall(X0) | happy(X0))) [flattening 51]
55. ! [X0] : ((patient(X0) | (~wise(X0) | ~brave(X0))) & ((wise(X0) & brave(X0)) | ~patient(X0))) [nnf transformation 13]
56. ! [X0] : ((patient(X0) | ~wise(X0) | ~brave(X0)) & ((wise(X0) & brave(X0)) | ~patient(X0))) [flattening 55]
89. ~brave(X0) | quiet(X0) [cnf transformation 34]
95. patient(sK0) | humble(X1) | generous(X1) [cnf transformation 50]
97. ~quiet(sK0) | humble(X1) | generous(X1) [cnf transformation 50]
99. ~tall(X0) | ~humble(X0) | ~tall(X0) | happy(X0) [cnf transformation 52]
102. tall(X0) | tall(X0) | ~humble(X0) [cnf transformation 52]
107. ~patient(X0) | brave(X0) [cnf transformation 56]
119. ~happy(john) | generous(john) [cnf transformation 20]
125. ~generous(john) [cnf transformation 25]
126. ~tall(X0) | ~humble(X0) | happy(X0) [duplicate literal removal 99]
127. ~humble(X0) | tall(X0) [duplicate literal removal 102]
145. 4 <=> ! [X1] : (humble(X1) | generous(X1)) [avatar definition]
146. generous(X1) | humble(X1) <- (4) [avatar component clause 145]
148. 5 <=> quiet(sK0) [avatar definition]
150. ~quiet(sK0) <- (~5) [avatar component clause 148]
151. 4 | ~5 [avatar split clause 97,148,145]
157. 7 <=> patient(sK0) [avatar definition]
159. patient(sK0) <- (7) [avatar component clause 157]
160. 4 | 7 [avatar split clause 95,157,145]
175. ~humble(X0) | happy(X0) [subsumption resolution 126,127]
189. 13 <=> generous(john) [avatar definition]
190. ~generous(john) <- (~13) [avatar component clause 189]
193. 14 <=> happy(john) [avatar definition]
195. ~happy(john) <- (~14) [avatar component clause 193]
196. 13 | ~14 [avatar split clause 119,193,189]
216. ~13 [avatar split clause 125,189]
224. brave(sK0) <- (7) [resolution 159,107]
228. quiet(sK0) <- (7) [resolution 224,89]
229. $false <- (~5, 7) [subsumption resolution 228,150]
230. 5 | ~7 [avatar contradiction clause 229]
234. humble(john) <- (4, ~13) [resolution 146,190]
237. happy(john) <- (4, ~13) [resolution 234,175]
239. $false <- (4, ~13, ~14) [subsumption resolution 237,195]
240. ~4 | 13 | 14 [avatar contradiction clause 239]
241. $false [avatar sat refutation 151,160,196,216,230,240]
% SZS output end Proof for 6655719545497846499237454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old is patient.
If someone is tall then someone is kind and vice versa.
Everyone who is humble or rich is either not strong or not happy.
Everyone who is either not generous or not creative is strong or wise and vice versa.
Everyone who is curious is not wise and vice versa.
Everyone who is both not old and kind is both rich and curious.
If someone is not old then alice is either not curious or wise.
If someone is wise or not rich then someone is both not quiet and not patient.
Everyone who is either curious or not generous is patient.
If john is either not wise or not patient then someone is quiet or not happy.
Everyone who is both funny and not curious is creative or not happy and vice versa.
If lucy is calm or not humble then someone is both not brave and not kind.
Everyone who is both not tall and brave is both rich and wise and vice versa.
Everyone who is either not brave or not quiet is both not curious and not happy.
Susan is generous or not quiet.
Paul is not happy or happy.
Someone is both not calm and patient.
Paul is not calm or kind.
Someone is not brave.
Lucy is not tall or creative. | John is wise. | contradiction | (![X]:((~creative(X)<~>~old(X))=>patient(X)))&
((?[X]:(tall(X)))<=>(?[X]:(kind(X))))&
(![X]:((humble(X)|rich(X))=>(~strong(X)<~>~happy(X))))&
(![X]:((~generous(X)<~>~creative(X))<=>(strong(X)|wise(X))))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~old(X)&kind(X))=>(rich(X)&curious(X))))&
((?[X]:(~old(X)))=>((~curious(alice)<~>wise(alice))))&
((?[X]:((wise(X)|~rich(X))))=>(?[X]:((~quiet(X)&~patient(X)))))&
(![X]:((curious(X)<~>~generous(X))=>patient(X)))&
(((~wise(john)<~>~patient(john)))=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((funny(X)&~curious(X))<=>(creative(X)|~happy(X))))&
(((calm(lucy)|~humble(lucy)))=>(?[X]:((~brave(X)&~kind(X)))))&
(![X]:((~tall(X)&brave(X))<=>(rich(X)&wise(X))))&
(![X]:((~brave(X)<~>~quiet(X))=>(~curious(X)&~happy(X))))&
((generous(susan)|~quiet(susan)))&
((~happy(paul)|happy(paul)))&
(?[X]:((~calm(X)&patient(X))))&
((~calm(paul)|kind(paul)))&
(?[X]:(~brave(X)))&
((~tall(lucy)|creative(lucy))) | wise(john) | [
"p0",
"p3",
"p4",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 7509714960623053928557007
% SZS output start Proof for 7509714960623053928557007
1. ! [X0] : ((~creative(X0) <~> ~old(X0)) => patient(X0)) [input p0]
4. ! [X0] : ((~generous(X0) <~> ~creative(X0)) <=> (wise(X0) | strong(X0))) [input p3]
5. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p4]
7. ? [X0] : ~old(X0) => (~curious(alice) <~> wise(alice)) [input p6]
8. ? [X0] : (~rich(X0) | wise(X0)) => ? [X0] : (~patient(X0) & ~quiet(X0)) [input p7]
9. ! [X0] : ((curious(X0) <~> ~generous(X0)) => patient(X0)) [input p8]
11. ! [X0] : ((~curious(X0) & funny(X0)) <=> (~happy(X0) | creative(X0))) [input p10]
21. wise(john) [input hypothesis]
23. ? [X0] : (~rich(X0) | wise(X0)) => ? [X1] : (~patient(X1) & ~quiet(X1)) [rectify 8]
27. ! [X0] : (patient(X0) | (~creative(X0) <=> ~old(X0))) [ennf transformation 1]
31. (~curious(alice) <~> wise(alice)) | ! [X0] : old(X0) [ennf transformation 7]
32. ? [X1] : (~patient(X1) & ~quiet(X1)) | ! [X0] : (rich(X0) & ~wise(X0)) [ennf transformation 23]
33. ! [X0] : (patient(X0) | (curious(X0) <=> ~generous(X0))) [ennf transformation 9]
37. ! [X0] : (patient(X0) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) [nnf transformation 27]
44. ! [X0] : ((((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~wise(X0) & ~strong(X0))) & ((wise(X0) | strong(X0)) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))))) [nnf transformation 4]
45. ! [X0] : ((((creative(X0) | generous(X0)) & (~creative(X0) | ~generous(X0))) | (~wise(X0) & ~strong(X0))) & (wise(X0) | strong(X0) | ((~generous(X0) | creative(X0)) & (~creative(X0) | generous(X0))))) [flattening 44]
46. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 5]
47. ((~wise(alice) | curious(alice)) & (wise(alice) | ~curious(alice))) | ! [X0] : old(X0) [nnf transformation 31]
48. ? [X0] : (~patient(X0) & ~quiet(X0)) | ! [X1] : (rich(X1) & ~wise(X1)) [rectify 32]
49. ? [X0] : (~patient(X0) & ~quiet(X0)) => (~patient(sK2) & ~quiet(sK2)) [choice axiom]
50. (~patient(sK2) & ~quiet(sK2)) | ! [X1] : (rich(X1) & ~wise(X1)) [skolemisation 48,49]
51. ! [X0] : (patient(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) [nnf transformation 33]
55. ! [X0] : (((~curious(X0) & funny(X0)) | (happy(X0) & ~creative(X0))) & ((~happy(X0) | creative(X0)) | (curious(X0) | ~funny(X0)))) [nnf transformation 11]
56. ! [X0] : (((~curious(X0) & funny(X0)) | (happy(X0) & ~creative(X0))) & (~happy(X0) | creative(X0) | curious(X0) | ~funny(X0))) [flattening 55]
66. ~old(X0) | patient(X0) | creative(X0) [cnf transformation 37]
77. ~wise(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 45]
80. ~curious(X0) | ~wise(X0) [cnf transformation 46]
81. curious(X0) | wise(X0) [cnf transformation 46]
84. wise(alice) | ~curious(alice) | old(X0) [cnf transformation 47]
85. ~wise(alice) | curious(alice) | old(X0) [cnf transformation 47]
88. ~patient(sK2) | ~wise(X1) [cnf transformation 50]
91. curious(X0) | patient(X0) | generous(X0) [cnf transformation 51]
97. ~curious(X0) | ~creative(X0) [cnf transformation 56]
114. wise(john) [cnf transformation 21]
131. curious(alice) | old(X0) [subsumption resolution 85,81]
133. 5 <=> ! [X0] : old(X0) [avatar definition]
134. old(X0) <- (5) [avatar component clause 133]
136. 6 <=> curious(alice) [avatar definition]
139. 5 | 6 [avatar split clause 131,136,133]
140. ~curious(alice) | old(X0) [subsumption resolution 84,80]
141. 5 | ~6 [avatar split clause 140,136,133]
146. 8 <=> patient(sK2) [avatar definition]
148. ~patient(sK2) <- (~8) [avatar component clause 146]
151. 9 <=> ! [X1] : ~wise(X1) [avatar definition]
152. ~wise(X1) <- (9) [avatar component clause 151]
153. 9 | ~8 [avatar split clause 88,146,151]
165. 12 <=> wise(john) [avatar definition]
166. wise(john) <- (12) [avatar component clause 165]
210. 12 [avatar split clause 114,165]
214. ~creative(X0) | wise(X0) [resolution 97,81]
216. patient(X0) | creative(X0) <- (5) [resolution 66,134]
217. creative(sK2) <- (5, ~8) [resolution 216,148]
219. wise(sK2) <- (5, ~8) [resolution 217,214]
223. ~generous(sK2) | ~creative(sK2) <- (5, ~8) [resolution 77,219]
233. ~generous(sK2) <- (5, ~8) [subsumption resolution 223,217]
246. patient(X2) | generous(X2) | ~creative(X2) [resolution 91,97]
249. generous(X2) | patient(X2) <- (5) [subsumption resolution 246,216]
252. patient(sK2) <- (5, ~8) [resolution 249,233]
255. $false <- (5, ~8) [subsumption resolution 252,148]
256. ~5 | 8 [avatar contradiction clause 255]
258. $false <- (9, 12) [resolution 152,166]
260. ~9 | ~12 [avatar contradiction clause 258]
261. $false [avatar sat refutation 139,141,153,210,256,260]
% SZS output end Proof for 7509714960623053928557007
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not creative is strong and vice versa.
Everyone who is both quiet and wise is both not calm and calm and vice versa.
If someone is not creative or quiet then fred is both not creative and not kind and vice versa.
Everyone who is both not wise and brave is brave or quiet.
Everyone who is wise is either funny or not old and vice versa.
If fred is both not kind and quiet then paul is either rich or generous and vice versa.
Everyone who is either curious or not quiet is both not quiet and not wise.
Everyone who is not calm or happy is rich and vice versa.
If susan is either quiet or generous then someone is not creative or not generous.
If someone is not quiet then someone is not calm or old and vice versa.
If someone is not happy or not rich then lucy is either happy or not wise and vice versa.
Everyone who is either not brave or not tall is both wise and not kind and vice versa.
Everyone who is both wise and patient is either not wise or funny.
If susan is both old and not curious then someone is humble.
Everyone who is not wise is creative and vice versa.
Everyone who is calm or happy is both not creative and not happy and vice versa.
Someone is either not tall or creative.
Someone is curious or tall.
Fred is both not strong and not quiet.
Someone is both not kind and funny.
Someone is either not generous or not calm.
Someone is either kind or not brave.
Someone is both tall and wise. | Fred is brave. | entailment | (![X]:((tall(X)&~creative(X))<=>strong(X)))&
(![X]:((quiet(X)&wise(X))<=>(~calm(X)&calm(X))))&
((?[X]:((~creative(X)|quiet(X))))<=>((~creative(fred)&~kind(fred))))&
(![X]:((~wise(X)&brave(X))=>(brave(X)|quiet(X))))&
(![X]:(wise(X)<=>(funny(X)<~>~old(X))))&
(((~kind(fred)&quiet(fred)))<=>((rich(paul)<~>generous(paul))))&
(![X]:((curious(X)<~>~quiet(X))=>(~quiet(X)&~wise(X))))&
(![X]:((~calm(X)|happy(X))<=>rich(X)))&
(((quiet(susan)<~>generous(susan)))=>(?[X]:((~creative(X)|~generous(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~calm(X)|old(X)))))&
((?[X]:((~happy(X)|~rich(X))))<=>((happy(lucy)<~>~wise(lucy))))&
(![X]:((~brave(X)<~>~tall(X))<=>(wise(X)&~kind(X))))&
(![X]:((wise(X)&patient(X))=>(~wise(X)<~>funny(X))))&
(((old(susan)&~curious(susan)))=>(?[X]:(humble(X))))&
(![X]:(~wise(X)<=>creative(X)))&
(![X]:((calm(X)|happy(X))<=>(~creative(X)&~happy(X))))&
(?[X]:((~tall(X)<~>creative(X))))&
(?[X]:((curious(X)|tall(X))))&
((~strong(fred)&~quiet(fred)))&
(?[X]:((~kind(X)&funny(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:((kind(X)<~>~brave(X))))&
(?[X]:((tall(X)&wise(X)))) | brave(fred) | [
"p0",
"p2",
"p11",
"p14",
"p18",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8048311449051922900767519
% SZS output start Proof for 8048311449051922900767519
1. ! [X0] : ((~creative(X0) & tall(X0)) <=> strong(X0)) [input p0]
3. ? [X0] : (quiet(X0) | ~creative(X0)) <=> (~kind(fred) & ~creative(fred)) [input p2]
12. ! [X0] : ((~brave(X0) <~> ~tall(X0)) <=> (~kind(X0) & wise(X0))) [input p11]
15. ! [X0] : (~wise(X0) <=> creative(X0)) [input p14]
19. ~quiet(fred) & ~strong(fred) [input p18]
23. ? [X0] : (wise(X0) & tall(X0)) [input p22]
24. ~brave(fred) [input hypothesis]
26. ! [X0] : ((~creative(X0) & tall(X0)) => strong(X0)) [unused predicate definition removal 1]
29. ! [X0] : (strong(X0) | (creative(X0) | ~tall(X0))) [ennf transformation 26]
30. ! [X0] : (strong(X0) | creative(X0) | ~tall(X0)) [flattening 29]
37. (? [X0] : (quiet(X0) | ~creative(X0)) | (kind(fred) | creative(fred))) & ((~kind(fred) & ~creative(fred)) | ! [X0] : (~quiet(X0) & creative(X0))) [nnf transformation 3]
38. (? [X0] : (quiet(X0) | ~creative(X0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X0] : (~quiet(X0) & creative(X0))) [flattening 37]
39. (? [X0] : (quiet(X0) | ~creative(X0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X1] : (~quiet(X1) & creative(X1))) [rectify 38]
40. ? [X0] : (quiet(X0) | ~creative(X0)) => (quiet(sK0) | ~creative(sK0)) [choice axiom]
41. ((quiet(sK0) | ~creative(sK0)) | kind(fred) | creative(fred)) & ((~kind(fred) & ~creative(fred)) | ! [X1] : (~quiet(X1) & creative(X1))) [skolemisation 39,40]
60. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | (kind(X0) | ~wise(X0))) & ((~kind(X0) & wise(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [nnf transformation 12]
61. ! [X0] : ((((tall(X0) | brave(X0)) & (~tall(X0) | ~brave(X0))) | kind(X0) | ~wise(X0)) & ((~kind(X0) & wise(X0)) | ((~brave(X0) | tall(X0)) & (~tall(X0) | brave(X0))))) [flattening 60]
62. ! [X0] : ((~wise(X0) | ~creative(X0)) & (creative(X0) | wise(X0))) [nnf transformation 15]
78. ? [X0] : (wise(X0) & tall(X0)) => (wise(sK10) & tall(sK10)) [choice axiom]
79. wise(sK10) & tall(sK10) [skolemisation 23,78]
80. ~tall(X0) | creative(X0) | strong(X0) [cnf transformation 30]
85. ~creative(fred) | creative(X1) [cnf transformation 41]
87. ~kind(fred) | creative(X1) [cnf transformation 41]
124. ~wise(X0) | brave(X0) | kind(X0) | tall(X0) [cnf transformation 61]
125. wise(X0) | creative(X0) [cnf transformation 62]
126. ~wise(X0) | ~creative(X0) [cnf transformation 62]
135. ~strong(fred) [cnf transformation 19]
144. wise(sK10) [cnf transformation 79]
145. ~brave(fred) [cnf transformation 24]
151. 1 <=> creative(fred) [avatar definition]
152. ~creative(fred) <- (~1) [avatar component clause 151]
155. 2 <=> kind(fred) [avatar definition]
156. ~kind(fred) <- (~2) [avatar component clause 155]
172. 6 <=> ! [X1] : creative(X1) [avatar definition]
173. creative(X1) <- (6) [avatar component clause 172]
174. 6 | ~2 [avatar split clause 87,155,172]
176. 6 | ~1 [avatar split clause 85,151,172]
306. ~creative(sK10) [resolution 126,144]
343. brave(X0) | kind(X0) | tall(X0) | creative(X0) [resolution 124,125]
344. kind(fred) | tall(fred) | creative(fred) [resolution 343,145]
352. tall(fred) | creative(fred) <- (~2) [subsumption resolution 344,156]
353. tall(fred) <- (~1, ~2) [subsumption resolution 352,152]
376. creative(fred) | strong(fred) <- (~1, ~2) [resolution 353,80]
378. strong(fred) <- (~1, ~2) [subsumption resolution 376,152]
379. $false <- (~1, ~2) [subsumption resolution 378,135]
380. 1 | 2 [avatar contradiction clause 379]
395. $false <- (6) [resolution 173,306]
396. ~6 [avatar contradiction clause 395]
402. $false [avatar sat refutation 174,176,380,396]
% SZS output end Proof for 8048311449051922900767519
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not happy or curious is both quiet and not creative.
If fred is either not kind or not rich then alice is either not tall or patient.
Everyone who is both not tall and calm is brave or not rich and vice versa.
If paul is tall then alice is both curious and wise and vice versa.
Everyone who is tall or humble is kind or creative and vice versa.
Everyone who is old is either rich or funny and vice versa.
Everyone who is both not happy and brave is wise or not tall.
Everyone who is both not kind and not generous is both creative and not wise.
Everyone who is both generous and humble is both old and not brave.
Everyone who is either not curious or tall is not calm or calm.
Everyone who is funny is either calm or brave and vice versa.
If someone is both not quiet and tall then someone is calm.
Everyone who is curious or not funny is creative or not happy and vice versa.
If someone is either calm or not kind then alice is both not generous and old.
If someone is not calm or not old then someone is patient.
Someone is either not rich or creative.
Paul is not rich.
John is both not creative and not curious.
Paul is brave or not happy.
Lucy is both not quiet and not brave.
Someone is either not brave or not generous.
Fred is generous.
John is either not tall or generous. | Alice is creative. | neutral | (![X]:((~happy(X)|curious(X))=>(quiet(X)&~creative(X))))&
(((~kind(fred)<~>~rich(fred)))=>((~tall(alice)<~>patient(alice))))&
(![X]:((~tall(X)&calm(X))<=>(brave(X)|~rich(X))))&
((tall(paul))<=>((curious(alice)&wise(alice))))&
(![X]:((tall(X)|humble(X))<=>(kind(X)|creative(X))))&
(![X]:(old(X)<=>(rich(X)<~>funny(X))))&
(![X]:((~happy(X)&brave(X))=>(wise(X)|~tall(X))))&
(![X]:((~kind(X)&~generous(X))=>(creative(X)&~wise(X))))&
(![X]:((generous(X)&humble(X))=>(old(X)&~brave(X))))&
(![X]:((~curious(X)<~>tall(X))=>(~calm(X)|calm(X))))&
(![X]:(funny(X)<=>(calm(X)<~>brave(X))))&
((?[X]:((~quiet(X)&tall(X))))=>(?[X]:(calm(X))))&
(![X]:((curious(X)|~funny(X))<=>(creative(X)|~happy(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>((~generous(alice)&old(alice))))&
((?[X]:((~calm(X)|~old(X))))=>(?[X]:(patient(X))))&
(?[X]:((~rich(X)<~>creative(X))))&
(~rich(paul))&
((~creative(john)&~curious(john)))&
((brave(paul)|~happy(paul)))&
((~quiet(lucy)&~brave(lucy)))&
(?[X]:((~brave(X)<~>~generous(X))))&
(generous(fred))&
((~tall(john)<~>generous(john))) | creative(alice) | [] | null | 0 |
Everyone who is not curious or generous is strong or quiet and vice versa.
If someone is both not old and kind then john is wise.
Everyone who is not rich is rich or not brave and vice versa.
Everyone who is either not tall or not kind is both not tall and not humble and vice versa.
Everyone who is either curious or not kind is both brave and not strong and vice versa.
If alice is both old and generous then someone is generous and vice versa.
Everyone who is either not funny or not old is not happy and vice versa.
If someone is either not brave or not wise then lucy is not kind or brave.
If john is not old or quiet then paul is not wise or not humble and vice versa.
If someone is either happy or patient then alice is not humble or calm.
Everyone who is not humble or kind is both not wise and strong.
If susan is both strong and brave then alice is humble and vice versa.
Everyone who is patient is both not creative and not humble and vice versa.
Everyone who is both patient and strong is both brave and rich.
If paul is either creative or calm then mary is both not humble and brave and vice versa.
If someone is either creative or rich then lucy is either not generous or generous and vice versa.
Someone is not creative.
Someone is quiet or humble.
Mary is either calm or tall.
Someone is not happy.
Someone is both not humble and tall.
Someone is either not quiet or not humble.
Someone is not funny.
Lucy is both not funny and not happy. | Alice is humble. | contradiction | (![X]:((~curious(X)|generous(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~old(X)&kind(X))))=>(wise(john)))&
(![X]:(~rich(X)<=>(rich(X)|~brave(X))))&
(![X]:((~tall(X)<~>~kind(X))<=>(~tall(X)&~humble(X))))&
(![X]:((curious(X)<~>~kind(X))<=>(brave(X)&~strong(X))))&
(((old(alice)&generous(alice)))<=>(?[X]:(generous(X))))&
(![X]:((~funny(X)<~>~old(X))<=>~happy(X)))&
((?[X]:((~brave(X)<~>~wise(X))))=>((~kind(lucy)|brave(lucy))))&
(((~old(john)|quiet(john)))<=>((~wise(paul)|~humble(paul))))&
((?[X]:((happy(X)<~>patient(X))))=>((~humble(alice)|calm(alice))))&
(![X]:((~humble(X)|kind(X))=>(~wise(X)&strong(X))))&
(((strong(susan)&brave(susan)))<=>(humble(alice)))&
(![X]:(patient(X)<=>(~creative(X)&~humble(X))))&
(![X]:((patient(X)&strong(X))=>(brave(X)&rich(X))))&
(((creative(paul)<~>calm(paul)))<=>((~humble(mary)&brave(mary))))&
((?[X]:((creative(X)<~>rich(X))))<=>((~generous(lucy)<~>generous(lucy))))&
(?[X]:(~creative(X)))&
(?[X]:((quiet(X)|humble(X))))&
((calm(mary)<~>tall(mary)))&
(?[X]:(~happy(X)))&
(?[X]:((~humble(X)&tall(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:(~funny(X)))&
((~funny(lucy)&~happy(lucy))) | humble(alice) | [
"p2",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8574149310139035754923849
% SZS output start Proof for 8574149310139035754923849
3. ! [X0] : (~rich(X0) <=> (~brave(X0) | rich(X0))) [input p2]
12. (brave(susan) & strong(susan)) <=> humble(alice) [input p11]
25. humble(alice) [input hypothesis]
36. ! [X0] : ((~rich(X0) | (brave(X0) & ~rich(X0))) & ((~brave(X0) | rich(X0)) | rich(X0))) [nnf transformation 3]
37. ! [X0] : ((~rich(X0) | (brave(X0) & ~rich(X0))) & (~brave(X0) | rich(X0) | rich(X0))) [flattening 36]
52. ((brave(susan) & strong(susan)) | ~humble(alice)) & (humble(alice) | (~brave(susan) | ~strong(susan))) [nnf transformation 12]
53. ((brave(susan) & strong(susan)) | ~humble(alice)) & (humble(alice) | ~brave(susan) | ~strong(susan)) [flattening 52]
81. ~brave(X0) | rich(X0) | rich(X0) [cnf transformation 37]
82. ~rich(X0) | ~rich(X0) [cnf transformation 37]
117. brave(susan) | ~humble(alice) [cnf transformation 53]
149. humble(alice) [cnf transformation 25]
156. ~brave(X0) | rich(X0) [duplicate literal removal 81]
157. ~rich(X0) [duplicate literal removal 82]
166. ~brave(X0) [subsumption resolution 156,157]
221. 14 <=> humble(alice) [avatar definition]
233. ~humble(alice) [subsumption resolution 117,166]
234. ~14 [avatar split clause 233,221]
300. 14 [avatar split clause 149,221]
301. $false [avatar sat refutation 234,300]
% SZS output end Proof for 8574149310139035754923849
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not curious or quiet is either not old or not tall.
If lucy is either not tall or strong then someone is either not strong or not creative and vice versa.
Everyone who is not calm is old or kind and vice versa.
Everyone who is both quiet and happy is curious or creative.
If someone is not happy then someone is patient or not humble and vice versa.
If mary is strong then susan is both calm and not generous and vice versa.
Everyone who is both funny and not wise is not creative or generous and vice versa.
Everyone who is either not brave or happy is either curious or strong and vice versa.
Everyone who is not generous or kind is both tall and not calm and vice versa.
If lucy is funny or tall then john is not kind or funny.
If someone is either rich or wise then someone is not brave and vice versa.
Everyone who is curious is both wise and kind and vice versa.
If someone is not quiet then someone is both rich and quiet and vice versa.
If someone is either not calm or not quiet then someone is either tall or creative.
Everyone who is calm is both curious and calm.
If fred is not quiet or not humble then someone is either curious or happy.
Someone is rich.
Someone is both not strong and not generous.
Lucy is humble or not kind.
Someone is either not generous or not tall.
Someone is not curious or not creative.
Paul is patient.
Mary is either not funny or patient. | John is funny. | neutral | (![X]:((~curious(X)<~>quiet(X))=>(~old(X)<~>~tall(X))))&
(((~tall(lucy)<~>strong(lucy)))<=>(?[X]:((~strong(X)<~>~creative(X)))))&
(![X]:(~calm(X)<=>(old(X)|kind(X))))&
(![X]:((quiet(X)&happy(X))=>(curious(X)|creative(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((patient(X)|~humble(X)))))&
((strong(mary))<=>((calm(susan)&~generous(susan))))&
(![X]:((funny(X)&~wise(X))<=>(~creative(X)|generous(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(curious(X)<~>strong(X))))&
(![X]:((~generous(X)|kind(X))<=>(tall(X)&~calm(X))))&
(((funny(lucy)|tall(lucy)))=>((~kind(john)|funny(john))))&
((?[X]:((rich(X)<~>wise(X))))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)<=>(wise(X)&kind(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((rich(X)&quiet(X)))))&
((?[X]:((~calm(X)<~>~quiet(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:(calm(X)=>(curious(X)&calm(X))))&
(((~quiet(fred)|~humble(fred)))=>(?[X]:((curious(X)<~>happy(X)))))&
(?[X]:(rich(X)))&
(?[X]:((~strong(X)&~generous(X))))&
((humble(lucy)|~kind(lucy)))&
(?[X]:((~generous(X)<~>~tall(X))))&
(?[X]:((~curious(X)|~creative(X))))&
(patient(paul))&
((~funny(mary)<~>patient(mary))) | funny(john) | [] | null | 0 |
Everyone who is quiet is either brave or not creative and vice versa.
Everyone who is both calm and not humble is not wise or not calm.
Everyone who is not tall is both not creative and not curious and vice versa.
Everyone who is not curious is not funny or tall.
Everyone who is both patient and not humble is not strong and vice versa.
Everyone who is creative is not wise and vice versa.
Everyone who is generous is wise or not funny.
If fred is not strong or not calm then lucy is strong or not rich.
Everyone who is either funny or creative is not humble.
Everyone who is either not happy or generous is old or not patient and vice versa.
If susan is old or not calm then someone is not rich or generous and vice versa.
If paul is either happy or patient then john is generous.
Everyone who is either happy or kind is both quiet and not funny and vice versa.
Everyone who is wise or kind is either generous or not wise.
If fred is kind then someone is either funny or not brave and vice versa.
Everyone who is either curious or happy is quiet and vice versa.
Susan is both happy and humble.
Someone is both not brave and old.
Paul is both funny and not quiet.
Lucy is not happy or wise.
Someone is either curious or not kind.
Someone is not generous.
Lucy is both not generous and not old.
Susan is both kind and brave. | Lucy is not patient. | entailment | (![X]:(quiet(X)<=>(brave(X)<~>~creative(X))))&
(![X]:((calm(X)&~humble(X))=>(~wise(X)|~calm(X))))&
(![X]:(~tall(X)<=>(~creative(X)&~curious(X))))&
(![X]:(~curious(X)=>(~funny(X)|tall(X))))&
(![X]:((patient(X)&~humble(X))<=>~strong(X)))&
(![X]:(creative(X)<=>~wise(X)))&
(![X]:(generous(X)=>(wise(X)|~funny(X))))&
(((~strong(fred)|~calm(fred)))=>((strong(lucy)|~rich(lucy))))&
(![X]:((funny(X)<~>creative(X))=>~humble(X)))&
(![X]:((~happy(X)<~>generous(X))<=>(old(X)|~patient(X))))&
(((old(susan)|~calm(susan)))<=>(?[X]:((~rich(X)|generous(X)))))&
(((happy(paul)<~>patient(paul)))=>(generous(john)))&
(![X]:((happy(X)<~>kind(X))<=>(quiet(X)&~funny(X))))&
(![X]:((wise(X)|kind(X))=>(generous(X)<~>~wise(X))))&
((kind(fred))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((curious(X)<~>happy(X))<=>quiet(X)))&
((happy(susan)&humble(susan)))&
(?[X]:((~brave(X)&old(X))))&
((funny(paul)&~quiet(paul)))&
((~happy(lucy)|wise(lucy)))&
(?[X]:((curious(X)<~>~kind(X))))&
(?[X]:(~generous(X)))&
((~generous(lucy)&~old(lucy)))&
((kind(susan)&brave(susan))) | ~patient(lucy) | [
"p5",
"p9",
"p13",
"p19",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5480315898407912999903467
% SZS output start Proof for 5480315898407912999903467
6. ! [X0] : (creative(X0) <=> ~wise(X0)) [input p5]
10. ! [X0] : ((~happy(X0) <~> generous(X0)) <=> (~patient(X0) | old(X0))) [input p9]
14. ! [X0] : ((kind(X0) | wise(X0)) => (generous(X0) <~> ~wise(X0))) [input p13]
20. wise(lucy) | ~happy(lucy) [input p19]
23. ~old(lucy) & ~generous(lucy) [input p22]
25. patient(lucy) [input hypothesis]
42. ! [X0] : ((generous(X0) <~> ~wise(X0)) | (~kind(X0) & ~wise(X0))) [ennf transformation 14]
44. ! [X0] : ((creative(X0) | wise(X0)) & (~wise(X0) | ~creative(X0))) [nnf transformation 6]
46. ! [X0] : ((((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (patient(X0) & ~old(X0))) & ((~patient(X0) | old(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))))) [nnf transformation 10]
47. ! [X0] : ((((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (patient(X0) & ~old(X0))) & (~patient(X0) | old(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))))) [flattening 46]
56. ! [X0] : (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (~kind(X0) & ~wise(X0))) [nnf transformation 42]
77. ~wise(X0) | ~creative(X0) [cnf transformation 44]
78. wise(X0) | creative(X0) [cnf transformation 44]
84. ~patient(X0) | old(X0) | generous(X0) | happy(X0) [cnf transformation 47]
102. ~wise(X0) | generous(X0) | ~wise(X0) [cnf transformation 56]
120. wise(lucy) | ~happy(lucy) [cnf transformation 20]
124. ~generous(lucy) [cnf transformation 23]
125. ~old(lucy) [cnf transformation 23]
128. patient(lucy) [cnf transformation 25]
129. ~wise(X0) | generous(X0) [duplicate literal removal 102]
212. 19 <=> happy(lucy) [avatar definition]
216. 20 <=> wise(lucy) [avatar definition]
218. wise(lucy) <- (20) [avatar component clause 216]
219. ~19 | 20 [avatar split clause 120,216,212]
231. generous(X0) | creative(X0) [resolution 129,78]
233. creative(lucy) [resolution 231,124]
425. old(lucy) | generous(lucy) | happy(lucy) [resolution 84,128]
427. generous(lucy) | happy(lucy) [subsumption resolution 425,125]
428. happy(lucy) [subsumption resolution 427,124]
431. 19 [avatar split clause 428,212]
451. ~creative(lucy) <- (20) [resolution 218,77]
463. $false <- (20) [subsumption resolution 451,233]
464. ~20 [avatar contradiction clause 463]
465. $false [avatar sat refutation 219,431,464]
% SZS output end Proof for 5480315898407912999903467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not brave is both not tall and creative.
Everyone who is strong is funny.
Everyone who is both quiet and not humble is old and vice versa.
Everyone who is not brave is either not rich or wise.
If someone is happy or funny then someone is not happy and vice versa.
If john is not wise or not happy then susan is tall.
Everyone who is both not wise and rich is not calm.
Everyone who is either not funny or funny is both not kind and not tall.
If paul is not happy or old then someone is either not patient or not happy.
Everyone who is both humble and not quiet is both not funny and not calm and vice versa.
Everyone who is not humble is either not quiet or old and vice versa.
If someone is not quiet then someone is either patient or not quiet.
If someone is kind or not quiet then paul is quiet or not quiet and vice versa.
Everyone who is either not strong or not tall is not rich or quiet and vice versa.
If someone is both not rich and tall then someone is either not creative or not generous and vice versa.
Someone is both not patient and rich.
Mary is creative.
Someone is not creative.
Paul is not wise.
Lucy is old.
Someone is both strong and not quiet.
Someone is both not old and quiet. | Paul is funny. | entailment | (![X]:((~calm(X)<~>~brave(X))=>(~tall(X)&creative(X))))&
(![X]:(strong(X)=>funny(X)))&
(![X]:((quiet(X)&~humble(X))<=>old(X)))&
(![X]:(~brave(X)=>(~rich(X)<~>wise(X))))&
((?[X]:((happy(X)|funny(X))))<=>(?[X]:(~happy(X))))&
(((~wise(john)|~happy(john)))=>(tall(susan)))&
(![X]:((~wise(X)&rich(X))=>~calm(X)))&
(![X]:((~funny(X)<~>funny(X))=>(~kind(X)&~tall(X))))&
(((~happy(paul)|old(paul)))=>(?[X]:((~patient(X)<~>~happy(X)))))&
(![X]:((humble(X)&~quiet(X))<=>(~funny(X)&~calm(X))))&
(![X]:(~humble(X)<=>(~quiet(X)<~>old(X))))&
((?[X]:(~quiet(X)))=>(?[X]:((patient(X)<~>~quiet(X)))))&
((?[X]:((kind(X)|~quiet(X))))<=>((quiet(paul)|~quiet(paul))))&
(![X]:((~strong(X)<~>~tall(X))<=>(~rich(X)|quiet(X))))&
((?[X]:((~rich(X)&tall(X))))<=>(?[X]:((~creative(X)<~>~generous(X)))))&
(?[X]:((~patient(X)&rich(X))))&
(creative(mary))&
(?[X]:(~creative(X)))&
(~wise(paul))&
(old(lucy))&
(?[X]:((strong(X)&~quiet(X))))&
(?[X]:((~old(X)&quiet(X)))) | funny(paul) | [
"p1",
"p2",
"p6",
"p7",
"p9",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8442191326080090100878585
% SZS output start Proof for 8442191326080090100878585
2. ! [X0] : (strong(X0) => funny(X0)) [input p1]
3. ! [X0] : ((~humble(X0) & quiet(X0)) <=> old(X0)) [input p2]
7. ! [X0] : ((rich(X0) & ~wise(X0)) => ~calm(X0)) [input p6]
8. ! [X0] : ((~funny(X0) <~> funny(X0)) => (~tall(X0) & ~kind(X0))) [input p7]
10. ! [X0] : ((~quiet(X0) & humble(X0)) <=> (~calm(X0) & ~funny(X0))) [input p9]
11. ! [X0] : (~humble(X0) <=> (~quiet(X0) <~> old(X0))) [input p10]
14. ! [X0] : ((~strong(X0) <~> ~tall(X0)) <=> (quiet(X0) | ~rich(X0))) [input p13]
19. ~wise(paul) [input p18]
23. ~funny(paul) [input hypothesis]
28. ! [X0] : (funny(X0) | ~strong(X0)) [ennf transformation 2]
31. ! [X0] : (~calm(X0) | (~rich(X0) | wise(X0))) [ennf transformation 7]
32. ! [X0] : (~calm(X0) | ~rich(X0) | wise(X0)) [flattening 31]
33. ! [X0] : ((~tall(X0) & ~kind(X0)) | (~funny(X0) <=> funny(X0))) [ennf transformation 8]
37. ! [X0] : (((~humble(X0) & quiet(X0)) | ~old(X0)) & (old(X0) | (humble(X0) | ~quiet(X0)))) [nnf transformation 3]
38. ! [X0] : (((~humble(X0) & quiet(X0)) | ~old(X0)) & (old(X0) | humble(X0) | ~quiet(X0))) [flattening 37]
45. ! [X0] : ((~tall(X0) & ~kind(X0)) | ((~funny(X0) | ~funny(X0)) & (funny(X0) | funny(X0)))) [nnf transformation 33]
49. ! [X0] : (((~quiet(X0) & humble(X0)) | (calm(X0) | funny(X0))) & ((~calm(X0) & ~funny(X0)) | (quiet(X0) | ~humble(X0)))) [nnf transformation 10]
50. ! [X0] : (((~quiet(X0) & humble(X0)) | calm(X0) | funny(X0)) & ((~calm(X0) & ~funny(X0)) | quiet(X0) | ~humble(X0))) [flattening 49]
51. ! [X0] : ((~humble(X0) | ((~quiet(X0) | ~old(X0)) & (old(X0) | quiet(X0)))) & (((~old(X0) | quiet(X0)) & (old(X0) | ~quiet(X0))) | humble(X0))) [nnf transformation 11]
61. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | (~quiet(X0) & rich(X0))) & ((quiet(X0) | ~rich(X0)) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [nnf transformation 14]
62. ! [X0] : ((((tall(X0) | strong(X0)) & (~tall(X0) | ~strong(X0))) | (~quiet(X0) & rich(X0))) & (quiet(X0) | ~rich(X0) | ((~strong(X0) | tall(X0)) & (~tall(X0) | strong(X0))))) [flattening 61]
80. ~strong(X0) | funny(X0) [cnf transformation 28]
82. ~old(X0) | quiet(X0) [cnf transformation 38]
91. ~rich(X0) | ~calm(X0) | wise(X0) [cnf transformation 32]
94. ~tall(X0) | funny(X0) | funny(X0) [cnf transformation 45]
95. ~tall(X0) | ~funny(X0) | ~funny(X0) [cnf transformation 45]
102. humble(X0) | calm(X0) | funny(X0) [cnf transformation 50]
103. ~quiet(X0) | calm(X0) | funny(X0) [cnf transformation 50]
106. ~humble(X0) | old(X0) | quiet(X0) [cnf transformation 51]
118. tall(X0) | strong(X0) | rich(X0) [cnf transformation 62]
130. ~wise(paul) [cnf transformation 19]
136. ~funny(paul) [cnf transformation 23]
139. ~tall(X0) | funny(X0) [duplicate literal removal 94]
140. ~funny(X0) | ~tall(X0) [duplicate literal removal 95]
179. ~tall(X0) [subsumption resolution 139,140]
201. ~humble(X0) | quiet(X0) [subsumption resolution 106,82]
228. rich(X0) | strong(X0) [subsumption resolution 118,179]
282. ~calm(X0) | wise(X0) | strong(X0) [resolution 91,228]
299. calm(X2) | funny(X2) | quiet(X2) [resolution 102,201]
300. funny(X2) | calm(X2) [subsumption resolution 299,103]
305. calm(paul) [resolution 300,136]
332. 31 <=> strong(paul) [avatar definition]
334. strong(paul) <- (31) [avatar component clause 332]
346. wise(paul) | strong(paul) [resolution 282,305]
347. funny(paul) <- (31) [resolution 334,80]
348. $false <- (31) [subsumption resolution 347,136]
349. ~31 [avatar contradiction clause 348]
350. strong(paul) [subsumption resolution 346,130]
351. 31 [avatar split clause 350,332]
352. $false [avatar sat refutation 349,351]
% SZS output end Proof for 8442191326080090100878585
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient and not creative is not tall or not humble.
Everyone who is not funny or old is happy or not funny and vice versa.
Everyone who is not patient is brave or strong and vice versa.
Everyone who is either rich or wise is either not brave or not generous.
If john is not humble then john is not calm and vice versa.
Everyone who is not kind or not quiet is wise or not tall.
If someone is not tall or not wise then lucy is either not strong or rich.
If john is not rich then paul is either funny or patient.
If someone is both not curious and not wise then susan is not quiet and vice versa.
Everyone who is both not rich and not kind is not wise and vice versa.
Everyone who is both not wise and not kind is happy and vice versa.
Everyone who is not tall or not wise is generous and vice versa.
Everyone who is either not happy or kind is humble or not quiet and vice versa.
Everyone who is brave is humble or not curious.
Everyone who is not rich or not curious is wise or not tall.
If mary is either not happy or not creative then lucy is not calm and vice versa.
John is not creative.
Someone is either not old or happy.
Fred is tall or not curious.
John is brave.
Someone is not curious.
Someone is either patient or kind.
Someone is patient or creative.
Lucy is not brave or not calm. | Susan is not funny. | neutral | (![X]:((~patient(X)&~creative(X))=>(~tall(X)|~humble(X))))&
(![X]:((~funny(X)|old(X))<=>(happy(X)|~funny(X))))&
(![X]:(~patient(X)<=>(brave(X)|strong(X))))&
(![X]:((rich(X)<~>wise(X))=>(~brave(X)<~>~generous(X))))&
((~humble(john))<=>(~calm(john)))&
(![X]:((~kind(X)|~quiet(X))=>(wise(X)|~tall(X))))&
((?[X]:((~tall(X)|~wise(X))))=>((~strong(lucy)<~>rich(lucy))))&
((~rich(john))=>((funny(paul)<~>patient(paul))))&
((?[X]:((~curious(X)&~wise(X))))<=>(~quiet(susan)))&
(![X]:((~rich(X)&~kind(X))<=>~wise(X)))&
(![X]:((~wise(X)&~kind(X))<=>happy(X)))&
(![X]:((~tall(X)|~wise(X))<=>generous(X)))&
(![X]:((~happy(X)<~>kind(X))<=>(humble(X)|~quiet(X))))&
(![X]:(brave(X)=>(humble(X)|~curious(X))))&
(![X]:((~rich(X)|~curious(X))=>(wise(X)|~tall(X))))&
(((~happy(mary)<~>~creative(mary)))<=>(~calm(lucy)))&
(~creative(john))&
(?[X]:((~old(X)<~>happy(X))))&
((tall(fred)|~curious(fred)))&
(brave(john))&
(?[X]:(~curious(X)))&
(?[X]:((patient(X)<~>kind(X))))&
(?[X]:((patient(X)|creative(X))))&
((~brave(lucy)|~calm(lucy))) | ~funny(susan) | [] | null | 0 |
If alice is strong then someone is both wise and quiet. If john is creative then someone is both wise and quiet and vice versa. If someone is both happy and old then someone is wise and vice versa. Everyone who is generous is either old or not calm and vice versa. Everyone who is not old is both quiet and strong. If someone is either rich or kind then john is either kind or wise. Everyone who is patient or not happy is calm and vice versa. If alice is calm then someone is wise. Everyone who is rich or creative is happy. If someone is either creative or not generous then mary is either not curious or not creative and vice versa. Everyone who is brave or rich is not quiet. Everyone who is rich or not wise is either not strong or tall and vice versa. Everyone who is strong is not generous or brave and vice versa. Everyone who is both not old and curious is not quiet or rich and vice versa. If someone is not old or not calm then alice is not quiet or creative and vice versa. If someone is either not generous or kind then alice is curious or not kind and vice versa. Someone is not brave. Paul is both not patient and not strong. Someone is either kind or not calm. Susan is brave or not old. Someone is not generous or old. Someone is both not rich and not patient. John is both creative and not tall. | Alice is not happy. | contradiction | ((strong(alice))=>(?[X]:((wise(X)&quiet(X)))))&
((creative(john))<=>(?[X]:((wise(X)&quiet(X)))))&
((?[X]:((happy(X)&old(X))))<=>(?[X]:(wise(X))))&
(![X]:(generous(X)<=>(old(X)<~>~calm(X))))&
(![X]:(~old(X)=>(quiet(X)&strong(X))))&
((?[X]:((rich(X)<~>kind(X))))=>((kind(john)<~>wise(john))))&
(![X]:((patient(X)|~happy(X))<=>calm(X)))&
((calm(alice))=>(?[X]:(wise(X))))&
(![X]:((rich(X)|creative(X))=>happy(X)))&
((?[X]:((creative(X)<~>~generous(X))))<=>((~curious(mary)<~>~creative(mary))))&
(![X]:((brave(X)|rich(X))=>~quiet(X)))&
(![X]:((rich(X)|~wise(X))<=>(~strong(X)<~>tall(X))))&
(![X]:(strong(X)<=>(~generous(X)|brave(X))))&
(![X]:((~old(X)&curious(X))<=>(~quiet(X)|rich(X))))&
((?[X]:((~old(X)|~calm(X))))<=>((~quiet(alice)|creative(alice))))&
((?[X]:((~generous(X)<~>kind(X))))<=>((curious(alice)|~kind(alice))))&
(?[X]:(~brave(X)))&
((~patient(paul)&~strong(paul)))&
(?[X]:((kind(X)<~>~calm(X))))&
((brave(susan)|~old(susan)))&
(?[X]:((~generous(X)|old(X))))&
(?[X]:((~rich(X)&~patient(X))))&
((creative(john)&~tall(john))) | ~happy(alice) | [
"p4",
"p8",
"p10",
"p13",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 473904149968672462453873
% SZS output start Proof for 473904149968672462453873
5. ! [X0] : (~old(X0) => (strong(X0) & quiet(X0))) [input p4]
9. ! [X0] : ((creative(X0) | rich(X0)) => happy(X0)) [input p8]
11. ! [X0] : ((rich(X0) | brave(X0)) => ~quiet(X0)) [input p10]
14. ! [X0] : ((curious(X0) & ~old(X0)) <=> (rich(X0) | ~quiet(X0))) [input p13]
15. ? [X0] : (~calm(X0) | ~old(X0)) <=> (creative(alice) | ~quiet(alice)) [input p14]
20. ~old(susan) | brave(susan) [input p19]
24. ~happy(alice) [input hypothesis]
27. ! [X0] : ((strong(X0) & quiet(X0)) | old(X0)) [ennf transformation 5]
30. ! [X0] : (happy(X0) | (~creative(X0) & ~rich(X0))) [ennf transformation 9]
31. ! [X0] : (~quiet(X0) | (~rich(X0) & ~brave(X0))) [ennf transformation 11]
57. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & ((rich(X0) | ~quiet(X0)) | (~curious(X0) | old(X0)))) [nnf transformation 14]
58. ! [X0] : (((curious(X0) & ~old(X0)) | (~rich(X0) & quiet(X0))) & (rich(X0) | ~quiet(X0) | ~curious(X0) | old(X0))) [flattening 57]
59. (? [X0] : (~calm(X0) | ~old(X0)) | (~creative(alice) & quiet(alice))) & ((creative(alice) | ~quiet(alice)) | ! [X0] : (calm(X0) & old(X0))) [nnf transformation 15]
60. (? [X0] : (~calm(X0) | ~old(X0)) | (~creative(alice) & quiet(alice))) & (creative(alice) | ~quiet(alice) | ! [X0] : (calm(X0) & old(X0))) [flattening 59]
61. (? [X0] : (~calm(X0) | ~old(X0)) | (~creative(alice) & quiet(alice))) & (creative(alice) | ~quiet(alice) | ! [X1] : (calm(X1) & old(X1))) [rectify 60]
62. ? [X0] : (~calm(X0) | ~old(X0)) => (~calm(sK6) | ~old(sK6)) [choice axiom]
63. ((~calm(sK6) | ~old(sK6)) | (~creative(alice) & quiet(alice))) & (creative(alice) | ~quiet(alice) | ! [X1] : (calm(X1) & old(X1))) [skolemisation 61,62]
90. old(X0) | quiet(X0) [cnf transformation 27]
101. ~creative(X0) | happy(X0) [cnf transformation 30]
110. ~brave(X0) | ~quiet(X0) [cnf transformation 31]
122. ~old(X0) | quiet(X0) [cnf transformation 58]
126. creative(alice) | ~quiet(alice) | old(X1) [cnf transformation 63]
141. ~old(susan) | brave(susan) [cnf transformation 20]
147. ~happy(alice) [cnf transformation 24]
258. quiet(X0) [subsumption resolution 122,90]
261. 25 <=> creative(alice) [avatar definition]
262. creative(alice) <- (25) [avatar component clause 261]
278. creative(alice) | old(X1) [subsumption resolution 126,258]
280. 29 <=> ! [X1] : old(X1) [avatar definition]
281. old(X1) <- (29) [avatar component clause 280]
282. 29 | 25 [avatar split clause 278,261,280]
322. 38 <=> brave(susan) [avatar definition]
324. brave(susan) <- (38) [avatar component clause 322]
326. 39 <=> old(susan) [avatar definition]
328. ~old(susan) <- (~39) [avatar component clause 326]
329. 38 | ~39 [avatar split clause 141,326,322]
352. happy(alice) <- (25) [resolution 101,262]
353. $false <- (25) [subsumption resolution 352,147]
354. ~25 [avatar contradiction clause 353]
358. $false <- (29, ~39) [resolution 281,328]
359. ~29 | 39 [avatar contradiction clause 358]
361. ~quiet(susan) <- (38) [resolution 110,324]
362. $false <- (38) [subsumption resolution 361,258]
363. ~38 [avatar contradiction clause 362]
364. $false [avatar sat refutation 282,329,354,359,363]
% SZS output end Proof for 473904149968672462453873
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If alice is either not humble or not funny then someone is calm and vice versa.
Everyone who is not old is either not calm or not brave and vice versa.
If someone is not patient or rich then someone is both not creative and funny.
If fred is either not rich or generous then someone is kind and vice versa.
Everyone who is either not strong or not humble is either rich or not quiet.
Everyone who is not happy is both not rich and humble and vice versa.
Everyone who is both kind and not brave is either calm or not kind.
Everyone who is both not tall and not creative is not funny and vice versa.
Everyone who is tall or not calm is old or quiet and vice versa.
Everyone who is either not calm or curious is both curious and old and vice versa.
Everyone who is both curious and generous is both patient and quiet and vice versa.
Everyone who is either strong or not calm is brave or wise and vice versa.
Everyone who is not strong or not wise is both not kind and not patient.
If someone is both not humble and brave then someone is either calm or creative.
Everyone who is either brave or not strong is not strong or tall.
If someone is both not wise and not old then john is wise.
Lucy is both not kind and not old.
Someone is both brave and generous.
Paul is not patient or strong.
Alice is humble.
Alice is either not wise or not patient.
Susan is either not old or not creative.
Someone is both strong and old.
Someone is funny. | Susan is not brave. | neutral | (((~humble(alice)<~>~funny(alice)))<=>(?[X]:(calm(X))))&
(![X]:(~old(X)<=>(~calm(X)<~>~brave(X))))&
((?[X]:((~patient(X)|rich(X))))=>(?[X]:((~creative(X)&funny(X)))))&
(((~rich(fred)<~>generous(fred)))<=>(?[X]:(kind(X))))&
(![X]:((~strong(X)<~>~humble(X))=>(rich(X)<~>~quiet(X))))&
(![X]:(~happy(X)<=>(~rich(X)&humble(X))))&
(![X]:((kind(X)&~brave(X))=>(calm(X)<~>~kind(X))))&
(![X]:((~tall(X)&~creative(X))<=>~funny(X)))&
(![X]:((tall(X)|~calm(X))<=>(old(X)|quiet(X))))&
(![X]:((~calm(X)<~>curious(X))<=>(curious(X)&old(X))))&
(![X]:((curious(X)&generous(X))<=>(patient(X)&quiet(X))))&
(![X]:((strong(X)<~>~calm(X))<=>(brave(X)|wise(X))))&
(![X]:((~strong(X)|~wise(X))=>(~kind(X)&~patient(X))))&
((?[X]:((~humble(X)&brave(X))))=>(?[X]:((calm(X)<~>creative(X)))))&
(![X]:((brave(X)<~>~strong(X))=>(~strong(X)|tall(X))))&
((?[X]:((~wise(X)&~old(X))))=>(wise(john)))&
((~kind(lucy)&~old(lucy)))&
(?[X]:((brave(X)&generous(X))))&
((~patient(paul)|strong(paul)))&
(humble(alice))&
((~wise(alice)<~>~patient(alice)))&
((~old(susan)<~>~creative(susan)))&
(?[X]:((strong(X)&old(X))))&
(?[X]:(funny(X))) | ~brave(susan) | [] | null | 0 |
Everyone who is either old or not patient is both kind and calm.
Everyone who is both not wise and not humble is both not generous and quiet.
Everyone who is old or not kind is not strong.
If someone is both brave and kind then someone is both not funny and not creative.
Everyone who is not funny or calm is tall.
If someone is rich or not patient then lucy is both not humble and humble.
Everyone who is both not generous and tall is both curious and not strong and vice versa.
Everyone who is both patient and kind is not happy or generous and vice versa.
Everyone who is not tall or not patient is both happy and brave.
Everyone who is not happy or not kind is both creative and kind and vice versa.
Everyone who is not generous is not wise or funny and vice versa.
Everyone who is not quiet or humble is both generous and not wise.
Everyone who is calm or patient is either not humble or not tall and vice versa.
Lucy is either tall or not creative.
Mary is either generous or old.
Someone is either not strong or calm.
Paul is not wise or wise.
Fred is tall or wise. | Mary is not patient. | contradiction | (![X]:((old(X)<~>~patient(X))=>(kind(X)&calm(X))))&
(![X]:((~wise(X)&~humble(X))=>(~generous(X)&quiet(X))))&
(![X]:((old(X)|~kind(X))=>~strong(X)))&
((?[X]:((brave(X)&kind(X))))=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((~funny(X)|calm(X))=>tall(X)))&
((?[X]:((rich(X)|~patient(X))))=>((~humble(lucy)&humble(lucy))))&
(![X]:((~generous(X)&tall(X))<=>(curious(X)&~strong(X))))&
(![X]:((patient(X)&kind(X))<=>(~happy(X)|generous(X))))&
(![X]:((~tall(X)|~patient(X))=>(happy(X)&brave(X))))&
(![X]:((~happy(X)|~kind(X))<=>(creative(X)&kind(X))))&
(![X]:(~generous(X)<=>(~wise(X)|funny(X))))&
(![X]:((~quiet(X)|humble(X))=>(generous(X)&~wise(X))))&
(![X]:((calm(X)|patient(X))<=>(~humble(X)<~>~tall(X))))&
((tall(lucy)<~>~creative(lucy)))&
((generous(mary)<~>old(mary)))&
(?[X]:((~strong(X)<~>calm(X))))&
((~wise(paul)|wise(paul)))&
((tall(fred)|wise(fred))) | ~patient(mary) | [
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 5765402918023495053577053
% SZS output start Proof for 5765402918023495053577053
6. ? [X0] : (~patient(X0) | rich(X0)) => (humble(lucy) & ~humble(lucy)) [input p5]
19. ~patient(mary) [input hypothesis]
21. ? [X0] : ~patient(X0) => (humble(lucy) & ~humble(lucy)) [pure predicate removal 6]
30. (humble(lucy) & ~humble(lucy)) | ! [X0] : patient(X0) [ennf transformation 21]
63. ~humble(lucy) | patient(X0) [cnf transformation 30]
64. humble(lucy) | patient(X0) [cnf transformation 30]
102. ~patient(mary) [cnf transformation 19]
119. 4 <=> ! [X0] : patient(X0) [avatar definition]
120. patient(X0) <- (4) [avatar component clause 119]
122. 5 <=> humble(lucy) [avatar definition]
125. 4 | 5 [avatar split clause 64,122,119]
126. 4 | ~5 [avatar split clause 63,122,119]
168. $false <- (4) [resolution 120,102]
169. ~4 [avatar contradiction clause 168]
170. $false [avatar sat refutation 125,126,169]
% SZS output end Proof for 5765402918023495053577053
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or funny is both patient and not happy.
Everyone who is old or not quiet is not wise.
Everyone who is kind or not wise is both kind and not wise.
Everyone who is not strong or not rich is both not brave and not humble.
Everyone who is either not happy or generous is either humble or generous and vice versa.
Everyone who is either not quiet or strong is not happy and vice versa.
If paul is patient or not funny then someone is not patient.
If lucy is not calm then paul is not strong.
Everyone who is either wise or not old is either creative or not creative and vice versa.
Everyone who is either tall or not old is not strong or not old and vice versa.
Everyone who is either rich or creative is not kind or patient and vice versa.
If someone is strong then someone is either curious or not brave and vice versa.
If mary is strong then john is either brave or quiet and vice versa.
Everyone who is not strong or generous is either wise or kind and vice versa.
Someone is both not creative and rich.
Lucy is either not generous or not old.
Fred is patient or not funny.
Fred is not quiet or rich.
Someone is strong or old.
Paul is curious.
Fred is calm or creative. | Fred is strong. | entailment | (![X]:((happy(X)|funny(X))=>(patient(X)&~happy(X))))&
(![X]:((old(X)|~quiet(X))=>~wise(X)))&
(![X]:((kind(X)|~wise(X))=>(kind(X)&~wise(X))))&
(![X]:((~strong(X)|~rich(X))=>(~brave(X)&~humble(X))))&
(![X]:((~happy(X)<~>generous(X))<=>(humble(X)<~>generous(X))))&
(![X]:((~quiet(X)<~>strong(X))<=>~happy(X)))&
(((patient(paul)|~funny(paul)))=>(?[X]:(~patient(X))))&
((~calm(lucy))=>(~strong(paul)))&
(![X]:((wise(X)<~>~old(X))<=>(creative(X)<~>~creative(X))))&
(![X]:((tall(X)<~>~old(X))<=>(~strong(X)|~old(X))))&
(![X]:((rich(X)<~>creative(X))<=>(~kind(X)|patient(X))))&
((?[X]:(strong(X)))<=>(?[X]:((curious(X)<~>~brave(X)))))&
((strong(mary))<=>((brave(john)<~>quiet(john))))&
(![X]:((~strong(X)|generous(X))<=>(wise(X)<~>kind(X))))&
(?[X]:((~creative(X)&rich(X))))&
((~generous(lucy)<~>~old(lucy)))&
((patient(fred)|~funny(fred)))&
((~quiet(fred)|rich(fred)))&
(?[X]:((strong(X)|old(X))))&
(curious(paul))&
((calm(fred)|creative(fred))) | strong(fred) | [
"p0",
"p3",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 258074080555594653727639
% SZS output start Proof for 258074080555594653727639
1. ! [X0] : ((funny(X0) | happy(X0)) => (~happy(X0) & patient(X0))) [input p0]
4. ! [X0] : ((~rich(X0) | ~strong(X0)) => (~humble(X0) & ~brave(X0))) [input p3]
5. ! [X0] : ((~happy(X0) <~> generous(X0)) <=> (humble(X0) <~> generous(X0))) [input p4]
22. ~strong(fred) [input hypothesis]
26. ! [X0] : ((~happy(X0) & patient(X0)) | (~funny(X0) & ~happy(X0))) [ennf transformation 1]
29. ! [X0] : ((~humble(X0) & ~brave(X0)) | (rich(X0) & strong(X0))) [ennf transformation 4]
31. ! [X0] : ((((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((humble(X0) | ~generous(X0)) & (generous(X0) | ~humble(X0)))) & (((~generous(X0) | ~humble(X0)) & (generous(X0) | humble(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0))))) [nnf transformation 5]
55. ~happy(X0) | ~happy(X0) [cnf transformation 26]
65. ~humble(X0) | strong(X0) [cnf transformation 29]
67. generous(X0) | humble(X0) | generous(X0) | happy(X0) [cnf transformation 31]
74. ~generous(X0) | happy(X0) | humble(X0) | ~generous(X0) [cnf transformation 31]
123. ~strong(fred) [cnf transformation 22]
130. generous(X0) | humble(X0) | happy(X0) [duplicate literal removal 67]
133. ~generous(X0) | happy(X0) | humble(X0) [duplicate literal removal 74]
134. ~happy(X0) [duplicate literal removal 55]
135. ~generous(X0) | humble(X0) [subsumption resolution 133,134]
136. generous(X0) | humble(X0) [subsumption resolution 130,134]
137. humble(X0) [subsumption resolution 136,135]
215. strong(X0) [resolution 65,137]
216. $false [resolution 215,123]
% SZS output end Proof for 258074080555594653727639
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or not kind is both not kind and not strong and vice versa.
Everyone who is rich is wise.
Everyone who is brave is both funny and humble and vice versa.
Everyone who is either not humble or brave is not happy or curious.
If fred is both rich and not calm then someone is either generous or not humble.
Everyone who is either not quiet or not creative is either kind or not rich and vice versa.
If lucy is either not brave or not strong then someone is both wise and humble and vice versa.
If someone is not tall then someone is calm and vice versa.
Everyone who is both patient and tall is generous.
Everyone who is either creative or strong is either funny or not humble.
If lucy is both humble and creative then fred is patient.
Everyone who is both tall and not strong is both wise and not humble and vice versa.
Everyone who is either brave or not wise is rich.
If someone is either tall or not old then lucy is not humble.
Everyone who is curious or not old is not calm or generous and vice versa.
Everyone who is not strong or brave is tall or not kind and vice versa.
Mary is happy.
Alice is both old and not strong.
Someone is either humble or not kind.
John is either not strong or happy.
Fred is both generous and not patient.
Fred is both wise and humble.
Someone is brave.
Mary is tall. | Lucy is not creative. | entailment | (![X]:((~calm(X)<~>~kind(X))<=>(~kind(X)&~strong(X))))&
(![X]:(rich(X)=>wise(X)))&
(![X]:(brave(X)<=>(funny(X)&humble(X))))&
(![X]:((~humble(X)<~>brave(X))=>(~happy(X)|curious(X))))&
(((rich(fred)&~calm(fred)))=>(?[X]:((generous(X)<~>~humble(X)))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(kind(X)<~>~rich(X))))&
(((~brave(lucy)<~>~strong(lucy)))<=>(?[X]:((wise(X)&humble(X)))))&
((?[X]:(~tall(X)))<=>(?[X]:(calm(X))))&
(![X]:((patient(X)&tall(X))=>generous(X)))&
(![X]:((creative(X)<~>strong(X))=>(funny(X)<~>~humble(X))))&
(((humble(lucy)&creative(lucy)))=>(patient(fred)))&
(![X]:((tall(X)&~strong(X))<=>(wise(X)&~humble(X))))&
(![X]:((brave(X)<~>~wise(X))=>rich(X)))&
((?[X]:((tall(X)<~>~old(X))))=>(~humble(lucy)))&
(![X]:((curious(X)|~old(X))<=>(~calm(X)|generous(X))))&
(![X]:((~strong(X)|brave(X))<=>(tall(X)|~kind(X))))&
(happy(mary))&
((old(alice)&~strong(alice)))&
(?[X]:((humble(X)<~>~kind(X))))&
((~strong(john)<~>happy(john)))&
((generous(fred)&~patient(fred)))&
((wise(fred)&humble(fred)))&
(?[X]:(brave(X)))&
(tall(mary)) | ~creative(lucy) | [
"p1",
"p2",
"p6",
"p10",
"p11",
"p12",
"p20",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 3769351114584494410358103
% SZS output start Proof for 3769351114584494410358103
2. ! [X0] : (rich(X0) => wise(X0)) [input p1]
3. ! [X0] : (brave(X0) <=> (humble(X0) & funny(X0))) [input p2]
7. (~brave(lucy) <~> ~strong(lucy)) <=> ? [X0] : (humble(X0) & wise(X0)) [input p6]
11. (creative(lucy) & humble(lucy)) => patient(fred) [input p10]
12. ! [X0] : ((~strong(X0) & tall(X0)) <=> (~humble(X0) & wise(X0))) [input p11]
13. ! [X0] : ((brave(X0) <~> ~wise(X0)) => rich(X0)) [input p12]
21. ~patient(fred) & generous(fred) [input p20]
22. humble(fred) & wise(fred) [input p21]
25. creative(lucy) [input hypothesis]
27. ! [X0] : (wise(X0) | ~rich(X0)) [ennf transformation 2]
35. patient(fred) | (~creative(lucy) | ~humble(lucy)) [ennf transformation 11]
36. patient(fred) | ~creative(lucy) | ~humble(lucy) [flattening 35]
37. ! [X0] : (rich(X0) | (brave(X0) <=> ~wise(X0))) [ennf transformation 13]
41. ! [X0] : ((brave(X0) | (~humble(X0) | ~funny(X0))) & ((humble(X0) & funny(X0)) | ~brave(X0))) [nnf transformation 3]
42. ! [X0] : ((brave(X0) | ~humble(X0) | ~funny(X0)) & ((humble(X0) & funny(X0)) | ~brave(X0))) [flattening 41]
48. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & (? [X0] : (humble(X0) & wise(X0)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [nnf transformation 7]
49. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & (? [X1] : (humble(X1) & wise(X1)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [rectify 48]
50. ? [X1] : (humble(X1) & wise(X1)) => (humble(sK1) & wise(sK1)) [choice axiom]
51. (((strong(lucy) | brave(lucy)) & (~strong(lucy) | ~brave(lucy))) | ! [X0] : (~humble(X0) | ~wise(X0))) & ((humble(sK1) & wise(sK1)) | ((~brave(lucy) | strong(lucy)) & (~strong(lucy) | brave(lucy)))) [skolemisation 49,50]
58. ! [X0] : (((~strong(X0) & tall(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (strong(X0) | ~tall(X0)))) [nnf transformation 12]
59. ! [X0] : (((~strong(X0) & tall(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | strong(X0) | ~tall(X0))) [flattening 58]
60. ! [X0] : (rich(X0) | ((brave(X0) | wise(X0)) & (~wise(X0) | ~brave(X0)))) [nnf transformation 37]
78. ~rich(X0) | wise(X0) [cnf transformation 27]
80. ~brave(X0) | humble(X0) [cnf transformation 42]
99. strong(lucy) | brave(lucy) | ~humble(X0) | ~wise(X0) [cnf transformation 51]
107. patient(fred) | ~creative(lucy) | ~humble(lucy) [cnf transformation 36]
111. ~wise(X0) | humble(X0) | ~strong(X0) [cnf transformation 59]
113. rich(X0) | brave(X0) | wise(X0) [cnf transformation 60]
132. ~patient(fred) [cnf transformation 21]
133. wise(fred) [cnf transformation 22]
134. humble(fred) [cnf transformation 22]
137. creative(lucy) [cnf transformation 25]
161. 5 <=> ! [X0] : (~humble(X0) | ~wise(X0)) [avatar definition]
162. ~humble(X0) | ~wise(X0) <- (5) [avatar component clause 161]
164. 6 <=> brave(lucy) [avatar definition]
165. ~brave(lucy) <- (~6) [avatar component clause 164]
166. brave(lucy) <- (6) [avatar component clause 164]
168. 7 <=> strong(lucy) [avatar definition]
170. strong(lucy) <- (7) [avatar component clause 168]
171. 5 | 6 | 7 [avatar split clause 99,168,164,161]
202. 14 <=> humble(lucy) [avatar definition]
204. ~humble(lucy) <- (~14) [avatar component clause 202]
206. 15 <=> creative(lucy) [avatar definition]
210. 16 <=> patient(fred) [avatar definition]
213. ~14 | ~15 | 16 [avatar split clause 107,210,206,202]
214. brave(X0) | wise(X0) [subsumption resolution 113,78]
243. ~16 [avatar split clause 132,210]
244. 15 [avatar split clause 137,206]
249. ~wise(fred) <- (5) [resolution 162,134]
251. $false <- (5) [subsumption resolution 249,133]
252. ~5 [avatar contradiction clause 251]
253. humble(lucy) <- (6) [resolution 166,80]
255. $false <- (6, ~14) [subsumption resolution 253,204]
256. ~6 | 14 [avatar contradiction clause 255]
259. wise(lucy) <- (~6) [resolution 214,165]
311. humble(lucy) | ~strong(lucy) <- (~6) [resolution 111,259]
315. ~strong(lucy) <- (~6, ~14) [subsumption resolution 311,204]
316. $false <- (~6, 7, ~14) [subsumption resolution 315,170]
317. 6 | ~7 | 14 [avatar contradiction clause 316]
321. $false [avatar sat refutation 171,213,243,244,252,256,317]
% SZS output end Proof for 3769351114584494410358103
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or funny is both not generous and not quiet and vice versa.
If lucy is rich then paul is either tall or generous and vice versa.
Everyone who is not brave is patient or wise and vice versa.
If someone is generous then someone is both not humble and not patient and vice versa.
Everyone who is generous or not rich is either not creative or funny.
Everyone who is either rich or not humble is strong or brave.
Everyone who is not generous or creative is not strong or not happy and vice versa.
If mary is both not quiet and not funny then lucy is both not curious and not funny.
Everyone who is brave or kind is either patient or wise.
Everyone who is old or curious is rich and vice versa.
Everyone who is both kind and not happy is either not funny or happy.
If alice is both kind and not kind then paul is either happy or tall and vice versa.
Everyone who is both quiet and not happy is both creative and calm.
Everyone who is either curious or brave is not brave or not humble.
Everyone who is either curious or not happy is not quiet and vice versa.
Everyone who is old or tall is either not rich or brave and vice versa.
Someone is either generous or not calm.
Paul is wise.
Paul is rich or not old.
Alice is both not curious and not brave.
Someone is generous or not tall.
Someone is both not tall and not old.
Someone is both curious and kind.
Someone is not wise. | Alice is not generous. | neutral | (![X]:((old(X)|funny(X))<=>(~generous(X)&~quiet(X))))&
((rich(lucy))<=>((tall(paul)<~>generous(paul))))&
(![X]:(~brave(X)<=>(patient(X)|wise(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~humble(X)&~patient(X)))))&
(![X]:((generous(X)|~rich(X))=>(~creative(X)<~>funny(X))))&
(![X]:((rich(X)<~>~humble(X))=>(strong(X)|brave(X))))&
(![X]:((~generous(X)|creative(X))<=>(~strong(X)|~happy(X))))&
(((~quiet(mary)&~funny(mary)))=>((~curious(lucy)&~funny(lucy))))&
(![X]:((brave(X)|kind(X))=>(patient(X)<~>wise(X))))&
(![X]:((old(X)|curious(X))<=>rich(X)))&
(![X]:((kind(X)&~happy(X))=>(~funny(X)<~>happy(X))))&
(((kind(alice)&~kind(alice)))<=>((happy(paul)<~>tall(paul))))&
(![X]:((quiet(X)&~happy(X))=>(creative(X)&calm(X))))&
(![X]:((curious(X)<~>brave(X))=>(~brave(X)|~humble(X))))&
(![X]:((curious(X)<~>~happy(X))<=>~quiet(X)))&
(![X]:((old(X)|tall(X))<=>(~rich(X)<~>brave(X))))&
(?[X]:((generous(X)<~>~calm(X))))&
(wise(paul))&
((rich(paul)|~old(paul)))&
((~curious(alice)&~brave(alice)))&
(?[X]:((generous(X)|~tall(X))))&
(?[X]:((~tall(X)&~old(X))))&
(?[X]:((curious(X)&kind(X))))&
(?[X]:(~wise(X))) | ~generous(alice) | [] | null | 0 |
If someone is both not wise and calm then someone is not strong or not old and vice versa.
If someone is either not rich or not quiet then alice is not rich and vice versa.
Everyone who is either not rich or calm is not rich and vice versa.
Everyone who is not tall or not creative is both not quiet and not happy.
If someone is either generous or not wise then someone is creative or not quiet.
Everyone who is not quiet is either strong or calm and vice versa.
Everyone who is wise is either not generous or creative.
If susan is either not creative or not wise then lucy is both not strong and not happy and vice versa.
If mary is both not patient and not wise then alice is both not tall and generous.
If john is both strong and kind then someone is both not quiet and funny.
Everyone who is not happy is both not funny and creative.
If someone is either not old or not funny then susan is either generous or humble and vice versa.
If someone is not strong or not wise then paul is either curious or quiet and vice versa.
If paul is not generous or not rich then someone is not happy or strong.
Everyone who is either not humble or not rich is either not creative or wise.
Everyone who is either not funny or not quiet is both generous and not quiet.
Paul is wise.
Someone is not quiet or happy.
Someone is humble or wise.
John is both happy and creative.
Fred is both kind and not humble.
Someone is either curious or humble.
Someone is both rich and kind.
Someone is rich or not quiet. | Lucy is not calm. | entailment | ((?[X]:((~wise(X)&calm(X))))<=>(?[X]:((~strong(X)|~old(X)))))&
((?[X]:((~rich(X)<~>~quiet(X))))<=>(~rich(alice)))&
(![X]:((~rich(X)<~>calm(X))<=>~rich(X)))&
(![X]:((~tall(X)|~creative(X))=>(~quiet(X)&~happy(X))))&
((?[X]:((generous(X)<~>~wise(X))))=>(?[X]:((creative(X)|~quiet(X)))))&
(![X]:(~quiet(X)<=>(strong(X)<~>calm(X))))&
(![X]:(wise(X)=>(~generous(X)<~>creative(X))))&
(((~creative(susan)<~>~wise(susan)))<=>((~strong(lucy)&~happy(lucy))))&
(((~patient(mary)&~wise(mary)))=>((~tall(alice)&generous(alice))))&
(((strong(john)&kind(john)))=>(?[X]:((~quiet(X)&funny(X)))))&
(![X]:(~happy(X)=>(~funny(X)&creative(X))))&
((?[X]:((~old(X)<~>~funny(X))))<=>((generous(susan)<~>humble(susan))))&
((?[X]:((~strong(X)|~wise(X))))<=>((curious(paul)<~>quiet(paul))))&
(((~generous(paul)|~rich(paul)))=>(?[X]:((~happy(X)|strong(X)))))&
(![X]:((~humble(X)<~>~rich(X))=>(~creative(X)<~>wise(X))))&
(![X]:((~funny(X)<~>~quiet(X))=>(generous(X)&~quiet(X))))&
(wise(paul))&
(?[X]:((~quiet(X)|happy(X))))&
(?[X]:((humble(X)|wise(X))))&
((happy(john)&creative(john)))&
((kind(fred)&~humble(fred)))&
(?[X]:((curious(X)<~>humble(X))))&
(?[X]:((rich(X)&kind(X))))&
(?[X]:((rich(X)|~quiet(X)))) | ~calm(lucy) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 3312986443368066128903117
% SZS output start Proof for 3312986443368066128903117
3. ! [X0] : ((~rich(X0) <~> calm(X0)) <=> ~rich(X0)) [input p2]
25. calm(lucy) [input hypothesis]
48. ! [X0] : ((((~calm(X0) | rich(X0)) & (calm(X0) | ~rich(X0))) | rich(X0)) & (~rich(X0) | ((~rich(X0) | ~calm(X0)) & (calm(X0) | rich(X0))))) [nnf transformation 3]
92. ~rich(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 48]
94. ~calm(X0) | rich(X0) | rich(X0) [cnf transformation 48]
151. calm(lucy) [cnf transformation 25]
153. ~rich(X0) | ~calm(X0) [duplicate literal removal 92]
154. ~calm(X0) | rich(X0) [duplicate literal removal 94]
207. ~calm(X0) [subsumption resolution 153,154]
363. $false [subsumption resolution 151,207]
% SZS output end Proof for 3312986443368066128903117
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not calm or brave then lucy is not funny.
Everyone who is either not strong or tall is either not happy or not quiet.
Everyone who is rich or generous is not patient and vice versa.
Everyone who is either not patient or not tall is not kind and vice versa.
Everyone who is rich is both not patient and not kind and vice versa.
If someone is rich or not patient then someone is either not wise or not rich and vice versa.
If someone is either happy or not patient then paul is not rich and vice versa.
Everyone who is not kind is either not old or tall and vice versa.
Everyone who is either wise or creative is not funny.
Everyone who is not generous or generous is not kind and vice versa.
If lucy is funny then someone is both not generous and not happy and vice versa.
Everyone who is either patient or not old is both not funny and generous.
Everyone who is not humble or not calm is either strong or happy.
Everyone who is not generous is not brave or quiet and vice versa.
Everyone who is either not happy or kind is either calm or humble and vice versa.
Someone is either not patient or patient.
Someone is not creative.
Someone is both calm and not humble.
Susan is either not curious or funny.
Alice is strong or not funny.
Lucy is either not creative or curious. | Alice is calm. | entailment | ((?[X]:((~calm(X)|brave(X))))=>(~funny(lucy)))&
(![X]:((~strong(X)<~>tall(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((rich(X)|generous(X))<=>~patient(X)))&
(![X]:((~patient(X)<~>~tall(X))<=>~kind(X)))&
(![X]:(rich(X)<=>(~patient(X)&~kind(X))))&
((?[X]:((rich(X)|~patient(X))))<=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:((happy(X)<~>~patient(X))))<=>(~rich(paul)))&
(![X]:(~kind(X)<=>(~old(X)<~>tall(X))))&
(![X]:((wise(X)<~>creative(X))=>~funny(X)))&
(![X]:((~generous(X)|generous(X))<=>~kind(X)))&
((funny(lucy))<=>(?[X]:((~generous(X)&~happy(X)))))&
(![X]:((patient(X)<~>~old(X))=>(~funny(X)&generous(X))))&
(![X]:((~humble(X)|~calm(X))=>(strong(X)<~>happy(X))))&
(![X]:(~generous(X)<=>(~brave(X)|quiet(X))))&
(![X]:((~happy(X)<~>kind(X))<=>(calm(X)<~>humble(X))))&
(?[X]:((~patient(X)<~>patient(X))))&
(?[X]:(~creative(X)))&
(?[X]:((calm(X)&~humble(X))))&
((~curious(susan)<~>funny(susan)))&
((strong(alice)|~funny(alice)))&
((~creative(lucy)<~>curious(lucy))) | calm(alice) | [
"p0",
"p1",
"p2",
"p3",
"p9",
"p10",
"p12",
"p13",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3998683778714328672626002
% SZS output start Proof for 3998683778714328672626002
1. ? [X0] : (brave(X0) | ~calm(X0)) => ~funny(lucy) [input p0]
2. ! [X0] : ((~strong(X0) <~> tall(X0)) => (~happy(X0) <~> ~quiet(X0))) [input p1]
3. ! [X0] : ((generous(X0) | rich(X0)) <=> ~patient(X0)) [input p2]
4. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> ~kind(X0)) [input p3]
10. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~kind(X0)) [input p9]
11. funny(lucy) <=> ? [X0] : (~happy(X0) & ~generous(X0)) [input p10]
13. ! [X0] : ((~calm(X0) | ~humble(X0)) => (strong(X0) <~> happy(X0))) [input p12]
14. ! [X0] : (~generous(X0) <=> (quiet(X0) | ~brave(X0))) [input p13]
15. ! [X0] : ((~happy(X0) <~> kind(X0)) <=> (calm(X0) <~> humble(X0))) [input p14]
18. ? [X0] : (~humble(X0) & calm(X0)) [input p17]
22. ~calm(alice) [input hypothesis]
24. ~funny(lucy) | ! [X0] : (~brave(X0) & calm(X0)) [ennf transformation 1]
25. ! [X0] : ((~happy(X0) <~> ~quiet(X0)) | (~strong(X0) <=> tall(X0))) [ennf transformation 2]
28. ! [X0] : ((strong(X0) <~> happy(X0)) | (calm(X0) & humble(X0))) [ennf transformation 13]
29. ! [X0] : (((quiet(X0) | happy(X0)) & (~quiet(X0) | ~happy(X0))) | ((~strong(X0) | ~tall(X0)) & (tall(X0) | strong(X0)))) [nnf transformation 25]
30. ! [X0] : (((generous(X0) | rich(X0)) | patient(X0)) & (~patient(X0) | (~generous(X0) & ~rich(X0)))) [nnf transformation 3]
31. ! [X0] : ((generous(X0) | rich(X0) | patient(X0)) & (~patient(X0) | (~generous(X0) & ~rich(X0)))) [flattening 30]
32. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | kind(X0)) & (~kind(X0) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 4]
46. ! [X0] : (((generous(X0) | ~generous(X0)) | kind(X0)) & (~kind(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 10]
47. ! [X0] : ((generous(X0) | ~generous(X0) | kind(X0)) & (~kind(X0) | (~generous(X0) & generous(X0)))) [flattening 46]
48. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & (? [X0] : (~happy(X0) & ~generous(X0)) | ~funny(lucy)) [nnf transformation 11]
49. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & (? [X1] : (~happy(X1) & ~generous(X1)) | ~funny(lucy)) [rectify 48]
50. ? [X1] : (~happy(X1) & ~generous(X1)) => (~happy(sK3) & ~generous(sK3)) [choice axiom]
51. (funny(lucy) | ! [X0] : (happy(X0) | generous(X0))) & ((~happy(sK3) & ~generous(sK3)) | ~funny(lucy)) [skolemisation 49,50]
53. ! [X0] : (((~happy(X0) | ~strong(X0)) & (happy(X0) | strong(X0))) | (calm(X0) & humble(X0))) [nnf transformation 28]
54. ! [X0] : ((~generous(X0) | (~quiet(X0) & brave(X0))) & ((quiet(X0) | ~brave(X0)) | generous(X0))) [nnf transformation 14]
55. ! [X0] : ((~generous(X0) | (~quiet(X0) & brave(X0))) & (quiet(X0) | ~brave(X0) | generous(X0))) [flattening 54]
56. ! [X0] : ((((~kind(X0) | happy(X0)) & (kind(X0) | ~happy(X0))) | ((calm(X0) | ~humble(X0)) & (humble(X0) | ~calm(X0)))) & (((~humble(X0) | ~calm(X0)) & (humble(X0) | calm(X0))) | ((~happy(X0) | ~kind(X0)) & (kind(X0) | happy(X0))))) [nnf transformation 15]
62. ? [X0] : (~humble(X0) & calm(X0)) => (~humble(sK6) & calm(sK6)) [choice axiom]
63. ~humble(sK6) & calm(sK6) [skolemisation 18,62]
66. ~funny(lucy) | calm(X0) [cnf transformation 24]
71. ~tall(X0) | happy(X0) | ~strong(X0) | quiet(X0) [cnf transformation 29]
73. ~patient(X0) | ~generous(X0) [cnf transformation 31]
78. kind(X0) | patient(X0) | tall(X0) [cnf transformation 32]
98. ~kind(X0) | generous(X0) [cnf transformation 47]
99. ~kind(X0) | ~generous(X0) [cnf transformation 47]
103. funny(lucy) | happy(X0) | generous(X0) [cnf transformation 51]
108. humble(X0) | strong(X0) | happy(X0) [cnf transformation 53]
114. ~generous(X0) | ~quiet(X0) [cnf transformation 55]
119. kind(X0) | ~happy(X0) | humble(X0) | ~calm(X0) [cnf transformation 56]
126. calm(sK6) [cnf transformation 63]
127. ~humble(sK6) [cnf transformation 63]
133. ~calm(alice) [cnf transformation 22]
138. 2 <=> funny(lucy) [avatar definition]
143. 3 <=> ! [X0] : calm(X0) [avatar definition]
144. calm(X0) <- (3) [avatar component clause 143]
145. 3 | ~2 [avatar split clause 66,138,143]
200. ~kind(X0) [subsumption resolution 98,99]
202. 16 <=> ! [X0] : (happy(X0) | generous(X0)) [avatar definition]
203. generous(X0) | happy(X0) <- (16) [avatar component clause 202]
204. 16 | 2 [avatar split clause 103,138,202]
217. ~happy(X0) | humble(X0) | ~calm(X0) [subsumption resolution 119,200]
294. patient(X2) | tall(X2) | ~generous(X2) [resolution 78,99]
299. ~generous(X2) | tall(X2) [subsumption resolution 294,73]
335. strong(sK6) | happy(sK6) [resolution 108,127]
337. 31 <=> happy(sK6) [avatar definition]
338. ~happy(sK6) <- (~31) [avatar component clause 337]
339. happy(sK6) <- (31) [avatar component clause 337]
341. 32 <=> strong(sK6) [avatar definition]
343. strong(sK6) <- (32) [avatar component clause 341]
344. 31 | 32 [avatar split clause 335,341,337]
380. humble(sK6) | ~calm(sK6) <- (31) [resolution 217,339]
386. ~calm(sK6) <- (31) [subsumption resolution 380,127]
387. $false <- (31) [subsumption resolution 386,126]
388. ~31 [avatar contradiction clause 387]
411. 38 <=> generous(sK6) [avatar definition]
412. ~generous(sK6) <- (~38) [avatar component clause 411]
413. generous(sK6) <- (38) [avatar component clause 411]
415. 39 <=> quiet(sK6) [avatar definition]
416. ~quiet(sK6) <- (~39) [avatar component clause 415]
431. $false <- (3) [resolution 144,133]
434. ~3 [avatar contradiction clause 431]
479. tall(sK6) <- (38) [resolution 413,299]
480. ~quiet(sK6) <- (38) [resolution 413,114]
482. ~39 | ~38 [avatar split clause 480,411,415]
510. happy(sK6) | ~strong(sK6) | quiet(sK6) <- (38) [resolution 479,71]
512. ~strong(sK6) | quiet(sK6) <- (~31, 38) [subsumption resolution 510,338]
513. quiet(sK6) <- (~31, 32, 38) [subsumption resolution 512,343]
514. $false <- (~31, 32, 38, ~39) [subsumption resolution 513,416]
515. 31 | ~32 | ~38 | 39 [avatar contradiction clause 514]
518. happy(sK6) <- (16, ~38) [resolution 412,203]
519. $false <- (16, ~31, ~38) [subsumption resolution 518,338]
520. ~16 | 31 | 38 [avatar contradiction clause 519]
521. $false [avatar sat refutation 145,204,344,388,434,482,515,520]
% SZS output end Proof for 3998683778714328672626002
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble is old or funny and vice versa.
If someone is both not strong and not curious then susan is not happy.
Everyone who is either brave or not wise is humble.
Everyone who is both brave and funny is old and vice versa.
Everyone who is calm or curious is creative and vice versa.
Everyone who is rich or not patient is not wise.
If someone is not rich or not old then someone is not calm or not curious and vice versa.
If someone is either creative or not quiet then someone is quiet or creative.
If someone is not happy or not humble then susan is not brave or not strong and vice versa.
If someone is both not curious and wise then someone is funny and vice versa.
Everyone who is not wise or happy is brave or not kind.
Everyone who is not brave is not humble.
Everyone who is calm or not generous is not funny or not strong.
If alice is not happy then someone is kind or rich and vice versa.
Everyone who is either not tall or not brave is either not curious or not rich and vice versa.
Everyone who is wise or not generous is not calm or not old and vice versa.
Mary is not patient.
Someone is either creative or rich.
Someone is calm or not patient.
Someone is both brave and calm.
Fred is brave.
Someone is humble.
Fred is tall.
Someone is both not rich and not curious. | Mary is not humble. | neutral | (![X]:(humble(X)<=>(old(X)|funny(X))))&
((?[X]:((~strong(X)&~curious(X))))=>(~happy(susan)))&
(![X]:((brave(X)<~>~wise(X))=>humble(X)))&
(![X]:((brave(X)&funny(X))<=>old(X)))&
(![X]:((calm(X)|curious(X))<=>creative(X)))&
(![X]:((rich(X)|~patient(X))=>~wise(X)))&
((?[X]:((~rich(X)|~old(X))))<=>(?[X]:((~calm(X)|~curious(X)))))&
((?[X]:((creative(X)<~>~quiet(X))))=>(?[X]:((quiet(X)|creative(X)))))&
((?[X]:((~happy(X)|~humble(X))))<=>((~brave(susan)|~strong(susan))))&
((?[X]:((~curious(X)&wise(X))))<=>(?[X]:(funny(X))))&
(![X]:((~wise(X)|happy(X))=>(brave(X)|~kind(X))))&
(![X]:(~brave(X)=>~humble(X)))&
(![X]:((calm(X)|~generous(X))=>(~funny(X)|~strong(X))))&
((~happy(alice))<=>(?[X]:((kind(X)|rich(X)))))&
(![X]:((~tall(X)<~>~brave(X))<=>(~curious(X)<~>~rich(X))))&
(![X]:((wise(X)|~generous(X))<=>(~calm(X)|~old(X))))&
(~patient(mary))&
(?[X]:((creative(X)<~>rich(X))))&
(?[X]:((calm(X)|~patient(X))))&
(?[X]:((brave(X)&calm(X))))&
(brave(fred))&
(?[X]:(humble(X)))&
(tall(fred))&
(?[X]:((~rich(X)&~curious(X)))) | ~humble(mary) | [] | null | 0 |
If someone is patient then someone is either not funny or old.
Everyone who is happy or tall is either not curious or creative.
Everyone who is both tall and creative is not humble.
Everyone who is old or not wise is either not funny or patient.
If someone is creative or not curious then someone is both old and wise and vice versa.
If paul is rich then john is both not wise and old.
Everyone who is either strong or not tall is strong.
If paul is both not rich and not humble then mary is both not funny and not curious.
Everyone who is both creative and tall is wise and vice versa.
If someone is either not tall or calm then mary is quiet and vice versa.
If someone is either not strong or brave then fred is either not humble or not brave and vice versa.
Everyone who is not quiet or old is happy or calm.
If susan is not patient or generous then someone is either kind or not curious.
Everyone who is both calm and humble is not funny or wise and vice versa.
Everyone who is either creative or kind is curious and vice versa.
Everyone who is both old and not humble is either brave or not wise.
Someone is both patient and calm.
Paul is both funny and not old.
Someone is curious or not calm.
Someone is either curious or not strong.
Someone is not tall or patient.
Someone is either funny or not wise. | Fred is not kind. | contradiction | ((?[X]:(patient(X)))=>(?[X]:((~funny(X)<~>old(X)))))&
(![X]:((happy(X)|tall(X))=>(~curious(X)<~>creative(X))))&
(![X]:((tall(X)&creative(X))=>~humble(X)))&
(![X]:((old(X)|~wise(X))=>(~funny(X)<~>patient(X))))&
((?[X]:((creative(X)|~curious(X))))<=>(?[X]:((old(X)&wise(X)))))&
((rich(paul))=>((~wise(john)&old(john))))&
(![X]:((strong(X)<~>~tall(X))=>strong(X)))&
(((~rich(paul)&~humble(paul)))=>((~funny(mary)&~curious(mary))))&
(![X]:((creative(X)&tall(X))<=>wise(X)))&
((?[X]:((~tall(X)<~>calm(X))))<=>(quiet(mary)))&
((?[X]:((~strong(X)<~>brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~quiet(X)|old(X))=>(happy(X)|calm(X))))&
(((~patient(susan)|generous(susan)))=>(?[X]:((kind(X)<~>~curious(X)))))&
(![X]:((calm(X)&humble(X))<=>(~funny(X)|wise(X))))&
(![X]:((creative(X)<~>kind(X))<=>curious(X)))&
(![X]:((old(X)&~humble(X))=>(brave(X)<~>~wise(X))))&
(?[X]:((patient(X)&calm(X))))&
((funny(paul)&~old(paul)))&
(?[X]:((curious(X)|~calm(X))))&
(?[X]:((curious(X)<~>~strong(X))))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:((funny(X)<~>~wise(X)))) | ~kind(fred) | [
"p2",
"p4",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 817327924991448446570134
% SZS output start Proof for 817327924991448446570134
3. ! [X0] : ((creative(X0) & tall(X0)) => ~humble(X0)) [input p2]
5. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X0] : (wise(X0) & old(X0)) [input p4]
9. ! [X0] : ((tall(X0) & creative(X0)) <=> wise(X0)) [input p8]
14. ! [X0] : ((humble(X0) & calm(X0)) <=> (wise(X0) | ~funny(X0))) [input p13]
15. ! [X0] : ((creative(X0) <~> kind(X0)) <=> curious(X0)) [input p14]
23. ~kind(fred) [input hypothesis]
25. ? [X0] : (~curious(X0) | creative(X0)) <=> ? [X1] : (wise(X1) & old(X1)) [rectify 5]
29. ! [X0] : (~humble(X0) | (~creative(X0) | ~tall(X0))) [ennf transformation 3]
30. ! [X0] : (~humble(X0) | ~creative(X0) | ~tall(X0)) [flattening 29]
47. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X1] : (wise(X1) & old(X1)) | ! [X0] : (curious(X0) & ~creative(X0))) [nnf transformation 25]
48. (? [X0] : (~curious(X0) | creative(X0)) | ! [X1] : (~wise(X1) | ~old(X1))) & (? [X2] : (wise(X2) & old(X2)) | ! [X3] : (curious(X3) & ~creative(X3))) [rectify 47]
49. ? [X0] : (~curious(X0) | creative(X0)) => (~curious(sK1) | creative(sK1)) [choice axiom]
50. ? [X2] : (wise(X2) & old(X2)) => (wise(sK2) & old(sK2)) [choice axiom]
51. ((~curious(sK1) | creative(sK1)) | ! [X1] : (~wise(X1) | ~old(X1))) & ((wise(sK2) & old(sK2)) | ! [X3] : (curious(X3) & ~creative(X3))) [skolemisation 48,50,49]
53. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | (~tall(X0) | ~creative(X0)))) [nnf transformation 9]
54. ! [X0] : (((tall(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | ~tall(X0) | ~creative(X0))) [flattening 53]
66. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & ((wise(X0) | ~funny(X0)) | (~humble(X0) | ~calm(X0)))) [nnf transformation 14]
67. ! [X0] : (((humble(X0) & calm(X0)) | (~wise(X0) & funny(X0))) & (wise(X0) | ~funny(X0) | ~humble(X0) | ~calm(X0))) [flattening 66]
68. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | ~curious(X0)) & (curious(X0) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 15]
88. ~humble(X0) | ~creative(X0) | ~tall(X0) [cnf transformation 30]
95. wise(sK2) | ~creative(X3) [cnf transformation 51]
96. wise(sK2) | curious(X3) [cnf transformation 51]
105. ~wise(X0) | creative(X0) [cnf transformation 54]
106. ~wise(X0) | tall(X0) [cnf transformation 54]
127. ~wise(X0) | humble(X0) [cnf transformation 67]
130. ~curious(X0) | creative(X0) | kind(X0) [cnf transformation 68]
144. ~kind(fred) [cnf transformation 23]
172. 7 <=> ! [X3] : curious(X3) [avatar definition]
173. curious(X3) <- (7) [avatar component clause 172]
175. 8 <=> wise(sK2) [avatar definition]
177. wise(sK2) <- (8) [avatar component clause 175]
178. 7 | 8 [avatar split clause 96,175,172]
180. 9 <=> ! [X3] : ~creative(X3) [avatar definition]
181. ~creative(X3) <- (9) [avatar component clause 180]
182. 9 | 8 [avatar split clause 95,175,180]
454. creative(X0) | kind(X0) <- (7) [resolution 130,173]
457. kind(X0) <- (7, 9) [subsumption resolution 454,181]
497. $false <- (7, 9) [resolution 457,144]
502. ~7 | ~9 [avatar contradiction clause 497]
553. humble(sK2) <- (8) [resolution 177,127]
555. tall(sK2) <- (8) [resolution 177,106]
556. creative(sK2) <- (8) [resolution 177,105]
568. ~creative(sK2) | ~tall(sK2) <- (8) [resolution 553,88]
569. ~tall(sK2) <- (8) [subsumption resolution 568,556]
570. $false <- (8) [subsumption resolution 569,555]
571. ~8 [avatar contradiction clause 570]
572. $false [avatar sat refutation 178,182,502,571]
% SZS output end Proof for 817327924991448446570134
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not funny or quiet then fred is happy.
If someone is brave or not wise then susan is both tall and not rich and vice versa.
If someone is humble then lucy is either humble or quiet.
Everyone who is strong is both not wise and strong.
Everyone who is not humble is not quiet or not old.
Everyone who is curious or creative is tall.
Everyone who is generous is curious and vice versa.
Everyone who is both not generous and not calm is not happy or not generous and vice versa.
Everyone who is not generous or not old is both quiet and calm.
If alice is both not calm and wise then paul is old.
If someone is either not patient or tall then someone is not tall or not curious and vice versa.
Everyone who is either not tall or generous is not calm or not generous.
Everyone who is both not strong and not tall is funny or not humble and vice versa.
If someone is both generous and not calm then someone is either not funny or not wise and vice versa.
If lucy is not generous then mary is not rich or not funny.
Everyone who is either generous or rich is either creative or old.
John is either brave or not calm.
Mary is strong or not happy.
John is rich or creative.
Someone is either not tall or not patient.
Fred is brave or not humble. | Paul is patient. | contradiction | (((~funny(john)<~>quiet(john)))=>(happy(fred)))&
((?[X]:((brave(X)|~wise(X))))<=>((tall(susan)&~rich(susan))))&
((?[X]:(humble(X)))=>((humble(lucy)<~>quiet(lucy))))&
(![X]:(strong(X)=>(~wise(X)&strong(X))))&
(![X]:(~humble(X)=>(~quiet(X)|~old(X))))&
(![X]:((curious(X)|creative(X))=>tall(X)))&
(![X]:(generous(X)<=>curious(X)))&
(![X]:((~generous(X)&~calm(X))<=>(~happy(X)|~generous(X))))&
(![X]:((~generous(X)|~old(X))=>(quiet(X)&calm(X))))&
(((~calm(alice)&wise(alice)))=>(old(paul)))&
((?[X]:((~patient(X)<~>tall(X))))<=>(?[X]:((~tall(X)|~curious(X)))))&
(![X]:((~tall(X)<~>generous(X))=>(~calm(X)|~generous(X))))&
(![X]:((~strong(X)&~tall(X))<=>(funny(X)|~humble(X))))&
((?[X]:((generous(X)&~calm(X))))<=>(?[X]:((~funny(X)<~>~wise(X)))))&
((~generous(lucy))=>((~rich(mary)|~funny(mary))))&
(![X]:((generous(X)<~>rich(X))=>(creative(X)<~>old(X))))&
((brave(john)<~>~calm(john)))&
((strong(mary)|~happy(mary)))&
((rich(john)|creative(john)))&
(?[X]:((~tall(X)<~>~patient(X))))&
((brave(fred)|~humble(fred))) | patient(paul) | [
"p5",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 1020328436458346900164450
% SZS output start Proof for 1020328436458346900164450
6. ! [X0] : ((creative(X0) | curious(X0)) => tall(X0)) [input p5]
7. ! [X0] : (generous(X0) <=> curious(X0)) [input p6]
8. ! [X0] : ((~calm(X0) & ~generous(X0)) <=> (~generous(X0) | ~happy(X0))) [input p7]
9. ! [X0] : ((~old(X0) | ~generous(X0)) => (calm(X0) & quiet(X0))) [input p8]
11. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X0] : (~curious(X0) | ~tall(X0)) [input p10]
22. patient(paul) [input hypothesis]
23. ? [X0] : (~patient(X0) <~> tall(X0)) <=> ? [X1] : (~curious(X1) | ~tall(X1)) [rectify 11]
30. ! [X0] : (tall(X0) | (~creative(X0) & ~curious(X0))) [ennf transformation 6]
31. ! [X0] : ((calm(X0) & quiet(X0)) | (old(X0) & generous(X0))) [ennf transformation 9]
46. ! [X0] : ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))) [nnf transformation 7]
47. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & ((~generous(X0) | ~happy(X0)) | (calm(X0) | generous(X0)))) [nnf transformation 8]
48. ! [X0] : (((~calm(X0) & ~generous(X0)) | (generous(X0) & happy(X0))) & (~generous(X0) | ~happy(X0) | calm(X0) | generous(X0))) [flattening 47]
49. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : (curious(X1) & tall(X1))) & (? [X1] : (~curious(X1) | ~tall(X1)) | ! [X0] : ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) [nnf transformation 23]
50. (? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | ! [X1] : (curious(X1) & tall(X1))) & (? [X2] : (~curious(X2) | ~tall(X2)) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [rectify 49]
51. ? [X0] : ((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) => ((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) [choice axiom]
52. ? [X2] : (~curious(X2) | ~tall(X2)) => (~curious(sK2) | ~tall(sK2)) [choice axiom]
53. (((~tall(sK1) | patient(sK1)) & (tall(sK1) | ~patient(sK1))) | ! [X1] : (curious(X1) & tall(X1))) & ((~curious(sK2) | ~tall(sK2)) | ! [X3] : ((~patient(X3) | ~tall(X3)) & (tall(X3) | patient(X3)))) [skolemisation 50,52,51]
79. ~curious(X0) | tall(X0) [cnf transformation 30]
81. ~generous(X0) | curious(X0) [cnf transformation 46]
87. ~calm(X0) | generous(X0) [cnf transformation 48]
90. calm(X0) | generous(X0) [cnf transformation 31]
94. ~curious(sK2) | ~tall(sK2) | ~patient(X3) | ~tall(X3) [cnf transformation 53]
124. patient(paul) [cnf transformation 22]
180. generous(X0) [subsumption resolution 90,87]
195. 16 <=> ! [X1] : curious(X1) [avatar definition]
196. curious(X1) <- (16) [avatar component clause 195]
207. 19 <=> ! [X1] : tall(X1) [avatar definition]
208. tall(X1) <- (19) [avatar component clause 207]
212. ~curious(sK2) | ~patient(X3) | ~tall(X3) [subsumption resolution 94,79]
214. 20 <=> ! [X3] : (~patient(X3) | ~tall(X3)) [avatar definition]
215. ~patient(X3) | ~tall(X3) <- (20) [avatar component clause 214]
217. 21 <=> curious(sK2) [avatar definition]
219. ~curious(sK2) <- (~21) [avatar component clause 217]
220. 20 | ~21 [avatar split clause 212,217,214]
307. curious(X0) [resolution 81,180]
308. 16 [avatar split clause 307,195]
309. $false <- (16, ~21) [resolution 196,219]
310. tall(X0) <- (16) [resolution 196,79]
311. ~16 | 21 [avatar contradiction clause 309]
312. 19 | ~16 [avatar split clause 310,195,207]
335. ~tall(paul) <- (20) [resolution 215,124]
336. $false <- (19, 20) [subsumption resolution 335,208]
337. ~19 | ~20 [avatar contradiction clause 336]
338. $false [avatar sat refutation 220,308,311,312,337]
% SZS output end Proof for 1020328436458346900164450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and strong is both patient and calm and vice versa.
Everyone who is not patient is either not tall or generous and vice versa.
Everyone who is not generous or not tall is either kind or not happy.
If someone is either not old or not generous then susan is quiet.
If mary is tall or not happy then someone is strong or not strong and vice versa.
If alice is happy then alice is both rich and not strong and vice versa.
Everyone who is both not old and quiet is strong or not calm.
If someone is not brave then someone is either rich or not generous.
If paul is old or kind then susan is both humble and creative.
Everyone who is generous or not old is rich or not quiet.
Everyone who is both happy and kind is not curious and vice versa.
Everyone who is funny is funny or not happy.
If lucy is not curious or not kind then fred is not funny and vice versa.
Everyone who is both rich and patient is both creative and not kind.
If fred is both not tall and generous then someone is wise or not old and vice versa.
Everyone who is not happy or quiet is not curious and vice versa.
Someone is not brave.
Someone is either tall or humble.
Mary is quiet.
Someone is generous or not kind.
Someone is both quiet and generous.
Someone is not old or not patient.
Alice is old.
Susan is rich or wise. | Fred is old. | entailment | (![X]:((~wise(X)&strong(X))<=>(patient(X)&calm(X))))&
(![X]:(~patient(X)<=>(~tall(X)<~>generous(X))))&
(![X]:((~generous(X)|~tall(X))=>(kind(X)<~>~happy(X))))&
((?[X]:((~old(X)<~>~generous(X))))=>(quiet(susan)))&
(((tall(mary)|~happy(mary)))<=>(?[X]:((strong(X)|~strong(X)))))&
((happy(alice))<=>((rich(alice)&~strong(alice))))&
(![X]:((~old(X)&quiet(X))=>(strong(X)|~calm(X))))&
((?[X]:(~brave(X)))=>(?[X]:((rich(X)<~>~generous(X)))))&
(((old(paul)|kind(paul)))=>((humble(susan)&creative(susan))))&
(![X]:((generous(X)|~old(X))=>(rich(X)|~quiet(X))))&
(![X]:((happy(X)&kind(X))<=>~curious(X)))&
(![X]:(funny(X)=>(funny(X)|~happy(X))))&
(((~curious(lucy)|~kind(lucy)))<=>(~funny(fred)))&
(![X]:((rich(X)&patient(X))=>(creative(X)&~kind(X))))&
(((~tall(fred)&generous(fred)))<=>(?[X]:((wise(X)|~old(X)))))&
(![X]:((~happy(X)|quiet(X))<=>~curious(X)))&
(?[X]:(~brave(X)))&
(?[X]:((tall(X)<~>humble(X))))&
(quiet(mary))&
(?[X]:((generous(X)|~kind(X))))&
(?[X]:((quiet(X)&generous(X))))&
(?[X]:((~old(X)|~patient(X))))&
(old(alice))&
((rich(susan)|wise(susan))) | old(fred) | [
"p1",
"p2",
"p9",
"p10",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2423159367273069555345348
% SZS output start Proof for 2423159367273069555345348
2. ! [X0] : (~patient(X0) <=> (~tall(X0) <~> generous(X0))) [input p1]
3. ! [X0] : ((~tall(X0) | ~generous(X0)) => (kind(X0) <~> ~happy(X0))) [input p2]
10. ! [X0] : ((~old(X0) | generous(X0)) => (~quiet(X0) | rich(X0))) [input p9]
11. ! [X0] : ((kind(X0) & happy(X0)) <=> ~curious(X0)) [input p10]
14. ! [X0] : ((patient(X0) & rich(X0)) => (~kind(X0) & creative(X0))) [input p13]
15. (generous(fred) & ~tall(fred)) <=> ? [X0] : (~old(X0) | wise(X0)) [input p14]
16. ! [X0] : ((quiet(X0) | ~happy(X0)) <=> ~curious(X0)) [input p15]
25. ~old(fred) [input hypothesis]
28. ! [X0] : ((patient(X0) & rich(X0)) => ~kind(X0)) [pure predicate removal 14]
29. ! [X0] : ((kind(X0) <~> ~happy(X0)) | (tall(X0) & generous(X0))) [ennf transformation 3]
35. ! [X0] : ((~quiet(X0) | rich(X0)) | (old(X0) & ~generous(X0))) [ennf transformation 10]
36. ! [X0] : (~quiet(X0) | rich(X0) | (old(X0) & ~generous(X0))) [flattening 35]
39. ! [X0] : (~kind(X0) | (~patient(X0) | ~rich(X0))) [ennf transformation 28]
40. ! [X0] : (~kind(X0) | ~patient(X0) | ~rich(X0)) [flattening 39]
43. ! [X0] : ((~patient(X0) | ((~tall(X0) | ~generous(X0)) & (generous(X0) | tall(X0)))) & (((~generous(X0) | tall(X0)) & (generous(X0) | ~tall(X0))) | patient(X0))) [nnf transformation 2]
44. ! [X0] : (((happy(X0) | ~kind(X0)) & (~happy(X0) | kind(X0))) | (tall(X0) & generous(X0))) [nnf transformation 29]
57. ! [X0] : (((kind(X0) & happy(X0)) | curious(X0)) & (~curious(X0) | (~kind(X0) | ~happy(X0)))) [nnf transformation 11]
58. ! [X0] : (((kind(X0) & happy(X0)) | curious(X0)) & (~curious(X0) | ~kind(X0) | ~happy(X0))) [flattening 57]
61. ((generous(fred) & ~tall(fred)) | ! [X0] : (old(X0) & ~wise(X0))) & (? [X0] : (~old(X0) | wise(X0)) | (~generous(fred) | tall(fred))) [nnf transformation 15]
62. ((generous(fred) & ~tall(fred)) | ! [X0] : (old(X0) & ~wise(X0))) & (? [X0] : (~old(X0) | wise(X0)) | ~generous(fred) | tall(fred)) [flattening 61]
63. ((generous(fred) & ~tall(fred)) | ! [X0] : (old(X0) & ~wise(X0))) & (? [X1] : (~old(X1) | wise(X1)) | ~generous(fred) | tall(fred)) [rectify 62]
64. ? [X1] : (~old(X1) | wise(X1)) => (~old(sK2) | wise(sK2)) [choice axiom]
65. ((generous(fred) & ~tall(fred)) | ! [X0] : (old(X0) & ~wise(X0))) & ((~old(sK2) | wise(sK2)) | ~generous(fred) | tall(fred)) [skolemisation 63,64]
66. ! [X0] : (((quiet(X0) | ~happy(X0)) | curious(X0)) & (~curious(X0) | (~quiet(X0) & happy(X0)))) [nnf transformation 16]
67. ! [X0] : ((quiet(X0) | ~happy(X0) | curious(X0)) & (~curious(X0) | (~quiet(X0) & happy(X0)))) [flattening 66]
84. ~generous(X0) | tall(X0) | patient(X0) [cnf transformation 43]
88. ~happy(X0) | kind(X0) | tall(X0) [cnf transformation 44]
105. ~quiet(X0) | rich(X0) | ~generous(X0) [cnf transformation 36]
107. ~curious(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 58]
108. curious(X0) | happy(X0) [cnf transformation 58]
114. ~rich(X0) | ~patient(X0) | ~kind(X0) [cnf transformation 40]
117. ~tall(fred) | old(X0) [cnf transformation 65]
119. generous(fred) | old(X0) [cnf transformation 65]
120. ~curious(X0) | happy(X0) [cnf transformation 67]
122. quiet(X0) | ~happy(X0) | curious(X0) [cnf transformation 67]
133. ~old(fred) [cnf transformation 25]
220. 20 <=> ! [X0] : old(X0) [avatar definition]
221. old(X0) <- (20) [avatar component clause 220]
223. 21 <=> generous(fred) [avatar definition]
225. generous(fred) <- (21) [avatar component clause 223]
226. 20 | 21 [avatar split clause 119,223,220]
232. 23 <=> tall(fred) [avatar definition]
234. ~tall(fred) <- (~23) [avatar component clause 232]
235. 20 | ~23 [avatar split clause 117,232,220]
246. curious(X0) | quiet(X0) [subsumption resolution 122,108]
247. happy(X0) [subsumption resolution 120,108]
323. tall(fred) | patient(fred) <- (21) [resolution 84,225]
333. patient(fred) <- (21, ~23) [subsumption resolution 323,234]
358. kind(X0) | tall(X0) [resolution 88,247]
410. ~kind(X0) | ~happy(X0) | quiet(X0) [resolution 107,246]
413. ~kind(X0) | quiet(X0) [subsumption resolution 410,247]
476. quiet(X0) | tall(X0) [resolution 413,358]
483. ~generous(X2) | rich(X2) | tall(X2) [resolution 476,105]
506. rich(fred) | tall(fred) <- (21) [resolution 483,225]
509. rich(fred) <- (21, ~23) [subsumption resolution 506,234]
531. ~patient(fred) | ~kind(fred) <- (21, ~23) [resolution 509,114]
532. ~kind(fred) <- (21, ~23) [subsumption resolution 531,333]
533. tall(fred) <- (21, ~23) [resolution 532,358]
535. $false <- (21, ~23) [subsumption resolution 533,234]
536. ~21 | 23 [avatar contradiction clause 535]
538. $false <- (20) [resolution 221,133]
543. ~20 [avatar contradiction clause 538]
545. $false [avatar sat refutation 226,235,536,543]
% SZS output end Proof for 2423159367273069555345348
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not wise or not strong is both not kind and funny and vice versa. If paul is curious or rich then someone is either not brave or not funny and vice versa. If alice is either brave or patient then alice is strong and vice versa. Everyone who is calm or not brave is both not humble and generous. If someone is not brave then alice is both not quiet and not strong. If someone is both not rich and brave then someone is both not generous and wise and vice versa. Everyone who is both kind and not creative is not patient or not brave. If someone is either not creative or tall then someone is not patient or calm. If mary is both not quiet and kind then fred is not tall. If someone is both strong and not tall then john is either not generous or not creative and vice versa. Everyone who is either curious or not rich is not rich and vice versa. Everyone who is either not wise or not old is either not wise or not tall and vice versa. Everyone who is happy or not quiet is both not curious and not happy and vice versa. If alice is both tall and not brave then paul is not quiet. If mary is not old then mary is both not strong and wise and vice versa. If mary is both not patient and strong then someone is both happy and generous. Someone is wise. Someone is both strong and not patient. Someone is either happy or rich. Susan is calm. Someone is not quiet. Fred is kind. | Susan is not generous. | contradiction | (![X]:((~wise(X)<~>~strong(X))<=>(~kind(X)&funny(X))))&
(((curious(paul)|rich(paul)))<=>(?[X]:((~brave(X)<~>~funny(X)))))&
(((brave(alice)<~>patient(alice)))<=>(strong(alice)))&
(![X]:((calm(X)|~brave(X))=>(~humble(X)&generous(X))))&
((?[X]:(~brave(X)))=>((~quiet(alice)&~strong(alice))))&
((?[X]:((~rich(X)&brave(X))))<=>(?[X]:((~generous(X)&wise(X)))))&
(![X]:((kind(X)&~creative(X))=>(~patient(X)|~brave(X))))&
((?[X]:((~creative(X)<~>tall(X))))=>(?[X]:((~patient(X)|calm(X)))))&
(((~quiet(mary)&kind(mary)))=>(~tall(fred)))&
((?[X]:((strong(X)&~tall(X))))<=>((~generous(john)<~>~creative(john))))&
(![X]:((curious(X)<~>~rich(X))<=>~rich(X)))&
(![X]:((~wise(X)<~>~old(X))<=>(~wise(X)<~>~tall(X))))&
(![X]:((happy(X)|~quiet(X))<=>(~curious(X)&~happy(X))))&
(((tall(alice)&~brave(alice)))=>(~quiet(paul)))&
((~old(mary))<=>((~strong(mary)&wise(mary))))&
(((~patient(mary)&strong(mary)))=>(?[X]:((happy(X)&generous(X)))))&
(?[X]:(wise(X)))&
(?[X]:((strong(X)&~patient(X))))&
(?[X]:((happy(X)<~>rich(X))))&
(calm(susan))&
(?[X]:(~quiet(X)))&
(kind(fred)) | ~generous(susan) | [
"p3",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 2609077594879880351259079
% SZS output start Proof for 2609077594879880351259079
4. ! [X0] : ((~brave(X0) | calm(X0)) => (generous(X0) & ~humble(X0))) [input p3]
20. calm(susan) [input p19]
23. ~generous(susan) [input hypothesis]
26. ! [X0] : ((~brave(X0) | calm(X0)) => generous(X0)) [pure predicate removal 4]
27. ! [X0] : (generous(X0) | (brave(X0) & ~calm(X0))) [ennf transformation 26]
92. ~calm(X0) | generous(X0) [cnf transformation 27]
138. calm(susan) [cnf transformation 20]
141. ~generous(susan) [cnf transformation 23]
325. generous(susan) [resolution 92,138]
326. $false [subsumption resolution 325,141]
% SZS output end Proof for 2609077594879880351259079
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not funny is either not generous or not creative.
If alice is both not rich and strong then someone is either not calm or brave.
Everyone who is not wise or not old is not rich.
If john is both not curious and not old then someone is brave and vice versa.
If someone is not funny or calm then someone is either happy or wise.
Everyone who is both curious and not humble is not generous or old.
If paul is both not rich and patient then someone is both not calm and brave and vice versa.
Everyone who is either calm or curious is humble.
Everyone who is patient is both rich and not wise and vice versa.
If someone is strong then someone is both humble and patient and vice versa.
Everyone who is brave is not kind and vice versa.
Everyone who is not quiet is calm or creative.
Everyone who is both quiet and old is either not humble or generous.
Everyone who is both not kind and not rich is both not curious and funny.
Everyone who is both old and happy is either strong or generous and vice versa.
Everyone who is not happy or kind is not humble.
John is calm or tall.
Someone is rich.
John is humble.
Someone is both tall and wise.
Alice is generous.
Someone is either creative or not happy.
Lucy is not calm or not old. | Lucy is not strong. | entailment | (![X]:((~patient(X)<~>~funny(X))=>(~generous(X)<~>~creative(X))))&
(((~rich(alice)&strong(alice)))=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:((~wise(X)|~old(X))=>~rich(X)))&
(((~curious(john)&~old(john)))<=>(?[X]:(brave(X))))&
((?[X]:((~funny(X)|calm(X))))=>(?[X]:((happy(X)<~>wise(X)))))&
(![X]:((curious(X)&~humble(X))=>(~generous(X)|old(X))))&
(((~rich(paul)&patient(paul)))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((calm(X)<~>curious(X))=>humble(X)))&
(![X]:(patient(X)<=>(rich(X)&~wise(X))))&
((?[X]:(strong(X)))<=>(?[X]:((humble(X)&patient(X)))))&
(![X]:(brave(X)<=>~kind(X)))&
(![X]:(~quiet(X)=>(calm(X)|creative(X))))&
(![X]:((quiet(X)&old(X))=>(~humble(X)<~>generous(X))))&
(![X]:((~kind(X)&~rich(X))=>(~curious(X)&funny(X))))&
(![X]:((old(X)&happy(X))<=>(strong(X)<~>generous(X))))&
(![X]:((~happy(X)|kind(X))=>~humble(X)))&
((calm(john)|tall(john)))&
(?[X]:(rich(X)))&
(humble(john))&
(?[X]:((tall(X)&wise(X))))&
(generous(alice))&
(?[X]:((creative(X)<~>~happy(X))))&
((~calm(lucy)|~old(lucy))) | ~strong(lucy) | [
"p2",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 1562849775364043852808494
% SZS output start Proof for 1562849775364043852808494
3. ! [X0] : ((~old(X0) | ~wise(X0)) => ~rich(X0)) [input p2]
9. ! [X0] : (patient(X0) <=> (~wise(X0) & rich(X0))) [input p8]
10. ? [X0] : strong(X0) <=> ? [X0] : (patient(X0) & humble(X0)) [input p9]
24. strong(lucy) [input hypothesis]
26. ? [X0] : strong(X0) <=> ? [X1] : (patient(X1) & humble(X1)) [rectify 10]
32. ! [X0] : (~rich(X0) | (old(X0) & wise(X0))) [ennf transformation 3]
63. ! [X0] : ((patient(X0) | (wise(X0) | ~rich(X0))) & ((~wise(X0) & rich(X0)) | ~patient(X0))) [nnf transformation 9]
64. ! [X0] : ((patient(X0) | wise(X0) | ~rich(X0)) & ((~wise(X0) & rich(X0)) | ~patient(X0))) [flattening 63]
65. (? [X0] : strong(X0) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X1] : (patient(X1) & humble(X1)) | ! [X0] : ~strong(X0)) [nnf transformation 26]
66. (? [X0] : strong(X0) | ! [X1] : (~patient(X1) | ~humble(X1))) & (? [X2] : (patient(X2) & humble(X2)) | ! [X3] : ~strong(X3)) [rectify 65]
67. ? [X0] : strong(X0) => strong(sK4) [choice axiom]
68. ? [X2] : (patient(X2) & humble(X2)) => (patient(sK5) & humble(sK5)) [choice axiom]
69. (strong(sK4) | ! [X1] : (~patient(X1) | ~humble(X1))) & ((patient(sK5) & humble(sK5)) | ! [X3] : ~strong(X3)) [skolemisation 66,68,67]
87. ~rich(X0) | wise(X0) [cnf transformation 32]
103. ~patient(X0) | rich(X0) [cnf transformation 64]
104. ~wise(X0) | ~patient(X0) [cnf transformation 64]
107. patient(sK5) | ~strong(X3) [cnf transformation 69]
131. strong(lucy) [cnf transformation 24]
218. 20 <=> ! [X3] : ~strong(X3) [avatar definition]
219. ~strong(X3) <- (20) [avatar component clause 218]
221. 21 <=> patient(sK5) [avatar definition]
223. patient(sK5) <- (21) [avatar component clause 221]
224. 20 | 21 [avatar split clause 107,221,218]
249. $false <- (20) [resolution 219,131]
250. ~20 [avatar contradiction clause 249]
253. rich(sK5) <- (21) [resolution 103,223]
255. wise(sK5) <- (21) [resolution 253,87]
259. ~patient(sK5) <- (21) [resolution 255,104]
260. $false <- (21) [subsumption resolution 259,223]
261. ~21 [avatar contradiction clause 260]
262. $false [avatar sat refutation 224,250,261]
% SZS output end Proof for 1562849775364043852808494
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.018 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both tall and kind then someone is both generous and funny. Everyone who is creative or not calm is not kind or not curious and vice versa. Everyone who is rich or not strong is not brave or not kind and vice versa. Everyone who is not kind or patient is both not brave and not tall. Everyone who is creative is rich and vice versa. If alice is rich then mary is both patient and not happy and vice versa. Everyone who is not kind is funny or creative. If susan is not happy then someone is both not happy and not kind. Everyone who is not generous or not calm is either funny or patient and vice versa. Everyone who is both quiet and not tall is both generous and not wise and vice versa. Everyone who is not curious or not generous is generous. Everyone who is either creative or not happy is old or happy. Everyone who is both not curious and not funny is not patient or happy and vice versa. Everyone who is either not old or not funny is both kind and not strong and vice versa. Everyone who is quiet is generous and vice versa. If fred is either creative or not wise then someone is both brave and not patient. Susan is not humble. Someone is humble or brave. Mary is either funny or patient. Someone is wise. Someone is either not rich or rich. Paul is both strong and not kind. Someone is not brave or calm. | Mary is not wise. | entailment | ((?[X]:((tall(X)&kind(X))))=>(?[X]:((generous(X)&funny(X)))))&
(![X]:((creative(X)|~calm(X))<=>(~kind(X)|~curious(X))))&
(![X]:((rich(X)|~strong(X))<=>(~brave(X)|~kind(X))))&
(![X]:((~kind(X)|patient(X))=>(~brave(X)&~tall(X))))&
(![X]:(creative(X)<=>rich(X)))&
((rich(alice))<=>((patient(mary)&~happy(mary))))&
(![X]:(~kind(X)=>(funny(X)|creative(X))))&
((~happy(susan))=>(?[X]:((~happy(X)&~kind(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(funny(X)<~>patient(X))))&
(![X]:((quiet(X)&~tall(X))<=>(generous(X)&~wise(X))))&
(![X]:((~curious(X)|~generous(X))=>generous(X)))&
(![X]:((creative(X)<~>~happy(X))=>(old(X)|happy(X))))&
(![X]:((~curious(X)&~funny(X))<=>(~patient(X)|happy(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(kind(X)&~strong(X))))&
(![X]:(quiet(X)<=>generous(X)))&
(((creative(fred)<~>~wise(fred)))=>(?[X]:((brave(X)&~patient(X)))))&
(~humble(susan))&
(?[X]:((humble(X)|brave(X))))&
((funny(mary)<~>patient(mary)))&
(?[X]:(wise(X)))&
(?[X]:((~rich(X)<~>rich(X))))&
((strong(paul)&~kind(paul)))&
(?[X]:((~brave(X)|calm(X)))) | ~wise(mary) | [
"p3",
"p9",
"p10",
"p12",
"p14",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1991396571306672396170757
% SZS output start Proof for 1991396571306672396170757
4. ! [X0] : ((patient(X0) | ~kind(X0)) => (~tall(X0) & ~brave(X0))) [input p3]
10. ! [X0] : ((~tall(X0) & quiet(X0)) <=> (~wise(X0) & generous(X0))) [input p9]
11. ! [X0] : ((~generous(X0) | ~curious(X0)) => generous(X0)) [input p10]
13. ! [X0] : ((~funny(X0) & ~curious(X0)) <=> (happy(X0) | ~patient(X0))) [input p12]
15. ! [X0] : (quiet(X0) <=> generous(X0)) [input p14]
19. funny(mary) <~> patient(mary) [input p18]
24. wise(mary) [input hypothesis]
27. ! [X0] : ((~tall(X0) & ~brave(X0)) | (~patient(X0) & kind(X0))) [ennf transformation 4]
31. ! [X0] : (generous(X0) | (generous(X0) & curious(X0))) [ennf transformation 11]
49. ! [X0] : (((~tall(X0) & quiet(X0)) | (wise(X0) | ~generous(X0))) & ((~wise(X0) & generous(X0)) | (tall(X0) | ~quiet(X0)))) [nnf transformation 10]
50. ! [X0] : (((~tall(X0) & quiet(X0)) | wise(X0) | ~generous(X0)) & ((~wise(X0) & generous(X0)) | tall(X0) | ~quiet(X0))) [flattening 49]
52. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & ((happy(X0) | ~patient(X0)) | (funny(X0) | curious(X0)))) [nnf transformation 13]
53. ! [X0] : (((~funny(X0) & ~curious(X0)) | (~happy(X0) & patient(X0))) & (happy(X0) | ~patient(X0) | funny(X0) | curious(X0))) [flattening 52]
56. ! [X0] : ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0))) [nnf transformation 15]
62. (~patient(mary) | ~funny(mary)) & (patient(mary) | funny(mary)) [nnf transformation 19]
83. ~patient(X0) | ~tall(X0) [cnf transformation 27]
99. ~wise(X0) | tall(X0) | ~quiet(X0) [cnf transformation 50]
103. generous(X0) | generous(X0) [cnf transformation 31]
109. ~funny(X0) | patient(X0) [cnf transformation 53]
118. quiet(X0) | ~generous(X0) [cnf transformation 56]
125. patient(mary) | funny(mary) [cnf transformation 62]
126. ~patient(mary) | ~funny(mary) [cnf transformation 62]
133. wise(mary) [cnf transformation 24]
135. generous(X0) [duplicate literal removal 103]
150. 4 <=> patient(mary) [avatar definition]
151. patient(mary) <- (4) [avatar component clause 150]
178. quiet(X0) [subsumption resolution 118,135]
208. ~funny(mary) [subsumption resolution 126,109]
209. patient(mary) [subsumption resolution 125,208]
210. 4 [avatar split clause 209,150]
221. ~tall(mary) <- (4) [resolution 83,151]
294. tall(mary) | ~quiet(mary) [resolution 99,133]
298. ~quiet(mary) <- (4) [subsumption resolution 294,221]
299. $false <- (4) [subsumption resolution 298,178]
300. ~4 [avatar contradiction clause 299]
301. $false [avatar sat refutation 210,300]
% SZS output end Proof for 1991396571306672396170757
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative or brave then someone is both wise and happy.
Everyone who is either brave or not strong is either not old or quiet and vice versa.
Everyone who is patient is tall or not quiet and vice versa.
Everyone who is both rich and not creative is either wise or creative and vice versa.
Everyone who is both not patient and not quiet is either calm or funny and vice versa.
If someone is old or strong then someone is either generous or patient and vice versa.
Everyone who is not kind or happy is both not humble and happy.
Everyone who is kind is humble and vice versa.
Everyone who is both not wise and not patient is either not happy or not quiet.
Everyone who is strong or not quiet is not old.
If fred is both not strong and curious then someone is not humble or kind and vice versa.
Everyone who is either old or not kind is both funny and not happy and vice versa.
Everyone who is not happy is curious or not wise and vice versa.
Everyone who is both calm and funny is quiet or not calm and vice versa.
Everyone who is both not funny and calm is generous or not happy.
Susan is not curious.
Someone is not humble or not brave.
Someone is either not happy or creative.
Someone is either happy or calm.
Someone is rich.
Someone is not kind or strong.
Someone is not wise or not quiet. | Fred is old. | entailment | ((?[X]:((~creative(X)|brave(X))))=>(?[X]:((wise(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>(~old(X)<~>quiet(X))))&
(![X]:(patient(X)<=>(tall(X)|~quiet(X))))&
(![X]:((rich(X)&~creative(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)&~quiet(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((old(X)|strong(X))))<=>(?[X]:((generous(X)<~>patient(X)))))&
(![X]:((~kind(X)|happy(X))=>(~humble(X)&happy(X))))&
(![X]:(kind(X)<=>humble(X)))&
(![X]:((~wise(X)&~patient(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|~quiet(X))=>~old(X)))&
(((~strong(fred)&curious(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:(~happy(X)<=>(curious(X)|~wise(X))))&
(![X]:((calm(X)&funny(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~funny(X)&calm(X))=>(generous(X)|~happy(X))))&
(~curious(susan))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~wise(X)|~quiet(X)))) | old(fred) | [
"p2",
"p4",
"p6",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1374831299624024092469324
% SZS output start Proof for 1374831299624024092469324
3. ! [X0] : (patient(X0) <=> (~quiet(X0) | tall(X0))) [input p2]
5. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (calm(X0) <~> funny(X0))) [input p4]
7. ! [X0] : ((happy(X0) | ~kind(X0)) => (happy(X0) & ~humble(X0))) [input p6]
8. ! [X0] : (kind(X0) <=> humble(X0)) [input p7]
12. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> (~happy(X0) & funny(X0))) [input p11]
14. ! [X0] : ((funny(X0) & calm(X0)) <=> (~calm(X0) | quiet(X0))) [input p13]
23. ~old(fred) [input hypothesis]
27. ! [X0] : ((happy(X0) & ~humble(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 7]
37. ! [X0] : ((patient(X0) | (quiet(X0) & ~tall(X0))) & ((~quiet(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 3]
38. ! [X0] : ((patient(X0) | (quiet(X0) & ~tall(X0))) & (~quiet(X0) | tall(X0) | ~patient(X0))) [flattening 37]
41. ! [X0] : (((~quiet(X0) & ~patient(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (quiet(X0) | patient(X0)))) [nnf transformation 5]
42. ! [X0] : (((~quiet(X0) & ~patient(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | quiet(X0) | patient(X0))) [flattening 41]
48. ! [X0] : ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))) [nnf transformation 8]
55. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 12]
56. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [flattening 55]
59. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 14]
60. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | ~funny(X0) | ~calm(X0))) [flattening 59]
89. patient(X0) | quiet(X0) [cnf transformation 38]
98. ~calm(X0) | funny(X0) | ~patient(X0) [cnf transformation 42]
109. ~humble(X0) | ~happy(X0) [cnf transformation 27]
110. kind(X0) | happy(X0) [cnf transformation 27]
112. ~kind(X0) | humble(X0) [cnf transformation 48]
126. ~happy(X0) | old(X0) | kind(X0) [cnf transformation 56]
127. ~kind(X0) | old(X0) | happy(X0) | ~funny(X0) [cnf transformation 56]
134. calm(X0) | calm(X0) [cnf transformation 60]
135. ~quiet(X0) | funny(X0) [cnf transformation 60]
147. ~old(fred) [cnf transformation 23]
149. calm(X0) [duplicate literal removal 134]
224. ~funny(X0) | happy(X0) | old(X0) [subsumption resolution 127,110]
225. kind(X0) | old(X0) [subsumption resolution 126,110]
279. humble(X0) | old(X0) [resolution 225,112]
316. ~patient(X0) | funny(X0) [resolution 98,149]
369. ~happy(X0) | old(X0) [resolution 279,109]
489. funny(X0) | quiet(X0) [resolution 316,89]
490. funny(X0) [subsumption resolution 489,135]
509. happy(X0) | old(X0) [resolution 490,224]
513. old(X0) [subsumption resolution 509,369]
554. $false [resolution 513,147]
% SZS output end Proof for 1374831299624024092469324
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not kind is not tall and vice versa.
Everyone who is either rich or not funny is not quiet and vice versa.
Everyone who is both brave and not rich is either happy or not tall and vice versa.
Everyone who is both not funny and calm is rich or creative.
Everyone who is not patient is both humble and not funny and vice versa.
Everyone who is both not brave and not quiet is either not brave or not creative.
Everyone who is either not happy or calm is funny.
Everyone who is funny or not wise is either wise or quiet.
Everyone who is either brave or old is humble or not tall and vice versa.
Everyone who is either tall or not funny is either brave or not generous.
If someone is calm or not quiet then fred is calm.
Everyone who is either not wise or not rich is funny.
Everyone who is both strong and not generous is not tall.
Everyone who is funny or not humble is not calm or generous and vice versa.
If someone is generous then john is tall and vice versa.
If alice is both not humble and not tall then fred is not rich or not humble.
Someone is brave or not brave.
Someone is either generous or not wise.
Someone is both not humble and happy.
John is creative.
Someone is kind.
Fred is either not generous or quiet.
John is tall or not humble.
Fred is both generous and not kind. | Alice is not tall. | neutral | (![X]:((quiet(X)&~kind(X))<=>~tall(X)))&
(![X]:((rich(X)<~>~funny(X))<=>~quiet(X)))&
(![X]:((brave(X)&~rich(X))<=>(happy(X)<~>~tall(X))))&
(![X]:((~funny(X)&calm(X))=>(rich(X)|creative(X))))&
(![X]:(~patient(X)<=>(humble(X)&~funny(X))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)<~>~creative(X))))&
(![X]:((~happy(X)<~>calm(X))=>funny(X)))&
(![X]:((funny(X)|~wise(X))=>(wise(X)<~>quiet(X))))&
(![X]:((brave(X)<~>old(X))<=>(humble(X)|~tall(X))))&
(![X]:((tall(X)<~>~funny(X))=>(brave(X)<~>~generous(X))))&
((?[X]:((calm(X)|~quiet(X))))=>(calm(fred)))&
(![X]:((~wise(X)<~>~rich(X))=>funny(X)))&
(![X]:((strong(X)&~generous(X))=>~tall(X)))&
(![X]:((funny(X)|~humble(X))<=>(~calm(X)|generous(X))))&
((?[X]:(generous(X)))<=>(tall(john)))&
(((~humble(alice)&~tall(alice)))=>((~rich(fred)|~humble(fred))))&
(?[X]:((brave(X)|~brave(X))))&
(?[X]:((generous(X)<~>~wise(X))))&
(?[X]:((~humble(X)&happy(X))))&
(creative(john))&
(?[X]:(kind(X)))&
((~generous(fred)<~>quiet(fred)))&
((tall(john)|~humble(john)))&
((generous(fred)&~kind(fred))) | ~tall(alice) | [] | null | 0 |
If paul is either happy or rich then someone is kind or wise. If susan is not kind then someone is either brave or not old and vice versa. If paul is curious then susan is both generous and not creative and vice versa. If someone is both not humble and not rich then susan is not curious. If someone is either strong or happy then someone is both generous and curious and vice versa. If mary is both rich and not quiet then someone is both not funny and not creative and vice versa. Everyone who is both curious and funny is not tall and vice versa. Everyone who is not wise is not rich or humble. Everyone who is not generous is both not tall and not quiet and vice versa. Everyone who is not patient or not creative is not curious and vice versa. Everyone who is humble or not brave is kind and vice versa. If someone is strong then someone is both wise and not wise. Everyone who is both not creative and funny is strong and vice versa. If fred is calm then lucy is either not generous or generous. Everyone who is both not strong and patient is both not patient and not quiet. If someone is not tall or not funny then someone is not strong or brave and vice versa. Susan is not calm or tall. Lucy is not creative. John is either not happy or not brave. Susan is both not patient and not happy. John is not humble or brave. Someone is both calm and not funny. Someone is both quiet and not calm. | Mary is quiet. | contradiction | (((happy(paul)<~>rich(paul)))=>(?[X]:((kind(X)|wise(X)))))&
((~kind(susan))<=>(?[X]:((brave(X)<~>~old(X)))))&
((curious(paul))<=>((generous(susan)&~creative(susan))))&
((?[X]:((~humble(X)&~rich(X))))=>(~curious(susan)))&
((?[X]:((strong(X)<~>happy(X))))<=>(?[X]:((generous(X)&curious(X)))))&
(((rich(mary)&~quiet(mary)))<=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((curious(X)&funny(X))<=>~tall(X)))&
(![X]:(~wise(X)=>(~rich(X)|humble(X))))&
(![X]:(~generous(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((~patient(X)|~creative(X))<=>~curious(X)))&
(![X]:((humble(X)|~brave(X))<=>kind(X)))&
((?[X]:(strong(X)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~creative(X)&funny(X))<=>strong(X)))&
((calm(fred))=>((~generous(lucy)<~>generous(lucy))))&
(![X]:((~strong(X)&patient(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
((~calm(susan)|tall(susan)))&
(~creative(lucy))&
((~happy(john)<~>~brave(john)))&
((~patient(susan)&~happy(susan)))&
((~humble(john)|brave(john)))&
(?[X]:((calm(X)&~funny(X))))&
(?[X]:((quiet(X)&~calm(X)))) | quiet(mary) | [
"p5",
"p11",
"p12",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2160509260978384197993714
% SZS output start Proof for 2160509260978384197993714
6. (~quiet(mary) & rich(mary)) <=> ? [X0] : (~creative(X0) & ~funny(X0)) [input p5]
12. ? [X0] : strong(X0) => ? [X0] : (~wise(X0) & wise(X0)) [input p11]
13. ! [X0] : ((funny(X0) & ~creative(X0)) <=> strong(X0)) [input p12]
18. ~creative(lucy) [input p17]
24. quiet(mary) [input hypothesis]
26. ? [X0] : strong(X0) => ? [X1] : (~wise(X1) & wise(X1)) [rectify 12]
32. ? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : ~strong(X0) [ennf transformation 26]
50. ((~quiet(mary) & rich(mary)) | ! [X0] : (creative(X0) | funny(X0))) & (? [X0] : (~creative(X0) & ~funny(X0)) | (quiet(mary) | ~rich(mary))) [nnf transformation 6]
51. ((~quiet(mary) & rich(mary)) | ! [X0] : (creative(X0) | funny(X0))) & (? [X0] : (~creative(X0) & ~funny(X0)) | quiet(mary) | ~rich(mary)) [flattening 50]
52. ((~quiet(mary) & rich(mary)) | ! [X0] : (creative(X0) | funny(X0))) & (? [X1] : (~creative(X1) & ~funny(X1)) | quiet(mary) | ~rich(mary)) [rectify 51]
53. ? [X1] : (~creative(X1) & ~funny(X1)) => (~creative(sK4) & ~funny(sK4)) [choice axiom]
54. ((~quiet(mary) & rich(mary)) | ! [X0] : (creative(X0) | funny(X0))) & ((~creative(sK4) & ~funny(sK4)) | quiet(mary) | ~rich(mary)) [skolemisation 52,53]
63. ? [X0] : (~wise(X0) & wise(X0)) | ! [X1] : ~strong(X1) [rectify 32]
64. ? [X0] : (~wise(X0) & wise(X0)) => (~wise(sK5) & wise(sK5)) [choice axiom]
65. (~wise(sK5) & wise(sK5)) | ! [X1] : ~strong(X1) [skolemisation 63,64]
66. ! [X0] : (((funny(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | (~funny(X0) | creative(X0)))) [nnf transformation 13]
67. ! [X0] : (((funny(X0) & ~creative(X0)) | ~strong(X0)) & (strong(X0) | ~funny(X0) | creative(X0))) [flattening 66]
98. ~quiet(mary) | creative(X0) | funny(X0) [cnf transformation 54]
112. wise(sK5) | ~strong(X1) [cnf transformation 65]
113. ~wise(sK5) | ~strong(X1) [cnf transformation 65]
114. ~funny(X0) | strong(X0) | creative(X0) [cnf transformation 67]
126. ~creative(lucy) [cnf transformation 18]
136. quiet(mary) [cnf transformation 24]
233. 22 <=> ! [X0] : (creative(X0) | funny(X0)) [avatar definition]
234. funny(X0) | creative(X0) <- (22) [avatar component clause 233]
236. 23 <=> quiet(mary) [avatar definition]
239. 22 | ~23 [avatar split clause 98,236,233]
256. 27 <=> ! [X1] : ~strong(X1) [avatar definition]
257. ~strong(X1) <- (27) [avatar component clause 256]
259. 28 <=> wise(sK5) [avatar definition]
262. 27 | ~28 [avatar split clause 113,259,256]
263. 27 | 28 [avatar split clause 112,259,256]
320. 23 [avatar split clause 136,236]
365. strong(X0) | creative(X0) | creative(X0) <- (22) [resolution 114,234]
366. strong(X0) | creative(X0) <- (22) [duplicate literal removal 365]
367. creative(X0) <- (22, 27) [subsumption resolution 366,257]
368. $false <- (22, 27) [resolution 367,126]
369. ~22 | ~27 [avatar contradiction clause 368]
370. $false [avatar sat refutation 239,262,263,320,369]
% SZS output end Proof for 2160509260978384197993714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or not calm is tall.
Everyone who is not tall is either not tall or not quiet and vice versa.
If fred is either not brave or not quiet then someone is both not old and not kind.
Everyone who is humble is not rich or wise and vice versa.
Everyone who is not rich or rich is happy or curious.
If someone is curious or not generous then someone is not brave and vice versa.
If alice is not wise or wise then someone is either generous or rich.
If someone is strong then john is either funny or not generous.
Everyone who is either humble or not brave is either humble or calm and vice versa.
Everyone who is either funny or not generous is both not calm and not curious and vice versa.
Everyone who is wise or quiet is not curious and vice versa.
Everyone who is not calm or tall is either not wise or not creative.
If alice is both kind and brave then paul is not generous and vice versa.
If someone is calm or strong then mary is both curious and tall and vice versa.
Everyone who is old is both not rich and kind.
Everyone who is not quiet or not creative is generous and vice versa.
Fred is curious or brave.
Someone is either not funny or old.
Someone is either curious or not curious.
Mary is brave.
Someone is both not patient and tall.
Susan is either not curious or not humble. | Fred is humble. | entailment | (![X]:((patient(X)<~>~calm(X))=>tall(X)))&
(![X]:(~tall(X)<=>(~tall(X)<~>~quiet(X))))&
(((~brave(fred)<~>~quiet(fred)))=>(?[X]:((~old(X)&~kind(X)))))&
(![X]:(humble(X)<=>(~rich(X)|wise(X))))&
(![X]:((~rich(X)|rich(X))=>(happy(X)|curious(X))))&
((?[X]:((curious(X)|~generous(X))))<=>(?[X]:(~brave(X))))&
(((~wise(alice)|wise(alice)))=>(?[X]:((generous(X)<~>rich(X)))))&
((?[X]:(strong(X)))=>((funny(john)<~>~generous(john))))&
(![X]:((humble(X)<~>~brave(X))<=>(humble(X)<~>calm(X))))&
(![X]:((funny(X)<~>~generous(X))<=>(~calm(X)&~curious(X))))&
(![X]:((wise(X)|quiet(X))<=>~curious(X)))&
(![X]:((~calm(X)|tall(X))=>(~wise(X)<~>~creative(X))))&
(((kind(alice)&brave(alice)))<=>(~generous(paul)))&
((?[X]:((calm(X)|strong(X))))<=>((curious(mary)&tall(mary))))&
(![X]:(old(X)=>(~rich(X)&kind(X))))&
(![X]:((~quiet(X)|~creative(X))<=>generous(X)))&
((curious(fred)|brave(fred)))&
(?[X]:((~funny(X)<~>old(X))))&
(?[X]:((curious(X)<~>~curious(X))))&
(brave(mary))&
(?[X]:((~patient(X)&tall(X))))&
((~curious(susan)<~>~humble(susan))) | humble(fred) | [
"p1",
"p3",
"p5",
"p8",
"p10",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3951306107463031728811062
% SZS output start Proof for 3951306107463031728811062
2. ! [X0] : (~tall(X0) <=> (~tall(X0) <~> ~quiet(X0))) [input p1]
4. ! [X0] : (humble(X0) <=> (wise(X0) | ~rich(X0))) [input p3]
6. ? [X0] : (~generous(X0) | curious(X0)) <=> ? [X0] : ~brave(X0) [input p5]
9. ! [X0] : ((humble(X0) <~> ~brave(X0)) <=> (humble(X0) <~> calm(X0))) [input p8]
11. ! [X0] : ((quiet(X0) | wise(X0)) <=> ~curious(X0)) [input p10]
12. ! [X0] : ((tall(X0) | ~calm(X0)) => (~wise(X0) <~> ~creative(X0))) [input p11]
14. ? [X0] : (strong(X0) | calm(X0)) <=> (tall(mary) & curious(mary)) [input p13]
16. ! [X0] : ((~creative(X0) | ~quiet(X0)) <=> generous(X0)) [input p15]
23. ~humble(fred) [input hypothesis]
24. ? [X0] : (~generous(X0) | curious(X0)) <=> ? [X1] : ~brave(X1) [rectify 6]
30. ! [X0] : ((~wise(X0) <~> ~creative(X0)) | (~tall(X0) & calm(X0))) [ennf transformation 12]
33. ! [X0] : ((~tall(X0) | ((~tall(X0) | quiet(X0)) & (~quiet(X0) | tall(X0)))) & (((quiet(X0) | tall(X0)) & (~quiet(X0) | ~tall(X0))) | tall(X0))) [nnf transformation 2]
37. ! [X0] : ((humble(X0) | (~wise(X0) & rich(X0))) & ((wise(X0) | ~rich(X0)) | ~humble(X0))) [nnf transformation 4]
38. ! [X0] : ((humble(X0) | (~wise(X0) & rich(X0))) & (wise(X0) | ~rich(X0) | ~humble(X0))) [flattening 37]
39. (? [X0] : (~generous(X0) | curious(X0)) | ! [X1] : brave(X1)) & (? [X1] : ~brave(X1) | ! [X0] : (generous(X0) & ~curious(X0))) [nnf transformation 24]
40. (? [X0] : (~generous(X0) | curious(X0)) | ! [X1] : brave(X1)) & (? [X2] : ~brave(X2) | ! [X3] : (generous(X3) & ~curious(X3))) [rectify 39]
41. ? [X0] : (~generous(X0) | curious(X0)) => (~generous(sK1) | curious(sK1)) [choice axiom]
42. ? [X2] : ~brave(X2) => ~brave(sK2) [choice axiom]
43. ((~generous(sK1) | curious(sK1)) | ! [X1] : brave(X1)) & (~brave(sK2) | ! [X3] : (generous(X3) & ~curious(X3))) [skolemisation 40,42,41]
48. ! [X0] : ((((brave(X0) | ~humble(X0)) & (~brave(X0) | humble(X0))) | ((humble(X0) | ~calm(X0)) & (calm(X0) | ~humble(X0)))) & (((~calm(X0) | ~humble(X0)) & (calm(X0) | humble(X0))) | ((humble(X0) | brave(X0)) & (~brave(X0) | ~humble(X0))))) [nnf transformation 9]
51. ! [X0] : (((quiet(X0) | wise(X0)) | curious(X0)) & (~curious(X0) | (~quiet(X0) & ~wise(X0)))) [nnf transformation 11]
52. ! [X0] : ((quiet(X0) | wise(X0) | curious(X0)) & (~curious(X0) | (~quiet(X0) & ~wise(X0)))) [flattening 51]
53. ! [X0] : (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | (~tall(X0) & calm(X0))) [nnf transformation 30]
56. (? [X0] : (strong(X0) | calm(X0)) | (~tall(mary) | ~curious(mary))) & ((tall(mary) & curious(mary)) | ! [X0] : (~strong(X0) & ~calm(X0))) [nnf transformation 14]
57. (? [X0] : (strong(X0) | calm(X0)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X0] : (~strong(X0) & ~calm(X0))) [flattening 56]
58. (? [X0] : (strong(X0) | calm(X0)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X1] : (~strong(X1) & ~calm(X1))) [rectify 57]
59. ? [X0] : (strong(X0) | calm(X0)) => (strong(sK4) | calm(sK4)) [choice axiom]
60. ((strong(sK4) | calm(sK4)) | ~tall(mary) | ~curious(mary)) & ((tall(mary) & curious(mary)) | ! [X1] : (~strong(X1) & ~calm(X1))) [skolemisation 58,59]
61. ! [X0] : (((~creative(X0) | ~quiet(X0)) | ~generous(X0)) & (generous(X0) | (creative(X0) & quiet(X0)))) [nnf transformation 16]
62. ! [X0] : ((~creative(X0) | ~quiet(X0) | ~generous(X0)) & (generous(X0) | (creative(X0) & quiet(X0)))) [flattening 61]
75. quiet(X0) | tall(X0) | tall(X0) [cnf transformation 33]
77. ~tall(X0) | ~tall(X0) | quiet(X0) [cnf transformation 33]
84. ~wise(X0) | humble(X0) [cnf transformation 38]
86. ~brave(sK2) | generous(X3) [cnf transformation 43]
95. calm(X0) | humble(X0) | humble(X0) | brave(X0) [cnf transformation 48]
100. brave(X0) | ~humble(X0) | calm(X0) | ~humble(X0) [cnf transformation 48]
109. ~curious(X0) | ~quiet(X0) [cnf transformation 52]
113. creative(X0) | wise(X0) | calm(X0) [cnf transformation 53]
118. curious(mary) | ~calm(X1) [cnf transformation 60]
127. ~creative(X0) | ~quiet(X0) | ~generous(X0) [cnf transformation 62]
138. ~humble(fred) [cnf transformation 23]
139. calm(X0) | humble(X0) | brave(X0) [duplicate literal removal 95]
142. brave(X0) | ~humble(X0) | calm(X0) [duplicate literal removal 100]
143. quiet(X0) | tall(X0) [duplicate literal removal 75]
144. ~tall(X0) | quiet(X0) [duplicate literal removal 77]
145. quiet(X0) [subsumption resolution 143,144]
175. 7 <=> ! [X3] : generous(X3) [avatar definition]
176. generous(X3) <- (7) [avatar component clause 175]
178. 8 <=> brave(sK2) [avatar definition]
180. ~brave(sK2) <- (~8) [avatar component clause 178]
181. 7 | ~8 [avatar split clause 86,178,175]
183. 9 <=> ! [X3] : ~curious(X3) [avatar definition]
184. ~curious(X3) <- (9) [avatar component clause 183]
216. brave(X0) | calm(X0) [subsumption resolution 139,142]
217. ~curious(X0) [subsumption resolution 109,145]
218. 9 [avatar split clause 217,183]
235. 19 <=> curious(mary) [avatar definition]
236. curious(mary) <- (19) [avatar component clause 235]
253. 23 <=> ! [X1] : ~calm(X1) [avatar definition]
254. ~calm(X1) <- (23) [avatar component clause 253]
257. 23 | 19 [avatar split clause 118,235,253]
258. ~creative(X0) | ~generous(X0) [subsumption resolution 127,145]
284. $false <- (9, 19) [resolution 236,184]
285. ~9 | ~19 [avatar contradiction clause 284]
298. calm(sK2) <- (~8) [resolution 216,180]
300. $false <- (~8, 23) [subsumption resolution 298,254]
301. 8 | ~23 [avatar contradiction clause 300]
317. wise(X2) | calm(X2) | ~generous(X2) [resolution 113,258]
319. wise(X2) | ~generous(X2) <- (23) [subsumption resolution 317,254]
320. wise(X2) <- (7, 23) [subsumption resolution 319,176]
325. humble(X0) <- (7, 23) [resolution 320,84]
332. $false <- (7, 23) [resolution 325,138]
333. ~7 | ~23 [avatar contradiction clause 332]
334. $false [avatar sat refutation 181,218,257,285,301,333]
% SZS output end Proof for 3951306107463031728811062
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either not calm or generous is both funny and quiet and vice versa. If paul is either not rich or tall then lucy is either kind or not old and vice versa. Everyone who is either patient or not humble is calm. If fred is either kind or not brave then someone is not old and vice versa. Everyone who is not creative or patient is both tall and generous and vice versa. If someone is both calm and patient then someone is patient. If paul is kind or not wise then fred is wise or not strong and vice versa. Everyone who is not creative is humble. Everyone who is not quiet is both not rich and curious. Everyone who is not funny or rich is both not creative and not patient and vice versa. If someone is either not kind or patient then someone is not rich or patient. Everyone who is either not tall or not old is not funny and vice versa. Everyone who is either not funny or wise is rich or not old. Everyone who is wise or not brave is both not wise and not curious and vice versa. If lucy is generous or not happy then alice is not humble. Everyone who is both not calm and old is wise or humble. Someone is rich. Fred is not quiet or calm. Fred is both not kind and humble. Someone is funny. Fred is both tall and not creative. Someone is brave or not patient. Mary is either not brave or not tall. Someone is not calm. | Fred is calm. | entailment | (![X]:((~calm(X)<~>generous(X))<=>(funny(X)&quiet(X))))&
(((~rich(paul)<~>tall(paul)))<=>((kind(lucy)<~>~old(lucy))))&
(![X]:((patient(X)<~>~humble(X))=>calm(X)))&
(((kind(fred)<~>~brave(fred)))<=>(?[X]:(~old(X))))&
(![X]:((~creative(X)|patient(X))<=>(tall(X)&generous(X))))&
((?[X]:((calm(X)&patient(X))))=>(?[X]:(patient(X))))&
(((kind(paul)|~wise(paul)))<=>((wise(fred)|~strong(fred))))&
(![X]:(~creative(X)=>humble(X)))&
(![X]:(~quiet(X)=>(~rich(X)&curious(X))))&
(![X]:((~funny(X)|rich(X))<=>(~creative(X)&~patient(X))))&
((?[X]:((~kind(X)<~>patient(X))))=>(?[X]:((~rich(X)|patient(X)))))&
(![X]:((~tall(X)<~>~old(X))<=>~funny(X)))&
(![X]:((~funny(X)<~>wise(X))=>(rich(X)|~old(X))))&
(![X]:((wise(X)|~brave(X))<=>(~wise(X)&~curious(X))))&
(((generous(lucy)|~happy(lucy)))=>(~humble(alice)))&
(![X]:((~calm(X)&old(X))=>(wise(X)|humble(X))))&
(?[X]:(rich(X)))&
((~quiet(fred)|calm(fred)))&
((~kind(fred)&humble(fred)))&
(?[X]:(funny(X)))&
((tall(fred)&~creative(fred)))&
(?[X]:((brave(X)|~patient(X))))&
((~brave(mary)<~>~tall(mary)))&
(?[X]:(~calm(X))) | calm(fred) | [
"p2",
"p3",
"p4",
"p8",
"p9",
"p11",
"p13",
"p17",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5408666427965023342100744
% SZS output start Proof for 5408666427965023342100744
3. ! [X0] : ((patient(X0) <~> ~humble(X0)) => calm(X0)) [input p2]
4. (kind(fred) <~> ~brave(fred)) <=> ? [X0] : ~old(X0) [input p3]
5. ! [X0] : ((patient(X0) | ~creative(X0)) <=> (generous(X0) & tall(X0))) [input p4]
9. ! [X0] : (~quiet(X0) => (curious(X0) & ~rich(X0))) [input p8]
10. ! [X0] : ((rich(X0) | ~funny(X0)) <=> (~patient(X0) & ~creative(X0))) [input p9]
12. ! [X0] : ((~tall(X0) <~> ~old(X0)) <=> ~funny(X0)) [input p11]
14. ! [X0] : ((~brave(X0) | wise(X0)) <=> (~curious(X0) & ~wise(X0))) [input p13]
18. calm(fred) | ~quiet(fred) [input p17]
19. humble(fred) & ~kind(fred) [input p18]
21. ~creative(fred) & tall(fred) [input p20]
25. ~calm(fred) [input hypothesis]
29. ! [X0] : (calm(X0) | (patient(X0) <=> ~humble(X0))) [ennf transformation 3]
32. ! [X0] : ((curious(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 9]
42. ! [X0] : (calm(X0) | ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0)))) [nnf transformation 29]
43. (((brave(fred) | ~kind(fred)) & (~brave(fred) | kind(fred))) | ! [X0] : old(X0)) & (? [X0] : ~old(X0) | ((kind(fred) | brave(fred)) & (~brave(fred) | ~kind(fred)))) [nnf transformation 4]
44. (((brave(fred) | ~kind(fred)) & (~brave(fred) | kind(fred))) | ! [X0] : old(X0)) & (? [X1] : ~old(X1) | ((kind(fred) | brave(fred)) & (~brave(fred) | ~kind(fred)))) [rectify 43]
45. ? [X1] : ~old(X1) => ~old(sK0) [choice axiom]
46. (((brave(fred) | ~kind(fred)) & (~brave(fred) | kind(fred))) | ! [X0] : old(X0)) & (~old(sK0) | ((kind(fred) | brave(fred)) & (~brave(fred) | ~kind(fred)))) [skolemisation 44,45]
47. ! [X0] : (((patient(X0) | ~creative(X0)) | (~generous(X0) | ~tall(X0))) & ((generous(X0) & tall(X0)) | (~patient(X0) & creative(X0)))) [nnf transformation 5]
48. ! [X0] : ((patient(X0) | ~creative(X0) | ~generous(X0) | ~tall(X0)) & ((generous(X0) & tall(X0)) | (~patient(X0) & creative(X0)))) [flattening 47]
54. ! [X0] : (((rich(X0) | ~funny(X0)) | (patient(X0) | creative(X0))) & ((~patient(X0) & ~creative(X0)) | (~rich(X0) & funny(X0)))) [nnf transformation 10]
55. ! [X0] : ((rich(X0) | ~funny(X0) | patient(X0) | creative(X0)) & ((~patient(X0) & ~creative(X0)) | (~rich(X0) & funny(X0)))) [flattening 54]
60. ! [X0] : ((((old(X0) | tall(X0)) & (~old(X0) | ~tall(X0))) | funny(X0)) & (~funny(X0) | ((~tall(X0) | old(X0)) & (~old(X0) | tall(X0))))) [nnf transformation 12]
62. ! [X0] : (((~brave(X0) | wise(X0)) | (curious(X0) | wise(X0))) & ((~curious(X0) & ~wise(X0)) | (brave(X0) & ~wise(X0)))) [nnf transformation 14]
63. ! [X0] : ((~brave(X0) | wise(X0) | curious(X0) | wise(X0)) & ((~curious(X0) & ~wise(X0)) | (brave(X0) & ~wise(X0)))) [flattening 62]
87. ~humble(X0) | calm(X0) | ~patient(X0) [cnf transformation 42]
91. ~brave(fred) | kind(fred) | old(X0) [cnf transformation 46]
93. creative(X0) | tall(X0) [cnf transformation 48]
104. ~rich(X0) | quiet(X0) [cnf transformation 32]
105. curious(X0) | quiet(X0) [cnf transformation 32]
106. ~creative(X0) | funny(X0) [cnf transformation 55]
110. ~funny(X0) | rich(X0) | patient(X0) | creative(X0) [cnf transformation 55]
115. ~old(X0) | ~tall(X0) | funny(X0) [cnf transformation 60]
122. ~curious(X0) | brave(X0) [cnf transformation 63]
127. calm(fred) | ~quiet(fred) [cnf transformation 18]
128. ~kind(fred) [cnf transformation 19]
129. humble(fred) [cnf transformation 19]
132. ~creative(fred) [cnf transformation 21]
137. ~calm(fred) [cnf transformation 25]
165. 5 <=> ! [X0] : old(X0) [avatar definition]
166. old(X0) <- (5) [avatar component clause 165]
168. 6 <=> kind(fred) [avatar definition]
172. 7 <=> brave(fred) [avatar definition]
173. ~brave(fred) <- (~7) [avatar component clause 172]
176. 5 | 6 | ~7 [avatar split clause 91,172,168,165]
236. 20 <=> quiet(fred) [avatar definition]
238. ~quiet(fred) <- (~20) [avatar component clause 236]
240. 21 <=> calm(fred) [avatar definition]
241. ~calm(fred) <- (~21) [avatar component clause 240]
243. ~20 | 21 [avatar split clause 127,240,236]
244. ~6 [avatar split clause 128,168]
264. ~21 [avatar split clause 137,240]
271. tall(X2) | funny(X2) [resolution 106,93]
276. brave(X0) | quiet(X0) [resolution 122,105]
282. calm(fred) | ~patient(fred) [resolution 87,129]
284. ~patient(fred) <- (~21) [subsumption resolution 282,241]
449. quiet(fred) <- (~7) [resolution 276,173]
452. $false <- (~7, ~20) [subsumption resolution 449,238]
453. 7 | 20 [avatar contradiction clause 452]
456. ~tall(X2) | funny(X2) <- (5) [resolution 166,115]
463. funny(X2) <- (5) [subsumption resolution 456,271]
472. creative(X0) | patient(X0) | rich(X0) <- (5) [resolution 463,110]
531. patient(fred) | rich(fred) <- (5) [resolution 472,132]
536. rich(fred) <- (5, ~21) [subsumption resolution 531,284]
569. quiet(fred) <- (5, ~21) [resolution 536,104]
570. $false <- (5, ~20, ~21) [subsumption resolution 569,238]
571. ~5 | 20 | 21 [avatar contradiction clause 570]
572. $false [avatar sat refutation 176,243,244,264,453,571]
% SZS output end Proof for 5408666427965023342100744
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not rich or not kind then someone is old.
Everyone who is not strong or not creative is happy or not happy.
Everyone who is creative is not wise or kind.
If susan is kind or not curious then someone is both not quiet and old.
If alice is generous or not brave then someone is tall and vice versa.
If fred is not funny then alice is tall or rich and vice versa.
If someone is brave then fred is either not tall or not creative.
Everyone who is either not humble or curious is either generous or not curious and vice versa.
Everyone who is funny or not calm is wise and vice versa.
If fred is either not quiet or kind then someone is not rich or not curious and vice versa.
If someone is not humble or not creative then someone is old and vice versa.
If mary is either not calm or quiet then someone is tall or not funny and vice versa.
Everyone who is both patient and not brave is either not creative or calm and vice versa.
Everyone who is either not humble or generous is both not curious and funny and vice versa.
Everyone who is both old and not calm is curious.
If someone is rich or creative then mary is both patient and curious and vice versa.
Someone is not wise or not curious.
Mary is both tall and old.
Fred is not humble or strong.
Fred is brave or not brave.
Someone is both not generous and wise.
Someone is not patient or calm.
Mary is both not happy and not generous.
John is not curious. | Alice is not curious. | entailment | ((?[X]:((~rich(X)|~kind(X))))=>(?[X]:(old(X))))&
(![X]:((~strong(X)|~creative(X))=>(happy(X)|~happy(X))))&
(![X]:(creative(X)=>(~wise(X)|kind(X))))&
(((kind(susan)|~curious(susan)))=>(?[X]:((~quiet(X)&old(X)))))&
(((generous(alice)|~brave(alice)))<=>(?[X]:(tall(X))))&
((~funny(fred))<=>((tall(alice)|rich(alice))))&
((?[X]:(brave(X)))=>((~tall(fred)<~>~creative(fred))))&
(![X]:((~humble(X)<~>curious(X))<=>(generous(X)<~>~curious(X))))&
(![X]:((funny(X)|~calm(X))<=>wise(X)))&
(((~quiet(fred)<~>kind(fred)))<=>(?[X]:((~rich(X)|~curious(X)))))&
((?[X]:((~humble(X)|~creative(X))))<=>(?[X]:(old(X))))&
(((~calm(mary)<~>quiet(mary)))<=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((patient(X)&~brave(X))<=>(~creative(X)<~>calm(X))))&
(![X]:((~humble(X)<~>generous(X))<=>(~curious(X)&funny(X))))&
(![X]:((old(X)&~calm(X))=>curious(X)))&
((?[X]:((rich(X)|creative(X))))<=>((patient(mary)&curious(mary))))&
(?[X]:((~wise(X)|~curious(X))))&
((tall(mary)&old(mary)))&
((~humble(fred)|strong(fred)))&
((brave(fred)|~brave(fred)))&
(?[X]:((~generous(X)&wise(X))))&
(?[X]:((~patient(X)|calm(X))))&
((~happy(mary)&~generous(mary)))&
(~curious(john)) | ~curious(alice) | [
"p7",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1658439786396139821447331
% SZS output start Proof for 1658439786396139821447331
8. ! [X0] : ((~humble(X0) <~> curious(X0)) <=> (generous(X0) <~> ~curious(X0))) [input p7]
14. ! [X0] : ((~humble(X0) <~> generous(X0)) <=> (funny(X0) & ~curious(X0))) [input p13]
25. curious(alice) [input hypothesis]
52. ! [X0] : ((((~curious(X0) | humble(X0)) & (curious(X0) | ~humble(X0))) | ((generous(X0) | curious(X0)) & (~curious(X0) | ~generous(X0)))) & (((curious(X0) | ~generous(X0)) & (~curious(X0) | generous(X0))) | ((~humble(X0) | ~curious(X0)) & (curious(X0) | humble(X0))))) [nnf transformation 8]
70. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | (~funny(X0) | curious(X0))) & ((funny(X0) & ~curious(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [nnf transformation 14]
71. ! [X0] : ((((~generous(X0) | humble(X0)) & (generous(X0) | ~humble(X0))) | ~funny(X0) | curious(X0)) & ((funny(X0) & ~curious(X0)) | ((~humble(X0) | ~generous(X0)) & (generous(X0) | humble(X0))))) [flattening 70]
100. ~curious(X0) | generous(X0) | ~humble(X0) | ~curious(X0) [cnf transformation 52]
104. curious(X0) | ~humble(X0) | generous(X0) | curious(X0) [cnf transformation 52]
105. ~curious(X0) | humble(X0) | ~curious(X0) | ~generous(X0) [cnf transformation 52]
131. ~curious(X0) | generous(X0) | humble(X0) [cnf transformation 71]
132. ~curious(X0) | ~humble(X0) | ~generous(X0) [cnf transformation 71]
153. curious(alice) [cnf transformation 25]
154. ~curious(X0) | generous(X0) | ~humble(X0) [duplicate literal removal 100]
156. curious(X0) | ~humble(X0) | generous(X0) [duplicate literal removal 104]
157. ~curious(X0) | humble(X0) | ~generous(X0) [duplicate literal removal 105]
237. generous(X0) | ~humble(X0) [subsumption resolution 154,156]
316. ~curious(X0) | ~generous(X0) [subsumption resolution 132,157]
317. ~curious(X0) | generous(X0) [subsumption resolution 131,237]
318. ~curious(X0) [subsumption resolution 317,316]
331. $false [subsumption resolution 153,318]
% SZS output end Proof for 1658439786396139821447331
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or tall is not generous and vice versa.
Everyone who is not quiet or not happy is either not happy or not calm.
If john is old then mary is calm or brave.
If someone is brave or calm then someone is both not calm and not quiet.
Everyone who is generous is either not curious or not calm.
Everyone who is not old is creative.
Everyone who is both not curious and not calm is either not happy or brave and vice versa.
Everyone who is strong or tall is both humble and brave.
If lucy is either generous or not strong then someone is old or not calm and vice versa.
Everyone who is generous is rich or not happy and vice versa.
Everyone who is either not calm or curious is not quiet or humble.
Everyone who is not kind or funny is not brave.
Everyone who is either not creative or tall is either calm or not generous and vice versa.
Everyone who is not wise or not happy is either not generous or not wise and vice versa.
Everyone who is either not wise or quiet is either not generous or wise.
Everyone who is strong is tall or not wise and vice versa.
Fred is not tall or not old.
Someone is not curious or not patient.
Mary is either not creative or tall.
Susan is curious or strong.
Someone is not kind or generous. | John is generous. | entailment | (![X]:((~patient(X)|tall(X))<=>~generous(X)))&
(![X]:((~quiet(X)|~happy(X))=>(~happy(X)<~>~calm(X))))&
((old(john))=>((calm(mary)|brave(mary))))&
((?[X]:((brave(X)|calm(X))))=>(?[X]:((~calm(X)&~quiet(X)))))&
(![X]:(generous(X)=>(~curious(X)<~>~calm(X))))&
(![X]:(~old(X)=>creative(X)))&
(![X]:((~curious(X)&~calm(X))<=>(~happy(X)<~>brave(X))))&
(![X]:((strong(X)|tall(X))=>(humble(X)&brave(X))))&
(((generous(lucy)<~>~strong(lucy)))<=>(?[X]:((old(X)|~calm(X)))))&
(![X]:(generous(X)<=>(rich(X)|~happy(X))))&
(![X]:((~calm(X)<~>curious(X))=>(~quiet(X)|humble(X))))&
(![X]:((~kind(X)|funny(X))=>~brave(X)))&
(![X]:((~creative(X)<~>tall(X))<=>(calm(X)<~>~generous(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~generous(X)<~>~wise(X))))&
(![X]:((~wise(X)<~>quiet(X))=>(~generous(X)<~>wise(X))))&
(![X]:(strong(X)<=>(tall(X)|~wise(X))))&
((~tall(fred)|~old(fred)))&
(?[X]:((~curious(X)|~patient(X))))&
((~creative(mary)<~>tall(mary)))&
((curious(susan)|strong(susan)))&
(?[X]:((~kind(X)|generous(X)))) | generous(john) | [
"p9",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 179597170919615063159923
% SZS output start Proof for 179597170919615063159923
10. ! [X0] : (generous(X0) <=> (~happy(X0) | rich(X0))) [input p9]
14. ! [X0] : ((~happy(X0) | ~wise(X0)) <=> (~generous(X0) <~> ~wise(X0))) [input p13]
22. ~generous(john) [input hypothesis]
49. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & ((~happy(X0) | rich(X0)) | ~generous(X0))) [nnf transformation 10]
50. ! [X0] : ((generous(X0) | (happy(X0) & ~rich(X0))) & (~happy(X0) | rich(X0) | ~generous(X0))) [flattening 49]
52. ! [X0] : (((~happy(X0) | ~wise(X0)) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [nnf transformation 14]
53. ! [X0] : ((~happy(X0) | ~wise(X0) | ((~generous(X0) | wise(X0)) & (~wise(X0) | generous(X0)))) & (((wise(X0) | generous(X0)) & (~wise(X0) | ~generous(X0))) | (happy(X0) & wise(X0)))) [flattening 52]
93. generous(X0) | happy(X0) [cnf transformation 50]
105. wise(X0) | generous(X0) | wise(X0) [cnf transformation 53]
107. ~happy(X0) | ~wise(X0) | ~wise(X0) | generous(X0) [cnf transformation 53]
122. ~generous(john) [cnf transformation 22]
125. wise(X0) | generous(X0) [duplicate literal removal 105]
126. ~happy(X0) | ~wise(X0) | generous(X0) [duplicate literal removal 107]
193. ~wise(X0) | generous(X0) [subsumption resolution 126,93]
194. generous(X0) [subsumption resolution 125,193]
234. $false [subsumption resolution 122,194]
% SZS output end Proof for 179597170919615063159923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not old or not kind then lucy is both not curious and tall and vice versa.
If someone is both happy and kind then alice is both calm and wise.
Everyone who is both not curious and wise is rich and vice versa.
If lucy is either kind or wise then someone is creative and vice versa.
If alice is both humble and not wise then john is either not old or quiet.
If someone is wise then paul is not funny and vice versa.
Everyone who is both not old and tall is either not happy or not rich and vice versa.
Everyone who is wise or not humble is either quiet or not rich and vice versa.
If susan is strong or old then susan is strong or brave and vice versa.
Everyone who is either not curious or old is either old or not funny and vice versa.
Everyone who is both not humble and quiet is calm or not old and vice versa.
If someone is either humble or patient then someone is either not funny or curious.
If lucy is calm or generous then alice is not humble and vice versa.
Everyone who is not calm or tall is calm and vice versa.
Everyone who is not rich or not curious is not tall or not humble.
If someone is not quiet then mary is both happy and not calm and vice versa.
Someone is patient or not curious.
Paul is either not happy or not generous.
Lucy is not brave or curious.
Lucy is not creative.
Someone is both not curious and creative. | Alice is humble. | contradiction | (((~old(susan)<~>~kind(susan)))<=>((~curious(lucy)&tall(lucy))))&
((?[X]:((happy(X)&kind(X))))=>((calm(alice)&wise(alice))))&
(![X]:((~curious(X)&wise(X))<=>rich(X)))&
(((kind(lucy)<~>wise(lucy)))<=>(?[X]:(creative(X))))&
(((humble(alice)&~wise(alice)))=>((~old(john)<~>quiet(john))))&
((?[X]:(wise(X)))<=>(~funny(paul)))&
(![X]:((~old(X)&tall(X))<=>(~happy(X)<~>~rich(X))))&
(![X]:((wise(X)|~humble(X))<=>(quiet(X)<~>~rich(X))))&
(((strong(susan)|old(susan)))<=>((strong(susan)|brave(susan))))&
(![X]:((~curious(X)<~>old(X))<=>(old(X)<~>~funny(X))))&
(![X]:((~humble(X)&quiet(X))<=>(calm(X)|~old(X))))&
((?[X]:((humble(X)<~>patient(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(((calm(lucy)|generous(lucy)))<=>(~humble(alice)))&
(![X]:((~calm(X)|tall(X))<=>calm(X)))&
(![X]:((~rich(X)|~curious(X))=>(~tall(X)|~humble(X))))&
((?[X]:(~quiet(X)))<=>((happy(mary)&~calm(mary))))&
(?[X]:((patient(X)|~curious(X))))&
((~happy(paul)<~>~generous(paul)))&
((~brave(lucy)|curious(lucy)))&
(~creative(lucy))&
(?[X]:((~curious(X)&creative(X)))) | humble(alice) | [
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4802698919589786153945064
% SZS output start Proof for 4802698919589786153945064
13. (generous(lucy) | calm(lucy)) <=> ~humble(alice) [input p12]
14. ! [X0] : ((tall(X0) | ~calm(X0)) <=> calm(X0)) [input p13]
22. humble(alice) [input hypothesis]
56. ((generous(lucy) | calm(lucy)) | humble(alice)) & (~humble(alice) | (~generous(lucy) & ~calm(lucy))) [nnf transformation 13]
57. (generous(lucy) | calm(lucy) | humble(alice)) & (~humble(alice) | (~generous(lucy) & ~calm(lucy))) [flattening 56]
58. ! [X0] : (((tall(X0) | ~calm(X0)) | ~calm(X0)) & (calm(X0) | (~tall(X0) & calm(X0)))) [nnf transformation 14]
59. ! [X0] : ((tall(X0) | ~calm(X0) | ~calm(X0)) & (calm(X0) | (~tall(X0) & calm(X0)))) [flattening 58]
122. ~humble(alice) | ~calm(lucy) [cnf transformation 57]
125. calm(X0) | calm(X0) [cnf transformation 59]
140. humble(alice) [cnf transformation 22]
141. calm(X0) [duplicate literal removal 125]
202. 12 <=> humble(alice) [avatar definition]
243. 20 <=> calm(lucy) [avatar definition]
244. ~calm(lucy) <- (~20) [avatar component clause 243]
252. ~20 | ~12 [avatar split clause 122,202,243]
278. 12 [avatar split clause 140,202]
279. $false <- (~20) [subsumption resolution 244,141]
280. 20 [avatar contradiction clause 279]
283. $false [avatar sat refutation 252,278,280]
% SZS output end Proof for 4802698919589786153945064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not wise is not rich or humble.
Everyone who is not generous is both not tall and not quiet and vice versa.
Everyone who is not patient or not creative is not curious and vice versa.
Everyone who is humble or not brave is kind and vice versa.
If someone is strong then someone is both wise and not wise.
Everyone who is both not creative and funny is strong and vice versa.
If fred is calm then lucy is either not generous or generous.
Everyone who is both not strong and patient is both not patient and not quiet.
If someone is not tall or not funny then someone is not strong or brave and vice versa.
Everyone who is creative is either tall or humble and vice versa.
If someone is not happy then someone is quiet or not happy and vice versa.
Everyone who is either not happy or not funny is patient or not humble and vice versa.
If someone is creative then someone is not humble or creative.
If paul is not old then someone is either not calm or not happy.
Everyone who is both not kind and brave is both not quiet and old and vice versa.
If alice is either not generous or happy then lucy is both not generous and not humble.
Someone is either rich or curious.
Susan is both not strong and rich.
Alice is tall or not kind.
John is not rich.
Alice is both not funny and old.
Someone is not strong or wise. | Alice is tall. | neutral | (![X]:(~wise(X)=>(~rich(X)|humble(X))))&
(![X]:(~generous(X)<=>(~tall(X)&~quiet(X))))&
(![X]:((~patient(X)|~creative(X))<=>~curious(X)))&
(![X]:((humble(X)|~brave(X))<=>kind(X)))&
((?[X]:(strong(X)))=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:((~creative(X)&funny(X))<=>strong(X)))&
((calm(fred))=>((~generous(lucy)<~>generous(lucy))))&
(![X]:((~strong(X)&patient(X))=>(~patient(X)&~quiet(X))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~strong(X)|brave(X)))))&
(![X]:(creative(X)<=>(tall(X)<~>humble(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((~happy(X)<~>~funny(X))<=>(patient(X)|~humble(X))))&
((?[X]:(creative(X)))=>(?[X]:((~humble(X)|creative(X)))))&
((~old(paul))=>(?[X]:((~calm(X)<~>~happy(X)))))&
(![X]:((~kind(X)&brave(X))<=>(~quiet(X)&old(X))))&
(((~generous(alice)<~>happy(alice)))=>((~generous(lucy)&~humble(lucy))))&
(?[X]:((rich(X)<~>curious(X))))&
((~strong(susan)&rich(susan)))&
((tall(alice)|~kind(alice)))&
(~rich(john))&
((~funny(alice)&old(alice)))&
(?[X]:((~strong(X)|wise(X)))) | tall(alice) | [] | null | 0 |
If susan is both not strong and not rich then fred is both not strong and wise and vice versa.
If alice is either calm or brave then someone is tall and vice versa.
Everyone who is both old and not rich is tall or strong and vice versa.
Everyone who is either brave or strong is old and vice versa.
Everyone who is either not curious or not quiet is both not quiet and generous.
If someone is both rich and funny then someone is either creative or brave and vice versa.
If someone is both not patient and not rich then someone is not humble and vice versa.
If someone is both strong and not humble then fred is not quiet.
If someone is either calm or not strong then someone is not strong or not tall and vice versa.
If someone is calm or not curious then someone is both old and not quiet and vice versa.
Everyone who is both not funny and not kind is not humble.
Everyone who is both generous and not quiet is not old or not curious.
Everyone who is not calm or not curious is both not strong and rich.
Everyone who is not generous or strong is both generous and tall and vice versa.
If paul is patient then someone is both not curious and not creative.
Everyone who is not funny is strong.
Paul is not rich or tall.
Someone is not kind or not happy.
Lucy is not strong.
Someone is brave or not quiet.
Mary is both not brave and not kind.
Fred is not humble or not happy.
Someone is old or not humble.
Alice is both not tall and not rich. | Fred is generous. | entailment | (((~strong(susan)&~rich(susan)))<=>((~strong(fred)&wise(fred))))&
(((calm(alice)<~>brave(alice)))<=>(?[X]:(tall(X))))&
(![X]:((old(X)&~rich(X))<=>(tall(X)|strong(X))))&
(![X]:((brave(X)<~>strong(X))<=>old(X)))&
(![X]:((~curious(X)<~>~quiet(X))=>(~quiet(X)&generous(X))))&
((?[X]:((rich(X)&funny(X))))<=>(?[X]:((creative(X)<~>brave(X)))))&
((?[X]:((~patient(X)&~rich(X))))<=>(?[X]:(~humble(X))))&
((?[X]:((strong(X)&~humble(X))))=>(~quiet(fred)))&
((?[X]:((calm(X)<~>~strong(X))))<=>(?[X]:((~strong(X)|~tall(X)))))&
((?[X]:((calm(X)|~curious(X))))<=>(?[X]:((old(X)&~quiet(X)))))&
(![X]:((~funny(X)&~kind(X))=>~humble(X)))&
(![X]:((generous(X)&~quiet(X))=>(~old(X)|~curious(X))))&
(![X]:((~calm(X)|~curious(X))=>(~strong(X)&rich(X))))&
(![X]:((~generous(X)|strong(X))<=>(generous(X)&tall(X))))&
((patient(paul))=>(?[X]:((~curious(X)&~creative(X)))))&
(![X]:(~funny(X)=>strong(X)))&
((~rich(paul)|tall(paul)))&
(?[X]:((~kind(X)|~happy(X))))&
(~strong(lucy))&
(?[X]:((brave(X)|~quiet(X))))&
((~brave(mary)&~kind(mary)))&
((~humble(fred)|~happy(fred)))&
(?[X]:((old(X)|~humble(X))))&
((~tall(alice)&~rich(alice))) | generous(fred) | [
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3357039056353912260434076
% SZS output start Proof for 3357039056353912260434076
14. ! [X0] : ((strong(X0) | ~generous(X0)) <=> (tall(X0) & generous(X0))) [input p13]
25. ~generous(fred) [input hypothesis]
71. ! [X0] : (((strong(X0) | ~generous(X0)) | (~tall(X0) | ~generous(X0))) & ((tall(X0) & generous(X0)) | (~strong(X0) & generous(X0)))) [nnf transformation 14]
72. ! [X0] : ((strong(X0) | ~generous(X0) | ~tall(X0) | ~generous(X0)) & ((tall(X0) & generous(X0)) | (~strong(X0) & generous(X0)))) [flattening 71]
127. generous(X0) | generous(X0) [cnf transformation 72]
143. ~generous(fred) [cnf transformation 25]
144. generous(X0) [duplicate literal removal 127]
346. $false [subsumption resolution 143,144]
% SZS output end Proof for 3357039056353912260434076
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is curious or not old then mary is curious or not old.
If paul is not patient then paul is either not wise or not rich.
Everyone who is both patient and not kind is either not calm or happy and vice versa.
Everyone who is both creative and not creative is kind and vice versa.
If mary is not wise then someone is wise and vice versa.
If susan is generous then alice is either old or curious and vice versa.
If someone is either calm or not curious then someone is not strong and vice versa.
If someone is both not curious and not kind then someone is either not funny or not generous.
Everyone who is patient or not brave is old and vice versa.
Everyone who is both not humble and not old is both not wise and calm.
Everyone who is both not kind and strong is either not creative or not quiet and vice versa.
Everyone who is funny is both not kind and rich and vice versa.
If mary is kind then someone is brave and vice versa.
If someone is either not calm or not tall then mary is both not quiet and humble and vice versa.
Everyone who is either not kind or not curious is both calm and wise and vice versa.
Everyone who is both not generous and not kind is not calm and vice versa.
Someone is either not funny or not quiet.
Susan is both rich and not curious.
Lucy is not humble.
Someone is old. | Susan is wise. | neutral | (((curious(lucy)|~old(lucy)))=>((curious(mary)|~old(mary))))&
((~patient(paul))=>((~wise(paul)<~>~rich(paul))))&
(![X]:((patient(X)&~kind(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((creative(X)&~creative(X))<=>kind(X)))&
((~wise(mary))<=>(?[X]:(wise(X))))&
((generous(susan))<=>((old(alice)<~>curious(alice))))&
((?[X]:((calm(X)<~>~curious(X))))<=>(?[X]:(~strong(X))))&
((?[X]:((~curious(X)&~kind(X))))=>(?[X]:((~funny(X)<~>~generous(X)))))&
(![X]:((patient(X)|~brave(X))<=>old(X)))&
(![X]:((~humble(X)&~old(X))=>(~wise(X)&calm(X))))&
(![X]:((~kind(X)&strong(X))<=>(~creative(X)<~>~quiet(X))))&
(![X]:(funny(X)<=>(~kind(X)&rich(X))))&
((kind(mary))<=>(?[X]:(brave(X))))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((~quiet(mary)&humble(mary))))&
(![X]:((~kind(X)<~>~curious(X))<=>(calm(X)&wise(X))))&
(![X]:((~generous(X)&~kind(X))<=>~calm(X)))&
(?[X]:((~funny(X)<~>~quiet(X))))&
((rich(susan)&~curious(susan)))&
(~humble(lucy))&
(?[X]:(old(X))) | wise(susan) | [] | null | 0 |
Everyone who is either generous or curious is either not funny or rich and vice versa. Everyone who is brave or not brave is not funny or humble. Everyone who is either curious or kind is either not kind or not patient and vice versa. Everyone who is both not old and not kind is not strong and vice versa. Everyone who is not tall is both not old and calm and vice versa. Everyone who is not curious or not humble is rich. Everyone who is both not quiet and wise is curious and vice versa. If john is not generous then someone is either tall or curious. Everyone who is not generous is both not rich and brave. Everyone who is not patient or not brave is tall and vice versa. If susan is both brave and wise then someone is not humble or calm and vice versa. Everyone who is either generous or old is either not patient or creative and vice versa. Everyone who is not funny or not curious is either wise or not calm. Everyone who is either not humble or not funny is humble or kind. Everyone who is either not brave or not calm is not quiet or wise and vice versa. Everyone who is not brave is either old or creative. Someone is both not quiet and not curious. Fred is either not creative or brave. Mary is both brave and funny. John is both not quiet and kind. Someone is both not curious and old. | John is not tall. | contradiction | (![X]:((generous(X)<~>curious(X))<=>(~funny(X)<~>rich(X))))&
(![X]:((brave(X)|~brave(X))=>(~funny(X)|humble(X))))&
(![X]:((curious(X)<~>kind(X))<=>(~kind(X)<~>~patient(X))))&
(![X]:((~old(X)&~kind(X))<=>~strong(X)))&
(![X]:(~tall(X)<=>(~old(X)&calm(X))))&
(![X]:((~curious(X)|~humble(X))=>rich(X)))&
(![X]:((~quiet(X)&wise(X))<=>curious(X)))&
((~generous(john))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(~rich(X)&brave(X))))&
(![X]:((~patient(X)|~brave(X))<=>tall(X)))&
(((brave(susan)&wise(susan)))<=>(?[X]:((~humble(X)|calm(X)))))&
(![X]:((generous(X)<~>old(X))<=>(~patient(X)<~>creative(X))))&
(![X]:((~funny(X)|~curious(X))=>(wise(X)<~>~calm(X))))&
(![X]:((~humble(X)<~>~funny(X))=>(humble(X)|kind(X))))&
(![X]:((~brave(X)<~>~calm(X))<=>(~quiet(X)|wise(X))))&
(![X]:(~brave(X)=>(old(X)<~>creative(X))))&
(?[X]:((~quiet(X)&~curious(X))))&
((~creative(fred)<~>brave(fred)))&
((brave(mary)&funny(mary)))&
((~quiet(john)&kind(john)))&
(?[X]:((~curious(X)&old(X)))) | ~tall(john) | [
"p4",
"p6",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1983095839788766778141464
% SZS output start Proof for 1983095839788766778141464
5. ! [X0] : (~tall(X0) <=> (calm(X0) & ~old(X0))) [input p4]
7. ! [X0] : ((wise(X0) & ~quiet(X0)) <=> curious(X0)) [input p6]
10. ! [X0] : ((~brave(X0) | ~patient(X0)) <=> tall(X0)) [input p9]
13. ! [X0] : ((~curious(X0) | ~funny(X0)) => (wise(X0) <~> ~calm(X0))) [input p12]
15. ! [X0] : ((~brave(X0) <~> ~calm(X0)) <=> (wise(X0) | ~quiet(X0))) [input p14]
22. ~tall(john) [input hypothesis]
28. ! [X0] : ((wise(X0) <~> ~calm(X0)) | (curious(X0) & funny(X0))) [ennf transformation 13]
34. ! [X0] : ((~tall(X0) | (~calm(X0) | old(X0))) & ((calm(X0) & ~old(X0)) | tall(X0))) [nnf transformation 5]
35. ! [X0] : ((~tall(X0) | ~calm(X0) | old(X0)) & ((calm(X0) & ~old(X0)) | tall(X0))) [flattening 34]
36. ! [X0] : (((wise(X0) & ~quiet(X0)) | ~curious(X0)) & (curious(X0) | (~wise(X0) | quiet(X0)))) [nnf transformation 7]
37. ! [X0] : (((wise(X0) & ~quiet(X0)) | ~curious(X0)) & (curious(X0) | ~wise(X0) | quiet(X0))) [flattening 36]
41. ! [X0] : (((~brave(X0) | ~patient(X0)) | ~tall(X0)) & (tall(X0) | (brave(X0) & patient(X0)))) [nnf transformation 10]
42. ! [X0] : ((~brave(X0) | ~patient(X0) | ~tall(X0)) & (tall(X0) | (brave(X0) & patient(X0)))) [flattening 41]
49. ! [X0] : (((calm(X0) | ~wise(X0)) & (~calm(X0) | wise(X0))) | (curious(X0) & funny(X0))) [nnf transformation 28]
51. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~wise(X0) & quiet(X0))) & ((wise(X0) | ~quiet(X0)) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [nnf transformation 15]
52. ! [X0] : ((((calm(X0) | brave(X0)) & (~calm(X0) | ~brave(X0))) | (~wise(X0) & quiet(X0))) & (wise(X0) | ~quiet(X0) | ((~brave(X0) | calm(X0)) & (~calm(X0) | brave(X0))))) [flattening 51]
78. calm(X0) | tall(X0) [cnf transformation 35]
84. ~curious(X0) | wise(X0) [cnf transformation 37]
90. tall(X0) | brave(X0) [cnf transformation 42]
106. ~calm(X0) | wise(X0) | curious(X0) [cnf transformation 49]
114. ~calm(X0) | ~brave(X0) | ~wise(X0) [cnf transformation 52]
129. ~tall(john) [cnf transformation 22]
179. ~calm(X0) | wise(X0) [subsumption resolution 106,84]
180. ~calm(X0) | ~brave(X0) [subsumption resolution 114,179]
209. ~brave(X0) | tall(X0) [resolution 180,78]
210. tall(X0) [subsumption resolution 209,90]
211. $false [resolution 210,129]
% SZS output end Proof for 1983095839788766778141464
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both tall and not brave is both not humble and not funny.
If someone is both calm and not calm then john is either not old or kind.
Everyone who is both not quiet and wise is both not wise and not patient and vice versa.
Everyone who is either strong or not patient is either not patient or not old and vice versa.
If someone is strong or not generous then someone is both calm and rich and vice versa.
If someone is not strong then someone is either not calm or calm and vice versa.
Everyone who is both not old and not calm is not generous or brave.
If lucy is both calm and strong then susan is both patient and not wise.
Everyone who is strong is both patient and not calm and vice versa.
If lucy is tall then someone is humble or patient and vice versa.
Everyone who is not patient or old is funny.
Everyone who is both not calm and curious is either not strong or quiet.
Everyone who is both generous and not tall is happy or calm.
If susan is both curious and not calm then someone is both calm and patient and vice versa.
Everyone who is quiet or generous is both quiet and not patient and vice versa.
If paul is wise or rich then someone is not quiet.
Someone is funny or not wise.
Paul is both not quiet and rich.
John is either not quiet or not strong.
Paul is either not wise or kind.
Mary is brave or wise.
Someone is both curious and quiet.
Someone is either not tall or not wise.
Alice is not calm. | Susan is curious. | neutral | (![X]:((tall(X)&~brave(X))=>(~humble(X)&~funny(X))))&
((?[X]:((calm(X)&~calm(X))))=>((~old(john)<~>kind(john))))&
(![X]:((~quiet(X)&wise(X))<=>(~wise(X)&~patient(X))))&
(![X]:((strong(X)<~>~patient(X))<=>(~patient(X)<~>~old(X))))&
((?[X]:((strong(X)|~generous(X))))<=>(?[X]:((calm(X)&rich(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((~calm(X)<~>calm(X)))))&
(![X]:((~old(X)&~calm(X))=>(~generous(X)|brave(X))))&
(((calm(lucy)&strong(lucy)))=>((patient(susan)&~wise(susan))))&
(![X]:(strong(X)<=>(patient(X)&~calm(X))))&
((tall(lucy))<=>(?[X]:((humble(X)|patient(X)))))&
(![X]:((~patient(X)|old(X))=>funny(X)))&
(![X]:((~calm(X)&curious(X))=>(~strong(X)<~>quiet(X))))&
(![X]:((generous(X)&~tall(X))=>(happy(X)|calm(X))))&
(((curious(susan)&~calm(susan)))<=>(?[X]:((calm(X)&patient(X)))))&
(![X]:((quiet(X)|generous(X))<=>(quiet(X)&~patient(X))))&
(((wise(paul)|rich(paul)))=>(?[X]:(~quiet(X))))&
(?[X]:((funny(X)|~wise(X))))&
((~quiet(paul)&rich(paul)))&
((~quiet(john)<~>~strong(john)))&
((~wise(paul)<~>kind(paul)))&
((brave(mary)|wise(mary)))&
(?[X]:((curious(X)&quiet(X))))&
(?[X]:((~tall(X)<~>~wise(X))))&
(~calm(alice)) | curious(susan) | [] | null | 0 |
If someone is kind then alice is curious and vice versa.
Everyone who is quiet is brave and vice versa.
If paul is not happy or not kind then mary is not old or not quiet.
If susan is both strong and not happy then someone is not calm and vice versa.
If fred is either curious or not calm then john is tall or not calm.
If someone is either rich or humble then someone is kind or not happy.
If mary is strong or tall then john is brave or not rich and vice versa.
If someone is both not old and wise then mary is either quiet or not generous and vice versa.
If someone is both kind and not calm then someone is not tall or not wise and vice versa.
If paul is funny or not brave then someone is either not rich or not curious and vice versa.
If someone is not humble then mary is not tall and vice versa.
If someone is patient or not calm then fred is either old or not patient and vice versa.
Everyone who is either happy or wise is both not creative and creative and vice versa.
If someone is both not happy and not creative then someone is either quiet or not patient.
Everyone who is either not creative or humble is both quiet and not calm and vice versa.
If someone is tall or not curious then alice is either old or not rich and vice versa.
Mary is either not brave or calm.
Someone is creative or not humble.
Fred is either not wise or generous.
Paul is not calm.
Fred is creative.
Someone is both wise and old.
Someone is both kind and brave.
Someone is either not quiet or happy. | Susan is not wise. | entailment | ((?[X]:(kind(X)))<=>(curious(alice)))&
(![X]:(quiet(X)<=>brave(X)))&
(((~happy(paul)|~kind(paul)))=>((~old(mary)|~quiet(mary))))&
(((strong(susan)&~happy(susan)))<=>(?[X]:(~calm(X))))&
(((curious(fred)<~>~calm(fred)))=>((tall(john)|~calm(john))))&
((?[X]:((rich(X)<~>humble(X))))=>(?[X]:((kind(X)|~happy(X)))))&
(((strong(mary)|tall(mary)))<=>((brave(john)|~rich(john))))&
((?[X]:((~old(X)&wise(X))))<=>((quiet(mary)<~>~generous(mary))))&
((?[X]:((kind(X)&~calm(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
(((funny(paul)|~brave(paul)))<=>(?[X]:((~rich(X)<~>~curious(X)))))&
((?[X]:(~humble(X)))<=>(~tall(mary)))&
((?[X]:((patient(X)|~calm(X))))<=>((old(fred)<~>~patient(fred))))&
(![X]:((happy(X)<~>wise(X))<=>(~creative(X)&creative(X))))&
((?[X]:((~happy(X)&~creative(X))))=>(?[X]:((quiet(X)<~>~patient(X)))))&
(![X]:((~creative(X)<~>humble(X))<=>(quiet(X)&~calm(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((old(alice)<~>~rich(alice))))&
((~brave(mary)<~>calm(mary)))&
(?[X]:((creative(X)|~humble(X))))&
((~wise(fred)<~>generous(fred)))&
(~calm(paul))&
(creative(fred))&
(?[X]:((wise(X)&old(X))))&
(?[X]:((kind(X)&brave(X))))&
(?[X]:((~quiet(X)<~>happy(X)))) | ~wise(susan) | [
"p3",
"p12",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 4038816467350865679230858
% SZS output start Proof for 4038816467350865679230858
4. (~happy(susan) & strong(susan)) <=> ? [X0] : ~calm(X0) [input p3]
13. ! [X0] : ((happy(X0) <~> wise(X0)) <=> (creative(X0) & ~creative(X0))) [input p12]
20. ~calm(paul) [input p19]
25. wise(susan) [input hypothesis]
40. ((~happy(susan) & strong(susan)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | (happy(susan) | ~strong(susan))) [nnf transformation 4]
41. ((~happy(susan) & strong(susan)) | ! [X0] : calm(X0)) & (? [X0] : ~calm(X0) | happy(susan) | ~strong(susan)) [flattening 40]
42. ((~happy(susan) & strong(susan)) | ! [X0] : calm(X0)) & (? [X1] : ~calm(X1) | happy(susan) | ~strong(susan)) [rectify 41]
43. ? [X1] : ~calm(X1) => ~calm(sK1) [choice axiom]
44. ((~happy(susan) & strong(susan)) | ! [X0] : calm(X0)) & (~calm(sK1) | happy(susan) | ~strong(susan)) [skolemisation 42,43]
74. ! [X0] : ((((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | (~creative(X0) | creative(X0))) & ((creative(X0) & ~creative(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))))) [nnf transformation 13]
75. ! [X0] : ((((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | ~creative(X0) | creative(X0)) & ((creative(X0) & ~creative(X0)) | ((happy(X0) | ~wise(X0)) & (wise(X0) | ~happy(X0))))) [flattening 74]
105. ~happy(susan) | calm(X0) [cnf transformation 44]
140. ~creative(X0) | happy(X0) | ~wise(X0) [cnf transformation 75]
142. creative(X0) | happy(X0) | ~wise(X0) [cnf transformation 75]
164. ~calm(paul) [cnf transformation 20]
172. wise(susan) [cnf transformation 25]
205. 8 <=> ! [X0] : calm(X0) [avatar definition]
206. calm(X0) <- (8) [avatar component clause 205]
208. 9 <=> happy(susan) [avatar definition]
211. 8 | ~9 [avatar split clause 105,208,205]
389. ~wise(X0) | happy(X0) [subsumption resolution 140,142]
488. happy(susan) [resolution 389,172]
492. 9 [avatar split clause 488,208]
493. $false <- (8) [resolution 206,164]
502. ~8 [avatar contradiction clause 493]
503. $false [avatar sat refutation 211,492,502]
% SZS output end Proof for 4038816467350865679230858
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either strong or not calm is not curious or not funny and vice versa.
If fred is either patient or not humble then someone is not happy or humble and vice versa.
Everyone who is both not happy and kind is both not curious and not wise and vice versa.
Everyone who is not strong or not kind is calm.
Everyone who is strong or calm is either humble or tall and vice versa.
Everyone who is either wise or strong is creative or brave.
Everyone who is not curious is both creative and happy.
If someone is both not old and humble then fred is not humble or not happy.
Everyone who is old or generous is not tall and vice versa.
Everyone who is both quiet and not kind is either not old or generous and vice versa.
Everyone who is curious is not happy or not quiet and vice versa.
If someone is rich or funny then john is either not old or brave.
Everyone who is creative is happy.
If someone is strong then someone is calm or not strong and vice versa.
If susan is wise or not kind then someone is not curious and vice versa.
Everyone who is humble is not old or strong and vice versa.
Alice is tall or strong.
Someone is strong.
Alice is not tall.
Lucy is both not happy and quiet.
Alice is not brave or not happy.
Someone is both not calm and rich.
Fred is quiet.
Someone is either not curious or humble. | Fred is old. | entailment | (![X]:((strong(X)<~>~calm(X))<=>(~curious(X)|~funny(X))))&
(((patient(fred)<~>~humble(fred)))<=>(?[X]:((~happy(X)|humble(X)))))&
(![X]:((~happy(X)&kind(X))<=>(~curious(X)&~wise(X))))&
(![X]:((~strong(X)|~kind(X))=>calm(X)))&
(![X]:((strong(X)|calm(X))<=>(humble(X)<~>tall(X))))&
(![X]:((wise(X)<~>strong(X))=>(creative(X)|brave(X))))&
(![X]:(~curious(X)=>(creative(X)&happy(X))))&
((?[X]:((~old(X)&humble(X))))=>((~humble(fred)|~happy(fred))))&
(![X]:((old(X)|generous(X))<=>~tall(X)))&
(![X]:((quiet(X)&~kind(X))<=>(~old(X)<~>generous(X))))&
(![X]:(curious(X)<=>(~happy(X)|~quiet(X))))&
((?[X]:((rich(X)|funny(X))))=>((~old(john)<~>brave(john))))&
(![X]:(creative(X)=>happy(X)))&
((?[X]:(strong(X)))<=>(?[X]:((calm(X)|~strong(X)))))&
(((wise(susan)|~kind(susan)))<=>(?[X]:(~curious(X))))&
(![X]:(humble(X)<=>(~old(X)|strong(X))))&
((tall(alice)|strong(alice)))&
(?[X]:(strong(X)))&
(~tall(alice))&
((~happy(lucy)&quiet(lucy)))&
((~brave(alice)|~happy(alice)))&
(?[X]:((~calm(X)&rich(X))))&
(quiet(fred))&
(?[X]:((~curious(X)<~>humble(X)))) | old(fred) | [
"p2",
"p3",
"p4",
"p6",
"p7",
"p8",
"p9",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7869010065396060165146853
% SZS output start Proof for 7869010065396060165146853
3. ! [X0] : ((kind(X0) & ~happy(X0)) <=> (~wise(X0) & ~curious(X0))) [input p2]
4. ! [X0] : ((~kind(X0) | ~strong(X0)) => calm(X0)) [input p3]
5. ! [X0] : ((calm(X0) | strong(X0)) <=> (humble(X0) <~> tall(X0))) [input p4]
7. ! [X0] : (~curious(X0) => (happy(X0) & creative(X0))) [input p6]
8. ? [X0] : (humble(X0) & ~old(X0)) => (~happy(fred) | ~humble(fred)) [input p7]
9. ! [X0] : ((generous(X0) | old(X0)) <=> ~tall(X0)) [input p8]
10. ! [X0] : ((~kind(X0) & quiet(X0)) <=> (~old(X0) <~> generous(X0))) [input p9]
16. ! [X0] : (humble(X0) <=> (strong(X0) | ~old(X0))) [input p15]
23. quiet(fred) [input p22]
25. ~old(fred) [input hypothesis]
27. ! [X0] : (calm(X0) | (kind(X0) & strong(X0))) [ennf transformation 4]
30. ! [X0] : ((happy(X0) & creative(X0)) | curious(X0)) [ennf transformation 7]
31. (~happy(fred) | ~humble(fred)) | ! [X0] : (~humble(X0) | old(X0)) [ennf transformation 8]
32. ~happy(fred) | ~humble(fred) | ! [X0] : (~humble(X0) | old(X0)) [flattening 31]
41. ! [X0] : (((kind(X0) & ~happy(X0)) | (wise(X0) | curious(X0))) & ((~wise(X0) & ~curious(X0)) | (~kind(X0) | happy(X0)))) [nnf transformation 3]
42. ! [X0] : (((kind(X0) & ~happy(X0)) | wise(X0) | curious(X0)) & ((~wise(X0) & ~curious(X0)) | ~kind(X0) | happy(X0))) [flattening 41]
43. ! [X0] : (((calm(X0) | strong(X0)) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~calm(X0) & ~strong(X0)))) [nnf transformation 5]
44. ! [X0] : ((calm(X0) | strong(X0) | ((humble(X0) | ~tall(X0)) & (tall(X0) | ~humble(X0)))) & (((~tall(X0) | ~humble(X0)) & (tall(X0) | humble(X0))) | (~calm(X0) & ~strong(X0)))) [flattening 43]
46. ! [X0] : (((generous(X0) | old(X0)) | tall(X0)) & (~tall(X0) | (~generous(X0) & ~old(X0)))) [nnf transformation 9]
47. ! [X0] : ((generous(X0) | old(X0) | tall(X0)) & (~tall(X0) | (~generous(X0) & ~old(X0)))) [flattening 46]
48. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0)))) & (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | (kind(X0) | ~quiet(X0)))) [nnf transformation 10]
49. ! [X0] : (((~kind(X0) & quiet(X0)) | ((~old(X0) | ~generous(X0)) & (generous(X0) | old(X0)))) & (((~generous(X0) | old(X0)) & (generous(X0) | ~old(X0))) | kind(X0) | ~quiet(X0))) [flattening 48]
63. ! [X0] : ((humble(X0) | (~strong(X0) & old(X0))) & ((strong(X0) | ~old(X0)) | ~humble(X0))) [nnf transformation 16]
64. ! [X0] : ((humble(X0) | (~strong(X0) & old(X0))) & (strong(X0) | ~old(X0) | ~humble(X0))) [flattening 63]
84. ~kind(X0) | ~curious(X0) | happy(X0) [cnf transformation 42]
88. calm(X0) | strong(X0) [cnf transformation 27]
89. kind(X0) | calm(X0) [cnf transformation 27]
90. ~strong(X0) | humble(X0) | tall(X0) [cnf transformation 44]
91. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 44]
93. ~tall(X0) | ~humble(X0) | ~calm(X0) [cnf transformation 44]
99. happy(X0) | curious(X0) [cnf transformation 30]
100. ~happy(fred) | ~humble(fred) | ~humble(X0) | old(X0) [cnf transformation 32]
101. ~old(X0) | ~tall(X0) [cnf transformation 47]
103. generous(X0) | old(X0) | tall(X0) [cnf transformation 47]
105. ~quiet(X0) | old(X0) | kind(X0) | ~generous(X0) [cnf transformation 49]
108. ~kind(X0) | generous(X0) | old(X0) [cnf transformation 49]
125. old(X0) | humble(X0) [cnf transformation 64]
135. quiet(fred) [cnf transformation 23]
138. ~old(fred) [cnf transformation 25]
147. 3 <=> humble(fred) [avatar definition]
149. humble(fred) <- (3) [avatar component clause 147]
168. 7 <=> ! [X0] : (~humble(X0) | old(X0)) [avatar definition]
169. ~humble(X0) | old(X0) <- (7) [avatar component clause 168]
171. 8 <=> happy(fred) [avatar definition]
173. ~happy(fred) <- (~8) [avatar component clause 171]
174. 7 | ~3 | ~8 [avatar split clause 100,171,147,168]
273. humble(fred) [resolution 125,138]
275. ~tall(X0) | humble(X0) [resolution 125,101]
278. 3 [avatar split clause 273,147]
378. humble(X0) | tall(X0) | strong(X0) [resolution 91,88]
383. humble(X0) | tall(X0) [subsumption resolution 378,90]
384. humble(X0) [subsumption resolution 383,275]
389. generous(X0) | old(X0) | calm(X0) [resolution 108,89]
561. old(fred) | kind(fred) | ~generous(fred) [resolution 105,135]
567. kind(fred) | ~generous(fred) [subsumption resolution 561,138]
569. 64 <=> generous(fred) [avatar definition]
571. ~generous(fred) <- (~64) [avatar component clause 569]
573. 65 <=> kind(fred) [avatar definition]
575. kind(fred) <- (65) [avatar component clause 573]
576. ~64 | 65 [avatar split clause 567,573,569]
584. old(fred) | tall(fred) <- (~64) [resolution 571,103]
585. tall(fred) <- (~64) [subsumption resolution 584,138]
602. old(fred) | calm(fred) <- (~64) [resolution 389,571]
680. ~humble(fred) | ~calm(fred) <- (~64) [resolution 585,93]
682. ~calm(fred) <- (3, ~64) [subsumption resolution 680,149]
686. calm(fred) <- (~64) [subsumption resolution 602,138]
687. $false <- (3, ~64) [subsumption resolution 686,682]
688. ~3 | 64 [avatar contradiction clause 687]
691. old(X0) <- (7) [subsumption resolution 169,384]
702. $false <- (7) [resolution 691,138]
707. ~7 [avatar contradiction clause 702]
711. 72 <=> curious(fred) [avatar definition]
712. curious(fred) <- (72) [avatar component clause 711]
716. curious(fred) <- (~8) [resolution 173,99]
717. 72 | 8 [avatar split clause 716,171,711]
722. ~curious(fred) | happy(fred) <- (65) [resolution 575,84]
723. happy(fred) <- (65, 72) [subsumption resolution 722,712]
724. $false <- (~8, 65, 72) [subsumption resolution 723,173]
725. 8 | ~65 | ~72 [avatar contradiction clause 724]
726. $false [avatar sat refutation 174,278,576,688,707,717,725]
% SZS output end Proof for 7869010065396060165146853
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is humble then someone is strong. If fred is both rich and not old then someone is both not old and not wise and vice versa. Everyone who is both not curious and not wise is not happy. Everyone who is either not curious or wise is not old or patient. If someone is not quiet or generous then alice is either wise or not calm and vice versa. Everyone who is not quiet or strong is both calm and not calm and vice versa. Everyone who is not tall is generous and vice versa. If someone is not creative then lucy is generous and vice versa. If fred is either strong or old then someone is either kind or humble. If lucy is strong or generous then someone is not generous. If mary is both not happy and humble then alice is not patient or not brave and vice versa. If mary is happy or not tall then someone is not old. If alice is both quiet and not patient then someone is not calm. If someone is both not patient and not funny then someone is either not kind or not happy and vice versa. If someone is both not brave and strong then someone is both old and quiet. If someone is both not tall and not rich then lucy is not old. Paul is both not curious and not patient. Susan is calm. Paul is brave. John is happy or not funny. Someone is both not strong and patient. Someone is either not generous or happy. Paul is not strong. John is either not happy or wise. | Alice is not humble. | entailment | ((?[X]:(humble(X)))=>(?[X]:(strong(X))))&
(((rich(fred)&~old(fred)))<=>(?[X]:((~old(X)&~wise(X)))))&
(![X]:((~curious(X)&~wise(X))=>~happy(X)))&
(![X]:((~curious(X)<~>wise(X))=>(~old(X)|patient(X))))&
((?[X]:((~quiet(X)|generous(X))))<=>((wise(alice)<~>~calm(alice))))&
(![X]:((~quiet(X)|strong(X))<=>(calm(X)&~calm(X))))&
(![X]:(~tall(X)<=>generous(X)))&
((?[X]:(~creative(X)))<=>(generous(lucy)))&
(((strong(fred)<~>old(fred)))=>(?[X]:((kind(X)<~>humble(X)))))&
(((strong(lucy)|generous(lucy)))=>(?[X]:(~generous(X))))&
(((~happy(mary)&humble(mary)))<=>((~patient(alice)|~brave(alice))))&
(((happy(mary)|~tall(mary)))=>(?[X]:(~old(X))))&
(((quiet(alice)&~patient(alice)))=>(?[X]:(~calm(X))))&
((?[X]:((~patient(X)&~funny(X))))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((~brave(X)&strong(X))))=>(?[X]:((old(X)&quiet(X)))))&
((?[X]:((~tall(X)&~rich(X))))=>(~old(lucy)))&
((~curious(paul)&~patient(paul)))&
(calm(susan))&
(brave(paul))&
((happy(john)|~funny(john)))&
(?[X]:((~strong(X)&patient(X))))&
(?[X]:((~generous(X)<~>happy(X))))&
(~strong(paul))&
((~happy(john)<~>wise(john))) | ~humble(alice) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1639513998270920332754738
% SZS output start Proof for 1639513998270920332754738
1. ? [X0] : humble(X0) => ? [X0] : strong(X0) [input p0]
6. ! [X0] : ((strong(X0) | ~quiet(X0)) <=> (~calm(X0) & calm(X0))) [input p5]
25. humble(alice) [input hypothesis]
26. ? [X0] : humble(X0) => ? [X1] : strong(X1) [rectify 1]
30. ? [X1] : strong(X1) | ! [X0] : ~humble(X0) [ennf transformation 26]
43. ? [X0] : strong(X0) | ! [X1] : ~humble(X1) [rectify 30]
44. ? [X0] : strong(X0) => strong(sK0) [choice axiom]
45. strong(sK0) | ! [X1] : ~humble(X1) [skolemisation 43,44]
56. ! [X0] : (((strong(X0) | ~quiet(X0)) | (calm(X0) | ~calm(X0))) & ((~calm(X0) & calm(X0)) | (~strong(X0) & quiet(X0)))) [nnf transformation 6]
57. ! [X0] : ((strong(X0) | ~quiet(X0) | calm(X0) | ~calm(X0)) & ((~calm(X0) & calm(X0)) | (~strong(X0) & quiet(X0)))) [flattening 56]
87. strong(sK0) | ~humble(X1) [cnf transformation 45]
102. calm(X0) | ~strong(X0) [cnf transformation 57]
104. ~calm(X0) | ~strong(X0) [cnf transformation 57]
144. humble(alice) [cnf transformation 25]
146. 1 <=> ! [X1] : ~humble(X1) [avatar definition]
147. ~humble(X1) <- (1) [avatar component clause 146]
149. 2 <=> strong(sK0) [avatar definition]
151. strong(sK0) <- (2) [avatar component clause 149]
152. 1 | 2 [avatar split clause 87,149,146]
204. ~strong(X0) [subsumption resolution 102,104]
343. $false <- (2) [subsumption resolution 151,204]
344. ~2 [avatar contradiction clause 343]
345. $false <- (1) [resolution 147,144]
346. ~1 [avatar contradiction clause 345]
347. $false [avatar sat refutation 152,344,346]
% SZS output end Proof for 1639513998270920332754738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous and not rich then susan is strong.
If susan is not brave then lucy is both not patient and patient.
Everyone who is either humble or rich is either humble or not creative and vice versa.
If mary is old then someone is not quiet.
If someone is either quiet or generous then john is happy.
If someone is not generous then someone is funny or kind and vice versa.
If paul is calm then susan is not brave and vice versa.
Everyone who is both calm and not brave is both not kind and creative and vice versa.
Everyone who is both not patient and calm is rich.
If someone is either not curious or happy then someone is either humble or quiet.
If mary is curious then paul is not kind and vice versa.
Everyone who is not brave is not humble and vice versa.
Everyone who is either calm or curious is either not patient or patient and vice versa.
Everyone who is either humble or not kind is both not curious and kind.
Everyone who is not humble is either calm or not kind.
Susan is brave or wise.
Someone is creative.
John is either not brave or happy.
Someone is either generous or kind.
Someone is either not wise or quiet.
Someone is wise.
Paul is either kind or quiet. | Mary is creative. | contradiction | ((?[X]:((generous(X)&~rich(X))))=>(strong(susan)))&
((~brave(susan))=>((~patient(lucy)&patient(lucy))))&
(![X]:((humble(X)<~>rich(X))<=>(humble(X)<~>~creative(X))))&
((old(mary))=>(?[X]:(~quiet(X))))&
((?[X]:((quiet(X)<~>generous(X))))=>(happy(john)))&
((?[X]:(~generous(X)))<=>(?[X]:((funny(X)|kind(X)))))&
((calm(paul))<=>(~brave(susan)))&
(![X]:((calm(X)&~brave(X))<=>(~kind(X)&creative(X))))&
(![X]:((~patient(X)&calm(X))=>rich(X)))&
((?[X]:((~curious(X)<~>happy(X))))=>(?[X]:((humble(X)<~>quiet(X)))))&
((curious(mary))<=>(~kind(paul)))&
(![X]:(~brave(X)<=>~humble(X)))&
(![X]:((calm(X)<~>curious(X))<=>(~patient(X)<~>patient(X))))&
(![X]:((humble(X)<~>~kind(X))=>(~curious(X)&kind(X))))&
(![X]:(~humble(X)=>(calm(X)<~>~kind(X))))&
((brave(susan)|wise(susan)))&
(?[X]:(creative(X)))&
((~brave(john)<~>happy(john)))&
(?[X]:((generous(X)<~>kind(X))))&
(?[X]:((~wise(X)<~>quiet(X))))&
(?[X]:(wise(X)))&
((kind(paul)<~>quiet(paul))) | creative(mary) | [
"p1",
"p6",
"p7",
"p10",
"p11",
"p12",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 503557791423632101286714
% SZS output start Proof for 503557791423632101286714
2. ~brave(susan) => (patient(lucy) & ~patient(lucy)) [input p1]
7. calm(paul) <=> ~brave(susan) [input p6]
8. ! [X0] : ((~brave(X0) & calm(X0)) <=> (creative(X0) & ~kind(X0))) [input p7]
11. curious(mary) <=> ~kind(paul) [input p10]
12. ! [X0] : (~brave(X0) <=> ~humble(X0)) [input p11]
13. ! [X0] : ((calm(X0) <~> curious(X0)) <=> (~patient(X0) <~> patient(X0))) [input p12]
14. ! [X0] : ((humble(X0) <~> ~kind(X0)) => (kind(X0) & ~curious(X0))) [input p13]
15. ! [X0] : (~humble(X0) => (calm(X0) <~> ~kind(X0))) [input p14]
23. creative(mary) [input hypothesis]
28. (patient(lucy) & ~patient(lucy)) | brave(susan) [ennf transformation 2]
33. ! [X0] : ((kind(X0) & ~curious(X0)) | (humble(X0) <=> ~kind(X0))) [ennf transformation 14]
34. ! [X0] : ((calm(X0) <~> ~kind(X0)) | humble(X0)) [ennf transformation 15]
42. (calm(paul) | brave(susan)) & (~brave(susan) | ~calm(paul)) [nnf transformation 7]
43. ! [X0] : (((~brave(X0) & calm(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (brave(X0) | ~calm(X0)))) [nnf transformation 8]
44. ! [X0] : (((~brave(X0) & calm(X0)) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | brave(X0) | ~calm(X0))) [flattening 43]
49. (curious(mary) | kind(paul)) & (~kind(paul) | ~curious(mary)) [nnf transformation 11]
50. ! [X0] : ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0))) [nnf transformation 12]
51. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ((~patient(X0) | ~patient(X0)) & (patient(X0) | patient(X0)))) & (((~patient(X0) | patient(X0)) & (patient(X0) | ~patient(X0))) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 13]
52. ! [X0] : ((kind(X0) & ~curious(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) [nnf transformation 33]
53. ! [X0] : (((kind(X0) | ~calm(X0)) & (~kind(X0) | calm(X0))) | humble(X0)) [nnf transformation 34]
66. ~patient(lucy) | brave(susan) [cnf transformation 28]
67. patient(lucy) | brave(susan) [cnf transformation 28]
81. ~brave(susan) | ~calm(paul) [cnf transformation 42]
83. ~calm(X0) | brave(X0) | ~kind(X0) [cnf transformation 44]
86. ~creative(X0) | ~brave(X0) | kind(X0) [cnf transformation 44]
93. curious(mary) | kind(paul) [cnf transformation 49]
94. ~humble(X0) | brave(X0) [cnf transformation 50]
95. ~brave(X0) | humble(X0) [cnf transformation 50]
100. curious(X0) | calm(X0) | patient(X0) | patient(X0) [cnf transformation 51]
101. curious(X0) | calm(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 51]
104. ~curious(X0) | ~kind(X0) | ~humble(X0) [cnf transformation 52]
107. kind(X0) | humble(X0) | kind(X0) [cnf transformation 52]
108. ~kind(X0) | calm(X0) | humble(X0) [cnf transformation 53]
121. creative(mary) [cnf transformation 23]
122. kind(X0) | humble(X0) [duplicate literal removal 107]
123. curious(X0) | calm(X0) | patient(X0) [duplicate literal removal 100]
124. ~patient(X0) | calm(X0) | curious(X0) [duplicate literal removal 101]
132. 1 <=> brave(susan) [avatar definition]
136. 2 <=> patient(lucy) [avatar definition]
139. 1 | 2 [avatar split clause 67,136,132]
140. 1 | ~2 [avatar split clause 66,136,132]
180. 12 <=> calm(paul) [avatar definition]
181. ~calm(paul) <- (~12) [avatar component clause 180]
184. ~12 | ~1 [avatar split clause 81,132,180]
204. 17 <=> kind(paul) [avatar definition]
206. kind(paul) <- (17) [avatar component clause 204]
208. 18 <=> curious(mary) [avatar definition]
210. curious(mary) <- (18) [avatar component clause 208]
211. 17 | 18 [avatar split clause 93,208,204]
214. curious(X0) | calm(X0) [subsumption resolution 123,124]
215. calm(X0) | humble(X0) [subsumption resolution 108,122]
273. brave(X0) | ~kind(X0) | humble(X0) [resolution 83,215]
275. 26 <=> kind(mary) [avatar definition]
276. kind(mary) <- (26) [avatar component clause 275]
283. ~kind(X0) | humble(X0) [subsumption resolution 273,95]
284. humble(X0) [subsumption resolution 283,122]
285. brave(X0) [resolution 284,94]
302. ~brave(mary) | kind(mary) [resolution 86,121]
304. kind(mary) [subsumption resolution 302,285]
313. 26 [avatar split clause 304,275]
320. ~kind(X0) | ~humble(X0) | calm(X0) [resolution 104,214]
321. ~kind(mary) | ~humble(mary) <- (18) [resolution 104,210]
322. ~kind(X0) | calm(X0) [subsumption resolution 320,284]
323. ~humble(mary) <- (18, 26) [subsumption resolution 321,276]
324. $false <- (18, 26) [subsumption resolution 323,284]
325. ~18 | ~26 [avatar contradiction clause 324]
350. calm(paul) <- (17) [resolution 322,206]
352. $false <- (~12, 17) [subsumption resolution 350,181]
353. 12 | ~17 [avatar contradiction clause 352]
355. $false [avatar sat refutation 139,140,184,211,313,325,353]
% SZS output end Proof for 503557791423632101286714
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not rich is both generous and quiet. Everyone who is generous is either not calm or not creative and vice versa. Everyone who is both not patient and not strong is both not tall and rich. If john is both not calm and not creative then john is either not tall or not patient. If alice is humble then john is either not tall or creative. If someone is not humble then someone is both curious and happy and vice versa. Everyone who is not tall is both generous and creative. If paul is not patient then lucy is not quiet or not funny and vice versa. Everyone who is not curious or old is either not brave or kind and vice versa. Everyone who is both generous and not curious is both not rich and not quiet. If mary is both patient and not strong then someone is both not quiet and not funny and vice versa. If mary is patient or brave then paul is both creative and not generous and vice versa. Everyone who is not kind or not calm is either funny or calm and vice versa. Everyone who is not funny is either not calm or not tall. Everyone who is creative or not generous is not creative or rich and vice versa. Everyone who is calm or not humble is patient or kind and vice versa. Someone is both creative and patient. Someone is not patient or kind. Alice is humble. Lucy is both curious and wise. Someone is not happy or not curious. Lucy is curious or patient. Alice is either wise or not curious. | Lucy is not quiet. | neutral | (![X]:((~curious(X)&~rich(X))=>(generous(X)&quiet(X))))&
(![X]:(generous(X)<=>(~calm(X)<~>~creative(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)&rich(X))))&
(((~calm(john)&~creative(john)))=>((~tall(john)<~>~patient(john))))&
((humble(alice))=>((~tall(john)<~>creative(john))))&
((?[X]:(~humble(X)))<=>(?[X]:((curious(X)&happy(X)))))&
(![X]:(~tall(X)=>(generous(X)&creative(X))))&
((~patient(paul))<=>((~quiet(lucy)|~funny(lucy))))&
(![X]:((~curious(X)|old(X))<=>(~brave(X)<~>kind(X))))&
(![X]:((generous(X)&~curious(X))=>(~rich(X)&~quiet(X))))&
(((patient(mary)&~strong(mary)))<=>(?[X]:((~quiet(X)&~funny(X)))))&
(((patient(mary)|brave(mary)))<=>((creative(paul)&~generous(paul))))&
(![X]:((~kind(X)|~calm(X))<=>(funny(X)<~>calm(X))))&
(![X]:(~funny(X)=>(~calm(X)<~>~tall(X))))&
(![X]:((creative(X)|~generous(X))<=>(~creative(X)|rich(X))))&
(![X]:((calm(X)|~humble(X))<=>(patient(X)|kind(X))))&
(?[X]:((creative(X)&patient(X))))&
(?[X]:((~patient(X)|kind(X))))&
(humble(alice))&
((curious(lucy)&wise(lucy)))&
(?[X]:((~happy(X)|~curious(X))))&
((curious(lucy)|patient(lucy)))&
((wise(alice)<~>~curious(alice))) | ~quiet(lucy) | [] | null | 0 |
If someone is old then mary is either not kind or not curious.
Everyone who is tall is calm and vice versa.
Everyone who is both not tall and strong is quiet or not curious and vice versa.
If john is curious or not wise then someone is either patient or rich and vice versa.
Everyone who is both not old and not calm is not quiet.
If susan is both happy and humble then someone is calm or funny.
If mary is both old and patient then someone is happy or quiet.
Everyone who is old is either not humble or not generous.
Everyone who is not tall is not brave or kind and vice versa.
Everyone who is either not kind or happy is generous.
If someone is both brave and not old then someone is either not patient or calm.
If lucy is old or not creative then alice is tall and vice versa.
Everyone who is either calm or quiet is either not brave or rich and vice versa.
Everyone who is not generous or not brave is not rich and vice versa.
Everyone who is both not brave and old is both funny and happy and vice versa.
If paul is both not rich and not creative then lucy is both not generous and not creative.
Susan is both not creative and quiet.
Someone is kind or not humble.
Alice is both rich and not funny.
Someone is wise or humble.
Someone is not funny or happy.
Paul is both not calm and generous.
Fred is either funny or not calm. | Susan is not strong. | contradiction | ((?[X]:(old(X)))=>((~kind(mary)<~>~curious(mary))))&
(![X]:(tall(X)<=>calm(X)))&
(![X]:((~tall(X)&strong(X))<=>(quiet(X)|~curious(X))))&
(((curious(john)|~wise(john)))<=>(?[X]:((patient(X)<~>rich(X)))))&
(![X]:((~old(X)&~calm(X))=>~quiet(X)))&
(((happy(susan)&humble(susan)))=>(?[X]:((calm(X)|funny(X)))))&
(((old(mary)&patient(mary)))=>(?[X]:((happy(X)|quiet(X)))))&
(![X]:(old(X)=>(~humble(X)<~>~generous(X))))&
(![X]:(~tall(X)<=>(~brave(X)|kind(X))))&
(![X]:((~kind(X)<~>happy(X))=>generous(X)))&
((?[X]:((brave(X)&~old(X))))=>(?[X]:((~patient(X)<~>calm(X)))))&
(((old(lucy)|~creative(lucy)))<=>(tall(alice)))&
(![X]:((calm(X)<~>quiet(X))<=>(~brave(X)<~>rich(X))))&
(![X]:((~generous(X)|~brave(X))<=>~rich(X)))&
(![X]:((~brave(X)&old(X))<=>(funny(X)&happy(X))))&
(((~rich(paul)&~creative(paul)))=>((~generous(lucy)&~creative(lucy))))&
((~creative(susan)&quiet(susan)))&
(?[X]:((kind(X)|~humble(X))))&
((rich(alice)&~funny(alice)))&
(?[X]:((wise(X)|humble(X))))&
(?[X]:((~funny(X)|happy(X))))&
((~calm(paul)&generous(paul)))&
((funny(fred)<~>~calm(fred))) | ~strong(susan) | [
"p2",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 363930370455611046476451
% SZS output start Proof for 363930370455611046476451
3. ! [X0] : ((strong(X0) & ~tall(X0)) <=> (~curious(X0) | quiet(X0))) [input p2]
17. quiet(susan) & ~creative(susan) [input p16]
24. ~strong(susan) [input hypothesis]
40. ! [X0] : (((strong(X0) & ~tall(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~strong(X0) | tall(X0)))) [nnf transformation 3]
41. ! [X0] : (((strong(X0) & ~tall(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~strong(X0) | tall(X0))) [flattening 40]
80. ~quiet(X0) | strong(X0) [cnf transformation 41]
121. quiet(susan) [cnf transformation 17]
131. ~strong(susan) [cnf transformation 24]
290. strong(susan) [resolution 80,121]
291. $false [subsumption resolution 290,131]
% SZS output end Proof for 363930370455611046476451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not tall is patient and vice versa.
If mary is not rich or happy then someone is not funny.
Everyone who is either happy or patient is not funny and vice versa.
If someone is not patient or not generous then someone is rich or not happy and vice versa.
Everyone who is not kind is either patient or generous.
Everyone who is both not brave and strong is either generous or not old.
Everyone who is either strong or not brave is either not calm or happy and vice versa.
Everyone who is both quiet and not creative is creative.
Everyone who is both not humble and wise is both brave and patient.
If alice is not happy then lucy is either rich or not brave and vice versa.
If susan is both strong and not quiet then someone is brave or not kind and vice versa.
If someone is either generous or tall then john is both not kind and not wise and vice versa.
Everyone who is either calm or creative is either wise or old and vice versa.
If mary is both not wise and not old then someone is not tall.
Everyone who is either calm or generous is either not wise or not happy and vice versa.
Everyone who is not wise or not patient is either funny or kind.
Someone is either tall or not tall.
Susan is both old and brave.
Someone is rich or strong.
Alice is both creative and humble.
Someone is either not funny or old.
John is not funny.
Lucy is not rich. | Mary is old. | neutral | (![X]:((~humble(X)|~tall(X))<=>patient(X)))&
(((~rich(mary)|happy(mary)))=>(?[X]:(~funny(X))))&
(![X]:((happy(X)<~>patient(X))<=>~funny(X)))&
((?[X]:((~patient(X)|~generous(X))))<=>(?[X]:((rich(X)|~happy(X)))))&
(![X]:(~kind(X)=>(patient(X)<~>generous(X))))&
(![X]:((~brave(X)&strong(X))=>(generous(X)<~>~old(X))))&
(![X]:((strong(X)<~>~brave(X))<=>(~calm(X)<~>happy(X))))&
(![X]:((quiet(X)&~creative(X))=>creative(X)))&
(![X]:((~humble(X)&wise(X))=>(brave(X)&patient(X))))&
((~happy(alice))<=>((rich(lucy)<~>~brave(lucy))))&
(((strong(susan)&~quiet(susan)))<=>(?[X]:((brave(X)|~kind(X)))))&
((?[X]:((generous(X)<~>tall(X))))<=>((~kind(john)&~wise(john))))&
(![X]:((calm(X)<~>creative(X))<=>(wise(X)<~>old(X))))&
(((~wise(mary)&~old(mary)))=>(?[X]:(~tall(X))))&
(![X]:((calm(X)<~>generous(X))<=>(~wise(X)<~>~happy(X))))&
(![X]:((~wise(X)|~patient(X))=>(funny(X)<~>kind(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((old(susan)&brave(susan)))&
(?[X]:((rich(X)|strong(X))))&
((creative(alice)&humble(alice)))&
(?[X]:((~funny(X)<~>old(X))))&
(~funny(john))&
(~rich(lucy)) | old(mary) | [] | null | 0 |
Everyone who is both rich and not happy is either creative or not happy and vice versa. If someone is funny then someone is not happy or calm. If alice is both kind and brave then someone is patient or not generous. Everyone who is both not old and wise is not tall. Everyone who is either patient or not tall is both wise and not strong and vice versa. Everyone who is either not strong or rich is both not strong and not kind. If someone is not strong then someone is either old or generous and vice versa. If someone is not brave then someone is not curious and vice versa. If fred is not old or tall then fred is patient or not quiet. If john is both not tall and not generous then someone is not tall. If someone is humble then someone is either curious or tall. If mary is either not calm or funny then lucy is not old or strong and vice versa. If someone is not happy or not old then susan is both generous and curious and vice versa. If someone is both not kind and brave then fred is wise and vice versa. Everyone who is patient is both humble and not humble and vice versa. Everyone who is not strong is either not patient or not strong. Susan is both creative and funny. Mary is not creative. Fred is not brave or calm. Someone is either not curious or wise. Someone is both not calm and old. Lucy is old or generous. Susan is wise or strong. Someone is not creative or happy. | Alice is rich. | contradiction | (![X]:((rich(X)&~happy(X))<=>(creative(X)<~>~happy(X))))&
((?[X]:(funny(X)))=>(?[X]:((~happy(X)|calm(X)))))&
(((kind(alice)&brave(alice)))=>(?[X]:((patient(X)|~generous(X)))))&
(![X]:((~old(X)&wise(X))=>~tall(X)))&
(![X]:((patient(X)<~>~tall(X))<=>(wise(X)&~strong(X))))&
(![X]:((~strong(X)<~>rich(X))=>(~strong(X)&~kind(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((old(X)<~>generous(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:(~curious(X))))&
(((~old(fred)|tall(fred)))=>((patient(fred)|~quiet(fred))))&
(((~tall(john)&~generous(john)))=>(?[X]:(~tall(X))))&
((?[X]:(humble(X)))=>(?[X]:((curious(X)<~>tall(X)))))&
(((~calm(mary)<~>funny(mary)))<=>((~old(lucy)|strong(lucy))))&
((?[X]:((~happy(X)|~old(X))))<=>((generous(susan)&curious(susan))))&
((?[X]:((~kind(X)&brave(X))))<=>(wise(fred)))&
(![X]:(patient(X)<=>(humble(X)&~humble(X))))&
(![X]:(~strong(X)=>(~patient(X)<~>~strong(X))))&
((creative(susan)&funny(susan)))&
(~creative(mary))&
((~brave(fred)|calm(fred)))&
(?[X]:((~curious(X)<~>wise(X))))&
(?[X]:((~calm(X)&old(X))))&
((old(lucy)|generous(lucy)))&
((wise(susan)|strong(susan)))&
(?[X]:((~creative(X)|happy(X)))) | rich(alice) | [
"p5",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 44349932417218648118370
% SZS output start Proof for 44349932417218648118370
6. ! [X0] : ((~strong(X0) <~> rich(X0)) => (~kind(X0) & ~strong(X0))) [input p5]
15. ! [X0] : (patient(X0) <=> (~humble(X0) & humble(X0))) [input p14]
16. ! [X0] : (~strong(X0) => (~patient(X0) <~> ~strong(X0))) [input p15]
25. rich(alice) [input hypothesis]
36. ! [X0] : ((~kind(X0) & ~strong(X0)) | (~strong(X0) <=> rich(X0))) [ennf transformation 6]
40. ! [X0] : ((~patient(X0) <~> ~strong(X0)) | strong(X0)) [ennf transformation 16]
50. ! [X0] : ((~kind(X0) & ~strong(X0)) | ((~strong(X0) | ~rich(X0)) & (rich(X0) | strong(X0)))) [nnf transformation 36]
78. ! [X0] : ((patient(X0) | (humble(X0) | ~humble(X0))) & ((~humble(X0) & humble(X0)) | ~patient(X0))) [nnf transformation 15]
79. ! [X0] : ((patient(X0) | humble(X0) | ~humble(X0)) & ((~humble(X0) & humble(X0)) | ~patient(X0))) [flattening 78]
80. ! [X0] : (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | strong(X0)) [nnf transformation 40]
104. ~strong(X0) | ~strong(X0) | ~rich(X0) [cnf transformation 50]
130. humble(X0) | ~patient(X0) [cnf transformation 79]
131. ~humble(X0) | ~patient(X0) [cnf transformation 79]
134. strong(X0) | patient(X0) | strong(X0) [cnf transformation 80]
146. rich(alice) [cnf transformation 25]
147. strong(X0) | patient(X0) [duplicate literal removal 134]
148. ~strong(X0) | ~rich(X0) [duplicate literal removal 104]
194. 11 <=> ! [X3] : strong(X3) [avatar definition]
195. strong(X3) <- (11) [avatar component clause 194]
315. ~patient(X0) [subsumption resolution 130,131]
316. strong(X0) [subsumption resolution 147,315]
317. 11 [avatar split clause 316,194]
354. ~rich(X0) <- (11) [resolution 148,195]
357. $false <- (11) [resolution 354,146]
358. ~11 [avatar contradiction clause 357]
359. $false [avatar sat refutation 317,358]
% SZS output end Proof for 44349932417218648118370
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is curious and vice versa.
Everyone who is not rich or brave is both calm and kind and vice versa.
Everyone who is not funny or not quiet is either not quiet or brave and vice versa.
If someone is both not rich and kind then fred is both tall and not calm and vice versa.
Everyone who is not quiet is rich.
If someone is not strong or not quiet then someone is not old or humble and vice versa.
If someone is both not calm and generous then someone is both not generous and not patient.
Everyone who is not calm or not creative is wise or not generous.
Everyone who is either curious or not wise is either not happy or not wise and vice versa.
If someone is not strong or rich then someone is wise.
Everyone who is both not wise and generous is either strong or not old and vice versa.
If someone is humble or curious then fred is either humble or not curious and vice versa.
Everyone who is not generous is not happy or wise and vice versa.
Everyone who is quiet is both not generous and not quiet.
Everyone who is not quiet is not tall or humble.
Everyone who is not calm is either brave or curious.
Mary is either not quiet or not happy.
Someone is either not calm or not kind.
Someone is both patient and not brave.
John is old or not curious.
Mary is both old and tall.
Someone is either not tall or not kind.
Mary is either kind or tall. | John is not tall. | neutral | ((?[X]:(~strong(X)))<=>(?[X]:(curious(X))))&
(![X]:((~rich(X)|brave(X))<=>(calm(X)&kind(X))))&
(![X]:((~funny(X)|~quiet(X))<=>(~quiet(X)<~>brave(X))))&
((?[X]:((~rich(X)&kind(X))))<=>((tall(fred)&~calm(fred))))&
(![X]:(~quiet(X)=>rich(X)))&
((?[X]:((~strong(X)|~quiet(X))))<=>(?[X]:((~old(X)|humble(X)))))&
((?[X]:((~calm(X)&generous(X))))=>(?[X]:((~generous(X)&~patient(X)))))&
(![X]:((~calm(X)|~creative(X))=>(wise(X)|~generous(X))))&
(![X]:((curious(X)<~>~wise(X))<=>(~happy(X)<~>~wise(X))))&
((?[X]:((~strong(X)|rich(X))))=>(?[X]:(wise(X))))&
(![X]:((~wise(X)&generous(X))<=>(strong(X)<~>~old(X))))&
((?[X]:((humble(X)|curious(X))))<=>((humble(fred)<~>~curious(fred))))&
(![X]:(~generous(X)<=>(~happy(X)|wise(X))))&
(![X]:(quiet(X)=>(~generous(X)&~quiet(X))))&
(![X]:(~quiet(X)=>(~tall(X)|humble(X))))&
(![X]:(~calm(X)=>(brave(X)<~>curious(X))))&
((~quiet(mary)<~>~happy(mary)))&
(?[X]:((~calm(X)<~>~kind(X))))&
(?[X]:((patient(X)&~brave(X))))&
((old(john)|~curious(john)))&
((old(mary)&tall(mary)))&
(?[X]:((~tall(X)<~>~kind(X))))&
((kind(mary)<~>tall(mary))) | ~tall(john) | [] | null | 0 |
Everyone who is both not brave and old is either not quiet or not creative and vice versa. Everyone who is creative or not generous is both not curious and not creative and vice versa. If lucy is either kind or tall then lucy is either quiet or old. Everyone who is either not strong or happy is not funny or not rich and vice versa. Everyone who is generous or not creative is not wise and vice versa. If someone is not calm or wise then someone is curious or not humble and vice versa. If someone is creative or not strong then mary is either not wise or not generous and vice versa. Everyone who is both patient and brave is not strong or calm. Everyone who is not strong or rich is creative. Everyone who is old or not happy is brave or not calm and vice versa. If someone is happy or not calm then mary is tall or strong and vice versa. If someone is funny or not kind then someone is either wise or rich. If someone is both not funny and funny then someone is either not old or not creative. Everyone who is tall is both not wise and not patient. If lucy is not generous or not funny then someone is either humble or brave and vice versa. Everyone who is not tall is curious or not old. Someone is brave or not creative. Fred is either patient or not creative. Someone is old or not humble. Lucy is either not rich or humble. Someone is both not creative and calm. | Fred is happy. | entailment | (![X]:((~brave(X)&old(X))<=>(~quiet(X)<~>~creative(X))))&
(![X]:((creative(X)|~generous(X))<=>(~curious(X)&~creative(X))))&
(((kind(lucy)<~>tall(lucy)))=>((quiet(lucy)<~>old(lucy))))&
(![X]:((~strong(X)<~>happy(X))<=>(~funny(X)|~rich(X))))&
(![X]:((generous(X)|~creative(X))<=>~wise(X)))&
((?[X]:((~calm(X)|wise(X))))<=>(?[X]:((curious(X)|~humble(X)))))&
((?[X]:((creative(X)|~strong(X))))<=>((~wise(mary)<~>~generous(mary))))&
(![X]:((patient(X)&brave(X))=>(~strong(X)|calm(X))))&
(![X]:((~strong(X)|rich(X))=>creative(X)))&
(![X]:((old(X)|~happy(X))<=>(brave(X)|~calm(X))))&
((?[X]:((happy(X)|~calm(X))))<=>((tall(mary)|strong(mary))))&
((?[X]:((funny(X)|~kind(X))))=>(?[X]:((wise(X)<~>rich(X)))))&
((?[X]:((~funny(X)&funny(X))))=>(?[X]:((~old(X)<~>~creative(X)))))&
(![X]:(tall(X)=>(~wise(X)&~patient(X))))&
(((~generous(lucy)|~funny(lucy)))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
(?[X]:((brave(X)|~creative(X))))&
((patient(fred)<~>~creative(fred)))&
(?[X]:((old(X)|~humble(X))))&
((~rich(lucy)<~>humble(lucy)))&
(?[X]:((~creative(X)&calm(X)))) | happy(fred) | [
"p1",
"p3",
"p4",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 7781510816091602254881245
% SZS output start Proof for 7781510816091602254881245
2. ! [X0] : ((~generous(X0) | creative(X0)) <=> (~creative(X0) & ~curious(X0))) [input p1]
4. ! [X0] : ((~strong(X0) <~> happy(X0)) <=> (~rich(X0) | ~funny(X0))) [input p3]
5. ! [X0] : ((~creative(X0) | generous(X0)) <=> ~wise(X0)) [input p4]
9. ! [X0] : ((rich(X0) | ~strong(X0)) => creative(X0)) [input p8]
12. ? [X0] : (~kind(X0) | funny(X0)) => ? [X0] : (wise(X0) <~> rich(X0)) [input p11]
22. ~happy(fred) [input hypothesis]
24. ? [X0] : (~kind(X0) | funny(X0)) => ? [X1] : (wise(X1) <~> rich(X1)) [rectify 12]
29. ! [X0] : (creative(X0) | (~rich(X0) & strong(X0))) [ennf transformation 9]
30. ? [X1] : (wise(X1) <~> rich(X1)) | ! [X0] : (kind(X0) & ~funny(X0)) [ennf transformation 24]
37. ! [X0] : (((~generous(X0) | creative(X0)) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | (generous(X0) & ~creative(X0)))) [nnf transformation 2]
38. ! [X0] : ((~generous(X0) | creative(X0) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | (generous(X0) & ~creative(X0)))) [flattening 37]
40. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (rich(X0) & funny(X0))) & ((~rich(X0) | ~funny(X0)) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~happy(X0) | strong(X0)) & (happy(X0) | ~strong(X0))) | (rich(X0) & funny(X0))) & (~rich(X0) | ~funny(X0) | ((~strong(X0) | ~happy(X0)) & (happy(X0) | strong(X0))))) [flattening 40]
42. ! [X0] : (((~creative(X0) | generous(X0)) | wise(X0)) & (~wise(X0) | (creative(X0) & ~generous(X0)))) [nnf transformation 5]
43. ! [X0] : ((~creative(X0) | generous(X0) | wise(X0)) & (~wise(X0) | (creative(X0) & ~generous(X0)))) [flattening 42]
60. ? [X1] : ((~rich(X1) | ~wise(X1)) & (rich(X1) | wise(X1))) | ! [X0] : (kind(X0) & ~funny(X0)) [nnf transformation 30]
61. ? [X0] : ((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ! [X1] : (kind(X1) & ~funny(X1)) [rectify 60]
62. ? [X0] : ((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) => ((~rich(sK4) | ~wise(sK4)) & (rich(sK4) | wise(sK4))) [choice axiom]
63. ((~rich(sK4) | ~wise(sK4)) & (rich(sK4) | wise(sK4))) | ! [X1] : (kind(X1) & ~funny(X1)) [skolemisation 61,62]
89. ~creative(X0) | ~creative(X0) [cnf transformation 38]
98. ~strong(X0) | happy(X0) | funny(X0) [cnf transformation 41]
103. ~wise(X0) | creative(X0) [cnf transformation 43]
116. creative(X0) | strong(X0) [cnf transformation 29]
117. creative(X0) | ~rich(X0) [cnf transformation 29]
126. rich(sK4) | wise(sK4) | ~funny(X1) [cnf transformation 63]
149. ~happy(fred) [cnf transformation 22]
150. ~creative(X0) [duplicate literal removal 89]
172. ~wise(X0) [subsumption resolution 103,150]
212. 13 <=> ! [X1] : strong(X1) [avatar definition]
213. strong(X1) <- (13) [avatar component clause 212]
215. ~rich(X0) [subsumption resolution 117,150]
216. strong(X0) [subsumption resolution 116,150]
217. 13 [avatar split clause 216,212]
243. wise(sK4) | ~funny(X1) [subsumption resolution 126,215]
244. ~funny(X1) [subsumption resolution 243,172]
286. happy(X0) | funny(X0) <- (13) [resolution 98,213]
288. happy(X0) <- (13) [subsumption resolution 286,244]
289. $false <- (13) [resolution 288,149]
290. ~13 [avatar contradiction clause 289]
291. $false [avatar sat refutation 217,290]
% SZS output end Proof for 7781510816091602254881245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not strong is either quiet or generous and vice versa.
Everyone who is both wise and not calm is not generous.
Everyone who is curious is both not brave and quiet and vice versa.
If someone is creative or not rich then lucy is patient or brave.
If paul is not tall then susan is funny or curious.
Everyone who is both not humble and quiet is both not calm and generous and vice versa.
Everyone who is not strong is either not generous or funny and vice versa.
If alice is not curious then someone is either not humble or not strong and vice versa.
Everyone who is not wise or calm is both not old and not rich and vice versa.
Everyone who is either not calm or not generous is both not strong and kind and vice versa.
Everyone who is curious or old is both strong and not generous.
If someone is brave then mary is not generous or quiet.
If mary is both not tall and tall then alice is humble or curious and vice versa.
Everyone who is generous or tall is both not humble and brave and vice versa.
Everyone who is both not kind and not patient is not patient.
If paul is either patient or quiet then someone is both tall and creative and vice versa.
Paul is generous.
John is not generous.
Paul is both creative and funny.
Someone is either not patient or not strong.
Lucy is curious or tall.
Someone is either funny or brave.
Fred is not strong or not calm. | Paul is kind. | contradiction | (![X]:((~tall(X)|~strong(X))<=>(quiet(X)<~>generous(X))))&
(![X]:((wise(X)&~calm(X))=>~generous(X)))&
(![X]:(curious(X)<=>(~brave(X)&quiet(X))))&
((?[X]:((creative(X)|~rich(X))))=>((patient(lucy)|brave(lucy))))&
((~tall(paul))=>((funny(susan)|curious(susan))))&
(![X]:((~humble(X)&quiet(X))<=>(~calm(X)&generous(X))))&
(![X]:(~strong(X)<=>(~generous(X)<~>funny(X))))&
((~curious(alice))<=>(?[X]:((~humble(X)<~>~strong(X)))))&
(![X]:((~wise(X)|calm(X))<=>(~old(X)&~rich(X))))&
(![X]:((~calm(X)<~>~generous(X))<=>(~strong(X)&kind(X))))&
(![X]:((curious(X)|old(X))=>(strong(X)&~generous(X))))&
((?[X]:(brave(X)))=>((~generous(mary)|quiet(mary))))&
(((~tall(mary)&tall(mary)))<=>((humble(alice)|curious(alice))))&
(![X]:((generous(X)|tall(X))<=>(~humble(X)&brave(X))))&
(![X]:((~kind(X)&~patient(X))=>~patient(X)))&
(((patient(paul)<~>quiet(paul)))<=>(?[X]:((tall(X)&creative(X)))))&
(generous(paul))&
(~generous(john))&
((creative(paul)&funny(paul)))&
(?[X]:((~patient(X)<~>~strong(X))))&
((curious(lucy)|tall(lucy)))&
(?[X]:((funny(X)<~>brave(X))))&
((~strong(fred)|~calm(fred))) | kind(paul) | [
"p0",
"p5",
"p6",
"p9",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 5709401684073627080188948
% SZS output start Proof for 5709401684073627080188948
1. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (quiet(X0) <~> generous(X0))) [input p0]
6. ! [X0] : ((quiet(X0) & ~humble(X0)) <=> (generous(X0) & ~calm(X0))) [input p5]
7. ! [X0] : (~strong(X0) <=> (~generous(X0) <~> funny(X0))) [input p6]
10. ! [X0] : ((~calm(X0) <~> ~generous(X0)) <=> (kind(X0) & ~strong(X0))) [input p9]
17. generous(paul) [input p16]
19. funny(paul) & creative(paul) [input p18]
24. kind(paul) [input hypothesis]
36. ! [X0] : (((~strong(X0) | ~tall(X0)) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) & (((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (strong(X0) & tall(X0)))) [nnf transformation 1]
37. ! [X0] : ((~strong(X0) | ~tall(X0) | ((quiet(X0) | ~generous(X0)) & (generous(X0) | ~quiet(X0)))) & (((~generous(X0) | ~quiet(X0)) & (generous(X0) | quiet(X0))) | (strong(X0) & tall(X0)))) [flattening 36]
40. ! [X0] : (((quiet(X0) & ~humble(X0)) | (~generous(X0) | calm(X0))) & ((generous(X0) & ~calm(X0)) | (~quiet(X0) | humble(X0)))) [nnf transformation 6]
41. ! [X0] : (((quiet(X0) & ~humble(X0)) | ~generous(X0) | calm(X0)) & ((generous(X0) & ~calm(X0)) | ~quiet(X0) | humble(X0))) [flattening 40]
42. ! [X0] : ((~strong(X0) | ((~generous(X0) | ~funny(X0)) & (funny(X0) | generous(X0)))) & (((~funny(X0) | generous(X0)) & (funny(X0) | ~generous(X0))) | strong(X0))) [nnf transformation 7]
49. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | (~kind(X0) | strong(X0))) & ((kind(X0) & ~strong(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [nnf transformation 10]
50. ! [X0] : ((((generous(X0) | calm(X0)) & (~generous(X0) | ~calm(X0))) | ~kind(X0) | strong(X0)) & ((kind(X0) & ~strong(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0))))) [flattening 49]
68. ~generous(X0) | ~quiet(X0) | strong(X0) [cnf transformation 37]
81. ~generous(X0) | quiet(X0) | calm(X0) [cnf transformation 41]
85. ~funny(X0) | ~generous(X0) | ~strong(X0) [cnf transformation 42]
99. ~kind(X0) | ~calm(X0) | ~generous(X0) | strong(X0) [cnf transformation 50]
123. generous(paul) [cnf transformation 17]
126. funny(paul) [cnf transformation 19]
133. kind(paul) [cnf transformation 24]
217. 20 <=> quiet(paul) [avatar definition]
324. ~quiet(paul) | strong(paul) [resolution 68,123]
371. quiet(paul) | calm(paul) [resolution 81,123]
410. ~generous(paul) | ~strong(paul) [resolution 85,126]
412. ~strong(paul) [subsumption resolution 410,123]
450. ~calm(paul) | ~generous(paul) | strong(paul) [resolution 99,133]
455. ~calm(paul) | strong(paul) [subsumption resolution 450,123]
456. ~calm(paul) [subsumption resolution 455,412]
457. quiet(paul) [subsumption resolution 371,456]
458. 20 [avatar split clause 457,217]
459. ~quiet(paul) [subsumption resolution 324,412]
460. ~20 [avatar split clause 459,217]
463. $false [avatar sat refutation 458,460]
% SZS output end Proof for 5709401684073627080188948
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not 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. | Alice is not quiet. | 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)))) | ~quiet(alice) | [
"p0",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 4838312352890115832463928
% SZS output start Proof for 4838312352890115832463928
1. ? [X0] : ~old(X0) <=> (~humble(alice) <~> ~quiet(alice)) [input p0]
11. ! [X0] : (~old(X0) => ~brave(X0)) [input p10]
12. ! [X0] : ((~brave(X0) | humble(X0)) => (happy(X0) & ~happy(X0))) [input p11]
23. quiet(alice) [input hypothesis]
36. ! [X0] : (~brave(X0) | old(X0)) [ennf transformation 11]
37. ! [X0] : ((happy(X0) & ~happy(X0)) | (brave(X0) & ~humble(X0))) [ennf transformation 12]
41. (? [X0] : ~old(X0) | ((~humble(alice) | quiet(alice)) & (~quiet(alice) | humble(alice)))) & (((quiet(alice) | humble(alice)) & (~quiet(alice) | ~humble(alice))) | ! [X0] : old(X0)) [nnf transformation 1]
42. (? [X0] : ~old(X0) | ((~humble(alice) | quiet(alice)) & (~quiet(alice) | humble(alice)))) & (((quiet(alice) | humble(alice)) & (~quiet(alice) | ~humble(alice))) | ! [X1] : old(X1)) [rectify 41]
43. ? [X0] : ~old(X0) => ~old(sK0) [choice axiom]
44. (~old(sK0) | ((~humble(alice) | quiet(alice)) & (~quiet(alice) | humble(alice)))) & (((quiet(alice) | humble(alice)) & (~quiet(alice) | ~humble(alice))) | ! [X1] : old(X1)) [skolemisation 42,43]
72. ~old(sK0) | ~quiet(alice) | humble(alice) [cnf transformation 44]
92. ~brave(X0) | old(X0) [cnf transformation 36]
93. ~happy(X0) | ~humble(X0) [cnf transformation 37]
94. ~happy(X0) | brave(X0) [cnf transformation 37]
95. happy(X0) | ~humble(X0) [cnf transformation 37]
96. happy(X0) | brave(X0) [cnf transformation 37]
121. quiet(alice) [cnf transformation 23]
124. 1 <=> quiet(alice) [avatar definition]
128. 2 <=> humble(alice) [avatar definition]
129. humble(alice) <- (2) [avatar component clause 128]
132. 3 <=> old(sK0) [avatar definition]
134. ~old(sK0) <- (~3) [avatar component clause 132]
136. 2 | ~1 | ~3 [avatar split clause 72,132,124,128]
138. 4 <=> ! [X1] : old(X1) [avatar definition]
139. old(X1) <- (4) [avatar component clause 138]
177. brave(X0) [subsumption resolution 94,96]
178. ~humble(X0) [subsumption resolution 93,95]
217. 1 [avatar split clause 121,124]
223. old(X0) [resolution 92,177]
224. 4 [avatar split clause 223,138]
225. $false <- (~3, 4) [resolution 139,134]
228. 3 | ~4 [avatar contradiction clause 225]
229. $false <- (2) [subsumption resolution 129,178]
230. ~2 [avatar contradiction clause 229]
231. $false [avatar sat refutation 136,217,224,228,230]
% SZS output end Proof for 4838312352890115832463928
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
If someone is kind then someone is not tall. If someone is brave then someone is either not kind or not happy and vice versa. If someone is both rich and generous then alice is calm and vice versa. Everyone who is happy or tall is humble and vice versa. Everyone who is not happy or rich is either funny or rich. Everyone who is both patient and old is humble or not humble and vice versa. Everyone who is not quiet or curious is not tall or not patient and vice versa. If john is both brave and funny then mary is either patient or humble and vice versa. If mary is tall then fred is either brave or not strong and vice versa. Everyone who is tall is both humble and not wise. If someone is both not old and happy then john is tall and vice versa. Everyone who is not brave or not rich is either quiet or not generous and vice versa. Everyone who is curious is either not rich or rich. Everyone who is old or rich is tall or not happy. Everyone who is not curious or quiet is both not creative and not old. Everyone who is either kind or not wise is not happy or calm. Alice is generous. Someone is either wise or not brave. Someone is either rich or not patient. Someone is not tall. Someone is either old or brave. Mary is either not strong or not wise. | John is curious. | entailment | ((?[X]:(kind(X)))=>(?[X]:(~tall(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((rich(X)&generous(X))))<=>(calm(alice)))&
(![X]:((happy(X)|tall(X))<=>humble(X)))&
(![X]:((~happy(X)|rich(X))=>(funny(X)<~>rich(X))))&
(![X]:((patient(X)&old(X))<=>(humble(X)|~humble(X))))&
(![X]:((~quiet(X)|curious(X))<=>(~tall(X)|~patient(X))))&
(((brave(john)&funny(john)))<=>((patient(mary)<~>humble(mary))))&
((tall(mary))<=>((brave(fred)<~>~strong(fred))))&
(![X]:(tall(X)=>(humble(X)&~wise(X))))&
((?[X]:((~old(X)&happy(X))))<=>(tall(john)))&
(![X]:((~brave(X)|~rich(X))<=>(quiet(X)<~>~generous(X))))&
(![X]:(curious(X)=>(~rich(X)<~>rich(X))))&
(![X]:((old(X)|rich(X))=>(tall(X)|~happy(X))))&
(![X]:((~curious(X)|quiet(X))=>(~creative(X)&~old(X))))&
(![X]:((kind(X)<~>~wise(X))=>(~happy(X)|calm(X))))&
(generous(alice))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((rich(X)<~>~patient(X))))&
(?[X]:(~tall(X)))&
(?[X]:((old(X)<~>brave(X))))&
((~strong(mary)<~>~wise(mary))) | curious(john) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6534474493922430683628120
% SZS output start Proof for 6534474493922430683628120
6. ! [X0] : ((old(X0) & patient(X0)) <=> (~humble(X0) | humble(X0))) [input p5]
15. ! [X0] : ((quiet(X0) | ~curious(X0)) => (~old(X0) & ~creative(X0))) [input p14]
23. ~curious(john) [input hypothesis]
26. ! [X0] : ((quiet(X0) | ~curious(X0)) => ~old(X0)) [pure predicate removal 15]
33. ! [X0] : (~old(X0) | (~quiet(X0) & curious(X0))) [ennf transformation 26]
51. ! [X0] : (((old(X0) & patient(X0)) | (humble(X0) & ~humble(X0))) & ((~humble(X0) | humble(X0)) | (~old(X0) | ~patient(X0)))) [nnf transformation 6]
52. ! [X0] : (((old(X0) & patient(X0)) | (humble(X0) & ~humble(X0))) & (~humble(X0) | humble(X0) | ~old(X0) | ~patient(X0))) [flattening 51]
96. old(X0) | ~humble(X0) [cnf transformation 52]
97. old(X0) | humble(X0) [cnf transformation 52]
127. ~old(X0) | curious(X0) [cnf transformation 33]
141. ~curious(john) [cnf transformation 23]
194. old(X0) [subsumption resolution 96,97]
245. curious(X0) [subsumption resolution 127,194]
268. $false [subsumption resolution 141,245]
% SZS output end Proof for 6534474493922430683628120
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then mary is both funny and generous and vice versa. Everyone who is creative is both not patient and not brave. If someone is not curious or not wise then someone is either not quiet or patient and vice versa. Everyone who is not quiet is either not brave or not funny. If someone is both generous and not wise then susan is either not rich or not curious. Everyone who is happy is either generous or not humble and vice versa. If paul is funny then mary is humble or not kind and vice versa. Everyone who is not kind or not rich is both not tall and patient. If lucy is creative then lucy is brave or patient and vice versa. If someone is not generous then lucy is not creative and vice versa. If alice is not quiet or kind then someone is not patient or not humble and vice versa. Everyone who is both old and quiet is rich or not rich. If paul is both creative and not creative then someone is quiet. Everyone who is happy is either not quiet or happy. Everyone who is not wise or not happy is either wise or generous. If someone is not tall then someone is either curious or strong and vice versa. John is both not curious and old. Someone is not happy or not creative. Someone is not strong or humble. Paul is not humble or not quiet. Someone is either kind or wise. Someone is not tall or wise. Someone is rich. Someone is funny. | Susan is not rich. | neutral | ((?[X]:(~old(X)))<=>((funny(mary)&generous(mary))))&
(![X]:(creative(X)=>(~patient(X)&~brave(X))))&
((?[X]:((~curious(X)|~wise(X))))<=>(?[X]:((~quiet(X)<~>patient(X)))))&
(![X]:(~quiet(X)=>(~brave(X)<~>~funny(X))))&
((?[X]:((generous(X)&~wise(X))))=>((~rich(susan)<~>~curious(susan))))&
(![X]:(happy(X)<=>(generous(X)<~>~humble(X))))&
((funny(paul))<=>((humble(mary)|~kind(mary))))&
(![X]:((~kind(X)|~rich(X))=>(~tall(X)&patient(X))))&
((creative(lucy))<=>((brave(lucy)|patient(lucy))))&
((?[X]:(~generous(X)))<=>(~creative(lucy)))&
(((~quiet(alice)|kind(alice)))<=>(?[X]:((~patient(X)|~humble(X)))))&
(![X]:((old(X)&quiet(X))=>(rich(X)|~rich(X))))&
(((creative(paul)&~creative(paul)))=>(?[X]:(quiet(X))))&
(![X]:(happy(X)=>(~quiet(X)<~>happy(X))))&
(![X]:((~wise(X)|~happy(X))=>(wise(X)<~>generous(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((curious(X)<~>strong(X)))))&
((~curious(john)&old(john)))&
(?[X]:((~happy(X)|~creative(X))))&
(?[X]:((~strong(X)|humble(X))))&
((~humble(paul)|~quiet(paul)))&
(?[X]:((kind(X)<~>wise(X))))&
(?[X]:((~tall(X)|wise(X))))&
(?[X]:(rich(X)))&
(?[X]:(funny(X))) | ~rich(susan) | [] | null | 0 |
Everyone who is either patient or brave is either funny or tall and vice versa.
Everyone who is both patient and strong is both not brave and rich.
If lucy is quiet then someone is not strong and vice versa.
Everyone who is funny or kind is not patient or not quiet and vice versa.
If someone is either humble or rich then someone is not curious or rich.
Everyone who is not calm is not tall and vice versa.
If someone is either patient or generous then someone is both wise and humble and vice versa.
If alice is not wise then someone is curious or not kind and vice versa.
Everyone who is either quiet or not humble is not patient.
Everyone who is both not old and happy is either curious or not happy and vice versa.
Everyone who is both wise and not old is happy.
If someone is not wise or strong then john is either tall or not wise and vice versa.
Everyone who is not curious is brave or curious and vice versa.
If fred is either funny or calm then someone is either not calm or brave and vice versa.
Everyone who is not strong is not curious or not quiet.
Someone is both not strong and not kind.
Paul is not wise or old.
Someone is quiet.
Susan is not happy or not strong.
Someone is both not humble and not quiet.
Lucy is not curious or not happy.
Someone is rich.
Fred is kind or patient. | Alice is not tall. | neutral | (![X]:((patient(X)<~>brave(X))<=>(funny(X)<~>tall(X))))&
(![X]:((patient(X)&strong(X))=>(~brave(X)&rich(X))))&
((quiet(lucy))<=>(?[X]:(~strong(X))))&
(![X]:((funny(X)|kind(X))<=>(~patient(X)|~quiet(X))))&
((?[X]:((humble(X)<~>rich(X))))=>(?[X]:((~curious(X)|rich(X)))))&
(![X]:(~calm(X)<=>~tall(X)))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((wise(X)&humble(X)))))&
((~wise(alice))<=>(?[X]:((curious(X)|~kind(X)))))&
(![X]:((quiet(X)<~>~humble(X))=>~patient(X)))&
(![X]:((~old(X)&happy(X))<=>(curious(X)<~>~happy(X))))&
(![X]:((wise(X)&~old(X))=>happy(X)))&
((?[X]:((~wise(X)|strong(X))))<=>((tall(john)<~>~wise(john))))&
(![X]:(~curious(X)<=>(brave(X)|curious(X))))&
(((funny(fred)<~>calm(fred)))<=>(?[X]:((~calm(X)<~>brave(X)))))&
(![X]:(~strong(X)=>(~curious(X)|~quiet(X))))&
(?[X]:((~strong(X)&~kind(X))))&
((~wise(paul)|old(paul)))&
(?[X]:(quiet(X)))&
((~happy(susan)|~strong(susan)))&
(?[X]:((~humble(X)&~quiet(X))))&
((~curious(lucy)|~happy(lucy)))&
(?[X]:(rich(X)))&
((kind(fred)|patient(fred))) | ~tall(alice) | [] | null | 0 |
Everyone who is both curious and not brave is not happy or humble and vice versa.
Everyone who is not patient or not rich is not humble and vice versa.
If someone is happy or not funny then someone is both not old and not happy.
Everyone who is either strong or funny is both brave and strong.
Everyone who is strong is either wise or not old.
If paul is not humble or not rich then john is either not rich or not funny.
Everyone who is both calm and old is not funny or curious and vice versa.
If someone is rich then someone is not kind.
If someone is both not tall and old then alice is either not curious or not humble.
If mary is rich or not old then alice is either not quiet or creative.
If someone is either humble or not happy then mary is either not wise or not strong and vice versa.
If someone is not wise or happy then someone is either calm or patient and vice versa.
If susan is not curious or brave then someone is either quiet or not rich.
Everyone who is creative is not humble and vice versa.
If alice is either tall or patient then paul is not kind.
If someone is both not old and strong then someone is not brave or not patient.
Someone is both old and generous.
John is rich or not rich.
Alice is old.
Lucy is either patient or generous.
Susan is either not generous or old. | Alice is curious. | entailment | (![X]:((curious(X)&~brave(X))<=>(~happy(X)|humble(X))))&
(![X]:((~patient(X)|~rich(X))<=>~humble(X)))&
((?[X]:((happy(X)|~funny(X))))=>(?[X]:((~old(X)&~happy(X)))))&
(![X]:((strong(X)<~>funny(X))=>(brave(X)&strong(X))))&
(![X]:(strong(X)=>(wise(X)<~>~old(X))))&
(((~humble(paul)|~rich(paul)))=>((~rich(john)<~>~funny(john))))&
(![X]:((calm(X)&old(X))<=>(~funny(X)|curious(X))))&
((?[X]:(rich(X)))=>(?[X]:(~kind(X))))&
((?[X]:((~tall(X)&old(X))))=>((~curious(alice)<~>~humble(alice))))&
(((rich(mary)|~old(mary)))=>((~quiet(alice)<~>creative(alice))))&
((?[X]:((humble(X)<~>~happy(X))))<=>((~wise(mary)<~>~strong(mary))))&
((?[X]:((~wise(X)|happy(X))))<=>(?[X]:((calm(X)<~>patient(X)))))&
(((~curious(susan)|brave(susan)))=>(?[X]:((quiet(X)<~>~rich(X)))))&
(![X]:(creative(X)<=>~humble(X)))&
(((tall(alice)<~>patient(alice)))=>(~kind(paul)))&
((?[X]:((~old(X)&strong(X))))=>(?[X]:((~brave(X)|~patient(X)))))&
(?[X]:((old(X)&generous(X))))&
((rich(john)|~rich(john)))&
(old(alice))&
((patient(lucy)<~>generous(lucy)))&
((~generous(susan)<~>old(susan))) | curious(alice) | [
"p0",
"p2",
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 1412410456900970559969451
% SZS output start Proof for 1412410456900970559969451
1. ! [X0] : ((~brave(X0) & curious(X0)) <=> (humble(X0) | ~happy(X0))) [input p0]
3. ? [X0] : (~funny(X0) | happy(X0)) => ? [X0] : (~happy(X0) & ~old(X0)) [input p2]
7. ! [X0] : ((old(X0) & calm(X0)) <=> (curious(X0) | ~funny(X0))) [input p6]
22. ~curious(alice) [input hypothesis]
23. ? [X0] : (~funny(X0) | happy(X0)) => ? [X1] : (~happy(X1) & ~old(X1)) [rectify 3]
30. ? [X1] : (~happy(X1) & ~old(X1)) | ! [X0] : (funny(X0) & ~happy(X0)) [ennf transformation 23]
37. ! [X0] : (((~brave(X0) & curious(X0)) | (~humble(X0) & happy(X0))) & ((humble(X0) | ~happy(X0)) | (brave(X0) | ~curious(X0)))) [nnf transformation 1]
38. ! [X0] : (((~brave(X0) & curious(X0)) | (~humble(X0) & happy(X0))) & (humble(X0) | ~happy(X0) | brave(X0) | ~curious(X0))) [flattening 37]
41. ? [X0] : (~happy(X0) & ~old(X0)) | ! [X1] : (funny(X1) & ~happy(X1)) [rectify 30]
42. ? [X0] : (~happy(X0) & ~old(X0)) => (~happy(sK0) & ~old(sK0)) [choice axiom]
43. (~happy(sK0) & ~old(sK0)) | ! [X1] : (funny(X1) & ~happy(X1)) [skolemisation 41,42]
47. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & funny(X0))) & ((curious(X0) | ~funny(X0)) | (~old(X0) | ~calm(X0)))) [nnf transformation 7]
48. ! [X0] : (((old(X0) & calm(X0)) | (~curious(X0) & funny(X0))) & (curious(X0) | ~funny(X0) | ~old(X0) | ~calm(X0))) [flattening 47]
71. happy(X0) | curious(X0) [cnf transformation 38]
78. ~old(sK0) | ~happy(X1) [cnf transformation 43]
80. ~happy(sK0) | ~happy(X1) [cnf transformation 43]
96. ~curious(X0) | old(X0) [cnf transformation 48]
130. ~curious(alice) [cnf transformation 22]
136. 2 <=> happy(sK0) [avatar definition]
138. ~happy(sK0) <- (~2) [avatar component clause 136]
141. 3 <=> ! [X1] : ~happy(X1) [avatar definition]
142. ~happy(X1) <- (3) [avatar component clause 141]
143. 3 | ~2 [avatar split clause 80,136,141]
145. 4 <=> old(sK0) [avatar definition]
147. ~old(sK0) <- (~4) [avatar component clause 145]
149. 3 | ~4 [avatar split clause 78,145,141]
303. curious(sK0) <- (~2) [resolution 71,138]
309. old(sK0) <- (~2) [resolution 96,303]
311. $false <- (~2, ~4) [subsumption resolution 309,147]
312. 2 | 4 [avatar contradiction clause 311]
317. curious(X0) <- (3) [resolution 142,71]
318. $false <- (3) [resolution 317,130]
321. ~3 [avatar contradiction clause 318]
322. $false [avatar sat refutation 143,149,312,321]
% SZS output end Proof for 1412410456900970559969451
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not tall and not calm then someone is not brave or not curious.
Everyone who is not calm or rich is both quiet and patient.
Everyone who is both not wise and tall is either not wise or not calm and vice versa.
If susan is kind or not calm then someone is both wise and not generous.
Everyone who is not calm is creative and vice versa.
If paul is not creative then fred is calm and vice versa.
If someone is both not rich and humble then mary is not strong.
Everyone who is either not funny or not tall is both funny and not brave and vice versa.
Everyone who is either not old or not humble is not strong or not tall and vice versa.
If someone is either not patient or not old then someone is calm or not happy and vice versa.
If someone is both old and happy then alice is both not wise and not humble.
If someone is both not curious and brave then alice is not old or not humble.
Everyone who is not humble is generous or not tall.
Everyone who is both not generous and not humble is patient.
Someone is either patient or wise.
Someone is humble.
Someone is not calm or brave.
John is tall.
Paul is rich.
Someone is not wise or not brave. | Mary is curious. | neutral | ((?[X]:((~tall(X)&~calm(X))))=>(?[X]:((~brave(X)|~curious(X)))))&
(![X]:((~calm(X)|rich(X))=>(quiet(X)&patient(X))))&
(![X]:((~wise(X)&tall(X))<=>(~wise(X)<~>~calm(X))))&
(((kind(susan)|~calm(susan)))=>(?[X]:((wise(X)&~generous(X)))))&
(![X]:(~calm(X)<=>creative(X)))&
((~creative(paul))<=>(calm(fred)))&
((?[X]:((~rich(X)&humble(X))))=>(~strong(mary)))&
(![X]:((~funny(X)<~>~tall(X))<=>(funny(X)&~brave(X))))&
(![X]:((~old(X)<~>~humble(X))<=>(~strong(X)|~tall(X))))&
((?[X]:((~patient(X)<~>~old(X))))<=>(?[X]:((calm(X)|~happy(X)))))&
((?[X]:((old(X)&happy(X))))=>((~wise(alice)&~humble(alice))))&
((?[X]:((~curious(X)&brave(X))))=>((~old(alice)|~humble(alice))))&
(![X]:(~humble(X)=>(generous(X)|~tall(X))))&
(![X]:((~generous(X)&~humble(X))=>patient(X)))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:(humble(X)))&
(?[X]:((~calm(X)|brave(X))))&
(tall(john))&
(rich(paul))&
(?[X]:((~wise(X)|~brave(X)))) | curious(mary) | [] | null | 0 |
If alice is rich then mary is either wise or not happy and vice versa. If someone is either wise or patient then mary is both not calm and not generous. If lucy is wise then susan is not creative. Everyone who is not brave is both not kind and generous. If someone is not wise or not kind then someone is both creative and not curious. Everyone who is not wise is not creative. Everyone who is both brave and curious is both not brave and not kind. If someone is either happy or not tall then lucy is not creative. Everyone who is not calm or not creative is calm and vice versa. Everyone who is not tall is curious or not wise. If alice is not kind then someone is either tall or strong and vice versa. Everyone who is strong or not strong is either humble or not happy. If someone is quiet or not funny then someone is old and vice versa. Everyone who is not wise or not calm is either creative or wise. If someone is either not happy or patient then someone is both not humble and creative. Everyone who is both not happy and not curious is either not humble or curious and vice versa. Someone is not quiet or not kind. Someone is not strong or not funny. Susan is not curious. Someone is either creative or not generous. | Mary is humble. | contradiction | ((rich(alice))<=>((wise(mary)<~>~happy(mary))))&
((?[X]:((wise(X)<~>patient(X))))=>((~calm(mary)&~generous(mary))))&
((wise(lucy))=>(~creative(susan)))&
(![X]:(~brave(X)=>(~kind(X)&generous(X))))&
((?[X]:((~wise(X)|~kind(X))))=>(?[X]:((creative(X)&~curious(X)))))&
(![X]:(~wise(X)=>~creative(X)))&
(![X]:((brave(X)&curious(X))=>(~brave(X)&~kind(X))))&
((?[X]:((happy(X)<~>~tall(X))))=>(~creative(lucy)))&
(![X]:((~calm(X)|~creative(X))<=>calm(X)))&
(![X]:(~tall(X)=>(curious(X)|~wise(X))))&
((~kind(alice))<=>(?[X]:((tall(X)<~>strong(X)))))&
(![X]:((strong(X)|~strong(X))=>(humble(X)<~>~happy(X))))&
((?[X]:((quiet(X)|~funny(X))))<=>(?[X]:(old(X))))&
(![X]:((~wise(X)|~calm(X))=>(creative(X)<~>wise(X))))&
((?[X]:((~happy(X)<~>patient(X))))=>(?[X]:((~humble(X)&creative(X)))))&
(![X]:((~happy(X)&~curious(X))<=>(~humble(X)<~>curious(X))))&
(?[X]:((~quiet(X)|~kind(X))))&
(?[X]:((~strong(X)|~funny(X))))&
(~curious(susan))&
(?[X]:((creative(X)<~>~generous(X)))) | humble(mary) | [
"p1",
"p5",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1830039510924630881820328
% SZS output start Proof for 1830039510924630881820328
2. ? [X0] : (wise(X0) <~> patient(X0)) => (~generous(mary) & ~calm(mary)) [input p1]
6. ! [X0] : (~wise(X0) => ~creative(X0)) [input p5]
9. ! [X0] : ((~creative(X0) | ~calm(X0)) <=> calm(X0)) [input p8]
12. ! [X0] : ((~strong(X0) | strong(X0)) => (humble(X0) <~> ~happy(X0))) [input p11]
14. ! [X0] : ((~calm(X0) | ~wise(X0)) => (creative(X0) <~> wise(X0))) [input p13]
15. ? [X0] : (~happy(X0) <~> patient(X0)) => ? [X0] : (creative(X0) & ~humble(X0)) [input p14]
21. humble(mary) [input hypothesis]
24. ? [X0] : (~happy(X0) <~> patient(X0)) => ? [X1] : (creative(X1) & ~humble(X1)) [rectify 15]
25. (~generous(mary) & ~calm(mary)) | ! [X0] : (wise(X0) <=> patient(X0)) [ennf transformation 2]
29. ! [X0] : (~creative(X0) | wise(X0)) [ennf transformation 6]
35. ! [X0] : ((humble(X0) <~> ~happy(X0)) | (strong(X0) & ~strong(X0))) [ennf transformation 12]
36. ! [X0] : ((creative(X0) <~> wise(X0)) | (calm(X0) & wise(X0))) [ennf transformation 14]
37. ? [X1] : (creative(X1) & ~humble(X1)) | ! [X0] : (~happy(X0) <=> patient(X0)) [ennf transformation 24]
39. (~generous(mary) & ~calm(mary)) | ! [X0] : ((wise(X0) | ~patient(X0)) & (patient(X0) | ~wise(X0))) [nnf transformation 25]
44. ! [X0] : (((~creative(X0) | ~calm(X0)) | ~calm(X0)) & (calm(X0) | (creative(X0) & calm(X0)))) [nnf transformation 9]
45. ! [X0] : ((~creative(X0) | ~calm(X0) | ~calm(X0)) & (calm(X0) | (creative(X0) & calm(X0)))) [flattening 44]
50. ! [X0] : (((happy(X0) | ~humble(X0)) & (~happy(X0) | humble(X0))) | (strong(X0) & ~strong(X0))) [nnf transformation 35]
56. ! [X0] : (((~wise(X0) | ~creative(X0)) & (wise(X0) | creative(X0))) | (calm(X0) & wise(X0))) [nnf transformation 36]
57. ? [X1] : (creative(X1) & ~humble(X1)) | ! [X0] : ((~happy(X0) | ~patient(X0)) & (patient(X0) | happy(X0))) [nnf transformation 37]
58. ? [X0] : (creative(X0) & ~humble(X0)) | ! [X1] : ((~happy(X1) | ~patient(X1)) & (patient(X1) | happy(X1))) [rectify 57]
59. ? [X0] : (creative(X0) & ~humble(X0)) => (creative(sK4) & ~humble(sK4)) [choice axiom]
60. (creative(sK4) & ~humble(sK4)) | ! [X1] : ((~happy(X1) | ~patient(X1)) & (patient(X1) | happy(X1))) [skolemisation 58,59]
74. ~calm(mary) | patient(X0) | ~wise(X0) [cnf transformation 39]
85. ~creative(X0) | wise(X0) [cnf transformation 29]
90. calm(X0) | calm(X0) [cnf transformation 45]
92. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
100. happy(X0) | ~humble(X0) | ~strong(X0) [cnf transformation 50]
101. happy(X0) | ~humble(X0) | strong(X0) [cnf transformation 50]
105. wise(X0) | creative(X0) | wise(X0) [cnf transformation 56]
112. creative(sK4) | ~happy(X1) | ~patient(X1) [cnf transformation 60]
124. humble(mary) [cnf transformation 21]
127. wise(X0) | creative(X0) [duplicate literal removal 105]
128. calm(X0) [duplicate literal removal 90]
129. ~creative(X0) | ~calm(X0) [duplicate literal removal 92]
156. 6 <=> ! [X0] : (patient(X0) | ~wise(X0)) [avatar definition]
157. patient(X0) | ~wise(X0) <- (6) [avatar component clause 156]
160. 7 <=> calm(mary) [avatar definition]
162. ~calm(mary) <- (~7) [avatar component clause 160]
164. 6 | ~7 [avatar split clause 74,160,156]
183. 12 <=> ! [X1] : wise(X1) [avatar definition]
184. wise(X1) <- (12) [avatar component clause 183]
227. ~humble(X0) | happy(X0) [subsumption resolution 100,101]
253. wise(X0) [subsumption resolution 127,85]
254. 12 [avatar split clause 253,183]
256. 28 <=> ! [X1] : (~happy(X1) | ~patient(X1)) [avatar definition]
257. ~happy(X1) | ~patient(X1) <- (28) [avatar component clause 256]
259. 29 <=> creative(sK4) [avatar definition]
261. creative(sK4) <- (29) [avatar component clause 259]
262. 28 | 29 [avatar split clause 112,259,256]
303. $false <- (~7) [subsumption resolution 162,128]
304. 7 [avatar contradiction clause 303]
305. patient(X0) <- (6, 12) [subsumption resolution 157,184]
314. ~calm(sK4) <- (29) [resolution 129,261]
316. $false <- (29) [subsumption resolution 314,128]
317. ~29 [avatar contradiction clause 316]
318. ~happy(X1) <- (6, 12, 28) [subsumption resolution 257,305]
320. happy(mary) [resolution 227,124]
323. $false <- (6, 12, 28) [subsumption resolution 320,318]
324. ~6 | ~12 | ~28 [avatar contradiction clause 323]
327. $false [avatar sat refutation 164,254,262,304,317,324]
% SZS output end Proof for 1830039510924630881820328
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 either calm or kind is either tall or not tall and vice versa.
If someone is both wise and curious then someone is not tall or not kind and vice versa.
Everyone who is both happy and not humble is not quiet or funny.
Everyone who is curious is not wise.
Everyone who is strong or not brave is not kind.
If someone is kind or curious then someone is curious.
If someone is both happy and tall then fred is brave or not wise.
If john is either not creative or wise then someone is either brave or not tall and vice versa.
Everyone who is both not creative and tall is both generous and creative.
If someone is brave then someone is not patient or not rich.
Everyone who is both not funny and not strong is either strong or not calm.
Everyone who is not humble is both not strong and not calm and vice versa.
If someone is either rich or not wise then someone is wise.
Everyone who is not creative or not generous is quiet or humble and vice versa.
If paul is old then fred is old.
If someone is both not generous and not funny then mary is either not wise or patient.
Someone is kind.
Someone is brave.
Susan is either not calm or not creative.
Someone is not kind or not calm.
Paul is either patient or happy.
Someone is either not rich or not kind.
Alice is either patient or brave. | Mary is not tall. | contradiction | (![X]:((calm(X)<~>kind(X))<=>(tall(X)<~>~tall(X))))&
((?[X]:((wise(X)&curious(X))))<=>(?[X]:((~tall(X)|~kind(X)))))&
(![X]:((happy(X)&~humble(X))=>(~quiet(X)|funny(X))))&
(![X]:(curious(X)=>~wise(X)))&
(![X]:((strong(X)|~brave(X))=>~kind(X)))&
((?[X]:((kind(X)|curious(X))))=>(?[X]:(curious(X))))&
((?[X]:((happy(X)&tall(X))))=>((brave(fred)|~wise(fred))))&
(((~creative(john)<~>wise(john)))<=>(?[X]:((brave(X)<~>~tall(X)))))&
(![X]:((~creative(X)&tall(X))=>(generous(X)&creative(X))))&
((?[X]:(brave(X)))=>(?[X]:((~patient(X)|~rich(X)))))&
(![X]:((~funny(X)&~strong(X))=>(strong(X)<~>~calm(X))))&
(![X]:(~humble(X)<=>(~strong(X)&~calm(X))))&
((?[X]:((rich(X)<~>~wise(X))))=>(?[X]:(wise(X))))&
(![X]:((~creative(X)|~generous(X))<=>(quiet(X)|humble(X))))&
((old(paul))=>(old(fred)))&
((?[X]:((~generous(X)&~funny(X))))=>((~wise(mary)<~>patient(mary))))&
(?[X]:(kind(X)))&
(?[X]:(brave(X)))&
((~calm(susan)<~>~creative(susan)))&
(?[X]:((~kind(X)|~calm(X))))&
((patient(paul)<~>happy(paul)))&
(?[X]:((~rich(X)<~>~kind(X))))&
((patient(alice)<~>brave(alice))) | ~tall(mary) | [
"p1",
"p3",
"hypothesis"
] | % SZS status Unsatisfiable for 1942912802067100166260
% SZS output start Proof for 1942912802067100166260
2. ? [X0] : (curious(X0) & wise(X0)) <=> ? [X0] : (~kind(X0) | ~tall(X0)) [input p1]
4. ! [X0] : (curious(X0) => ~wise(X0)) [input p3]
24. ~tall(mary) [input hypothesis]
25. ? [X0] : (curious(X0) & wise(X0)) <=> ? [X1] : (~kind(X1) | ~tall(X1)) [rectify 2]
32. ! [X0] : (~wise(X0) | ~curious(X0)) [ennf transformation 4]
43. (? [X0] : (curious(X0) & wise(X0)) | ! [X1] : (kind(X1) & tall(X1))) & (? [X1] : (~kind(X1) | ~tall(X1)) | ! [X0] : (~curious(X0) | ~wise(X0))) [nnf transformation 25]
44. (? [X0] : (curious(X0) & wise(X0)) | ! [X1] : (kind(X1) & tall(X1))) & (? [X2] : (~kind(X2) | ~tall(X2)) | ! [X3] : (~curious(X3) | ~wise(X3))) [rectify 43]
45. ? [X0] : (curious(X0) & wise(X0)) => (curious(sK0) & wise(sK0)) [choice axiom]
46. ? [X2] : (~kind(X2) | ~tall(X2)) => (~kind(sK1) | ~tall(sK1)) [choice axiom]
47. ((curious(sK0) & wise(sK0)) | ! [X1] : (kind(X1) & tall(X1))) & ((~kind(sK1) | ~tall(sK1)) | ! [X3] : (~curious(X3) | ~wise(X3))) [skolemisation 44,46,45]
87. wise(sK0) | tall(X1) [cnf transformation 47]
89. curious(sK0) | tall(X1) [cnf transformation 47]
91. ~wise(X0) | ~curious(X0) [cnf transformation 32]
129. ~tall(mary) [cnf transformation 24]
141. 2 <=> curious(sK0) [avatar definition]
143. curious(sK0) <- (2) [avatar component clause 141]
146. 3 <=> ! [X1] : tall(X1) [avatar definition]
147. tall(X1) <- (3) [avatar component clause 146]
148. 3 | 2 [avatar split clause 89,141,146]
150. 4 <=> wise(sK0) [avatar definition]
152. wise(sK0) <- (4) [avatar component clause 150]
154. 3 | 4 [avatar split clause 87,150,146]
156. 5 <=> ! [X3] : (~curious(X3) | ~wise(X3)) [avatar definition]
157. ~curious(X3) | ~wise(X3) <- (5) [avatar component clause 156]
167. 5 [avatar split clause 91,156]
302. ~wise(sK0) <- (2, 5) [resolution 157,143]
304. $false <- (2, 4, 5) [subsumption resolution 302,152]
305. ~2 | ~4 | ~5 [avatar contradiction clause 304]
310. $false <- (3) [resolution 147,129]
314. ~3 [avatar contradiction clause 310]
315. $false [avatar sat refutation 148,154,167,305,314]
% SZS output end Proof for 1942912802067100166260
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
If someone is happy then paul is not strong.
Everyone who is either not rich or funny is not tall and vice versa.
Everyone who is both not patient and rich is not generous or not curious and vice versa.
If someone is not strong then someone is generous or not strong and vice versa.
Everyone who is not tall or not curious is quiet or humble and vice versa.
If paul is rich or not creative then lucy is either not kind or not patient and vice versa.
Everyone who is patient is funny or not kind.
Everyone who is not funny is both not generous and not rich and vice versa.
If someone is either not generous or generous then someone is not patient or rich.
Everyone who is both calm and not rich is either humble or rich.
If someone is generous then lucy is not old or funny and vice versa.
Everyone who is not brave or patient is either not generous or happy and vice versa.
Everyone who is either funny or not humble is tall.
Everyone who is not funny or not tall is not patient or wise and vice versa.
Everyone who is not wise is not tall and vice versa.
Everyone who is curious is both generous and not creative and vice versa.
Someone is not happy or funny.
Mary is both quiet and strong.
Susan is strong.
Alice is either tall or funny.
John is happy. | John is not rich. | contradiction | ((?[X]:(happy(X)))=>(~strong(paul)))&
(![X]:((~rich(X)<~>funny(X))<=>~tall(X)))&
(![X]:((~patient(X)&rich(X))<=>(~generous(X)|~curious(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)|~strong(X)))))&
(![X]:((~tall(X)|~curious(X))<=>(quiet(X)|humble(X))))&
(((rich(paul)|~creative(paul)))<=>((~kind(lucy)<~>~patient(lucy))))&
(![X]:(patient(X)=>(funny(X)|~kind(X))))&
(![X]:(~funny(X)<=>(~generous(X)&~rich(X))))&
((?[X]:((~generous(X)<~>generous(X))))=>(?[X]:((~patient(X)|rich(X)))))&
(![X]:((calm(X)&~rich(X))=>(humble(X)<~>rich(X))))&
((?[X]:(generous(X)))<=>((~old(lucy)|funny(lucy))))&
(![X]:((~brave(X)|patient(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((funny(X)<~>~humble(X))=>tall(X)))&
(![X]:((~funny(X)|~tall(X))<=>(~patient(X)|wise(X))))&
(![X]:(~wise(X)<=>~tall(X)))&
(![X]:(curious(X)<=>(generous(X)&~creative(X))))&
(?[X]:((~happy(X)|funny(X))))&
((quiet(mary)&strong(mary)))&
(strong(susan))&
((tall(alice)<~>funny(alice)))&
(happy(john)) | ~rich(john) | [
"p1",
"p2",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1668434156208765483173229
% SZS output start Proof for 1668434156208765483173229
2. ! [X0] : ((~rich(X0) <~> funny(X0)) <=> ~tall(X0)) [input p1]
3. ! [X0] : ((rich(X0) & ~patient(X0)) <=> (~curious(X0) | ~generous(X0))) [input p2]
8. ! [X0] : (~funny(X0) <=> (~rich(X0) & ~generous(X0))) [input p7]
14. ! [X0] : ((~tall(X0) | ~funny(X0)) <=> (wise(X0) | ~patient(X0))) [input p13]
15. ! [X0] : (~wise(X0) <=> ~tall(X0)) [input p14]
22. ~rich(john) [input hypothesis]
31. ! [X0] : ((((~funny(X0) | rich(X0)) & (funny(X0) | ~rich(X0))) | tall(X0)) & (~tall(X0) | ((~rich(X0) | ~funny(X0)) & (funny(X0) | rich(X0))))) [nnf transformation 2]
32. ! [X0] : (((rich(X0) & ~patient(X0)) | (curious(X0) & generous(X0))) & ((~curious(X0) | ~generous(X0)) | (~rich(X0) | patient(X0)))) [nnf transformation 3]
33. ! [X0] : (((rich(X0) & ~patient(X0)) | (curious(X0) & generous(X0))) & (~curious(X0) | ~generous(X0) | ~rich(X0) | patient(X0))) [flattening 32]
43. ! [X0] : ((~funny(X0) | (rich(X0) | generous(X0))) & ((~rich(X0) & ~generous(X0)) | funny(X0))) [nnf transformation 8]
44. ! [X0] : ((~funny(X0) | rich(X0) | generous(X0)) & ((~rich(X0) & ~generous(X0)) | funny(X0))) [flattening 43]
57. ! [X0] : (((~tall(X0) | ~funny(X0)) | (~wise(X0) & patient(X0))) & ((wise(X0) | ~patient(X0)) | (tall(X0) & funny(X0)))) [nnf transformation 14]
58. ! [X0] : ((~tall(X0) | ~funny(X0) | (~wise(X0) & patient(X0))) & (wise(X0) | ~patient(X0) | (tall(X0) & funny(X0)))) [flattening 57]
59. ! [X0] : ((~wise(X0) | tall(X0)) & (~tall(X0) | wise(X0))) [nnf transformation 15]
69. ~funny(X0) | rich(X0) | tall(X0) [cnf transformation 31]
73. generous(X0) | rich(X0) [cnf transformation 33]
89. ~generous(X0) | funny(X0) [cnf transformation 44]
90. ~rich(X0) | funny(X0) [cnf transformation 44]
108. ~wise(X0) | ~funny(X0) | ~tall(X0) [cnf transformation 58]
109. ~tall(X0) | wise(X0) [cnf transformation 59]
121. ~rich(john) [cnf transformation 22]
228. funny(X0) | rich(X0) [resolution 89,73]
230. funny(X0) [subsumption resolution 228,90]
235. tall(X0) | rich(X0) [resolution 69,230]
305. wise(X2) | rich(X2) [resolution 235,109]
320. ~funny(X0) | ~tall(X0) | rich(X0) [resolution 108,305]
321. ~tall(X0) | rich(X0) [subsumption resolution 320,230]
322. rich(X0) [subsumption resolution 321,235]
399. $false [resolution 322,121]
% SZS output end Proof for 1668434156208765483173229
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny is curious or rich and vice versa. If fred is rich then alice is not calm or quiet and vice versa. Everyone who is both not wise and quiet is old. If susan is funny or not humble then someone is either generous or tall and vice versa. If susan is not calm or generous then john is both not old and tall. Everyone who is both happy and kind is not funny and vice versa. Everyone who is either not funny or funny is not strong or not brave. Everyone who is either happy or not generous is either happy or humble. Everyone who is either not funny or rich is not humble and vice versa. Everyone who is either not humble or happy is funny and vice versa. If someone is either not happy or happy then fred is either tall or calm and vice versa. Everyone who is tall is funny and vice versa. Everyone who is either not wise or funny is not funny or rich and vice versa. If someone is not brave then mary is humble or not tall and vice versa. If paul is both wise and not curious then someone is either generous or calm and vice versa. Someone is either old or not curious. Lucy is not patient or humble. Susan is patient. Susan is quiet. | Alice is not humble. | entailment | (![X]:(~funny(X)<=>(curious(X)|rich(X))))&
((rich(fred))<=>((~calm(alice)|quiet(alice))))&
(![X]:((~wise(X)&quiet(X))=>old(X)))&
(((funny(susan)|~humble(susan)))<=>(?[X]:((generous(X)<~>tall(X)))))&
(((~calm(susan)|generous(susan)))=>((~old(john)&tall(john))))&
(![X]:((happy(X)&kind(X))<=>~funny(X)))&
(![X]:((~funny(X)<~>funny(X))=>(~strong(X)|~brave(X))))&
(![X]:((happy(X)<~>~generous(X))=>(happy(X)<~>humble(X))))&
(![X]:((~funny(X)<~>rich(X))<=>~humble(X)))&
(![X]:((~humble(X)<~>happy(X))<=>funny(X)))&
((?[X]:((~happy(X)<~>happy(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:(tall(X)<=>funny(X)))&
(![X]:((~wise(X)<~>funny(X))<=>(~funny(X)|rich(X))))&
((?[X]:(~brave(X)))<=>((humble(mary)|~tall(mary))))&
(((wise(paul)&~curious(paul)))<=>(?[X]:((generous(X)<~>calm(X)))))&
(?[X]:((old(X)<~>~curious(X))))&
((~patient(lucy)|humble(lucy)))&
(patient(susan))&
(quiet(susan)) | ~humble(alice) | [
"p0",
"p1",
"p5",
"p7",
"p8",
"p9",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6257369755232281823948625
% SZS output start Proof for 6257369755232281823948625
1. ! [X0] : (~funny(X0) <=> (rich(X0) | curious(X0))) [input p0]
2. rich(fred) <=> (quiet(alice) | ~calm(alice)) [input p1]
6. ! [X0] : ((kind(X0) & happy(X0)) <=> ~funny(X0)) [input p5]
8. ! [X0] : ((happy(X0) <~> ~generous(X0)) => (happy(X0) <~> humble(X0))) [input p7]
9. ! [X0] : ((~funny(X0) <~> rich(X0)) <=> ~humble(X0)) [input p8]
10. ! [X0] : ((~humble(X0) <~> happy(X0)) <=> funny(X0)) [input p9]
13. ! [X0] : ((~wise(X0) <~> funny(X0)) <=> (rich(X0) | ~funny(X0))) [input p12]
15. (~curious(paul) & wise(paul)) <=> ? [X0] : (generous(X0) <~> calm(X0)) [input p14]
20. humble(alice) [input hypothesis]
25. ! [X0] : ((happy(X0) <~> humble(X0)) | (happy(X0) <=> ~generous(X0))) [ennf transformation 8]
26. ! [X0] : ((~funny(X0) | (~rich(X0) & ~curious(X0))) & ((rich(X0) | curious(X0)) | funny(X0))) [nnf transformation 1]
27. ! [X0] : ((~funny(X0) | (~rich(X0) & ~curious(X0))) & (rich(X0) | curious(X0) | funny(X0))) [flattening 26]
28. (rich(fred) | (~quiet(alice) & calm(alice))) & ((quiet(alice) | ~calm(alice)) | ~rich(fred)) [nnf transformation 2]
29. (rich(fred) | (~quiet(alice) & calm(alice))) & (quiet(alice) | ~calm(alice) | ~rich(fred)) [flattening 28]
35. ! [X0] : (((kind(X0) & happy(X0)) | funny(X0)) & (~funny(X0) | (~kind(X0) | ~happy(X0)))) [nnf transformation 6]
36. ! [X0] : (((kind(X0) & happy(X0)) | funny(X0)) & (~funny(X0) | ~kind(X0) | ~happy(X0))) [flattening 35]
37. ! [X0] : (((~humble(X0) | ~happy(X0)) & (humble(X0) | happy(X0))) | ((happy(X0) | generous(X0)) & (~generous(X0) | ~happy(X0)))) [nnf transformation 25]
38. ! [X0] : ((((~rich(X0) | funny(X0)) & (rich(X0) | ~funny(X0))) | humble(X0)) & (~humble(X0) | ((~funny(X0) | ~rich(X0)) & (rich(X0) | funny(X0))))) [nnf transformation 9]
39. ! [X0] : ((((~happy(X0) | humble(X0)) & (happy(X0) | ~humble(X0))) | ~funny(X0)) & (funny(X0) | ((~humble(X0) | ~happy(X0)) & (happy(X0) | humble(X0))))) [nnf transformation 10]
45. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (~rich(X0) & funny(X0))) & ((rich(X0) | ~funny(X0)) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [nnf transformation 13]
46. ! [X0] : ((((~funny(X0) | wise(X0)) & (funny(X0) | ~wise(X0))) | (~rich(X0) & funny(X0))) & (rich(X0) | ~funny(X0) | ((~wise(X0) | ~funny(X0)) & (funny(X0) | wise(X0))))) [flattening 45]
52. ((~curious(paul) & wise(paul)) | ! [X0] : ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (? [X0] : ((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | (curious(paul) | ~wise(paul))) [nnf transformation 15]
53. ((~curious(paul) & wise(paul)) | ! [X0] : ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (? [X0] : ((~calm(X0) | ~generous(X0)) & (calm(X0) | generous(X0))) | curious(paul) | ~wise(paul)) [flattening 52]
54. ((~curious(paul) & wise(paul)) | ! [X0] : ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (? [X1] : ((~calm(X1) | ~generous(X1)) & (calm(X1) | generous(X1))) | curious(paul) | ~wise(paul)) [rectify 53]
55. ? [X1] : ((~calm(X1) | ~generous(X1)) & (calm(X1) | generous(X1))) => ((~calm(sK3) | ~generous(sK3)) & (calm(sK3) | generous(sK3))) [choice axiom]
56. ((~curious(paul) & wise(paul)) | ! [X0] : ((generous(X0) | ~calm(X0)) & (calm(X0) | ~generous(X0)))) & (((~calm(sK3) | ~generous(sK3)) & (calm(sK3) | generous(sK3))) | curious(paul) | ~wise(paul)) [skolemisation 54,55]
62. ~rich(X0) | ~funny(X0) [cnf transformation 27]
64. rich(fred) | calm(alice) [cnf transformation 29]
78. happy(X0) | funny(X0) [cnf transformation 36]
82. ~humble(X0) | ~happy(X0) | ~generous(X0) | ~happy(X0) [cnf transformation 37]
87. ~rich(X0) | funny(X0) | humble(X0) [cnf transformation 38]
89. funny(X0) | ~humble(X0) | ~happy(X0) [cnf transformation 39]
90. happy(X0) | ~humble(X0) | ~funny(X0) [cnf transformation 39]
103. rich(X0) | ~funny(X0) | ~wise(X0) | ~funny(X0) [cnf transformation 46]
104. funny(X0) | ~wise(X0) | funny(X0) [cnf transformation 46]
105. funny(X0) | ~wise(X0) | ~rich(X0) [cnf transformation 46]
114. wise(paul) | generous(X0) | ~calm(X0) [cnf transformation 56]
122. humble(alice) [cnf transformation 20]
123. rich(X0) | ~funny(X0) | ~wise(X0) [duplicate literal removal 103]
124. ~wise(X0) | funny(X0) [duplicate literal removal 104]
130. ~happy(X0) | ~humble(X0) | ~generous(X0) [duplicate literal removal 82]
136. 2 <=> rich(fred) [avatar definition]
138. rich(fred) <- (2) [avatar component clause 136]
141. 3 <=> calm(alice) [avatar definition]
143. calm(alice) <- (3) [avatar component clause 141]
144. 3 | 2 [avatar split clause 64,136,141]
194. ~rich(X0) | humble(X0) [subsumption resolution 87,62]
196. ~humble(X0) | happy(X0) [subsumption resolution 90,78]
197. ~humble(X0) | funny(X0) [subsumption resolution 89,196]
216. ~wise(X0) | ~rich(X0) [subsumption resolution 105,62]
217. rich(X0) | ~wise(X0) [subsumption resolution 123,124]
218. ~wise(X0) [subsumption resolution 217,216]
238. 22 <=> ! [X0] : (generous(X0) | ~calm(X0)) [avatar definition]
239. ~calm(X0) | generous(X0) <- (22) [avatar component clause 238]
249. generous(X0) | ~calm(X0) [subsumption resolution 114,218]
250. 22 [avatar split clause 249,238]
272. ~funny(fred) <- (2) [resolution 62,138]
280. humble(fred) <- (2) [resolution 194,138]
283. happy(alice) [resolution 196,122]
286. funny(fred) <- (2) [resolution 197,280]
290. $false <- (2) [subsumption resolution 286,272]
291. ~2 [avatar contradiction clause 290]
302. generous(alice) <- (3, 22) [resolution 239,143]
333. ~humble(alice) | ~generous(alice) [resolution 130,283]
334. ~generous(alice) [subsumption resolution 333,122]
337. $false <- (3, 22) [subsumption resolution 302,334]
338. ~3 | ~22 [avatar contradiction clause 337]
339. $false [avatar sat refutation 144,250,291,338]
% SZS output end Proof for 6257369755232281823948625
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not creative or kind is both kind and creative and vice versa.
If someone is both brave and patient then someone is either not curious or not rich and vice versa.
If someone is tall then fred is not curious and vice versa.
Everyone who is both quiet and not patient is funny.
Everyone who is either not kind or not creative is either kind or generous and vice versa.
If someone is both kind and not humble then alice is tall and vice versa.
Everyone who is either strong or not humble is both generous and not quiet.
If fred is both creative and not tall then alice is either kind or not brave and vice versa.
Everyone who is both not curious and not humble is both not humble and old.
If john is both not patient and quiet then john is creative or not generous and vice versa.
If someone is not rich then someone is both not creative and generous and vice versa.
If lucy is happy then someone is either rich or old and vice versa.
Everyone who is patient is either not creative or quiet and vice versa.
Everyone who is either humble or old is not happy or rich and vice versa.
Everyone who is old or not old is both not wise and not happy.
If susan is either not generous or strong then lucy is not rich and vice versa.
Susan is either brave or not tall.
Someone is either generous or old.
Paul is both not wise and not patient.
Someone is both rich and not generous.
Someone is creative.
Someone is both kind and not tall.
Someone is not old or not funny. | Fred is humble. | contradiction | (![X]:((~creative(X)<~>kind(X))<=>(kind(X)&creative(X))))&
((?[X]:((brave(X)&patient(X))))<=>(?[X]:((~curious(X)<~>~rich(X)))))&
((?[X]:(tall(X)))<=>(~curious(fred)))&
(![X]:((quiet(X)&~patient(X))=>funny(X)))&
(![X]:((~kind(X)<~>~creative(X))<=>(kind(X)<~>generous(X))))&
((?[X]:((kind(X)&~humble(X))))<=>(tall(alice)))&
(![X]:((strong(X)<~>~humble(X))=>(generous(X)&~quiet(X))))&
(((creative(fred)&~tall(fred)))<=>((kind(alice)<~>~brave(alice))))&
(![X]:((~curious(X)&~humble(X))=>(~humble(X)&old(X))))&
(((~patient(john)&quiet(john)))<=>((creative(john)|~generous(john))))&
((?[X]:(~rich(X)))<=>(?[X]:((~creative(X)&generous(X)))))&
((happy(lucy))<=>(?[X]:((rich(X)<~>old(X)))))&
(![X]:(patient(X)<=>(~creative(X)<~>quiet(X))))&
(![X]:((humble(X)<~>old(X))<=>(~happy(X)|rich(X))))&
(![X]:((old(X)|~old(X))=>(~wise(X)&~happy(X))))&
(((~generous(susan)<~>strong(susan)))<=>(~rich(lucy)))&
((brave(susan)<~>~tall(susan)))&
(?[X]:((generous(X)<~>old(X))))&
((~wise(paul)&~patient(paul)))&
(?[X]:((rich(X)&~generous(X))))&
(?[X]:(creative(X)))&
(?[X]:((kind(X)&~tall(X))))&
(?[X]:((~old(X)|~funny(X)))) | humble(fred) | [
"p0",
"p4",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 7121752155556366673956284
% SZS output start Proof for 7121752155556366673956284
1. ! [X0] : ((~creative(X0) <~> kind(X0)) <=> (creative(X0) & kind(X0))) [input p0]
5. ! [X0] : ((~kind(X0) <~> ~creative(X0)) <=> (kind(X0) <~> generous(X0))) [input p4]
11. ? [X0] : ~rich(X0) <=> ? [X0] : (generous(X0) & ~creative(X0)) [input p10]
12. happy(lucy) <=> ? [X0] : (rich(X0) <~> old(X0)) [input p11]
14. ! [X0] : ((humble(X0) <~> old(X0)) <=> (rich(X0) | ~happy(X0))) [input p13]
15. ! [X0] : ((~old(X0) | old(X0)) => (~happy(X0) & ~wise(X0))) [input p14]
24. humble(fred) [input hypothesis]
26. ? [X0] : ~rich(X0) <=> ? [X1] : (generous(X1) & ~creative(X1)) [rectify 11]
28. ! [X0] : ((~old(X0) | old(X0)) => ~happy(X0)) [pure predicate removal 15]
34. ! [X0] : (~happy(X0) | (old(X0) & ~old(X0))) [ennf transformation 28]
35. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | (~creative(X0) | ~kind(X0))) & ((creative(X0) & kind(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [nnf transformation 1]
36. ! [X0] : ((((~kind(X0) | creative(X0)) & (kind(X0) | ~creative(X0))) | ~creative(X0) | ~kind(X0)) & ((creative(X0) & kind(X0)) | ((~creative(X0) | ~kind(X0)) & (kind(X0) | creative(X0))))) [flattening 35]
46. ! [X0] : ((((creative(X0) | kind(X0)) & (~creative(X0) | ~kind(X0))) | ((kind(X0) | ~generous(X0)) & (generous(X0) | ~kind(X0)))) & (((~generous(X0) | ~kind(X0)) & (generous(X0) | kind(X0))) | ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))))) [nnf transformation 5]
56. (? [X0] : ~rich(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X1] : (generous(X1) & ~creative(X1)) | ! [X0] : rich(X0)) [nnf transformation 26]
57. (? [X0] : ~rich(X0) | ! [X1] : (~generous(X1) | creative(X1))) & (? [X2] : (generous(X2) & ~creative(X2)) | ! [X3] : rich(X3)) [rectify 56]
58. ? [X0] : ~rich(X0) => ~rich(sK4) [choice axiom]
59. ? [X2] : (generous(X2) & ~creative(X2)) => (generous(sK5) & ~creative(sK5)) [choice axiom]
60. (~rich(sK4) | ! [X1] : (~generous(X1) | creative(X1))) & ((generous(sK5) & ~creative(sK5)) | ! [X3] : rich(X3)) [skolemisation 57,59,58]
61. (happy(lucy) | ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (? [X0] : ((~old(X0) | ~rich(X0)) & (old(X0) | rich(X0))) | ~happy(lucy)) [nnf transformation 12]
62. (happy(lucy) | ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (? [X1] : ((~old(X1) | ~rich(X1)) & (old(X1) | rich(X1))) | ~happy(lucy)) [rectify 61]
63. ? [X1] : ((~old(X1) | ~rich(X1)) & (old(X1) | rich(X1))) => ((~old(sK6) | ~rich(sK6)) & (old(sK6) | rich(sK6))) [choice axiom]
64. (happy(lucy) | ! [X0] : ((rich(X0) | ~old(X0)) & (old(X0) | ~rich(X0)))) & (((~old(sK6) | ~rich(sK6)) & (old(sK6) | rich(sK6))) | ~happy(lucy)) [skolemisation 62,63]
66. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [nnf transformation 14]
67. ! [X0] : ((((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0))))) [flattening 66]
83. creative(X0) | kind(X0) | creative(X0) [cnf transformation 36]
99. ~generous(X0) | ~kind(X0) | ~kind(X0) | creative(X0) [cnf transformation 46]
124. ~creative(sK5) | rich(X3) [cnf transformation 60]
125. generous(sK5) | rich(X3) [cnf transformation 60]
129. happy(lucy) | old(X0) | ~rich(X0) [cnf transformation 64]
139. ~old(X0) | ~humble(X0) | happy(X0) [cnf transformation 67]
141. ~happy(X0) | ~old(X0) [cnf transformation 34]
142. ~happy(X0) | old(X0) [cnf transformation 34]
158. humble(fred) [cnf transformation 24]
160. ~generous(X0) | ~kind(X0) | creative(X0) [duplicate literal removal 99]
164. kind(X0) | creative(X0) [duplicate literal removal 83]
211. ~generous(X0) | creative(X0) [subsumption resolution 160,164]
274. 23 <=> ! [X3] : rich(X3) [avatar definition]
275. rich(X3) <- (23) [avatar component clause 274]
277. 24 <=> generous(sK5) [avatar definition]
279. generous(sK5) <- (24) [avatar component clause 277]
280. 23 | 24 [avatar split clause 125,277,274]
282. 25 <=> creative(sK5) [avatar definition]
285. 23 | ~25 [avatar split clause 124,282,274]
290. 27 <=> happy(lucy) [avatar definition]
292. happy(lucy) <- (27) [avatar component clause 290]
295. 28 <=> ! [X0] : (old(X0) | ~rich(X0)) [avatar definition]
296. ~rich(X0) | old(X0) <- (28) [avatar component clause 295]
297. 28 | 27 [avatar split clause 129,290,295]
308. ~happy(X0) [subsumption resolution 141,142]
363. creative(sK5) <- (24) [resolution 211,279]
369. 25 | ~24 [avatar split clause 363,277,282]
444. $false <- (27) [subsumption resolution 292,308]
445. ~27 [avatar contradiction clause 444]
455. old(X0) <- (23, 28) [subsumption resolution 296,275]
477. ~humble(X0) | happy(X0) <- (23, 28) [resolution 455,139]
479. ~humble(X0) <- (23, 28) [subsumption resolution 477,308]
517. $false <- (23, 28) [resolution 479,158]
520. ~23 | ~28 [avatar contradiction clause 517]
521. $false [avatar sat refutation 280,285,297,369,445,520]
% SZS output end Proof for 7121752155556366673956284
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind or not patient is either not patient or old and vice versa.
If someone is either not old or humble then paul is brave or funny and vice versa.
If lucy is either rich or happy then alice is strong or rich and vice versa.
If susan is both not creative and quiet then paul is either not generous or kind.
If someone is strong then fred is patient.
If paul is either not patient or generous then someone is not patient or not quiet and vice versa.
If someone is curious or not old then paul is not brave.
If mary is either not strong or not old then someone is quiet or not rich and vice versa.
Everyone who is both rich and not wise is curious and vice versa.
If mary is both funny and not strong then fred is both old and patient.
Everyone who is either not calm or not strong is not kind.
If susan is either not strong or not humble then someone is not rich or happy and vice versa.
If alice is either generous or not kind then someone is either not calm or humble and vice versa.
If alice is not quiet or not funny then mary is either not patient or not kind.
Everyone who is either not creative or creative is either brave or not generous.
If susan is either happy or not funny then lucy is either creative or not curious and vice versa.
Someone is not funny or not wise.
Paul is either not creative or brave.
Paul is not humble or not patient.
Susan is both not wise and not patient.
Someone is either not rich or strong.
Someone is either happy or not patient.
Someone is not humble or not patient.
Someone is not old or not quiet. | Mary is wise. | neutral | (![X]:((~kind(X)|~patient(X))<=>(~patient(X)<~>old(X))))&
((?[X]:((~old(X)<~>humble(X))))<=>((brave(paul)|funny(paul))))&
(((rich(lucy)<~>happy(lucy)))<=>((strong(alice)|rich(alice))))&
(((~creative(susan)&quiet(susan)))=>((~generous(paul)<~>kind(paul))))&
((?[X]:(strong(X)))=>(patient(fred)))&
(((~patient(paul)<~>generous(paul)))<=>(?[X]:((~patient(X)|~quiet(X)))))&
((?[X]:((curious(X)|~old(X))))=>(~brave(paul)))&
(((~strong(mary)<~>~old(mary)))<=>(?[X]:((quiet(X)|~rich(X)))))&
(![X]:((rich(X)&~wise(X))<=>curious(X)))&
(((funny(mary)&~strong(mary)))=>((old(fred)&patient(fred))))&
(![X]:((~calm(X)<~>~strong(X))=>~kind(X)))&
(((~strong(susan)<~>~humble(susan)))<=>(?[X]:((~rich(X)|happy(X)))))&
(((generous(alice)<~>~kind(alice)))<=>(?[X]:((~calm(X)<~>humble(X)))))&
(((~quiet(alice)|~funny(alice)))=>((~patient(mary)<~>~kind(mary))))&
(![X]:((~creative(X)<~>creative(X))=>(brave(X)<~>~generous(X))))&
(((happy(susan)<~>~funny(susan)))<=>((creative(lucy)<~>~curious(lucy))))&
(?[X]:((~funny(X)|~wise(X))))&
((~creative(paul)<~>brave(paul)))&
((~humble(paul)|~patient(paul)))&
((~wise(susan)&~patient(susan)))&
(?[X]:((~rich(X)<~>strong(X))))&
(?[X]:((happy(X)<~>~patient(X))))&
(?[X]:((~humble(X)|~patient(X))))&
(?[X]:((~old(X)|~quiet(X)))) | wise(mary) | [] | null | 0 |
If lucy is patient then someone is either not quiet or humble and vice versa. Everyone who is not creative is both not curious and quiet. Everyone who is both generous and not wise is not tall or generous. Everyone who is humble is either patient or quiet. Everyone who is not rich is either not rich or happy and vice versa. Everyone who is both not happy and not rich is tall. Everyone who is not humble is both not happy and kind and vice versa. Everyone who is either creative or not brave is not strong. If susan is patient or not wise then someone is either tall or wise. If fred is either brave or not calm then john is either brave or not brave and vice versa. Everyone who is both not humble and tall is happy or not kind. If fred is either not old or calm then someone is old or rich. Everyone who is either not tall or creative is not patient or strong and vice versa. Everyone who is either tall or not strong is either not calm or not patient. Everyone who is either not old or tall is not strong and vice versa. Everyone who is not happy or not creative is both patient and not old. Susan is not funny or funny. Mary is not quiet. Mary is not humble. Someone is not tall or quiet. Someone is not strong. Someone is not kind or not quiet. | Mary is rich. | entailment | ((patient(lucy))<=>(?[X]:((~quiet(X)<~>humble(X)))))&
(![X]:(~creative(X)=>(~curious(X)&quiet(X))))&
(![X]:((generous(X)&~wise(X))=>(~tall(X)|generous(X))))&
(![X]:(humble(X)=>(patient(X)<~>quiet(X))))&
(![X]:(~rich(X)<=>(~rich(X)<~>happy(X))))&
(![X]:((~happy(X)&~rich(X))=>tall(X)))&
(![X]:(~humble(X)<=>(~happy(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))=>~strong(X)))&
(((patient(susan)|~wise(susan)))=>(?[X]:((tall(X)<~>wise(X)))))&
(((brave(fred)<~>~calm(fred)))<=>((brave(john)<~>~brave(john))))&
(![X]:((~humble(X)&tall(X))=>(happy(X)|~kind(X))))&
(((~old(fred)<~>calm(fred)))=>(?[X]:((old(X)|rich(X)))))&
(![X]:((~tall(X)<~>creative(X))<=>(~patient(X)|strong(X))))&
(![X]:((tall(X)<~>~strong(X))=>(~calm(X)<~>~patient(X))))&
(![X]:((~old(X)<~>tall(X))<=>~strong(X)))&
(![X]:((~happy(X)|~creative(X))=>(patient(X)&~old(X))))&
((~funny(susan)|funny(susan)))&
(~quiet(mary))&
(~humble(mary))&
(?[X]:((~tall(X)|quiet(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~kind(X)|~quiet(X)))) | rich(mary) | [
"p4",
"p5",
"p6",
"p10",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8435092196388481879731467
% SZS output start Proof for 8435092196388481879731467
5. ! [X0] : (~rich(X0) <=> (~rich(X0) <~> happy(X0))) [input p4]
6. ! [X0] : ((~rich(X0) & ~happy(X0)) => tall(X0)) [input p5]
7. ! [X0] : (~humble(X0) <=> (kind(X0) & ~happy(X0))) [input p6]
11. ! [X0] : ((tall(X0) & ~humble(X0)) => (~kind(X0) | happy(X0))) [input p10]
19. ~humble(mary) [input p18]
23. ~rich(mary) [input hypothesis]
29. ! [X0] : (tall(X0) | (rich(X0) | happy(X0))) [ennf transformation 6]
30. ! [X0] : (tall(X0) | rich(X0) | happy(X0)) [flattening 29]
33. ! [X0] : ((~kind(X0) | happy(X0)) | (~tall(X0) | humble(X0))) [ennf transformation 11]
34. ! [X0] : (~kind(X0) | happy(X0) | ~tall(X0) | humble(X0)) [flattening 33]
43. ! [X0] : ((~rich(X0) | ((~rich(X0) | ~happy(X0)) & (happy(X0) | rich(X0)))) & (((~happy(X0) | rich(X0)) & (happy(X0) | ~rich(X0))) | rich(X0))) [nnf transformation 5]
44. ! [X0] : ((~humble(X0) | (~kind(X0) | happy(X0))) & ((kind(X0) & ~happy(X0)) | humble(X0))) [nnf transformation 7]
45. ! [X0] : ((~humble(X0) | ~kind(X0) | happy(X0)) & ((kind(X0) & ~happy(X0)) | humble(X0))) [flattening 44]
73. ~happy(X0) | rich(X0) | rich(X0) [cnf transformation 43]
75. ~rich(X0) | ~rich(X0) | ~happy(X0) [cnf transformation 43]
76. tall(X0) | rich(X0) | happy(X0) [cnf transformation 30]
78. kind(X0) | humble(X0) [cnf transformation 45]
79. ~humble(X0) | ~kind(X0) | happy(X0) [cnf transformation 45]
94. ~kind(X0) | happy(X0) | ~tall(X0) | humble(X0) [cnf transformation 34]
117. ~humble(mary) [cnf transformation 19]
121. ~rich(mary) [cnf transformation 23]
126. ~happy(X0) | rich(X0) [duplicate literal removal 73]
127. ~happy(X0) | ~rich(X0) [duplicate literal removal 75]
150. ~happy(X0) [subsumption resolution 126,127]
151. rich(X0) | tall(X0) [subsumption resolution 76,150]
152. ~kind(X0) | ~humble(X0) [subsumption resolution 79,150]
189. ~kind(X0) | ~tall(X0) | humble(X0) [subsumption resolution 94,150]
190. ~kind(X0) | ~tall(X0) [subsumption resolution 189,152]
228. tall(mary) [resolution 151,121]
230. ~tall(X0) | humble(X0) [resolution 190,78]
231. humble(mary) [resolution 230,228]
232. $false [subsumption resolution 231,117]
% SZS output end Proof for 8435092196388481879731467
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or brave is kind or tall.
Everyone who is not wise or not tall is not funny or creative and vice versa.
If mary is either not calm or creative then someone is either humble or wise.
Everyone who is humble or not humble is kind.
Everyone who is either not creative or not funny is not brave.
If mary is both not generous and brave then someone is brave or not calm and vice versa.
Everyone who is either generous or not generous is both not happy and not quiet and vice versa.
Everyone who is either curious or not quiet is happy.
Everyone who is both not funny and not patient is not funny.
If paul is not quiet then someone is humble or quiet.
If fred is both happy and not generous then someone is both strong and calm.
Everyone who is not strong is happy and vice versa.
Everyone who is not funny is humble.
Everyone who is either not funny or tall is either rich or calm and vice versa.
Everyone who is both old and not kind is either not generous or wise and vice versa.
Someone is tall or happy.
Someone is not happy or not generous.
Lucy is not funny or not wise.
Someone is either not old or generous.
Fred is either not happy or not rich.
Someone is not calm or not curious. | Fred is not wise. | neutral | (![X]:((~curious(X)|brave(X))=>(kind(X)|tall(X))))&
(![X]:((~wise(X)|~tall(X))<=>(~funny(X)|creative(X))))&
(((~calm(mary)<~>creative(mary)))=>(?[X]:((humble(X)<~>wise(X)))))&
(![X]:((humble(X)|~humble(X))=>kind(X)))&
(![X]:((~creative(X)<~>~funny(X))=>~brave(X)))&
(((~generous(mary)&brave(mary)))<=>(?[X]:((brave(X)|~calm(X)))))&
(![X]:((generous(X)<~>~generous(X))<=>(~happy(X)&~quiet(X))))&
(![X]:((curious(X)<~>~quiet(X))=>happy(X)))&
(![X]:((~funny(X)&~patient(X))=>~funny(X)))&
((~quiet(paul))=>(?[X]:((humble(X)|quiet(X)))))&
(((happy(fred)&~generous(fred)))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:(~strong(X)<=>happy(X)))&
(![X]:(~funny(X)=>humble(X)))&
(![X]:((~funny(X)<~>tall(X))<=>(rich(X)<~>calm(X))))&
(![X]:((old(X)&~kind(X))<=>(~generous(X)<~>wise(X))))&
(?[X]:((tall(X)|happy(X))))&
(?[X]:((~happy(X)|~generous(X))))&
((~funny(lucy)|~wise(lucy)))&
(?[X]:((~old(X)<~>generous(X))))&
((~happy(fred)<~>~rich(fred)))&
(?[X]:((~calm(X)|~curious(X)))) | ~wise(fred) | [] | null | 0 |
If someone is both not funny and not curious then fred is brave or funny and vice versa.
Everyone who is not calm is not quiet and vice versa.
Everyone who is both tall and not brave is not generous.
Everyone who is not funny or not curious is both curious and not tall.
If lucy is both creative and not creative then mary is both generous and patient and vice versa.
If someone is kind or not patient then someone is quiet or curious and vice versa.
Everyone who is both not old and patient is old or creative.
Everyone who is either humble or old is not patient or tall.
If someone is not brave or not funny then someone is both creative and not quiet and vice versa.
Everyone who is not tall or curious is strong or not kind.
Everyone who is both not quiet and not calm is either not funny or not creative and vice versa.
Everyone who is either quiet or tall is not wise or brave and vice versa.
If lucy is not strong then mary is either quiet or not tall.
If someone is rich then susan is generous or not strong.
If someone is both not quiet and not strong then someone is not curious.
If someone is strong or not happy then someone is calm.
Someone is tall or not brave.
Someone is old.
Someone is both not tall and not kind.
Someone is quiet or old.
Someone is not calm or rich.
Mary is curious.
Someone is either quiet or patient.
Someone is both old and not quiet. | Susan is not funny. | neutral | ((?[X]:((~funny(X)&~curious(X))))<=>((brave(fred)|funny(fred))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(![X]:((tall(X)&~brave(X))=>~generous(X)))&
(![X]:((~funny(X)|~curious(X))=>(curious(X)&~tall(X))))&
(((creative(lucy)&~creative(lucy)))<=>((generous(mary)&patient(mary))))&
((?[X]:((kind(X)|~patient(X))))<=>(?[X]:((quiet(X)|curious(X)))))&
(![X]:((~old(X)&patient(X))=>(old(X)|creative(X))))&
(![X]:((humble(X)<~>old(X))=>(~patient(X)|tall(X))))&
((?[X]:((~brave(X)|~funny(X))))<=>(?[X]:((creative(X)&~quiet(X)))))&
(![X]:((~tall(X)|curious(X))=>(strong(X)|~kind(X))))&
(![X]:((~quiet(X)&~calm(X))<=>(~funny(X)<~>~creative(X))))&
(![X]:((quiet(X)<~>tall(X))<=>(~wise(X)|brave(X))))&
((~strong(lucy))=>((quiet(mary)<~>~tall(mary))))&
((?[X]:(rich(X)))=>((generous(susan)|~strong(susan))))&
((?[X]:((~quiet(X)&~strong(X))))=>(?[X]:(~curious(X))))&
((?[X]:((strong(X)|~happy(X))))=>(?[X]:(calm(X))))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:(old(X)))&
(?[X]:((~tall(X)&~kind(X))))&
(?[X]:((quiet(X)|old(X))))&
(?[X]:((~calm(X)|rich(X))))&
(curious(mary))&
(?[X]:((quiet(X)<~>patient(X))))&
(?[X]:((old(X)&~quiet(X)))) | ~funny(susan) | [] | null | 0 |
Everyone who is either wise or not wise is quiet.
Everyone who is both not generous and not creative is not creative and vice versa.
If john is either curious or happy then someone is not humble and vice versa.
Everyone who is both not happy and not curious is not tall and vice versa.
If susan is both happy and not strong then fred is either funny or not humble.
If someone is both not calm and not wise then someone is not creative or not generous and vice versa.
If someone is both generous and kind then someone is not wise.
Everyone who is either not quiet or curious is rich.
Everyone who is not creative is either kind or funny and vice versa.
If someone is either not tall or not patient then mary is not old.
If paul is not tall or patient then lucy is generous and vice versa.
If lucy is both not strong and not tall then alice is both calm and patient and vice versa.
If susan is both generous and wise then someone is not strong or humble and vice versa.
If someone is wise then someone is either humble or not rich.
If someone is both not calm and old then lucy is strong.
Everyone who is brave is both not curious and not strong.
Susan is both patient and tall.
Someone is not old or not humble.
Someone is creative.
Lucy is not humble.
Someone is not curious.
Susan is funny or not creative.
Someone is not old or not tall.
Susan is either quiet or generous. | John is not strong. | contradiction | (![X]:((wise(X)<~>~wise(X))=>quiet(X)))&
(![X]:((~generous(X)&~creative(X))<=>~creative(X)))&
(((curious(john)<~>happy(john)))<=>(?[X]:(~humble(X))))&
(![X]:((~happy(X)&~curious(X))<=>~tall(X)))&
(((happy(susan)&~strong(susan)))=>((funny(fred)<~>~humble(fred))))&
((?[X]:((~calm(X)&~wise(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
((?[X]:((generous(X)&kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~quiet(X)<~>curious(X))=>rich(X)))&
(![X]:(~creative(X)<=>(kind(X)<~>funny(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>(~old(mary)))&
(((~tall(paul)|patient(paul)))<=>(generous(lucy)))&
(((~strong(lucy)&~tall(lucy)))<=>((calm(alice)&patient(alice))))&
(((generous(susan)&wise(susan)))<=>(?[X]:((~strong(X)|humble(X)))))&
((?[X]:(wise(X)))=>(?[X]:((humble(X)<~>~rich(X)))))&
((?[X]:((~calm(X)&old(X))))=>(strong(lucy)))&
(![X]:(brave(X)=>(~curious(X)&~strong(X))))&
((patient(susan)&tall(susan)))&
(?[X]:((~old(X)|~humble(X))))&
(?[X]:(creative(X)))&
(~humble(lucy))&
(?[X]:(~curious(X)))&
((funny(susan)|~creative(susan)))&
(?[X]:((~old(X)|~tall(X))))&
((quiet(susan)<~>generous(susan))) | ~strong(john) | [
"p0",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 497569380840045184708060
% SZS output start Proof for 497569380840045184708060
1. ! [X0] : ((wise(X0) <~> ~wise(X0)) => quiet(X0)) [input p0]
13. (wise(susan) & generous(susan)) <=> ? [X0] : (humble(X0) | ~strong(X0)) [input p12]
24. quiet(susan) <~> generous(susan) [input p23]
25. ~strong(john) [input hypothesis]
34. ! [X0] : (quiet(X0) | (wise(X0) <=> ~wise(X0))) [ennf transformation 1]
40. ! [X0] : (quiet(X0) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 34]
64. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & (? [X0] : (humble(X0) | ~strong(X0)) | (~wise(susan) | ~generous(susan))) [nnf transformation 13]
65. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & (? [X0] : (humble(X0) | ~strong(X0)) | ~wise(susan) | ~generous(susan)) [flattening 64]
66. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & (? [X1] : (humble(X1) | ~strong(X1)) | ~wise(susan) | ~generous(susan)) [rectify 65]
67. ? [X1] : (humble(X1) | ~strong(X1)) => (humble(sK4) | ~strong(sK4)) [choice axiom]
68. ((wise(susan) & generous(susan)) | ! [X0] : (~humble(X0) & strong(X0))) & ((humble(sK4) | ~strong(sK4)) | ~wise(susan) | ~generous(susan)) [skolemisation 66,67]
77. (~generous(susan) | ~quiet(susan)) & (generous(susan) | quiet(susan)) [nnf transformation 24]
78. quiet(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 40]
79. quiet(X0) | wise(X0) | wise(X0) [cnf transformation 40]
112. generous(susan) | strong(X0) [cnf transformation 68]
125. ~generous(susan) | ~quiet(susan) [cnf transformation 77]
126. ~strong(john) [cnf transformation 25]
127. quiet(X0) | ~wise(X0) [duplicate literal removal 78]
128. quiet(X0) | wise(X0) [duplicate literal removal 79]
129. quiet(X0) [subsumption resolution 127,128]
247. 26 <=> ! [X0] : strong(X0) [avatar definition]
248. strong(X0) <- (26) [avatar component clause 247]
251. 27 <=> generous(susan) [avatar definition]
255. 26 | 27 [avatar split clause 112,251,247]
287. ~generous(susan) [subsumption resolution 125,129]
288. ~27 [avatar split clause 287,251]
291. $false <- (26) [resolution 248,126]
292. ~26 [avatar contradiction clause 291]
293. $false [avatar sat refutation 255,288,292]
% SZS output end Proof for 497569380840045184708060
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either kind or not creative then john is not rich.
Everyone who is both not quiet and not brave is either not humble or not happy and vice versa.
Everyone who is both quiet and not creative is not kind and vice versa.
Everyone who is either not rich or not generous is both not calm and patient.
Everyone who is not funny or not happy is both quiet and funny.
Everyone who is rich is not happy or kind.
Everyone who is either wise or not creative is both tall and wise and vice versa.
Everyone who is either not curious or curious is creative or not tall and vice versa.
If paul is creative or not brave then lucy is either tall or patient and vice versa.
Everyone who is happy is both not funny and not calm.
Everyone who is either curious or patient is either not wise or not calm.
If someone is both not generous and not creative then someone is both not generous and calm.
Everyone who is not rich is not happy or strong.
If someone is either generous or not tall then paul is not generous or not creative.
Everyone who is either not creative or strong is either tall or funny.
Everyone who is both brave and old is tall and vice versa.
Paul is rich or not rich.
Lucy is either creative or patient.
Someone is either not happy or not strong.
Someone is not patient or not brave.
Someone is kind.
Susan is not happy or not rich.
John is both quiet and not kind. | Paul is generous. | neutral | ((?[X]:((kind(X)<~>~creative(X))))=>(~rich(john)))&
(![X]:((~quiet(X)&~brave(X))<=>(~humble(X)<~>~happy(X))))&
(![X]:((quiet(X)&~creative(X))<=>~kind(X)))&
(![X]:((~rich(X)<~>~generous(X))=>(~calm(X)&patient(X))))&
(![X]:((~funny(X)|~happy(X))=>(quiet(X)&funny(X))))&
(![X]:(rich(X)=>(~happy(X)|kind(X))))&
(![X]:((wise(X)<~>~creative(X))<=>(tall(X)&wise(X))))&
(![X]:((~curious(X)<~>curious(X))<=>(creative(X)|~tall(X))))&
(((creative(paul)|~brave(paul)))<=>((tall(lucy)<~>patient(lucy))))&
(![X]:(happy(X)=>(~funny(X)&~calm(X))))&
(![X]:((curious(X)<~>patient(X))=>(~wise(X)<~>~calm(X))))&
((?[X]:((~generous(X)&~creative(X))))=>(?[X]:((~generous(X)&calm(X)))))&
(![X]:(~rich(X)=>(~happy(X)|strong(X))))&
((?[X]:((generous(X)<~>~tall(X))))=>((~generous(paul)|~creative(paul))))&
(![X]:((~creative(X)<~>strong(X))=>(tall(X)<~>funny(X))))&
(![X]:((brave(X)&old(X))<=>tall(X)))&
((rich(paul)|~rich(paul)))&
((creative(lucy)<~>patient(lucy)))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:((~patient(X)|~brave(X))))&
(?[X]:(kind(X)))&
((~happy(susan)|~rich(susan)))&
((quiet(john)&~kind(john))) | generous(paul) | [] | null | 0 |
Everyone who is both funny and not calm is not brave.
If someone is both not funny and quiet then someone is either generous or not quiet.
If susan is quiet then mary is not generous or strong.
If susan is both not tall and not generous then someone is either not wise or patient.
Everyone who is both not rich and strong is quiet or old and vice versa.
Everyone who is curious or calm is not wise.
Everyone who is both not funny and not generous is both not brave and patient and vice versa.
If someone is strong or happy then mary is either rich or funny and vice versa.
Everyone who is both not kind and not brave is not kind or not calm.
If fred is both wise and not tall then someone is not patient and vice versa.
Everyone who is both creative and curious is either happy or strong.
Everyone who is not curious or not funny is rich and vice versa.
If someone is either rich or not funny then paul is both not generous and rich and vice versa.
If alice is not calm or strong then alice is either strong or not rich.
Everyone who is both brave and not old is not happy or calm and vice versa.
Everyone who is wise is either not generous or creative.
Alice is not wise.
Someone is not tall.
Alice is rich.
Someone is patient.
Someone is old or patient.
Someone is both not humble and not calm.
Susan is either not wise or brave.
Alice is both brave and curious. | Susan is tall. | neutral | (![X]:((funny(X)&~calm(X))=>~brave(X)))&
((?[X]:((~funny(X)&quiet(X))))=>(?[X]:((generous(X)<~>~quiet(X)))))&
((quiet(susan))=>((~generous(mary)|strong(mary))))&
(((~tall(susan)&~generous(susan)))=>(?[X]:((~wise(X)<~>patient(X)))))&
(![X]:((~rich(X)&strong(X))<=>(quiet(X)|old(X))))&
(![X]:((curious(X)|calm(X))=>~wise(X)))&
(![X]:((~funny(X)&~generous(X))<=>(~brave(X)&patient(X))))&
((?[X]:((strong(X)|happy(X))))<=>((rich(mary)<~>funny(mary))))&
(![X]:((~kind(X)&~brave(X))=>(~kind(X)|~calm(X))))&
(((wise(fred)&~tall(fred)))<=>(?[X]:(~patient(X))))&
(![X]:((creative(X)&curious(X))=>(happy(X)<~>strong(X))))&
(![X]:((~curious(X)|~funny(X))<=>rich(X)))&
((?[X]:((rich(X)<~>~funny(X))))<=>((~generous(paul)&rich(paul))))&
(((~calm(alice)|strong(alice)))=>((strong(alice)<~>~rich(alice))))&
(![X]:((brave(X)&~old(X))<=>(~happy(X)|calm(X))))&
(![X]:(wise(X)=>(~generous(X)<~>creative(X))))&
(~wise(alice))&
(?[X]:(~tall(X)))&
(rich(alice))&
(?[X]:(patient(X)))&
(?[X]:((old(X)|patient(X))))&
(?[X]:((~humble(X)&~calm(X))))&
((~wise(susan)<~>brave(susan)))&
((brave(alice)&curious(alice))) | tall(susan) | [] | null | 0 |
If lucy is not calm then someone is either old or rich.
If someone is not patient then paul is both not old and creative.
Everyone who is both calm and not happy is not quiet or humble.
Everyone who is either quiet or happy is both not creative and not generous and vice versa.
Everyone who is either not funny or not rich is not quiet or calm and vice versa.
If john is brave then fred is brave.
Everyone who is either not tall or not patient is brave or humble.
Everyone who is rich or not calm is either humble or not kind and vice versa.
Everyone who is not kind or generous is both wise and funny and vice versa.
Everyone who is rich or not quiet is strong or not curious and vice versa.
If someone is either not humble or funny then susan is either brave or humble.
If someone is not rich or not strong then someone is kind.
Everyone who is either creative or not funny is curious and vice versa.
If fred is either kind or happy then lucy is both not strong and strong and vice versa.
Everyone who is not patient or not funny is old and vice versa.
If someone is not brave then someone is both not curious and patient and vice versa.
Someone is not curious.
Someone is either brave or not quiet.
Someone is calm.
Alice is brave.
Paul is both kind and old.
Someone is both not tall and old.
Someone is rich or not wise.
Susan is either not tall or old. | Paul is not humble. | contradiction | ((~calm(lucy))=>(?[X]:((old(X)<~>rich(X)))))&
((?[X]:(~patient(X)))=>((~old(paul)&creative(paul))))&
(![X]:((calm(X)&~happy(X))=>(~quiet(X)|humble(X))))&
(![X]:((quiet(X)<~>happy(X))<=>(~creative(X)&~generous(X))))&
(![X]:((~funny(X)<~>~rich(X))<=>(~quiet(X)|calm(X))))&
((brave(john))=>(brave(fred)))&
(![X]:((~tall(X)<~>~patient(X))=>(brave(X)|humble(X))))&
(![X]:((rich(X)|~calm(X))<=>(humble(X)<~>~kind(X))))&
(![X]:((~kind(X)|generous(X))<=>(wise(X)&funny(X))))&
(![X]:((rich(X)|~quiet(X))<=>(strong(X)|~curious(X))))&
((?[X]:((~humble(X)<~>funny(X))))=>((brave(susan)<~>humble(susan))))&
((?[X]:((~rich(X)|~strong(X))))=>(?[X]:(kind(X))))&
(![X]:((creative(X)<~>~funny(X))<=>curious(X)))&
(((kind(fred)<~>happy(fred)))<=>((~strong(lucy)&strong(lucy))))&
(![X]:((~patient(X)|~funny(X))<=>old(X)))&
((?[X]:(~brave(X)))<=>(?[X]:((~curious(X)&patient(X)))))&
(?[X]:(~curious(X)))&
(?[X]:((brave(X)<~>~quiet(X))))&
(?[X]:(calm(X)))&
(brave(alice))&
((kind(paul)&old(paul)))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:((rich(X)|~wise(X))))&
((~tall(susan)<~>old(susan))) | ~humble(paul) | [
"p1",
"p4",
"p7",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 4512550748302142440746711
% SZS output start Proof for 4512550748302142440746711
2. ? [X0] : ~patient(X0) => (creative(paul) & ~old(paul)) [input p1]
5. ! [X0] : ((~funny(X0) <~> ~rich(X0)) <=> (calm(X0) | ~quiet(X0))) [input p4]
8. ! [X0] : ((~calm(X0) | rich(X0)) <=> (humble(X0) <~> ~kind(X0))) [input p7]
15. ! [X0] : ((~funny(X0) | ~patient(X0)) <=> old(X0)) [input p14]
21. old(paul) & kind(paul) [input p20]
25. ~humble(paul) [input hypothesis]
29. (creative(paul) & ~old(paul)) | ! [X0] : patient(X0) [ennf transformation 2]
42. ! [X0] : ((((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | (~calm(X0) & quiet(X0))) & ((calm(X0) | ~quiet(X0)) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))))) [nnf transformation 5]
43. ! [X0] : ((((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | (~calm(X0) & quiet(X0))) & (calm(X0) | ~quiet(X0) | ((~funny(X0) | rich(X0)) & (~rich(X0) | funny(X0))))) [flattening 42]
45. ! [X0] : (((~calm(X0) | rich(X0)) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (calm(X0) & ~rich(X0)))) [nnf transformation 8]
46. ! [X0] : ((~calm(X0) | rich(X0) | ((humble(X0) | kind(X0)) & (~kind(X0) | ~humble(X0)))) & (((kind(X0) | ~humble(X0)) & (~kind(X0) | humble(X0))) | (calm(X0) & ~rich(X0)))) [flattening 45]
58. ! [X0] : (((~funny(X0) | ~patient(X0)) | ~old(X0)) & (old(X0) | (funny(X0) & patient(X0)))) [nnf transformation 15]
59. ! [X0] : ((~funny(X0) | ~patient(X0) | ~old(X0)) & (old(X0) | (funny(X0) & patient(X0)))) [flattening 58]
79. ~old(paul) | patient(X0) [cnf transformation 29]
93. ~calm(X0) | funny(X0) | rich(X0) [cnf transformation 43]
97. ~kind(X0) | humble(X0) | ~rich(X0) [cnf transformation 46]
98. ~kind(X0) | humble(X0) | calm(X0) [cnf transformation 46]
130. ~funny(X0) | ~patient(X0) | ~old(X0) [cnf transformation 59]
139. kind(paul) [cnf transformation 21]
140. old(paul) [cnf transformation 21]
146. ~humble(paul) [cnf transformation 25]
162. 4 <=> ! [X0] : patient(X0) [avatar definition]
163. patient(X0) <- (4) [avatar component clause 162]
170. 6 <=> old(paul) [avatar definition]
171. old(paul) <- (6) [avatar component clause 170]
173. 4 | ~6 [avatar split clause 79,170,162]
260. 6 [avatar split clause 140,170]
318. humble(paul) | ~rich(paul) [resolution 97,139]
321. ~rich(paul) [subsumption resolution 318,146]
337. humble(paul) | calm(paul) [resolution 98,139]
340. calm(paul) [subsumption resolution 337,146]
353. funny(paul) | rich(paul) [resolution 340,93]
354. funny(paul) [subsumption resolution 353,321]
472. ~patient(paul) | ~old(paul) [resolution 130,354]
477. ~old(paul) <- (4) [subsumption resolution 472,163]
478. $false <- (4, 6) [subsumption resolution 477,171]
479. ~4 | ~6 [avatar contradiction clause 478]
483. $false [avatar sat refutation 173,260,479]
% SZS output end Proof for 4512550748302142440746711
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not kind is not creative and vice versa. If alice is either not kind or quiet then someone is not strong or not brave and vice versa. Everyone who is either humble or brave is not brave and vice versa. Everyone who is either not patient or not quiet is either not humble or curious and vice versa. Everyone who is both humble and happy is either not tall or funny and vice versa. If someone is not funny then fred is either not tall or not old. If john is curious then john is not curious or calm. If someone is either quiet or kind then lucy is both not generous and not wise. Everyone who is humble is not happy or old. Everyone who is tall or old is not tall or strong and vice versa. If someone is quiet or not old then someone is both not wise and wise. If someone is both patient and not quiet then fred is calm. Everyone who is either not tall or not calm is both creative and not wise and vice versa. If someone is not creative or not generous then someone is both wise and not kind. If fred is both happy and old then john is funny and vice versa. Everyone who is both not happy and funny is not funny and vice versa. Alice is happy or funny. Mary is not creative. Someone is not calm or strong. Alice is not old or funny. Alice is both not quiet and creative. Someone is not calm. Someone is happy. | Mary is not kind. | entailment | (![X]:(~kind(X)<=>~creative(X)))&
(((~kind(alice)<~>quiet(alice)))<=>(?[X]:((~strong(X)|~brave(X)))))&
(![X]:((humble(X)<~>brave(X))<=>~brave(X)))&
(![X]:((~patient(X)<~>~quiet(X))<=>(~humble(X)<~>curious(X))))&
(![X]:((humble(X)&happy(X))<=>(~tall(X)<~>funny(X))))&
((?[X]:(~funny(X)))=>((~tall(fred)<~>~old(fred))))&
((curious(john))=>((~curious(john)|calm(john))))&
((?[X]:((quiet(X)<~>kind(X))))=>((~generous(lucy)&~wise(lucy))))&
(![X]:(humble(X)=>(~happy(X)|old(X))))&
(![X]:((tall(X)|old(X))<=>(~tall(X)|strong(X))))&
((?[X]:((quiet(X)|~old(X))))=>(?[X]:((~wise(X)&wise(X)))))&
((?[X]:((patient(X)&~quiet(X))))=>(calm(fred)))&
(![X]:((~tall(X)<~>~calm(X))<=>(creative(X)&~wise(X))))&
((?[X]:((~creative(X)|~generous(X))))=>(?[X]:((wise(X)&~kind(X)))))&
(((happy(fred)&old(fred)))<=>(funny(john)))&
(![X]:((~happy(X)&funny(X))<=>~funny(X)))&
((happy(alice)|funny(alice)))&
(~creative(mary))&
(?[X]:((~calm(X)|strong(X))))&
((~old(alice)|funny(alice)))&
((~quiet(alice)&creative(alice)))&
(?[X]:(~calm(X)))&
(?[X]:(happy(X))) | ~kind(mary) | [
"p0",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 8886711712878900715274730
% SZS output start Proof for 8886711712878900715274730
1. ! [X0] : (~kind(X0) <=> ~creative(X0)) [input p0]
18. ~creative(mary) [input p17]
24. kind(mary) [input hypothesis]
36. ! [X0] : ((~kind(X0) | creative(X0)) & (~creative(X0) | kind(X0))) [nnf transformation 1]
68. ~kind(X0) | creative(X0) [cnf transformation 36]
127. ~creative(mary) [cnf transformation 18]
134. kind(mary) [cnf transformation 24]
308. creative(mary) [resolution 68,134]
310. $false [subsumption resolution 308,127]
% SZS output end Proof for 8886711712878900715274730
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is creative is old and vice versa. If paul is wise or not happy then mary is not curious or quiet and vice versa. If mary is either old or tall then alice is not rich. If mary is either curious or not wise then someone is happy or not happy and vice versa. Everyone who is both not patient and not tall is both calm and not quiet. Everyone who is both not calm and kind is not kind or brave and vice versa. Everyone who is either not humble or happy is either curious or brave. If john is tall or not patient then someone is not brave or kind and vice versa. If someone is both not kind and funny then john is both not funny and kind and vice versa. Everyone who is tall or not humble is both humble and not curious and vice versa. Everyone who is either kind or humble is not brave. Everyone who is not calm is both not wise and not creative. If someone is not funny or not quiet then lucy is not humble or patient and vice versa. Everyone who is either not old or calm is both humble and not happy. If someone is both not happy and not old then paul is either brave or not strong. If john is either not patient or generous then someone is both not tall and kind. John is rich. Someone is both not happy and curious. Susan is either humble or brave. Someone is not curious or tall. Mary is not generous. Alice is either wise or strong. | Mary is rich. | neutral | (![X]:(creative(X)<=>old(X)))&
(((wise(paul)|~happy(paul)))<=>((~curious(mary)|quiet(mary))))&
(((old(mary)<~>tall(mary)))=>(~rich(alice)))&
(((curious(mary)<~>~wise(mary)))<=>(?[X]:((happy(X)|~happy(X)))))&
(![X]:((~patient(X)&~tall(X))=>(calm(X)&~quiet(X))))&
(![X]:((~calm(X)&kind(X))<=>(~kind(X)|brave(X))))&
(![X]:((~humble(X)<~>happy(X))=>(curious(X)<~>brave(X))))&
(((tall(john)|~patient(john)))<=>(?[X]:((~brave(X)|kind(X)))))&
((?[X]:((~kind(X)&funny(X))))<=>((~funny(john)&kind(john))))&
(![X]:((tall(X)|~humble(X))<=>(humble(X)&~curious(X))))&
(![X]:((kind(X)<~>humble(X))=>~brave(X)))&
(![X]:(~calm(X)=>(~wise(X)&~creative(X))))&
((?[X]:((~funny(X)|~quiet(X))))<=>((~humble(lucy)|patient(lucy))))&
(![X]:((~old(X)<~>calm(X))=>(humble(X)&~happy(X))))&
((?[X]:((~happy(X)&~old(X))))=>((brave(paul)<~>~strong(paul))))&
(((~patient(john)<~>generous(john)))=>(?[X]:((~tall(X)&kind(X)))))&
(rich(john))&
(?[X]:((~happy(X)&curious(X))))&
((humble(susan)<~>brave(susan)))&
(?[X]:((~curious(X)|tall(X))))&
(~generous(mary))&
((wise(alice)<~>strong(alice))) | rich(mary) | [] | null | 0 |
Everyone who is strong or not wise is not old or not calm.
If someone is strong or happy then susan is not kind.
Everyone who is humble is both generous and not rich.
Everyone who is old or brave is both not brave and brave.
If someone is curious or not generous then lucy is quiet or generous and vice versa.
If alice is both brave and not curious then paul is old or not funny.
Everyone who is not calm is not quiet and vice versa.
If alice is either not happy or not old then someone is both not rich and not patient.
Everyone who is not rich is curious or not curious and vice versa.
Everyone who is not happy or funny is either generous or rich.
If john is tall then someone is not curious or not old and vice versa.
If someone is either not wise or patient then susan is rich and vice versa.
If susan is either not tall or calm then mary is either not curious or not funny.
If someone is calm then someone is either tall or not patient.
Everyone who is kind is either not happy or strong and vice versa.
If fred is not old or not rich then susan is both not curious and wise and vice versa.
Someone is both humble and not quiet.
Susan is tall or rich.
Someone is either not happy or not tall.
Fred is both wise and strong.
Someone is both calm and not curious.
Fred is not quiet or not old. | Susan is strong. | neutral | (![X]:((strong(X)|~wise(X))=>(~old(X)|~calm(X))))&
((?[X]:((strong(X)|happy(X))))=>(~kind(susan)))&
(![X]:(humble(X)=>(generous(X)&~rich(X))))&
(![X]:((old(X)|brave(X))=>(~brave(X)&brave(X))))&
((?[X]:((curious(X)|~generous(X))))<=>((quiet(lucy)|generous(lucy))))&
(((brave(alice)&~curious(alice)))=>((old(paul)|~funny(paul))))&
(![X]:(~calm(X)<=>~quiet(X)))&
(((~happy(alice)<~>~old(alice)))=>(?[X]:((~rich(X)&~patient(X)))))&
(![X]:(~rich(X)<=>(curious(X)|~curious(X))))&
(![X]:((~happy(X)|funny(X))=>(generous(X)<~>rich(X))))&
((tall(john))<=>(?[X]:((~curious(X)|~old(X)))))&
((?[X]:((~wise(X)<~>patient(X))))<=>(rich(susan)))&
(((~tall(susan)<~>calm(susan)))=>((~curious(mary)<~>~funny(mary))))&
((?[X]:(calm(X)))=>(?[X]:((tall(X)<~>~patient(X)))))&
(![X]:(kind(X)<=>(~happy(X)<~>strong(X))))&
(((~old(fred)|~rich(fred)))<=>((~curious(susan)&wise(susan))))&
(?[X]:((humble(X)&~quiet(X))))&
((tall(susan)|rich(susan)))&
(?[X]:((~happy(X)<~>~tall(X))))&
((wise(fred)&strong(fred)))&
(?[X]:((calm(X)&~curious(X))))&
((~quiet(fred)|~old(fred))) | strong(susan) | [] | null | 0 |
Everyone who is not wise is not creative or wise and vice versa.
If someone is both generous and creative then fred is either not brave or wise.
Everyone who is either happy or not wise is either happy or rich and vice versa.
If someone is both not old and funny then someone is old and vice versa.
If john is both not patient and not strong then someone is quiet or not happy.
Everyone who is brave or rich is both generous and not wise.
Everyone who is not strong is either not calm or not tall and vice versa.
Everyone who is both not happy and not strong is calm and vice versa.
If someone is creative then someone is both wise and patient and vice versa.
Everyone who is either happy or not rich is either curious or not humble.
If susan is either funny or not happy then someone is either not old or kind and vice versa.
If alice is funny then lucy is kind or generous.
If someone is not rich or creative then susan is either not tall or happy.
Someone is either not generous or not old.
Someone is tall or not brave.
Someone is not strong.
Someone is either not happy or old.
Someone is both happy and not tall.
Paul is rich. | John is not humble. | neutral | (![X]:(~wise(X)<=>(~creative(X)|wise(X))))&
((?[X]:((generous(X)&creative(X))))=>((~brave(fred)<~>wise(fred))))&
(![X]:((happy(X)<~>~wise(X))<=>(happy(X)<~>rich(X))))&
((?[X]:((~old(X)&funny(X))))<=>(?[X]:(old(X))))&
(((~patient(john)&~strong(john)))=>(?[X]:((quiet(X)|~happy(X)))))&
(![X]:((brave(X)|rich(X))=>(generous(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~calm(X)<~>~tall(X))))&
(![X]:((~happy(X)&~strong(X))<=>calm(X)))&
((?[X]:(creative(X)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((happy(X)<~>~rich(X))=>(curious(X)<~>~humble(X))))&
(((funny(susan)<~>~happy(susan)))<=>(?[X]:((~old(X)<~>kind(X)))))&
((funny(alice))=>((kind(lucy)|generous(lucy))))&
((?[X]:((~rich(X)|creative(X))))=>((~tall(susan)<~>happy(susan))))&
(?[X]:((~generous(X)<~>~old(X))))&
(?[X]:((tall(X)|~brave(X))))&
(?[X]:(~strong(X)))&
(?[X]:((~happy(X)<~>old(X))))&
(?[X]:((happy(X)&~tall(X))))&
(rich(paul)) | ~humble(john) | [] | null | 0 |
Everyone who is either strong or not curious is both not happy and humble and vice versa. Everyone who is not humble is either not humble or calm. Everyone who is both generous and not wise is calm. Everyone who is both not rich and not generous is calm or kind. Everyone who is both not kind and old is both brave and not happy. If someone is not old or humble then someone is kind and vice versa. If mary is not rich or not old then mary is both tall and not strong. If someone is happy then someone is both funny and not creative and vice versa. If someone is not generous then mary is tall or not humble. Everyone who is generous or quiet is both funny and rich and vice versa. If fred is both brave and not quiet then someone is not generous and vice versa. Everyone who is both patient and not old is either quiet or not old and vice versa. Everyone who is both not strong and wise is both not funny and not rich. If mary is either funny or not creative then someone is either not kind or not quiet and vice versa. If someone is not rich then susan is either not tall or funny and vice versa. If someone is either not tall or not old then someone is not funny or wise. Someone is not tall or not wise. Someone is either tall or quiet. Fred is both not old and quiet. John is brave or not calm. Mary is not calm. Someone is both funny and quiet. Someone is funny or not old. Lucy is tall or not brave. | Mary is not old. | contradiction | (![X]:((strong(X)<~>~curious(X))<=>(~happy(X)&humble(X))))&
(![X]:(~humble(X)=>(~humble(X)<~>calm(X))))&
(![X]:((generous(X)&~wise(X))=>calm(X)))&
(![X]:((~rich(X)&~generous(X))=>(calm(X)|kind(X))))&
(![X]:((~kind(X)&old(X))=>(brave(X)&~happy(X))))&
((?[X]:((~old(X)|humble(X))))<=>(?[X]:(kind(X))))&
(((~rich(mary)|~old(mary)))=>((tall(mary)&~strong(mary))))&
((?[X]:(happy(X)))<=>(?[X]:((funny(X)&~creative(X)))))&
((?[X]:(~generous(X)))=>((tall(mary)|~humble(mary))))&
(![X]:((generous(X)|quiet(X))<=>(funny(X)&rich(X))))&
(((brave(fred)&~quiet(fred)))<=>(?[X]:(~generous(X))))&
(![X]:((patient(X)&~old(X))<=>(quiet(X)<~>~old(X))))&
(![X]:((~strong(X)&wise(X))=>(~funny(X)&~rich(X))))&
(((funny(mary)<~>~creative(mary)))<=>(?[X]:((~kind(X)<~>~quiet(X)))))&
((?[X]:(~rich(X)))<=>((~tall(susan)<~>funny(susan))))&
((?[X]:((~tall(X)<~>~old(X))))=>(?[X]:((~funny(X)|wise(X)))))&
(?[X]:((~tall(X)|~wise(X))))&
(?[X]:((tall(X)<~>quiet(X))))&
((~old(fred)&quiet(fred)))&
((brave(john)|~calm(john)))&
(~calm(mary))&
(?[X]:((funny(X)&quiet(X))))&
(?[X]:((funny(X)|~old(X))))&
((tall(lucy)|~brave(lucy))) | ~old(mary) | [
"p2",
"p6",
"p9",
"p10",
"p12",
"p18",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 1170181533863553395675875
% SZS output start Proof for 1170181533863553395675875
3. ! [X0] : ((~wise(X0) & generous(X0)) => calm(X0)) [input p2]
7. (~old(mary) | ~rich(mary)) => (~strong(mary) & tall(mary)) [input p6]
10. ! [X0] : ((quiet(X0) | generous(X0)) <=> (rich(X0) & funny(X0))) [input p9]
11. (~quiet(fred) & brave(fred)) <=> ? [X0] : ~generous(X0) [input p10]
13. ! [X0] : ((wise(X0) & ~strong(X0)) => (~rich(X0) & ~funny(X0))) [input p12]
19. quiet(fred) & ~old(fred) [input p18]
21. ~calm(mary) [input p20]
25. ~old(mary) [input hypothesis]
30. ! [X0] : (calm(X0) | (wise(X0) | ~generous(X0))) [ennf transformation 3]
31. ! [X0] : (calm(X0) | wise(X0) | ~generous(X0)) [flattening 30]
36. (~strong(mary) & tall(mary)) | (old(mary) & rich(mary)) [ennf transformation 7]
39. ! [X0] : ((~rich(X0) & ~funny(X0)) | (~wise(X0) | strong(X0))) [ennf transformation 13]
40. ! [X0] : ((~rich(X0) & ~funny(X0)) | ~wise(X0) | strong(X0)) [flattening 39]
55. ! [X0] : (((quiet(X0) | generous(X0)) | (~rich(X0) | ~funny(X0))) & ((rich(X0) & funny(X0)) | (~quiet(X0) & ~generous(X0)))) [nnf transformation 10]
56. ! [X0] : ((quiet(X0) | generous(X0) | ~rich(X0) | ~funny(X0)) & ((rich(X0) & funny(X0)) | (~quiet(X0) & ~generous(X0)))) [flattening 55]
57. ((~quiet(fred) & brave(fred)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | (quiet(fred) | ~brave(fred))) [nnf transformation 11]
58. ((~quiet(fred) & brave(fred)) | ! [X0] : generous(X0)) & (? [X0] : ~generous(X0) | quiet(fred) | ~brave(fred)) [flattening 57]
59. ((~quiet(fred) & brave(fred)) | ! [X0] : generous(X0)) & (? [X1] : ~generous(X1) | quiet(fred) | ~brave(fred)) [rectify 58]
60. ? [X1] : ~generous(X1) => ~generous(sK4) [choice axiom]
61. ((~quiet(fred) & brave(fred)) | ! [X0] : generous(X0)) & (~generous(sK4) | quiet(fred) | ~brave(fred)) [skolemisation 59,60]
93. ~generous(X0) | wise(X0) | calm(X0) [cnf transformation 31]
103. ~strong(mary) | old(mary) [cnf transformation 36]
108. ~generous(X0) | funny(X0) [cnf transformation 56]
115. ~quiet(fred) | generous(X0) [cnf transformation 61]
122. ~funny(X0) | ~wise(X0) | strong(X0) [cnf transformation 40]
142. quiet(fred) [cnf transformation 19]
144. ~calm(mary) [cnf transformation 21]
149. ~old(mary) [cnf transformation 25]
178. 7 <=> old(mary) [avatar definition]
182. 8 <=> strong(mary) [avatar definition]
184. ~strong(mary) <- (~8) [avatar component clause 182]
185. 7 | ~8 [avatar split clause 103,182,178]
219. 16 <=> ! [X0] : generous(X0) [avatar definition]
220. generous(X0) <- (16) [avatar component clause 219]
227. 18 <=> quiet(fred) [avatar definition]
230. 16 | ~18 [avatar split clause 115,227,219]
246. 22 <=> funny(mary) [avatar definition]
247. funny(mary) <- (22) [avatar component clause 246]
248. ~funny(mary) <- (~22) [avatar component clause 246]
326. 18 [avatar split clause 142,227]
354. ~7 [avatar split clause 149,178]
355. funny(X0) <- (16) [resolution 108,220]
400. wise(X0) | calm(X0) <- (16) [resolution 93,220]
405. ~wise(mary) | strong(mary) <- (22) [resolution 122,247]
416. ~wise(mary) <- (~8, 22) [subsumption resolution 405,184]
419. calm(mary) <- (~8, 16, 22) [resolution 416,400]
420. $false <- (~8, 16, 22) [subsumption resolution 419,144]
421. 8 | ~16 | ~22 [avatar contradiction clause 420]
422. $false <- (16, ~22) [subsumption resolution 248,355]
423. ~16 | 22 [avatar contradiction clause 422]
424. $false [avatar sat refutation 185,230,326,354,421,423]
% SZS output end Proof for 1170181533863553395675875
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is strong or quiet is strong. If alice is both not rich and patient then someone is tall or not strong and vice versa. If paul is kind then mary is rich and vice versa. If someone is not wise then paul is not kind or old. Everyone who is both wise and rich is both not patient and not calm and vice versa. Everyone who is both not strong and old is either wise or curious. Everyone who is funny is both brave and not happy. Everyone who is either not humble or not wise is strong or kind and vice versa. Everyone who is either not quiet or wise is not creative or tall. If fred is not curious then mary is either brave or not old. If john is not curious then lucy is not funny. If someone is both generous and curious then susan is not patient or quiet. If susan is not quiet or brave then someone is either not patient or not creative. Everyone who is happy or not wise is generous and vice versa. Everyone who is both generous and not tall is not generous. Everyone who is both creative and not curious is both not old and not creative. Paul is both generous and humble. John is not strong or not creative. Paul is not creative or not humble. Alice is both not kind and not happy. Paul is not kind. Someone is not curious or kind. Someone is either not curious or patient. | Lucy is patient. | neutral | (![X]:((strong(X)|quiet(X))=>strong(X)))&
(((~rich(alice)&patient(alice)))<=>(?[X]:((tall(X)|~strong(X)))))&
((kind(paul))<=>(rich(mary)))&
((?[X]:(~wise(X)))=>((~kind(paul)|old(paul))))&
(![X]:((wise(X)&rich(X))<=>(~patient(X)&~calm(X))))&
(![X]:((~strong(X)&old(X))=>(wise(X)<~>curious(X))))&
(![X]:(funny(X)=>(brave(X)&~happy(X))))&
(![X]:((~humble(X)<~>~wise(X))<=>(strong(X)|kind(X))))&
(![X]:((~quiet(X)<~>wise(X))=>(~creative(X)|tall(X))))&
((~curious(fred))=>((brave(mary)<~>~old(mary))))&
((~curious(john))=>(~funny(lucy)))&
((?[X]:((generous(X)&curious(X))))=>((~patient(susan)|quiet(susan))))&
(((~quiet(susan)|brave(susan)))=>(?[X]:((~patient(X)<~>~creative(X)))))&
(![X]:((happy(X)|~wise(X))<=>generous(X)))&
(![X]:((generous(X)&~tall(X))=>~generous(X)))&
(![X]:((creative(X)&~curious(X))=>(~old(X)&~creative(X))))&
((generous(paul)&humble(paul)))&
((~strong(john)|~creative(john)))&
((~creative(paul)|~humble(paul)))&
((~kind(alice)&~happy(alice)))&
(~kind(paul))&
(?[X]:((~curious(X)|kind(X))))&
(?[X]:((~curious(X)<~>patient(X)))) | patient(lucy) | [] | null | 0 |
If alice is brave or not funny then paul is brave or calm.
Everyone who is either not old or old is both tall and not curious and vice versa.
Everyone who is both calm and generous is either not old or not curious.
Everyone who is not kind or rich is both funny and creative.
If someone is happy then john is both not patient and happy.
Everyone who is either rich or strong is either calm or happy and vice versa.
If lucy is either patient or wise then susan is both generous and not creative and vice versa.
Everyone who is both rich and not wise is not happy and vice versa.
Everyone who is either happy or not patient is not tall or brave.
If mary is either not funny or wise then lucy is either not kind or not curious.
Everyone who is wise is either tall or not tall and vice versa.
Everyone who is either not old or not rich is both not curious and calm and vice versa.
Everyone who is either not strong or curious is either calm or happy and vice versa.
Everyone who is calm is not tall.
Everyone who is either not calm or curious is not happy or not humble.
John is either tall or not rich.
John is brave or not rich.
Fred is either not funny or not humble.
Someone is either not strong or humble.
Mary is not patient or rich.
Someone is tall.
John is either quiet or brave. | Mary is creative. | entailment | (((brave(alice)|~funny(alice)))=>((brave(paul)|calm(paul))))&
(![X]:((~old(X)<~>old(X))<=>(tall(X)&~curious(X))))&
(![X]:((calm(X)&generous(X))=>(~old(X)<~>~curious(X))))&
(![X]:((~kind(X)|rich(X))=>(funny(X)&creative(X))))&
((?[X]:(happy(X)))=>((~patient(john)&happy(john))))&
(![X]:((rich(X)<~>strong(X))<=>(calm(X)<~>happy(X))))&
(((patient(lucy)<~>wise(lucy)))<=>((generous(susan)&~creative(susan))))&
(![X]:((rich(X)&~wise(X))<=>~happy(X)))&
(![X]:((happy(X)<~>~patient(X))=>(~tall(X)|brave(X))))&
(((~funny(mary)<~>wise(mary)))=>((~kind(lucy)<~>~curious(lucy))))&
(![X]:(wise(X)<=>(tall(X)<~>~tall(X))))&
(![X]:((~old(X)<~>~rich(X))<=>(~curious(X)&calm(X))))&
(![X]:((~strong(X)<~>curious(X))<=>(calm(X)<~>happy(X))))&
(![X]:(calm(X)=>~tall(X)))&
(![X]:((~calm(X)<~>curious(X))=>(~happy(X)|~humble(X))))&
((tall(john)<~>~rich(john)))&
((brave(john)|~rich(john)))&
((~funny(fred)<~>~humble(fred)))&
(?[X]:((~strong(X)<~>humble(X))))&
((~patient(mary)|rich(mary)))&
(?[X]:(tall(X)))&
((quiet(john)<~>brave(john))) | creative(mary) | [
"p1",
"p3",
"p5",
"p7",
"p10",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 8769703464217680826528637
% SZS output start Proof for 8769703464217680826528637
2. ! [X0] : ((~old(X0) <~> old(X0)) <=> (~curious(X0) & tall(X0))) [input p1]
4. ! [X0] : ((rich(X0) | ~kind(X0)) => (creative(X0) & funny(X0))) [input p3]
6. ! [X0] : ((rich(X0) <~> strong(X0)) <=> (calm(X0) <~> happy(X0))) [input p5]
8. ! [X0] : ((~wise(X0) & rich(X0)) <=> ~happy(X0)) [input p7]
11. ! [X0] : (wise(X0) <=> (tall(X0) <~> ~tall(X0))) [input p10]
13. ! [X0] : ((~strong(X0) <~> curious(X0)) <=> (calm(X0) <~> happy(X0))) [input p12]
14. ! [X0] : (calm(X0) => ~tall(X0)) [input p13]
23. ~creative(mary) [input hypothesis]
28. ! [X0] : ((creative(X0) & funny(X0)) | (~rich(X0) & kind(X0))) [ennf transformation 4]
33. ! [X0] : (~tall(X0) | ~calm(X0)) [ennf transformation 14]
36. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | (curious(X0) | ~tall(X0))) & ((~curious(X0) & tall(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [nnf transformation 2]
37. ! [X0] : ((((~old(X0) | old(X0)) & (old(X0) | ~old(X0))) | curious(X0) | ~tall(X0)) & ((~curious(X0) & tall(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0))))) [flattening 36]
39. ! [X0] : ((((~strong(X0) | ~rich(X0)) & (strong(X0) | rich(X0))) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0))))) [nnf transformation 6]
42. ! [X0] : (((~wise(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | (wise(X0) | ~rich(X0)))) [nnf transformation 8]
43. ! [X0] : (((~wise(X0) & rich(X0)) | happy(X0)) & (~happy(X0) | wise(X0) | ~rich(X0))) [flattening 42]
46. ! [X0] : ((wise(X0) | ((tall(X0) | tall(X0)) & (~tall(X0) | ~tall(X0)))) & (((tall(X0) | ~tall(X0)) & (~tall(X0) | tall(X0))) | ~wise(X0))) [nnf transformation 11]
49. ! [X0] : ((((~curious(X0) | strong(X0)) & (curious(X0) | ~strong(X0))) | ((calm(X0) | ~happy(X0)) & (happy(X0) | ~calm(X0)))) & (((~happy(X0) | ~calm(X0)) & (happy(X0) | calm(X0))) | ((~strong(X0) | ~curious(X0)) & (curious(X0) | strong(X0))))) [nnf transformation 13]
61. tall(X0) | old(X0) | old(X0) [cnf transformation 37]
62. tall(X0) | ~old(X0) | ~old(X0) [cnf transformation 37]
63. ~curious(X0) | old(X0) | old(X0) [cnf transformation 37]
64. ~curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 37]
72. ~rich(X0) | creative(X0) [cnf transformation 28]
80. ~happy(X0) | rich(X0) | calm(X0) | strong(X0) [cnf transformation 39]
91. ~wise(X0) | happy(X0) [cnf transformation 43]
100. wise(X0) | ~tall(X0) | ~tall(X0) [cnf transformation 46]
113. curious(X0) | ~strong(X0) | calm(X0) | ~happy(X0) [cnf transformation 49]
116. ~tall(X0) | ~calm(X0) [cnf transformation 33]
130. ~creative(mary) [cnf transformation 23]
131. wise(X0) | ~tall(X0) [duplicate literal removal 100]
133. tall(X0) | old(X0) [duplicate literal removal 61]
134. ~old(X0) | tall(X0) [duplicate literal removal 62]
135. ~curious(X0) | old(X0) [duplicate literal removal 63]
136. ~curious(X0) | ~old(X0) [duplicate literal removal 64]
155. ~curious(X0) [subsumption resolution 135,136]
156. tall(X0) [subsumption resolution 133,134]
211. wise(X0) [subsumption resolution 131,156]
214. ~strong(X0) | calm(X0) | ~happy(X0) [subsumption resolution 113,155]
218. ~calm(X0) [subsumption resolution 116,156]
260. happy(X0) [resolution 91,211]
289. rich(X0) | calm(X0) | strong(X0) [resolution 80,260]
292. strong(X0) | rich(X0) [subsumption resolution 289,218]
300. rich(X4) | calm(X4) | ~happy(X4) [resolution 292,214]
303. rich(X4) | ~happy(X4) [subsumption resolution 300,218]
304. rich(X4) [subsumption resolution 303,260]
317. creative(X3) [resolution 304,72]
322. $false [resolution 317,130]
% SZS output end Proof for 8769703464217680826528637
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong is not wise or quiet and vice versa.
If paul is both patient and not funny then susan is either not patient or not happy.
Everyone who is kind or not quiet is either calm or not kind and vice versa.
If paul is both not old and not humble then fred is rich.
Everyone who is not tall or wise is not quiet.
Everyone who is either humble or creative is happy.
If john is either not funny or not wise then someone is either not funny or not brave.
Everyone who is both tall and not humble is not wise or not strong and vice versa.
Everyone who is not strong or not brave is not brave.
If lucy is not funny then lucy is either patient or not funny and vice versa.
Everyone who is both rich and not brave is either quiet or generous.
Everyone who is generous or wise is both not brave and not happy and vice versa.
If someone is either brave or rich then alice is either quiet or happy.
Everyone who is generous or strong is not happy or not humble and vice versa.
Everyone who is happy or old is either happy or kind and vice versa.
Everyone who is curious or not creative is patient.
Someone is either not patient or not strong.
Alice is not curious.
Someone is either not creative or not curious.
John is either generous or wise.
Someone is not generous.
Susan is strong or old.
Someone is generous or not creative. | Lucy is wise. | entailment | (![X]:((~tall(X)|~strong(X))<=>(~wise(X)|quiet(X))))&
(((patient(paul)&~funny(paul)))=>((~patient(susan)<~>~happy(susan))))&
(![X]:((kind(X)|~quiet(X))<=>(calm(X)<~>~kind(X))))&
(((~old(paul)&~humble(paul)))=>(rich(fred)))&
(![X]:((~tall(X)|wise(X))=>~quiet(X)))&
(![X]:((humble(X)<~>creative(X))=>happy(X)))&
(((~funny(john)<~>~wise(john)))=>(?[X]:((~funny(X)<~>~brave(X)))))&
(![X]:((tall(X)&~humble(X))<=>(~wise(X)|~strong(X))))&
(![X]:((~strong(X)|~brave(X))=>~brave(X)))&
((~funny(lucy))<=>((patient(lucy)<~>~funny(lucy))))&
(![X]:((rich(X)&~brave(X))=>(quiet(X)<~>generous(X))))&
(![X]:((generous(X)|wise(X))<=>(~brave(X)&~happy(X))))&
((?[X]:((brave(X)<~>rich(X))))=>((quiet(alice)<~>happy(alice))))&
(![X]:((generous(X)|strong(X))<=>(~happy(X)|~humble(X))))&
(![X]:((happy(X)|old(X))<=>(happy(X)<~>kind(X))))&
(![X]:((curious(X)|~creative(X))=>patient(X)))&
(?[X]:((~patient(X)<~>~strong(X))))&
(~curious(alice))&
(?[X]:((~creative(X)<~>~curious(X))))&
((generous(john)<~>wise(john)))&
(?[X]:(~generous(X)))&
((strong(susan)|old(susan)))&
(?[X]:((generous(X)|~creative(X)))) | wise(lucy) | [
"p0",
"p5",
"p7",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1088926662182512967606591
% SZS output start Proof for 1088926662182512967606591
1. ! [X0] : ((~strong(X0) | ~tall(X0)) <=> (quiet(X0) | ~wise(X0))) [input p0]
6. ! [X0] : ((humble(X0) <~> creative(X0)) => happy(X0)) [input p5]
8. ! [X0] : ((~humble(X0) & tall(X0)) <=> (~strong(X0) | ~wise(X0))) [input p7]
10. ~funny(lucy) <=> (patient(lucy) <~> ~funny(lucy)) [input p9]
12. ! [X0] : ((wise(X0) | generous(X0)) <=> (~happy(X0) & ~brave(X0))) [input p11]
14. ! [X0] : ((strong(X0) | generous(X0)) <=> (~humble(X0) | ~happy(X0))) [input p13]
16. ! [X0] : ((~creative(X0) | curious(X0)) => patient(X0)) [input p15]
24. ~wise(lucy) [input hypothesis]
30. ! [X0] : (happy(X0) | (humble(X0) <=> creative(X0))) [ennf transformation 6]
36. ! [X0] : (patient(X0) | (creative(X0) & ~curious(X0))) [ennf transformation 16]
37. ! [X0] : (((~strong(X0) | ~tall(X0)) | (~quiet(X0) & wise(X0))) & ((quiet(X0) | ~wise(X0)) | (strong(X0) & tall(X0)))) [nnf transformation 1]
38. ! [X0] : ((~strong(X0) | ~tall(X0) | (~quiet(X0) & wise(X0))) & (quiet(X0) | ~wise(X0) | (strong(X0) & tall(X0)))) [flattening 37]
42. ! [X0] : (happy(X0) | ((humble(X0) | ~creative(X0)) & (creative(X0) | ~humble(X0)))) [nnf transformation 30]
46. ! [X0] : (((~humble(X0) & tall(X0)) | (strong(X0) & wise(X0))) & ((~strong(X0) | ~wise(X0)) | (humble(X0) | ~tall(X0)))) [nnf transformation 8]
47. ! [X0] : (((~humble(X0) & tall(X0)) | (strong(X0) & wise(X0))) & (~strong(X0) | ~wise(X0) | humble(X0) | ~tall(X0))) [flattening 46]
48. (~funny(lucy) | ((patient(lucy) | funny(lucy)) & (~funny(lucy) | ~patient(lucy)))) & (((funny(lucy) | ~patient(lucy)) & (~funny(lucy) | patient(lucy))) | funny(lucy)) [nnf transformation 10]
50. ! [X0] : (((wise(X0) | generous(X0)) | (happy(X0) | brave(X0))) & ((~happy(X0) & ~brave(X0)) | (~wise(X0) & ~generous(X0)))) [nnf transformation 12]
51. ! [X0] : ((wise(X0) | generous(X0) | happy(X0) | brave(X0)) & ((~happy(X0) & ~brave(X0)) | (~wise(X0) & ~generous(X0)))) [flattening 50]
53. ! [X0] : (((strong(X0) | generous(X0)) | (humble(X0) & happy(X0))) & ((~humble(X0) | ~happy(X0)) | (~strong(X0) & ~generous(X0)))) [nnf transformation 14]
54. ! [X0] : ((strong(X0) | generous(X0) | (humble(X0) & happy(X0))) & (~humble(X0) | ~happy(X0) | (~strong(X0) & ~generous(X0)))) [flattening 53]
70. ~strong(X0) | ~tall(X0) | wise(X0) [cnf transformation 38]
84. ~creative(X0) | humble(X0) | happy(X0) [cnf transformation 42]
90. wise(X0) | tall(X0) [cnf transformation 47]
93. ~humble(X0) | strong(X0) [cnf transformation 47]
97. funny(lucy) | ~patient(lucy) | funny(lucy) [cnf transformation 48]
98. ~funny(lucy) | ~funny(lucy) | ~patient(lucy) [cnf transformation 48]
104. ~generous(X0) | ~happy(X0) [cnf transformation 51]
114. strong(X0) | generous(X0) | humble(X0) [cnf transformation 54]
122. creative(X0) | patient(X0) [cnf transformation 36]
133. ~wise(lucy) [cnf transformation 24]
136. funny(lucy) | ~patient(lucy) [duplicate literal removal 97]
137. ~funny(lucy) | ~patient(lucy) [duplicate literal removal 98]
193. 12 <=> patient(lucy) [avatar definition]
195. ~patient(lucy) <- (~12) [avatar component clause 193]
197. 13 <=> funny(lucy) [avatar definition]
200. ~12 | ~13 [avatar split clause 137,197,193]
201. ~12 | 13 [avatar split clause 136,197,193]
220. generous(X0) | strong(X0) [subsumption resolution 114,93]
268. tall(lucy) [resolution 90,133]
274. ~happy(X0) | strong(X0) [resolution 220,104]
297. humble(X0) | happy(X0) | patient(X0) [resolution 84,122]
420. happy(X2) | patient(X2) | strong(X2) [resolution 297,93]
424. patient(X2) | strong(X2) [subsumption resolution 420,274]
467. strong(lucy) <- (~12) [resolution 424,195]
489. ~tall(lucy) | wise(lucy) <- (~12) [resolution 467,70]
491. wise(lucy) <- (~12) [subsumption resolution 489,268]
492. $false <- (~12) [subsumption resolution 491,133]
493. 12 [avatar contradiction clause 492]
494. $false [avatar sat refutation 200,201,493]
% SZS output end Proof for 1088926662182512967606591
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either curious or not humble is generous or funny and vice versa. Everyone who is calm or humble is happy or not wise. Everyone who is not tall or not creative is not kind and vice versa. Everyone who is strong or not creative is not wise or not kind. Everyone who is brave or patient is old or not calm and vice versa. Everyone who is tall is calm or not creative and vice versa. If mary is calm then someone is not brave or creative and vice versa. If someone is funny or quiet then someone is not curious or not wise and vice versa. If lucy is not generous or not strong then someone is not happy or brave. If john is either curious or calm then lucy is calm or kind. If someone is not curious then someone is both calm and funny. Everyone who is both not patient and not strong is quiet or curious. Everyone who is either not wise or not funny is either quiet or creative. If fred is brave then fred is either funny or old. Everyone who is curious or not tall is either calm or creative. Everyone who is both not curious and not rich is not calm and vice versa. Susan is not generous. Someone is not calm. John is both not quiet and not curious. Paul is either not old or not quiet. Fred is not generous. Fred is calm. Paul is both not brave and not humble. | Lucy is not strong. | neutral | (![X]:((curious(X)<~>~humble(X))<=>(generous(X)|funny(X))))&
(![X]:((calm(X)|humble(X))=>(happy(X)|~wise(X))))&
(![X]:((~tall(X)|~creative(X))<=>~kind(X)))&
(![X]:((strong(X)|~creative(X))=>(~wise(X)|~kind(X))))&
(![X]:((brave(X)|patient(X))<=>(old(X)|~calm(X))))&
(![X]:(tall(X)<=>(calm(X)|~creative(X))))&
((calm(mary))<=>(?[X]:((~brave(X)|creative(X)))))&
((?[X]:((funny(X)|quiet(X))))<=>(?[X]:((~curious(X)|~wise(X)))))&
(((~generous(lucy)|~strong(lucy)))=>(?[X]:((~happy(X)|brave(X)))))&
(((curious(john)<~>calm(john)))=>((calm(lucy)|kind(lucy))))&
((?[X]:(~curious(X)))=>(?[X]:((calm(X)&funny(X)))))&
(![X]:((~patient(X)&~strong(X))=>(quiet(X)|curious(X))))&
(![X]:((~wise(X)<~>~funny(X))=>(quiet(X)<~>creative(X))))&
((brave(fred))=>((funny(fred)<~>old(fred))))&
(![X]:((curious(X)|~tall(X))=>(calm(X)<~>creative(X))))&
(![X]:((~curious(X)&~rich(X))<=>~calm(X)))&
(~generous(susan))&
(?[X]:(~calm(X)))&
((~quiet(john)&~curious(john)))&
((~old(paul)<~>~quiet(paul)))&
(~generous(fred))&
(calm(fred))&
((~brave(paul)&~humble(paul))) | ~strong(lucy) | [] | null | 0 |
Everyone who is both not brave and tall is not rich or strong and vice versa. If someone is funny or humble then susan is quiet or not kind. Everyone who is either not humble or humble is either not happy or generous and vice versa. Everyone who is not curious or not kind is either patient or not curious and vice versa. If someone is rich or not kind then someone is calm. Everyone who is either generous or rich is either humble or not old and vice versa. Everyone who is both not rich and not humble is both not patient and not wise. Everyone who is either patient or happy is both humble and not curious. Everyone who is both not rich and not old is both not funny and not tall. If someone is both curious and not creative then fred is either kind or brave and vice versa. Everyone who is rich is either kind or wise. Everyone who is not strong is strong. Everyone who is not funny or not patient is curious. If alice is both brave and happy then mary is old. Everyone who is curious is both not quiet and creative and vice versa. If someone is either kind or not brave then paul is not wise or strong and vice versa. Alice is quiet or rich. John is both curious and not happy. Someone is creative or not patient. John is curious or not kind. Someone is tall. Fred is not humble. Mary is both curious and not patient. Someone is either old or not quiet. | Fred is generous. | entailment | (![X]:((~brave(X)&tall(X))<=>(~rich(X)|strong(X))))&
((?[X]:((funny(X)|humble(X))))=>((quiet(susan)|~kind(susan))))&
(![X]:((~humble(X)<~>humble(X))<=>(~happy(X)<~>generous(X))))&
(![X]:((~curious(X)|~kind(X))<=>(patient(X)<~>~curious(X))))&
((?[X]:((rich(X)|~kind(X))))=>(?[X]:(calm(X))))&
(![X]:((generous(X)<~>rich(X))<=>(humble(X)<~>~old(X))))&
(![X]:((~rich(X)&~humble(X))=>(~patient(X)&~wise(X))))&
(![X]:((patient(X)<~>happy(X))=>(humble(X)&~curious(X))))&
(![X]:((~rich(X)&~old(X))=>(~funny(X)&~tall(X))))&
((?[X]:((curious(X)&~creative(X))))<=>((kind(fred)<~>brave(fred))))&
(![X]:(rich(X)=>(kind(X)<~>wise(X))))&
(![X]:(~strong(X)=>strong(X)))&
(![X]:((~funny(X)|~patient(X))=>curious(X)))&
(((brave(alice)&happy(alice)))=>(old(mary)))&
(![X]:(curious(X)<=>(~quiet(X)&creative(X))))&
((?[X]:((kind(X)<~>~brave(X))))<=>((~wise(paul)|strong(paul))))&
((quiet(alice)|rich(alice)))&
((curious(john)&~happy(john)))&
(?[X]:((creative(X)|~patient(X))))&
((curious(john)|~kind(john)))&
(?[X]:(tall(X)))&
(~humble(fred))&
((curious(mary)&~patient(mary)))&
(?[X]:((old(X)<~>~quiet(X)))) | generous(fred) | [
"p0",
"p2",
"p3",
"p7",
"p9",
"p11",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 4107631558457982342715313
% SZS output start Proof for 4107631558457982342715313
1. ! [X0] : ((tall(X0) & ~brave(X0)) <=> (strong(X0) | ~rich(X0))) [input p0]
3. ! [X0] : ((~humble(X0) <~> humble(X0)) <=> (~happy(X0) <~> generous(X0))) [input p2]
4. ! [X0] : ((~kind(X0) | ~curious(X0)) <=> (patient(X0) <~> ~curious(X0))) [input p3]
8. ! [X0] : ((patient(X0) <~> happy(X0)) => (~curious(X0) & humble(X0))) [input p7]
10. ? [X0] : (~creative(X0) & curious(X0)) <=> (kind(fred) <~> brave(fred)) [input p9]
12. ! [X0] : (~strong(X0) => strong(X0)) [input p11]
13. ! [X0] : ((~patient(X0) | ~funny(X0)) => curious(X0)) [input p12]
15. ! [X0] : (curious(X0) <=> (creative(X0) & ~quiet(X0))) [input p14]
25. ~generous(fred) [input hypothesis]
32. ! [X0] : ((~curious(X0) & humble(X0)) | (patient(X0) <=> happy(X0))) [ennf transformation 8]
36. ! [X0] : (strong(X0) | strong(X0)) [ennf transformation 12]
37. ! [X0] : (curious(X0) | (patient(X0) & funny(X0))) [ennf transformation 13]
40. ! [X0] : (((tall(X0) & ~brave(X0)) | (~strong(X0) & rich(X0))) & ((strong(X0) | ~rich(X0)) | (~tall(X0) | brave(X0)))) [nnf transformation 1]
41. ! [X0] : (((tall(X0) & ~brave(X0)) | (~strong(X0) & rich(X0))) & (strong(X0) | ~rich(X0) | ~tall(X0) | brave(X0))) [flattening 40]
42. ! [X0] : ((((~humble(X0) | humble(X0)) & (humble(X0) | ~humble(X0))) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | ((~humble(X0) | ~humble(X0)) & (humble(X0) | humble(X0))))) [nnf transformation 3]
43. ! [X0] : (((~kind(X0) | ~curious(X0)) | ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | (kind(X0) & curious(X0)))) [nnf transformation 4]
44. ! [X0] : ((~kind(X0) | ~curious(X0) | ((patient(X0) | curious(X0)) & (~curious(X0) | ~patient(X0)))) & (((curious(X0) | ~patient(X0)) & (~curious(X0) | patient(X0))) | (kind(X0) & curious(X0)))) [flattening 43]
46. ! [X0] : ((~curious(X0) & humble(X0)) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) [nnf transformation 32]
47. (? [X0] : (~creative(X0) & curious(X0)) | ((kind(fred) | ~brave(fred)) & (brave(fred) | ~kind(fred)))) & (((~brave(fred) | ~kind(fred)) & (brave(fred) | kind(fred))) | ! [X0] : (creative(X0) | ~curious(X0))) [nnf transformation 10]
48. (? [X0] : (~creative(X0) & curious(X0)) | ((kind(fred) | ~brave(fred)) & (brave(fred) | ~kind(fred)))) & (((~brave(fred) | ~kind(fred)) & (brave(fred) | kind(fred))) | ! [X1] : (creative(X1) | ~curious(X1))) [rectify 47]
49. ? [X0] : (~creative(X0) & curious(X0)) => (~creative(sK0) & curious(sK0)) [choice axiom]
50. ((~creative(sK0) & curious(sK0)) | ((kind(fred) | ~brave(fred)) & (brave(fred) | ~kind(fred)))) & (((~brave(fred) | ~kind(fred)) & (brave(fred) | kind(fred))) | ! [X1] : (creative(X1) | ~curious(X1))) [skolemisation 48,49]
52. ! [X0] : ((curious(X0) | (~creative(X0) | quiet(X0))) & ((creative(X0) & ~quiet(X0)) | ~curious(X0))) [nnf transformation 15]
53. ! [X0] : ((curious(X0) | ~creative(X0) | quiet(X0)) & ((creative(X0) & ~quiet(X0)) | ~curious(X0))) [flattening 52]
68. ~strong(X0) | ~brave(X0) [cnf transformation 41]
73. generous(X0) | ~happy(X0) | humble(X0) | humble(X0) [cnf transformation 42]
74. generous(X0) | ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 42]
82. ~curious(X0) | patient(X0) | kind(X0) [cnf transformation 44]
83. curious(X0) | ~patient(X0) | curious(X0) [cnf transformation 44]
99. ~curious(X0) | happy(X0) | ~patient(X0) [cnf transformation 46]
107. ~creative(sK0) | brave(fred) | ~kind(fred) [cnf transformation 50]
111. strong(X0) | strong(X0) [cnf transformation 36]
113. curious(X0) | patient(X0) [cnf transformation 37]
116. creative(X0) | ~curious(X0) [cnf transformation 53]
135. ~generous(fred) [cnf transformation 25]
136. strong(X0) [duplicate literal removal 111]
137. ~patient(X0) | curious(X0) [duplicate literal removal 83]
139. generous(X0) | ~happy(X0) | humble(X0) [duplicate literal removal 73]
140. generous(X0) | ~happy(X0) | ~humble(X0) [duplicate literal removal 74]
160. ~happy(X0) | generous(X0) [subsumption resolution 139,140]
161. ~patient(X0) | happy(X0) [subsumption resolution 99,137]
164. 5 <=> brave(fred) [avatar definition]
165. brave(fred) <- (5) [avatar component clause 164]
168. 6 <=> kind(fred) [avatar definition]
172. 7 <=> creative(sK0) [avatar definition]
174. ~creative(sK0) <- (~7) [avatar component clause 172]
176. ~6 | 5 | ~7 [avatar split clause 107,172,164,168]
188. curious(X0) [subsumption resolution 113,137]
202. creative(X0) [subsumption resolution 116,188]
224. $false <- (~7) [subsumption resolution 174,202]
225. 7 [avatar contradiction clause 224]
226. ~brave(X0) [resolution 68,136]
229. patient(X0) | kind(X0) [resolution 82,188]
231. happy(X0) | kind(X0) [resolution 229,161]
237. generous(X0) | kind(X0) [resolution 231,160]
239. kind(fred) [resolution 237,135]
243. 6 [avatar split clause 239,168]
244. $false <- (5) [subsumption resolution 165,226]
245. ~5 [avatar contradiction clause 244]
246. $false [avatar sat refutation 176,225,243,245]
% SZS output end Proof for 4107631558457982342715313
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either kind or calm is quiet and vice versa. Everyone who is funny or not kind is happy. If susan is either not strong or brave then susan is not tall or not brave. If fred is not humble then alice is quiet or not wise and vice versa. If john is either old or not calm then mary is either strong or tall. If lucy is not wise or not rich then mary is either not funny or creative. Everyone who is both wise and rich is either not kind or not curious and vice versa. Everyone who is either kind or strong is not quiet or wise. Everyone who is rich is strong or creative and vice versa. Everyone who is not funny or patient is not rich or rich. If alice is both kind and funny then john is curious. Everyone who is calm is rich and vice versa. If someone is quiet then someone is either not creative or not humble and vice versa. Everyone who is wise is both not old and not creative and vice versa. Everyone who is not old is both tall and not brave. If mary is either curious or humble then someone is brave or curious. Someone is either patient or not wise. Mary is patient. Fred is either not funny or quiet. Susan is both tall and generous. Someone is not wise. Someone is either generous or wise. Mary is patient or funny. | Susan is not humble. | neutral | (![X]:((kind(X)<~>calm(X))<=>quiet(X)))&
(![X]:((funny(X)|~kind(X))=>happy(X)))&
(((~strong(susan)<~>brave(susan)))=>((~tall(susan)|~brave(susan))))&
((~humble(fred))<=>((quiet(alice)|~wise(alice))))&
(((old(john)<~>~calm(john)))=>((strong(mary)<~>tall(mary))))&
(((~wise(lucy)|~rich(lucy)))=>((~funny(mary)<~>creative(mary))))&
(![X]:((wise(X)&rich(X))<=>(~kind(X)<~>~curious(X))))&
(![X]:((kind(X)<~>strong(X))=>(~quiet(X)|wise(X))))&
(![X]:(rich(X)<=>(strong(X)|creative(X))))&
(![X]:((~funny(X)|patient(X))=>(~rich(X)|rich(X))))&
(((kind(alice)&funny(alice)))=>(curious(john)))&
(![X]:(calm(X)<=>rich(X)))&
((?[X]:(quiet(X)))<=>(?[X]:((~creative(X)<~>~humble(X)))))&
(![X]:(wise(X)<=>(~old(X)&~creative(X))))&
(![X]:(~old(X)=>(tall(X)&~brave(X))))&
(((curious(mary)<~>humble(mary)))=>(?[X]:((brave(X)|curious(X)))))&
(?[X]:((patient(X)<~>~wise(X))))&
(patient(mary))&
((~funny(fred)<~>quiet(fred)))&
((tall(susan)&generous(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((generous(X)<~>wise(X))))&
((patient(mary)|funny(mary))) | ~humble(susan) | [] | null | 0 |
If lucy is both brave and patient then mary is humble. Everyone who is either wise or not humble is both not old and not wise. If someone is both not humble and funny then paul is either not funny or not curious. If mary is not happy or not humble then someone is either creative or curious. Everyone who is not generous is wise or not quiet. Everyone who is not happy is not generous or not strong. Everyone who is old or brave is both strong and not old and vice versa. If mary is both funny and not brave then someone is tall. Everyone who is both tall and not funny is rich or not rich and vice versa. Everyone who is either not kind or creative is either not patient or not creative and vice versa. Everyone who is both quiet and rich is both not creative and rich and vice versa. Everyone who is either not happy or humble is not humble. If alice is either not wise or calm then someone is both wise and patient and vice versa. Everyone who is either calm or rich is either curious or not quiet. Everyone who is strong or humble is either wise or not creative and vice versa. Everyone who is not quiet or creative is either patient or creative. Mary is not curious. Someone is not patient. Someone is not funny. Someone is wise or not generous. Someone is patient. | Alice is happy. | neutral | (((brave(lucy)&patient(lucy)))=>(humble(mary)))&
(![X]:((wise(X)<~>~humble(X))=>(~old(X)&~wise(X))))&
((?[X]:((~humble(X)&funny(X))))=>((~funny(paul)<~>~curious(paul))))&
(((~happy(mary)|~humble(mary)))=>(?[X]:((creative(X)<~>curious(X)))))&
(![X]:(~generous(X)=>(wise(X)|~quiet(X))))&
(![X]:(~happy(X)=>(~generous(X)|~strong(X))))&
(![X]:((old(X)|brave(X))<=>(strong(X)&~old(X))))&
(((funny(mary)&~brave(mary)))=>(?[X]:(tall(X))))&
(![X]:((tall(X)&~funny(X))<=>(rich(X)|~rich(X))))&
(![X]:((~kind(X)<~>creative(X))<=>(~patient(X)<~>~creative(X))))&
(![X]:((quiet(X)&rich(X))<=>(~creative(X)&rich(X))))&
(![X]:((~happy(X)<~>humble(X))=>~humble(X)))&
(((~wise(alice)<~>calm(alice)))<=>(?[X]:((wise(X)&patient(X)))))&
(![X]:((calm(X)<~>rich(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((strong(X)|humble(X))<=>(wise(X)<~>~creative(X))))&
(![X]:((~quiet(X)|creative(X))=>(patient(X)<~>creative(X))))&
(~curious(mary))&
(?[X]:(~patient(X)))&
(?[X]:(~funny(X)))&
(?[X]:((wise(X)|~generous(X))))&
(?[X]:(patient(X))) | happy(alice) | [] | null | 0 |
Everyone who is both not quiet and rich is not humble.
Everyone who is not rich is brave and vice versa.
If fred is both not wise and not humble then someone is old or brave.
Everyone who is either calm or not wise is not kind or not old and vice versa.
Everyone who is both creative and calm is not patient or patient.
Everyone who is both not funny and not calm is both not funny and not curious and vice versa.
Everyone who is not patient or humble is not creative and vice versa.
Everyone who is both not happy and not old is either calm or not rich and vice versa.
Everyone who is both quiet and rich is both strong and not funny and vice versa.
Everyone who is both not curious and not tall is strong and vice versa.
If mary is both not old and not tall then someone is both not funny and generous.
Everyone who is both wise and old is either not creative or not rich and vice versa.
Everyone who is both calm and not rich is not wise.
Everyone who is either strong or kind is not calm or not happy and vice versa.
If someone is both humble and not brave then lucy is brave or kind and vice versa.
Someone is strong or not creative.
John is both not wise and tall.
Someone is not patient or creative.
Someone is patient.
Paul is both wise and curious.
Alice is funny. | Lucy is curious. | contradiction | (![X]:((~quiet(X)&rich(X))=>~humble(X)))&
(![X]:(~rich(X)<=>brave(X)))&
(((~wise(fred)&~humble(fred)))=>(?[X]:((old(X)|brave(X)))))&
(![X]:((calm(X)<~>~wise(X))<=>(~kind(X)|~old(X))))&
(![X]:((creative(X)&calm(X))=>(~patient(X)|patient(X))))&
(![X]:((~funny(X)&~calm(X))<=>(~funny(X)&~curious(X))))&
(![X]:((~patient(X)|humble(X))<=>~creative(X)))&
(![X]:((~happy(X)&~old(X))<=>(calm(X)<~>~rich(X))))&
(![X]:((quiet(X)&rich(X))<=>(strong(X)&~funny(X))))&
(![X]:((~curious(X)&~tall(X))<=>strong(X)))&
(((~old(mary)&~tall(mary)))=>(?[X]:((~funny(X)&generous(X)))))&
(![X]:((wise(X)&old(X))<=>(~creative(X)<~>~rich(X))))&
(![X]:((calm(X)&~rich(X))=>~wise(X)))&
(![X]:((strong(X)<~>kind(X))<=>(~calm(X)|~happy(X))))&
((?[X]:((humble(X)&~brave(X))))<=>((brave(lucy)|kind(lucy))))&
(?[X]:((strong(X)|~creative(X))))&
((~wise(john)&tall(john)))&
(?[X]:((~patient(X)|creative(X))))&
(?[X]:(patient(X)))&
((wise(paul)&curious(paul)))&
(funny(alice)) | curious(lucy) | [
"p0",
"p1",
"p3",
"p6",
"p7",
"p8",
"p9",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8503379465818576642528670
% SZS output start Proof for 8503379465818576642528670
1. ! [X0] : ((rich(X0) & ~quiet(X0)) => ~humble(X0)) [input p0]
2. ! [X0] : (~rich(X0) <=> brave(X0)) [input p1]
4. ! [X0] : ((calm(X0) <~> ~wise(X0)) <=> (~old(X0) | ~kind(X0))) [input p3]
7. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~creative(X0)) [input p6]
8. ! [X0] : ((~old(X0) & ~happy(X0)) <=> (calm(X0) <~> ~rich(X0))) [input p7]
9. ! [X0] : ((rich(X0) & quiet(X0)) <=> (~funny(X0) & strong(X0))) [input p8]
10. ! [X0] : ((~tall(X0) & ~curious(X0)) <=> strong(X0)) [input p9]
12. ! [X0] : ((old(X0) & wise(X0)) <=> (~creative(X0) <~> ~rich(X0))) [input p11]
14. ! [X0] : ((strong(X0) <~> kind(X0)) <=> (~happy(X0) | ~calm(X0))) [input p13]
15. ? [X0] : (~brave(X0) & humble(X0)) <=> (kind(lucy) | brave(lucy)) [input p14]
22. curious(lucy) [input hypothesis]
24. ! [X0] : (~humble(X0) | (~rich(X0) | quiet(X0))) [ennf transformation 1]
25. ! [X0] : (~humble(X0) | ~rich(X0) | quiet(X0)) [flattening 24]
34. ! [X0] : ((~rich(X0) | ~brave(X0)) & (brave(X0) | rich(X0))) [nnf transformation 2]
37. ! [X0] : ((((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (old(X0) & kind(X0))) & ((~old(X0) | ~kind(X0)) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))))) [nnf transformation 4]
38. ! [X0] : ((((wise(X0) | ~calm(X0)) & (~wise(X0) | calm(X0))) | (old(X0) & kind(X0))) & (~old(X0) | ~kind(X0) | ((calm(X0) | wise(X0)) & (~wise(X0) | ~calm(X0))))) [flattening 37]
41. ! [X0] : (((humble(X0) | ~patient(X0)) | creative(X0)) & (~creative(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 7]
42. ! [X0] : ((humble(X0) | ~patient(X0) | creative(X0)) & (~creative(X0) | (~humble(X0) & patient(X0)))) [flattening 41]
43. ! [X0] : (((~old(X0) & ~happy(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | (old(X0) | happy(X0)))) [nnf transformation 8]
44. ! [X0] : (((~old(X0) & ~happy(X0)) | ((calm(X0) | rich(X0)) & (~rich(X0) | ~calm(X0)))) & (((rich(X0) | ~calm(X0)) & (~rich(X0) | calm(X0))) | old(X0) | happy(X0))) [flattening 43]
45. ! [X0] : (((rich(X0) & quiet(X0)) | (funny(X0) | ~strong(X0))) & ((~funny(X0) & strong(X0)) | (~rich(X0) | ~quiet(X0)))) [nnf transformation 9]
46. ! [X0] : (((rich(X0) & quiet(X0)) | funny(X0) | ~strong(X0)) & ((~funny(X0) & strong(X0)) | ~rich(X0) | ~quiet(X0))) [flattening 45]
47. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~strong(X0)) & (strong(X0) | (tall(X0) | curious(X0)))) [nnf transformation 10]
48. ! [X0] : (((~tall(X0) & ~curious(X0)) | ~strong(X0)) & (strong(X0) | tall(X0) | curious(X0))) [flattening 47]
51. ! [X0] : (((old(X0) & wise(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | (~old(X0) | ~wise(X0)))) [nnf transformation 12]
52. ! [X0] : (((old(X0) & wise(X0)) | ((~creative(X0) | rich(X0)) & (~rich(X0) | creative(X0)))) & (((rich(X0) | creative(X0)) & (~rich(X0) | ~creative(X0))) | ~old(X0) | ~wise(X0))) [flattening 51]
53. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (happy(X0) & calm(X0))) & ((~happy(X0) | ~calm(X0)) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [nnf transformation 14]
54. ! [X0] : ((((~kind(X0) | ~strong(X0)) & (kind(X0) | strong(X0))) | (happy(X0) & calm(X0))) & (~happy(X0) | ~calm(X0) | ((strong(X0) | ~kind(X0)) & (kind(X0) | ~strong(X0))))) [flattening 53]
55. (? [X0] : (~brave(X0) & humble(X0)) | (~kind(lucy) & ~brave(lucy))) & ((kind(lucy) | brave(lucy)) | ! [X0] : (brave(X0) | ~humble(X0))) [nnf transformation 15]
56. (? [X0] : (~brave(X0) & humble(X0)) | (~kind(lucy) & ~brave(lucy))) & (kind(lucy) | brave(lucy) | ! [X0] : (brave(X0) | ~humble(X0))) [flattening 55]
57. (? [X0] : (~brave(X0) & humble(X0)) | (~kind(lucy) & ~brave(lucy))) & (kind(lucy) | brave(lucy) | ! [X1] : (brave(X1) | ~humble(X1))) [rectify 56]
58. ? [X0] : (~brave(X0) & humble(X0)) => (~brave(sK2) & humble(sK2)) [choice axiom]
59. ((~brave(sK2) & humble(sK2)) | (~kind(lucy) & ~brave(lucy))) & (kind(lucy) | brave(lucy) | ! [X1] : (brave(X1) | ~humble(X1))) [skolemisation 57,58]
66. ~humble(X0) | ~rich(X0) | quiet(X0) [cnf transformation 25]
67. brave(X0) | rich(X0) [cnf transformation 34]
72. ~wise(X0) | calm(X0) | kind(X0) [cnf transformation 38]
82. ~creative(X0) | ~humble(X0) [cnf transformation 42]
86. ~happy(X0) | ~rich(X0) | ~calm(X0) [cnf transformation 44]
88. ~calm(X0) | ~rich(X0) | ~old(X0) [cnf transformation 44]
90. ~rich(X0) | strong(X0) | ~quiet(X0) [cnf transformation 46]
95. ~strong(X0) | ~curious(X0) [cnf transformation 48]
100. ~rich(X0) | wise(X0) | creative(X0) [cnf transformation 52]
102. ~rich(X0) | old(X0) | creative(X0) [cnf transformation 52]
107. strong(X0) | kind(X0) | calm(X0) [cnf transformation 54]
108. strong(X0) | kind(X0) | happy(X0) [cnf transformation 54]
109. ~strong(X0) | ~kind(X0) | calm(X0) [cnf transformation 54]
112. humble(sK2) | ~brave(lucy) [cnf transformation 59]
113. humble(sK2) | ~kind(lucy) [cnf transformation 59]
114. ~brave(sK2) | ~brave(lucy) [cnf transformation 59]
115. ~brave(sK2) | ~kind(lucy) [cnf transformation 59]
124. curious(lucy) [cnf transformation 22]
156. 8 <=> kind(lucy) [avatar definition]
158. ~kind(lucy) <- (~8) [avatar component clause 156]
160. 9 <=> brave(sK2) [avatar definition]
162. ~brave(sK2) <- (~9) [avatar component clause 160]
163. ~8 | ~9 [avatar split clause 115,160,156]
165. 10 <=> brave(lucy) [avatar definition]
167. ~brave(lucy) <- (~10) [avatar component clause 165]
168. ~10 | ~9 [avatar split clause 114,160,165]
170. 11 <=> humble(sK2) [avatar definition]
172. humble(sK2) <- (11) [avatar component clause 170]
173. ~8 | 11 [avatar split clause 113,170,156]
174. ~10 | 11 [avatar split clause 112,170,165]
197. rich(sK2) <- (~9) [resolution 67,162]
200. ~rich(sK2) | quiet(sK2) <- (11) [resolution 66,172]
201. quiet(sK2) <- (~9, 11) [subsumption resolution 200,197]
227. 21 <=> calm(lucy) [avatar definition]
229. calm(lucy) <- (21) [avatar component clause 227]
261. strong(sK2) | ~quiet(sK2) <- (~9) [resolution 90,197]
262. strong(sK2) <- (~9, 11) [subsumption resolution 261,201]
289. 32 <=> rich(lucy) [avatar definition]
290. rich(lucy) <- (32) [avatar component clause 289]
297. wise(sK2) | creative(sK2) <- (~9) [resolution 100,197]
300. 33 <=> creative(sK2) [avatar definition]
302. creative(sK2) <- (33) [avatar component clause 300]
304. 34 <=> wise(sK2) [avatar definition]
306. wise(sK2) <- (34) [avatar component clause 304]
307. 33 | 34 | 9 [avatar split clause 297,160,304,300]
318. calm(sK2) | kind(sK2) <- (34) [resolution 306,72]
320. 37 <=> old(sK2) [avatar definition]
324. 38 <=> calm(sK2) [avatar definition]
326. calm(sK2) <- (38) [avatar component clause 324]
329. 39 <=> kind(sK2) [avatar definition]
332. 39 | 38 | ~34 [avatar split clause 318,304,324,329]
350. old(sK2) | creative(sK2) <- (~9) [resolution 102,197]
352. 33 | 37 | 9 [avatar split clause 350,160,320,300]
380. ~curious(X2) | calm(X2) | kind(X2) [resolution 107,95]
396. ~curious(X2) | happy(X2) | kind(X2) [resolution 108,95]
405. ~kind(sK2) | calm(sK2) <- (~9, 11) [resolution 109,262]
509. calm(lucy) | kind(lucy) [resolution 380,124]
513. happy(lucy) | kind(lucy) [resolution 396,124]
516. ~rich(sK2) | ~old(sK2) <- (38) [resolution 326,88]
520. ~old(sK2) <- (~9, 38) [subsumption resolution 516,197]
524. ~37 | 9 | ~38 [avatar split clause 520,324,160,320]
543. ~humble(sK2) <- (33) [resolution 302,82]
545. $false <- (11, 33) [subsumption resolution 543,172]
546. ~11 | ~33 [avatar contradiction clause 545]
549. 38 | ~39 | 9 | ~11 [avatar split clause 405,170,160,329,324]
551. 64 <=> happy(lucy) [avatar definition]
553. happy(lucy) <- (64) [avatar component clause 551]
554. 8 | 64 [avatar split clause 513,551,156]
566. calm(lucy) <- (~8) [subsumption resolution 509,158]
567. 21 | 8 [avatar split clause 566,156,227]
569. rich(lucy) <- (~10) [resolution 167,67]
572. 32 | 10 [avatar split clause 569,165,289]
615. ~rich(lucy) | ~calm(lucy) <- (64) [resolution 553,86]
616. ~calm(lucy) <- (32, 64) [subsumption resolution 615,290]
617. $false <- (21, 32, 64) [subsumption resolution 616,229]
618. ~21 | ~32 | ~64 [avatar contradiction clause 617]
619. $false [avatar sat refutation 163,168,173,174,307,332,352,524,546,549,554,567,572,618]
% SZS output end Proof for 8503379465818576642528670
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and not generous is either humble or brave.
If mary is not rich or kind then alice is both wise and rich.
Everyone who is not happy or not humble is both not kind and wise and vice versa.
If someone is patient or not wise then someone is not old or not generous.
If someone is happy then alice is either not kind or not brave and vice versa.
Everyone who is patient is not wise or patient and vice versa.
If alice is not funny then fred is curious or happy and vice versa.
Everyone who is wise is not strong or not patient.
Everyone who is not kind is brave and vice versa.
If someone is not generous or not patient then someone is humble or not happy and vice versa.
If someone is either not brave or wise then john is not creative or humble and vice versa.
If someone is both humble and creative then someone is funny or generous and vice versa.
Everyone who is either calm or strong is either strong or not happy and vice versa.
If someone is not generous then john is brave or not creative and vice versa.
Everyone who is funny or brave is creative or not rich.
Everyone who is both tall and brave is rich and vice versa.
Someone is calm.
Paul is strong.
Someone is not old or not rich.
Someone is both creative and old.
Someone is not generous. | Fred is not generous. | neutral | (![X]:((kind(X)&~generous(X))=>(humble(X)<~>brave(X))))&
(((~rich(mary)|kind(mary)))=>((wise(alice)&rich(alice))))&
(![X]:((~happy(X)|~humble(X))<=>(~kind(X)&wise(X))))&
((?[X]:((patient(X)|~wise(X))))=>(?[X]:((~old(X)|~generous(X)))))&
((?[X]:(happy(X)))<=>((~kind(alice)<~>~brave(alice))))&
(![X]:(patient(X)<=>(~wise(X)|patient(X))))&
((~funny(alice))<=>((curious(fred)|happy(fred))))&
(![X]:(wise(X)=>(~strong(X)|~patient(X))))&
(![X]:(~kind(X)<=>brave(X)))&
((?[X]:((~generous(X)|~patient(X))))<=>(?[X]:((humble(X)|~happy(X)))))&
((?[X]:((~brave(X)<~>wise(X))))<=>((~creative(john)|humble(john))))&
((?[X]:((humble(X)&creative(X))))<=>(?[X]:((funny(X)|generous(X)))))&
(![X]:((calm(X)<~>strong(X))<=>(strong(X)<~>~happy(X))))&
((?[X]:(~generous(X)))<=>((brave(john)|~creative(john))))&
(![X]:((funny(X)|brave(X))=>(creative(X)|~rich(X))))&
(![X]:((tall(X)&brave(X))<=>rich(X)))&
(?[X]:(calm(X)))&
(strong(paul))&
(?[X]:((~old(X)|~rich(X))))&
(?[X]:((creative(X)&old(X))))&
(?[X]:(~generous(X))) | ~generous(fred) | [] | null | 0 |
If susan is not kind then john is either quiet or not calm. Everyone who is creative is humble and vice versa. Everyone who is both kind and not happy is either not happy or rich and vice versa. Everyone who is not quiet or not brave is calm or not wise. Everyone who is not tall or tall is brave and vice versa. If john is either quiet or not tall then someone is not old or happy and vice versa. If alice is creative then mary is curious and vice versa. Everyone who is quiet or generous is not curious. Everyone who is not kind is both not brave and funny. If someone is either humble or not tall then susan is both brave and patient and vice versa. If someone is wise or rich then someone is either old or not calm and vice versa. Everyone who is rich or funny is not quiet and vice versa. If someone is either not calm or not tall then mary is both not rich and tall and vice versa. If fred is both patient and calm then john is creative. Everyone who is not rich or rich is either patient or quiet. Everyone who is not tall is not quiet or not wise. John is either not generous or happy. Someone is either not generous or not strong. Someone is humble. Someone is either not brave or not curious. John is both not patient and creative. Someone is either old or patient. John is either not quiet or generous. Someone is either not brave or not happy. | John is tall. | entailment | ((~kind(susan))=>((quiet(john)<~>~calm(john))))&
(![X]:(creative(X)<=>humble(X)))&
(![X]:((kind(X)&~happy(X))<=>(~happy(X)<~>rich(X))))&
(![X]:((~quiet(X)|~brave(X))=>(calm(X)|~wise(X))))&
(![X]:((~tall(X)|tall(X))<=>brave(X)))&
(((quiet(john)<~>~tall(john)))<=>(?[X]:((~old(X)|happy(X)))))&
((creative(alice))<=>(curious(mary)))&
(![X]:((quiet(X)|generous(X))=>~curious(X)))&
(![X]:(~kind(X)=>(~brave(X)&funny(X))))&
((?[X]:((humble(X)<~>~tall(X))))<=>((brave(susan)&patient(susan))))&
((?[X]:((wise(X)|rich(X))))<=>(?[X]:((old(X)<~>~calm(X)))))&
(![X]:((rich(X)|funny(X))<=>~quiet(X)))&
((?[X]:((~calm(X)<~>~tall(X))))<=>((~rich(mary)&tall(mary))))&
(((patient(fred)&calm(fred)))=>(creative(john)))&
(![X]:((~rich(X)|rich(X))=>(patient(X)<~>quiet(X))))&
(![X]:(~tall(X)=>(~quiet(X)|~wise(X))))&
((~generous(john)<~>happy(john)))&
(?[X]:((~generous(X)<~>~strong(X))))&
(?[X]:(humble(X)))&
(?[X]:((~brave(X)<~>~curious(X))))&
((~patient(john)&creative(john)))&
(?[X]:((old(X)<~>patient(X))))&
((~quiet(john)<~>generous(john)))&
(?[X]:((~brave(X)<~>~happy(X)))) | tall(john) | [
"p5",
"p11",
"p14",
"p16",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 9037231298409978831510213
% SZS output start Proof for 9037231298409978831510213
6. (quiet(john) <~> ~tall(john)) <=> ? [X0] : (happy(X0) | ~old(X0)) [input p5]
12. ! [X0] : ((funny(X0) | rich(X0)) <=> ~quiet(X0)) [input p11]
15. ! [X0] : ((rich(X0) | ~rich(X0)) => (patient(X0) <~> quiet(X0))) [input p14]
17. ~generous(john) <~> happy(john) [input p16]
21. creative(john) & ~patient(john) [input p20]
23. ~quiet(john) <~> generous(john) [input p22]
25. ~tall(john) [input hypothesis]
34. ! [X0] : ((patient(X0) <~> quiet(X0)) | (~rich(X0) & rich(X0))) [ennf transformation 15]
43. (((tall(john) | ~quiet(john)) & (~tall(john) | quiet(john))) | ! [X0] : (~happy(X0) & old(X0))) & (? [X0] : (happy(X0) | ~old(X0)) | ((quiet(john) | tall(john)) & (~tall(john) | ~quiet(john)))) [nnf transformation 6]
44. (((tall(john) | ~quiet(john)) & (~tall(john) | quiet(john))) | ! [X0] : (~happy(X0) & old(X0))) & (? [X1] : (happy(X1) | ~old(X1)) | ((quiet(john) | tall(john)) & (~tall(john) | ~quiet(john)))) [rectify 43]
45. ? [X1] : (happy(X1) | ~old(X1)) => (happy(sK0) | ~old(sK0)) [choice axiom]
46. (((tall(john) | ~quiet(john)) & (~tall(john) | quiet(john))) | ! [X0] : (~happy(X0) & old(X0))) & ((happy(sK0) | ~old(sK0)) | ((quiet(john) | tall(john)) & (~tall(john) | ~quiet(john)))) [skolemisation 44,45]
58. ! [X0] : (((funny(X0) | rich(X0)) | quiet(X0)) & (~quiet(X0) | (~funny(X0) & ~rich(X0)))) [nnf transformation 12]
59. ! [X0] : ((funny(X0) | rich(X0) | quiet(X0)) & (~quiet(X0) | (~funny(X0) & ~rich(X0)))) [flattening 58]
65. ! [X0] : (((~quiet(X0) | ~patient(X0)) & (quiet(X0) | patient(X0))) | (~rich(X0) & rich(X0))) [nnf transformation 34]
66. (~happy(john) | generous(john)) & (happy(john) | ~generous(john)) [nnf transformation 17]
78. (~generous(john) | quiet(john)) & (generous(john) | ~quiet(john)) [nnf transformation 23]
102. tall(john) | ~quiet(john) | ~happy(X0) [cnf transformation 46]
121. ~rich(X0) | ~quiet(X0) [cnf transformation 59]
131. quiet(X0) | patient(X0) | rich(X0) [cnf transformation 65]
132. quiet(X0) | patient(X0) | ~rich(X0) [cnf transformation 65]
136. happy(john) | ~generous(john) [cnf transformation 66]
143. ~patient(john) [cnf transformation 21]
147. generous(john) | ~quiet(john) [cnf transformation 78]
151. ~tall(john) [cnf transformation 25]
159. 2 <=> quiet(john) [avatar definition]
171. 4 <=> ! [X0] : ~happy(X0) [avatar definition]
172. ~happy(X0) <- (4) [avatar component clause 171]
174. 5 <=> tall(john) [avatar definition]
177. 4 | ~2 | 5 [avatar split clause 102,174,159,171]
305. ~rich(X0) | patient(X0) [subsumption resolution 132,121]
306. patient(X0) | quiet(X0) [subsumption resolution 131,305]
308. 33 <=> generous(john) [avatar definition]
312. 34 <=> happy(john) [avatar definition]
313. happy(john) <- (34) [avatar component clause 312]
316. ~33 | 34 [avatar split clause 136,312,308]
340. ~2 | 33 [avatar split clause 147,308,159]
342. ~5 [avatar split clause 151,174]
351. quiet(john) [resolution 306,143]
356. 2 [avatar split clause 351,159]
362. $false <- (4, 34) [resolution 313,172]
363. ~4 | ~34 [avatar contradiction clause 362]
364. $false [avatar sat refutation 177,316,340,342,356,363]
% SZS output end Proof for 9037231298409978831510213
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old then fred is not generous or not rich and vice versa. If mary is generous then someone is both quiet and tall. Everyone who is calm or quiet is both not patient and creative and vice versa. Everyone who is not calm is not creative or not happy. Everyone who is not happy or not curious is both calm and not rich. Everyone who is both not curious and not old is either not calm or not funny and vice versa. Everyone who is either tall or not tall is either not brave or not quiet and vice versa. If someone is old or quiet then fred is rich or curious and vice versa. Everyone who is curious is either rich or humble and vice versa. Everyone who is both brave and tall is not tall or not curious. Everyone who is humble is either old or not patient and vice versa. Everyone who is not wise or not funny is either not humble or not brave and vice versa. If john is either not humble or not generous then alice is tall. If paul is both not generous and not funny then john is either creative or not brave. Someone is not wise or curious. Alice is creative. Paul is strong. Someone is not tall or kind. Someone is kind or tall. Someone is tall. | Alice is not funny. | contradiction | ((?[X]:(old(X)))<=>((~generous(fred)|~rich(fred))))&
((generous(mary))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((calm(X)|quiet(X))<=>(~patient(X)&creative(X))))&
(![X]:(~calm(X)=>(~creative(X)|~happy(X))))&
(![X]:((~happy(X)|~curious(X))=>(calm(X)&~rich(X))))&
(![X]:((~curious(X)&~old(X))<=>(~calm(X)<~>~funny(X))))&
(![X]:((tall(X)<~>~tall(X))<=>(~brave(X)<~>~quiet(X))))&
((?[X]:((old(X)|quiet(X))))<=>((rich(fred)|curious(fred))))&
(![X]:(curious(X)<=>(rich(X)<~>humble(X))))&
(![X]:((brave(X)&tall(X))=>(~tall(X)|~curious(X))))&
(![X]:(humble(X)<=>(old(X)<~>~patient(X))))&
(![X]:((~wise(X)|~funny(X))<=>(~humble(X)<~>~brave(X))))&
(((~humble(john)<~>~generous(john)))=>(tall(alice)))&
(((~generous(paul)&~funny(paul)))=>((creative(john)<~>~brave(john))))&
(?[X]:((~wise(X)|curious(X))))&
(creative(alice))&
(strong(paul))&
(?[X]:((~tall(X)|kind(X))))&
(?[X]:((kind(X)|tall(X))))&
(?[X]:(tall(X))) | ~funny(alice) | [
"p2",
"p3",
"p4",
"p5",
"p8",
"p10",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3655139078010507206392090
% SZS output start Proof for 3655139078010507206392090
3. ! [X0] : ((quiet(X0) | calm(X0)) <=> (creative(X0) & ~patient(X0))) [input p2]
4. ! [X0] : (~calm(X0) => (~happy(X0) | ~creative(X0))) [input p3]
5. ! [X0] : ((~curious(X0) | ~happy(X0)) => (~rich(X0) & calm(X0))) [input p4]
6. ! [X0] : ((~old(X0) & ~curious(X0)) <=> (~calm(X0) <~> ~funny(X0))) [input p5]
9. ! [X0] : (curious(X0) <=> (rich(X0) <~> humble(X0))) [input p8]
11. ! [X0] : (humble(X0) <=> (old(X0) <~> ~patient(X0))) [input p10]
16. creative(alice) [input p15]
21. ~funny(alice) [input hypothesis]
26. ! [X0] : ((~happy(X0) | ~creative(X0)) | calm(X0)) [ennf transformation 4]
27. ! [X0] : (~happy(X0) | ~creative(X0) | calm(X0)) [flattening 26]
28. ! [X0] : ((~rich(X0) & calm(X0)) | (curious(X0) & happy(X0))) [ennf transformation 5]
41. ! [X0] : (((quiet(X0) | calm(X0)) | (~creative(X0) | patient(X0))) & ((creative(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [nnf transformation 3]
42. ! [X0] : ((quiet(X0) | calm(X0) | ~creative(X0) | patient(X0)) & ((creative(X0) & ~patient(X0)) | (~quiet(X0) & ~calm(X0)))) [flattening 41]
43. ! [X0] : (((~old(X0) & ~curious(X0)) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) & (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | (old(X0) | curious(X0)))) [nnf transformation 6]
44. ! [X0] : (((~old(X0) & ~curious(X0)) | ((~calm(X0) | funny(X0)) & (~funny(X0) | calm(X0)))) & (((funny(X0) | calm(X0)) & (~funny(X0) | ~calm(X0))) | old(X0) | curious(X0))) [flattening 43]
51. ! [X0] : ((curious(X0) | ((rich(X0) | ~humble(X0)) & (humble(X0) | ~rich(X0)))) & (((~humble(X0) | ~rich(X0)) & (humble(X0) | rich(X0))) | ~curious(X0))) [nnf transformation 9]
52. ! [X0] : ((humble(X0) | ((old(X0) | patient(X0)) & (~patient(X0) | ~old(X0)))) & (((patient(X0) | ~old(X0)) & (~patient(X0) | old(X0))) | ~humble(X0))) [nnf transformation 11]
66. ~patient(X0) | ~calm(X0) [cnf transformation 42]
71. ~happy(X0) | ~creative(X0) | calm(X0) [cnf transformation 27]
72. happy(X0) | calm(X0) [cnf transformation 28]
75. ~rich(X0) | curious(X0) [cnf transformation 28]
79. ~curious(X0) | ~calm(X0) | funny(X0) [cnf transformation 44]
81. ~calm(X0) | ~old(X0) | funny(X0) [cnf transformation 44]
97. curious(X0) | rich(X0) | ~humble(X0) [cnf transformation 51]
102. humble(X0) | old(X0) | patient(X0) [cnf transformation 52]
114. creative(alice) [cnf transformation 16]
116. ~funny(alice) [cnf transformation 21]
179. ~humble(X0) | curious(X0) [subsumption resolution 97,75]
228. ~creative(X0) | calm(X0) | calm(X0) [resolution 71,72]
229. ~creative(X0) | calm(X0) [duplicate literal removal 228]
230. calm(alice) [resolution 229,114]
279. curious(X3) | patient(X3) | old(X3) [resolution 102,179]
469. patient(X1) | old(X1) | ~calm(X1) | funny(X1) [resolution 279,79]
472. patient(X1) | ~calm(X1) | funny(X1) [subsumption resolution 469,81]
473. ~calm(X1) | funny(X1) [subsumption resolution 472,66]
604. funny(alice) [resolution 473,230]
606. $false [subsumption resolution 604,116]
% SZS output end Proof for 3655139078010507206392090
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not tall and not creative then alice is both tall and not old. If someone is old or not brave then susan is not rich and vice versa. If someone is both wise and kind then someone is not happy and vice versa. Everyone who is not funny is not creative and vice versa. If someone is either brave or strong then someone is not brave or not quiet and vice versa. If someone is rich or not rich then john is not funny or funny. If someone is brave or strong then alice is not curious or tall and vice versa. Everyone who is not strong is funny and vice versa. Everyone who is either not wise or not generous is either humble or strong and vice versa. Everyone who is patient or humble is not funny or not humble. Everyone who is either kind or wise is rich or wise and vice versa. If someone is brave then someone is either not rich or creative and vice versa. Everyone who is either creative or not brave is both rich and not patient. If paul is both not brave and humble then susan is humble. Everyone who is brave or wise is not tall or not strong. Everyone who is either not calm or quiet is both not creative and kind and vice versa. Fred is generous. John is either not happy or not tall. Fred is not generous or humble. Mary is creative or wise. John is not tall or not curious. Someone is generous or rich. Lucy is either tall or old. Lucy is old or not creative. | Fred is tall. | contradiction | ((?[X]:((~tall(X)&~creative(X))))=>((tall(alice)&~old(alice))))&
((?[X]:((old(X)|~brave(X))))<=>(~rich(susan)))&
((?[X]:((wise(X)&kind(X))))<=>(?[X]:(~happy(X))))&
(![X]:(~funny(X)<=>~creative(X)))&
((?[X]:((brave(X)<~>strong(X))))<=>(?[X]:((~brave(X)|~quiet(X)))))&
((?[X]:((rich(X)|~rich(X))))=>((~funny(john)|funny(john))))&
((?[X]:((brave(X)|strong(X))))<=>((~curious(alice)|tall(alice))))&
(![X]:(~strong(X)<=>funny(X)))&
(![X]:((~wise(X)<~>~generous(X))<=>(humble(X)<~>strong(X))))&
(![X]:((patient(X)|humble(X))=>(~funny(X)|~humble(X))))&
(![X]:((kind(X)<~>wise(X))<=>(rich(X)|wise(X))))&
((?[X]:(brave(X)))<=>(?[X]:((~rich(X)<~>creative(X)))))&
(![X]:((creative(X)<~>~brave(X))=>(rich(X)&~patient(X))))&
(((~brave(paul)&humble(paul)))=>(humble(susan)))&
(![X]:((brave(X)|wise(X))=>(~tall(X)|~strong(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(~creative(X)&kind(X))))&
(generous(fred))&
((~happy(john)<~>~tall(john)))&
((~generous(fred)|humble(fred)))&
((creative(mary)|wise(mary)))&
((~tall(john)|~curious(john)))&
(?[X]:((generous(X)|rich(X))))&
((tall(lucy)<~>old(lucy)))&
((old(lucy)|~creative(lucy))) | tall(fred) | [
"p7",
"p8",
"p9",
"p14",
"p16",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2957024471148816449356910
% SZS output start Proof for 2957024471148816449356910
8. ! [X0] : (~strong(X0) <=> funny(X0)) [input p7]
9. ! [X0] : ((~wise(X0) <~> ~generous(X0)) <=> (humble(X0) <~> strong(X0))) [input p8]
10. ! [X0] : ((humble(X0) | patient(X0)) => (~humble(X0) | ~funny(X0))) [input p9]
15. ! [X0] : ((wise(X0) | brave(X0)) => (~strong(X0) | ~tall(X0))) [input p14]
17. generous(fred) [input p16]
19. humble(fred) | ~generous(fred) [input p18]
25. tall(fred) [input hypothesis]
29. ! [X0] : (humble(X0) => (~humble(X0) | ~funny(X0))) [pure predicate removal 10]
34. ! [X0] : ((~humble(X0) | ~funny(X0)) | ~humble(X0)) [ennf transformation 29]
35. ! [X0] : (~humble(X0) | ~funny(X0) | ~humble(X0)) [flattening 34]
39. ! [X0] : ((~strong(X0) | ~tall(X0)) | (~wise(X0) & ~brave(X0))) [ennf transformation 15]
40. ! [X0] : (~strong(X0) | ~tall(X0) | (~wise(X0) & ~brave(X0))) [flattening 39]
61. ! [X0] : ((~strong(X0) | ~funny(X0)) & (funny(X0) | strong(X0))) [nnf transformation 8]
62. ! [X0] : ((((generous(X0) | wise(X0)) & (~generous(X0) | ~wise(X0))) | ((humble(X0) | ~strong(X0)) & (strong(X0) | ~humble(X0)))) & (((~strong(X0) | ~humble(X0)) & (strong(X0) | humble(X0))) | ((~wise(X0) | generous(X0)) & (~generous(X0) | wise(X0))))) [nnf transformation 9]
99. strong(X0) | funny(X0) [cnf transformation 61]
103. ~humble(X0) | ~strong(X0) | ~generous(X0) | wise(X0) [cnf transformation 62]
109. ~humble(X0) | ~funny(X0) | ~humble(X0) [cnf transformation 35]
124. ~strong(X0) | ~tall(X0) | ~wise(X0) [cnf transformation 40]
131. generous(fred) [cnf transformation 17]
134. humble(fred) | ~generous(fred) [cnf transformation 19]
141. tall(fred) [cnf transformation 25]
144. ~humble(X0) | ~funny(X0) [duplicate literal removal 109]
299. humble(fred) [subsumption resolution 134,131]
347. ~funny(fred) [resolution 144,299]
458. ~strong(fred) | ~generous(fred) | wise(fred) [resolution 103,299]
460. ~strong(fred) | wise(fred) [subsumption resolution 458,131]
462. 62 <=> wise(fred) [avatar definition]
464. wise(fred) <- (62) [avatar component clause 462]
466. 63 <=> strong(fred) [avatar definition]
467. strong(fred) <- (63) [avatar component clause 466]
468. ~strong(fred) <- (~63) [avatar component clause 466]
469. 62 | ~63 [avatar split clause 460,466,462]
491. funny(fred) <- (~63) [resolution 468,99]
492. $false <- (~63) [subsumption resolution 491,347]
493. 63 [avatar contradiction clause 492]
513. ~tall(fred) | ~wise(fred) <- (63) [resolution 467,124]
516. ~wise(fred) <- (63) [subsumption resolution 513,141]
517. $false <- (62, 63) [subsumption resolution 516,464]
518. ~62 | ~63 [avatar contradiction clause 517]
520. $false [avatar sat refutation 469,493,518]
% SZS output end Proof for 2957024471148816449356910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either humble or not happy is both not old and kind.
Everyone who is both wise and happy is humble.
If someone is wise then someone is both generous and not quiet.
If john is either rich or creative then alice is either patient or curious and vice versa.
Everyone who is kind or not happy is strong and vice versa.
Everyone who is either tall or not humble is not strong or not brave and vice versa.
Everyone who is both not generous and not kind is happy or wise and vice versa.
If alice is not tall or not humble then lucy is not calm or brave.
If john is calm then someone is either calm or not old and vice versa.
Everyone who is funny is creative or not tall.
Everyone who is either not strong or quiet is tall and vice versa.
Everyone who is not quiet is curious.
Everyone who is both not funny and tall is both patient and quiet.
Everyone who is either not funny or not patient is both calm and wise.
If mary is wise or tall then someone is old or not curious and vice versa.
If susan is either rich or not brave then someone is both not wise and humble.
Paul is curious.
Susan is patient or not kind.
Lucy is not strong or happy.
Paul is either happy or rich.
Susan is not quiet.
Fred is not calm or tall.
Susan is either not quiet or old.
Mary is both not strong and quiet. | Mary is not old. | entailment | (![X]:((humble(X)<~>~happy(X))=>(~old(X)&kind(X))))&
(![X]:((wise(X)&happy(X))=>humble(X)))&
((?[X]:(wise(X)))=>(?[X]:((generous(X)&~quiet(X)))))&
(((rich(john)<~>creative(john)))<=>((patient(alice)<~>curious(alice))))&
(![X]:((kind(X)|~happy(X))<=>strong(X)))&
(![X]:((tall(X)<~>~humble(X))<=>(~strong(X)|~brave(X))))&
(![X]:((~generous(X)&~kind(X))<=>(happy(X)|wise(X))))&
(((~tall(alice)|~humble(alice)))=>((~calm(lucy)|brave(lucy))))&
((calm(john))<=>(?[X]:((calm(X)<~>~old(X)))))&
(![X]:(funny(X)=>(creative(X)|~tall(X))))&
(![X]:((~strong(X)<~>quiet(X))<=>tall(X)))&
(![X]:(~quiet(X)=>curious(X)))&
(![X]:((~funny(X)&tall(X))=>(patient(X)&quiet(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(calm(X)&wise(X))))&
(((wise(mary)|tall(mary)))<=>(?[X]:((old(X)|~curious(X)))))&
(((rich(susan)<~>~brave(susan)))=>(?[X]:((~wise(X)&humble(X)))))&
(curious(paul))&
((patient(susan)|~kind(susan)))&
((~strong(lucy)|happy(lucy)))&
((happy(paul)<~>rich(paul)))&
(~quiet(susan))&
((~calm(fred)|tall(fred)))&
((~quiet(susan)<~>old(susan)))&
((~strong(mary)&quiet(mary))) | ~old(mary) | [
"p0",
"p1",
"p4",
"p5",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5605722276639561976820009
% SZS output start Proof for 5605722276639561976820009
1. ! [X0] : ((humble(X0) <~> ~happy(X0)) => (kind(X0) & ~old(X0))) [input p0]
2. ! [X0] : ((happy(X0) & wise(X0)) => humble(X0)) [input p1]
5. ! [X0] : ((~happy(X0) | kind(X0)) <=> strong(X0)) [input p4]
6. ! [X0] : ((tall(X0) <~> ~humble(X0)) <=> (~brave(X0) | ~strong(X0))) [input p5]
15. (tall(mary) | wise(mary)) <=> ? [X0] : (~curious(X0) | old(X0)) [input p14]
24. quiet(mary) & ~strong(mary) [input p23]
25. old(mary) [input hypothesis]
27. ! [X0] : ((kind(X0) & ~old(X0)) | (humble(X0) <=> ~happy(X0))) [ennf transformation 1]
28. ! [X0] : (humble(X0) | (~happy(X0) | ~wise(X0))) [ennf transformation 2]
29. ! [X0] : (humble(X0) | ~happy(X0) | ~wise(X0)) [flattening 28]
40. ! [X0] : ((kind(X0) & ~old(X0)) | ((humble(X0) | happy(X0)) & (~happy(X0) | ~humble(X0)))) [nnf transformation 27]
45. ! [X0] : (((~happy(X0) | kind(X0)) | ~strong(X0)) & (strong(X0) | (happy(X0) & ~kind(X0)))) [nnf transformation 5]
46. ! [X0] : ((~happy(X0) | kind(X0) | ~strong(X0)) & (strong(X0) | (happy(X0) & ~kind(X0)))) [flattening 45]
47. ! [X0] : ((((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (brave(X0) & strong(X0))) & ((~brave(X0) | ~strong(X0)) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))))) [nnf transformation 6]
48. ! [X0] : ((((humble(X0) | ~tall(X0)) & (~humble(X0) | tall(X0))) | (brave(X0) & strong(X0))) & (~brave(X0) | ~strong(X0) | ((tall(X0) | humble(X0)) & (~humble(X0) | ~tall(X0))))) [flattening 47]
57. ((tall(mary) | wise(mary)) | ! [X0] : (curious(X0) & ~old(X0))) & (? [X0] : (~curious(X0) | old(X0)) | (~tall(mary) & ~wise(mary))) [nnf transformation 15]
58. (tall(mary) | wise(mary) | ! [X0] : (curious(X0) & ~old(X0))) & (? [X0] : (~curious(X0) | old(X0)) | (~tall(mary) & ~wise(mary))) [flattening 57]
59. (tall(mary) | wise(mary) | ! [X0] : (curious(X0) & ~old(X0))) & (? [X1] : (~curious(X1) | old(X1)) | (~tall(mary) & ~wise(mary))) [rectify 58]
60. ? [X1] : (~curious(X1) | old(X1)) => (~curious(sK2) | old(sK2)) [choice axiom]
61. (tall(mary) | wise(mary) | ! [X0] : (curious(X0) & ~old(X0))) & ((~curious(sK2) | old(sK2)) | (~tall(mary) & ~wise(mary))) [skolemisation 59,60]
67. ~old(X0) | ~happy(X0) | ~humble(X0) [cnf transformation 40]
71. ~wise(X0) | ~happy(X0) | humble(X0) [cnf transformation 29]
83. strong(X0) | happy(X0) [cnf transformation 46]
89. ~tall(X0) | humble(X0) | strong(X0) [cnf transformation 48]
116. tall(mary) | wise(mary) | ~old(X0) [cnf transformation 61]
131. ~strong(mary) [cnf transformation 24]
133. old(mary) [cnf transformation 25]
215. 18 <=> wise(mary) [avatar definition]
217. wise(mary) <- (18) [avatar component clause 215]
219. 19 <=> tall(mary) [avatar definition]
221. tall(mary) <- (19) [avatar component clause 219]
224. 20 <=> ! [X0] : ~old(X0) [avatar definition]
225. ~old(X0) <- (20) [avatar component clause 224]
226. 20 | 18 | 19 [avatar split clause 116,219,215,224]
287. happy(mary) [resolution 83,131]
293. ~happy(mary) | ~humble(mary) [resolution 67,133]
294. ~humble(mary) [subsumption resolution 293,287]
333. ~happy(mary) | humble(mary) <- (18) [resolution 71,217]
334. humble(mary) <- (18) [subsumption resolution 333,287]
335. $false <- (18) [subsumption resolution 334,294]
336. ~18 [avatar contradiction clause 335]
339. humble(mary) | strong(mary) <- (19) [resolution 89,221]
340. strong(mary) <- (19) [subsumption resolution 339,294]
341. $false <- (19) [subsumption resolution 340,131]
342. ~19 [avatar contradiction clause 341]
347. $false <- (20) [resolution 225,133]
348. ~20 [avatar contradiction clause 347]
349. $false [avatar sat refutation 226,336,342,348]
% SZS output end Proof for 5605722276639561976820009
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either humble or old then lucy is either rich or generous. Everyone who is both happy and kind is strong. Everyone who is curious is both not kind and funny and vice versa. If someone is either happy or generous then lucy is wise. If paul is either rich or not tall then someone is either not calm or generous. Everyone who is curious is wise and vice versa. Everyone who is funny is either patient or funny. If someone is either generous or funny then lucy is both generous and creative. If susan is either not rich or not generous then john is both not brave and curious. If lucy is not strong then someone is humble or not creative. Everyone who is both not brave and strong is both tall and wise. If paul is generous or tall then mary is either brave or kind. Everyone who is both not patient and not generous is not humble or not kind. If mary is both wise and generous then paul is both rich and not kind and vice versa. Everyone who is not generous is either not old or not rich. If someone is not funny then susan is both brave and humble. Fred is both tall and generous. Someone is either brave or patient. Susan is either not old or not rich. Someone is either not humble or humble. Someone is creative or not brave. Someone is funny. Someone is both curious and not brave. | Susan is not rich. | neutral | (((humble(fred)<~>old(fred)))=>((rich(lucy)<~>generous(lucy))))&
(![X]:((happy(X)&kind(X))=>strong(X)))&
(![X]:(curious(X)<=>(~kind(X)&funny(X))))&
((?[X]:((happy(X)<~>generous(X))))=>(wise(lucy)))&
(((rich(paul)<~>~tall(paul)))=>(?[X]:((~calm(X)<~>generous(X)))))&
(![X]:(curious(X)<=>wise(X)))&
(![X]:(funny(X)=>(patient(X)<~>funny(X))))&
((?[X]:((generous(X)<~>funny(X))))=>((generous(lucy)&creative(lucy))))&
(((~rich(susan)<~>~generous(susan)))=>((~brave(john)&curious(john))))&
((~strong(lucy))=>(?[X]:((humble(X)|~creative(X)))))&
(![X]:((~brave(X)&strong(X))=>(tall(X)&wise(X))))&
(((generous(paul)|tall(paul)))=>((brave(mary)<~>kind(mary))))&
(![X]:((~patient(X)&~generous(X))=>(~humble(X)|~kind(X))))&
(((wise(mary)&generous(mary)))<=>((rich(paul)&~kind(paul))))&
(![X]:(~generous(X)=>(~old(X)<~>~rich(X))))&
((?[X]:(~funny(X)))=>((brave(susan)&humble(susan))))&
((tall(fred)&generous(fred)))&
(?[X]:((brave(X)<~>patient(X))))&
((~old(susan)<~>~rich(susan)))&
(?[X]:((~humble(X)<~>humble(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:(funny(X)))&
(?[X]:((curious(X)&~brave(X)))) | ~rich(susan) | [] | null | 0 |
Everyone who is strong is either happy or not old.
Everyone who is not patient is both rich and curious.
Everyone who is either happy or tall is not creative or creative and vice versa.
Everyone who is both not humble and tall is either patient or old and vice versa.
If someone is wise then susan is both old and tall.
Everyone who is not quiet is not tall or not generous and vice versa.
Everyone who is either not brave or curious is either not creative or wise and vice versa.
Everyone who is both not strong and not patient is both rich and kind.
If someone is not generous or kind then john is strong and vice versa.
Everyone who is both not tall and not old is either not rich or brave and vice versa.
Everyone who is curious is either quiet or humble and vice versa.
If lucy is brave or not brave then john is either calm or not patient and vice versa.
Everyone who is not happy or funny is both calm and funny and vice versa.
Everyone who is calm or not tall is not old and vice versa.
Everyone who is not kind is humble or quiet.
Everyone who is not rich or not brave is not patient or funny and vice versa.
Someone is both quiet and kind.
Someone is kind.
Someone is both curious and not creative.
John is both not quiet and not rich.
Someone is brave.
Someone is humble or not wise.
Lucy is both not kind and not strong. | John is wise. | contradiction | (![X]:(strong(X)=>(happy(X)<~>~old(X))))&
(![X]:(~patient(X)=>(rich(X)&curious(X))))&
(![X]:((happy(X)<~>tall(X))<=>(~creative(X)|creative(X))))&
(![X]:((~humble(X)&tall(X))<=>(patient(X)<~>old(X))))&
((?[X]:(wise(X)))=>((old(susan)&tall(susan))))&
(![X]:(~quiet(X)<=>(~tall(X)|~generous(X))))&
(![X]:((~brave(X)<~>curious(X))<=>(~creative(X)<~>wise(X))))&
(![X]:((~strong(X)&~patient(X))=>(rich(X)&kind(X))))&
((?[X]:((~generous(X)|kind(X))))<=>(strong(john)))&
(![X]:((~tall(X)&~old(X))<=>(~rich(X)<~>brave(X))))&
(![X]:(curious(X)<=>(quiet(X)<~>humble(X))))&
(((brave(lucy)|~brave(lucy)))<=>((calm(john)<~>~patient(john))))&
(![X]:((~happy(X)|funny(X))<=>(calm(X)&funny(X))))&
(![X]:((calm(X)|~tall(X))<=>~old(X)))&
(![X]:(~kind(X)=>(humble(X)|quiet(X))))&
(![X]:((~rich(X)|~brave(X))<=>(~patient(X)|funny(X))))&
(?[X]:((quiet(X)&kind(X))))&
(?[X]:(kind(X)))&
(?[X]:((curious(X)&~creative(X))))&
((~quiet(john)&~rich(john)))&
(?[X]:(brave(X)))&
(?[X]:((humble(X)|~wise(X))))&
((~kind(lucy)&~strong(lucy))) | wise(john) | [
"p2",
"p4",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 4195188539595594337274573
% SZS output start Proof for 4195188539595594337274573
3. ! [X0] : ((happy(X0) <~> tall(X0)) <=> (creative(X0) | ~creative(X0))) [input p2]
5. ? [X0] : wise(X0) => (tall(susan) & old(susan)) [input p4]
13. ! [X0] : ((funny(X0) | ~happy(X0)) <=> (funny(X0) & calm(X0))) [input p12]
14. ! [X0] : ((~tall(X0) | calm(X0)) <=> ~old(X0)) [input p13]
24. wise(john) [input hypothesis]
27. (tall(susan) & old(susan)) | ! [X0] : ~wise(X0) [ennf transformation 5]
33. ! [X0] : ((((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~creative(X0) & creative(X0))) & ((creative(X0) | ~creative(X0)) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0))))) [nnf transformation 3]
34. ! [X0] : ((((~tall(X0) | ~happy(X0)) & (tall(X0) | happy(X0))) | (~creative(X0) & creative(X0))) & (creative(X0) | ~creative(X0) | ((happy(X0) | ~tall(X0)) & (tall(X0) | ~happy(X0))))) [flattening 33]
49. ! [X0] : (((funny(X0) | ~happy(X0)) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | (~funny(X0) & happy(X0)))) [nnf transformation 13]
50. ! [X0] : ((funny(X0) | ~happy(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | (~funny(X0) & happy(X0)))) [flattening 49]
51. ! [X0] : (((~tall(X0) | calm(X0)) | old(X0)) & (~old(X0) | (tall(X0) & ~calm(X0)))) [nnf transformation 14]
52. ! [X0] : ((~tall(X0) | calm(X0) | old(X0)) & (~old(X0) | (tall(X0) & ~calm(X0)))) [flattening 51]
73. ~tall(X0) | ~happy(X0) | creative(X0) [cnf transformation 34]
74. ~tall(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 34]
81. old(susan) | ~wise(X0) [cnf transformation 27]
115. calm(X0) | happy(X0) [cnf transformation 50]
120. ~calm(X0) | ~old(X0) [cnf transformation 52]
121. ~old(X0) | tall(X0) [cnf transformation 52]
139. wise(john) [cnf transformation 24]
140. ~tall(X0) | ~happy(X0) [subsumption resolution 73,74]
143. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
144. ~wise(X0) <- (1) [avatar component clause 143]
146. 2 <=> tall(susan) [avatar definition]
148. tall(susan) <- (2) [avatar component clause 146]
151. 3 <=> old(susan) [avatar definition]
153. old(susan) <- (3) [avatar component clause 151]
154. 1 | 3 [avatar split clause 81,151,143]
211. ~old(X0) | happy(X0) [resolution 120,115]
212. tall(susan) <- (3) [resolution 121,153]
213. ~happy(susan) <- (2) [resolution 140,148]
218. happy(susan) <- (3) [resolution 211,153]
219. $false <- (2, 3) [subsumption resolution 218,213]
220. ~2 | ~3 [avatar contradiction clause 219]
221. 2 | ~3 [avatar split clause 212,151,146]
222. $false <- (1) [resolution 144,139]
223. ~1 [avatar contradiction clause 222]
224. $false [avatar sat refutation 154,220,221,223]
% SZS output end Proof for 4195188539595594337274573
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is either not calm or not kind then someone is not generous and vice versa.
Everyone who is either quiet or not brave is not old or not calm and vice versa.
Everyone who is not rich or not calm is both not humble and happy.
If fred is kind then susan is both not calm and not patient.
If john is both patient and calm then someone is both wise and brave and vice versa.
Everyone who is tall is either not creative or kind and vice versa.
If someone is both not kind and not creative then someone is either not calm or not wise.
If john is both generous and not generous then mary is tall or rich.
Everyone who is wise is both happy and not generous and vice versa.
If someone is either not rich or not strong then someone is either not wise or calm and vice versa.
If someone is either not quiet or not strong then fred is either rich or old.
Everyone who is not rich or not happy is either not old or not kind.
If john is either generous or strong then john is creative and vice versa.
Everyone who is not wise or not generous is not calm or brave.
If alice is strong then someone is either not calm or wise and vice versa.
Everyone who is kind or brave is both not tall and not generous and vice versa.
Mary is both not calm and not old.
Fred is quiet.
Alice is either strong or creative.
John is either not calm or not wise.
Someone is not rich.
Mary is not quiet or not curious.
Fred is both not creative and not strong. | Alice is not old. | neutral | (((~calm(susan)<~>~kind(susan)))<=>(?[X]:(~generous(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~old(X)|~calm(X))))&
(![X]:((~rich(X)|~calm(X))=>(~humble(X)&happy(X))))&
((kind(fred))=>((~calm(susan)&~patient(susan))))&
(((patient(john)&calm(john)))<=>(?[X]:((wise(X)&brave(X)))))&
(![X]:(tall(X)<=>(~creative(X)<~>kind(X))))&
((?[X]:((~kind(X)&~creative(X))))=>(?[X]:((~calm(X)<~>~wise(X)))))&
(((generous(john)&~generous(john)))=>((tall(mary)|rich(mary))))&
(![X]:(wise(X)<=>(happy(X)&~generous(X))))&
((?[X]:((~rich(X)<~>~strong(X))))<=>(?[X]:((~wise(X)<~>calm(X)))))&
((?[X]:((~quiet(X)<~>~strong(X))))=>((rich(fred)<~>old(fred))))&
(![X]:((~rich(X)|~happy(X))=>(~old(X)<~>~kind(X))))&
(((generous(john)<~>strong(john)))<=>(creative(john)))&
(![X]:((~wise(X)|~generous(X))=>(~calm(X)|brave(X))))&
((strong(alice))<=>(?[X]:((~calm(X)<~>wise(X)))))&
(![X]:((kind(X)|brave(X))<=>(~tall(X)&~generous(X))))&
((~calm(mary)&~old(mary)))&
(quiet(fred))&
((strong(alice)<~>creative(alice)))&
((~calm(john)<~>~wise(john)))&
(?[X]:(~rich(X)))&
((~quiet(mary)|~curious(mary)))&
((~creative(fred)&~strong(fred))) | ~old(alice) | [] | null | 0 |
Everyone who is both not calm and humble is both not wise and quiet and vice versa.
If someone is not wise or not old then fred is either creative or not brave and vice versa.
If alice is not calm or not happy then john is patient.
Everyone who is not generous is quiet or not kind and vice versa.
If someone is happy then someone is either kind or funny and vice versa.
Everyone who is not curious is either not curious or funny and vice versa.
Everyone who is not happy is curious and vice versa.
If fred is patient or quiet then someone is both not generous and tall.
Everyone who is not curious or not funny is either not old or not quiet.
If someone is either calm or not brave then someone is both not calm and not brave and vice versa.
Everyone who is both quiet and not kind is both not creative and kind.
If someone is not tall then someone is both not strong and kind.
If lucy is calm or not quiet then alice is both calm and curious and vice versa.
Everyone who is not kind or strong is either not humble or patient and vice versa.
If someone is not rich then alice is calm.
Everyone who is either quiet or not calm is not humble or wise.
Lucy is not happy or not tall.
Someone is quiet.
Someone is not old or not generous.
Someone is either not wise or curious.
Lucy is rich or kind.
Someone is strong.
Someone is either old or not curious.
Lucy is not kind or tall. | Lucy is not old. | neutral | (![X]:((~calm(X)&humble(X))<=>(~wise(X)&quiet(X))))&
((?[X]:((~wise(X)|~old(X))))<=>((creative(fred)<~>~brave(fred))))&
(((~calm(alice)|~happy(alice)))=>(patient(john)))&
(![X]:(~generous(X)<=>(quiet(X)|~kind(X))))&
((?[X]:(happy(X)))<=>(?[X]:((kind(X)<~>funny(X)))))&
(![X]:(~curious(X)<=>(~curious(X)<~>funny(X))))&
(![X]:(~happy(X)<=>curious(X)))&
(((patient(fred)|quiet(fred)))=>(?[X]:((~generous(X)&tall(X)))))&
(![X]:((~curious(X)|~funny(X))=>(~old(X)<~>~quiet(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((~calm(X)&~brave(X)))))&
(![X]:((quiet(X)&~kind(X))=>(~creative(X)&kind(X))))&
((?[X]:(~tall(X)))=>(?[X]:((~strong(X)&kind(X)))))&
(((calm(lucy)|~quiet(lucy)))<=>((calm(alice)&curious(alice))))&
(![X]:((~kind(X)|strong(X))<=>(~humble(X)<~>patient(X))))&
((?[X]:(~rich(X)))=>(calm(alice)))&
(![X]:((quiet(X)<~>~calm(X))=>(~humble(X)|wise(X))))&
((~happy(lucy)|~tall(lucy)))&
(?[X]:(quiet(X)))&
(?[X]:((~old(X)|~generous(X))))&
(?[X]:((~wise(X)<~>curious(X))))&
((rich(lucy)|kind(lucy)))&
(?[X]:(strong(X)))&
(?[X]:((old(X)<~>~curious(X))))&
((~kind(lucy)|tall(lucy))) | ~old(lucy) | [] | null | 0 |
Subsets and Splits
No saved queries yet
Save your SQL queries to embed, download, and access them later. Queries will appear here once saved.