premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
listlengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
If someone is both not calm and old then someone is either rich or not tall. Everyone who is not old is not wise and vice versa. Everyone who is both not patient and not wise is funny and vice versa. Everyone who is not curious or funny is both not calm and wise. Everyone who is old or not strong is tall. Everyone who is either not old or not quiet is not curious. If alice is wise or quiet then someone is either tall or curious. Everyone who is not kind is both strong and calm. Everyone who is not creative is not brave and vice versa. Everyone who is both not quiet and not patient is patient or not calm. Everyone who is humble or quiet is either old or not happy. Everyone who is not funny is both rich and not wise. Everyone who is not funny is funny or patient and vice versa. Everyone who is not tall or happy is rich or strong. If someone is patient then fred is curious. John is both not creative and not old. Alice is kind. Someone is generous or patient. Susan is not curious or not strong. Someone is not kind. | Alice is not old. | entailment | ((?[X]:((~calm(X)&old(X))))=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(~old(X)<=>~wise(X)))&
(![X]:((~patient(X)&~wise(X))<=>funny(X)))&
(![X]:((~curious(X)|funny(X))=>(~calm(X)&wise(X))))&
(![X]:((old(X)|~strong(X))=>tall(X)))&
(![X]:((~old(X)<~>~quiet(X))=>~curious(X)))&
(((wise(alice)|quiet(alice)))=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:(~kind(X)=>(strong(X)&calm(X))))&
(![X]:(~creative(X)<=>~brave(X)))&
(![X]:((~quiet(X)&~patient(X))=>(patient(X)|~calm(X))))&
(![X]:((humble(X)|quiet(X))=>(old(X)<~>~happy(X))))&
(![X]:(~funny(X)=>(rich(X)&~wise(X))))&
(![X]:(~funny(X)<=>(funny(X)|patient(X))))&
(![X]:((~tall(X)|happy(X))=>(rich(X)|strong(X))))&
((?[X]:(patient(X)))=>(curious(fred)))&
((~creative(john)&~old(john)))&
(kind(alice))&
(?[X]:((generous(X)|patient(X))))&
((~curious(susan)|~strong(susan)))&
(?[X]:(~kind(X))) | ~old(alice) | [
"p1",
"p2",
"p3",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 87827793202660500206782
% SZS output start Proof for 87827793202660500206782
2. ! [X0] : (~old(X0) <=> ~wise(X0)) [input p1]
3. ! [X0] : ((~wise(X0) & ~patient(X0)) <=> funny(X0)) [input p2]
4. ! [X0] : ((funny(X0) | ~curious(X0)) => (wise(X0) & ~calm(X0))) [input p3]
12. ! [X0] : (~funny(X0) => (~wise(X0) & rich(X0))) [input p11]
21. old(alice) [input hypothesis]
29. ! [X0] : ((wise(X0) & ~calm(X0)) | (~funny(X0) & curious(X0))) [ennf transformation 4]
37. ! [X0] : ((~wise(X0) & rich(X0)) | funny(X0)) [ennf transformation 12]
45. ! [X0] : ((~old(X0) | wise(X0)) & (~wise(X0) | old(X0))) [nnf transformation 2]
46. ! [X0] : (((~wise(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | (wise(X0) | patient(X0)))) [nnf transformation 3]
47. ! [X0] : (((~wise(X0) & ~patient(X0)) | ~funny(X0)) & (funny(X0) | wise(X0) | patient(X0))) [flattening 46]
60. ~old(X0) | wise(X0) [cnf transformation 45]
63. ~wise(X0) | ~funny(X0) [cnf transformation 47]
67. wise(X0) | ~funny(X0) [cnf transformation 29]
82. ~wise(X0) | funny(X0) [cnf transformation 37]
93. old(alice) [cnf transformation 21]
110. ~funny(X0) [subsumption resolution 67,63]
131. ~wise(X0) [subsumption resolution 82,110]
146. wise(alice) [resolution 60,93]
147. $false [subsumption resolution 146,131]
% SZS output end Proof for 87827793202660500206782
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not strong is both not rich and not old.
Everyone who is strong is not strong or brave and vice versa.
Everyone who is either funny or creative is not calm or brave and vice versa.
Everyone who is both not tall and not brave is either not quiet or generous and vice versa.
If alice is not rich then someone is brave or creative.
Everyone who is not kind or tall is both tall and funny.
Everyone who is rich or not humble is both not curious and kind and vice versa.
If john is both not funny and not rich then someone is not quiet and vice versa.
If someone is curious then someone is wise.
Everyone who is not patient is either curious or not generous and vice versa.
Everyone who is both strong and not humble is both funny and old.
If lucy is funny then mary is rich and vice versa.
Everyone who is not quiet or creative is either not wise or not creative.
If someone is not creative then fred is both not tall and calm and vice versa.
If someone is calm then susan is not funny or happy and vice versa.
If someone is not patient or quiet then lucy is not patient or not rich and vice versa.
John is brave or happy.
Someone is not brave or calm.
Someone is patient or curious.
Someone is both strong and calm.
Fred is both quiet and humble.
Someone is either generous or quiet.
Paul is brave.
Paul is not funny. | Paul is not brave. | contradiction | (![X]:(~strong(X)=>(~rich(X)&~old(X))))&
(![X]:(strong(X)<=>(~strong(X)|brave(X))))&
(![X]:((funny(X)<~>creative(X))<=>(~calm(X)|brave(X))))&
(![X]:((~tall(X)&~brave(X))<=>(~quiet(X)<~>generous(X))))&
((~rich(alice))=>(?[X]:((brave(X)|creative(X)))))&
(![X]:((~kind(X)|tall(X))=>(tall(X)&funny(X))))&
(![X]:((rich(X)|~humble(X))<=>(~curious(X)&kind(X))))&
(((~funny(john)&~rich(john)))<=>(?[X]:(~quiet(X))))&
((?[X]:(curious(X)))=>(?[X]:(wise(X))))&
(![X]:(~patient(X)<=>(curious(X)<~>~generous(X))))&
(![X]:((strong(X)&~humble(X))=>(funny(X)&old(X))))&
((funny(lucy))<=>(rich(mary)))&
(![X]:((~quiet(X)|creative(X))=>(~wise(X)<~>~creative(X))))&
((?[X]:(~creative(X)))<=>((~tall(fred)&calm(fred))))&
((?[X]:(calm(X)))<=>((~funny(susan)|happy(susan))))&
((?[X]:((~patient(X)|quiet(X))))<=>((~patient(lucy)|~rich(lucy))))&
((brave(john)|happy(john)))&
(?[X]:((~brave(X)|calm(X))))&
(?[X]:((patient(X)|curious(X))))&
(?[X]:((strong(X)&calm(X))))&
((quiet(fred)&humble(fred)))&
(?[X]:((generous(X)<~>quiet(X))))&
(brave(paul))&
(~funny(paul)) | ~brave(paul) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 7009976444547412716554742
% SZS output start Proof for 7009976444547412716554742
2. ! [X0] : (strong(X0) <=> (brave(X0) | ~strong(X0))) [input p1]
25. ~brave(paul) [input hypothesis]
34. ! [X0] : ((strong(X0) | (~brave(X0) & strong(X0))) & ((brave(X0) | ~strong(X0)) | ~strong(X0))) [nnf transformation 2]
35. ! [X0] : ((strong(X0) | (~brave(X0) & strong(X0))) & (brave(X0) | ~strong(X0) | ~strong(X0))) [flattening 34]
81. brave(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 35]
82. strong(X0) | strong(X0) [cnf transformation 35]
143. ~brave(paul) [cnf transformation 25]
145. brave(X0) | ~strong(X0) [duplicate literal removal 81]
146. strong(X0) [duplicate literal removal 82]
147. brave(X0) [subsumption resolution 145,146]
262. $false [subsumption resolution 143,147]
% SZS output end Proof for 7009976444547412716554742
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is rich or not old then someone is both tall and humble.
Everyone who is humble or not happy is not creative and vice versa.
If lucy is both strong and not creative then someone is not rich or funny and vice versa.
Everyone who is old or creative is either not quiet or not rich.
Everyone who is funny or creative is either not creative or strong.
Everyone who is both not wise and patient is both not calm and not old.
Everyone who is both funny and old is funny or wise.
If john is both funny and calm then fred is funny or not rich and vice versa.
Everyone who is kind is wise.
Everyone who is happy is both curious and humble and vice versa.
Everyone who is calm or not kind is either kind or happy and vice versa.
Everyone who is old or tall is both kind and funny and vice versa.
Everyone who is both not patient and funny is both funny and not brave.
If mary is strong then paul is both not calm and not generous.
If someone is either not creative or not quiet then someone is either not brave or brave and vice versa.
Everyone who is not funny is not tall and vice versa.
Someone is not old or wise.
Someone is both kind and patient.
Lucy is not rich.
John is either not funny or not patient.
Someone is both humble and wise.
Alice is not strong or humble.
Someone is not happy.
Someone is calm. | Lucy is not funny. | entailment | (((rich(lucy)|~old(lucy)))=>(?[X]:((tall(X)&humble(X)))))&
(![X]:((humble(X)|~happy(X))<=>~creative(X)))&
(((strong(lucy)&~creative(lucy)))<=>(?[X]:((~rich(X)|funny(X)))))&
(![X]:((old(X)|creative(X))=>(~quiet(X)<~>~rich(X))))&
(![X]:((funny(X)|creative(X))=>(~creative(X)<~>strong(X))))&
(![X]:((~wise(X)&patient(X))=>(~calm(X)&~old(X))))&
(![X]:((funny(X)&old(X))=>(funny(X)|wise(X))))&
(((funny(john)&calm(john)))<=>((funny(fred)|~rich(fred))))&
(![X]:(kind(X)=>wise(X)))&
(![X]:(happy(X)<=>(curious(X)&humble(X))))&
(![X]:((calm(X)|~kind(X))<=>(kind(X)<~>happy(X))))&
(![X]:((old(X)|tall(X))<=>(kind(X)&funny(X))))&
(![X]:((~patient(X)&funny(X))=>(funny(X)&~brave(X))))&
((strong(mary))=>((~calm(paul)&~generous(paul))))&
((?[X]:((~creative(X)<~>~quiet(X))))<=>(?[X]:((~brave(X)<~>brave(X)))))&
(![X]:(~funny(X)<=>~tall(X)))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:((kind(X)&patient(X))))&
(~rich(lucy))&
((~funny(john)<~>~patient(john)))&
(?[X]:((humble(X)&wise(X))))&
((~strong(alice)|humble(alice)))&
(?[X]:(~happy(X)))&
(?[X]:(calm(X))) | ~funny(lucy) | [
"p2",
"p4",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 22840862132810594821159
% SZS output start Proof for 22840862132810594821159
3. (~creative(lucy) & strong(lucy)) <=> ? [X0] : (funny(X0) | ~rich(X0)) [input p2]
5. ! [X0] : ((creative(X0) | funny(X0)) => (~creative(X0) <~> strong(X0))) [input p4]
19. ~rich(lucy) [input p18]
25. funny(lucy) [input hypothesis]
35. ! [X0] : ((~creative(X0) <~> strong(X0)) | (~creative(X0) & ~funny(X0))) [ennf transformation 5]
43. ((~creative(lucy) & strong(lucy)) | ! [X0] : (~funny(X0) & rich(X0))) & (? [X0] : (funny(X0) | ~rich(X0)) | (creative(lucy) | ~strong(lucy))) [nnf transformation 3]
44. ((~creative(lucy) & strong(lucy)) | ! [X0] : (~funny(X0) & rich(X0))) & (? [X0] : (funny(X0) | ~rich(X0)) | creative(lucy) | ~strong(lucy)) [flattening 43]
45. ((~creative(lucy) & strong(lucy)) | ! [X0] : (~funny(X0) & rich(X0))) & (? [X1] : (funny(X1) | ~rich(X1)) | creative(lucy) | ~strong(lucy)) [rectify 44]
46. ? [X1] : (funny(X1) | ~rich(X1)) => (funny(sK1) | ~rich(sK1)) [choice axiom]
47. ((~creative(lucy) & strong(lucy)) | ! [X0] : (~funny(X0) & rich(X0))) & ((funny(sK1) | ~rich(sK1)) | creative(lucy) | ~strong(lucy)) [skolemisation 45,46]
49. ! [X0] : (((~strong(X0) | creative(X0)) & (strong(X0) | ~creative(X0))) | (~creative(X0) & ~funny(X0))) [nnf transformation 35]
81. strong(lucy) | rich(X0) [cnf transformation 47]
83. ~creative(lucy) | rich(X0) [cnf transformation 47]
91. ~funny(X0) | creative(X0) | ~strong(X0) [cnf transformation 49]
127. ~rich(lucy) [cnf transformation 19]
134. funny(lucy) [cnf transformation 25]
152. 3 <=> rich(lucy) [avatar definition]
154. ~rich(lucy) <- (~3) [avatar component clause 152]
166. 6 <=> creative(lucy) [avatar definition]
168. ~creative(lucy) <- (~6) [avatar component clause 166]
171. 7 <=> ! [X0] : rich(X0) [avatar definition]
172. rich(X0) <- (7) [avatar component clause 171]
173. 7 | ~6 [avatar split clause 83,166,171]
175. 8 <=> strong(lucy) [avatar definition]
177. strong(lucy) <- (8) [avatar component clause 175]
179. 7 | 8 [avatar split clause 81,175,171]
237. ~3 [avatar split clause 127,152]
253. $false <- (~3, 7) [subsumption resolution 154,172]
254. 3 | ~7 [avatar contradiction clause 253]
283. creative(lucy) | ~strong(lucy) [resolution 91,134]
286. ~strong(lucy) <- (~6) [subsumption resolution 283,168]
287. $false <- (~6, 8) [subsumption resolution 286,177]
288. 6 | ~8 [avatar contradiction clause 287]
307. $false [avatar sat refutation 173,179,237,254,288]
% SZS output end Proof for 22840862132810594821159
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not humble and not creative then someone is either funny or humble and vice versa.
Everyone who is either not curious or generous is not calm and vice versa.
Everyone who is rich is either not old or wise.
Everyone who is either wise or not wise is strong or quiet and vice versa.
If someone is not humble then paul is not calm or not tall.
Everyone who is not happy is either humble or not creative.
Everyone who is not calm is either not creative or kind.
Everyone who is not patient or not calm is either funny or not humble.
If someone is both generous and wise then paul is old or not kind.
Everyone who is both curious and not rich is not curious and vice versa.
Everyone who is not wise is humble and vice versa.
Everyone who is either not creative or creative is tall.
If someone is not creative or quiet then someone is both generous and not strong and vice versa.
If someone is both not humble and brave then someone is either not wise or rich.
If someone is both not wise and brave then someone is both kind and not kind.
Everyone who is both not tall and rich is either strong or humble.
Paul is not calm or not funny.
Someone is not calm.
Lucy is either curious or happy.
John is either not wise or rich.
Someone is patient or not strong.
Paul is either not generous or not humble.
Someone is not creative.
Paul is curious or not kind. | Paul is not generous. | contradiction | ((?[X]:((~humble(X)&~creative(X))))<=>(?[X]:((funny(X)<~>humble(X)))))&
(![X]:((~curious(X)<~>generous(X))<=>~calm(X)))&
(![X]:(rich(X)=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)<~>~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:(~humble(X)))=>((~calm(paul)|~tall(paul))))&
(![X]:(~happy(X)=>(humble(X)<~>~creative(X))))&
(![X]:(~calm(X)=>(~creative(X)<~>kind(X))))&
(![X]:((~patient(X)|~calm(X))=>(funny(X)<~>~humble(X))))&
((?[X]:((generous(X)&wise(X))))=>((old(paul)|~kind(paul))))&
(![X]:((curious(X)&~rich(X))<=>~curious(X)))&
(![X]:(~wise(X)<=>humble(X)))&
(![X]:((~creative(X)<~>creative(X))=>tall(X)))&
((?[X]:((~creative(X)|quiet(X))))<=>(?[X]:((generous(X)&~strong(X)))))&
((?[X]:((~humble(X)&brave(X))))=>(?[X]:((~wise(X)<~>rich(X)))))&
((?[X]:((~wise(X)&brave(X))))=>(?[X]:((kind(X)&~kind(X)))))&
(![X]:((~tall(X)&rich(X))=>(strong(X)<~>humble(X))))&
((~calm(paul)|~funny(paul)))&
(?[X]:(~calm(X)))&
((curious(lucy)<~>happy(lucy)))&
((~wise(john)<~>rich(john)))&
(?[X]:((patient(X)|~strong(X))))&
((~generous(paul)<~>~humble(paul)))&
(?[X]:(~creative(X)))&
((curious(paul)|~kind(paul))) | ~generous(paul) | [
"p1",
"p4",
"p9",
"p10",
"p11",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 6148416324814274471939734
% SZS output start Proof for 6148416324814274471939734
2. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> ~calm(X0)) [input p1]
5. ? [X0] : ~humble(X0) => (~tall(paul) | ~calm(paul)) [input p4]
10. ! [X0] : ((~rich(X0) & curious(X0)) <=> ~curious(X0)) [input p9]
11. ! [X0] : (~wise(X0) <=> humble(X0)) [input p10]
12. ! [X0] : ((~creative(X0) <~> creative(X0)) => tall(X0)) [input p11]
20. ~wise(john) <~> rich(john) [input p19]
25. ~generous(paul) [input hypothesis]
35. (~tall(paul) | ~calm(paul)) | ! [X0] : humble(X0) [ennf transformation 5]
36. ~tall(paul) | ~calm(paul) | ! [X0] : humble(X0) [flattening 35]
42. ! [X0] : (tall(X0) | (~creative(X0) <=> creative(X0))) [ennf transformation 12]
50. ! [X0] : ((((~generous(X0) | curious(X0)) & (generous(X0) | ~curious(X0))) | calm(X0)) & (~calm(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0))))) [nnf transformation 2]
57. ! [X0] : (((~rich(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | (rich(X0) | ~curious(X0)))) [nnf transformation 10]
58. ! [X0] : (((~rich(X0) & curious(X0)) | curious(X0)) & (~curious(X0) | rich(X0) | ~curious(X0))) [flattening 57]
59. ! [X0] : ((~wise(X0) | ~humble(X0)) & (humble(X0) | wise(X0))) [nnf transformation 11]
60. ! [X0] : (tall(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) [nnf transformation 42]
70. (~rich(john) | wise(john)) & (rich(john) | ~wise(john)) [nnf transformation 20]
82. ~curious(X0) | generous(X0) | calm(X0) [cnf transformation 50]
92. ~tall(paul) | ~calm(paul) | humble(X0) [cnf transformation 36]
100. ~curious(X0) | rich(X0) | ~curious(X0) [cnf transformation 58]
101. curious(X0) | curious(X0) [cnf transformation 58]
104. ~wise(X0) | ~humble(X0) [cnf transformation 59]
105. tall(X0) | creative(X0) | creative(X0) [cnf transformation 60]
106. tall(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 60]
119. ~rich(john) | wise(john) [cnf transformation 70]
124. ~generous(paul) [cnf transformation 25]
125. tall(X0) | creative(X0) [duplicate literal removal 105]
126. ~creative(X0) | tall(X0) [duplicate literal removal 106]
127. ~curious(X0) | rich(X0) [duplicate literal removal 100]
128. curious(X0) [duplicate literal removal 101]
164. 8 <=> ! [X0] : humble(X0) [avatar definition]
165. humble(X0) <- (8) [avatar component clause 164]
167. 9 <=> calm(paul) [avatar definition]
169. ~calm(paul) <- (~9) [avatar component clause 167]
171. 10 <=> tall(paul) [avatar definition]
173. ~tall(paul) <- (~10) [avatar component clause 171]
174. 8 | ~9 | ~10 [avatar split clause 92,171,167,164]
187. rich(X0) [subsumption resolution 127,128]
188. tall(X0) [subsumption resolution 125,126]
225. wise(john) [subsumption resolution 119,187]
227. 22 <=> generous(paul) [avatar definition]
228. ~generous(paul) <- (~22) [avatar component clause 227]
236. ~22 [avatar split clause 124,227]
242. ~humble(john) [resolution 104,225]
261. calm(X0) | generous(X0) [resolution 82,128]
263. generous(paul) <- (~9) [resolution 261,169]
267. $false <- (~9, ~22) [subsumption resolution 263,228]
268. 9 | 22 [avatar contradiction clause 267]
269. $false <- (~10) [subsumption resolution 173,188]
270. 10 [avatar contradiction clause 269]
273. $false <- (8) [resolution 165,242]
276. ~8 [avatar contradiction clause 273]
278. $false [avatar sat refutation 174,236,268,270,276]
% SZS output end Proof for 6148416324814274471939734
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both strong and not creative then someone is either not calm or patient.
Everyone who is not old is not kind or not tall.
Everyone who is both not quiet and not funny is funny or wise and vice versa.
Everyone who is either happy or not quiet is either not funny or creative.
Everyone who is either quiet or not creative is calm or not funny.
Everyone who is either strong or funny is both rich and brave.
If alice is either curious or not curious then someone is tall and vice versa.
Everyone who is both curious and not calm is not creative or not strong and vice versa.
If someone is either patient or generous then someone is strong or kind and vice versa.
If someone is tall or rich then someone is both not curious and not kind.
Everyone who is brave or generous is not happy and vice versa.
Everyone who is curious is calm or not creative.
If fred is rich then someone is brave or not generous.
If someone is either kind or creative then john is either not kind or not funny.
If paul is not old then someone is either curious or not old.
Lucy is both patient and humble.
Mary is either not calm or not curious.
Someone is not creative.
Someone is happy. | Lucy is patient. | entailment | ((?[X]:((strong(X)&~creative(X))))=>(?[X]:((~calm(X)<~>patient(X)))))&
(![X]:(~old(X)=>(~kind(X)|~tall(X))))&
(![X]:((~quiet(X)&~funny(X))<=>(funny(X)|wise(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(~funny(X)<~>creative(X))))&
(![X]:((quiet(X)<~>~creative(X))=>(calm(X)|~funny(X))))&
(![X]:((strong(X)<~>funny(X))=>(rich(X)&brave(X))))&
(((curious(alice)<~>~curious(alice)))<=>(?[X]:(tall(X))))&
(![X]:((curious(X)&~calm(X))<=>(~creative(X)|~strong(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:((strong(X)|kind(X)))))&
((?[X]:((tall(X)|rich(X))))=>(?[X]:((~curious(X)&~kind(X)))))&
(![X]:((brave(X)|generous(X))<=>~happy(X)))&
(![X]:(curious(X)=>(calm(X)|~creative(X))))&
((rich(fred))=>(?[X]:((brave(X)|~generous(X)))))&
((?[X]:((kind(X)<~>creative(X))))=>((~kind(john)<~>~funny(john))))&
((~old(paul))=>(?[X]:((curious(X)<~>~old(X)))))&
((patient(lucy)&humble(lucy)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:(~creative(X)))&
(?[X]:(happy(X))) | patient(lucy) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 9194395238056254888133633
% SZS output start Proof for 9194395238056254888133633
16. humble(lucy) & patient(lucy) [input p15]
20. ~patient(lucy) [input hypothesis]
24. patient(lucy) [pure predicate removal 16]
122. patient(lucy) [cnf transformation 24]
127. ~patient(lucy) [cnf transformation 20]
263. $false [subsumption resolution 127,122]
% SZS output end Proof for 9194395238056254888133633
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or not generous then someone is not creative or kind and vice versa.
Everyone who is either funny or not humble is patient or not generous and vice versa.
Everyone who is humble or kind is both calm and tall and vice versa.
Everyone who is both generous and not brave is either creative or not creative and vice versa.
If someone is either calm or wise then fred is both rich and not curious.
Everyone who is both not rich and not quiet is strong or not creative and vice versa.
If mary is not tall or funny then susan is both not happy and kind and vice versa.
Everyone who is humble is both rich and patient.
If someone is both not tall and not patient then someone is both curious and not rich and vice versa.
Everyone who is old or not calm is both not calm and humble.
Everyone who is both old and not curious is happy or not rich and vice versa.
If fred is both old and kind then someone is both tall and not brave.
Everyone who is either not old or rich is not kind or not rich and vice versa.
If susan is not wise then lucy is either calm or not curious and vice versa.
Everyone who is either not creative or not curious is patient.
Everyone who is rich is creative or not happy.
Lucy is not curious or rich.
Susan is both not old and calm.
Someone is both not funny and not brave.
John is either happy or not humble.
Paul is not tall or kind.
Someone is either calm or happy. | Fred is not strong. | entailment | ((?[X]:((~old(X)|~generous(X))))<=>(?[X]:((~creative(X)|kind(X)))))&
(![X]:((funny(X)<~>~humble(X))<=>(patient(X)|~generous(X))))&
(![X]:((humble(X)|kind(X))<=>(calm(X)&tall(X))))&
(![X]:((generous(X)&~brave(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:((calm(X)<~>wise(X))))=>((rich(fred)&~curious(fred))))&
(![X]:((~rich(X)&~quiet(X))<=>(strong(X)|~creative(X))))&
(((~tall(mary)|funny(mary)))<=>((~happy(susan)&kind(susan))))&
(![X]:(humble(X)=>(rich(X)&patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((old(X)|~calm(X))=>(~calm(X)&humble(X))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)|~rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(~kind(X)|~rich(X))))&
((~wise(susan))<=>((calm(lucy)<~>~curious(lucy))))&
(![X]:((~creative(X)<~>~curious(X))=>patient(X)))&
(![X]:(rich(X)=>(creative(X)|~happy(X))))&
((~curious(lucy)|rich(lucy)))&
((~old(susan)&calm(susan)))&
(?[X]:((~funny(X)&~brave(X))))&
((happy(john)<~>~humble(john)))&
((~tall(paul)|kind(paul)))&
(?[X]:((calm(X)<~>happy(X)))) | ~strong(fred) | [
"p2",
"p5",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 2882722968086870884234367
% SZS output start Proof for 2882722968086870884234367
3. ! [X0] : ((kind(X0) | humble(X0)) <=> (tall(X0) & calm(X0))) [input p2]
6. ! [X0] : ((~quiet(X0) & ~rich(X0)) <=> (~creative(X0) | strong(X0))) [input p5]
10. ! [X0] : ((~calm(X0) | old(X0)) => (humble(X0) & ~calm(X0))) [input p9]
11. ! [X0] : ((~curious(X0) & old(X0)) <=> (~rich(X0) | happy(X0))) [input p10]
23. strong(fred) [input hypothesis]
28. ! [X0] : ((humble(X0) & ~calm(X0)) | (calm(X0) & ~old(X0))) [ennf transformation 10]
41. ! [X0] : (((kind(X0) | humble(X0)) | (~tall(X0) | ~calm(X0))) & ((tall(X0) & calm(X0)) | (~kind(X0) & ~humble(X0)))) [nnf transformation 3]
42. ! [X0] : ((kind(X0) | humble(X0) | ~tall(X0) | ~calm(X0)) & ((tall(X0) & calm(X0)) | (~kind(X0) & ~humble(X0)))) [flattening 41]
46. ! [X0] : (((~quiet(X0) & ~rich(X0)) | (creative(X0) & ~strong(X0))) & ((~creative(X0) | strong(X0)) | (quiet(X0) | rich(X0)))) [nnf transformation 6]
47. ! [X0] : (((~quiet(X0) & ~rich(X0)) | (creative(X0) & ~strong(X0))) & (~creative(X0) | strong(X0) | quiet(X0) | rich(X0))) [flattening 46]
55. ! [X0] : (((~curious(X0) & old(X0)) | (rich(X0) & ~happy(X0))) & ((~rich(X0) | happy(X0)) | (curious(X0) | ~old(X0)))) [nnf transformation 11]
56. ! [X0] : (((~curious(X0) & old(X0)) | (rich(X0) & ~happy(X0))) & (~rich(X0) | happy(X0) | curious(X0) | ~old(X0))) [flattening 55]
79. ~humble(X0) | calm(X0) [cnf transformation 42]
95. ~strong(X0) | ~rich(X0) [cnf transformation 47]
110. ~calm(X0) | ~old(X0) [cnf transformation 28]
113. humble(X0) | calm(X0) [cnf transformation 28]
116. old(X0) | rich(X0) [cnf transformation 56]
144. strong(fred) [cnf transformation 23]
251. calm(X0) [subsumption resolution 113,79]
252. ~old(X0) [subsumption resolution 110,251]
254. rich(X0) [subsumption resolution 116,252]
282. ~rich(fred) [resolution 95,144]
283. $false [subsumption resolution 282,254]
% SZS output end Proof for 2882722968086870884234367
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not brave and brave then someone is not creative or not generous and vice versa. Everyone who is not kind or kind is both not brave and not kind. Everyone who is not humble or not brave is strong or not generous. Everyone who is not strong is both happy and not quiet. If lucy is either not generous or generous then susan is either not wise or not strong and vice versa. If alice is brave or calm then mary is both humble and creative and vice versa. If someone is not quiet or not strong then someone is funny. If john is brave then someone is either patient or not patient. Everyone who is both not patient and not old is both patient and tall and vice versa. Everyone who is curious is rich or happy. Everyone who is not calm or wise is rich. If someone is tall or not rich then mary is either not old or not generous and vice versa. If someone is both strong and tall then someone is calm or not calm and vice versa. Everyone who is either funny or not generous is not quiet. If paul is either happy or not kind then someone is either old or not creative and vice versa. If paul is either rich or curious then someone is both not funny and calm. Paul is calm or kind. John is both not humble and old. Someone is both not tall and not wise. Someone is not rich. Paul is not happy. Someone is creative. Paul is either not curious or rich. Someone is both old and curious. | Mary is strong. | entailment | ((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((~creative(X)|~generous(X)))))&
(![X]:((~kind(X)|kind(X))=>(~brave(X)&~kind(X))))&
(![X]:((~humble(X)|~brave(X))=>(strong(X)|~generous(X))))&
(![X]:(~strong(X)=>(happy(X)&~quiet(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>((~wise(susan)<~>~strong(susan))))&
(((brave(alice)|calm(alice)))<=>((humble(mary)&creative(mary))))&
((?[X]:((~quiet(X)|~strong(X))))=>(?[X]:(funny(X))))&
((brave(john))=>(?[X]:((patient(X)<~>~patient(X)))))&
(![X]:((~patient(X)&~old(X))<=>(patient(X)&tall(X))))&
(![X]:(curious(X)=>(rich(X)|happy(X))))&
(![X]:((~calm(X)|wise(X))=>rich(X)))&
((?[X]:((tall(X)|~rich(X))))<=>((~old(mary)<~>~generous(mary))))&
((?[X]:((strong(X)&tall(X))))<=>(?[X]:((calm(X)|~calm(X)))))&
(![X]:((funny(X)<~>~generous(X))=>~quiet(X)))&
(((happy(paul)<~>~kind(paul)))<=>(?[X]:((old(X)<~>~creative(X)))))&
(((rich(paul)<~>curious(paul)))=>(?[X]:((~funny(X)&calm(X)))))&
((calm(paul)|kind(paul)))&
((~humble(john)&old(john)))&
(?[X]:((~tall(X)&~wise(X))))&
(?[X]:(~rich(X)))&
(~happy(paul))&
(?[X]:(creative(X)))&
((~curious(paul)<~>rich(paul)))&
(?[X]:((old(X)&curious(X)))) | strong(mary) | [
"p0",
"p1",
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 250512004719238125558396
% SZS output start Proof for 250512004719238125558396
1. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X0] : (~generous(X0) | ~creative(X0)) [input p0]
2. ! [X0] : ((kind(X0) | ~kind(X0)) => (~kind(X0) & ~brave(X0))) [input p1]
3. ! [X0] : ((~brave(X0) | ~humble(X0)) => (~generous(X0) | strong(X0))) [input p2]
25. ~strong(mary) [input hypothesis]
26. ? [X0] : (brave(X0) & ~brave(X0)) <=> ? [X1] : (~generous(X1) | ~creative(X1)) [rectify 1]
29. ! [X0] : ((~kind(X0) & ~brave(X0)) | (~kind(X0) & kind(X0))) [ennf transformation 2]
30. ! [X0] : ((~generous(X0) | strong(X0)) | (brave(X0) & humble(X0))) [ennf transformation 3]
31. ! [X0] : (~generous(X0) | strong(X0) | (brave(X0) & humble(X0))) [flattening 30]
40. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : (generous(X1) & creative(X1))) & (? [X1] : (~generous(X1) | ~creative(X1)) | ! [X0] : (~brave(X0) | brave(X0))) [nnf transformation 26]
41. (? [X0] : (brave(X0) & ~brave(X0)) | ! [X1] : (generous(X1) & creative(X1))) & (? [X2] : (~generous(X2) | ~creative(X2)) | ! [X3] : (~brave(X3) | brave(X3))) [rectify 40]
42. ? [X0] : (brave(X0) & ~brave(X0)) => (brave(sK0) & ~brave(sK0)) [choice axiom]
43. ? [X2] : (~generous(X2) | ~creative(X2)) => (~generous(sK1) | ~creative(sK1)) [choice axiom]
44. ((brave(sK0) & ~brave(sK0)) | ! [X1] : (generous(X1) & creative(X1))) & ((~generous(sK1) | ~creative(sK1)) | ! [X3] : (~brave(X3) | brave(X3))) [skolemisation 41,43,42]
84. ~brave(sK0) | generous(X1) [cnf transformation 44]
86. brave(sK0) | generous(X1) [cnf transformation 44]
87. ~brave(X0) | kind(X0) [cnf transformation 29]
90. ~kind(X0) | ~kind(X0) [cnf transformation 29]
92. ~generous(X0) | strong(X0) | brave(X0) [cnf transformation 31]
156. ~strong(mary) [cnf transformation 25]
163. ~kind(X0) [duplicate literal removal 90]
165. 1 <=> ! [X1] : generous(X1) [avatar definition]
166. generous(X1) <- (1) [avatar component clause 165]
168. 2 <=> brave(sK0) [avatar definition]
171. 1 | 2 [avatar split clause 86,168,165]
176. 1 | ~2 [avatar split clause 84,168,165]
178. ~brave(X0) [subsumption resolution 87,163]
179. ~generous(X0) | strong(X0) [subsumption resolution 92,178]
225. 13 <=> generous(mary) [avatar definition]
226. ~generous(mary) <- (~13) [avatar component clause 225]
227. generous(mary) <- (13) [avatar component clause 225]
334. strong(mary) <- (13) [resolution 179,227]
336. $false <- (13) [subsumption resolution 334,156]
337. ~13 [avatar contradiction clause 336]
338. $false <- (1, ~13) [subsumption resolution 226,166]
339. ~1 | 13 [avatar contradiction clause 338]
340. $false [avatar sat refutation 171,176,337,339]
% SZS output end Proof for 250512004719238125558396
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise and humble is not old and vice versa. If someone is both kind and not curious then alice is either not generous or old. Everyone who is not generous is rich or patient. If someone is not patient then mary is not patient or creative and vice versa. Everyone who is strong is old or tall and vice versa. Everyone who is not generous is not kind or quiet and vice versa. If fred is not curious or not quiet then john is not patient. Everyone who is either not kind or creative is both patient and humble. If someone is either wise or not old then someone is both not kind and not generous and vice versa. If john is either not funny or old then alice is not brave or not creative and vice versa. Everyone who is not brave or kind is both old and tall and vice versa. Everyone who is both quiet and funny is either kind or funny and vice versa. Everyone who is either happy or not patient is calm. Everyone who is either generous or old is not curious and vice versa. If alice is either not kind or not brave then paul is not happy or rich and vice versa. Everyone who is kind is either not quiet or not curious. Paul is not happy or wise. Paul is not happy or calm. Someone is funny or not brave. Mary is either generous or not strong. Someone is brave or not wise. Paul is not patient. Susan is not brave or not happy. Susan is both not generous and not quiet. | Mary is not wise. | neutral | (![X]:((wise(X)&humble(X))<=>~old(X)))&
((?[X]:((kind(X)&~curious(X))))=>((~generous(alice)<~>old(alice))))&
(![X]:(~generous(X)=>(rich(X)|patient(X))))&
((?[X]:(~patient(X)))<=>((~patient(mary)|creative(mary))))&
(![X]:(strong(X)<=>(old(X)|tall(X))))&
(![X]:(~generous(X)<=>(~kind(X)|quiet(X))))&
(((~curious(fred)|~quiet(fred)))=>(~patient(john)))&
(![X]:((~kind(X)<~>creative(X))=>(patient(X)&humble(X))))&
((?[X]:((wise(X)<~>~old(X))))<=>(?[X]:((~kind(X)&~generous(X)))))&
(((~funny(john)<~>old(john)))<=>((~brave(alice)|~creative(alice))))&
(![X]:((~brave(X)|kind(X))<=>(old(X)&tall(X))))&
(![X]:((quiet(X)&funny(X))<=>(kind(X)<~>funny(X))))&
(![X]:((happy(X)<~>~patient(X))=>calm(X)))&
(![X]:((generous(X)<~>old(X))<=>~curious(X)))&
(((~kind(alice)<~>~brave(alice)))<=>((~happy(paul)|rich(paul))))&
(![X]:(kind(X)=>(~quiet(X)<~>~curious(X))))&
((~happy(paul)|wise(paul)))&
((~happy(paul)|calm(paul)))&
(?[X]:((funny(X)|~brave(X))))&
((generous(mary)<~>~strong(mary)))&
(?[X]:((brave(X)|~wise(X))))&
(~patient(paul))&
((~brave(susan)|~happy(susan)))&
((~generous(susan)&~quiet(susan))) | ~wise(mary) | []
| null | 0 |
If fred is not generous or not quiet then someone is both quiet and not quiet and vice versa.
Everyone who is not brave is both brave and wise.
If someone is not humble then someone is both not curious and not wise and vice versa.
If lucy is either not funny or not calm then someone is funny.
If john is not patient or not curious then lucy is both wise and funny.
Everyone who is both brave and wise is both wise and kind.
If someone is humble then someone is either not old or brave.
Everyone who is curious or not generous is not brave and vice versa.
If fred is both generous and old then john is both generous and patient.
If someone is not funny or not quiet then someone is happy or humble.
If lucy is curious then alice is happy.
If someone is either not strong or not generous then john is either creative or curious.
Everyone who is not brave is both humble and kind and vice versa.
Everyone who is humble is both not generous and not patient.
Everyone who is both not creative and curious is not patient or not rich and vice versa.
Someone is either strong or not quiet.
Alice is both old and tall.
Susan is either not humble or not calm.
Someone is either not generous or not creative.
Someone is not happy.
Someone is either not happy or not funny.
Mary is either not brave or generous. | Susan is brave. | entailment | (((~generous(fred)|~quiet(fred)))<=>(?[X]:((quiet(X)&~quiet(X)))))&
(![X]:(~brave(X)=>(brave(X)&wise(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~curious(X)&~wise(X)))))&
(((~funny(lucy)<~>~calm(lucy)))=>(?[X]:(funny(X))))&
(((~patient(john)|~curious(john)))=>((wise(lucy)&funny(lucy))))&
(![X]:((brave(X)&wise(X))=>(wise(X)&kind(X))))&
((?[X]:(humble(X)))=>(?[X]:((~old(X)<~>brave(X)))))&
(![X]:((curious(X)|~generous(X))<=>~brave(X)))&
(((generous(fred)&old(fred)))=>((generous(john)&patient(john))))&
((?[X]:((~funny(X)|~quiet(X))))=>(?[X]:((happy(X)|humble(X)))))&
((curious(lucy))=>(happy(alice)))&
((?[X]:((~strong(X)<~>~generous(X))))=>((creative(john)<~>curious(john))))&
(![X]:(~brave(X)<=>(humble(X)&kind(X))))&
(![X]:(humble(X)=>(~generous(X)&~patient(X))))&
(![X]:((~creative(X)&curious(X))<=>(~patient(X)|~rich(X))))&
(?[X]:((strong(X)<~>~quiet(X))))&
((old(alice)&tall(alice)))&
((~humble(susan)<~>~calm(susan)))&
(?[X]:((~generous(X)<~>~creative(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~happy(X)<~>~funny(X))))&
((~brave(mary)<~>generous(mary))) | brave(susan) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 1133347174572207508987879
% SZS output start Proof for 1133347174572207508987879
2. ! [X0] : (~brave(X0) => (wise(X0) & brave(X0))) [input p1]
23. ~brave(susan) [input hypothesis]
28. ! [X0] : ((wise(X0) & brave(X0)) | brave(X0)) [ennf transformation 2]
85. brave(X0) | brave(X0) [cnf transformation 28]
134. ~brave(susan) [cnf transformation 23]
135. brave(X0) [duplicate literal removal 85]
283. $false [subsumption resolution 134,135]
% SZS output end Proof for 1133347174572207508987879
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or old then someone is both kind and not old and vice versa.
Everyone who is brave or funny is both brave and quiet and vice versa.
Everyone who is not patient is both funny and not quiet.
Everyone who is either curious or kind is either not tall or brave.
If susan is either creative or funny then someone is not old and vice versa.
If fred is quiet or patient then fred is either not patient or not happy and vice versa.
If someone is generous or brave then someone is not rich or generous.
If someone is not curious or not funny then alice is both patient and not calm and vice versa.
Everyone who is humble or not generous is either not humble or not happy and vice versa.
If john is brave then someone is generous.
Everyone who is both wise and not humble is generous.
Everyone who is either not rich or not tall is either kind or not happy and vice versa.
Everyone who is strong or not creative is both not wise and not creative and vice versa.
If someone is both not creative and funny then someone is patient.
If someone is either not tall or not patient then alice is either kind or not brave.
Everyone who is creative or not old is strong or patient.
Someone is either not patient or kind.
Paul is not tall.
Someone is creative or wise.
Someone is rich or tall.
Susan is either generous or not wise.
Susan is either kind or humble.
Someone is funny or brave.
Paul is happy. | Paul is patient. | entailment | ((?[X]:((patient(X)<~>old(X))))<=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((brave(X)|funny(X))<=>(brave(X)&quiet(X))))&
(![X]:(~patient(X)=>(funny(X)&~quiet(X))))&
(![X]:((curious(X)<~>kind(X))=>(~tall(X)<~>brave(X))))&
(((creative(susan)<~>funny(susan)))<=>(?[X]:(~old(X))))&
(((quiet(fred)|patient(fred)))<=>((~patient(fred)<~>~happy(fred))))&
((?[X]:((generous(X)|brave(X))))=>(?[X]:((~rich(X)|generous(X)))))&
((?[X]:((~curious(X)|~funny(X))))<=>((patient(alice)&~calm(alice))))&
(![X]:((humble(X)|~generous(X))<=>(~humble(X)<~>~happy(X))))&
((brave(john))=>(?[X]:(generous(X))))&
(![X]:((wise(X)&~humble(X))=>generous(X)))&
(![X]:((~rich(X)<~>~tall(X))<=>(kind(X)<~>~happy(X))))&
(![X]:((strong(X)|~creative(X))<=>(~wise(X)&~creative(X))))&
((?[X]:((~creative(X)&funny(X))))=>(?[X]:(patient(X))))&
((?[X]:((~tall(X)<~>~patient(X))))=>((kind(alice)<~>~brave(alice))))&
(![X]:((creative(X)|~old(X))=>(strong(X)|patient(X))))&
(?[X]:((~patient(X)<~>kind(X))))&
(~tall(paul))&
(?[X]:((creative(X)|wise(X))))&
(?[X]:((rich(X)|tall(X))))&
((generous(susan)<~>~wise(susan)))&
((kind(susan)<~>humble(susan)))&
(?[X]:((funny(X)|brave(X))))&
(happy(paul)) | patient(paul) | [
"p1",
"p2",
"hypothesis"
]
| % SZS status Unsatisfiable for 5429271701480955567894454
% SZS output start Proof for 5429271701480955567894454
2. ! [X0] : ((funny(X0) | brave(X0)) <=> (quiet(X0) & brave(X0))) [input p1]
3. ! [X0] : (~patient(X0) => (~quiet(X0) & funny(X0))) [input p2]
25. ~patient(paul) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & funny(X0)) | patient(X0)) [ennf transformation 3]
44. ! [X0] : (((funny(X0) | brave(X0)) | (~quiet(X0) | ~brave(X0))) & ((quiet(X0) & brave(X0)) | (~funny(X0) & ~brave(X0)))) [nnf transformation 2]
45. ! [X0] : ((funny(X0) | brave(X0) | ~quiet(X0) | ~brave(X0)) & ((quiet(X0) & brave(X0)) | (~funny(X0) & ~brave(X0)))) [flattening 44]
92. ~funny(X0) | quiet(X0) [cnf transformation 45]
94. funny(X0) | patient(X0) [cnf transformation 29]
95. ~quiet(X0) | patient(X0) [cnf transformation 29]
156. ~patient(paul) [cnf transformation 25]
356. patient(X0) | quiet(X0) [resolution 94,92]
358. patient(X0) [subsumption resolution 356,95]
360. $false [resolution 358,156]
% SZS output end Proof for 5429271701480955567894454
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not curious or strong then fred is not wise or not patient and vice versa.
Everyone who is calm or not happy is brave.
Everyone who is old is both not calm and tall.
Everyone who is old or not old is both patient and old and vice versa.
If susan is either wise or curious then someone is either not funny or not old and vice versa.
Everyone who is both humble and not humble is not kind or patient.
If someone is happy then lucy is both tall and not kind.
Everyone who is not tall is either strong or patient.
If someone is not tall then mary is both not generous and creative and vice versa.
Everyone who is both brave and not strong is either curious or tall and vice versa.
If someone is not humble or not creative then fred is either patient or generous and vice versa.
Everyone who is both not kind and not strong is either generous or not funny and vice versa.
If someone is not tall or old then susan is both not happy and curious.
If fred is either not brave or not creative then someone is curious and vice versa.
Everyone who is both quiet and old is kind.
If fred is either not calm or not tall then fred is kind or happy.
Paul is not kind or generous.
Someone is both not wise and not happy.
Lucy is not calm.
Someone is both curious and not kind. | Mary is quiet. | neutral | (((~curious(mary)<~>strong(mary)))<=>((~wise(fred)|~patient(fred))))&
(![X]:((calm(X)|~happy(X))=>brave(X)))&
(![X]:(old(X)=>(~calm(X)&tall(X))))&
(![X]:((old(X)|~old(X))<=>(patient(X)&old(X))))&
(((wise(susan)<~>curious(susan)))<=>(?[X]:((~funny(X)<~>~old(X)))))&
(![X]:((humble(X)&~humble(X))=>(~kind(X)|patient(X))))&
((?[X]:(happy(X)))=>((tall(lucy)&~kind(lucy))))&
(![X]:(~tall(X)=>(strong(X)<~>patient(X))))&
((?[X]:(~tall(X)))<=>((~generous(mary)&creative(mary))))&
(![X]:((brave(X)&~strong(X))<=>(curious(X)<~>tall(X))))&
((?[X]:((~humble(X)|~creative(X))))<=>((patient(fred)<~>generous(fred))))&
(![X]:((~kind(X)&~strong(X))<=>(generous(X)<~>~funny(X))))&
((?[X]:((~tall(X)|old(X))))=>((~happy(susan)&curious(susan))))&
(((~brave(fred)<~>~creative(fred)))<=>(?[X]:(curious(X))))&
(![X]:((quiet(X)&old(X))=>kind(X)))&
(((~calm(fred)<~>~tall(fred)))=>((kind(fred)|happy(fred))))&
((~kind(paul)|generous(paul)))&
(?[X]:((~wise(X)&~happy(X))))&
(~calm(lucy))&
(?[X]:((curious(X)&~kind(X)))) | quiet(mary) | []
| null | 0 |
If someone is either calm or patient then mary is calm.
Everyone who is both tall and strong is kind.
Everyone who is not calm is not wise or not curious and vice versa.
Everyone who is either creative or quiet is curious.
If paul is strong or not happy then someone is not quiet.
If susan is both not curious and not brave then someone is both happy and not wise.
Everyone who is either not wise or not calm is quiet or curious and vice versa.
Everyone who is either tall or not happy is not rich and vice versa.
Everyone who is not generous or brave is both generous and not kind.
Everyone who is either not creative or not brave is either not creative or strong and vice versa.
Everyone who is both patient and curious is strong or not wise and vice versa.
Everyone who is either humble or not old is either not generous or happy and vice versa.
Everyone who is either not humble or calm is happy.
If alice is both not old and not tall then someone is happy and vice versa.
If someone is either not brave or patient then mary is generous.
If john is not strong or not brave then someone is humble.
Someone is either not old or brave.
Susan is brave or quiet.
Someone is wise or generous. | Alice is rich. | neutral | ((?[X]:((calm(X)<~>patient(X))))=>(calm(mary)))&
(![X]:((tall(X)&strong(X))=>kind(X)))&
(![X]:(~calm(X)<=>(~wise(X)|~curious(X))))&
(![X]:((creative(X)<~>quiet(X))=>curious(X)))&
(((strong(paul)|~happy(paul)))=>(?[X]:(~quiet(X))))&
(((~curious(susan)&~brave(susan)))=>(?[X]:((happy(X)&~wise(X)))))&
(![X]:((~wise(X)<~>~calm(X))<=>(quiet(X)|curious(X))))&
(![X]:((tall(X)<~>~happy(X))<=>~rich(X)))&
(![X]:((~generous(X)|brave(X))=>(generous(X)&~kind(X))))&
(![X]:((~creative(X)<~>~brave(X))<=>(~creative(X)<~>strong(X))))&
(![X]:((patient(X)&curious(X))<=>(strong(X)|~wise(X))))&
(![X]:((humble(X)<~>~old(X))<=>(~generous(X)<~>happy(X))))&
(![X]:((~humble(X)<~>calm(X))=>happy(X)))&
(((~old(alice)&~tall(alice)))<=>(?[X]:(happy(X))))&
((?[X]:((~brave(X)<~>patient(X))))=>(generous(mary)))&
(((~strong(john)|~brave(john)))=>(?[X]:(humble(X))))&
(?[X]:((~old(X)<~>brave(X))))&
((brave(susan)|quiet(susan)))&
(?[X]:((wise(X)|generous(X)))) | rich(alice) | []
| null | 0 |
Everyone who is rich is not brave or not funny.
Everyone who is strong or curious is not funny.
Everyone who is creative or calm is not patient.
If mary is both funny and not happy then someone is not generous or tall.
If someone is not humble then alice is either not tall or funny and vice versa.
Everyone who is both not strong and rich is both happy and not creative and vice versa.
Everyone who is either quiet or strong is humble.
Everyone who is old is both not happy and not patient.
If lucy is happy or not quiet then john is either not happy or not rich and vice versa.
If someone is both not funny and not old then someone is patient and vice versa.
Everyone who is both patient and not calm is quiet or not kind and vice versa.
Everyone who is either strong or not strong is curious and vice versa.
If someone is not tall or humble then lucy is humble.
Everyone who is either brave or not humble is both kind and not old.
Everyone who is happy is both not funny and not brave and vice versa.
If alice is both not curious and not funny then someone is either brave or not old.
Alice is both not tall and rich.
Someone is either not happy or kind.
Paul is quiet or tall.
Someone is either humble or not brave.
Someone is quiet or generous.
Someone is both not calm and happy.
Someone is not happy. | John is kind. | neutral | (![X]:(rich(X)=>(~brave(X)|~funny(X))))&
(![X]:((strong(X)|curious(X))=>~funny(X)))&
(![X]:((creative(X)|calm(X))=>~patient(X)))&
(((funny(mary)&~happy(mary)))=>(?[X]:((~generous(X)|tall(X)))))&
((?[X]:(~humble(X)))<=>((~tall(alice)<~>funny(alice))))&
(![X]:((~strong(X)&rich(X))<=>(happy(X)&~creative(X))))&
(![X]:((quiet(X)<~>strong(X))=>humble(X)))&
(![X]:(old(X)=>(~happy(X)&~patient(X))))&
(((happy(lucy)|~quiet(lucy)))<=>((~happy(john)<~>~rich(john))))&
((?[X]:((~funny(X)&~old(X))))<=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~calm(X))<=>(quiet(X)|~kind(X))))&
(![X]:((strong(X)<~>~strong(X))<=>curious(X)))&
((?[X]:((~tall(X)|humble(X))))=>(humble(lucy)))&
(![X]:((brave(X)<~>~humble(X))=>(kind(X)&~old(X))))&
(![X]:(happy(X)<=>(~funny(X)&~brave(X))))&
(((~curious(alice)&~funny(alice)))=>(?[X]:((brave(X)<~>~old(X)))))&
((~tall(alice)&rich(alice)))&
(?[X]:((~happy(X)<~>kind(X))))&
((quiet(paul)|tall(paul)))&
(?[X]:((humble(X)<~>~brave(X))))&
(?[X]:((quiet(X)|generous(X))))&
(?[X]:((~calm(X)&happy(X))))&
(?[X]:(~happy(X))) | kind(john) | []
| null | 0 |
If someone is either not strong or not creative then someone is funny. Everyone who is calm or old is both not patient and creative and vice versa. If susan is curious then fred is either not tall or not brave and vice versa. Everyone who is both creative and kind is calm and vice versa. Everyone who is either old or wise is not wise or not rich and vice versa. If alice is either tall or not wise then someone is either strong or not calm and vice versa. If someone is not humble then someone is not generous and vice versa. Everyone who is calm is both rich and strong and vice versa. If susan is both calm and not rich then mary is both calm and not curious and vice versa. Everyone who is calm is either not humble or not funny. Everyone who is strong is not patient or not funny. Everyone who is either happy or not quiet is either funny or tall. Everyone who is both curious and not happy is either happy or not patient. If alice is either not generous or patient then someone is not happy or not strong and vice versa. Everyone who is patient is not curious or wise and vice versa. Everyone who is funny is either not kind or not brave and vice versa. Someone is brave or tall. John is not old. Someone is funny. Someone is either patient or quiet. Susan is either wise or curious. Alice is calm. John is either generous or patient. | Mary is not brave. | neutral | ((?[X]:((~strong(X)<~>~creative(X))))=>(?[X]:(funny(X))))&
(![X]:((calm(X)|old(X))<=>(~patient(X)&creative(X))))&
((curious(susan))<=>((~tall(fred)<~>~brave(fred))))&
(![X]:((creative(X)&kind(X))<=>calm(X)))&
(![X]:((old(X)<~>wise(X))<=>(~wise(X)|~rich(X))))&
(((tall(alice)<~>~wise(alice)))<=>(?[X]:((strong(X)<~>~calm(X)))))&
((?[X]:(~humble(X)))<=>(?[X]:(~generous(X))))&
(![X]:(calm(X)<=>(rich(X)&strong(X))))&
(((calm(susan)&~rich(susan)))<=>((calm(mary)&~curious(mary))))&
(![X]:(calm(X)=>(~humble(X)<~>~funny(X))))&
(![X]:(strong(X)=>(~patient(X)|~funny(X))))&
(![X]:((happy(X)<~>~quiet(X))=>(funny(X)<~>tall(X))))&
(![X]:((curious(X)&~happy(X))=>(happy(X)<~>~patient(X))))&
(((~generous(alice)<~>patient(alice)))<=>(?[X]:((~happy(X)|~strong(X)))))&
(![X]:(patient(X)<=>(~curious(X)|wise(X))))&
(![X]:(funny(X)<=>(~kind(X)<~>~brave(X))))&
(?[X]:((brave(X)|tall(X))))&
(~old(john))&
(?[X]:(funny(X)))&
(?[X]:((patient(X)<~>quiet(X))))&
((wise(susan)<~>curious(susan)))&
(calm(alice))&
((generous(john)<~>patient(john))) | ~brave(mary) | []
| null | 0 |
Everyone who is both curious and kind is both brave and happy.
If susan is not curious then john is either not rich or not happy.
If lucy is strong then john is either not creative or not calm and vice versa.
Everyone who is wise is humble and vice versa.
Everyone who is not quiet is both happy and tall.
If paul is calm then someone is patient or creative and vice versa.
Everyone who is either wise or strong is either humble or old and vice versa.
Everyone who is not brave is both quiet and curious.
If lucy is humble or strong then someone is funny.
Everyone who is not happy is either kind or not brave.
Everyone who is both not brave and patient is either not kind or not calm and vice versa.
Everyone who is not strong or not generous is either not curious or not wise.
If alice is not old then john is both not funny and not quiet.
Everyone who is both wise and not creative is either not strong or creative and vice versa.
If someone is either old or not happy then paul is both happy and not calm and vice versa.
If fred is both wise and not happy then lucy is rich and vice versa.
Mary is both tall and funny.
Fred is funny.
Someone is wise or not rich.
Someone is either kind or old.
Someone is wise.
Someone is funny.
John is either brave or quiet.
Someone is calm. | John is not creative. | neutral | (![X]:((curious(X)&kind(X))=>(brave(X)&happy(X))))&
((~curious(susan))=>((~rich(john)<~>~happy(john))))&
((strong(lucy))<=>((~creative(john)<~>~calm(john))))&
(![X]:(wise(X)<=>humble(X)))&
(![X]:(~quiet(X)=>(happy(X)&tall(X))))&
((calm(paul))<=>(?[X]:((patient(X)|creative(X)))))&
(![X]:((wise(X)<~>strong(X))<=>(humble(X)<~>old(X))))&
(![X]:(~brave(X)=>(quiet(X)&curious(X))))&
(((humble(lucy)|strong(lucy)))=>(?[X]:(funny(X))))&
(![X]:(~happy(X)=>(kind(X)<~>~brave(X))))&
(![X]:((~brave(X)&patient(X))<=>(~kind(X)<~>~calm(X))))&
(![X]:((~strong(X)|~generous(X))=>(~curious(X)<~>~wise(X))))&
((~old(alice))=>((~funny(john)&~quiet(john))))&
(![X]:((wise(X)&~creative(X))<=>(~strong(X)<~>creative(X))))&
((?[X]:((old(X)<~>~happy(X))))<=>((happy(paul)&~calm(paul))))&
(((wise(fred)&~happy(fred)))<=>(rich(lucy)))&
((tall(mary)&funny(mary)))&
(funny(fred))&
(?[X]:((wise(X)|~rich(X))))&
(?[X]:((kind(X)<~>old(X))))&
(?[X]:(wise(X)))&
(?[X]:(funny(X)))&
((brave(john)<~>quiet(john)))&
(?[X]:(calm(X))) | ~creative(john) | []
| null | 0 |
If someone is either patient or not rich then someone is tall and vice versa. Everyone who is humble is generous. Everyone who is both wise and not humble is either patient or not tall and vice versa. If alice is both happy and not brave then someone is both patient and not kind and vice versa. If alice is both old and humble then someone is not curious or patient and vice versa. If someone is both not quiet and not happy then someone is happy or funny and vice versa. If susan is not funny or not rich then susan is either not humble or not old and vice versa. Everyone who is not generous or old is not brave. Everyone who is not creative or not brave is not rich. If someone is old or not rich then someone is not creative or not quiet. Everyone who is both not generous and rich is both creative and funny and vice versa. Everyone who is both happy and creative is kind or not generous. Everyone who is either brave or not old is funny. If john is both quiet and brave then paul is calm or kind and vice versa. If someone is both not brave and strong then mary is creative. Everyone who is calm or patient is either not kind or not patient. John is brave or creative. Someone is strong. Someone is either not funny or not humble. Mary is both quiet and not tall. Someone is curious. Someone is both strong and tall. Someone is not curious. Someone is either not calm or old. | Susan is rich. | neutral | ((?[X]:((patient(X)<~>~rich(X))))<=>(?[X]:(tall(X))))&
(![X]:(humble(X)=>generous(X)))&
(![X]:((wise(X)&~humble(X))<=>(patient(X)<~>~tall(X))))&
(((happy(alice)&~brave(alice)))<=>(?[X]:((patient(X)&~kind(X)))))&
(((old(alice)&humble(alice)))<=>(?[X]:((~curious(X)|patient(X)))))&
((?[X]:((~quiet(X)&~happy(X))))<=>(?[X]:((happy(X)|funny(X)))))&
(((~funny(susan)|~rich(susan)))<=>((~humble(susan)<~>~old(susan))))&
(![X]:((~generous(X)|old(X))=>~brave(X)))&
(![X]:((~creative(X)|~brave(X))=>~rich(X)))&
((?[X]:((old(X)|~rich(X))))=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((~generous(X)&rich(X))<=>(creative(X)&funny(X))))&
(![X]:((happy(X)&creative(X))=>(kind(X)|~generous(X))))&
(![X]:((brave(X)<~>~old(X))=>funny(X)))&
(((quiet(john)&brave(john)))<=>((calm(paul)|kind(paul))))&
((?[X]:((~brave(X)&strong(X))))=>(creative(mary)))&
(![X]:((calm(X)|patient(X))=>(~kind(X)<~>~patient(X))))&
((brave(john)|creative(john)))&
(?[X]:(strong(X)))&
(?[X]:((~funny(X)<~>~humble(X))))&
((quiet(mary)&~tall(mary)))&
(?[X]:(curious(X)))&
(?[X]:((strong(X)&tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~calm(X)<~>old(X)))) | rich(susan) | []
| null | 0 |
If susan is not wise then fred is not funny.
Everyone who is patient or not rich is both generous and not patient and vice versa.
If john is either not old or curious then someone is either not curious or wise and vice versa.
Everyone who is not brave is either not generous or generous and vice versa.
Everyone who is either old or tall is either quiet or not brave.
Everyone who is not funny is both not humble and brave.
Everyone who is both quiet and not funny is either not quiet or creative.
Everyone who is either not humble or quiet is both not rich and happy and vice versa.
If someone is not patient then someone is either generous or patient and vice versa.
If paul is not brave then someone is both not kind and curious.
Everyone who is not kind is either not humble or brave and vice versa.
If someone is not generous or strong then someone is either not generous or not brave.
Everyone who is either not calm or not generous is both not creative and not kind.
Everyone who is not strong or strong is generous and vice versa.
Everyone who is both not strong and generous is not brave or not humble and vice versa.
Someone is not brave.
Someone is not brave or not curious.
John is either not wise or calm.
Lucy is kind or rich.
Fred is either patient or creative.
Someone is patient or not tall. | Lucy is calm. | entailment | ((~wise(susan))=>(~funny(fred)))&
(![X]:((patient(X)|~rich(X))<=>(generous(X)&~patient(X))))&
(((~old(john)<~>curious(john)))<=>(?[X]:((~curious(X)<~>wise(X)))))&
(![X]:(~brave(X)<=>(~generous(X)<~>generous(X))))&
(![X]:((old(X)<~>tall(X))=>(quiet(X)<~>~brave(X))))&
(![X]:(~funny(X)=>(~humble(X)&brave(X))))&
(![X]:((quiet(X)&~funny(X))=>(~quiet(X)<~>creative(X))))&
(![X]:((~humble(X)<~>quiet(X))<=>(~rich(X)&happy(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)<~>patient(X)))))&
((~brave(paul))=>(?[X]:((~kind(X)&curious(X)))))&
(![X]:(~kind(X)<=>(~humble(X)<~>brave(X))))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:((~generous(X)<~>~brave(X)))))&
(![X]:((~calm(X)<~>~generous(X))=>(~creative(X)&~kind(X))))&
(![X]:((~strong(X)|strong(X))<=>generous(X)))&
(![X]:((~strong(X)&generous(X))<=>(~brave(X)|~humble(X))))&
(?[X]:(~brave(X)))&
(?[X]:((~brave(X)|~curious(X))))&
((~wise(john)<~>calm(john)))&
((kind(lucy)|rich(lucy)))&
((patient(fred)<~>creative(fred)))&
(?[X]:((patient(X)|~tall(X)))) | calm(lucy) | [
"p1",
"p3",
"p12",
"p14",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 6684342851265410805743354
% SZS output start Proof for 6684342851265410805743354
2. ! [X0] : ((~rich(X0) | patient(X0)) <=> (~patient(X0) & generous(X0))) [input p1]
4. ! [X0] : (~brave(X0) <=> (~generous(X0) <~> generous(X0))) [input p3]
13. ! [X0] : ((~calm(X0) <~> ~generous(X0)) => (~kind(X0) & ~creative(X0))) [input p12]
15. ! [X0] : ((generous(X0) & ~strong(X0)) <=> (~humble(X0) | ~brave(X0))) [input p14]
19. rich(lucy) | kind(lucy) [input p18]
22. ~calm(lucy) [input hypothesis]
32. ! [X0] : ((~kind(X0) & ~creative(X0)) | (~calm(X0) <=> ~generous(X0))) [ennf transformation 13]
33. ! [X0] : (((~rich(X0) | patient(X0)) | (patient(X0) | ~generous(X0))) & ((~patient(X0) & generous(X0)) | (rich(X0) & ~patient(X0)))) [nnf transformation 2]
34. ! [X0] : ((~rich(X0) | patient(X0) | patient(X0) | ~generous(X0)) & ((~patient(X0) & generous(X0)) | (rich(X0) & ~patient(X0)))) [flattening 33]
39. ! [X0] : ((~brave(X0) | ((~generous(X0) | ~generous(X0)) & (generous(X0) | generous(X0)))) & (((~generous(X0) | generous(X0)) & (generous(X0) | ~generous(X0))) | brave(X0))) [nnf transformation 4]
56. ! [X0] : ((~kind(X0) & ~creative(X0)) | ((~calm(X0) | generous(X0)) & (~generous(X0) | calm(X0)))) [nnf transformation 32]
59. ! [X0] : (((generous(X0) & ~strong(X0)) | (humble(X0) & brave(X0))) & ((~humble(X0) | ~brave(X0)) | (~generous(X0) | strong(X0)))) [nnf transformation 15]
60. ! [X0] : (((generous(X0) & ~strong(X0)) | (humble(X0) & brave(X0))) & (~humble(X0) | ~brave(X0) | ~generous(X0) | strong(X0))) [flattening 59]
72. ~patient(X0) | ~patient(X0) [cnf transformation 34]
74. ~rich(X0) | patient(X0) | patient(X0) | ~generous(X0) [cnf transformation 34]
85. ~brave(X0) | generous(X0) | generous(X0) [cnf transformation 39]
86. ~brave(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 39]
117. ~kind(X0) | ~generous(X0) | calm(X0) [cnf transformation 56]
125. generous(X0) | brave(X0) [cnf transformation 60]
131. rich(lucy) | kind(lucy) [cnf transformation 19]
135. ~calm(lucy) [cnf transformation 22]
137. ~brave(X0) | generous(X0) [duplicate literal removal 85]
138. ~brave(X0) | ~generous(X0) [duplicate literal removal 86]
139. ~patient(X0) [duplicate literal removal 72]
140. ~generous(X0) | patient(X0) | ~rich(X0) [duplicate literal removal 74]
180. ~brave(X0) [subsumption resolution 137,138]
201. 11 <=> ! [X1] : generous(X1) [avatar definition]
202. generous(X1) <- (11) [avatar component clause 201]
206. generous(X0) [subsumption resolution 125,180]
207. 11 [avatar split clause 206,201]
221. 14 <=> kind(lucy) [avatar definition]
223. kind(lucy) <- (14) [avatar component clause 221]
225. 15 <=> rich(lucy) [avatar definition]
227. rich(lucy) <- (15) [avatar component clause 225]
228. 14 | 15 [avatar split clause 131,225,221]
253. ~generous(lucy) | calm(lucy) <- (14) [resolution 117,223]
254. calm(lucy) <- (11, 14) [subsumption resolution 253,202]
255. $false <- (11, 14) [subsumption resolution 254,135]
256. ~11 | ~14 [avatar contradiction clause 255]
272. patient(X1) | ~rich(X1) <- (11) [resolution 140,202]
274. ~rich(X1) <- (11) [subsumption resolution 272,139]
285. $false <- (11, 15) [resolution 274,227]
286. ~11 | ~15 [avatar contradiction clause 285]
287. $false [avatar sat refutation 207,228,256,286]
% SZS output end Proof for 6684342851265410805743354
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not wise is either not funny or not quiet and vice versa. Everyone who is brave is both not quiet and happy and vice versa. If someone is not wise then john is both not patient and not funny and vice versa. If someone is either not old or curious then lucy is either not calm or not happy and vice versa. Everyone who is not old is old or strong. Everyone who is either not patient or happy is calm or not patient and vice versa. Everyone who is either kind or humble is tall and vice versa. Everyone who is both tall and not happy is not humble or not patient. Everyone who is not curious or curious is either curious or brave and vice versa. Everyone who is both brave and not kind is not old. If someone is not creative then someone is curious and vice versa. If someone is not quiet then mary is both not strong and not patient and vice versa. Everyone who is humble or old is both humble and quiet. Everyone who is tall or not old is not happy or not tall and vice versa. Everyone who is both not humble and not rich is strong or generous and vice versa. Everyone who is not rich or wise is not rich and vice versa. Fred is either not curious or humble. Someone is not happy or brave. Someone is both not wise and calm. Mary is either not rich or not creative. Someone is strong. Someone is not rich or funny. Someone is either not wise or funny. Fred is both tall and not kind. | Fred is not curious. | contradiction | (![X]:((~strong(X)&~wise(X))<=>(~funny(X)<~>~quiet(X))))&
(![X]:(brave(X)<=>(~quiet(X)&happy(X))))&
((?[X]:(~wise(X)))<=>((~patient(john)&~funny(john))))&
((?[X]:((~old(X)<~>curious(X))))<=>((~calm(lucy)<~>~happy(lucy))))&
(![X]:(~old(X)=>(old(X)|strong(X))))&
(![X]:((~patient(X)<~>happy(X))<=>(calm(X)|~patient(X))))&
(![X]:((kind(X)<~>humble(X))<=>tall(X)))&
(![X]:((tall(X)&~happy(X))=>(~humble(X)|~patient(X))))&
(![X]:((~curious(X)|curious(X))<=>(curious(X)<~>brave(X))))&
(![X]:((brave(X)&~kind(X))=>~old(X)))&
((?[X]:(~creative(X)))<=>(?[X]:(curious(X))))&
((?[X]:(~quiet(X)))<=>((~strong(mary)&~patient(mary))))&
(![X]:((humble(X)|old(X))=>(humble(X)&quiet(X))))&
(![X]:((tall(X)|~old(X))<=>(~happy(X)|~tall(X))))&
(![X]:((~humble(X)&~rich(X))<=>(strong(X)|generous(X))))&
(![X]:((~rich(X)|wise(X))<=>~rich(X)))&
((~curious(fred)<~>humble(fred)))&
(?[X]:((~happy(X)|brave(X))))&
(?[X]:((~wise(X)&calm(X))))&
((~rich(mary)<~>~creative(mary)))&
(?[X]:(strong(X)))&
(?[X]:((~rich(X)|funny(X))))&
(?[X]:((~wise(X)<~>funny(X))))&
((tall(fred)&~kind(fred))) | ~curious(fred) | [
"p1",
"p8",
"p13",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 8443247622698962542190198
% SZS output start Proof for 8443247622698962542190198
2. ! [X0] : (brave(X0) <=> (happy(X0) & ~quiet(X0))) [input p1]
9. ! [X0] : ((curious(X0) | ~curious(X0)) <=> (curious(X0) <~> brave(X0))) [input p8]
14. ! [X0] : ((~old(X0) | tall(X0)) <=> (~tall(X0) | ~happy(X0))) [input p13]
24. ~kind(fred) & tall(fred) [input p23]
25. ~curious(fred) [input hypothesis]
36. ! [X0] : ((brave(X0) | (~happy(X0) | quiet(X0))) & ((happy(X0) & ~quiet(X0)) | ~brave(X0))) [nnf transformation 2]
37. ! [X0] : ((brave(X0) | ~happy(X0) | quiet(X0)) & ((happy(X0) & ~quiet(X0)) | ~brave(X0))) [flattening 36]
50. ! [X0] : (((curious(X0) | ~curious(X0)) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0)))) & (((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | (~curious(X0) & curious(X0)))) [nnf transformation 9]
51. ! [X0] : ((curious(X0) | ~curious(X0) | ((curious(X0) | ~brave(X0)) & (brave(X0) | ~curious(X0)))) & (((~brave(X0) | ~curious(X0)) & (brave(X0) | curious(X0))) | (~curious(X0) & curious(X0)))) [flattening 50]
62. ! [X0] : (((~old(X0) | tall(X0)) | (tall(X0) & happy(X0))) & ((~tall(X0) | ~happy(X0)) | (old(X0) & ~tall(X0)))) [nnf transformation 14]
63. ! [X0] : ((~old(X0) | tall(X0) | (tall(X0) & happy(X0))) & (~tall(X0) | ~happy(X0) | (old(X0) & ~tall(X0)))) [flattening 62]
88. ~brave(X0) | happy(X0) [cnf transformation 37]
113. brave(X0) | curious(X0) | curious(X0) [cnf transformation 51]
129. ~tall(X0) | ~happy(X0) | ~tall(X0) [cnf transformation 63]
152. tall(fred) [cnf transformation 24]
154. ~curious(fred) [cnf transformation 25]
155. ~tall(X0) | ~happy(X0) [duplicate literal removal 129]
157. curious(X0) | brave(X0) [duplicate literal removal 113]
248. 19 <=> curious(fred) [avatar definition]
249. ~curious(fred) <- (~19) [avatar component clause 248]
295. ~19 [avatar split clause 154,248]
304. ~happy(fred) [resolution 155,152]
306. brave(fred) <- (~19) [resolution 157,249]
311. happy(fred) <- (~19) [resolution 306,88]
313. $false <- (~19) [subsumption resolution 311,304]
314. 19 [avatar contradiction clause 313]
315. $false [avatar sat refutation 295,314]
% SZS output end Proof for 8443247622698962542190198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall is quiet and vice versa. If someone is not strong or not kind then someone is not wise. Everyone who is both not humble and not strong is both not calm and not strong. If someone is both wise and not humble then mary is humble. If alice is both old and rich then someone is both not funny and quiet. If paul is not calm then susan is either old or not rich. Everyone who is both funny and not patient is rich and vice versa. Everyone who is both not brave and humble is kind or not calm. If john is happy then fred is either not old or not happy and vice versa. If someone is either brave or creative then someone is not brave and vice versa. Everyone who is curious is funny. If lucy is funny then fred is not quiet and vice versa. Everyone who is calm is either funny or not rich and vice versa. If john is not kind then someone is either quiet or old. Everyone who is not strong is both generous and old and vice versa. If someone is either patient or kind then fred is both curious and not rich and vice versa. Someone is either creative or not strong. Someone is calm or not creative. Paul is not brave. Susan is not tall. Fred is not funny or not creative. Susan is happy. Someone is either not generous or strong. | John is rich. | neutral | (![X]:(tall(X)<=>quiet(X)))&
((?[X]:((~strong(X)|~kind(X))))=>(?[X]:(~wise(X))))&
(![X]:((~humble(X)&~strong(X))=>(~calm(X)&~strong(X))))&
((?[X]:((wise(X)&~humble(X))))=>(humble(mary)))&
(((old(alice)&rich(alice)))=>(?[X]:((~funny(X)&quiet(X)))))&
((~calm(paul))=>((old(susan)<~>~rich(susan))))&
(![X]:((funny(X)&~patient(X))<=>rich(X)))&
(![X]:((~brave(X)&humble(X))=>(kind(X)|~calm(X))))&
((happy(john))<=>((~old(fred)<~>~happy(fred))))&
((?[X]:((brave(X)<~>creative(X))))<=>(?[X]:(~brave(X))))&
(![X]:(curious(X)=>funny(X)))&
((funny(lucy))<=>(~quiet(fred)))&
(![X]:(calm(X)<=>(funny(X)<~>~rich(X))))&
((~kind(john))=>(?[X]:((quiet(X)<~>old(X)))))&
(![X]:(~strong(X)<=>(generous(X)&old(X))))&
((?[X]:((patient(X)<~>kind(X))))<=>((curious(fred)&~rich(fred))))&
(?[X]:((creative(X)<~>~strong(X))))&
(?[X]:((calm(X)|~creative(X))))&
(~brave(paul))&
(~tall(susan))&
((~funny(fred)|~creative(fred)))&
(happy(susan))&
(?[X]:((~generous(X)<~>strong(X)))) | rich(john) | []
| null | 0 |
If someone is not tall or not generous then someone is both funny and curious. Everyone who is kind is both quiet and not brave and vice versa. Everyone who is happy is either calm or not tall and vice versa. If someone is patient or not happy then someone is not wise or patient and vice versa. If paul is either not happy or not old then someone is either old or not humble. Everyone who is calm is not rich or not tall. Everyone who is both not quiet and strong is not calm and vice versa. Everyone who is both not kind and not calm is not happy. If fred is not tall or not brave then alice is not calm or generous. Everyone who is both creative and quiet is either tall or not wise and vice versa. Everyone who is either not strong or not old is funny and vice versa. If someone is both tall and not old then someone is not patient. Everyone who is not brave or wise is not generous. Everyone who is not curious or kind is not quiet. If someone is both not patient and creative then someone is funny or creative. Everyone who is both not tall and curious is brave and vice versa. Mary is quiet. Paul is either not quiet or not creative. Mary is creative or old. Mary is both not strong and patient. Someone is both not rich and funny. John is both old and funny. Lucy is patient. Alice is wise or not calm. | Alice is strong. | entailment | ((?[X]:((~tall(X)|~generous(X))))=>(?[X]:((funny(X)&curious(X)))))&
(![X]:(kind(X)<=>(quiet(X)&~brave(X))))&
(![X]:(happy(X)<=>(calm(X)<~>~tall(X))))&
((?[X]:((patient(X)|~happy(X))))<=>(?[X]:((~wise(X)|patient(X)))))&
(((~happy(paul)<~>~old(paul)))=>(?[X]:((old(X)<~>~humble(X)))))&
(![X]:(calm(X)=>(~rich(X)|~tall(X))))&
(![X]:((~quiet(X)&strong(X))<=>~calm(X)))&
(![X]:((~kind(X)&~calm(X))=>~happy(X)))&
(((~tall(fred)|~brave(fred)))=>((~calm(alice)|generous(alice))))&
(![X]:((creative(X)&quiet(X))<=>(tall(X)<~>~wise(X))))&
(![X]:((~strong(X)<~>~old(X))<=>funny(X)))&
((?[X]:((tall(X)&~old(X))))=>(?[X]:(~patient(X))))&
(![X]:((~brave(X)|wise(X))=>~generous(X)))&
(![X]:((~curious(X)|kind(X))=>~quiet(X)))&
((?[X]:((~patient(X)&creative(X))))=>(?[X]:((funny(X)|creative(X)))))&
(![X]:((~tall(X)&curious(X))<=>brave(X)))&
(quiet(mary))&
((~quiet(paul)<~>~creative(paul)))&
((creative(mary)|old(mary)))&
((~strong(mary)&patient(mary)))&
(?[X]:((~rich(X)&funny(X))))&
((old(john)&funny(john)))&
(patient(lucy))&
((wise(alice)|~calm(alice))) | strong(alice) | [
"p6",
"p8",
"p12",
"p15",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 310700888048945273470745
% SZS output start Proof for 310700888048945273470745
7. ! [X0] : ((strong(X0) & ~quiet(X0)) <=> ~calm(X0)) [input p6]
9. (~brave(fred) | ~tall(fred)) => (generous(alice) | ~calm(alice)) [input p8]
13. ! [X0] : ((wise(X0) | ~brave(X0)) => ~generous(X0)) [input p12]
16. ! [X0] : ((curious(X0) & ~tall(X0)) <=> brave(X0)) [input p15]
24. ~calm(alice) | wise(alice) [input p23]
25. ~strong(alice) [input hypothesis]
37. (generous(alice) | ~calm(alice)) | (brave(fred) & tall(fred)) [ennf transformation 9]
38. generous(alice) | ~calm(alice) | (brave(fred) & tall(fred)) [flattening 37]
41. ! [X0] : (~generous(X0) | (~wise(X0) & brave(X0))) [ennf transformation 13]
58. ! [X0] : (((strong(X0) & ~quiet(X0)) | calm(X0)) & (~calm(X0) | (~strong(X0) | quiet(X0)))) [nnf transformation 7]
59. ! [X0] : (((strong(X0) & ~quiet(X0)) | calm(X0)) & (~calm(X0) | ~strong(X0) | quiet(X0))) [flattening 58]
69. ! [X0] : (((curious(X0) & ~tall(X0)) | ~brave(X0)) & (brave(X0) | (~curious(X0) | tall(X0)))) [nnf transformation 16]
70. ! [X0] : (((curious(X0) & ~tall(X0)) | ~brave(X0)) & (brave(X0) | ~curious(X0) | tall(X0))) [flattening 69]
95. strong(X0) | calm(X0) [cnf transformation 59]
97. generous(alice) | ~calm(alice) | tall(fred) [cnf transformation 38]
98. generous(alice) | ~calm(alice) | brave(fred) [cnf transformation 38]
109. ~wise(X0) | ~generous(X0) [cnf transformation 41]
114. ~brave(X0) | ~tall(X0) [cnf transformation 70]
126. ~calm(alice) | wise(alice) [cnf transformation 24]
127. ~strong(alice) [cnf transformation 25]
196. 16 <=> brave(fred) [avatar definition]
198. brave(fred) <- (16) [avatar component clause 196]
200. 17 <=> calm(alice) [avatar definition]
204. 18 <=> generous(alice) [avatar definition]
207. 16 | ~17 | 18 [avatar split clause 98,204,200,196]
209. 19 <=> tall(fred) [avatar definition]
211. tall(fred) <- (19) [avatar component clause 209]
212. 19 | ~17 | 18 [avatar split clause 97,204,200,209]
254. 29 <=> wise(alice) [avatar definition]
256. wise(alice) <- (29) [avatar component clause 254]
257. 29 | ~17 [avatar split clause 126,200,254]
261. calm(alice) [resolution 95,127]
264. 17 [avatar split clause 261,200]
266. ~generous(alice) <- (29) [resolution 109,256]
269. ~18 | ~29 [avatar split clause 266,254,204]
273. ~tall(fred) <- (16) [resolution 114,198]
274. $false <- (16, 19) [subsumption resolution 273,211]
275. ~16 | ~19 [avatar contradiction clause 274]
276. $false [avatar sat refutation 207,212,257,264,269,275]
% SZS output end Proof for 310700888048945273470745
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is both curious and wise then lucy is not curious and vice versa. Everyone who is quiet or not funny is patient or not humble and vice versa. Everyone who is both happy and calm is wise or not brave and vice versa. If lucy is both happy and not old then someone is both not wise and not strong. If someone is both funny and not rich then lucy is not tall. Everyone who is either rich or not funny is patient and vice versa. Everyone who is both not funny and rich is not wise or strong and vice versa. If susan is either curious or tall then someone is both not strong and calm. If someone is both not curious and funny then susan is both happy and not kind and vice versa. Everyone who is rich or not strong is generous and vice versa. Everyone who is not quiet or humble is brave or not calm. Everyone who is not tall is either not calm or humble and vice versa. Everyone who is either calm or humble is both creative and generous and vice versa. Everyone who is both not funny and not brave is not funny or strong and vice versa. If someone is not wise then someone is either funny or not tall. Everyone who is either not patient or not tall is both tall and not brave and vice versa. Mary is not brave. Alice is not wise or not rich. John is either wise or quiet. Someone is quiet or not wise. Someone is either calm or curious. Someone is either not old or not patient. Mary is patient or curious. Someone is either old or not old. | John is funny. | contradiction | (((curious(lucy)&wise(lucy)))<=>(~curious(lucy)))&
(![X]:((quiet(X)|~funny(X))<=>(patient(X)|~humble(X))))&
(![X]:((happy(X)&calm(X))<=>(wise(X)|~brave(X))))&
(((happy(lucy)&~old(lucy)))=>(?[X]:((~wise(X)&~strong(X)))))&
((?[X]:((funny(X)&~rich(X))))=>(~tall(lucy)))&
(![X]:((rich(X)<~>~funny(X))<=>patient(X)))&
(![X]:((~funny(X)&rich(X))<=>(~wise(X)|strong(X))))&
(((curious(susan)<~>tall(susan)))=>(?[X]:((~strong(X)&calm(X)))))&
((?[X]:((~curious(X)&funny(X))))<=>((happy(susan)&~kind(susan))))&
(![X]:((rich(X)|~strong(X))<=>generous(X)))&
(![X]:((~quiet(X)|humble(X))=>(brave(X)|~calm(X))))&
(![X]:(~tall(X)<=>(~calm(X)<~>humble(X))))&
(![X]:((calm(X)<~>humble(X))<=>(creative(X)&generous(X))))&
(![X]:((~funny(X)&~brave(X))<=>(~funny(X)|strong(X))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>~tall(X)))))&
(![X]:((~patient(X)<~>~tall(X))<=>(tall(X)&~brave(X))))&
(~brave(mary))&
((~wise(alice)|~rich(alice)))&
((wise(john)<~>quiet(john)))&
(?[X]:((quiet(X)|~wise(X))))&
(?[X]:((calm(X)<~>curious(X))))&
(?[X]:((~old(X)<~>~patient(X))))&
((patient(mary)|curious(mary)))&
(?[X]:((old(X)<~>~old(X)))) | funny(john) | [
"p0",
"p1",
"p2",
"p4",
"p5",
"p6",
"p10",
"p11",
"p13",
"p15",
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 7992862637543536890752541
% SZS output start Proof for 7992862637543536890752541
1. (wise(lucy) & curious(lucy)) <=> ~curious(lucy) [input p0]
2. ! [X0] : ((~funny(X0) | quiet(X0)) <=> (~humble(X0) | patient(X0))) [input p1]
3. ! [X0] : ((calm(X0) & happy(X0)) <=> (~brave(X0) | wise(X0))) [input p2]
5. ? [X0] : (~rich(X0) & funny(X0)) => ~tall(lucy) [input p4]
6. ! [X0] : ((rich(X0) <~> ~funny(X0)) <=> patient(X0)) [input p5]
7. ! [X0] : ((rich(X0) & ~funny(X0)) <=> (strong(X0) | ~wise(X0))) [input p6]
11. ! [X0] : ((humble(X0) | ~quiet(X0)) => (~calm(X0) | brave(X0))) [input p10]
12. ! [X0] : (~tall(X0) <=> (~calm(X0) <~> humble(X0))) [input p11]
14. ! [X0] : ((~brave(X0) & ~funny(X0)) <=> (strong(X0) | ~funny(X0))) [input p13]
16. ! [X0] : ((~patient(X0) <~> ~tall(X0)) <=> (~brave(X0) & tall(X0))) [input p15]
19. wise(john) <~> quiet(john) [input p18]
25. funny(john) [input hypothesis]
29. ~tall(lucy) | ! [X0] : (rich(X0) | ~funny(X0)) [ennf transformation 5]
31. ! [X0] : ((~calm(X0) | brave(X0)) | (~humble(X0) & quiet(X0))) [ennf transformation 11]
32. ! [X0] : (~calm(X0) | brave(X0) | (~humble(X0) & quiet(X0))) [flattening 31]
34. ((wise(lucy) & curious(lucy)) | curious(lucy)) & (~curious(lucy) | (~wise(lucy) | ~curious(lucy))) [nnf transformation 1]
35. ((wise(lucy) & curious(lucy)) | curious(lucy)) & (~curious(lucy) | ~wise(lucy) | ~curious(lucy)) [flattening 34]
36. ! [X0] : (((~funny(X0) | quiet(X0)) | (humble(X0) & ~patient(X0))) & ((~humble(X0) | patient(X0)) | (funny(X0) & ~quiet(X0)))) [nnf transformation 2]
37. ! [X0] : ((~funny(X0) | quiet(X0) | (humble(X0) & ~patient(X0))) & (~humble(X0) | patient(X0) | (funny(X0) & ~quiet(X0)))) [flattening 36]
38. ! [X0] : (((calm(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & ((~brave(X0) | wise(X0)) | (~calm(X0) | ~happy(X0)))) [nnf transformation 3]
39. ! [X0] : (((calm(X0) & happy(X0)) | (brave(X0) & ~wise(X0))) & (~brave(X0) | wise(X0) | ~calm(X0) | ~happy(X0))) [flattening 38]
42. ! [X0] : ((((funny(X0) | ~rich(X0)) & (~funny(X0) | rich(X0))) | ~patient(X0)) & (patient(X0) | ((rich(X0) | funny(X0)) & (~funny(X0) | ~rich(X0))))) [nnf transformation 6]
43. ! [X0] : (((rich(X0) & ~funny(X0)) | (~strong(X0) & wise(X0))) & ((strong(X0) | ~wise(X0)) | (~rich(X0) | funny(X0)))) [nnf transformation 7]
44. ! [X0] : (((rich(X0) & ~funny(X0)) | (~strong(X0) & wise(X0))) & (strong(X0) | ~wise(X0) | ~rich(X0) | funny(X0))) [flattening 43]
55. ! [X0] : ((~tall(X0) | ((~calm(X0) | ~humble(X0)) & (humble(X0) | calm(X0)))) & (((~humble(X0) | calm(X0)) & (humble(X0) | ~calm(X0))) | tall(X0))) [nnf transformation 12]
58. ! [X0] : (((~brave(X0) & ~funny(X0)) | (~strong(X0) & funny(X0))) & ((strong(X0) | ~funny(X0)) | (brave(X0) | funny(X0)))) [nnf transformation 14]
59. ! [X0] : (((~brave(X0) & ~funny(X0)) | (~strong(X0) & funny(X0))) & (strong(X0) | ~funny(X0) | brave(X0) | funny(X0))) [flattening 58]
64. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | (brave(X0) | ~tall(X0))) & ((~brave(X0) & tall(X0)) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [nnf transformation 16]
65. ! [X0] : ((((tall(X0) | patient(X0)) & (~tall(X0) | ~patient(X0))) | brave(X0) | ~tall(X0)) & ((~brave(X0) & tall(X0)) | ((~patient(X0) | tall(X0)) & (~tall(X0) | patient(X0))))) [flattening 64]
66. (~quiet(john) | ~wise(john)) & (quiet(john) | wise(john)) [nnf transformation 19]
78. ~curious(lucy) | ~wise(lucy) | ~curious(lucy) [cnf transformation 35]
79. curious(lucy) | curious(lucy) [cnf transformation 35]
82. ~humble(X0) | patient(X0) | funny(X0) [cnf transformation 37]
83. ~patient(X0) | quiet(X0) | ~funny(X0) [cnf transformation 37]
89. brave(X0) | calm(X0) [cnf transformation 39]
92. ~tall(lucy) | rich(X0) | ~funny(X0) [cnf transformation 29]
93. ~rich(X0) | ~funny(X0) | patient(X0) [cnf transformation 42]
98. ~funny(X0) | wise(X0) [cnf transformation 44]
114. ~calm(X0) | brave(X0) | ~humble(X0) [cnf transformation 32]
115. ~calm(X0) | humble(X0) | tall(X0) [cnf transformation 55]
128. ~brave(X0) | funny(X0) [cnf transformation 59]
136. ~tall(X0) | ~patient(X0) | brave(X0) | ~tall(X0) [cnf transformation 65]
141. ~quiet(john) | ~wise(john) [cnf transformation 66]
150. funny(john) [cnf transformation 25]
152. ~tall(X0) | ~patient(X0) | brave(X0) [duplicate literal removal 136]
153. ~curious(lucy) | ~wise(lucy) [duplicate literal removal 78]
154. curious(lucy) [duplicate literal removal 79]
156. 1 <=> curious(lucy) [avatar definition]
160. 2 <=> wise(lucy) [avatar definition]
161. ~wise(lucy) <- (~2) [avatar component clause 160]
164. 1 [avatar split clause 154,156]
165. ~2 | ~1 [avatar split clause 153,156,160]
185. 7 <=> ! [X0] : (rich(X0) | ~funny(X0)) [avatar definition]
186. ~funny(X0) | rich(X0) <- (7) [avatar component clause 185]
188. 8 <=> tall(lucy) [avatar definition]
190. ~tall(lucy) <- (~8) [avatar component clause 188]
191. 7 | ~8 [avatar split clause 92,188,185]
235. ~humble(X0) | brave(X0) [subsumption resolution 114,89]
260. 23 <=> wise(john) [avatar definition]
264. 24 <=> quiet(john) [avatar definition]
267. ~23 | ~24 [avatar split clause 141,264,260]
311. wise(john) [resolution 98,150]
320. calm(X0) | funny(X0) [resolution 128,89]
383. tall(X0) | humble(X0) | funny(X0) [resolution 115,320]
537. humble(X0) | funny(X0) | ~patient(X0) | brave(X0) [resolution 383,152]
541. humble(lucy) | funny(lucy) <- (~8) [resolution 383,190]
545. funny(X0) | ~patient(X0) | brave(X0) [subsumption resolution 537,235]
546. funny(X0) | ~patient(X0) [subsumption resolution 545,128]
548. 49 <=> funny(lucy) [avatar definition]
550. funny(lucy) <- (49) [avatar component clause 548]
552. 50 <=> humble(lucy) [avatar definition]
554. humble(lucy) <- (50) [avatar component clause 552]
555. 49 | 50 | 8 [avatar split clause 541,188,552,548]
572. patient(lucy) | funny(lucy) <- (50) [resolution 554,82]
591. funny(lucy) <- (50) [subsumption resolution 572,546]
592. 49 | ~50 [avatar split clause 591,552,548]
669. wise(lucy) <- (49) [resolution 550,98]
670. $false <- (~2, 49) [subsumption resolution 669,161]
671. 2 | ~49 [avatar contradiction clause 670]
681. rich(john) <- (7) [resolution 186,150]
684. ~funny(john) | patient(john) <- (7) [resolution 681,93]
686. patient(john) <- (7) [subsumption resolution 684,150]
689. quiet(john) | ~funny(john) <- (7) [resolution 686,83]
695. 23 [avatar split clause 311,260]
696. quiet(john) <- (7) [subsumption resolution 689,150]
697. 24 | ~7 [avatar split clause 696,185,264]
698. $false [avatar sat refutation 164,165,191,267,555,592,671,695,697]
% SZS output end Proof for 7992862637543536890752541
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
If susan is both not tall and not rich then someone is generous or not calm.
If someone is not generous or not rich then someone is not quiet and vice versa.
If someone is not generous then john is both curious and patient and vice versa.
Everyone who is not happy is both not strong and patient and vice versa.
If someone is wise or patient then someone is kind or happy and vice versa.
If john is brave or not quiet then someone is calm.
If someone is creative then someone is either kind or not humble and vice versa.
If susan is happy or not generous then someone is patient.
Everyone who is both strong and old is either not kind or strong and vice versa.
If someone is not creative then lucy is kind.
Everyone who is both quiet and rich is not tall.
Everyone who is either brave or creative is both calm and creative and vice versa.
If someone is not quiet or not tall then alice is both humble and not wise and vice versa.
Everyone who is not rich or humble is either not happy or patient.
If someone is humble or not kind then mary is both patient and quiet.
Everyone who is not brave or not tall is old or rich.
Someone is not wise.
Someone is calm.
John is not patient.
Alice is not brave.
Mary is both kind and brave.
Someone is either not funny or happy. | Alice is not humble. | contradiction | (((~tall(susan)&~rich(susan)))=>(?[X]:((generous(X)|~calm(X)))))&
((?[X]:((~generous(X)|~rich(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:(~generous(X)))<=>((curious(john)&patient(john))))&
(![X]:(~happy(X)<=>(~strong(X)&patient(X))))&
((?[X]:((wise(X)|patient(X))))<=>(?[X]:((kind(X)|happy(X)))))&
(((brave(john)|~quiet(john)))=>(?[X]:(calm(X))))&
((?[X]:(creative(X)))<=>(?[X]:((kind(X)<~>~humble(X)))))&
(((happy(susan)|~generous(susan)))=>(?[X]:(patient(X))))&
(![X]:((strong(X)&old(X))<=>(~kind(X)<~>strong(X))))&
((?[X]:(~creative(X)))=>(kind(lucy)))&
(![X]:((quiet(X)&rich(X))=>~tall(X)))&
(![X]:((brave(X)<~>creative(X))<=>(calm(X)&creative(X))))&
((?[X]:((~quiet(X)|~tall(X))))<=>((humble(alice)&~wise(alice))))&
(![X]:((~rich(X)|humble(X))=>(~happy(X)<~>patient(X))))&
((?[X]:((humble(X)|~kind(X))))=>((patient(mary)&quiet(mary))))&
(![X]:((~brave(X)|~tall(X))=>(old(X)|rich(X))))&
(?[X]:(~wise(X)))&
(?[X]:(calm(X)))&
(~patient(john))&
(~brave(alice))&
((kind(mary)&brave(mary)))&
(?[X]:((~funny(X)<~>happy(X)))) | ~humble(alice) | [
"p1",
"p10",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 3902880546653434287796088
% SZS output start Proof for 3902880546653434287796088
2. ? [X0] : (~rich(X0) | ~generous(X0)) <=> ? [X0] : ~quiet(X0) [input p1]
11. ! [X0] : ((rich(X0) & quiet(X0)) => ~tall(X0)) [input p10]
13. ? [X0] : (~tall(X0) | ~quiet(X0)) <=> (~wise(alice) & humble(alice)) [input p12]
23. ~humble(alice) [input hypothesis]
24. ? [X0] : (~rich(X0) | ~generous(X0)) <=> ? [X1] : ~quiet(X1) [rectify 2]
32. ! [X0] : (~tall(X0) | (~rich(X0) | ~quiet(X0))) [ennf transformation 11]
33. ! [X0] : (~tall(X0) | ~rich(X0) | ~quiet(X0)) [flattening 32]
40. (? [X0] : (~rich(X0) | ~generous(X0)) | ! [X1] : quiet(X1)) & (? [X1] : ~quiet(X1) | ! [X0] : (rich(X0) & generous(X0))) [nnf transformation 24]
41. (? [X0] : (~rich(X0) | ~generous(X0)) | ! [X1] : quiet(X1)) & (? [X2] : ~quiet(X2) | ! [X3] : (rich(X3) & generous(X3))) [rectify 40]
42. ? [X0] : (~rich(X0) | ~generous(X0)) => (~rich(sK1) | ~generous(sK1)) [choice axiom]
43. ? [X2] : ~quiet(X2) => ~quiet(sK2) [choice axiom]
44. ((~rich(sK1) | ~generous(sK1)) | ! [X1] : quiet(X1)) & (~quiet(sK2) | ! [X3] : (rich(X3) & generous(X3))) [skolemisation 41,43,42]
70. (? [X0] : (~tall(X0) | ~quiet(X0)) | (wise(alice) | ~humble(alice))) & ((~wise(alice) & humble(alice)) | ! [X0] : (tall(X0) & quiet(X0))) [nnf transformation 13]
71. (? [X0] : (~tall(X0) | ~quiet(X0)) | wise(alice) | ~humble(alice)) & ((~wise(alice) & humble(alice)) | ! [X0] : (tall(X0) & quiet(X0))) [flattening 70]
72. (? [X0] : (~tall(X0) | ~quiet(X0)) | wise(alice) | ~humble(alice)) & ((~wise(alice) & humble(alice)) | ! [X1] : (tall(X1) & quiet(X1))) [rectify 71]
73. ? [X0] : (~tall(X0) | ~quiet(X0)) => (~tall(sK10) | ~quiet(sK10)) [choice axiom]
74. ((~tall(sK10) | ~quiet(sK10)) | wise(alice) | ~humble(alice)) & ((~wise(alice) & humble(alice)) | ! [X1] : (tall(X1) & quiet(X1))) [skolemisation 72,73]
85. ~quiet(sK2) | rich(X3) [cnf transformation 44]
112. ~quiet(X0) | ~rich(X0) | ~tall(X0) [cnf transformation 33]
119. humble(alice) | quiet(X1) [cnf transformation 74]
120. humble(alice) | tall(X1) [cnf transformation 74]
142. ~humble(alice) [cnf transformation 23]
165. 5 <=> ! [X1] : quiet(X1) [avatar definition]
166. quiet(X1) <- (5) [avatar component clause 165]
177. 8 <=> ! [X3] : rich(X3) [avatar definition]
178. rich(X3) <- (8) [avatar component clause 177]
180. 9 <=> quiet(sK2) [avatar definition]
182. ~quiet(sK2) <- (~9) [avatar component clause 180]
183. 8 | ~9 [avatar split clause 85,180,177]
298. 36 <=> humble(alice) [avatar definition]
315. 40 <=> ! [X1] : tall(X1) [avatar definition]
316. tall(X1) <- (40) [avatar component clause 315]
319. 40 | 36 [avatar split clause 120,298,315]
320. 5 | 36 [avatar split clause 119,298,165]
354. ~36 [avatar split clause 142,298]
361. $false <- (5, ~9) [resolution 182,166]
362. ~5 | 9 [avatar contradiction clause 361]
413. ~rich(X0) | ~tall(X0) <- (5) [resolution 112,166]
415. ~tall(X0) <- (5, 8) [subsumption resolution 413,178]
416. $false <- (5, 8, 40) [subsumption resolution 415,316]
417. ~5 | ~8 | ~40 [avatar contradiction clause 416]
421. $false [avatar sat refutation 183,319,320,354,362,417]
% SZS output end Proof for 3902880546653434287796088
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or not curious is either not kind or humble and vice versa.
Everyone who is both not quiet and not wise is strong or quiet and vice versa.
If someone is not strong or rich then mary is not curious or not tall.
Everyone who is either not curious or strong is not kind and vice versa.
If paul is either not kind or not strong then mary is not old or brave and vice versa.
Everyone who is either not old or not humble is both rich and not funny and vice versa.
If someone is strong then john is generous or quiet and vice versa.
Everyone who is either patient or not brave is not tall or old.
Everyone who is either not tall or generous is not quiet and vice versa.
If someone is brave then someone is kind or patient and vice versa.
Everyone who is kind or not kind is humble and vice versa.
Everyone who is either rich or not calm is not wise or creative.
If someone is either brave or curious then alice is brave or funny.
If paul is either quiet or not creative then mary is humble.
Everyone who is not curious or kind is not patient or not rich and vice versa.
Everyone who is both not humble and happy is both not kind and not curious.
Paul is either rich or happy.
Lucy is either calm or not patient.
Someone is either not brave or creative.
John is either generous or curious.
Mary is either humble or wise. | Lucy is quiet. | contradiction | (![X]:((happy(X)<~>~curious(X))<=>(~kind(X)<~>humble(X))))&
(![X]:((~quiet(X)&~wise(X))<=>(strong(X)|quiet(X))))&
((?[X]:((~strong(X)|rich(X))))=>((~curious(mary)|~tall(mary))))&
(![X]:((~curious(X)<~>strong(X))<=>~kind(X)))&
(((~kind(paul)<~>~strong(paul)))<=>((~old(mary)|brave(mary))))&
(![X]:((~old(X)<~>~humble(X))<=>(rich(X)&~funny(X))))&
((?[X]:(strong(X)))<=>((generous(john)|quiet(john))))&
(![X]:((patient(X)<~>~brave(X))=>(~tall(X)|old(X))))&
(![X]:((~tall(X)<~>generous(X))<=>~quiet(X)))&
((?[X]:(brave(X)))<=>(?[X]:((kind(X)|patient(X)))))&
(![X]:((kind(X)|~kind(X))<=>humble(X)))&
(![X]:((rich(X)<~>~calm(X))=>(~wise(X)|creative(X))))&
((?[X]:((brave(X)<~>curious(X))))=>((brave(alice)|funny(alice))))&
(((quiet(paul)<~>~creative(paul)))=>(humble(mary)))&
(![X]:((~curious(X)|kind(X))<=>(~patient(X)|~rich(X))))&
(![X]:((~humble(X)&happy(X))=>(~kind(X)&~curious(X))))&
((rich(paul)<~>happy(paul)))&
((calm(lucy)<~>~patient(lucy)))&
(?[X]:((~brave(X)<~>creative(X))))&
((generous(john)<~>curious(john)))&
((humble(mary)<~>wise(mary))) | quiet(lucy) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 7917260291086892062463300
% SZS output start Proof for 7917260291086892062463300
2. ! [X0] : ((~wise(X0) & ~quiet(X0)) <=> (quiet(X0) | strong(X0))) [input p1]
22. quiet(lucy) [input hypothesis]
36. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & ((quiet(X0) | strong(X0)) | (wise(X0) | quiet(X0)))) [nnf transformation 2]
37. ! [X0] : (((~wise(X0) & ~quiet(X0)) | (~quiet(X0) & ~strong(X0))) & (quiet(X0) | strong(X0) | wise(X0) | quiet(X0))) [flattening 36]
79. ~quiet(X0) | ~quiet(X0) [cnf transformation 37]
137. quiet(lucy) [cnf transformation 22]
139. ~quiet(X0) [duplicate literal removal 79]
273. $false [subsumption resolution 137,139]
% SZS output end Proof for 7917260291086892062463300
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or curious is generous or humble and vice versa.
If someone is both not strong and not humble then alice is both not strong and not kind and vice versa.
If susan is not humble then someone is not funny.
If fred is both not calm and not generous then someone is both not old and not generous and vice versa.
Everyone who is not tall is both humble and generous and vice versa.
If someone is both strong and not old then someone is not generous or brave.
Everyone who is humble or brave is funny.
If susan is not curious or not old then someone is either curious or not old and vice versa.
If mary is both tall and not happy then fred is strong and vice versa.
Everyone who is either brave or curious is both not patient and brave and vice versa.
If someone is quiet or brave then fred is not funny or not strong and vice versa.
If susan is both not kind and funny then someone is both not funny and humble and vice versa.
Everyone who is kind or quiet is not happy or happy.
Everyone who is not patient is either brave or not curious.
If john is not rich then susan is either not humble or not funny.
If someone is old or wise then someone is not rich and vice versa.
Someone is generous.
Someone is both not wise and rich.
Someone is both not brave and calm.
Paul is quiet.
Someone is not generous.
Susan is both not kind and patient.
Someone is both not humble and brave.
Paul is tall. | Susan is curious. | contradiction | (![X]:((strong(X)<~>curious(X))<=>(generous(X)|humble(X))))&
((?[X]:((~strong(X)&~humble(X))))<=>((~strong(alice)&~kind(alice))))&
((~humble(susan))=>(?[X]:(~funny(X))))&
(((~calm(fred)&~generous(fred)))<=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:(~tall(X)<=>(humble(X)&generous(X))))&
((?[X]:((strong(X)&~old(X))))=>(?[X]:((~generous(X)|brave(X)))))&
(![X]:((humble(X)|brave(X))=>funny(X)))&
(((~curious(susan)|~old(susan)))<=>(?[X]:((curious(X)<~>~old(X)))))&
(((tall(mary)&~happy(mary)))<=>(strong(fred)))&
(![X]:((brave(X)<~>curious(X))<=>(~patient(X)&brave(X))))&
((?[X]:((quiet(X)|brave(X))))<=>((~funny(fred)|~strong(fred))))&
(((~kind(susan)&funny(susan)))<=>(?[X]:((~funny(X)&humble(X)))))&
(![X]:((kind(X)|quiet(X))=>(~happy(X)|happy(X))))&
(![X]:(~patient(X)=>(brave(X)<~>~curious(X))))&
((~rich(john))=>((~humble(susan)<~>~funny(susan))))&
((?[X]:((old(X)|wise(X))))<=>(?[X]:(~rich(X))))&
(?[X]:(generous(X)))&
(?[X]:((~wise(X)&rich(X))))&
(?[X]:((~brave(X)&calm(X))))&
(quiet(paul))&
(?[X]:(~generous(X)))&
((~kind(susan)&patient(susan)))&
(?[X]:((~humble(X)&brave(X))))&
(tall(paul)) | curious(susan) | [
"p6",
"p9",
"p11",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 3965102751219846955198403
% SZS output start Proof for 3965102751219846955198403
7. ! [X0] : ((brave(X0) | humble(X0)) => funny(X0)) [input p6]
10. ! [X0] : ((brave(X0) <~> curious(X0)) <=> (brave(X0) & ~patient(X0))) [input p9]
12. (funny(susan) & ~kind(susan)) <=> ? [X0] : (humble(X0) & ~funny(X0)) [input p11]
22. patient(susan) & ~kind(susan) [input p21]
25. curious(susan) [input hypothesis]
30. ! [X0] : (funny(X0) | (~brave(X0) & ~humble(X0))) [ennf transformation 7]
61. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | (~brave(X0) | patient(X0))) & ((brave(X0) & ~patient(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [nnf transformation 10]
62. ! [X0] : ((((~curious(X0) | ~brave(X0)) & (curious(X0) | brave(X0))) | ~brave(X0) | patient(X0)) & ((brave(X0) & ~patient(X0)) | ((brave(X0) | ~curious(X0)) & (curious(X0) | ~brave(X0))))) [flattening 61]
68. ((funny(susan) & ~kind(susan)) | ! [X0] : (~humble(X0) | funny(X0))) & (? [X0] : (humble(X0) & ~funny(X0)) | (~funny(susan) | kind(susan))) [nnf transformation 12]
69. ((funny(susan) & ~kind(susan)) | ! [X0] : (~humble(X0) | funny(X0))) & (? [X0] : (humble(X0) & ~funny(X0)) | ~funny(susan) | kind(susan)) [flattening 68]
70. ((funny(susan) & ~kind(susan)) | ! [X0] : (~humble(X0) | funny(X0))) & (? [X1] : (humble(X1) & ~funny(X1)) | ~funny(susan) | kind(susan)) [rectify 69]
71. ? [X1] : (humble(X1) & ~funny(X1)) => (humble(sK6) & ~funny(sK6)) [choice axiom]
72. ((funny(susan) & ~kind(susan)) | ! [X0] : (~humble(X0) | funny(X0))) & ((humble(sK6) & ~funny(sK6)) | ~funny(susan) | kind(susan)) [skolemisation 70,71]
109. ~humble(X0) | funny(X0) [cnf transformation 30]
110. ~brave(X0) | funny(X0) [cnf transformation 30]
123. brave(X0) | brave(X0) | ~curious(X0) [cnf transformation 62]
130. ~funny(sK6) | ~funny(susan) | kind(susan) [cnf transformation 72]
131. humble(sK6) | ~funny(susan) | kind(susan) [cnf transformation 72]
150. ~kind(susan) [cnf transformation 22]
155. curious(susan) [cnf transformation 25]
156. ~curious(X0) | brave(X0) [duplicate literal removal 123]
229. 17 <=> curious(susan) [avatar definition]
230. curious(susan) <- (17) [avatar component clause 229]
291. 30 <=> kind(susan) [avatar definition]
295. 31 <=> funny(susan) [avatar definition]
297. ~funny(susan) <- (~31) [avatar component clause 295]
299. 32 <=> humble(sK6) [avatar definition]
301. humble(sK6) <- (32) [avatar component clause 299]
302. 30 | ~31 | 32 [avatar split clause 131,299,295,291]
304. 33 <=> funny(sK6) [avatar definition]
307. 30 | ~31 | ~33 [avatar split clause 130,304,295,291]
341. ~30 [avatar split clause 150,291]
342. 17 [avatar split clause 155,229]
347. funny(sK6) <- (32) [resolution 109,301]
351. 33 | ~32 [avatar split clause 347,299,304]
353. brave(susan) <- (17) [resolution 156,230]
356. funny(susan) <- (17) [resolution 353,110]
357. $false <- (17, ~31) [subsumption resolution 356,297]
358. ~17 | 31 [avatar contradiction clause 357]
359. $false [avatar sat refutation 302,307,341,342,351,358]
% SZS output end Proof for 3965102751219846955198403
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If paul is old then paul is not quiet or not wise.
Everyone who is both old and creative is generous and vice versa.
Everyone who is not happy or not kind is either not old or not wise.
If someone is either calm or not brave then someone is either curious or not wise and vice versa.
If john is old then lucy is both not calm and creative and vice versa.
Everyone who is not strong or not patient is either strong or not old.
Everyone who is not humble or not brave is both humble and not generous and vice versa.
Everyone who is not kind or not brave is quiet or not rich.
Everyone who is not wise is not curious and vice versa.
If someone is not kind or wise then mary is both wise and not wise and vice versa.
Everyone who is not generous is humble and vice versa.
If paul is both not creative and not kind then mary is either not quiet or not patient.
If susan is not kind then someone is curious and vice versa.
Everyone who is not generous is not kind or strong and vice versa.
If john is old or not rich then someone is not happy and vice versa.
Everyone who is not quiet is not quiet or funny and vice versa.
Someone is rich.
Alice is either not kind or not tall.
John is either not humble or not tall.
Paul is not strong or calm.
Someone is not rich. | Susan is not quiet. | neutral | ((old(paul))=>((~quiet(paul)|~wise(paul))))&
(![X]:((old(X)&creative(X))<=>generous(X)))&
(![X]:((~happy(X)|~kind(X))=>(~old(X)<~>~wise(X))))&
((?[X]:((calm(X)<~>~brave(X))))<=>(?[X]:((curious(X)<~>~wise(X)))))&
((old(john))<=>((~calm(lucy)&creative(lucy))))&
(![X]:((~strong(X)|~patient(X))=>(strong(X)<~>~old(X))))&
(![X]:((~humble(X)|~brave(X))<=>(humble(X)&~generous(X))))&
(![X]:((~kind(X)|~brave(X))=>(quiet(X)|~rich(X))))&
(![X]:(~wise(X)<=>~curious(X)))&
((?[X]:((~kind(X)|wise(X))))<=>((wise(mary)&~wise(mary))))&
(![X]:(~generous(X)<=>humble(X)))&
(((~creative(paul)&~kind(paul)))=>((~quiet(mary)<~>~patient(mary))))&
((~kind(susan))<=>(?[X]:(curious(X))))&
(![X]:(~generous(X)<=>(~kind(X)|strong(X))))&
(((old(john)|~rich(john)))<=>(?[X]:(~happy(X))))&
(![X]:(~quiet(X)<=>(~quiet(X)|funny(X))))&
(?[X]:(rich(X)))&
((~kind(alice)<~>~tall(alice)))&
((~humble(john)<~>~tall(john)))&
((~strong(paul)|calm(paul)))&
(?[X]:(~rich(X))) | ~quiet(susan) | []
| null | 0 |
Everyone who is both not generous and not kind is kind.
If alice is both wise and calm then someone is funny or wise and vice versa.
If someone is not old then someone is both wise and not rich.
If someone is either calm or not rich then someone is not kind or curious and vice versa.
Everyone who is not rich or not curious is not quiet and vice versa.
If paul is not old then someone is both kind and not old and vice versa.
If someone is tall or brave then someone is either not strong or old and vice versa.
Everyone who is either not calm or generous is rich and vice versa.
If paul is either not old or strong then someone is both generous and kind.
Everyone who is not happy or tall is not tall.
If alice is strong or not brave then someone is either tall or curious and vice versa.
Everyone who is both not strong and not creative is both rich and calm and vice versa.
If mary is either calm or not patient then someone is both brave and not generous and vice versa.
Everyone who is either not old or not happy is quiet.
If mary is either not creative or patient then mary is both brave and not humble and vice versa.
If lucy is either not calm or not tall then alice is not brave or not wise and vice versa.
Someone is not humble or strong.
Someone is either not wise or not humble.
Fred is both wise and creative.
Paul is not brave or not wise.
Mary is not calm.
Lucy is both not creative and rich.
Someone is not kind or not quiet.
Someone is either quiet or tall. | Lucy is not creative. | entailment | (![X]:((~generous(X)&~kind(X))=>kind(X)))&
(((wise(alice)&calm(alice)))<=>(?[X]:((funny(X)|wise(X)))))&
((?[X]:(~old(X)))=>(?[X]:((wise(X)&~rich(X)))))&
((?[X]:((calm(X)<~>~rich(X))))<=>(?[X]:((~kind(X)|curious(X)))))&
(![X]:((~rich(X)|~curious(X))<=>~quiet(X)))&
((~old(paul))<=>(?[X]:((kind(X)&~old(X)))))&
((?[X]:((tall(X)|brave(X))))<=>(?[X]:((~strong(X)<~>old(X)))))&
(![X]:((~calm(X)<~>generous(X))<=>rich(X)))&
(((~old(paul)<~>strong(paul)))=>(?[X]:((generous(X)&kind(X)))))&
(![X]:((~happy(X)|tall(X))=>~tall(X)))&
(((strong(alice)|~brave(alice)))<=>(?[X]:((tall(X)<~>curious(X)))))&
(![X]:((~strong(X)&~creative(X))<=>(rich(X)&calm(X))))&
(((calm(mary)<~>~patient(mary)))<=>(?[X]:((brave(X)&~generous(X)))))&
(![X]:((~old(X)<~>~happy(X))=>quiet(X)))&
(((~creative(mary)<~>patient(mary)))<=>((brave(mary)&~humble(mary))))&
(((~calm(lucy)<~>~tall(lucy)))<=>((~brave(alice)|~wise(alice))))&
(?[X]:((~humble(X)|strong(X))))&
(?[X]:((~wise(X)<~>~humble(X))))&
((wise(fred)&creative(fred)))&
((~brave(paul)|~wise(paul)))&
(~calm(mary))&
((~creative(lucy)&rich(lucy)))&
(?[X]:((~kind(X)|~quiet(X))))&
(?[X]:((quiet(X)<~>tall(X)))) | ~creative(lucy) | [
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 1222202050406310871882602
% SZS output start Proof for 1222202050406310871882602
22. rich(lucy) & ~creative(lucy) [input p21]
25. creative(lucy) [input hypothesis]
162. ~creative(lucy) [cnf transformation 22]
167. creative(lucy) [cnf transformation 25]
446. $false [subsumption resolution 167,162]
% SZS output end Proof for 1222202050406310871882602
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or wise is either kind or rich and vice versa.
If someone is either not kind or wise then someone is calm and vice versa.
If someone is not happy then someone is creative or brave and vice versa.
If john is both happy and creative then fred is not humble or not calm and vice versa.
If mary is not generous then john is not patient.
If someone is both not calm and rich then someone is not generous or tall.
Everyone who is both brave and wise is not wise and vice versa.
Everyone who is calm is quiet or kind and vice versa.
Everyone who is both not strong and kind is both rich and tall and vice versa.
Everyone who is both not kind and tall is both not curious and creative.
Everyone who is both not curious and not kind is not brave or humble and vice versa.
Everyone who is rich or not patient is either wise or kind and vice versa.
If someone is curious then fred is not funny.
If fred is both not quiet and not old then someone is either not quiet or not happy and vice versa.
Everyone who is not tall is not funny or funny and vice versa.
Everyone who is either not patient or not kind is rich.
Someone is not curious.
Someone is both strong and not rich.
Alice is either not generous or not creative.
John is not curious or brave.
Alice is both not quiet and not calm.
Someone is either kind or not quiet.
Alice is generous. | Mary is not rich. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(kind(X)<~>rich(X))))&
((?[X]:((~kind(X)<~>wise(X))))<=>(?[X]:(calm(X))))&
((?[X]:(~happy(X)))<=>(?[X]:((creative(X)|brave(X)))))&
(((happy(john)&creative(john)))<=>((~humble(fred)|~calm(fred))))&
((~generous(mary))=>(~patient(john)))&
((?[X]:((~calm(X)&rich(X))))=>(?[X]:((~generous(X)|tall(X)))))&
(![X]:((brave(X)&wise(X))<=>~wise(X)))&
(![X]:(calm(X)<=>(quiet(X)|kind(X))))&
(![X]:((~strong(X)&kind(X))<=>(rich(X)&tall(X))))&
(![X]:((~kind(X)&tall(X))=>(~curious(X)&creative(X))))&
(![X]:((~curious(X)&~kind(X))<=>(~brave(X)|humble(X))))&
(![X]:((rich(X)|~patient(X))<=>(wise(X)<~>kind(X))))&
((?[X]:(curious(X)))=>(~funny(fred)))&
(((~quiet(fred)&~old(fred)))<=>(?[X]:((~quiet(X)<~>~happy(X)))))&
(![X]:(~tall(X)<=>(~funny(X)|funny(X))))&
(![X]:((~patient(X)<~>~kind(X))=>rich(X)))&
(?[X]:(~curious(X)))&
(?[X]:((strong(X)&~rich(X))))&
((~generous(alice)<~>~creative(alice)))&
((~curious(john)|brave(john)))&
((~quiet(alice)&~calm(alice)))&
(?[X]:((kind(X)<~>~quiet(X))))&
(generous(alice)) | ~rich(mary) | [
"p0",
"p1",
"p6",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 654101865629019204592491
% SZS output start Proof for 654101865629019204592491
1. ! [X0] : ((~curious(X0) <~> wise(X0)) <=> (kind(X0) <~> rich(X0))) [input p0]
2. ? [X0] : (~kind(X0) <~> wise(X0)) <=> ? [X0] : calm(X0) [input p1]
7. ! [X0] : ((wise(X0) & brave(X0)) <=> ~wise(X0)) [input p6]
11. ! [X0] : ((~kind(X0) & ~curious(X0)) <=> (humble(X0) | ~brave(X0))) [input p10]
24. rich(mary) [input hypothesis]
25. ? [X0] : (~kind(X0) <~> wise(X0)) <=> ? [X1] : calm(X1) [rectify 2]
34. ! [X0] : ((((~wise(X0) | curious(X0)) & (wise(X0) | ~curious(X0))) | ((kind(X0) | ~rich(X0)) & (rich(X0) | ~kind(X0)))) & (((~rich(X0) | ~kind(X0)) & (rich(X0) | kind(X0))) | ((~curious(X0) | ~wise(X0)) & (wise(X0) | curious(X0))))) [nnf transformation 1]
35. (? [X0] : ((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : ((~kind(X0) | ~wise(X0)) & (wise(X0) | kind(X0)))) [nnf transformation 25]
36. (? [X0] : ((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : ((~kind(X3) | ~wise(X3)) & (wise(X3) | kind(X3)))) [rectify 35]
37. ? [X0] : ((~wise(X0) | kind(X0)) & (wise(X0) | ~kind(X0))) => ((~wise(sK0) | kind(sK0)) & (wise(sK0) | ~kind(sK0))) [choice axiom]
38. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
39. (((~wise(sK0) | kind(sK0)) & (wise(sK0) | ~kind(sK0))) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : ((~kind(X3) | ~wise(X3)) & (wise(X3) | kind(X3)))) [skolemisation 36,38,37]
50. ! [X0] : (((wise(X0) & brave(X0)) | wise(X0)) & (~wise(X0) | (~wise(X0) | ~brave(X0)))) [nnf transformation 7]
51. ! [X0] : (((wise(X0) & brave(X0)) | wise(X0)) & (~wise(X0) | ~wise(X0) | ~brave(X0))) [flattening 50]
56. ! [X0] : (((~kind(X0) & ~curious(X0)) | (~humble(X0) & brave(X0))) & ((humble(X0) | ~brave(X0)) | (kind(X0) | curious(X0)))) [nnf transformation 11]
57. ! [X0] : (((~kind(X0) & ~curious(X0)) | (~humble(X0) & brave(X0))) & (humble(X0) | ~brave(X0) | kind(X0) | curious(X0))) [flattening 56]
83. ~rich(X0) | curious(X0) | kind(X0) | ~wise(X0) [cnf transformation 34]
85. calm(sK1) | ~kind(X3) | ~wise(X3) [cnf transformation 39]
87. ~wise(sK0) | kind(sK0) | ~calm(X1) [cnf transformation 39]
98. ~wise(X0) | ~wise(X0) | ~brave(X0) [cnf transformation 51]
100. wise(X0) | wise(X0) [cnf transformation 51]
111. ~curious(X0) | brave(X0) [cnf transformation 57]
113. ~kind(X0) | brave(X0) [cnf transformation 57]
144. rich(mary) [cnf transformation 24]
145. ~wise(X0) | ~brave(X0) [duplicate literal removal 98]
146. wise(X0) [duplicate literal removal 100]
148. 1 <=> ! [X1] : ~calm(X1) [avatar definition]
149. ~calm(X1) <- (1) [avatar component clause 148]
151. 2 <=> kind(sK0) [avatar definition]
153. kind(sK0) <- (2) [avatar component clause 151]
155. 3 <=> wise(sK0) [avatar definition]
157. ~wise(sK0) <- (~3) [avatar component clause 155]
158. 1 | 2 | ~3 [avatar split clause 87,155,151,148]
161. 4 <=> ! [X3] : (~kind(X3) | ~wise(X3)) [avatar definition]
162. ~kind(X3) | ~wise(X3) <- (4) [avatar component clause 161]
164. 5 <=> calm(sK1) [avatar definition]
166. calm(sK1) <- (5) [avatar component clause 164]
167. 4 | 5 [avatar split clause 85,164,161]
173. 7 <=> ! [X1] : ~brave(X1) [avatar definition]
174. ~brave(X1) <- (7) [avatar component clause 173]
238. ~brave(X0) [subsumption resolution 145,146]
239. 7 [avatar split clause 238,173]
303. $false <- (~3) [subsumption resolution 157,146]
304. 3 [avatar contradiction clause 303]
305. $false <- (1, 5) [resolution 166,149]
306. ~1 | ~5 [avatar contradiction clause 305]
316. brave(sK0) <- (2) [resolution 113,153]
317. $false <- (2, 7) [subsumption resolution 316,174]
318. ~2 | ~7 [avatar contradiction clause 317]
321. ~kind(X3) <- (4) [subsumption resolution 162,146]
348. curious(mary) | kind(mary) | ~wise(mary) [resolution 83,144]
351. curious(mary) | ~wise(mary) <- (4) [subsumption resolution 348,321]
352. curious(mary) <- (4) [subsumption resolution 351,146]
354. brave(mary) <- (4) [resolution 352,111]
355. $false <- (4, 7) [subsumption resolution 354,174]
356. ~4 | ~7 [avatar contradiction clause 355]
357. $false [avatar sat refutation 158,167,239,304,306,318,356]
% SZS output end Proof for 654101865629019204592491
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not strong and not tall is either not patient or not creative.
Everyone who is either curious or not humble is both happy and generous and vice versa.
If mary is both not generous and old then someone is both old and tall.
Everyone who is both funny and not quiet is both not tall and wise and vice versa.
If lucy is not generous then someone is strong and vice versa.
Everyone who is not generous or not humble is either not calm or not tall and vice versa.
Everyone who is both not funny and not patient is humble and vice versa.
Everyone who is both not quiet and not rich is generous and vice versa.
Everyone who is wise is both not wise and rich.
If fred is either not wise or not creative then someone is not tall or wise and vice versa.
Everyone who is happy or not kind is either rich or not tall.
If mary is both creative and not creative then someone is either curious or not patient.
Everyone who is both tall and wise is either brave or creative and vice versa.
Everyone who is both not happy and not kind is not kind and vice versa.
If fred is both not tall and not strong then john is not brave or funny.
Everyone who is not curious or old is either wise or brave.
Alice is creative or old.
Someone is not tall or patient.
Someone is tall.
Lucy is funny.
Someone is happy or not tall.
Susan is not strong or not old.
Someone is both not happy and kind. | Lucy is not strong. | neutral | (![X]:((~strong(X)&~tall(X))=>(~patient(X)<~>~creative(X))))&
(![X]:((curious(X)<~>~humble(X))<=>(happy(X)&generous(X))))&
(((~generous(mary)&old(mary)))=>(?[X]:((old(X)&tall(X)))))&
(![X]:((funny(X)&~quiet(X))<=>(~tall(X)&wise(X))))&
((~generous(lucy))<=>(?[X]:(strong(X))))&
(![X]:((~generous(X)|~humble(X))<=>(~calm(X)<~>~tall(X))))&
(![X]:((~funny(X)&~patient(X))<=>humble(X)))&
(![X]:((~quiet(X)&~rich(X))<=>generous(X)))&
(![X]:(wise(X)=>(~wise(X)&rich(X))))&
(((~wise(fred)<~>~creative(fred)))<=>(?[X]:((~tall(X)|wise(X)))))&
(![X]:((happy(X)|~kind(X))=>(rich(X)<~>~tall(X))))&
(((creative(mary)&~creative(mary)))=>(?[X]:((curious(X)<~>~patient(X)))))&
(![X]:((tall(X)&wise(X))<=>(brave(X)<~>creative(X))))&
(![X]:((~happy(X)&~kind(X))<=>~kind(X)))&
(((~tall(fred)&~strong(fred)))=>((~brave(john)|funny(john))))&
(![X]:((~curious(X)|old(X))=>(wise(X)<~>brave(X))))&
((creative(alice)|old(alice)))&
(?[X]:((~tall(X)|patient(X))))&
(?[X]:(tall(X)))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | ~strong(lucy) | []
| null | 0 |
If someone is calm then john is not humble and vice versa.
Everyone who is either quiet or not curious is both strong and curious and vice versa.
Everyone who is not strong or not funny is not curious and vice versa.
If susan is not quiet then someone is both not brave and not funny and vice versa.
If someone is not funny then paul is patient.
Everyone who is not creative or strong is not quiet.
Everyone who is both not tall and not funny is either not strong or calm and vice versa.
Everyone who is not quiet is either generous or calm and vice versa.
Everyone who is brave or generous is calm or generous.
Everyone who is funny is not creative and vice versa.
If john is old then someone is either rich or not humble.
Everyone who is both humble and old is either curious or wise and vice versa.
Everyone who is not tall is either calm or not old.
If someone is wise or not kind then alice is tall or patient.
If someone is wise then john is either quiet or not curious and vice versa.
If someone is not calm then lucy is either tall or funny.
Paul is not rich.
Someone is either not old or not humble.
Someone is quiet.
Alice is either brave or not tall.
Someone is both creative and not old.
Someone is either generous or patient.
Someone is either curious or not wise.
Alice is either not quiet or generous. | John is wise. | contradiction | ((?[X]:(calm(X)))<=>(~humble(john)))&
(![X]:((quiet(X)<~>~curious(X))<=>(strong(X)&curious(X))))&
(![X]:((~strong(X)|~funny(X))<=>~curious(X)))&
((~quiet(susan))<=>(?[X]:((~brave(X)&~funny(X)))))&
((?[X]:(~funny(X)))=>(patient(paul)))&
(![X]:((~creative(X)|strong(X))=>~quiet(X)))&
(![X]:((~tall(X)&~funny(X))<=>(~strong(X)<~>calm(X))))&
(![X]:(~quiet(X)<=>(generous(X)<~>calm(X))))&
(![X]:((brave(X)|generous(X))=>(calm(X)|generous(X))))&
(![X]:(funny(X)<=>~creative(X)))&
((old(john))=>(?[X]:((rich(X)<~>~humble(X)))))&
(![X]:((humble(X)&old(X))<=>(curious(X)<~>wise(X))))&
(![X]:(~tall(X)=>(calm(X)<~>~old(X))))&
((?[X]:((wise(X)|~kind(X))))=>((tall(alice)|patient(alice))))&
((?[X]:(wise(X)))<=>((quiet(john)<~>~curious(john))))&
((?[X]:(~calm(X)))=>((tall(lucy)<~>funny(lucy))))&
(~rich(paul))&
(?[X]:((~old(X)<~>~humble(X))))&
(?[X]:(quiet(X)))&
((brave(alice)<~>~tall(alice)))&
(?[X]:((creative(X)&~old(X))))&
(?[X]:((generous(X)<~>patient(X))))&
(?[X]:((curious(X)<~>~wise(X))))&
((~quiet(alice)<~>generous(alice))) | wise(john) | [
"p1",
"p2",
"p5",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 1845223120831332171383266
% SZS output start Proof for 1845223120831332171383266
2. ! [X0] : ((quiet(X0) <~> ~curious(X0)) <=> (curious(X0) & strong(X0))) [input p1]
3. ! [X0] : ((~funny(X0) | ~strong(X0)) <=> ~curious(X0)) [input p2]
6. ! [X0] : ((strong(X0) | ~creative(X0)) => ~quiet(X0)) [input p5]
15. ? [X0] : wise(X0) <=> (quiet(john) <~> ~curious(john)) [input p14]
25. wise(john) [input hypothesis]
28. ! [X0] : (~quiet(X0) | (~strong(X0) & creative(X0))) [ennf transformation 6]
40. ! [X0] : ((((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | (~curious(X0) | ~strong(X0))) & ((curious(X0) & strong(X0)) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))))) [nnf transformation 2]
41. ! [X0] : ((((curious(X0) | ~quiet(X0)) & (~curious(X0) | quiet(X0))) | ~curious(X0) | ~strong(X0)) & ((curious(X0) & strong(X0)) | ((quiet(X0) | curious(X0)) & (~curious(X0) | ~quiet(X0))))) [flattening 40]
42. ! [X0] : (((~funny(X0) | ~strong(X0)) | curious(X0)) & (~curious(X0) | (funny(X0) & strong(X0)))) [nnf transformation 3]
43. ! [X0] : ((~funny(X0) | ~strong(X0) | curious(X0)) & (~curious(X0) | (funny(X0) & strong(X0)))) [flattening 42]
58. (? [X0] : wise(X0) | ((quiet(john) | curious(john)) & (~curious(john) | ~quiet(john)))) & (((curious(john) | ~quiet(john)) & (~curious(john) | quiet(john))) | ! [X0] : ~wise(X0)) [nnf transformation 15]
59. (? [X0] : wise(X0) | ((quiet(john) | curious(john)) & (~curious(john) | ~quiet(john)))) & (((curious(john) | ~quiet(john)) & (~curious(john) | quiet(john))) | ! [X1] : ~wise(X1)) [rectify 58]
60. ? [X0] : wise(X0) => wise(sK3) [choice axiom]
61. (wise(sK3) | ((quiet(john) | curious(john)) & (~curious(john) | ~quiet(john)))) & (((curious(john) | ~quiet(john)) & (~curious(john) | quiet(john))) | ! [X1] : ~wise(X1)) [skolemisation 59,60]
83. curious(X0) | quiet(X0) | curious(X0) [cnf transformation 41]
86. ~curious(X0) | strong(X0) [cnf transformation 43]
94. ~strong(X0) | ~quiet(X0) [cnf transformation 28]
120. ~curious(john) | quiet(john) | ~wise(X1) [cnf transformation 61]
121. curious(john) | ~quiet(john) | ~wise(X1) [cnf transformation 61]
140. wise(john) [cnf transformation 25]
141. curious(X0) | quiet(X0) [duplicate literal removal 83]
197. 13 <=> ! [X0] : ~wise(X0) [avatar definition]
198. ~wise(X0) <- (13) [avatar component clause 197]
209. 16 <=> quiet(john) [avatar definition]
210. quiet(john) <- (16) [avatar component clause 209]
213. 17 <=> curious(john) [avatar definition]
214. curious(john) <- (17) [avatar component clause 213]
221. curious(john) | ~wise(X1) [subsumption resolution 121,141]
222. 13 | 17 [avatar split clause 221,213,197]
223. quiet(john) | ~wise(X1) [subsumption resolution 120,141]
224. 13 | 16 [avatar split clause 223,209,197]
286. $false <- (13) [resolution 198,140]
287. ~13 [avatar contradiction clause 286]
288. strong(john) <- (17) [resolution 86,214]
293. ~quiet(john) <- (17) [resolution 94,288]
294. $false <- (16, 17) [subsumption resolution 293,210]
295. ~16 | ~17 [avatar contradiction clause 294]
296. $false [avatar sat refutation 222,224,287,295]
% SZS output end Proof for 1845223120831332171383266
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is old or not tall then paul is wise or curious.
Everyone who is humble is both not calm and not generous and vice versa.
Everyone who is quiet or not brave is rich and vice versa.
If paul is either creative or funny then paul is tall.
Everyone who is curious is not strong.
If lucy is not brave then lucy is either rich or not tall.
If mary is brave then paul is either humble or funny.
Everyone who is curious is not funny and vice versa.
If someone is tall or funny then someone is not funny or quiet and vice versa.
Everyone who is not old or not creative is either tall or not calm and vice versa.
Everyone who is not generous is not happy.
Everyone who is not old is not curious.
Everyone who is either not happy or strong is not tall.
If someone is both not old and happy then someone is funny.
If someone is not happy then someone is generous.
Everyone who is either old or not wise is not humble.
Someone is brave.
Lucy is not old or not rich.
Paul is not funny.
John is not old.
Someone is either rich or not patient.
Lucy is not happy.
John is rich or kind.
Paul is either not quiet or not tall. | John is strong. | neutral | (((old(lucy)|~tall(lucy)))=>((wise(paul)|curious(paul))))&
(![X]:(humble(X)<=>(~calm(X)&~generous(X))))&
(![X]:((quiet(X)|~brave(X))<=>rich(X)))&
(((creative(paul)<~>funny(paul)))=>(tall(paul)))&
(![X]:(curious(X)=>~strong(X)))&
((~brave(lucy))=>((rich(lucy)<~>~tall(lucy))))&
((brave(mary))=>((humble(paul)<~>funny(paul))))&
(![X]:(curious(X)<=>~funny(X)))&
((?[X]:((tall(X)|funny(X))))<=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~old(X)|~creative(X))<=>(tall(X)<~>~calm(X))))&
(![X]:(~generous(X)=>~happy(X)))&
(![X]:(~old(X)=>~curious(X)))&
(![X]:((~happy(X)<~>strong(X))=>~tall(X)))&
((?[X]:((~old(X)&happy(X))))=>(?[X]:(funny(X))))&
((?[X]:(~happy(X)))=>(?[X]:(generous(X))))&
(![X]:((old(X)<~>~wise(X))=>~humble(X)))&
(?[X]:(brave(X)))&
((~old(lucy)|~rich(lucy)))&
(~funny(paul))&
(~old(john))&
(?[X]:((rich(X)<~>~patient(X))))&
(~happy(lucy))&
((rich(john)|kind(john)))&
((~quiet(paul)<~>~tall(paul))) | strong(john) | []
| null | 0 |
Everyone who is either happy or tall is both not strong and funny. If fred is both rich and not creative then someone is not quiet or curious and vice versa. Everyone who is not strong is either not old or strong. Everyone who is not patient or creative is either not generous or not creative and vice versa. Everyone who is wise is brave or not wise and vice versa. If susan is calm then fred is not humble or not calm and vice versa. Everyone who is both generous and calm is brave or not calm and vice versa. If someone is not wise then john is not kind or not calm and vice versa. If someone is either not quiet or rich then mary is not generous and vice versa. Everyone who is both rich and kind is old. If someone is either quiet or tall then someone is either calm or not generous and vice versa. If someone is both not tall and not calm then susan is wise or not happy. Everyone who is not brave is either curious or tall. Someone is not quiet or not creative. Someone is kind or not old. Mary is not funny. Alice is not patient or not rich. Someone is either not tall or humble. Someone is brave or generous. Someone is either calm or creative. | Fred is not funny. | neutral | (![X]:((happy(X)<~>tall(X))=>(~strong(X)&funny(X))))&
(((rich(fred)&~creative(fred)))<=>(?[X]:((~quiet(X)|curious(X)))))&
(![X]:(~strong(X)=>(~old(X)<~>strong(X))))&
(![X]:((~patient(X)|creative(X))<=>(~generous(X)<~>~creative(X))))&
(![X]:(wise(X)<=>(brave(X)|~wise(X))))&
((calm(susan))<=>((~humble(fred)|~calm(fred))))&
(![X]:((generous(X)&calm(X))<=>(brave(X)|~calm(X))))&
((?[X]:(~wise(X)))<=>((~kind(john)|~calm(john))))&
((?[X]:((~quiet(X)<~>rich(X))))<=>(~generous(mary)))&
(![X]:((rich(X)&kind(X))=>old(X)))&
((?[X]:((quiet(X)<~>tall(X))))<=>(?[X]:((calm(X)<~>~generous(X)))))&
((?[X]:((~tall(X)&~calm(X))))=>((wise(susan)|~happy(susan))))&
(![X]:(~brave(X)=>(curious(X)<~>tall(X))))&
(?[X]:((~quiet(X)|~creative(X))))&
(?[X]:((kind(X)|~old(X))))&
(~funny(mary))&
((~patient(alice)|~rich(alice)))&
(?[X]:((~tall(X)<~>humble(X))))&
(?[X]:((brave(X)|generous(X))))&
(?[X]:((calm(X)<~>creative(X)))) | ~funny(fred) | []
| null | 0 |
If mary is happy or not old then fred is either not quiet or kind and vice versa. Everyone who is wise is not generous or not quiet. If someone is either not creative or not quiet then fred is either funny or quiet. If someone is quiet or not kind then paul is not rich or not creative and vice versa. If susan is not funny or brave then someone is tall or quiet and vice versa. If john is either funny or calm then someone is both kind and not funny. If alice is either rich or calm then someone is both not humble and patient. If someone is both patient and strong then paul is not tall or not wise and vice versa. Everyone who is either not old or not humble is not old and vice versa. Everyone who is both patient and not patient is either not curious or not quiet. Everyone who is not creative is both not kind and rich. Everyone who is old is either not creative or not strong. Everyone who is patient or curious is not rich and vice versa. If someone is not humble then someone is not patient or not wise and vice versa. If susan is not brave then john is calm or patient. If alice is either not patient or tall then susan is both not old and not brave. Fred is either not calm or creative. Fred is both humble and strong. John is not calm or patient. John is calm or old. Mary is either not patient or not tall. | Alice is not calm. | entailment | (((happy(mary)|~old(mary)))<=>((~quiet(fred)<~>kind(fred))))&
(![X]:(wise(X)=>(~generous(X)|~quiet(X))))&
((?[X]:((~creative(X)<~>~quiet(X))))=>((funny(fred)<~>quiet(fred))))&
((?[X]:((quiet(X)|~kind(X))))<=>((~rich(paul)|~creative(paul))))&
(((~funny(susan)|brave(susan)))<=>(?[X]:((tall(X)|quiet(X)))))&
(((funny(john)<~>calm(john)))=>(?[X]:((kind(X)&~funny(X)))))&
(((rich(alice)<~>calm(alice)))=>(?[X]:((~humble(X)&patient(X)))))&
((?[X]:((patient(X)&strong(X))))<=>((~tall(paul)|~wise(paul))))&
(![X]:((~old(X)<~>~humble(X))<=>~old(X)))&
(![X]:((patient(X)&~patient(X))=>(~curious(X)<~>~quiet(X))))&
(![X]:(~creative(X)=>(~kind(X)&rich(X))))&
(![X]:(old(X)=>(~creative(X)<~>~strong(X))))&
(![X]:((patient(X)|curious(X))<=>~rich(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~patient(X)|~wise(X)))))&
((~brave(susan))=>((calm(john)|patient(john))))&
(((~patient(alice)<~>tall(alice)))=>((~old(susan)&~brave(susan))))&
((~calm(fred)<~>creative(fred)))&
((humble(fred)&strong(fred)))&
((~calm(john)|patient(john)))&
((calm(john)|old(john)))&
((~patient(mary)<~>~tall(mary))) | ~calm(alice) | [
"p6",
"p8",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 8550541706809635064532964
% SZS output start Proof for 8550541706809635064532964
7. (rich(alice) <~> calm(alice)) => ? [X0] : (patient(X0) & ~humble(X0)) [input p6]
9. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> ~old(X0)) [input p8]
13. ! [X0] : ((curious(X0) | patient(X0)) <=> ~rich(X0)) [input p12]
14. ? [X0] : ~humble(X0) <=> ? [X0] : (~wise(X0) | ~patient(X0)) [input p13]
22. calm(alice) [input hypothesis]
23. ? [X0] : ~humble(X0) <=> ? [X1] : (~wise(X1) | ~patient(X1)) [rectify 14]
27. ? [X0] : (patient(X0) & ~humble(X0)) | (rich(alice) <=> calm(alice)) [ennf transformation 7]
51. ? [X0] : (patient(X0) & ~humble(X0)) | ((rich(alice) | ~calm(alice)) & (calm(alice) | ~rich(alice))) [nnf transformation 27]
52. ? [X0] : (patient(X0) & ~humble(X0)) => (patient(sK3) & ~humble(sK3)) [choice axiom]
53. (patient(sK3) & ~humble(sK3)) | ((rich(alice) | ~calm(alice)) & (calm(alice) | ~rich(alice))) [skolemisation 51,52]
59. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | old(X0)) & (~old(X0) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 9]
62. ! [X0] : (((curious(X0) | patient(X0)) | rich(X0)) & (~rich(X0) | (~curious(X0) & ~patient(X0)))) [nnf transformation 13]
63. ! [X0] : ((curious(X0) | patient(X0) | rich(X0)) & (~rich(X0) | (~curious(X0) & ~patient(X0)))) [flattening 62]
64. (? [X0] : ~humble(X0) | ! [X1] : (wise(X1) & patient(X1))) & (? [X1] : (~wise(X1) | ~patient(X1)) | ! [X0] : humble(X0)) [nnf transformation 23]
65. (? [X0] : ~humble(X0) | ! [X1] : (wise(X1) & patient(X1))) & (? [X2] : (~wise(X2) | ~patient(X2)) | ! [X3] : humble(X3)) [rectify 64]
66. ? [X0] : ~humble(X0) => ~humble(sK5) [choice axiom]
67. ? [X2] : (~wise(X2) | ~patient(X2)) => (~wise(sK6) | ~patient(sK6)) [choice axiom]
68. (~humble(sK5) | ! [X1] : (wise(X1) & patient(X1))) & ((~wise(sK6) | ~patient(sK6)) | ! [X3] : humble(X3)) [skolemisation 65,67,66]
95. ~humble(sK3) | rich(alice) | ~calm(alice) [cnf transformation 53]
104. ~old(X0) | ~old(X0) | humble(X0) [cnf transformation 59]
106. humble(X0) | old(X0) | old(X0) [cnf transformation 59]
113. ~patient(X0) | ~rich(X0) [cnf transformation 63]
117. ~humble(sK5) | patient(X1) [cnf transformation 68]
132. calm(alice) [cnf transformation 22]
133. ~old(X0) | humble(X0) [duplicate literal removal 104]
134. humble(X0) | old(X0) [duplicate literal removal 106]
241. 23 <=> calm(alice) [avatar definition]
245. 24 <=> rich(alice) [avatar definition]
247. rich(alice) <- (24) [avatar component clause 245]
255. 26 <=> humble(sK3) [avatar definition]
257. ~humble(sK3) <- (~26) [avatar component clause 255]
258. ~23 | 24 | ~26 [avatar split clause 95,255,245,241]
284. humble(X0) [subsumption resolution 133,134]
286. patient(X1) [subsumption resolution 117,284]
315. 23 [avatar split clause 132,241]
325. ~rich(X0) [resolution 113,286]
326. $false <- (24) [resolution 325,247]
330. ~24 [avatar contradiction clause 326]
331. $false <- (~26) [subsumption resolution 257,284]
332. 26 [avatar contradiction clause 331]
333. $false [avatar sat refutation 258,315,330,332]
% SZS output end Proof for 8550541706809635064532964
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not calm is either not curious or patient and vice versa.
If someone is both not funny and brave then susan is both calm and rich.
Everyone who is not tall or patient is not curious and vice versa.
If someone is old then someone is not strong and vice versa.
Everyone who is happy or not strong is either creative or not humble and vice versa.
Everyone who is both not tall and not old is both not kind and generous.
If someone is either funny or not funny then john is either quiet or not curious and vice versa.
Everyone who is not patient is not calm or generous.
If fred is rich then susan is not quiet.
Everyone who is not funny is both kind and not patient and vice versa.
Everyone who is not tall or not funny is rich.
If someone is both tall and strong then fred is either old or brave.
If alice is both not rich and brave then someone is curious or not generous.
Everyone who is curious is either curious or funny and vice versa.
Everyone who is either happy or not patient is calm.
If someone is funny then mary is either brave or not curious.
John is not strong.
Lucy is kind or not funny.
Paul is both not strong and not tall.
Someone is wise or not patient.
Fred is both not funny and strong.
Someone is both rich and happy.
Someone is both not happy and creative. | Paul is not strong. | entailment | (![X]:(~calm(X)<=>(~curious(X)<~>patient(X))))&
((?[X]:((~funny(X)&brave(X))))=>((calm(susan)&rich(susan))))&
(![X]:((~tall(X)|patient(X))<=>~curious(X)))&
((?[X]:(old(X)))<=>(?[X]:(~strong(X))))&
(![X]:((happy(X)|~strong(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((~tall(X)&~old(X))=>(~kind(X)&generous(X))))&
((?[X]:((funny(X)<~>~funny(X))))<=>((quiet(john)<~>~curious(john))))&
(![X]:(~patient(X)=>(~calm(X)|generous(X))))&
((rich(fred))=>(~quiet(susan)))&
(![X]:(~funny(X)<=>(kind(X)&~patient(X))))&
(![X]:((~tall(X)|~funny(X))=>rich(X)))&
((?[X]:((tall(X)&strong(X))))=>((old(fred)<~>brave(fred))))&
(((~rich(alice)&brave(alice)))=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:(curious(X)<=>(curious(X)<~>funny(X))))&
(![X]:((happy(X)<~>~patient(X))=>calm(X)))&
((?[X]:(funny(X)))=>((brave(mary)<~>~curious(mary))))&
(~strong(john))&
((kind(lucy)|~funny(lucy)))&
((~strong(paul)&~tall(paul)))&
(?[X]:((wise(X)|~patient(X))))&
((~funny(fred)&strong(fred)))&
(?[X]:((rich(X)&happy(X))))&
(?[X]:((~happy(X)&creative(X)))) | ~strong(paul) | [
"p18",
"hypothesis"
]
| % SZS status Unsatisfiable for 5925911243917921766316567
% SZS output start Proof for 5925911243917921766316567
19. ~tall(paul) & ~strong(paul) [input p18]
24. strong(paul) [input hypothesis]
112. ~strong(paul) [cnf transformation 19]
120. strong(paul) [cnf transformation 24]
226. $false [subsumption resolution 120,112]
% SZS output end Proof for 5925911243917921766316567
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or not old is not generous.
Everyone who is either not old or curious is old or not strong and vice versa.
Everyone who is both happy and not old is not rich or not generous.
If mary is patient or humble then alice is not rich or not wise and vice versa.
If someone is both happy and not kind then fred is either happy or not kind.
If someone is not quiet then someone is either generous or tall.
If someone is either not quiet or strong then someone is not calm and vice versa.
If someone is both not rich and not patient then susan is kind and vice versa.
If someone is not calm or not old then someone is patient or not tall and vice versa.
If mary is curious or rich then someone is both calm and not humble.
Everyone who is both not calm and not brave is brave and vice versa.
Everyone who is old is rich or generous and vice versa.
If someone is funny then someone is either not tall or curious.
If lucy is not quiet then someone is either strong or tall and vice versa.
If susan is either strong or not wise then someone is calm or tall.
Everyone who is either not quiet or not generous is not funny or not quiet and vice versa.
Lucy is both humble and not patient.
Someone is not humble or not calm.
Someone is not curious.
Someone is wise or not funny. | Alice is not strong. | entailment | (![X]:((calm(X)|~old(X))=>~generous(X)))&
(![X]:((~old(X)<~>curious(X))<=>(old(X)|~strong(X))))&
(![X]:((happy(X)&~old(X))=>(~rich(X)|~generous(X))))&
(((patient(mary)|humble(mary)))<=>((~rich(alice)|~wise(alice))))&
((?[X]:((happy(X)&~kind(X))))=>((happy(fred)<~>~kind(fred))))&
((?[X]:(~quiet(X)))=>(?[X]:((generous(X)<~>tall(X)))))&
((?[X]:((~quiet(X)<~>strong(X))))<=>(?[X]:(~calm(X))))&
((?[X]:((~rich(X)&~patient(X))))<=>(kind(susan)))&
((?[X]:((~calm(X)|~old(X))))<=>(?[X]:((patient(X)|~tall(X)))))&
(((curious(mary)|rich(mary)))=>(?[X]:((calm(X)&~humble(X)))))&
(![X]:((~calm(X)&~brave(X))<=>brave(X)))&
(![X]:(old(X)<=>(rich(X)|generous(X))))&
((?[X]:(funny(X)))=>(?[X]:((~tall(X)<~>curious(X)))))&
((~quiet(lucy))<=>(?[X]:((strong(X)<~>tall(X)))))&
(((strong(susan)<~>~wise(susan)))=>(?[X]:((calm(X)|tall(X)))))&
(![X]:((~quiet(X)<~>~generous(X))<=>(~funny(X)|~quiet(X))))&
((humble(lucy)&~patient(lucy)))&
(?[X]:((~humble(X)|~calm(X))))&
(?[X]:(~curious(X)))&
(?[X]:((wise(X)|~funny(X)))) | ~strong(alice) | [
"p0",
"p5",
"p6",
"p10",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 6874560195967577759750473
% SZS output start Proof for 6874560195967577759750473
1. ! [X0] : ((~old(X0) | calm(X0)) => ~generous(X0)) [input p0]
6. ? [X0] : ~quiet(X0) => ? [X0] : (generous(X0) <~> tall(X0)) [input p5]
7. ? [X0] : (~quiet(X0) <~> strong(X0)) <=> ? [X0] : ~calm(X0) [input p6]
11. ! [X0] : ((~brave(X0) & ~calm(X0)) <=> brave(X0)) [input p10]
14. ~quiet(lucy) <=> ? [X0] : (strong(X0) <~> tall(X0)) [input p13]
16. ! [X0] : ((~quiet(X0) <~> ~generous(X0)) <=> (~quiet(X0) | ~funny(X0))) [input p15]
21. strong(alice) [input hypothesis]
22. ? [X0] : ~quiet(X0) => ? [X1] : (generous(X1) <~> tall(X1)) [rectify 6]
23. ? [X0] : (~quiet(X0) <~> strong(X0)) <=> ? [X1] : ~calm(X1) [rectify 7]
26. ! [X0] : (~generous(X0) | (old(X0) & ~calm(X0))) [ennf transformation 1]
30. ? [X1] : (generous(X1) <~> tall(X1)) | ! [X0] : quiet(X0) [ennf transformation 22]
39. ? [X1] : ((~tall(X1) | ~generous(X1)) & (tall(X1) | generous(X1))) | ! [X0] : quiet(X0) [nnf transformation 30]
40. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | ! [X1] : quiet(X1) [rectify 39]
41. ? [X0] : ((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) => ((~tall(sK0) | ~generous(sK0)) & (tall(sK0) | generous(sK0))) [choice axiom]
42. ((~tall(sK0) | ~generous(sK0)) & (tall(sK0) | generous(sK0))) | ! [X1] : quiet(X1) [skolemisation 40,41]
43. (? [X0] : ((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ! [X1] : calm(X1)) & (? [X1] : ~calm(X1) | ! [X0] : ((~quiet(X0) | ~strong(X0)) & (strong(X0) | quiet(X0)))) [nnf transformation 23]
44. (? [X0] : ((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) | ! [X1] : calm(X1)) & (? [X2] : ~calm(X2) | ! [X3] : ((~quiet(X3) | ~strong(X3)) & (strong(X3) | quiet(X3)))) [rectify 43]
45. ? [X0] : ((~strong(X0) | quiet(X0)) & (strong(X0) | ~quiet(X0))) => ((~strong(sK1) | quiet(sK1)) & (strong(sK1) | ~quiet(sK1))) [choice axiom]
46. ? [X2] : ~calm(X2) => ~calm(sK2) [choice axiom]
47. (((~strong(sK1) | quiet(sK1)) & (strong(sK1) | ~quiet(sK1))) | ! [X1] : calm(X1)) & (~calm(sK2) | ! [X3] : ((~quiet(X3) | ~strong(X3)) & (strong(X3) | quiet(X3)))) [skolemisation 44,46,45]
59. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~brave(X0)) & (brave(X0) | (brave(X0) | calm(X0)))) [nnf transformation 11]
60. ! [X0] : (((~brave(X0) & ~calm(X0)) | ~brave(X0)) & (brave(X0) | brave(X0) | calm(X0))) [flattening 59]
67. (~quiet(lucy) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (? [X0] : ((~tall(X0) | ~strong(X0)) & (tall(X0) | strong(X0))) | quiet(lucy)) [nnf transformation 14]
68. (~quiet(lucy) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (? [X1] : ((~tall(X1) | ~strong(X1)) & (tall(X1) | strong(X1))) | quiet(lucy)) [rectify 67]
69. ? [X1] : ((~tall(X1) | ~strong(X1)) & (tall(X1) | strong(X1))) => ((~tall(sK8) | ~strong(sK8)) & (tall(sK8) | strong(sK8))) [choice axiom]
70. (~quiet(lucy) | ! [X0] : ((strong(X0) | ~tall(X0)) & (tall(X0) | ~strong(X0)))) & (((~tall(sK8) | ~strong(sK8)) & (tall(sK8) | strong(sK8))) | quiet(lucy)) [skolemisation 68,69]
74. ! [X0] : ((((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (quiet(X0) & funny(X0))) & ((~quiet(X0) | ~funny(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0))))) [nnf transformation 16]
75. ! [X0] : ((((generous(X0) | quiet(X0)) & (~generous(X0) | ~quiet(X0))) | (quiet(X0) & funny(X0))) & (~quiet(X0) | ~funny(X0) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0))))) [flattening 74]
82. ~generous(X0) | ~calm(X0) [cnf transformation 26]
97. tall(sK0) | generous(sK0) | quiet(X1) [cnf transformation 42]
100. ~calm(sK2) | ~quiet(X3) | ~strong(X3) [cnf transformation 47]
114. brave(X0) | brave(X0) | calm(X0) [cnf transformation 60]
116. ~brave(X0) | ~brave(X0) [cnf transformation 60]
125. ~quiet(lucy) | strong(X0) | ~tall(X0) [cnf transformation 70]
133. generous(X0) | quiet(X0) | quiet(X0) [cnf transformation 75]
139. strong(alice) [cnf transformation 21]
141. quiet(X0) | generous(X0) [duplicate literal removal 133]
142. brave(X0) | calm(X0) [duplicate literal removal 114]
143. ~brave(X0) [duplicate literal removal 116]
181. 8 <=> ! [X1] : quiet(X1) [avatar definition]
182. quiet(X1) <- (8) [avatar component clause 181]
184. 9 <=> generous(sK0) [avatar definition]
185. generous(sK0) <- (9) [avatar component clause 184]
186. ~generous(sK0) <- (~9) [avatar component clause 184]
188. 10 <=> tall(sK0) [avatar definition]
189. tall(sK0) <- (10) [avatar component clause 188]
192. 8 | 9 | 10 [avatar split clause 97,188,184,181]
194. 11 <=> ! [X1] : calm(X1) [avatar definition]
195. calm(X1) <- (11) [avatar component clause 194]
207. 14 <=> ! [X3] : (~quiet(X3) | ~strong(X3)) [avatar definition]
208. ~quiet(X3) | ~strong(X3) <- (14) [avatar component clause 207]
210. 15 <=> calm(sK2) [avatar definition]
212. ~calm(sK2) <- (~15) [avatar component clause 210]
213. 14 | ~15 [avatar split clause 100,210,207]
285. calm(X0) [subsumption resolution 142,143]
286. 11 [avatar split clause 285,194]
301. 35 <=> ! [X0] : (strong(X0) | ~tall(X0)) [avatar definition]
302. ~tall(X0) | strong(X0) <- (35) [avatar component clause 301]
304. 36 <=> quiet(lucy) [avatar definition]
306. ~quiet(lucy) <- (~36) [avatar component clause 304]
307. 35 | ~36 [avatar split clause 125,304,301]
359. $false <- (11, ~15) [resolution 212,195]
360. ~11 | 15 [avatar contradiction clause 359]
361. ~strong(X3) <- (8, 14) [subsumption resolution 208,182]
364. $false <- (8, 14) [resolution 361,139]
365. ~8 | ~14 [avatar contradiction clause 364]
366. ~calm(sK0) <- (9) [resolution 82,185]
367. $false <- (9, 11) [subsumption resolution 366,195]
368. ~9 | ~11 [avatar contradiction clause 367]
371. ~strong(X0) | generous(X0) <- (14) [resolution 208,141]
373. strong(sK0) <- (10, 35) [resolution 302,189]
381. generous(sK0) <- (10, 14, 35) [resolution 371,373]
382. $false <- (~9, 10, 14, 35) [subsumption resolution 381,186]
383. 9 | ~10 | ~14 | ~35 [avatar contradiction clause 382]
385. generous(lucy) <- (~36) [resolution 306,141]
394. ~calm(lucy) <- (~36) [resolution 385,82]
395. $false <- (11, ~36) [subsumption resolution 394,195]
396. ~11 | 36 [avatar contradiction clause 395]
397. $false [avatar sat refutation 192,213,286,307,360,365,368,383,396]
% SZS output end Proof for 6874560195967577759750473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy is either not creative or rich and vice versa.
Everyone who is not generous or not creative is both tall and not calm.
If someone is calm or old then someone is strong and vice versa.
Everyone who is humble is both humble and brave.
If someone is either happy or humble then someone is not patient.
If paul is both not calm and old then someone is both not generous and not kind and vice versa.
Everyone who is curious or wise is rich or calm.
If someone is not calm or tall then paul is curious and vice versa.
Everyone who is rich is either funny or strong.
If fred is both wise and humble then alice is either not strong or tall.
Everyone who is patient is either not wise or not strong.
Everyone who is not calm is both not tall and not quiet and vice versa.
If john is either kind or not curious then someone is either not humble or generous.
If someone is not happy then someone is happy or patient.
If someone is not kind or strong then mary is either humble or not tall.
Everyone who is not rich is not old or not calm.
Someone is not quiet or funny.
Someone is either not calm or curious.
Alice is creative or not quiet.
Mary is both tall and patient.
Susan is happy.
John is both not curious and not happy.
Someone is either curious or strong.
Someone is either generous or not curious. | Mary is calm. | entailment | (![X]:(happy(X)<=>(~creative(X)<~>rich(X))))&
(![X]:((~generous(X)|~creative(X))=>(tall(X)&~calm(X))))&
((?[X]:((calm(X)|old(X))))<=>(?[X]:(strong(X))))&
(![X]:(humble(X)=>(humble(X)&brave(X))))&
((?[X]:((happy(X)<~>humble(X))))=>(?[X]:(~patient(X))))&
(((~calm(paul)&old(paul)))<=>(?[X]:((~generous(X)&~kind(X)))))&
(![X]:((curious(X)|wise(X))=>(rich(X)|calm(X))))&
((?[X]:((~calm(X)|tall(X))))<=>(curious(paul)))&
(![X]:(rich(X)=>(funny(X)<~>strong(X))))&
(((wise(fred)&humble(fred)))=>((~strong(alice)<~>tall(alice))))&
(![X]:(patient(X)=>(~wise(X)<~>~strong(X))))&
(![X]:(~calm(X)<=>(~tall(X)&~quiet(X))))&
(((kind(john)<~>~curious(john)))=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:(~happy(X)))=>(?[X]:((happy(X)|patient(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((humble(mary)<~>~tall(mary))))&
(![X]:(~rich(X)=>(~old(X)|~calm(X))))&
(?[X]:((~quiet(X)|funny(X))))&
(?[X]:((~calm(X)<~>curious(X))))&
((creative(alice)|~quiet(alice)))&
((tall(mary)&patient(mary)))&
(happy(susan))&
((~curious(john)&~happy(john)))&
(?[X]:((curious(X)<~>strong(X))))&
(?[X]:((generous(X)<~>~curious(X)))) | calm(mary) | [
"p11",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 8511972544483390749155738
% SZS output start Proof for 8511972544483390749155738
12. ! [X0] : (~calm(X0) <=> (~quiet(X0) & ~tall(X0))) [input p11]
20. patient(mary) & tall(mary) [input p19]
25. ~calm(mary) [input hypothesis]
66. ! [X0] : ((~calm(X0) | (quiet(X0) | tall(X0))) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [nnf transformation 12]
67. ! [X0] : ((~calm(X0) | quiet(X0) | tall(X0)) & ((~quiet(X0) & ~tall(X0)) | calm(X0))) [flattening 66]
115. ~tall(X0) | calm(X0) [cnf transformation 67]
132. tall(mary) [cnf transformation 20]
141. ~calm(mary) [cnf transformation 25]
277. 32 <=> tall(mary) [avatar definition]
279. tall(mary) <- (32) [avatar component clause 277]
315. 32 [avatar split clause 132,277]
341. calm(mary) <- (32) [resolution 115,279]
344. $false <- (32) [subsumption resolution 341,141]
345. ~32 [avatar contradiction clause 344]
348. $false [avatar sat refutation 315,345]
% SZS output end Proof for 8511972544483390749155738
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 humble or not rich is both not humble and kind.
Everyone who is either funny or rich is not funny.
Everyone who is both curious and not curious is both patient and creative and vice versa.
Everyone who is not curious is not brave and vice versa.
If john is either strong or not funny then paul is brave.
If alice is strong or funny then fred is either tall or not strong.
Everyone who is both not funny and curious is either curious or not brave and vice versa.
If someone is not creative or not generous then someone is calm and vice versa.
Everyone who is either not brave or quiet is happy or not happy.
If fred is either not creative or old then someone is old or not creative.
Everyone who is not tall or calm is strong and vice versa.
If fred is either not generous or brave then someone is both not patient and happy.
If someone is either strong or happy then paul is not wise or not creative and vice versa.
If someone is either curious or not humble then lucy is either not wise or not creative.
If lucy is both happy and not wise then someone is happy or not rich and vice versa.
Everyone who is not funny or not brave is generous or not strong and vice versa.
Someone is not curious or patient.
Mary is creative or old.
Alice is not humble.
Fred is both tall and not wise.
Mary is not patient.
Someone is not funny.
Fred is patient.
Mary is either funny or quiet. | Mary is not quiet. | contradiction | (![X]:((humble(X)<~>~rich(X))=>(~humble(X)&kind(X))))&
(![X]:((funny(X)<~>rich(X))=>~funny(X)))&
(![X]:((curious(X)&~curious(X))<=>(patient(X)&creative(X))))&
(![X]:(~curious(X)<=>~brave(X)))&
(((strong(john)<~>~funny(john)))=>(brave(paul)))&
(((strong(alice)|funny(alice)))=>((tall(fred)<~>~strong(fred))))&
(![X]:((~funny(X)&curious(X))<=>(curious(X)<~>~brave(X))))&
((?[X]:((~creative(X)|~generous(X))))<=>(?[X]:(calm(X))))&
(![X]:((~brave(X)<~>quiet(X))=>(happy(X)|~happy(X))))&
(((~creative(fred)<~>old(fred)))=>(?[X]:((old(X)|~creative(X)))))&
(![X]:((~tall(X)|calm(X))<=>strong(X)))&
(((~generous(fred)<~>brave(fred)))=>(?[X]:((~patient(X)&happy(X)))))&
((?[X]:((strong(X)<~>happy(X))))<=>((~wise(paul)|~creative(paul))))&
((?[X]:((curious(X)<~>~humble(X))))=>((~wise(lucy)<~>~creative(lucy))))&
(((happy(lucy)&~wise(lucy)))<=>(?[X]:((happy(X)|~rich(X)))))&
(![X]:((~funny(X)|~brave(X))<=>(generous(X)|~strong(X))))&
(?[X]:((~curious(X)|patient(X))))&
((creative(mary)|old(mary)))&
(~humble(alice))&
((tall(fred)&~wise(fred)))&
(~patient(mary))&
(?[X]:(~funny(X)))&
(patient(fred))&
((funny(mary)<~>quiet(mary))) | ~quiet(mary) | [
"p3",
"p6",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 4446127447723974680883796
% SZS output start Proof for 4446127447723974680883796
4. ! [X0] : (~curious(X0) <=> ~brave(X0)) [input p3]
7. ! [X0] : ((curious(X0) & ~funny(X0)) <=> (curious(X0) <~> ~brave(X0))) [input p6]
24. funny(mary) <~> quiet(mary) [input p23]
25. ~quiet(mary) [input hypothesis]
41. ! [X0] : ((~curious(X0) | brave(X0)) & (~brave(X0) | curious(X0))) [nnf transformation 4]
44. ! [X0] : (((curious(X0) & ~funny(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | (~curious(X0) | funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((curious(X0) & ~funny(X0)) | ((curious(X0) | brave(X0)) & (~brave(X0) | ~curious(X0)))) & (((brave(X0) | ~curious(X0)) & (~brave(X0) | curious(X0))) | ~curious(X0) | funny(X0))) [flattening 44]
77. (~quiet(mary) | ~funny(mary)) & (quiet(mary) | funny(mary)) [nnf transformation 24]
86. ~brave(X0) | curious(X0) [cnf transformation 41]
87. ~curious(X0) | brave(X0) [cnf transformation 41]
96. ~funny(X0) | ~brave(X0) | ~curious(X0) [cnf transformation 45]
99. curious(X0) | curious(X0) | brave(X0) [cnf transformation 45]
141. quiet(mary) | funny(mary) [cnf transformation 77]
143. ~quiet(mary) [cnf transformation 25]
145. curious(X0) | brave(X0) [duplicate literal removal 99]
183. brave(X0) [subsumption resolution 145,87]
184. ~curious(X0) | ~funny(X0) [subsumption resolution 96,183]
334. 40 <=> funny(mary) [avatar definition]
335. funny(mary) <- (40) [avatar component clause 334]
338. 41 <=> quiet(mary) [avatar definition]
342. 40 | 41 [avatar split clause 141,338,334]
343. ~41 [avatar split clause 143,338]
344. curious(X0) [resolution 86,183]
352. ~funny(X0) [resolution 184,344]
354. $false <- (40) [resolution 352,335]
355. ~40 [avatar contradiction clause 354]
356. $false [avatar sat refutation 342,343,355]
% SZS output end Proof for 4446127447723974680883796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or patient is quiet. If mary is either rich or not generous then john is both not strong and rich and vice versa. Everyone who is patient or strong is either not patient or not old and vice versa. Everyone who is either not happy or humble is not generous or generous. Everyone who is creative is not rich and vice versa. Everyone who is either strong or not tall is tall and vice versa. If john is either generous or funny then someone is not rich or not quiet. Everyone who is calm or not patient is not quiet or not old and vice versa. If alice is not quiet then someone is not quiet and vice versa. Everyone who is either curious or not old is both happy and tall. Everyone who is both patient and strong is either not patient or not brave. If someone is strong then someone is rich. Everyone who is not generous or funny is not funny or not tall. If someone is both not curious and not tall then lucy is both wise and not curious and vice versa. Everyone who is not quiet is both not rich and quiet. Everyone who is both not brave and not curious is humble. Mary is happy or not curious. Someone is strong or calm. Mary is both not funny and not humble. Someone is both curious and generous. John is not wise. Paul is not rich or funny. Someone is either not kind or funny. Someone is both calm and strong. | Mary is not brave. | entailment | (![X]:((~tall(X)<~>patient(X))=>quiet(X)))&
(((rich(mary)<~>~generous(mary)))<=>((~strong(john)&rich(john))))&
(![X]:((patient(X)|strong(X))<=>(~patient(X)<~>~old(X))))&
(![X]:((~happy(X)<~>humble(X))=>(~generous(X)|generous(X))))&
(![X]:(creative(X)<=>~rich(X)))&
(![X]:((strong(X)<~>~tall(X))<=>tall(X)))&
(((generous(john)<~>funny(john)))=>(?[X]:((~rich(X)|~quiet(X)))))&
(![X]:((calm(X)|~patient(X))<=>(~quiet(X)|~old(X))))&
((~quiet(alice))<=>(?[X]:(~quiet(X))))&
(![X]:((curious(X)<~>~old(X))=>(happy(X)&tall(X))))&
(![X]:((patient(X)&strong(X))=>(~patient(X)<~>~brave(X))))&
((?[X]:(strong(X)))=>(?[X]:(rich(X))))&
(![X]:((~generous(X)|funny(X))=>(~funny(X)|~tall(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>((wise(lucy)&~curious(lucy))))&
(![X]:(~quiet(X)=>(~rich(X)&quiet(X))))&
(![X]:((~brave(X)&~curious(X))=>humble(X)))&
((happy(mary)|~curious(mary)))&
(?[X]:((strong(X)|calm(X))))&
((~funny(mary)&~humble(mary)))&
(?[X]:((curious(X)&generous(X))))&
(~wise(john))&
((~rich(paul)|funny(paul)))&
(?[X]:((~kind(X)<~>funny(X))))&
(?[X]:((calm(X)&strong(X)))) | ~brave(mary) | [
"p2",
"p5",
"p7",
"p10",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3257401459575368745470938
% SZS output start Proof for 3257401459575368745470938
3. ! [X0] : ((strong(X0) | patient(X0)) <=> (~patient(X0) <~> ~old(X0))) [input p2]
6. ! [X0] : ((strong(X0) <~> ~tall(X0)) <=> tall(X0)) [input p5]
8. ! [X0] : ((~patient(X0) | calm(X0)) <=> (~old(X0) | ~quiet(X0))) [input p7]
11. ! [X0] : ((strong(X0) & patient(X0)) => (~patient(X0) <~> ~brave(X0))) [input p10]
15. ! [X0] : (~quiet(X0) => (quiet(X0) & ~rich(X0))) [input p14]
25. brave(mary) [input hypothesis]
32. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | (~strong(X0) | ~patient(X0))) [ennf transformation 11]
33. ! [X0] : ((~patient(X0) <~> ~brave(X0)) | ~strong(X0) | ~patient(X0)) [flattening 32]
37. ! [X0] : ((quiet(X0) & ~rich(X0)) | quiet(X0)) [ennf transformation 15]
43. ! [X0] : (((strong(X0) | patient(X0)) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~strong(X0) & ~patient(X0)))) [nnf transformation 3]
44. ! [X0] : ((strong(X0) | patient(X0) | ((~patient(X0) | old(X0)) & (~old(X0) | patient(X0)))) & (((old(X0) | patient(X0)) & (~old(X0) | ~patient(X0))) | (~strong(X0) & ~patient(X0)))) [flattening 43]
46. ! [X0] : ((((tall(X0) | ~strong(X0)) & (~tall(X0) | strong(X0))) | ~tall(X0)) & (tall(X0) | ((strong(X0) | tall(X0)) & (~tall(X0) | ~strong(X0))))) [nnf transformation 6]
50. ! [X0] : (((~patient(X0) | calm(X0)) | (old(X0) & quiet(X0))) & ((~old(X0) | ~quiet(X0)) | (patient(X0) & ~calm(X0)))) [nnf transformation 8]
51. ! [X0] : ((~patient(X0) | calm(X0) | (old(X0) & quiet(X0))) & (~old(X0) | ~quiet(X0) | (patient(X0) & ~calm(X0)))) [flattening 50]
57. ! [X0] : (((brave(X0) | patient(X0)) & (~brave(X0) | ~patient(X0))) | ~strong(X0) | ~patient(X0)) [nnf transformation 33]
83. ~old(X0) | ~patient(X0) | ~patient(X0) [cnf transformation 44]
86. ~strong(X0) | patient(X0) | old(X0) [cnf transformation 44]
92. tall(X0) | strong(X0) | tall(X0) [cnf transformation 46]
93. ~tall(X0) | strong(X0) | ~tall(X0) [cnf transformation 46]
98. ~old(X0) | ~quiet(X0) | patient(X0) [cnf transformation 51]
107. ~brave(X0) | ~patient(X0) | ~strong(X0) | ~patient(X0) [cnf transformation 57]
117. quiet(X0) | quiet(X0) [cnf transformation 37]
131. brave(mary) [cnf transformation 25]
132. quiet(X0) [duplicate literal removal 117]
134. ~brave(X0) | ~patient(X0) | ~strong(X0) [duplicate literal removal 107]
135. tall(X0) | strong(X0) [duplicate literal removal 92]
136. ~tall(X0) | strong(X0) [duplicate literal removal 93]
137. ~old(X0) | ~patient(X0) [duplicate literal removal 83]
161. strong(X0) [subsumption resolution 135,136]
181. ~old(X0) | ~quiet(X0) [subsumption resolution 98,137]
183. 9 <=> ! [X0] : quiet(X0) [avatar definition]
184. quiet(X0) <- (9) [avatar component clause 183]
195. ~brave(X0) | ~patient(X0) [subsumption resolution 134,161]
220. 9 [avatar split clause 132,183]
258. ~patient(mary) [resolution 195,131]
259. old(X0) | patient(X0) [resolution 86,161]
317. patient(X1) | ~quiet(X1) [resolution 259,181]
322. patient(X1) <- (9) [subsumption resolution 317,184]
327. $false <- (9) [resolution 322,258]
328. ~9 [avatar contradiction clause 327]
329. $false [avatar sat refutation 220,328]
% SZS output end Proof for 3257401459575368745470938
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 old or tall is either happy or curious and vice versa. Everyone who is both funny and old is not rich and vice versa. If someone is not humble or calm then alice is not strong and vice versa. If someone is either not kind or tall then someone is not humble. Everyone who is both humble and not funny is either not strong or not happy and vice versa. Everyone who is both not kind and creative is calm. If someone is both patient and calm then lucy is brave or quiet. If someone is both not creative and wise then mary is both wise and not old and vice versa. Everyone who is not strong or not calm is curious or not strong and vice versa. If susan is not generous then someone is not funny. Everyone who is generous or not generous is both not brave and not wise and vice versa. Everyone who is funny is both not strong and not kind and vice versa. If someone is either happy or not old then paul is both not quiet and not kind. Everyone who is kind or not strong is both not funny and not humble. Everyone who is either not patient or not brave is not patient or strong and vice versa. If mary is not generous or brave then alice is rich or calm. Mary is happy or not creative. Fred is strong or not generous. Someone is either humble or not curious. Someone is not kind or humble. | Alice is not funny. | entailment | (![X]:((~old(X)|tall(X))<=>(happy(X)<~>curious(X))))&
(![X]:((funny(X)&old(X))<=>~rich(X)))&
((?[X]:((~humble(X)|calm(X))))<=>(~strong(alice)))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~humble(X))))&
(![X]:((humble(X)&~funny(X))<=>(~strong(X)<~>~happy(X))))&
(![X]:((~kind(X)&creative(X))=>calm(X)))&
((?[X]:((patient(X)&calm(X))))=>((brave(lucy)|quiet(lucy))))&
((?[X]:((~creative(X)&wise(X))))<=>((wise(mary)&~old(mary))))&
(![X]:((~strong(X)|~calm(X))<=>(curious(X)|~strong(X))))&
((~generous(susan))=>(?[X]:(~funny(X))))&
(![X]:((generous(X)|~generous(X))<=>(~brave(X)&~wise(X))))&
(![X]:(funny(X)<=>(~strong(X)&~kind(X))))&
((?[X]:((happy(X)<~>~old(X))))=>((~quiet(paul)&~kind(paul))))&
(![X]:((kind(X)|~strong(X))=>(~funny(X)&~humble(X))))&
(![X]:((~patient(X)<~>~brave(X))<=>(~patient(X)|strong(X))))&
(((~generous(mary)|brave(mary)))=>((rich(alice)|calm(alice))))&
((happy(mary)|~creative(mary)))&
((strong(fred)|~generous(fred)))&
(?[X]:((humble(X)<~>~curious(X))))&
(?[X]:((~kind(X)|humble(X)))) | ~funny(alice) | [
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 3466697408581798759542674
% SZS output start Proof for 3466697408581798759542674
12. ! [X0] : (funny(X0) <=> (~kind(X0) & ~strong(X0))) [input p11]
14. ! [X0] : ((~strong(X0) | kind(X0)) => (~humble(X0) & ~funny(X0))) [input p13]
21. funny(alice) [input hypothesis]
33. ! [X0] : ((~humble(X0) & ~funny(X0)) | (strong(X0) & ~kind(X0))) [ennf transformation 14]
59. ! [X0] : ((funny(X0) | (kind(X0) | strong(X0))) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [nnf transformation 12]
60. ! [X0] : ((funny(X0) | kind(X0) | strong(X0)) & ((~kind(X0) & ~strong(X0)) | ~funny(X0))) [flattening 59]
103. ~strong(X0) | ~funny(X0) [cnf transformation 60]
111. ~funny(X0) | strong(X0) [cnf transformation 33]
127. funny(alice) [cnf transformation 21]
227. ~funny(X0) [subsumption resolution 111,103]
265. $false [subsumption resolution 127,227]
% SZS output end Proof for 3466697408581798759542674
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave or not quiet is both not tall and old and vice versa.
Everyone who is not strong or rich is not creative.
Everyone who is not tall is either quiet or curious.
If alice is not tall then alice is not kind and vice versa.
Everyone who is both humble and not strong is generous or calm and vice versa.
Everyone who is both not old and not generous is happy or not strong and vice versa.
If someone is old or not brave then paul is happy or not kind.
Everyone who is either not patient or not curious is funny or not generous and vice versa.
If someone is both not generous and not wise then alice is either not brave or not strong and vice versa.
If john is not happy or old then someone is not old.
If someone is not creative then someone is both not patient and rich and vice versa.
Everyone who is both not patient and calm is both not happy and strong.
If someone is not brave or not patient then paul is not curious.
If someone is brave then john is both not wise and generous.
If john is not wise then someone is not calm or kind and vice versa.
If someone is both not rich and old then fred is calm and vice versa.
Someone is not brave.
Someone is both not creative and wise.
Someone is humble or calm.
Lucy is not wise.
John is funny.
Someone is happy or not creative.
Fred is not rich or not funny.
John is not patient or not rich. | John is happy. | neutral | (![X]:((brave(X)<~>~quiet(X))<=>(~tall(X)&old(X))))&
(![X]:((~strong(X)|rich(X))=>~creative(X)))&
(![X]:(~tall(X)=>(quiet(X)<~>curious(X))))&
((~tall(alice))<=>(~kind(alice)))&
(![X]:((humble(X)&~strong(X))<=>(generous(X)|calm(X))))&
(![X]:((~old(X)&~generous(X))<=>(happy(X)|~strong(X))))&
((?[X]:((old(X)|~brave(X))))=>((happy(paul)|~kind(paul))))&
(![X]:((~patient(X)<~>~curious(X))<=>(funny(X)|~generous(X))))&
((?[X]:((~generous(X)&~wise(X))))<=>((~brave(alice)<~>~strong(alice))))&
(((~happy(john)|old(john)))=>(?[X]:(~old(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((~patient(X)&rich(X)))))&
(![X]:((~patient(X)&calm(X))=>(~happy(X)&strong(X))))&
((?[X]:((~brave(X)|~patient(X))))=>(~curious(paul)))&
((?[X]:(brave(X)))=>((~wise(john)&generous(john))))&
((~wise(john))<=>(?[X]:((~calm(X)|kind(X)))))&
((?[X]:((~rich(X)&old(X))))<=>(calm(fred)))&
(?[X]:(~brave(X)))&
(?[X]:((~creative(X)&wise(X))))&
(?[X]:((humble(X)|calm(X))))&
(~wise(lucy))&
(funny(john))&
(?[X]:((happy(X)|~creative(X))))&
((~rich(fred)|~funny(fred)))&
((~patient(john)|~rich(john))) | happy(john) | []
| null | 0 |
Everyone who is not rich is kind or quiet and vice versa.
Everyone who is both patient and humble is both not humble and humble and vice versa.
If john is kind then alice is either not kind or not patient and vice versa.
Everyone who is wise or brave is either not rich or old.
If someone is either not calm or not rich then fred is either wise or not tall and vice versa.
Everyone who is both generous and not patient is both tall and not happy and vice versa.
If someone is wise then fred is not happy.
Everyone who is wise or generous is not happy.
Everyone who is not wise or not happy is not kind or not funny.
Everyone who is either generous or not wise is either humble or not tall and vice versa.
If susan is both not strong and not brave then lucy is both not kind and brave and vice versa.
If mary is not rich or kind then someone is not funny or wise.
If someone is not humble or patient then lucy is tall or happy.
Everyone who is both creative and not old is creative and vice versa.
Everyone who is both funny and not generous is calm and vice versa.
If alice is funny then someone is rich and vice versa.
Lucy is not curious or humble.
John is either not generous or not patient.
Paul is not rich or wise.
Someone is both quiet and funny.
Someone is creative or brave.
Someone is not humble or wise.
Fred is not rich.
Paul is either not rich or happy. | Lucy is kind. | neutral | (![X]:(~rich(X)<=>(kind(X)|quiet(X))))&
(![X]:((patient(X)&humble(X))<=>(~humble(X)&humble(X))))&
((kind(john))<=>((~kind(alice)<~>~patient(alice))))&
(![X]:((wise(X)|brave(X))=>(~rich(X)<~>old(X))))&
((?[X]:((~calm(X)<~>~rich(X))))<=>((wise(fred)<~>~tall(fred))))&
(![X]:((generous(X)&~patient(X))<=>(tall(X)&~happy(X))))&
((?[X]:(wise(X)))=>(~happy(fred)))&
(![X]:((wise(X)|generous(X))=>~happy(X)))&
(![X]:((~wise(X)|~happy(X))=>(~kind(X)|~funny(X))))&
(![X]:((generous(X)<~>~wise(X))<=>(humble(X)<~>~tall(X))))&
(((~strong(susan)&~brave(susan)))<=>((~kind(lucy)&brave(lucy))))&
(((~rich(mary)|kind(mary)))=>(?[X]:((~funny(X)|wise(X)))))&
((?[X]:((~humble(X)|patient(X))))=>((tall(lucy)|happy(lucy))))&
(![X]:((creative(X)&~old(X))<=>creative(X)))&
(![X]:((funny(X)&~generous(X))<=>calm(X)))&
((funny(alice))<=>(?[X]:(rich(X))))&
((~curious(lucy)|humble(lucy)))&
((~generous(john)<~>~patient(john)))&
((~rich(paul)|wise(paul)))&
(?[X]:((quiet(X)&funny(X))))&
(?[X]:((creative(X)|brave(X))))&
(?[X]:((~humble(X)|wise(X))))&
(~rich(fred))&
((~rich(paul)<~>happy(paul))) | kind(lucy) | []
| null | 0 |
If someone is not humble then fred is either rich or not tall.
Everyone who is not kind or tall is both not old and not kind.
If someone is either old or not old then lucy is not generous.
Everyone who is both calm and not rich is funny or strong.
Everyone who is not creative is both calm and generous.
Everyone who is kind is not strong or rich.
If someone is either not strong or not curious then paul is not old or not generous.
Everyone who is not strong is brave or calm.
If alice is either not tall or funny then paul is either not strong or not brave and vice versa.
If someone is both not calm and wise then fred is patient and vice versa.
If someone is brave then alice is not quiet or not happy and vice versa.
Everyone who is not quiet is either quiet or tall and vice versa.
If john is either kind or humble then paul is both brave and tall and vice versa.
If someone is both not calm and not quiet then lucy is either funny or wise and vice versa.
If someone is patient then john is not calm or not strong.
Everyone who is not happy or not brave is happy and vice versa.
John is rich.
Someone is both calm and strong.
Someone is tall.
Susan is both tall and patient.
Alice is both not brave and not wise.
Someone is curious.
Someone is creative.
Mary is either not kind or strong. | Fred is not rich. | contradiction | ((?[X]:(~humble(X)))=>((rich(fred)<~>~tall(fred))))&
(![X]:((~kind(X)|tall(X))=>(~old(X)&~kind(X))))&
((?[X]:((old(X)<~>~old(X))))=>(~generous(lucy)))&
(![X]:((calm(X)&~rich(X))=>(funny(X)|strong(X))))&
(![X]:(~creative(X)=>(calm(X)&generous(X))))&
(![X]:(kind(X)=>(~strong(X)|rich(X))))&
((?[X]:((~strong(X)<~>~curious(X))))=>((~old(paul)|~generous(paul))))&
(![X]:(~strong(X)=>(brave(X)|calm(X))))&
(((~tall(alice)<~>funny(alice)))<=>((~strong(paul)<~>~brave(paul))))&
((?[X]:((~calm(X)&wise(X))))<=>(patient(fred)))&
((?[X]:(brave(X)))<=>((~quiet(alice)|~happy(alice))))&
(![X]:(~quiet(X)<=>(quiet(X)<~>tall(X))))&
(((kind(john)<~>humble(john)))<=>((brave(paul)&tall(paul))))&
((?[X]:((~calm(X)&~quiet(X))))<=>((funny(lucy)<~>wise(lucy))))&
((?[X]:(patient(X)))=>((~calm(john)|~strong(john))))&
(![X]:((~happy(X)|~brave(X))<=>happy(X)))&
(rich(john))&
(?[X]:((calm(X)&strong(X))))&
(?[X]:(tall(X)))&
((tall(susan)&patient(susan)))&
((~brave(alice)&~wise(alice)))&
(?[X]:(curious(X)))&
(?[X]:(creative(X)))&
((~kind(mary)<~>strong(mary))) | ~rich(fred) | [
"p0",
"p1",
"p11",
"p12",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 7691279046138710930102455
% SZS output start Proof for 7691279046138710930102455
1. ? [X0] : ~humble(X0) => (rich(fred) <~> ~tall(fred)) [input p0]
2. ! [X0] : ((tall(X0) | ~kind(X0)) => (~kind(X0) & ~old(X0))) [input p1]
12. ! [X0] : (~quiet(X0) <=> (quiet(X0) <~> tall(X0))) [input p11]
13. (kind(john) <~> humble(john)) <=> (tall(paul) & brave(paul)) [input p12]
16. ! [X0] : ((~brave(X0) | ~happy(X0)) <=> happy(X0)) [input p15]
25. ~rich(fred) [input hypothesis]
31. ! [X0] : ((tall(X0) | ~kind(X0)) => ~kind(X0)) [pure predicate removal 2]
32. (rich(fred) <~> ~tall(fred)) | ! [X0] : humble(X0) [ennf transformation 1]
33. ! [X0] : (~kind(X0) | (~tall(X0) & kind(X0))) [ennf transformation 31]
42. ((tall(fred) | ~rich(fred)) & (~tall(fred) | rich(fred))) | ! [X0] : humble(X0) [nnf transformation 32]
53. ! [X0] : ((~quiet(X0) | ((quiet(X0) | ~tall(X0)) & (tall(X0) | ~quiet(X0)))) & (((~tall(X0) | ~quiet(X0)) & (tall(X0) | quiet(X0))) | quiet(X0))) [nnf transformation 12]
54. (((~humble(john) | ~kind(john)) & (humble(john) | kind(john))) | (~tall(paul) | ~brave(paul))) & ((tall(paul) & brave(paul)) | ((kind(john) | ~humble(john)) & (humble(john) | ~kind(john)))) [nnf transformation 13]
55. (((~humble(john) | ~kind(john)) & (humble(john) | kind(john))) | ~tall(paul) | ~brave(paul)) & ((tall(paul) & brave(paul)) | ((kind(john) | ~humble(john)) & (humble(john) | ~kind(john)))) [flattening 54]
60. ! [X0] : (((~brave(X0) | ~happy(X0)) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [nnf transformation 16]
61. ! [X0] : ((~brave(X0) | ~happy(X0) | ~happy(X0)) & (happy(X0) | (brave(X0) & happy(X0)))) [flattening 60]
67. ~tall(fred) | rich(fred) | humble(X0) [cnf transformation 42]
70. ~kind(X0) | ~tall(X0) [cnf transformation 33]
88. tall(X0) | quiet(X0) | quiet(X0) [cnf transformation 53]
90. ~quiet(X0) | tall(X0) | ~quiet(X0) [cnf transformation 53]
93. brave(paul) | kind(john) | ~humble(john) [cnf transformation 55]
105. happy(X0) | happy(X0) [cnf transformation 61]
107. ~brave(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 61]
118. ~rich(fred) [cnf transformation 25]
119. happy(X0) [duplicate literal removal 105]
120. ~happy(X0) | ~brave(X0) [duplicate literal removal 107]
121. tall(X0) | quiet(X0) [duplicate literal removal 88]
122. ~quiet(X0) | tall(X0) [duplicate literal removal 90]
124. 1 <=> ! [X0] : humble(X0) [avatar definition]
125. humble(X0) <- (1) [avatar component clause 124]
127. 2 <=> rich(fred) [avatar definition]
131. 3 <=> tall(fred) [avatar definition]
132. ~tall(fred) <- (~3) [avatar component clause 131]
135. 1 | 2 | ~3 [avatar split clause 67,131,127,124]
137. 4 <=> brave(paul) [avatar definition]
139. brave(paul) <- (4) [avatar component clause 137]
193. 15 <=> ! [X1] : ~brave(X1) [avatar definition]
194. ~brave(X1) <- (15) [avatar component clause 193]
196. tall(X0) [subsumption resolution 121,122]
199. 16 <=> kind(john) [avatar definition]
200. kind(john) <- (16) [avatar component clause 199]
203. 17 <=> humble(john) [avatar definition]
205. ~humble(john) <- (~17) [avatar component clause 203]
209. ~17 | 16 | 4 [avatar split clause 93,137,199,203]
258. ~2 [avatar split clause 118,127]
261. $false <- (~3) [subsumption resolution 132,196]
262. 3 [avatar contradiction clause 261]
263. $false <- (1, ~17) [resolution 205,125]
264. ~1 | 17 [avatar contradiction clause 263]
266. ~brave(X1) [resolution 120,119]
267. 15 [avatar split clause 266,193]
269. $false <- (4, 15) [resolution 194,139]
270. ~4 | ~15 [avatar contradiction clause 269]
272. ~tall(john) <- (16) [resolution 200,70]
273. $false <- (16) [subsumption resolution 272,196]
274. ~16 [avatar contradiction clause 273]
275. $false [avatar sat refutation 135,209,258,262,264,267,270,274]
% SZS output end Proof for 7691279046138710930102455
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 lucy is both creative and tall then alice is both funny and generous.
If fred is rich or not calm then mary is either kind or not kind and vice versa.
Everyone who is either not curious or not rich is either not wise or wise and vice versa.
If paul is either happy or not wise then someone is both happy and rich.
If someone is patient or old then mary is both not quiet and funny and vice versa.
If someone is either wise or not strong then mary is rich or old.
Everyone who is both not calm and quiet is not old or funny and vice versa.
Everyone who is not kind is both not tall and humble and vice versa.
Everyone who is kind is both funny and calm and vice versa.
Everyone who is not creative is both happy and brave and vice versa.
Everyone who is either patient or not generous is not strong and vice versa.
Everyone who is creative or wise is not old and vice versa.
Everyone who is curious or not funny is not creative.
Everyone who is either not creative or calm is kind and vice versa.
If someone is either not rich or not wise then fred is both patient and not tall.
If lucy is both strong and not rich then lucy is either curious or quiet.
Someone is quiet.
Fred is brave or not curious.
Someone is generous or not happy.
Susan is not wise or not happy.
Susan is not patient or not creative. | Paul is wise. | entailment | (((creative(lucy)&tall(lucy)))=>((funny(alice)&generous(alice))))&
(((rich(fred)|~calm(fred)))<=>((kind(mary)<~>~kind(mary))))&
(![X]:((~curious(X)<~>~rich(X))<=>(~wise(X)<~>wise(X))))&
(((happy(paul)<~>~wise(paul)))=>(?[X]:((happy(X)&rich(X)))))&
((?[X]:((patient(X)|old(X))))<=>((~quiet(mary)&funny(mary))))&
((?[X]:((wise(X)<~>~strong(X))))=>((rich(mary)|old(mary))))&
(![X]:((~calm(X)&quiet(X))<=>(~old(X)|funny(X))))&
(![X]:(~kind(X)<=>(~tall(X)&humble(X))))&
(![X]:(kind(X)<=>(funny(X)&calm(X))))&
(![X]:(~creative(X)<=>(happy(X)&brave(X))))&
(![X]:((patient(X)<~>~generous(X))<=>~strong(X)))&
(![X]:((creative(X)|wise(X))<=>~old(X)))&
(![X]:((curious(X)|~funny(X))=>~creative(X)))&
(![X]:((~creative(X)<~>calm(X))<=>kind(X)))&
((?[X]:((~rich(X)<~>~wise(X))))=>((patient(fred)&~tall(fred))))&
(((strong(lucy)&~rich(lucy)))=>((curious(lucy)<~>quiet(lucy))))&
(?[X]:(quiet(X)))&
((brave(fred)|~curious(fred)))&
(?[X]:((generous(X)|~happy(X))))&
((~wise(susan)|~happy(susan)))&
((~patient(susan)|~creative(susan))) | wise(paul) | [
"p2",
"p4",
"p6",
"p8",
"p12",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3250957147908978711863101
% SZS output start Proof for 3250957147908978711863101
3. ! [X0] : ((~curious(X0) <~> ~rich(X0)) <=> (~wise(X0) <~> wise(X0))) [input p2]
5. ? [X0] : (old(X0) | patient(X0)) <=> (funny(mary) & ~quiet(mary)) [input p4]
7. ! [X0] : ((quiet(X0) & ~calm(X0)) <=> (funny(X0) | ~old(X0))) [input p6]
9. ! [X0] : (kind(X0) <=> (calm(X0) & funny(X0))) [input p8]
13. ! [X0] : ((~funny(X0) | curious(X0)) => ~creative(X0)) [input p12]
14. ! [X0] : ((~creative(X0) <~> calm(X0)) <=> kind(X0)) [input p13]
15. ? [X0] : (~rich(X0) <~> ~wise(X0)) => (~tall(fred) & patient(fred)) [input p14]
22. ~wise(paul) [input hypothesis]
28. ! [X0] : (~creative(X0) | (funny(X0) & ~curious(X0))) [ennf transformation 13]
29. (~tall(fred) & patient(fred)) | ! [X0] : (~rich(X0) <=> ~wise(X0)) [ennf transformation 15]
34. ! [X0] : ((((rich(X0) | curious(X0)) & (~rich(X0) | ~curious(X0))) | ((~wise(X0) | ~wise(X0)) & (wise(X0) | wise(X0)))) & (((~wise(X0) | wise(X0)) & (wise(X0) | ~wise(X0))) | ((~curious(X0) | rich(X0)) & (~rich(X0) | curious(X0))))) [nnf transformation 3]
38. (? [X0] : (old(X0) | patient(X0)) | (~funny(mary) | quiet(mary))) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [nnf transformation 5]
39. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X0] : (~old(X0) & ~patient(X0))) [flattening 38]
40. (? [X0] : (old(X0) | patient(X0)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [rectify 39]
41. ? [X0] : (old(X0) | patient(X0)) => (old(sK1) | patient(sK1)) [choice axiom]
42. ((old(sK1) | patient(sK1)) | ~funny(mary) | quiet(mary)) & ((funny(mary) & ~quiet(mary)) | ! [X1] : (~old(X1) & ~patient(X1))) [skolemisation 40,41]
44. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | (~quiet(X0) | calm(X0)))) [nnf transformation 7]
45. ! [X0] : (((quiet(X0) & ~calm(X0)) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ~quiet(X0) | calm(X0))) [flattening 44]
48. ! [X0] : ((kind(X0) | (~calm(X0) | ~funny(X0))) & ((calm(X0) & funny(X0)) | ~kind(X0))) [nnf transformation 9]
49. ! [X0] : ((kind(X0) | ~calm(X0) | ~funny(X0)) & ((calm(X0) & funny(X0)) | ~kind(X0))) [flattening 48]
55. ! [X0] : ((((~calm(X0) | creative(X0)) & (calm(X0) | ~creative(X0))) | ~kind(X0)) & (kind(X0) | ((~creative(X0) | ~calm(X0)) & (calm(X0) | creative(X0))))) [nnf transformation 14]
56. (~tall(fred) & patient(fred)) | ! [X0] : ((~rich(X0) | wise(X0)) & (~wise(X0) | rich(X0))) [nnf transformation 29]
76. rich(X0) | curious(X0) | wise(X0) | wise(X0) [cnf transformation 34]
77. rich(X0) | curious(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 34]
82. ~quiet(mary) | ~patient(X1) [cnf transformation 42]
83. ~quiet(mary) | ~old(X1) [cnf transformation 42]
85. funny(mary) | ~old(X1) [cnf transformation 42]
90. ~calm(X0) | old(X0) [cnf transformation 45]
92. quiet(X0) | old(X0) [cnf transformation 45]
93. ~funny(X0) | quiet(X0) [cnf transformation 45]
98. ~kind(X0) | calm(X0) [cnf transformation 49]
110. ~curious(X0) | ~creative(X0) [cnf transformation 28]
112. kind(X0) | calm(X0) | creative(X0) [cnf transformation 55]
115. ~calm(X0) | creative(X0) | ~kind(X0) [cnf transformation 55]
117. patient(fred) | ~rich(X0) | wise(X0) [cnf transformation 56]
127. ~wise(paul) [cnf transformation 22]
130. rich(X0) | curious(X0) | wise(X0) [duplicate literal removal 76]
131. rich(X0) | curious(X0) | ~wise(X0) [duplicate literal removal 77]
166. curious(X0) | rich(X0) [subsumption resolution 130,131]
169. 8 <=> wise(paul) [avatar definition]
170. ~wise(paul) <- (~8) [avatar component clause 169]
189. 12 <=> quiet(mary) [avatar definition]
190. ~quiet(mary) <- (~12) [avatar component clause 189]
193. 13 <=> funny(mary) [avatar definition]
194. funny(mary) <- (13) [avatar component clause 193]
206. 16 <=> ! [X1] : ~old(X1) [avatar definition]
207. ~old(X1) <- (16) [avatar component clause 206]
208. 16 | 13 [avatar split clause 85,193,206]
210. 17 <=> ! [X1] : ~patient(X1) [avatar definition]
211. ~patient(X1) <- (17) [avatar component clause 210]
213. 16 | ~12 [avatar split clause 83,189,206]
214. 17 | ~12 [avatar split clause 82,189,210]
223. 20 <=> old(mary) [avatar definition]
225. old(mary) <- (20) [avatar component clause 223]
231. ~kind(X0) | creative(X0) [subsumption resolution 115,98]
232. calm(X0) | creative(X0) [subsumption resolution 112,231]
234. 22 <=> ! [X0] : (~rich(X0) | wise(X0)) [avatar definition]
235. ~rich(X0) | wise(X0) <- (22) [avatar component clause 234]
246. 25 <=> patient(fred) [avatar definition]
248. patient(fred) <- (25) [avatar component clause 246]
249. 22 | 25 [avatar split clause 117,246,234]
301. ~8 [avatar split clause 127,169]
302. old(mary) <- (~12) [resolution 92,190]
304. 20 | 12 [avatar split clause 302,189,223]
310. quiet(mary) <- (13) [resolution 93,194]
311. $false <- (~12, 13) [subsumption resolution 310,190]
312. 12 | ~13 [avatar contradiction clause 311]
313. $false <- (16, 20) [resolution 207,225]
316. ~16 | ~20 [avatar contradiction clause 313]
322. ~creative(X0) | rich(X0) [resolution 166,110]
328. creative(X1) | old(X1) [resolution 232,90]
329. creative(X1) <- (16) [subsumption resolution 328,207]
346. rich(X0) <- (16) [resolution 322,329]
351. wise(X0) <- (16, 22) [resolution 346,235]
357. $false <- (~8, 16, 22) [resolution 351,170]
362. 8 | ~16 | ~22 [avatar contradiction clause 357]
363. $false <- (17, 25) [subsumption resolution 248,211]
364. ~17 | ~25 [avatar contradiction clause 363]
365. $false [avatar sat refutation 208,213,214,249,301,304,312,316,362,364]
% SZS output end Proof for 3250957147908978711863101
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is both not creative and not patient then mary is both generous and not generous and vice versa.
If mary is not humble or rich then someone is either not old or rich.
If john is either quiet or creative then paul is kind or not calm.
If someone is both not curious and patient then paul is both kind and funny and vice versa.
Everyone who is not creative or not generous is not funny or not kind.
If susan is not curious or wise then alice is humble.
Everyone who is either wise or not rich is both patient and creative.
If someone is not funny then alice is both not brave and old.
Everyone who is patient is creative and vice versa.
If someone is generous or creative then mary is happy.
If someone is both brave and generous then john is not kind or not wise.
Everyone who is not strong is both not patient and not kind and vice versa.
Everyone who is curious is both tall and not tall.
Everyone who is humble is both not generous and calm and vice versa.
Everyone who is creative or not quiet is both happy and quiet and vice versa.
Everyone who is not generous is calm or not wise.
Someone is wise.
Fred is either not brave or kind.
John is brave or not wise.
Someone is either not creative or kind.
Someone is both kind and not funny.
John is generous or quiet.
Someone is humble or not quiet.
Someone is not humble or not brave. | Mary is creative. | entailment | (((~creative(susan)&~patient(susan)))<=>((generous(mary)&~generous(mary))))&
(((~humble(mary)|rich(mary)))=>(?[X]:((~old(X)<~>rich(X)))))&
(((quiet(john)<~>creative(john)))=>((kind(paul)|~calm(paul))))&
((?[X]:((~curious(X)&patient(X))))<=>((kind(paul)&funny(paul))))&
(![X]:((~creative(X)|~generous(X))=>(~funny(X)|~kind(X))))&
(((~curious(susan)|wise(susan)))=>(humble(alice)))&
(![X]:((wise(X)<~>~rich(X))=>(patient(X)&creative(X))))&
((?[X]:(~funny(X)))=>((~brave(alice)&old(alice))))&
(![X]:(patient(X)<=>creative(X)))&
((?[X]:((generous(X)|creative(X))))=>(happy(mary)))&
((?[X]:((brave(X)&generous(X))))=>((~kind(john)|~wise(john))))&
(![X]:(~strong(X)<=>(~patient(X)&~kind(X))))&
(![X]:(curious(X)=>(tall(X)&~tall(X))))&
(![X]:(humble(X)<=>(~generous(X)&calm(X))))&
(![X]:((creative(X)|~quiet(X))<=>(happy(X)&quiet(X))))&
(![X]:(~generous(X)=>(calm(X)|~wise(X))))&
(?[X]:(wise(X)))&
((~brave(fred)<~>kind(fred)))&
((brave(john)|~wise(john)))&
(?[X]:((~creative(X)<~>kind(X))))&
(?[X]:((kind(X)&~funny(X))))&
((generous(john)|quiet(john)))&
(?[X]:((humble(X)|~quiet(X))))&
(?[X]:((~humble(X)|~brave(X)))) | creative(mary) | [
"p0",
"p8",
"p9",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 435109803460412706063851
% SZS output start Proof for 435109803460412706063851
1. (~patient(susan) & ~creative(susan)) <=> (~generous(mary) & generous(mary)) [input p0]
9. ! [X0] : (patient(X0) <=> creative(X0)) [input p8]
10. ? [X0] : (creative(X0) | generous(X0)) => happy(mary) [input p9]
15. ! [X0] : ((~quiet(X0) | creative(X0)) <=> (quiet(X0) & happy(X0))) [input p14]
25. ~creative(mary) [input hypothesis]
34. happy(mary) | ! [X0] : (~creative(X0) & ~generous(X0)) [ennf transformation 10]
40. ((~patient(susan) & ~creative(susan)) | (generous(mary) | ~generous(mary))) & ((~generous(mary) & generous(mary)) | (patient(susan) | creative(susan))) [nnf transformation 1]
41. ((~patient(susan) & ~creative(susan)) | generous(mary) | ~generous(mary)) & ((~generous(mary) & generous(mary)) | patient(susan) | creative(susan)) [flattening 40]
52. ! [X0] : ((patient(X0) | ~creative(X0)) & (creative(X0) | ~patient(X0))) [nnf transformation 9]
55. ! [X0] : (((~quiet(X0) | creative(X0)) | (~quiet(X0) | ~happy(X0))) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [nnf transformation 15]
56. ! [X0] : ((~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0)) & ((quiet(X0) & happy(X0)) | (quiet(X0) & ~creative(X0)))) [flattening 55]
69. generous(mary) | patient(susan) | creative(susan) [cnf transformation 41]
70. ~generous(mary) | patient(susan) | creative(susan) [cnf transformation 41]
93. ~patient(X0) | creative(X0) [cnf transformation 52]
96. happy(mary) | ~creative(X0) [cnf transformation 34]
106. quiet(X0) | quiet(X0) [cnf transformation 56]
107. ~quiet(X0) | creative(X0) | ~quiet(X0) | ~happy(X0) [cnf transformation 56]
120. ~creative(mary) [cnf transformation 25]
121. quiet(X0) [duplicate literal removal 106]
122. ~happy(X0) | creative(X0) | ~quiet(X0) [duplicate literal removal 107]
124. 1 <=> creative(susan) [avatar definition]
126. creative(susan) <- (1) [avatar component clause 124]
128. 2 <=> patient(susan) [avatar definition]
130. patient(susan) <- (2) [avatar component clause 128]
132. 3 <=> generous(mary) [avatar definition]
135. 1 | 2 | ~3 [avatar split clause 70,132,128,124]
136. 1 | 2 | 3 [avatar split clause 69,132,128,124]
222. 22 <=> ! [X0] : ~creative(X0) [avatar definition]
223. ~creative(X0) <- (22) [avatar component clause 222]
225. 23 <=> happy(mary) [avatar definition]
227. happy(mary) <- (23) [avatar component clause 225]
228. 22 | 23 [avatar split clause 96,225,222]
283. creative(susan) <- (2) [resolution 93,130]
285. 1 | ~2 [avatar split clause 283,128,124]
358. creative(mary) | ~quiet(mary) <- (23) [resolution 122,227]
360. ~quiet(mary) <- (23) [subsumption resolution 358,120]
361. $false <- (23) [subsumption resolution 360,121]
362. ~23 [avatar contradiction clause 361]
363. $false <- (1, 22) [resolution 223,126]
368. ~1 | ~22 [avatar contradiction clause 363]
369. $false [avatar sat refutation 135,136,228,285,362,368]
% SZS output end Proof for 435109803460412706063851
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is humble and vice versa.
Everyone who is old is either happy or not creative.
Everyone who is either not tall or not wise is either patient or tall and vice versa.
Everyone who is rich or curious is happy.
Everyone who is patient is either happy or creative and vice versa.
Everyone who is both not kind and not generous is either not curious or not wise.
Everyone who is wise is happy or brave and vice versa.
Everyone who is both not generous and not quiet is not tall or not old.
If someone is not wise then fred is both creative and not funny and vice versa.
If alice is rich or not creative then fred is both not patient and brave and vice versa.
If mary is both tall and not patient then someone is either not strong or not funny.
If john is not patient or not rich then someone is both not kind and kind and vice versa.
If someone is not wise then someone is either not calm or not quiet and vice versa.
If paul is either patient or not kind then someone is both tall and not creative.
Everyone who is either not happy or rich is not calm or rich and vice versa.
Fred is both not tall and not humble.
Someone is wise.
Someone is not brave or patient.
Susan is not generous.
Fred is both not rich and not generous.
Someone is calm. | Susan is not patient. | contradiction | (![X]:((~curious(X)<~>generous(X))<=>humble(X)))&
(![X]:(old(X)=>(happy(X)<~>~creative(X))))&
(![X]:((~tall(X)<~>~wise(X))<=>(patient(X)<~>tall(X))))&
(![X]:((rich(X)|curious(X))=>happy(X)))&
(![X]:(patient(X)<=>(happy(X)<~>creative(X))))&
(![X]:((~kind(X)&~generous(X))=>(~curious(X)<~>~wise(X))))&
(![X]:(wise(X)<=>(happy(X)|brave(X))))&
(![X]:((~generous(X)&~quiet(X))=>(~tall(X)|~old(X))))&
((?[X]:(~wise(X)))<=>((creative(fred)&~funny(fred))))&
(((rich(alice)|~creative(alice)))<=>((~patient(fred)&brave(fred))))&
(((tall(mary)&~patient(mary)))=>(?[X]:((~strong(X)<~>~funny(X)))))&
(((~patient(john)|~rich(john)))<=>(?[X]:((~kind(X)&kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~calm(X)<~>~quiet(X)))))&
(((patient(paul)<~>~kind(paul)))=>(?[X]:((tall(X)&~creative(X)))))&
(![X]:((~happy(X)<~>rich(X))<=>(~calm(X)|rich(X))))&
((~tall(fred)&~humble(fred)))&
(?[X]:(wise(X)))&
(?[X]:((~brave(X)|patient(X))))&
(~generous(susan))&
((~rich(fred)&~generous(fred)))&
(?[X]:(calm(X))) | ~patient(susan) | [
"p0",
"p2",
"p3",
"p4",
"p6",
"p8",
"p15",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 8748339689654356772102379
% SZS output start Proof for 8748339689654356772102379
1. ! [X0] : ((~curious(X0) <~> generous(X0)) <=> humble(X0)) [input p0]
3. ! [X0] : ((~tall(X0) <~> ~wise(X0)) <=> (patient(X0) <~> tall(X0))) [input p2]
4. ! [X0] : ((curious(X0) | rich(X0)) => happy(X0)) [input p3]
5. ! [X0] : (patient(X0) <=> (happy(X0) <~> creative(X0))) [input p4]
7. ! [X0] : (wise(X0) <=> (brave(X0) | happy(X0))) [input p6]
9. ? [X0] : ~wise(X0) <=> (~funny(fred) & creative(fred)) [input p8]
16. ~humble(fred) & ~tall(fred) [input p15]
20. ~generous(fred) & ~rich(fred) [input p19]
22. ~patient(susan) [input hypothesis]
24. ! [X0] : ((~curious(X0) <~> generous(X0)) => humble(X0)) [unused predicate definition removal 1]
27. ! [X0] : (humble(X0) | (~curious(X0) <=> generous(X0))) [ennf transformation 24]
28. ! [X0] : (happy(X0) | (~curious(X0) & ~rich(X0))) [ennf transformation 4]
34. ! [X0] : (humble(X0) | ((~curious(X0) | ~generous(X0)) & (generous(X0) | curious(X0)))) [nnf transformation 27]
35. ! [X0] : ((((wise(X0) | tall(X0)) & (~wise(X0) | ~tall(X0))) | ((patient(X0) | ~tall(X0)) & (tall(X0) | ~patient(X0)))) & (((~tall(X0) | ~patient(X0)) & (tall(X0) | patient(X0))) | ((~tall(X0) | wise(X0)) & (~wise(X0) | tall(X0))))) [nnf transformation 3]
36. ! [X0] : ((patient(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | ~patient(X0))) [nnf transformation 5]
38. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & ((brave(X0) | happy(X0)) | ~wise(X0))) [nnf transformation 7]
39. ! [X0] : ((wise(X0) | (~brave(X0) & ~happy(X0))) & (brave(X0) | happy(X0) | ~wise(X0))) [flattening 38]
40. (? [X0] : ~wise(X0) | (funny(fred) | ~creative(fred))) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [nnf transformation 9]
41. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X0] : wise(X0)) [flattening 40]
42. (? [X0] : ~wise(X0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [rectify 41]
43. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
44. (~wise(sK0) | funny(fred) | ~creative(fred)) & ((~funny(fred) & creative(fred)) | ! [X1] : wise(X1)) [skolemisation 42,43]
71. humble(X0) | generous(X0) | curious(X0) [cnf transformation 34]
73. tall(X0) | patient(X0) | ~wise(X0) | tall(X0) [cnf transformation 35]
78. ~wise(X0) | ~tall(X0) | patient(X0) | ~tall(X0) [cnf transformation 35]
82. ~curious(X0) | happy(X0) [cnf transformation 28]
84. ~patient(X0) | ~happy(X0) | ~creative(X0) [cnf transformation 36]
90. ~happy(X0) | wise(X0) [cnf transformation 39]
92. creative(fred) | wise(X1) [cnf transformation 44]
122. ~humble(fred) [cnf transformation 16]
127. ~generous(fred) [cnf transformation 20]
129. ~patient(susan) [cnf transformation 22]
132. tall(X0) | patient(X0) | ~wise(X0) [duplicate literal removal 73]
134. ~wise(X0) | ~tall(X0) | patient(X0) [duplicate literal removal 78]
137. ~wise(X0) | patient(X0) [subsumption resolution 132,134]
139. 1 <=> creative(fred) [avatar definition]
152. 4 <=> ! [X1] : wise(X1) [avatar definition]
153. wise(X1) <- (4) [avatar component clause 152]
155. 4 | 1 [avatar split clause 92,139,152]
157. 5 <=> patient(fred) [avatar definition]
159. patient(fred) <- (5) [avatar component clause 157]
277. generous(fred) | curious(fred) [resolution 71,122]
278. curious(fred) [subsumption resolution 277,127]
292. happy(fred) [resolution 278,82]
412. wise(fred) [resolution 292,90]
447. patient(fred) [resolution 412,137]
452. 5 [avatar split clause 447,157]
454. ~happy(fred) | ~creative(fred) <- (5) [resolution 159,84]
457. ~creative(fred) <- (5) [subsumption resolution 454,292]
460. ~1 | ~5 [avatar split clause 457,157,139]
464. patient(X3) <- (4) [resolution 153,137]
481. $false <- (4) [resolution 464,129]
482. ~4 [avatar contradiction clause 481]
484. $false [avatar sat refutation 155,452,460,482]
% SZS output end Proof for 8748339689654356772102379
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not humble is both not quiet and rich and vice versa.
Everyone who is either not generous or wise is curious or not quiet and vice versa.
Everyone who is tall is both not brave and not quiet.
If john is either not generous or quiet then someone is happy or funny.
Everyone who is both rich and tall is tall.
If fred is both not patient and funny then john is happy and vice versa.
If susan is either rich or patient then someone is both not old and rich.
Everyone who is both tall and curious is wise or patient and vice versa.
If fred is either tall or funny then lucy is generous or brave and vice versa.
If susan is humble then mary is either not kind or not old and vice versa.
Everyone who is both not humble and quiet is not brave and vice versa.
Everyone who is both funny and not funny is either not patient or not rich and vice versa.
If someone is either old or not rich then john is either not patient or humble.
Everyone who is tall is both generous and not brave and vice versa.
If someone is patient or strong then fred is wise or funny and vice versa.
Someone is not curious.
Someone is either not strong or not wise.
Lucy is both curious and not creative.
Someone is both not calm and quiet. | Mary is not old. | contradiction | (![X]:((~wise(X)&~humble(X))<=>(~quiet(X)&rich(X))))&
(![X]:((~generous(X)<~>wise(X))<=>(curious(X)|~quiet(X))))&
(![X]:(tall(X)=>(~brave(X)&~quiet(X))))&
(((~generous(john)<~>quiet(john)))=>(?[X]:((happy(X)|funny(X)))))&
(![X]:((rich(X)&tall(X))=>tall(X)))&
(((~patient(fred)&funny(fred)))<=>(happy(john)))&
(((rich(susan)<~>patient(susan)))=>(?[X]:((~old(X)&rich(X)))))&
(![X]:((tall(X)&curious(X))<=>(wise(X)|patient(X))))&
(((tall(fred)<~>funny(fred)))<=>((generous(lucy)|brave(lucy))))&
((humble(susan))<=>((~kind(mary)<~>~old(mary))))&
(![X]:((~humble(X)&quiet(X))<=>~brave(X)))&
(![X]:((funny(X)&~funny(X))<=>(~patient(X)<~>~rich(X))))&
((?[X]:((old(X)<~>~rich(X))))=>((~patient(john)<~>humble(john))))&
(![X]:(tall(X)<=>(generous(X)&~brave(X))))&
((?[X]:((patient(X)|strong(X))))<=>((wise(fred)|funny(fred))))&
(?[X]:(~curious(X)))&
(?[X]:((~strong(X)<~>~wise(X))))&
((curious(lucy)&~creative(lucy)))&
(?[X]:((~calm(X)&quiet(X)))) | ~old(mary) | [
"p0",
"p2",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
]
| % SZS status Unsatisfiable for 2613519682887584804394695
% SZS output start Proof for 2613519682887584804394695
1. ! [X0] : ((~humble(X0) & ~wise(X0)) <=> (rich(X0) & ~quiet(X0))) [input p0]
3. ! [X0] : (tall(X0) => (~quiet(X0) & ~brave(X0))) [input p2]
8. ! [X0] : ((curious(X0) & tall(X0)) <=> (patient(X0) | wise(X0))) [input p7]
11. ! [X0] : ((quiet(X0) & ~humble(X0)) <=> ~brave(X0)) [input p10]
12. ! [X0] : ((~funny(X0) & funny(X0)) <=> (~patient(X0) <~> ~rich(X0))) [input p11]
13. ? [X0] : (old(X0) <~> ~rich(X0)) => (~patient(john) <~> humble(john)) [input p12]
20. ~old(mary) [input hypothesis]
23. ! [X0] : ((~quiet(X0) & ~brave(X0)) | ~tall(X0)) [ennf transformation 3]
28. (~patient(john) <~> humble(john)) | ! [X0] : (old(X0) <=> ~rich(X0)) [ennf transformation 13]
29. ! [X0] : (((~humble(X0) & ~wise(X0)) | (~rich(X0) | quiet(X0))) & ((rich(X0) & ~quiet(X0)) | (humble(X0) | wise(X0)))) [nnf transformation 1]
30. ! [X0] : (((~humble(X0) & ~wise(X0)) | ~rich(X0) | quiet(X0)) & ((rich(X0) & ~quiet(X0)) | humble(X0) | wise(X0))) [flattening 29]
41. ! [X0] : (((curious(X0) & tall(X0)) | (~patient(X0) & ~wise(X0))) & ((patient(X0) | wise(X0)) | (~curious(X0) | ~tall(X0)))) [nnf transformation 8]
42. ! [X0] : (((curious(X0) & tall(X0)) | (~patient(X0) & ~wise(X0))) & (patient(X0) | wise(X0) | ~curious(X0) | ~tall(X0))) [flattening 41]
46. ! [X0] : (((quiet(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | (~quiet(X0) | humble(X0)))) [nnf transformation 11]
47. ! [X0] : (((quiet(X0) & ~humble(X0)) | brave(X0)) & (~brave(X0) | ~quiet(X0) | humble(X0))) [flattening 46]
48. ! [X0] : (((~funny(X0) & funny(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | (funny(X0) | ~funny(X0)))) [nnf transformation 12]
49. ! [X0] : (((~funny(X0) & funny(X0)) | ((~patient(X0) | rich(X0)) & (~rich(X0) | patient(X0)))) & (((rich(X0) | patient(X0)) & (~rich(X0) | ~patient(X0))) | funny(X0) | ~funny(X0))) [flattening 48]
50. ((~humble(john) | patient(john)) & (humble(john) | ~patient(john))) | ! [X0] : ((old(X0) | rich(X0)) & (~rich(X0) | ~old(X0))) [nnf transformation 28]
66. rich(X0) | humble(X0) | wise(X0) [cnf transformation 30]
75. ~brave(X0) | ~tall(X0) [cnf transformation 23]
76. ~tall(X0) | ~quiet(X0) [cnf transformation 23]
88. ~wise(X0) | tall(X0) [cnf transformation 42]
89. ~patient(X0) | tall(X0) [cnf transformation 42]
104. brave(X0) | quiet(X0) [cnf transformation 47]
107. funny(X0) | ~rich(X0) | patient(X0) [cnf transformation 49]
109. ~funny(X0) | ~rich(X0) | patient(X0) [cnf transformation 49]
114. ~humble(john) | patient(john) | old(X0) | rich(X0) [cnf transformation 50]
127. ~old(mary) [cnf transformation 20]
200. 15 <=> old(mary) [avatar definition]
201. ~old(mary) <- (~15) [avatar component clause 200]
216. ~rich(X0) | patient(X0) [subsumption resolution 107,109]
218. 18 <=> ! [X0] : (old(X0) | rich(X0)) [avatar definition]
219. old(X0) | rich(X0) <- (18) [avatar component clause 218]
221. 19 <=> patient(john) [avatar definition]
223. patient(john) <- (19) [avatar component clause 221]
225. 20 <=> humble(john) [avatar definition]
227. ~humble(john) <- (~20) [avatar component clause 225]
228. 18 | 19 | ~20 [avatar split clause 114,225,221,218]
267. ~15 [avatar split clause 127,200]
272. quiet(X0) | ~tall(X0) [resolution 104,75]
273. ~tall(X0) [subsumption resolution 272,76]
292. patient(X0) | wise(X0) | humble(X0) [resolution 66,216]
389. 39 <=> wise(john) [avatar definition]
391. wise(john) <- (39) [avatar component clause 389]
396. tall(john) <- (19) [resolution 223,89]
407. $false <- (19) [subsumption resolution 396,273]
408. ~19 [avatar contradiction clause 407]
413. rich(mary) <- (~15, 18) [resolution 219,201]
420. patient(mary) <- (~15, 18) [resolution 413,216]
464. wise(X3) | humble(X3) | tall(X3) [resolution 292,89]
470. humble(X3) | wise(X3) [subsumption resolution 464,273]
474. tall(mary) <- (~15, 18) [resolution 420,89]
475. $false <- (~15, 18) [subsumption resolution 474,273]
476. 15 | ~18 [avatar contradiction clause 475]
483. wise(john) <- (~20) [resolution 470,227]
489. 39 | 20 [avatar split clause 483,225,389]
492. tall(john) <- (39) [resolution 391,88]
496. $false <- (39) [subsumption resolution 492,273]
497. ~39 [avatar contradiction clause 496]
498. $false [avatar sat refutation 228,267,408,476,489,497]
% SZS output end Proof for 2613519682887584804394695
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or not humble then alice is not humble or rich.
Everyone who is either not creative or humble is not old or funny and vice versa.
If someone is both humble and not calm then someone is both not humble and not kind and vice versa.
If someone is both not kind and tall then someone is not wise and vice versa.
Everyone who is calm or creative is both not kind and not humble and vice versa.
If someone is both not funny and generous then someone is strong.
Everyone who is not generous or not humble is not kind or quiet.
If someone is both curious and not generous then someone is not quiet.
If mary is either calm or generous then alice is both not wise and not quiet and vice versa.
Everyone who is calm is patient or quiet and vice versa.
If alice is not brave then someone is rich.
If lucy is both not calm and not creative then someone is either not happy or not generous and vice versa.
If lucy is either generous or not happy then someone is not old or not rich.
Everyone who is calm is both creative and not old and vice versa.
Everyone who is calm is not funny or funny.
Everyone who is not calm is either not strong or not rich.
Alice is either quiet or not patient.
Someone is strong.
Someone is either kind or not funny.
Fred is curious or not happy.
Someone is curious.
Someone is not humble.
Someone is either not humble or old. | Alice is quiet. | contradiction | ((?[X]:((~brave(X)<~>~humble(X))))=>((~humble(alice)|rich(alice))))&
(![X]:((~creative(X)<~>humble(X))<=>(~old(X)|funny(X))))&
((?[X]:((humble(X)&~calm(X))))<=>(?[X]:((~humble(X)&~kind(X)))))&
((?[X]:((~kind(X)&tall(X))))<=>(?[X]:(~wise(X))))&
(![X]:((calm(X)|creative(X))<=>(~kind(X)&~humble(X))))&
((?[X]:((~funny(X)&generous(X))))=>(?[X]:(strong(X))))&
(![X]:((~generous(X)|~humble(X))=>(~kind(X)|quiet(X))))&
((?[X]:((curious(X)&~generous(X))))=>(?[X]:(~quiet(X))))&
(((calm(mary)<~>generous(mary)))<=>((~wise(alice)&~quiet(alice))))&
(![X]:(calm(X)<=>(patient(X)|quiet(X))))&
((~brave(alice))=>(?[X]:(rich(X))))&
(((~calm(lucy)&~creative(lucy)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(((generous(lucy)<~>~happy(lucy)))=>(?[X]:((~old(X)|~rich(X)))))&
(![X]:(calm(X)<=>(creative(X)&~old(X))))&
(![X]:(calm(X)=>(~funny(X)|funny(X))))&
(![X]:(~calm(X)=>(~strong(X)<~>~rich(X))))&
((quiet(alice)<~>~patient(alice)))&
(?[X]:(strong(X)))&
(?[X]:((kind(X)<~>~funny(X))))&
((curious(fred)|~happy(fred)))&
(?[X]:(curious(X)))&
(?[X]:(~humble(X)))&
(?[X]:((~humble(X)<~>old(X)))) | quiet(alice) | [
"p1",
"p4",
"p9",
"p13",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 155655855774664830760542
% SZS output start Proof for 155655855774664830760542
2. ! [X0] : ((~creative(X0) <~> humble(X0)) <=> (funny(X0) | ~old(X0))) [input p1]
5. ! [X0] : ((creative(X0) | calm(X0)) <=> (~humble(X0) & ~kind(X0))) [input p4]
10. ! [X0] : (calm(X0) <=> (quiet(X0) | patient(X0))) [input p9]
14. ! [X0] : (calm(X0) <=> (~old(X0) & creative(X0))) [input p13]
17. quiet(alice) <~> ~patient(alice) [input p16]
24. quiet(alice) [input hypothesis]
41. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (~funny(X0) & old(X0))) & ((funny(X0) | ~old(X0)) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [nnf transformation 2]
42. ! [X0] : ((((~humble(X0) | creative(X0)) & (humble(X0) | ~creative(X0))) | (~funny(X0) & old(X0))) & (funny(X0) | ~old(X0) | ((~creative(X0) | ~humble(X0)) & (humble(X0) | creative(X0))))) [flattening 41]
53. ! [X0] : (((creative(X0) | calm(X0)) | (humble(X0) | kind(X0))) & ((~humble(X0) & ~kind(X0)) | (~creative(X0) & ~calm(X0)))) [nnf transformation 5]
54. ! [X0] : ((creative(X0) | calm(X0) | humble(X0) | kind(X0)) & ((~humble(X0) & ~kind(X0)) | (~creative(X0) & ~calm(X0)))) [flattening 53]
63. ! [X0] : ((calm(X0) | (~quiet(X0) & ~patient(X0))) & ((quiet(X0) | patient(X0)) | ~calm(X0))) [nnf transformation 10]
64. ! [X0] : ((calm(X0) | (~quiet(X0) & ~patient(X0))) & (quiet(X0) | patient(X0) | ~calm(X0))) [flattening 63]
75. ! [X0] : ((calm(X0) | (old(X0) | ~creative(X0))) & ((~old(X0) & creative(X0)) | ~calm(X0))) [nnf transformation 14]
76. ! [X0] : ((calm(X0) | old(X0) | ~creative(X0)) & ((~old(X0) & creative(X0)) | ~calm(X0))) [flattening 75]
78. (patient(alice) | ~quiet(alice)) & (~patient(alice) | quiet(alice)) [nnf transformation 17]
95. ~creative(X0) | humble(X0) | old(X0) [cnf transformation 42]
108. ~calm(X0) | ~humble(X0) [cnf transformation 54]
122. ~patient(X0) | calm(X0) [cnf transformation 64]
133. ~calm(X0) | creative(X0) [cnf transformation 76]
134. ~calm(X0) | ~old(X0) [cnf transformation 76]
140. patient(alice) | ~quiet(alice) [cnf transformation 78]
149. quiet(alice) [cnf transformation 24]
154. 2 <=> humble(alice) [avatar definition]
234. 21 <=> quiet(alice) [avatar definition]
307. 36 <=> patient(alice) [avatar definition]
309. patient(alice) <- (36) [avatar component clause 307]
310. ~21 | 36 [avatar split clause 140,307,234]
341. 21 [avatar split clause 149,234]
345. calm(alice) <- (36) [resolution 122,309]
346. ~humble(alice) <- (36) [resolution 345,108]
348. creative(alice) <- (36) [resolution 133,345]
349. ~old(alice) <- (36) [resolution 134,345]
361. humble(alice) | old(alice) <- (36) [resolution 95,348]
366. humble(alice) <- (36) [subsumption resolution 361,349]
367. 2 | ~36 [avatar split clause 366,307,154]
369. ~2 | ~36 [avatar split clause 346,307,154]
370. $false [avatar sat refutation 310,341,367,369]
% SZS output end Proof for 155655855774664830760542
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong then someone is old or not old and vice versa.
If someone is either not generous or humble then susan is both not quiet and not old.
Everyone who is not curious or not humble is quiet and vice versa.
If someone is either wise or not tall then someone is generous or not quiet and vice versa.
Everyone who is both not curious and not wise is curious or not quiet and vice versa.
If someone is either not strong or tall then mary is humble or not happy and vice versa.
If someone is either not quiet or not curious then someone is either strong or quiet and vice versa.
Everyone who is curious or not old is wise or calm and vice versa.
Everyone who is both strong and tall is either not patient or quiet and vice versa.
If fred is humble then lucy is not wise and vice versa.
If john is either not generous or not rich then susan is not rich and vice versa.
Everyone who is either humble or happy is either not wise or happy and vice versa.
Everyone who is either curious or generous is patient or quiet.
If mary is either not patient or rich then someone is generous and vice versa.
Everyone who is humble or creative is tall and vice versa.
If fred is not wise or kind then someone is rich or patient.
Fred is either rich or not quiet.
John is wise or old.
Susan is funny.
Alice is either not calm or not generous.
Susan is not strong.
Someone is not calm or not patient.
Someone is kind. | John is not funny. | neutral | ((?[X]:(~strong(X)))<=>(?[X]:((old(X)|~old(X)))))&
((?[X]:((~generous(X)<~>humble(X))))=>((~quiet(susan)&~old(susan))))&
(![X]:((~curious(X)|~humble(X))<=>quiet(X)))&
((?[X]:((wise(X)<~>~tall(X))))<=>(?[X]:((generous(X)|~quiet(X)))))&
(![X]:((~curious(X)&~wise(X))<=>(curious(X)|~quiet(X))))&
((?[X]:((~strong(X)<~>tall(X))))<=>((humble(mary)|~happy(mary))))&
((?[X]:((~quiet(X)<~>~curious(X))))<=>(?[X]:((strong(X)<~>quiet(X)))))&
(![X]:((curious(X)|~old(X))<=>(wise(X)|calm(X))))&
(![X]:((strong(X)&tall(X))<=>(~patient(X)<~>quiet(X))))&
((humble(fred))<=>(~wise(lucy)))&
(((~generous(john)<~>~rich(john)))<=>(~rich(susan)))&
(![X]:((humble(X)<~>happy(X))<=>(~wise(X)<~>happy(X))))&
(![X]:((curious(X)<~>generous(X))=>(patient(X)|quiet(X))))&
(((~patient(mary)<~>rich(mary)))<=>(?[X]:(generous(X))))&
(![X]:((humble(X)|creative(X))<=>tall(X)))&
(((~wise(fred)|kind(fred)))=>(?[X]:((rich(X)|patient(X)))))&
((rich(fred)<~>~quiet(fred)))&
((wise(john)|old(john)))&
(funny(susan))&
((~calm(alice)<~>~generous(alice)))&
(~strong(susan))&
(?[X]:((~calm(X)|~patient(X))))&
(?[X]:(kind(X))) | ~funny(john) | []
| null | 0 |
Everyone who is patient or happy is not funny.
Everyone who is not patient or not quiet is both wise and calm and vice versa.
Everyone who is funny or not tall is both not calm and tall.
Everyone who is strong is rich or old and vice versa.
Everyone who is either funny or not wise is both not calm and old and vice versa.
Everyone who is not brave or not generous is both calm and wise.
Everyone who is both humble and curious is not curious.
If lucy is rich then john is generous or happy and vice versa.
Everyone who is either strong or not tall is either not rich or funny.
If john is either not curious or not wise then someone is not patient or not old.
Everyone who is curious or wise is either not rich or not old and vice versa.
If mary is either not generous or old then lucy is either patient or not old and vice versa.
Everyone who is wise or not tall is either not tall or curious and vice versa.
If someone is not rich or not curious then alice is either not calm or not rich and vice versa.
Everyone who is both not funny and wise is funny or tall.
Susan is not happy.
Someone is calm.
Mary is curious or not humble.
Someone is either creative or generous. | Alice is not creative. | neutral | (![X]:((patient(X)|happy(X))=>~funny(X)))&
(![X]:((~patient(X)|~quiet(X))<=>(wise(X)&calm(X))))&
(![X]:((funny(X)|~tall(X))=>(~calm(X)&tall(X))))&
(![X]:(strong(X)<=>(rich(X)|old(X))))&
(![X]:((funny(X)<~>~wise(X))<=>(~calm(X)&old(X))))&
(![X]:((~brave(X)|~generous(X))=>(calm(X)&wise(X))))&
(![X]:((humble(X)&curious(X))=>~curious(X)))&
((rich(lucy))<=>((generous(john)|happy(john))))&
(![X]:((strong(X)<~>~tall(X))=>(~rich(X)<~>funny(X))))&
(((~curious(john)<~>~wise(john)))=>(?[X]:((~patient(X)|~old(X)))))&
(![X]:((curious(X)|wise(X))<=>(~rich(X)<~>~old(X))))&
(((~generous(mary)<~>old(mary)))<=>((patient(lucy)<~>~old(lucy))))&
(![X]:((wise(X)|~tall(X))<=>(~tall(X)<~>curious(X))))&
((?[X]:((~rich(X)|~curious(X))))<=>((~calm(alice)<~>~rich(alice))))&
(![X]:((~funny(X)&wise(X))=>(funny(X)|tall(X))))&
(~happy(susan))&
(?[X]:(calm(X)))&
((curious(mary)|~humble(mary)))&
(?[X]:((creative(X)<~>generous(X)))) | ~creative(alice) | []
| null | 0 |
Everyone who is both happy and patient is calm.
If mary is both curious and tall then someone is either happy or not generous and vice versa.
Everyone who is both not wise and curious is both not wise and humble and vice versa.
If alice is happy then someone is curious or not generous and vice versa.
Everyone who is not creative or rich is both funny and not funny.
If john is both not generous and humble then lucy is patient or not tall and vice versa.
If someone is humble then john is not curious.
Everyone who is either not rich or not curious is patient or not kind.
If someone is not quiet then someone is either not wise or not strong and vice versa.
Everyone who is kind is both kind and not curious and vice versa.
If someone is either not tall or calm then someone is both not tall and old.
If someone is not quiet then someone is either not generous or kind and vice versa.
If someone is both not wise and old then lucy is not wise or not calm and vice versa.
Everyone who is both not generous and not calm is not wise and vice versa.
If john is both patient and not old then mary is both brave and not wise and vice versa.
Everyone who is not generous or generous is not funny and vice versa.
Someone is happy.
Fred is not strong.
Someone is old.
Susan is both not funny and not generous.
Alice is kind or not wise.
Susan is strong or kind.
Fred is either not wise or not old. | Mary is funny. | contradiction | (![X]:((happy(X)&patient(X))=>calm(X)))&
(((curious(mary)&tall(mary)))<=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:((~wise(X)&curious(X))<=>(~wise(X)&humble(X))))&
((happy(alice))<=>(?[X]:((curious(X)|~generous(X)))))&
(![X]:((~creative(X)|rich(X))=>(funny(X)&~funny(X))))&
(((~generous(john)&humble(john)))<=>((patient(lucy)|~tall(lucy))))&
((?[X]:(humble(X)))=>(~curious(john)))&
(![X]:((~rich(X)<~>~curious(X))=>(patient(X)|~kind(X))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
(![X]:(kind(X)<=>(kind(X)&~curious(X))))&
((?[X]:((~tall(X)<~>calm(X))))=>(?[X]:((~tall(X)&old(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~generous(X)<~>kind(X)))))&
((?[X]:((~wise(X)&old(X))))<=>((~wise(lucy)|~calm(lucy))))&
(![X]:((~generous(X)&~calm(X))<=>~wise(X)))&
(((patient(john)&~old(john)))<=>((brave(mary)&~wise(mary))))&
(![X]:((~generous(X)|generous(X))<=>~funny(X)))&
(?[X]:(happy(X)))&
(~strong(fred))&
(?[X]:(old(X)))&
((~funny(susan)&~generous(susan)))&
((kind(alice)|~wise(alice)))&
((strong(susan)|kind(susan)))&
((~wise(fred)<~>~old(fred))) | funny(mary) | [
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 4711263795768719656725414
% SZS output start Proof for 4711263795768719656725414
16. ! [X0] : ((generous(X0) | ~generous(X0)) <=> ~funny(X0)) [input p15]
24. funny(mary) [input hypothesis]
75. ! [X0] : (((generous(X0) | ~generous(X0)) | funny(X0)) & (~funny(X0) | (~generous(X0) & generous(X0)))) [nnf transformation 16]
76. ! [X0] : ((generous(X0) | ~generous(X0) | funny(X0)) & (~funny(X0) | (~generous(X0) & generous(X0)))) [flattening 75]
133. ~funny(X0) | generous(X0) [cnf transformation 76]
134. ~funny(X0) | ~generous(X0) [cnf transformation 76]
145. funny(mary) [cnf transformation 24]
335. ~funny(X0) [subsumption resolution 133,134]
364. $false [subsumption resolution 145,335]
% SZS output end Proof for 4711263795768719656725414
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is not funny or patient then someone is either not strong or not wise.
If alice is either not strong or creative then someone is not creative.
If someone is both not happy and funny then lucy is both not curious and not funny and vice versa.
If someone is both patient and funny then someone is quiet or not patient.
If mary is not humble then someone is not calm.
If john is either not strong or patient then fred is not calm or strong.
Everyone who is rich or not quiet is both not humble and not calm and vice versa.
Everyone who is not wise or not kind is either happy or not calm and vice versa.
If alice is not humble or curious then paul is either wise or creative and vice versa.
If fred is humble then alice is either not patient or not tall and vice versa.
If someone is both not strong and calm then someone is not creative or quiet.
If mary is both funny and humble then john is both not rich and wise.
Everyone who is not humble is calm.
Everyone who is both rich and not curious is not strong or not wise and vice versa.
Everyone who is old is either quiet or not strong.
Everyone who is not strong is either kind or not calm.
Paul is either funny or not strong.
Fred is old.
Someone is not creative or rich.
John is not creative or wise.
Someone is not quiet or not tall.
Someone is kind or wise.
Mary is either generous or not strong.
Paul is either creative or not generous. | John is not patient. | entailment | (((~funny(john)|patient(john)))=>(?[X]:((~strong(X)<~>~wise(X)))))&
(((~strong(alice)<~>creative(alice)))=>(?[X]:(~creative(X))))&
((?[X]:((~happy(X)&funny(X))))<=>((~curious(lucy)&~funny(lucy))))&
((?[X]:((patient(X)&funny(X))))=>(?[X]:((quiet(X)|~patient(X)))))&
((~humble(mary))=>(?[X]:(~calm(X))))&
(((~strong(john)<~>patient(john)))=>((~calm(fred)|strong(fred))))&
(![X]:((rich(X)|~quiet(X))<=>(~humble(X)&~calm(X))))&
(![X]:((~wise(X)|~kind(X))<=>(happy(X)<~>~calm(X))))&
(((~humble(alice)|curious(alice)))<=>((wise(paul)<~>creative(paul))))&
((humble(fred))<=>((~patient(alice)<~>~tall(alice))))&
((?[X]:((~strong(X)&calm(X))))=>(?[X]:((~creative(X)|quiet(X)))))&
(((funny(mary)&humble(mary)))=>((~rich(john)&wise(john))))&
(![X]:(~humble(X)=>calm(X)))&
(![X]:((rich(X)&~curious(X))<=>(~strong(X)|~wise(X))))&
(![X]:(old(X)=>(quiet(X)<~>~strong(X))))&
(![X]:(~strong(X)=>(kind(X)<~>~calm(X))))&
((funny(paul)<~>~strong(paul)))&
(old(fred))&
(?[X]:((~creative(X)|rich(X))))&
((~creative(john)|wise(john)))&
(?[X]:((~quiet(X)|~tall(X))))&
(?[X]:((kind(X)|wise(X))))&
((generous(mary)<~>~strong(mary)))&
((creative(paul)<~>~generous(paul))) | ~patient(john) | [
"p0",
"p6",
"p12",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 6364755427392188903884729
% SZS output start Proof for 6364755427392188903884729
1. (patient(john) | ~funny(john)) => ? [X0] : (~strong(X0) <~> ~wise(X0)) [input p0]
7. ! [X0] : ((~quiet(X0) | rich(X0)) <=> (~calm(X0) & ~humble(X0))) [input p6]
13. ! [X0] : (~humble(X0) => calm(X0)) [input p12]
14. ! [X0] : ((~curious(X0) & rich(X0)) <=> (~wise(X0) | ~strong(X0))) [input p13]
25. patient(john) [input hypothesis]
28. ? [X0] : (~strong(X0) <~> ~wise(X0)) | (~patient(john) & funny(john)) [ennf transformation 1]
37. ! [X0] : (calm(X0) | humble(X0)) [ennf transformation 13]
40. ? [X0] : ((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) | (~patient(john) & funny(john)) [nnf transformation 28]
41. ? [X0] : ((wise(X0) | strong(X0)) & (~wise(X0) | ~strong(X0))) => ((wise(sK0) | strong(sK0)) & (~wise(sK0) | ~strong(sK0))) [choice axiom]
42. ((wise(sK0) | strong(sK0)) & (~wise(sK0) | ~strong(sK0))) | (~patient(john) & funny(john)) [skolemisation 40,41]
57. ! [X0] : (((~quiet(X0) | rich(X0)) | (calm(X0) | humble(X0))) & ((~calm(X0) & ~humble(X0)) | (quiet(X0) & ~rich(X0)))) [nnf transformation 7]
58. ! [X0] : ((~quiet(X0) | rich(X0) | calm(X0) | humble(X0)) & ((~calm(X0) & ~humble(X0)) | (quiet(X0) & ~rich(X0)))) [flattening 57]
67. ! [X0] : (((~curious(X0) & rich(X0)) | (wise(X0) & strong(X0))) & ((~wise(X0) | ~strong(X0)) | (curious(X0) | ~rich(X0)))) [nnf transformation 14]
68. ! [X0] : (((~curious(X0) & rich(X0)) | (wise(X0) & strong(X0))) & (~wise(X0) | ~strong(X0) | curious(X0) | ~rich(X0))) [flattening 67]
81. ~wise(sK0) | ~strong(sK0) | ~patient(john) [cnf transformation 42]
94. ~rich(X0) | ~humble(X0) [cnf transformation 58]
96. ~rich(X0) | ~calm(X0) [cnf transformation 58]
118. calm(X0) | humble(X0) [cnf transformation 37]
120. rich(X0) | strong(X0) [cnf transformation 68]
121. rich(X0) | wise(X0) [cnf transformation 68]
139. patient(john) [cnf transformation 25]
141. 1 <=> patient(john) [avatar definition]
145. 2 <=> strong(sK0) [avatar definition]
146. ~strong(sK0) <- (~2) [avatar component clause 145]
149. 3 <=> wise(sK0) [avatar definition]
150. ~wise(sK0) <- (~3) [avatar component clause 149]
158. ~1 | ~2 | ~3 [avatar split clause 81,149,145,141]
271. 28 <=> ! [X1] : (~calm(X1) | strong(X1)) [avatar definition]
272. ~calm(X1) | strong(X1) <- (28) [avatar component clause 271]
354. 1 [avatar split clause 139,141]
359. strong(X0) | ~calm(X0) [resolution 120,96]
360. ~humble(X1) | strong(X1) [resolution 120,94]
361. 28 [avatar split clause 359,271]
364. ~calm(X0) | wise(X0) [resolution 121,96]
365. wise(X1) | ~humble(X1) [resolution 121,94]
366. strong(X0) | humble(X0) <- (28) [resolution 272,118]
367. strong(X0) <- (28) [subsumption resolution 366,360]
371. $false <- (~2, 28) [resolution 367,146]
372. 2 | ~28 [avatar contradiction clause 371]
385. wise(X0) | humble(X0) [resolution 364,118]
387. wise(X0) [subsumption resolution 385,365]
402. $false <- (~3) [resolution 387,150]
403. 3 [avatar contradiction clause 402]
404. $false [avatar sat refutation 158,354,361,372,403]
% SZS output end Proof for 6364755427392188903884729
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or not kind is kind and vice versa.
If someone is both not creative and not kind then lucy is not curious or not wise and vice versa.
If someone is tall or brave then susan is both not calm and brave.
Everyone who is either not curious or not creative is either not brave or not curious and vice versa.
Everyone who is humble or brave is both tall and generous.
If someone is wise then someone is both not humble and not kind.
Everyone who is funny or not humble is either not brave or old and vice versa.
Everyone who is either not kind or funny is strong or funny and vice versa.
If alice is either not curious or not rich then lucy is not rich and vice versa.
Everyone who is not wise is calm or creative.
Everyone who is either not tall or not generous is both not calm and not humble.
If lucy is not funny then someone is either tall or not curious and vice versa.
Everyone who is either not rich or not tall is brave.
Everyone who is humble is either not patient or generous.
Everyone who is either not humble or rich is both not funny and not old and vice versa.
Someone is wise or not generous.
John is either quiet or not curious.
Alice is happy.
Someone is both not patient and kind. | John is not old. | entailment | (![X]:((~generous(X)<~>~kind(X))<=>kind(X)))&
((?[X]:((~creative(X)&~kind(X))))<=>((~curious(lucy)|~wise(lucy))))&
((?[X]:((tall(X)|brave(X))))=>((~calm(susan)&brave(susan))))&
(![X]:((~curious(X)<~>~creative(X))<=>(~brave(X)<~>~curious(X))))&
(![X]:((humble(X)|brave(X))=>(tall(X)&generous(X))))&
((?[X]:(wise(X)))=>(?[X]:((~humble(X)&~kind(X)))))&
(![X]:((funny(X)|~humble(X))<=>(~brave(X)<~>old(X))))&
(![X]:((~kind(X)<~>funny(X))<=>(strong(X)|funny(X))))&
(((~curious(alice)<~>~rich(alice)))<=>(~rich(lucy)))&
(![X]:(~wise(X)=>(calm(X)|creative(X))))&
(![X]:((~tall(X)<~>~generous(X))=>(~calm(X)&~humble(X))))&
((~funny(lucy))<=>(?[X]:((tall(X)<~>~curious(X)))))&
(![X]:((~rich(X)<~>~tall(X))=>brave(X)))&
(![X]:(humble(X)=>(~patient(X)<~>generous(X))))&
(![X]:((~humble(X)<~>rich(X))<=>(~funny(X)&~old(X))))&
(?[X]:((wise(X)|~generous(X))))&
((quiet(john)<~>~curious(john)))&
(happy(alice))&
(?[X]:((~patient(X)&kind(X)))) | ~old(john) | [
"p0",
"p4",
"p6",
"hypothesis"
]
| % SZS status Unsatisfiable for 1111471324738647365135458
% SZS output start Proof for 1111471324738647365135458
1. ! [X0] : ((~generous(X0) <~> ~kind(X0)) <=> kind(X0)) [input p0]
5. ! [X0] : ((brave(X0) | humble(X0)) => (generous(X0) & tall(X0))) [input p4]
7. ! [X0] : ((~humble(X0) | funny(X0)) <=> (~brave(X0) <~> old(X0))) [input p6]
20. old(john) [input hypothesis]
24. ! [X0] : ((generous(X0) & tall(X0)) | (~brave(X0) & ~humble(X0))) [ennf transformation 5]
31. ! [X0] : ((((kind(X0) | generous(X0)) & (~kind(X0) | ~generous(X0))) | ~kind(X0)) & (kind(X0) | ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))))) [nnf transformation 1]
41. ! [X0] : (((~humble(X0) | funny(X0)) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (humble(X0) & ~funny(X0)))) [nnf transformation 7]
42. ! [X0] : ((~humble(X0) | funny(X0) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0)))) & (((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (humble(X0) & ~funny(X0)))) [flattening 41]
61. kind(X0) | ~generous(X0) | kind(X0) [cnf transformation 31]
62. ~kind(X0) | ~generous(X0) | ~kind(X0) [cnf transformation 31]
83. generous(X0) | ~humble(X0) [cnf transformation 24]
84. generous(X0) | ~brave(X0) [cnf transformation 24]
90. ~old(X0) | brave(X0) | humble(X0) [cnf transformation 42]
127. old(john) [cnf transformation 20]
134. kind(X0) | ~generous(X0) [duplicate literal removal 61]
135. ~kind(X0) | ~generous(X0) [duplicate literal removal 62]
136. ~generous(X0) [subsumption resolution 134,135]
162. 6 <=> ! [X0] : ~brave(X0) [avatar definition]
163. ~brave(X0) <- (6) [avatar component clause 162]
181. ~brave(X0) [subsumption resolution 84,136]
182. 6 [avatar split clause 181,162]
183. ~humble(X0) [subsumption resolution 83,136]
192. ~old(X0) | brave(X0) [subsumption resolution 90,183]
251. brave(john) [resolution 192,127]
252. $false <- (6) [subsumption resolution 251,163]
253. ~6 [avatar contradiction clause 252]
254. $false [avatar sat refutation 182,253]
% SZS output end Proof for 1111471324738647365135458
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not creative is both generous and not wise and vice versa. If mary is both calm and not funny then someone is not tall. If paul is not rich then someone is both not humble and quiet. Everyone who is either old or not quiet is either strong or brave and vice versa. Everyone who is not tall is both wise and humble and vice versa. Everyone who is humble is either not calm or not brave and vice versa. Everyone who is not strong is not patient or not strong and vice versa. Everyone who is both humble and not brave is either calm or not wise and vice versa. If alice is both generous and old then someone is patient or curious. Everyone who is both happy and not tall is calm. If paul is calm or not kind then mary is patient. Everyone who is humble is not kind or not tall and vice versa. Everyone who is tall is either not humble or not old and vice versa. If someone is either not old or not calm then someone is generous and vice versa. Everyone who is both not old and not kind is humble and vice versa. Fred is both curious and quiet. Mary is not humble or not happy. Susan is tall. Someone is not happy. Paul is not quiet. Someone is calm. Someone is both quiet and curious. | Paul is not tall. | contradiction | (![X]:((~brave(X)|~creative(X))<=>(generous(X)&~wise(X))))&
(((calm(mary)&~funny(mary)))=>(?[X]:(~tall(X))))&
((~rich(paul))=>(?[X]:((~humble(X)&quiet(X)))))&
(![X]:((old(X)<~>~quiet(X))<=>(strong(X)<~>brave(X))))&
(![X]:(~tall(X)<=>(wise(X)&humble(X))))&
(![X]:(humble(X)<=>(~calm(X)<~>~brave(X))))&
(![X]:(~strong(X)<=>(~patient(X)|~strong(X))))&
(![X]:((humble(X)&~brave(X))<=>(calm(X)<~>~wise(X))))&
(((generous(alice)&old(alice)))=>(?[X]:((patient(X)|curious(X)))))&
(![X]:((happy(X)&~tall(X))=>calm(X)))&
(((calm(paul)|~kind(paul)))=>(patient(mary)))&
(![X]:(humble(X)<=>(~kind(X)|~tall(X))))&
(![X]:(tall(X)<=>(~humble(X)<~>~old(X))))&
((?[X]:((~old(X)<~>~calm(X))))<=>(?[X]:(generous(X))))&
(![X]:((~old(X)&~kind(X))<=>humble(X)))&
((curious(fred)&quiet(fred)))&
((~humble(mary)|~happy(mary)))&
(tall(susan))&
(?[X]:(~happy(X)))&
(~quiet(paul))&
(?[X]:(calm(X)))&
(?[X]:((quiet(X)&curious(X)))) | ~tall(paul) | [
"p4",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5165537202900306360731756
% SZS output start Proof for 5165537202900306360731756
5. ! [X0] : (~tall(X0) <=> (humble(X0) & wise(X0))) [input p4]
13. ! [X0] : (tall(X0) <=> (~humble(X0) <~> ~old(X0))) [input p12]
15. ! [X0] : ((~kind(X0) & ~old(X0)) <=> humble(X0)) [input p14]
23. ~tall(paul) [input hypothesis]
37. ! [X0] : ((~tall(X0) | (~humble(X0) | ~wise(X0))) & ((humble(X0) & wise(X0)) | tall(X0))) [nnf transformation 5]
38. ! [X0] : ((~tall(X0) | ~humble(X0) | ~wise(X0)) & ((humble(X0) & wise(X0)) | tall(X0))) [flattening 37]
46. ! [X0] : ((tall(X0) | ((~humble(X0) | old(X0)) & (~old(X0) | humble(X0)))) & (((old(X0) | humble(X0)) & (~old(X0) | ~humble(X0))) | ~tall(X0))) [nnf transformation 13]
52. ! [X0] : (((~kind(X0) & ~old(X0)) | ~humble(X0)) & (humble(X0) | (kind(X0) | old(X0)))) [nnf transformation 15]
53. ! [X0] : (((~kind(X0) & ~old(X0)) | ~humble(X0)) & (humble(X0) | kind(X0) | old(X0))) [flattening 52]
72. humble(X0) | tall(X0) [cnf transformation 38]
95. tall(X0) | ~humble(X0) | old(X0) [cnf transformation 46]
101. ~old(X0) | ~humble(X0) [cnf transformation 53]
108. ~tall(paul) [cnf transformation 23]
126. old(X0) | tall(X0) [subsumption resolution 95,72]
163. tall(X0) | ~humble(X0) [resolution 126,101]
164. tall(X0) [subsumption resolution 163,72]
165. $false [resolution 164,108]
% SZS output end Proof for 5165537202900306360731756
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.024 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both rich and wise is both not wise and quiet. If susan is both not creative and funny then someone is strong. Everyone who is not rich or not generous is not happy or not old. If paul is both brave and not kind then paul is not kind. Everyone who is both not generous and funny is generous or not brave and vice versa. If someone is not old or tall then someone is both not kind and not humble. Everyone who is both calm and not calm is not funny or not old and vice versa. If john is either not rich or not quiet then someone is both calm and not strong and vice versa. If someone is humble or not patient then someone is both happy and not old. Everyone who is either wise or generous is not curious. Everyone who is either humble or quiet is not tall. Everyone who is calm or humble is humble or not strong. If fred is both strong and brave then mary is rich and vice versa. If mary is not funny or not generous then susan is either humble or not generous. Fred is either not kind or not humble. John is not generous or curious. Mary is not funny or curious. Alice is not kind. Alice is both not quiet and not creative. Someone is both funny and old. | Mary is not wise. | entailment | (![X]:((rich(X)&wise(X))=>(~wise(X)&quiet(X))))&
(((~creative(susan)&funny(susan)))=>(?[X]:(strong(X))))&
(![X]:((~rich(X)|~generous(X))=>(~happy(X)|~old(X))))&
(((brave(paul)&~kind(paul)))=>(~kind(paul)))&
(![X]:((~generous(X)&funny(X))<=>(generous(X)|~brave(X))))&
((?[X]:((~old(X)|tall(X))))=>(?[X]:((~kind(X)&~humble(X)))))&
(![X]:((calm(X)&~calm(X))<=>(~funny(X)|~old(X))))&
(((~rich(john)<~>~quiet(john)))<=>(?[X]:((calm(X)&~strong(X)))))&
((?[X]:((humble(X)|~patient(X))))=>(?[X]:((happy(X)&~old(X)))))&
(![X]:((wise(X)<~>generous(X))=>~curious(X)))&
(![X]:((humble(X)<~>quiet(X))=>~tall(X)))&
(![X]:((calm(X)|humble(X))=>(humble(X)|~strong(X))))&
(((strong(fred)&brave(fred)))<=>(rich(mary)))&
(((~funny(mary)|~generous(mary)))=>((humble(susan)<~>~generous(susan))))&
((~kind(fred)<~>~humble(fred)))&
((~generous(john)|curious(john)))&
((~funny(mary)|curious(mary)))&
(~kind(alice))&
((~quiet(alice)&~creative(alice)))&
(?[X]:((funny(X)&old(X)))) | ~wise(mary) | [
"p4",
"p6",
"p9",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 7081326367727786564227854
% SZS output start Proof for 7081326367727786564227854
5. ! [X0] : ((funny(X0) & ~generous(X0)) <=> (~brave(X0) | generous(X0))) [input p4]
7. ! [X0] : ((~calm(X0) & calm(X0)) <=> (~old(X0) | ~funny(X0))) [input p6]
10. ! [X0] : ((wise(X0) <~> generous(X0)) => ~curious(X0)) [input p9]
17. curious(mary) | ~funny(mary) [input p16]
21. wise(mary) [input hypothesis]
37. ! [X0] : (~curious(X0) | (wise(X0) <=> generous(X0))) [ennf transformation 10]
43. ! [X0] : (((funny(X0) & ~generous(X0)) | (brave(X0) & ~generous(X0))) & ((~brave(X0) | generous(X0)) | (~funny(X0) | generous(X0)))) [nnf transformation 5]
44. ! [X0] : (((funny(X0) & ~generous(X0)) | (brave(X0) & ~generous(X0))) & (~brave(X0) | generous(X0) | ~funny(X0) | generous(X0))) [flattening 43]
48. ! [X0] : (((~calm(X0) & calm(X0)) | (old(X0) & funny(X0))) & ((~old(X0) | ~funny(X0)) | (calm(X0) | ~calm(X0)))) [nnf transformation 7]
49. ! [X0] : (((~calm(X0) & calm(X0)) | (old(X0) & funny(X0))) & (~old(X0) | ~funny(X0) | calm(X0) | ~calm(X0))) [flattening 48]
57. ! [X0] : (~curious(X0) | ((wise(X0) | ~generous(X0)) & (generous(X0) | ~wise(X0)))) [nnf transformation 37]
71. ~generous(X0) | ~generous(X0) [cnf transformation 44]
78. calm(X0) | funny(X0) [cnf transformation 49]
80. ~calm(X0) | funny(X0) [cnf transformation 49]
90. ~curious(X0) | generous(X0) | ~wise(X0) [cnf transformation 57]
104. curious(mary) | ~funny(mary) [cnf transformation 17]
110. wise(mary) [cnf transformation 21]
112. ~generous(X0) [duplicate literal removal 71]
143. funny(X0) [subsumption resolution 78,80]
182. ~curious(X0) | ~wise(X0) [subsumption resolution 90,112]
210. curious(mary) [subsumption resolution 104,143]
216. ~wise(mary) [resolution 182,210]
217. $false [subsumption resolution 216,110]
% SZS output end Proof for 7081326367727786564227854
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either happy or not brave then susan is either not generous or generous.
Everyone who is both not wise and tall is either kind or old and vice versa.
If someone is kind then someone is not rich or strong.
If someone is rich or not patient then lucy is brave and vice versa.
Everyone who is both not brave and not calm is both humble and not funny and vice versa.
Everyone who is not creative is both not happy and quiet and vice versa.
Everyone who is either not quiet or not calm is both not funny and not generous and vice versa.
If susan is not calm or strong then someone is calm.
If someone is both generous and not generous then fred is not strong.
If mary is old or calm then mary is both not creative and patient and vice versa.
Everyone who is both not creative and quiet is happy and vice versa.
Everyone who is brave is either humble or wise and vice versa.
If susan is either not strong or rich then someone is either not humble or creative.
Everyone who is not patient or rich is patient and vice versa.
Everyone who is both not funny and not humble is either creative or not kind and vice versa.
Paul is funny.
Lucy is both not happy and generous.
Alice is not brave or not curious.
Someone is quiet or brave.
Someone is either quiet or curious.
Someone is not old. | Susan is kind. | neutral | ((?[X]:((happy(X)<~>~brave(X))))=>((~generous(susan)<~>generous(susan))))&
(![X]:((~wise(X)&tall(X))<=>(kind(X)<~>old(X))))&
((?[X]:(kind(X)))=>(?[X]:((~rich(X)|strong(X)))))&
((?[X]:((rich(X)|~patient(X))))<=>(brave(lucy)))&
(![X]:((~brave(X)&~calm(X))<=>(humble(X)&~funny(X))))&
(![X]:(~creative(X)<=>(~happy(X)&quiet(X))))&
(![X]:((~quiet(X)<~>~calm(X))<=>(~funny(X)&~generous(X))))&
(((~calm(susan)|strong(susan)))=>(?[X]:(calm(X))))&
((?[X]:((generous(X)&~generous(X))))=>(~strong(fred)))&
(((old(mary)|calm(mary)))<=>((~creative(mary)&patient(mary))))&
(![X]:((~creative(X)&quiet(X))<=>happy(X)))&
(![X]:(brave(X)<=>(humble(X)<~>wise(X))))&
(((~strong(susan)<~>rich(susan)))=>(?[X]:((~humble(X)<~>creative(X)))))&
(![X]:((~patient(X)|rich(X))<=>patient(X)))&
(![X]:((~funny(X)&~humble(X))<=>(creative(X)<~>~kind(X))))&
(funny(paul))&
((~happy(lucy)&generous(lucy)))&
((~brave(alice)|~curious(alice)))&
(?[X]:((quiet(X)|brave(X))))&
(?[X]:((quiet(X)<~>curious(X))))&
(?[X]:(~old(X))) | kind(susan) | []
| null | 0 |
If lucy is wise then paul is not tall and vice versa.
Everyone who is not kind is old.
If mary is both calm and strong then alice is either not calm or old and vice versa.
Everyone who is not generous or tall is not wise or curious.
If someone is both not kind and wise then someone is wise or not generous and vice versa.
Everyone who is not kind is both not generous and strong.
If fred is both funny and not brave then someone is either not happy or creative.
Everyone who is both quiet and not curious is either humble or calm and vice versa.
If mary is not curious then alice is old or quiet and vice versa.
Everyone who is both kind and creative is kind and vice versa.
If fred is either not old or not happy then someone is either not calm or kind.
Everyone who is both quiet and strong is not happy or quiet and vice versa.
Everyone who is either not old or not funny is either strong or humble and vice versa.
If paul is both not humble and not old then lucy is patient or not tall and vice versa.
Everyone who is either kind or creative is either old or not tall and vice versa.
Alice is happy.
Someone is either not curious or brave.
Someone is either not generous or not calm.
Someone is not brave or wise.
Someone is brave or not quiet.
Alice is generous or patient. | Mary is humble. | neutral | ((wise(lucy))<=>(~tall(paul)))&
(![X]:(~kind(X)=>old(X)))&
(((calm(mary)&strong(mary)))<=>((~calm(alice)<~>old(alice))))&
(![X]:((~generous(X)|tall(X))=>(~wise(X)|curious(X))))&
((?[X]:((~kind(X)&wise(X))))<=>(?[X]:((wise(X)|~generous(X)))))&
(![X]:(~kind(X)=>(~generous(X)&strong(X))))&
(((funny(fred)&~brave(fred)))=>(?[X]:((~happy(X)<~>creative(X)))))&
(![X]:((quiet(X)&~curious(X))<=>(humble(X)<~>calm(X))))&
((~curious(mary))<=>((old(alice)|quiet(alice))))&
(![X]:((kind(X)&creative(X))<=>kind(X)))&
(((~old(fred)<~>~happy(fred)))=>(?[X]:((~calm(X)<~>kind(X)))))&
(![X]:((quiet(X)&strong(X))<=>(~happy(X)|quiet(X))))&
(![X]:((~old(X)<~>~funny(X))<=>(strong(X)<~>humble(X))))&
(((~humble(paul)&~old(paul)))<=>((patient(lucy)|~tall(lucy))))&
(![X]:((kind(X)<~>creative(X))<=>(old(X)<~>~tall(X))))&
(happy(alice))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((~generous(X)<~>~calm(X))))&
(?[X]:((~brave(X)|wise(X))))&
(?[X]:((brave(X)|~quiet(X))))&
((generous(alice)|patient(alice))) | humble(mary) | []
| null | 0 |
If someone is either not strong or not brave then someone is strong or happy and vice versa.
If mary is either happy or not strong then someone is either generous or brave.
Everyone who is either not quiet or not humble is not creative or not brave and vice versa.
Everyone who is both not happy and old is not brave.
Everyone who is not humble is either rich or not tall and vice versa.
If john is rich or not wise then fred is both not generous and not humble.
Everyone who is humble or not kind is not quiet.
If someone is not quiet then paul is either not creative or not wise.
If paul is not humble or not old then someone is not funny.
Everyone who is strong or wise is both not quiet and not creative and vice versa.
Everyone who is strong or creative is either calm or creative and vice versa.
If someone is patient then john is both not wise and not funny and vice versa.
Everyone who is brave is both strong and not tall and vice versa.
If someone is either tall or wise then someone is generous or not happy.
Everyone who is not rich is not patient and vice versa.
If paul is both not funny and quiet then paul is not tall or wise.
Someone is both old and humble.
Someone is tall.
Someone is either happy or humble.
Someone is not generous.
Someone is calm.
Someone is either not calm or tall.
Someone is not strong.
Someone is not wise. | Mary is happy. | neutral | ((?[X]:((~strong(X)<~>~brave(X))))<=>(?[X]:((strong(X)|happy(X)))))&
(((happy(mary)<~>~strong(mary)))=>(?[X]:((generous(X)<~>brave(X)))))&
(![X]:((~quiet(X)<~>~humble(X))<=>(~creative(X)|~brave(X))))&
(![X]:((~happy(X)&old(X))=>~brave(X)))&
(![X]:(~humble(X)<=>(rich(X)<~>~tall(X))))&
(((rich(john)|~wise(john)))=>((~generous(fred)&~humble(fred))))&
(![X]:((humble(X)|~kind(X))=>~quiet(X)))&
((?[X]:(~quiet(X)))=>((~creative(paul)<~>~wise(paul))))&
(((~humble(paul)|~old(paul)))=>(?[X]:(~funny(X))))&
(![X]:((strong(X)|wise(X))<=>(~quiet(X)&~creative(X))))&
(![X]:((strong(X)|creative(X))<=>(calm(X)<~>creative(X))))&
((?[X]:(patient(X)))<=>((~wise(john)&~funny(john))))&
(![X]:(brave(X)<=>(strong(X)&~tall(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(?[X]:((generous(X)|~happy(X)))))&
(![X]:(~rich(X)<=>~patient(X)))&
(((~funny(paul)&quiet(paul)))=>((~tall(paul)|wise(paul))))&
(?[X]:((old(X)&humble(X))))&
(?[X]:(tall(X)))&
(?[X]:((happy(X)<~>humble(X))))&
(?[X]:(~generous(X)))&
(?[X]:(calm(X)))&
(?[X]:((~calm(X)<~>tall(X))))&
(?[X]:(~strong(X)))&
(?[X]:(~wise(X))) | happy(mary) | []
| null | 0 |
If mary is old then someone is wise or not patient. If someone is not brave or not rich then someone is either curious or generous and vice versa. If someone is not quiet or not generous then susan is both not curious and not creative and vice versa. Everyone who is either rich or not humble is not generous and vice versa. Everyone who is not calm or rich is either not old or generous and vice versa. If someone is not curious or rich then someone is not strong or curious and vice versa. Everyone who is not generous or not calm is both rich and not happy and vice versa. If someone is both funny and not funny then paul is either quiet or not creative and vice versa. If someone is humble then someone is old and vice versa. Everyone who is both not tall and not brave is either funny or quiet. Everyone who is not wise or not humble is either kind or not kind and vice versa. Everyone who is either rich or curious is either not rich or not generous. Everyone who is not creative is generous and vice versa. If someone is not humble then someone is both not funny and old and vice versa. If someone is both not quiet and calm then susan is wise or happy and vice versa. If someone is either wise or brave then fred is quiet or old and vice versa. Fred is either not brave or not curious. John is both not happy and not humble. Susan is either old or calm. Alice is either kind or not kind. Someone is quiet. Someone is tall. Someone is both tall and not curious. Someone is either generous or wise. | John is not creative. | entailment | ((old(mary))=>(?[X]:((wise(X)|~patient(X)))))&
((?[X]:((~brave(X)|~rich(X))))<=>(?[X]:((curious(X)<~>generous(X)))))&
((?[X]:((~quiet(X)|~generous(X))))<=>((~curious(susan)&~creative(susan))))&
(![X]:((rich(X)<~>~humble(X))<=>~generous(X)))&
(![X]:((~calm(X)|rich(X))<=>(~old(X)<~>generous(X))))&
((?[X]:((~curious(X)|rich(X))))<=>(?[X]:((~strong(X)|curious(X)))))&
(![X]:((~generous(X)|~calm(X))<=>(rich(X)&~happy(X))))&
((?[X]:((funny(X)&~funny(X))))<=>((quiet(paul)<~>~creative(paul))))&
((?[X]:(humble(X)))<=>(?[X]:(old(X))))&
(![X]:((~tall(X)&~brave(X))=>(funny(X)<~>quiet(X))))&
(![X]:((~wise(X)|~humble(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((rich(X)<~>curious(X))=>(~rich(X)<~>~generous(X))))&
(![X]:(~creative(X)<=>generous(X)))&
((?[X]:(~humble(X)))<=>(?[X]:((~funny(X)&old(X)))))&
((?[X]:((~quiet(X)&calm(X))))<=>((wise(susan)|happy(susan))))&
((?[X]:((wise(X)<~>brave(X))))<=>((quiet(fred)|old(fred))))&
((~brave(fred)<~>~curious(fred)))&
((~happy(john)&~humble(john)))&
((old(susan)<~>calm(susan)))&
((kind(alice)<~>~kind(alice)))&
(?[X]:(quiet(X)))&
(?[X]:(tall(X)))&
(?[X]:((tall(X)&~curious(X))))&
(?[X]:((generous(X)<~>wise(X)))) | ~creative(john) | [
"p3",
"p6",
"p12",
"p17",
"hypothesis"
]
| % SZS status Unsatisfiable for 4344425959680730545910027
% SZS output start Proof for 4344425959680730545910027
4. ! [X0] : ((rich(X0) <~> ~humble(X0)) <=> ~generous(X0)) [input p3]
7. ! [X0] : ((~calm(X0) | ~generous(X0)) <=> (~happy(X0) & rich(X0))) [input p6]
13. ! [X0] : (~creative(X0) <=> generous(X0)) [input p12]
18. ~humble(john) & ~happy(john) [input p17]
25. creative(john) [input hypothesis]
45. ! [X0] : ((((humble(X0) | ~rich(X0)) & (~humble(X0) | rich(X0))) | generous(X0)) & (~generous(X0) | ((rich(X0) | humble(X0)) & (~humble(X0) | ~rich(X0))))) [nnf transformation 4]
53. ! [X0] : (((~calm(X0) | ~generous(X0)) | (happy(X0) | ~rich(X0))) & ((~happy(X0) & rich(X0)) | (calm(X0) & generous(X0)))) [nnf transformation 7]
54. ! [X0] : ((~calm(X0) | ~generous(X0) | happy(X0) | ~rich(X0)) & ((~happy(X0) & rich(X0)) | (calm(X0) & generous(X0)))) [flattening 53]
67. ! [X0] : ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))) [nnf transformation 13]
107. ~rich(X0) | humble(X0) | generous(X0) [cnf transformation 45]
118. generous(X0) | rich(X0) [cnf transformation 54]
142. ~creative(X0) | ~generous(X0) [cnf transformation 67]
160. ~humble(john) [cnf transformation 18]
169. creative(john) [cnf transformation 25]
419. ~generous(john) [resolution 142,169]
422. rich(john) [resolution 419,118]
679. humble(john) | generous(john) [resolution 422,107]
681. generous(john) [subsumption resolution 679,160]
682. $false [subsumption resolution 681,419]
% SZS output end Proof for 4344425959680730545910027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is both quiet and tall.
Everyone who is either not old or not funny is strong or not generous.
Everyone who is either not humble or not funny is either calm or creative and vice versa.
Everyone who is not patient or not humble is either humble or not happy and vice versa.
If someone is both not strong and calm then someone is patient.
If mary is kind or not brave then fred is both old and not kind.
Everyone who is both not calm and not curious is both not patient and calm.
If someone is either kind or tall then someone is not quiet or brave.
If mary is either curious or not humble then mary is both not tall and not humble and vice versa.
Everyone who is quiet or kind is both not creative and not rich.
If susan is either tall or not wise then someone is rich or not quiet.
Everyone who is both not calm and not creative is either funny or not quiet and vice versa.
Everyone who is both not happy and strong is either brave or rich and vice versa.
Everyone who is curious or not rich is not humble.
If fred is brave or not funny then someone is both patient and wise.
Everyone who is creative is either not generous or not funny.
Someone is either not old or humble.
Lucy is either quiet or curious.
Susan is both calm and not quiet.
Fred is either not strong or funny.
Someone is either happy or rich.
Someone is wise.
Mary is either rich or brave. | Susan is not generous. | entailment | ((?[X]:(~creative(X)))=>(?[X]:((quiet(X)&tall(X)))))&
(![X]:((~old(X)<~>~funny(X))=>(strong(X)|~generous(X))))&
(![X]:((~humble(X)<~>~funny(X))<=>(calm(X)<~>creative(X))))&
(![X]:((~patient(X)|~humble(X))<=>(humble(X)<~>~happy(X))))&
((?[X]:((~strong(X)&calm(X))))=>(?[X]:(patient(X))))&
(((kind(mary)|~brave(mary)))=>((old(fred)&~kind(fred))))&
(![X]:((~calm(X)&~curious(X))=>(~patient(X)&calm(X))))&
((?[X]:((kind(X)<~>tall(X))))=>(?[X]:((~quiet(X)|brave(X)))))&
(((curious(mary)<~>~humble(mary)))<=>((~tall(mary)&~humble(mary))))&
(![X]:((quiet(X)|kind(X))=>(~creative(X)&~rich(X))))&
(((tall(susan)<~>~wise(susan)))=>(?[X]:((rich(X)|~quiet(X)))))&
(![X]:((~calm(X)&~creative(X))<=>(funny(X)<~>~quiet(X))))&
(![X]:((~happy(X)&strong(X))<=>(brave(X)<~>rich(X))))&
(![X]:((curious(X)|~rich(X))=>~humble(X)))&
(((brave(fred)|~funny(fred)))=>(?[X]:((patient(X)&wise(X)))))&
(![X]:(creative(X)=>(~generous(X)<~>~funny(X))))&
(?[X]:((~old(X)<~>humble(X))))&
((quiet(lucy)<~>curious(lucy)))&
((calm(susan)&~quiet(susan)))&
((~strong(fred)<~>funny(fred)))&
(?[X]:((happy(X)<~>rich(X))))&
(?[X]:(wise(X)))&
((rich(mary)<~>brave(mary))) | ~generous(susan) | [
"p0",
"p2",
"p6",
"p9",
"p11",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 1325501118840690418153198
% SZS output start Proof for 1325501118840690418153198
1. ? [X0] : ~creative(X0) => ? [X0] : (tall(X0) & quiet(X0)) [input p0]
3. ! [X0] : ((~humble(X0) <~> ~funny(X0)) <=> (calm(X0) <~> creative(X0))) [input p2]
7. ! [X0] : ((~curious(X0) & ~calm(X0)) => (calm(X0) & ~patient(X0))) [input p6]
10. ! [X0] : ((kind(X0) | quiet(X0)) => (~rich(X0) & ~creative(X0))) [input p9]
12. ! [X0] : ((~creative(X0) & ~calm(X0)) <=> (funny(X0) <~> ~quiet(X0))) [input p11]
14. ! [X0] : ((~rich(X0) | curious(X0)) => ~humble(X0)) [input p13]
16. ! [X0] : (creative(X0) => (~generous(X0) <~> ~funny(X0))) [input p15]
24. generous(susan) [input hypothesis]
25. ? [X0] : ~creative(X0) => ? [X1] : (tall(X1) & quiet(X1)) [rectify 1]
28. ? [X1] : (tall(X1) & quiet(X1)) | ! [X0] : creative(X0) [ennf transformation 25]
33. ! [X0] : ((calm(X0) & ~patient(X0)) | (curious(X0) | calm(X0))) [ennf transformation 7]
34. ! [X0] : ((calm(X0) & ~patient(X0)) | curious(X0) | calm(X0)) [flattening 33]
36. ! [X0] : ((~rich(X0) & ~creative(X0)) | (~kind(X0) & ~quiet(X0))) [ennf transformation 10]
38. ! [X0] : (~humble(X0) | (rich(X0) & ~curious(X0))) [ennf transformation 14]
40. ! [X0] : ((~generous(X0) <~> ~funny(X0)) | ~creative(X0)) [ennf transformation 16]
41. ? [X0] : (tall(X0) & quiet(X0)) | ! [X1] : creative(X1) [rectify 28]
42. ? [X0] : (tall(X0) & quiet(X0)) => (tall(sK0) & quiet(sK0)) [choice axiom]
43. (tall(sK0) & quiet(sK0)) | ! [X1] : creative(X1) [skolemisation 41,42]
45. ! [X0] : ((((funny(X0) | humble(X0)) & (~funny(X0) | ~humble(X0))) | ((calm(X0) | ~creative(X0)) & (creative(X0) | ~calm(X0)))) & (((~creative(X0) | ~calm(X0)) & (creative(X0) | calm(X0))) | ((~humble(X0) | funny(X0)) & (~funny(X0) | humble(X0))))) [nnf transformation 3]
60. ! [X0] : (((~creative(X0) & ~calm(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) & (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | (creative(X0) | calm(X0)))) [nnf transformation 12]
61. ! [X0] : (((~creative(X0) & ~calm(X0)) | ((funny(X0) | quiet(X0)) & (~quiet(X0) | ~funny(X0)))) & (((quiet(X0) | ~funny(X0)) & (~quiet(X0) | funny(X0))) | creative(X0) | calm(X0))) [flattening 60]
66. ! [X0] : (((funny(X0) | generous(X0)) & (~funny(X0) | ~generous(X0))) | ~creative(X0)) [nnf transformation 40]
78. quiet(sK0) | creative(X1) [cnf transformation 43]
82. ~funny(X0) | calm(X0) | creative(X0) | humble(X0) [cnf transformation 45]
88. ~calm(X0) | humble(X0) | creative(X0) | funny(X0) [cnf transformation 45]
102. calm(X0) | curious(X0) | calm(X0) [cnf transformation 34]
111. ~quiet(X0) | ~creative(X0) [cnf transformation 36]
113. ~rich(X0) | ~quiet(X0) [cnf transformation 36]
117. ~quiet(X0) | funny(X0) | creative(X0) | calm(X0) [cnf transformation 61]
119. ~calm(X0) | ~quiet(X0) | ~funny(X0) [cnf transformation 61]
122. ~creative(X0) | funny(X0) | quiet(X0) [cnf transformation 61]
129. ~curious(X0) | ~humble(X0) [cnf transformation 38]
130. ~humble(X0) | rich(X0) [cnf transformation 38]
135. ~funny(X0) | ~generous(X0) | ~creative(X0) [cnf transformation 66]
150. generous(susan) [cnf transformation 24]
153. curious(X0) | calm(X0) [duplicate literal removal 102]
157. 1 <=> ! [X1] : creative(X1) [avatar definition]
158. creative(X1) <- (1) [avatar component clause 157]
165. 3 <=> quiet(sK0) [avatar definition]
167. quiet(sK0) <- (3) [avatar component clause 165]
168. 1 | 3 [avatar split clause 78,165,157]
245. ~creative(X0) | funny(X0) [subsumption resolution 122,111]
246. ~quiet(X0) | funny(X0) | calm(X0) [subsumption resolution 117,245]
267. ~generous(X0) | ~creative(X0) [subsumption resolution 135,245]
314. ~humble(X0) | calm(X0) [resolution 153,129]
324. ~creative(susan) [resolution 267,150]
363. 36 <=> calm(sK0) [avatar definition]
364. ~calm(sK0) <- (~36) [avatar component clause 363]
365. calm(sK0) <- (36) [avatar component clause 363]
367. 37 <=> funny(sK0) [avatar definition]
368. ~funny(sK0) <- (~37) [avatar component clause 367]
369. funny(sK0) <- (37) [avatar component clause 367]
372. $false <- (1) [resolution 158,324]
375. ~1 [avatar contradiction clause 372]
376. funny(sK0) | calm(sK0) <- (3) [resolution 167,246]
377. ~creative(sK0) <- (3) [resolution 167,111]
379. ~quiet(sK0) | ~funny(sK0) <- (36) [resolution 365,119]
381. ~funny(sK0) <- (3, 36) [subsumption resolution 379,167]
382. ~37 | ~3 | ~36 [avatar split clause 381,363,165,367]
399. humble(sK0) | creative(sK0) | funny(sK0) <- (36) [resolution 88,365]
402. humble(sK0) | funny(sK0) <- (3, 36) [subsumption resolution 399,377]
403. humble(sK0) <- (3, 36, ~37) [subsumption resolution 402,368]
424. rich(sK0) <- (3, 36, ~37) [resolution 403,130]
471. ~quiet(sK0) <- (3, 36, ~37) [resolution 424,113]
479. $false <- (3, 36, ~37) [subsumption resolution 471,167]
480. ~3 | ~36 | 37 [avatar contradiction clause 479]
481. 36 | 37 | ~3 [avatar split clause 376,165,367,363]
483. calm(sK0) | creative(sK0) | humble(sK0) <- (37) [resolution 369,82]
484. creative(sK0) | humble(sK0) <- (~36, 37) [subsumption resolution 483,364]
485. humble(sK0) <- (3, ~36, 37) [subsumption resolution 484,377]
486. calm(sK0) <- (3, ~36, 37) [resolution 485,314]
491. $false <- (3, ~36, 37) [subsumption resolution 486,364]
492. ~3 | 36 | ~37 [avatar contradiction clause 491]
493. $false [avatar sat refutation 168,375,382,480,481,492]
% SZS output end Proof for 1325501118840690418153198
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not creative or not generous then someone is rich or humble and vice versa.
If susan is not happy or quiet then alice is either not patient or brave.
If alice is either funny or patient then mary is not generous.
Everyone who is tall or humble is not creative and vice versa.
Everyone who is not happy is either patient or quiet and vice versa.
Everyone who is both not funny and not curious is both not happy and generous and vice versa.
If someone is not funny then john is kind and vice versa.
If mary is funny or not curious then fred is either not rich or quiet and vice versa.
Everyone who is either not creative or curious is not humble or patient and vice versa.
Everyone who is not curious is either wise or funny and vice versa.
If paul is quiet then someone is either not brave or not generous and vice versa.
If someone is curious or rich then john is kind and vice versa.
Everyone who is humble is either strong or kind.
If susan is curious or generous then john is both not curious and not strong and vice versa.
Everyone who is not tall or kind is both not patient and humble.
Everyone who is not generous or patient is patient or wise.
Someone is tall.
John is kind or curious.
Someone is happy or curious.
Someone is either not quiet or not old.
Lucy is rich.
Someone is both not kind and rich.
Paul is calm. | Alice is not brave. | neutral | (((~creative(susan)|~generous(susan)))<=>(?[X]:((rich(X)|humble(X)))))&
(((~happy(susan)|quiet(susan)))=>((~patient(alice)<~>brave(alice))))&
(((funny(alice)<~>patient(alice)))=>(~generous(mary)))&
(![X]:((tall(X)|humble(X))<=>~creative(X)))&
(![X]:(~happy(X)<=>(patient(X)<~>quiet(X))))&
(![X]:((~funny(X)&~curious(X))<=>(~happy(X)&generous(X))))&
((?[X]:(~funny(X)))<=>(kind(john)))&
(((funny(mary)|~curious(mary)))<=>((~rich(fred)<~>quiet(fred))))&
(![X]:((~creative(X)<~>curious(X))<=>(~humble(X)|patient(X))))&
(![X]:(~curious(X)<=>(wise(X)<~>funny(X))))&
((quiet(paul))<=>(?[X]:((~brave(X)<~>~generous(X)))))&
((?[X]:((curious(X)|rich(X))))<=>(kind(john)))&
(![X]:(humble(X)=>(strong(X)<~>kind(X))))&
(((curious(susan)|generous(susan)))<=>((~curious(john)&~strong(john))))&
(![X]:((~tall(X)|kind(X))=>(~patient(X)&humble(X))))&
(![X]:((~generous(X)|patient(X))=>(patient(X)|wise(X))))&
(?[X]:(tall(X)))&
((kind(john)|curious(john)))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((~quiet(X)<~>~old(X))))&
(rich(lucy))&
(?[X]:((~kind(X)&rich(X))))&
(calm(paul)) | ~brave(alice) | []
| null | 0 |
If susan is patient or creative then someone is not creative or patient and vice versa.
If someone is either rich or not old then susan is both not quiet and not funny.
If alice is not funny then fred is both not generous and not strong.
If mary is both creative and not brave then paul is brave.
Everyone who is happy or not funny is both rich and not tall.
Everyone who is calm is both not quiet and not funny.
Everyone who is either not funny or brave is calm and vice versa.
If fred is patient then someone is both brave and quiet and vice versa.
If someone is not patient then fred is either calm or not creative.
Everyone who is either humble or kind is either not tall or not generous.
Everyone who is brave or not patient is not curious and vice versa.
Everyone who is both curious and tall is patient or curious.
Everyone who is either kind or not quiet is both funny and patient and vice versa.
If someone is either not happy or patient then someone is both happy and not kind.
If someone is either not old or old then john is both not happy and calm and vice versa.
Everyone who is not old or not strong is curious.
Alice is either curious or patient.
Someone is either strong or not patient.
Someone is funny or not strong.
Fred is both not rich and not happy.
Someone is not patient.
Someone is either patient or not creative.
John is not funny. | Susan is not tall. | entailment | (((patient(susan)|creative(susan)))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((rich(X)<~>~old(X))))=>((~quiet(susan)&~funny(susan))))&
((~funny(alice))=>((~generous(fred)&~strong(fred))))&
(((creative(mary)&~brave(mary)))=>(brave(paul)))&
(![X]:((happy(X)|~funny(X))=>(rich(X)&~tall(X))))&
(![X]:(calm(X)=>(~quiet(X)&~funny(X))))&
(![X]:((~funny(X)<~>brave(X))<=>calm(X)))&
((patient(fred))<=>(?[X]:((brave(X)&quiet(X)))))&
((?[X]:(~patient(X)))=>((calm(fred)<~>~creative(fred))))&
(![X]:((humble(X)<~>kind(X))=>(~tall(X)<~>~generous(X))))&
(![X]:((brave(X)|~patient(X))<=>~curious(X)))&
(![X]:((curious(X)&tall(X))=>(patient(X)|curious(X))))&
(![X]:((kind(X)<~>~quiet(X))<=>(funny(X)&patient(X))))&
((?[X]:((~happy(X)<~>patient(X))))=>(?[X]:((happy(X)&~kind(X)))))&
((?[X]:((~old(X)<~>old(X))))<=>((~happy(john)&calm(john))))&
(![X]:((~old(X)|~strong(X))=>curious(X)))&
((curious(alice)<~>patient(alice)))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:((funny(X)|~strong(X))))&
((~rich(fred)&~happy(fred)))&
(?[X]:(~patient(X)))&
(?[X]:((patient(X)<~>~creative(X))))&
(~funny(john)) | ~tall(susan) | [
"p1",
"p4",
"p5",
"p6",
"p10",
"p15",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 8346635622440306606354973
% SZS output start Proof for 8346635622440306606354973
2. ? [X0] : (rich(X0) <~> ~old(X0)) => (~funny(susan) & ~quiet(susan)) [input p1]
5. ! [X0] : ((~funny(X0) | happy(X0)) => (~tall(X0) & rich(X0))) [input p4]
6. ! [X0] : (calm(X0) => (~funny(X0) & ~quiet(X0))) [input p5]
7. ! [X0] : ((~funny(X0) <~> brave(X0)) <=> calm(X0)) [input p6]
11. ! [X0] : ((~patient(X0) | brave(X0)) <=> ~curious(X0)) [input p10]
16. ! [X0] : ((~strong(X0) | ~old(X0)) => curious(X0)) [input p15]
17. curious(alice) <~> patient(alice) [input p16]
24. tall(susan) [input hypothesis]
26. (~funny(susan) & ~quiet(susan)) | ! [X0] : (rich(X0) <=> ~old(X0)) [ennf transformation 2]
30. ! [X0] : ((~tall(X0) & rich(X0)) | (funny(X0) & ~happy(X0))) [ennf transformation 5]
31. ! [X0] : ((~funny(X0) & ~quiet(X0)) | ~calm(X0)) [ennf transformation 6]
37. ! [X0] : (curious(X0) | (strong(X0) & old(X0))) [ennf transformation 16]
43. (~funny(susan) & ~quiet(susan)) | ! [X0] : ((rich(X0) | old(X0)) & (~old(X0) | ~rich(X0))) [nnf transformation 26]
44. ! [X0] : ((((~brave(X0) | funny(X0)) & (brave(X0) | ~funny(X0))) | ~calm(X0)) & (calm(X0) | ((~funny(X0) | ~brave(X0)) & (brave(X0) | funny(X0))))) [nnf transformation 7]
51. ! [X0] : (((~patient(X0) | brave(X0)) | curious(X0)) & (~curious(X0) | (patient(X0) & ~brave(X0)))) [nnf transformation 11]
52. ! [X0] : ((~patient(X0) | brave(X0) | curious(X0)) & (~curious(X0) | (patient(X0) & ~brave(X0)))) [flattening 51]
64. (~patient(alice) | ~curious(alice)) & (patient(alice) | curious(alice)) [nnf transformation 17]
81. ~funny(susan) | ~old(X0) | ~rich(X0) [cnf transformation 43]
87. funny(X0) | rich(X0) [cnf transformation 30]
89. ~tall(X0) | funny(X0) [cnf transformation 30]
91. ~calm(X0) | ~funny(X0) [cnf transformation 31]
93. calm(X0) | ~funny(X0) | ~brave(X0) [cnf transformation 44]
95. ~brave(X0) | funny(X0) | ~calm(X0) [cnf transformation 44]
106. ~curious(X0) | patient(X0) [cnf transformation 52]
107. ~patient(X0) | brave(X0) | curious(X0) [cnf transformation 52]
125. curious(X0) | old(X0) [cnf transformation 37]
127. patient(alice) | curious(alice) [cnf transformation 64]
128. ~patient(alice) | ~curious(alice) [cnf transformation 64]
138. tall(susan) [cnf transformation 24]
173. 8 <=> funny(susan) [avatar definition]
178. 9 <=> ! [X0] : (~old(X0) | ~rich(X0)) [avatar definition]
179. ~old(X0) | ~rich(X0) <- (9) [avatar component clause 178]
180. 9 | ~8 [avatar split clause 81,173,178]
188. 11 <=> funny(alice) [avatar definition]
189. ~funny(alice) <- (~11) [avatar component clause 188]
214. ~calm(X0) | ~brave(X0) [subsumption resolution 95,91]
215. ~brave(X0) | ~funny(X0) [subsumption resolution 93,214]
283. ~curious(alice) [subsumption resolution 128,106]
284. patient(alice) [subsumption resolution 127,283]
317. funny(susan) [resolution 89,138]
320. 8 [avatar split clause 317,173]
323. old(alice) [resolution 125,283]
329. ~rich(alice) <- (9) [resolution 179,323]
369. brave(alice) | curious(alice) [resolution 107,284]
380. brave(alice) [subsumption resolution 369,283]
440. ~funny(alice) [resolution 380,215]
441. ~11 [avatar split clause 440,188]
442. rich(alice) <- (~11) [resolution 189,87]
443. $false <- (9, ~11) [subsumption resolution 442,329]
444. ~9 | 11 [avatar contradiction clause 443]
445. $false [avatar sat refutation 180,320,441,444]
% SZS output end Proof for 8346635622440306606354973
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.020 s
% ------------------------------
% ------------------------------
| 0 |
If someone is generous or not tall then someone is rich.
Everyone who is not kind or generous is generous and vice versa.
Everyone who is either old or kind is not wise or rich and vice versa.
If john is either humble or not strong then paul is both rich and not funny.
If mary is not generous then someone is either calm or humble.
If alice is either quiet or tall then someone is either wise or kind and vice versa.
If someone is not wise then someone is either not strong or patient and vice versa.
Everyone who is strong is generous and vice versa.
Everyone who is kind is both curious and humble and vice versa.
If someone is brave or not generous then someone is either strong or rich and vice versa.
If someone is both not happy and not generous then someone is not kind or old and vice versa.
Everyone who is both not generous and old is either generous or not wise and vice versa.
If someone is either not patient or not strong then someone is not calm.
Everyone who is tall or funny is old and vice versa.
Everyone who is funny or generous is both not happy and rich and vice versa.
If fred is either not humble or not patient then lucy is both creative and not old.
Alice is both brave and not patient.
Someone is generous or not patient.
Someone is both wise and not brave.
Someone is not strong.
Fred is brave or wise. | Alice is not old. | entailment | ((?[X]:((generous(X)|~tall(X))))=>(?[X]:(rich(X))))&
(![X]:((~kind(X)|generous(X))<=>generous(X)))&
(![X]:((old(X)<~>kind(X))<=>(~wise(X)|rich(X))))&
(((humble(john)<~>~strong(john)))=>((rich(paul)&~funny(paul))))&
((~generous(mary))=>(?[X]:((calm(X)<~>humble(X)))))&
(((quiet(alice)<~>tall(alice)))<=>(?[X]:((wise(X)<~>kind(X)))))&
((?[X]:(~wise(X)))<=>(?[X]:((~strong(X)<~>patient(X)))))&
(![X]:(strong(X)<=>generous(X)))&
(![X]:(kind(X)<=>(curious(X)&humble(X))))&
((?[X]:((brave(X)|~generous(X))))<=>(?[X]:((strong(X)<~>rich(X)))))&
((?[X]:((~happy(X)&~generous(X))))<=>(?[X]:((~kind(X)|old(X)))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)<~>~wise(X))))&
((?[X]:((~patient(X)<~>~strong(X))))=>(?[X]:(~calm(X))))&
(![X]:((tall(X)|funny(X))<=>old(X)))&
(![X]:((funny(X)|generous(X))<=>(~happy(X)&rich(X))))&
(((~humble(fred)<~>~patient(fred)))=>((creative(lucy)&~old(lucy))))&
((brave(alice)&~patient(alice)))&
(?[X]:((generous(X)|~patient(X))))&
(?[X]:((wise(X)&~brave(X))))&
(?[X]:(~strong(X)))&
((brave(fred)|wise(fred))) | ~old(alice) | [
"p1",
"p2",
"p10",
"p11",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 434391234546132017188466
% SZS output start Proof for 434391234546132017188466
2. ! [X0] : ((generous(X0) | ~kind(X0)) <=> generous(X0)) [input p1]
3. ! [X0] : ((old(X0) <~> kind(X0)) <=> (rich(X0) | ~wise(X0))) [input p2]
11. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X0] : (old(X0) | ~kind(X0)) [input p10]
12. ! [X0] : ((old(X0) & ~generous(X0)) <=> (generous(X0) <~> ~wise(X0))) [input p11]
14. ! [X0] : ((funny(X0) | tall(X0)) <=> old(X0)) [input p13]
15. ! [X0] : ((generous(X0) | funny(X0)) <=> (rich(X0) & ~happy(X0))) [input p14]
22. old(alice) [input hypothesis]
26. ? [X0] : (~generous(X0) & ~happy(X0)) <=> ? [X1] : (old(X1) | ~kind(X1)) [rectify 11]
37. ! [X0] : (((generous(X0) | ~kind(X0)) | ~generous(X0)) & (generous(X0) | (~generous(X0) & kind(X0)))) [nnf transformation 2]
38. ! [X0] : ((generous(X0) | ~kind(X0) | ~generous(X0)) & (generous(X0) | (~generous(X0) & kind(X0)))) [flattening 37]
39. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (~rich(X0) & wise(X0))) & ((rich(X0) | ~wise(X0)) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [nnf transformation 3]
40. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | (~rich(X0) & wise(X0))) & (rich(X0) | ~wise(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [flattening 39]
62. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (~old(X1) & kind(X1))) & (? [X1] : (old(X1) | ~kind(X1)) | ! [X0] : (generous(X0) | happy(X0))) [nnf transformation 26]
63. (? [X0] : (~generous(X0) & ~happy(X0)) | ! [X1] : (~old(X1) & kind(X1))) & (? [X2] : (old(X2) | ~kind(X2)) | ! [X3] : (generous(X3) | happy(X3))) [rectify 62]
64. ? [X0] : (~generous(X0) & ~happy(X0)) => (~generous(sK7) & ~happy(sK7)) [choice axiom]
65. ? [X2] : (old(X2) | ~kind(X2)) => (old(sK8) | ~kind(sK8)) [choice axiom]
66. ((~generous(sK7) & ~happy(sK7)) | ! [X1] : (~old(X1) & kind(X1))) & ((old(sK8) | ~kind(sK8)) | ! [X3] : (generous(X3) | happy(X3))) [skolemisation 63,65,64]
67. ! [X0] : (((old(X0) & ~generous(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | (~old(X0) | generous(X0)))) [nnf transformation 12]
68. ! [X0] : (((old(X0) & ~generous(X0)) | ((generous(X0) | wise(X0)) & (~wise(X0) | ~generous(X0)))) & (((wise(X0) | ~generous(X0)) & (~wise(X0) | generous(X0))) | ~old(X0) | generous(X0))) [flattening 67]
73. ! [X0] : (((funny(X0) | tall(X0)) | ~old(X0)) & (old(X0) | (~funny(X0) & ~tall(X0)))) [nnf transformation 14]
74. ! [X0] : ((funny(X0) | tall(X0) | ~old(X0)) & (old(X0) | (~funny(X0) & ~tall(X0)))) [flattening 73]
75. ! [X0] : (((generous(X0) | funny(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (~generous(X0) & ~funny(X0)))) [nnf transformation 15]
76. ! [X0] : ((generous(X0) | funny(X0) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | (~generous(X0) & ~funny(X0)))) [flattening 75]
86. kind(X0) | generous(X0) [cnf transformation 38]
90. ~wise(X0) | rich(X0) | old(X0) | ~kind(X0) [cnf transformation 40]
93. ~old(X0) | ~kind(X0) | wise(X0) [cnf transformation 40]
94. ~old(X0) | ~kind(X0) | ~rich(X0) [cnf transformation 40]
126. ~happy(sK7) | ~old(X1) [cnf transformation 66]
128. ~generous(sK7) | ~old(X1) [cnf transformation 66]
129. ~wise(X0) | generous(X0) | ~old(X0) | generous(X0) [cnf transformation 68]
131. ~generous(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 68]
134. wise(X0) | generous(X0) | old(X0) [cnf transformation 68]
137. ~tall(X0) | old(X0) [cnf transformation 74]
138. ~funny(X0) | old(X0) [cnf transformation 74]
139. ~old(X0) | tall(X0) | funny(X0) [cnf transformation 74]
142. ~funny(X0) | rich(X0) [cnf transformation 76]
143. ~generous(X0) | rich(X0) [cnf transformation 76]
144. ~rich(X0) | funny(X0) | generous(X0) | happy(X0) [cnf transformation 76]
154. old(alice) [cnf transformation 22]
155. ~wise(X0) | generous(X0) | ~old(X0) [duplicate literal removal 129]
156. ~wise(X0) | ~generous(X0) [duplicate literal removal 131]
293. 31 <=> ! [X1] : ~old(X1) [avatar definition]
294. ~old(X1) <- (31) [avatar component clause 293]
296. 32 <=> generous(sK7) [avatar definition]
298. ~generous(sK7) <- (~32) [avatar component clause 296]
299. 31 | ~32 [avatar split clause 128,296,293]
305. 34 <=> happy(sK7) [avatar definition]
307. ~happy(sK7) <- (~34) [avatar component clause 305]
308. 31 | ~34 [avatar split clause 126,305,293]
322. ~wise(X0) | ~old(X0) [subsumption resolution 155,156]
462. rich(X0) | old(X0) | ~kind(X0) | generous(X0) | old(X0) [resolution 90,134]
465. rich(X0) | old(X0) | ~kind(X0) | generous(X0) [duplicate literal removal 462]
632. 70 <=> tall(sK7) [avatar definition]
634. tall(sK7) <- (70) [avatar component clause 632]
636. 71 <=> funny(sK7) [avatar definition]
637. ~funny(sK7) <- (~71) [avatar component clause 636]
638. funny(sK7) <- (71) [avatar component clause 636]
693. $false <- (31) [resolution 294,154]
696. ~31 [avatar contradiction clause 693]
799. old(sK7) <- (71) [resolution 638,138]
805. ~kind(sK7) | ~rich(sK7) <- (71) [resolution 799,94]
817. 78 <=> kind(sK7) [avatar definition]
818. kind(sK7) <- (78) [avatar component clause 817]
819. ~kind(sK7) <- (~78) [avatar component clause 817]
822. 79 <=> rich(sK7) [avatar definition]
824. ~rich(sK7) <- (~79) [avatar component clause 822]
825. ~79 | ~78 | ~71 [avatar split clause 805,636,817,822]
827. rich(X0) | old(X0) | generous(X0) [subsumption resolution 465,86]
828. old(X0) | rich(X0) [subsumption resolution 827,143]
846. rich(X0) | tall(X0) | funny(X0) [resolution 828,139]
848. ~kind(X2) | rich(X2) | wise(X2) [resolution 828,93]
852. rich(X0) | tall(X0) [subsumption resolution 846,142]
864. happy(X0) | funny(X0) | generous(X0) | tall(X0) [resolution 852,144]
867. rich(X0) | wise(X0) | generous(X0) [resolution 848,86]
873. wise(X0) | rich(X0) [subsumption resolution 867,143]
874. generous(sK7) <- (~78) [resolution 819,86]
875. $false <- (~32, ~78) [subsumption resolution 874,298]
876. 32 | 78 [avatar contradiction clause 875]
888. rich(X3) | ~old(X3) [resolution 873,322]
894. rich(X3) [subsumption resolution 888,828]
899. funny(sK7) | generous(sK7) | tall(sK7) <- (~34) [resolution 864,307]
900. generous(sK7) | tall(sK7) <- (~34, ~71) [subsumption resolution 899,637]
901. tall(sK7) <- (~32, ~34, ~71) [subsumption resolution 900,298]
904. 70 | 32 | 34 | 71 [avatar split clause 901,636,305,296,632]
905. old(sK7) <- (70) [resolution 634,137]
914. ~kind(sK7) | ~rich(sK7) <- (70) [resolution 905,94]
916. ~rich(sK7) <- (70, 78) [subsumption resolution 914,818]
921. $false <- (70, 78) [subsumption resolution 916,894]
922. ~70 | ~78 [avatar contradiction clause 921]
923. $false <- (~79) [subsumption resolution 824,894]
924. 79 [avatar contradiction clause 923]
925. $false [avatar sat refutation 299,308,696,825,876,904,922,924]
% SZS output end Proof for 434391234546132017188466
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
If someone is calm then paul is either not generous or not funny and vice versa.
Everyone who is both old and not curious is not creative or calm.
If someone is not strong then lucy is both not strong and not curious.
Everyone who is not tall is not funny or generous and vice versa.
Everyone who is quiet or wise is funny or curious and vice versa.
If paul is either not quiet or quiet then susan is strong.
Everyone who is either not quiet or calm is generous.
Everyone who is both brave and not quiet is funny or wise and vice versa.
Everyone who is not wise is not quiet and vice versa.
Everyone who is either funny or tall is either generous or not kind.
If someone is both happy and not curious then paul is humble.
Everyone who is either not tall or quiet is either not funny or patient and vice versa.
Everyone who is both brave and tall is both old and not funny.
Someone is either not humble or not wise.
Susan is not rich.
Alice is happy or not rich.
John is not strong or creative.
Someone is either not funny or humble.
Alice is not tall. | John is not generous. | neutral | ((?[X]:(calm(X)))<=>((~generous(paul)<~>~funny(paul))))&
(![X]:((old(X)&~curious(X))=>(~creative(X)|calm(X))))&
((?[X]:(~strong(X)))=>((~strong(lucy)&~curious(lucy))))&
(![X]:(~tall(X)<=>(~funny(X)|generous(X))))&
(![X]:((quiet(X)|wise(X))<=>(funny(X)|curious(X))))&
(((~quiet(paul)<~>quiet(paul)))=>(strong(susan)))&
(![X]:((~quiet(X)<~>calm(X))=>generous(X)))&
(![X]:((brave(X)&~quiet(X))<=>(funny(X)|wise(X))))&
(![X]:(~wise(X)<=>~quiet(X)))&
(![X]:((funny(X)<~>tall(X))=>(generous(X)<~>~kind(X))))&
((?[X]:((happy(X)&~curious(X))))=>(humble(paul)))&
(![X]:((~tall(X)<~>quiet(X))<=>(~funny(X)<~>patient(X))))&
(![X]:((brave(X)&tall(X))=>(old(X)&~funny(X))))&
(?[X]:((~humble(X)<~>~wise(X))))&
(~rich(susan))&
((happy(alice)|~rich(alice)))&
((~strong(john)|creative(john)))&
(?[X]:((~funny(X)<~>humble(X))))&
(~tall(alice)) | ~generous(john) | []
| null | 0 |
If susan is patient then john is both not curious and kind and vice versa.
Everyone who is not calm is not wise or not old.
If someone is both calm and old then susan is either calm or not funny.
If someone is both strong and not rich then alice is either not kind or rich and vice versa.
If john is both rich and humble then someone is not happy or quiet.
Everyone who is rich or humble is either not curious or not tall and vice versa.
If someone is both not wise and not old then john is creative or not strong.
Everyone who is not humble or humble is either not tall or curious.
If someone is both strong and calm then someone is either not kind or not happy.
If someone is not brave or curious then lucy is rich and vice versa.
If someone is both not patient and happy then someone is not humble and vice versa.
Everyone who is either wise or rich is generous or not kind and vice versa.
If someone is both calm and creative then susan is both not happy and kind and vice versa.
Everyone who is not kind is not tall and vice versa.
Lucy is either not old or not humble.
Fred is either calm or not strong.
Someone is not kind or not quiet.
Fred is brave. | Susan is not generous. | neutral | ((patient(susan))<=>((~curious(john)&kind(john))))&
(![X]:(~calm(X)=>(~wise(X)|~old(X))))&
((?[X]:((calm(X)&old(X))))=>((calm(susan)<~>~funny(susan))))&
((?[X]:((strong(X)&~rich(X))))<=>((~kind(alice)<~>rich(alice))))&
(((rich(john)&humble(john)))=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((rich(X)|humble(X))<=>(~curious(X)<~>~tall(X))))&
((?[X]:((~wise(X)&~old(X))))=>((creative(john)|~strong(john))))&
(![X]:((~humble(X)|humble(X))=>(~tall(X)<~>curious(X))))&
((?[X]:((strong(X)&calm(X))))=>(?[X]:((~kind(X)<~>~happy(X)))))&
((?[X]:((~brave(X)|curious(X))))<=>(rich(lucy)))&
((?[X]:((~patient(X)&happy(X))))<=>(?[X]:(~humble(X))))&
(![X]:((wise(X)<~>rich(X))<=>(generous(X)|~kind(X))))&
((?[X]:((calm(X)&creative(X))))<=>((~happy(susan)&kind(susan))))&
(![X]:(~kind(X)<=>~tall(X)))&
((~old(lucy)<~>~humble(lucy)))&
((calm(fred)<~>~strong(fred)))&
(?[X]:((~kind(X)|~quiet(X))))&
(brave(fred)) | ~generous(susan) | []
| null | 0 |
If paul is either not creative or patient then someone is both calm and not rich.
If paul is rich or happy then lucy is not curious or tall.
Everyone who is wise is strong and vice versa.
Everyone who is either creative or rich is either not kind or quiet.
Everyone who is brave or humble is not generous and vice versa.
If susan is either old or funny then someone is kind.
If fred is old then someone is either generous or humble and vice versa.
If mary is not creative then mary is either calm or brave and vice versa.
Everyone who is old is funny and vice versa.
If someone is not old then fred is either not humble or not tall and vice versa.
Everyone who is either strong or not wise is brave and vice versa.
If alice is not wise then someone is curious.
Everyone who is quiet or not rich is patient or not generous.
Everyone who is either not humble or kind is both kind and curious and vice versa.
Everyone who is not strong is strong.
If john is not tall then mary is both not curious and not old.
Someone is tall.
Mary is both patient and not curious.
Susan is not rich or tall.
John is either curious or not old.
Mary is quiet.
Lucy is not creative. | Mary is kind. | neutral | (((~creative(paul)<~>patient(paul)))=>(?[X]:((calm(X)&~rich(X)))))&
(((rich(paul)|happy(paul)))=>((~curious(lucy)|tall(lucy))))&
(![X]:(wise(X)<=>strong(X)))&
(![X]:((creative(X)<~>rich(X))=>(~kind(X)<~>quiet(X))))&
(![X]:((brave(X)|humble(X))<=>~generous(X)))&
(((old(susan)<~>funny(susan)))=>(?[X]:(kind(X))))&
((old(fred))<=>(?[X]:((generous(X)<~>humble(X)))))&
((~creative(mary))<=>((calm(mary)<~>brave(mary))))&
(![X]:(old(X)<=>funny(X)))&
((?[X]:(~old(X)))<=>((~humble(fred)<~>~tall(fred))))&
(![X]:((strong(X)<~>~wise(X))<=>brave(X)))&
((~wise(alice))=>(?[X]:(curious(X))))&
(![X]:((quiet(X)|~rich(X))=>(patient(X)|~generous(X))))&
(![X]:((~humble(X)<~>kind(X))<=>(kind(X)&curious(X))))&
(![X]:(~strong(X)=>strong(X)))&
((~tall(john))=>((~curious(mary)&~old(mary))))&
(?[X]:(tall(X)))&
((patient(mary)&~curious(mary)))&
((~rich(susan)|tall(susan)))&
((curious(john)<~>~old(john)))&
(quiet(mary))&
(~creative(lucy)) | kind(mary) | []
| null | 0 |
Everyone who is patient is not generous or generous. If mary is either not tall or tall then someone is either patient or humble and vice versa. If someone is either not curious or generous then lucy is not kind or not happy and vice versa. If someone is both not kind and not patient then someone is both curious and quiet. If someone is not humble then john is either brave or rich and vice versa. If paul is not humble or old then someone is either not creative or not strong. If alice is both creative and tall then someone is funny and vice versa. If someone is both not curious and not tall then someone is either curious or not old and vice versa. Everyone who is not tall or not brave is both kind and curious. Everyone who is tall or happy is not brave or humble. If alice is not patient then mary is either not creative or brave and vice versa. Everyone who is not strong or not wise is both calm and not humble and vice versa. Everyone who is both not funny and patient is either wise or not wise and vice versa. Everyone who is both generous and brave is either wise or not calm. Everyone who is rich or not patient is old. Someone is either not funny or not humble. Someone is either brave or not old. Someone is not generous. John is calm. Mary is not quiet. Fred is not brave. Someone is both not old and quiet. | John is brave. | entailment | (![X]:(patient(X)=>(~generous(X)|generous(X))))&
(((~tall(mary)<~>tall(mary)))<=>(?[X]:((patient(X)<~>humble(X)))))&
((?[X]:((~curious(X)<~>generous(X))))<=>((~kind(lucy)|~happy(lucy))))&
((?[X]:((~kind(X)&~patient(X))))=>(?[X]:((curious(X)&quiet(X)))))&
((?[X]:(~humble(X)))<=>((brave(john)<~>rich(john))))&
(((~humble(paul)|old(paul)))=>(?[X]:((~creative(X)<~>~strong(X)))))&
(((creative(alice)&tall(alice)))<=>(?[X]:(funny(X))))&
((?[X]:((~curious(X)&~tall(X))))<=>(?[X]:((curious(X)<~>~old(X)))))&
(![X]:((~tall(X)|~brave(X))=>(kind(X)&curious(X))))&
(![X]:((tall(X)|happy(X))=>(~brave(X)|humble(X))))&
((~patient(alice))<=>((~creative(mary)<~>brave(mary))))&
(![X]:((~strong(X)|~wise(X))<=>(calm(X)&~humble(X))))&
(![X]:((~funny(X)&patient(X))<=>(wise(X)<~>~wise(X))))&
(![X]:((generous(X)&brave(X))=>(wise(X)<~>~calm(X))))&
(![X]:((rich(X)|~patient(X))=>old(X)))&
(?[X]:((~funny(X)<~>~humble(X))))&
(?[X]:((brave(X)<~>~old(X))))&
(?[X]:(~generous(X)))&
(calm(john))&
(~quiet(mary))&
(~brave(fred))&
(?[X]:((~old(X)&quiet(X)))) | brave(john) | [
"p1",
"p4",
"p7",
"p8",
"p12",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5327203191790802371226419
% SZS output start Proof for 5327203191790802371226419
2. (~tall(mary) <~> tall(mary)) <=> ? [X0] : (patient(X0) <~> humble(X0)) [input p1]
5. ? [X0] : ~humble(X0) <=> (brave(john) <~> rich(john)) [input p4]
8. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X0] : (curious(X0) <~> ~old(X0)) [input p7]
9. ! [X0] : ((~brave(X0) | ~tall(X0)) => (curious(X0) & kind(X0))) [input p8]
13. ! [X0] : ((patient(X0) & ~funny(X0)) <=> (wise(X0) <~> ~wise(X0))) [input p12]
15. ! [X0] : ((~patient(X0) | rich(X0)) => old(X0)) [input p14]
23. ~brave(john) [input hypothesis]
25. ? [X0] : (~tall(X0) & ~curious(X0)) <=> ? [X1] : (curious(X1) <~> ~old(X1)) [rectify 8]
30. ! [X0] : ((curious(X0) & kind(X0)) | (brave(X0) & tall(X0))) [ennf transformation 9]
35. ! [X0] : (old(X0) | (patient(X0) & ~rich(X0))) [ennf transformation 15]
36. (((~tall(mary) | tall(mary)) & (tall(mary) | ~tall(mary))) | ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (? [X0] : ((~humble(X0) | ~patient(X0)) & (humble(X0) | patient(X0))) | ((~tall(mary) | ~tall(mary)) & (tall(mary) | tall(mary)))) [nnf transformation 2]
37. (((~tall(mary) | tall(mary)) & (tall(mary) | ~tall(mary))) | ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (? [X1] : ((~humble(X1) | ~patient(X1)) & (humble(X1) | patient(X1))) | ((~tall(mary) | ~tall(mary)) & (tall(mary) | tall(mary)))) [rectify 36]
38. ? [X1] : ((~humble(X1) | ~patient(X1)) & (humble(X1) | patient(X1))) => ((~humble(sK0) | ~patient(sK0)) & (humble(sK0) | patient(sK0))) [choice axiom]
39. (((~tall(mary) | tall(mary)) & (tall(mary) | ~tall(mary))) | ! [X0] : ((patient(X0) | ~humble(X0)) & (humble(X0) | ~patient(X0)))) & (((~humble(sK0) | ~patient(sK0)) & (humble(sK0) | patient(sK0))) | ((~tall(mary) | ~tall(mary)) & (tall(mary) | tall(mary)))) [skolemisation 37,38]
48. (? [X0] : ~humble(X0) | ((brave(john) | ~rich(john)) & (rich(john) | ~brave(john)))) & (((~rich(john) | ~brave(john)) & (rich(john) | brave(john))) | ! [X0] : humble(X0)) [nnf transformation 5]
49. (? [X0] : ~humble(X0) | ((brave(john) | ~rich(john)) & (rich(john) | ~brave(john)))) & (((~rich(john) | ~brave(john)) & (rich(john) | brave(john))) | ! [X1] : humble(X1)) [rectify 48]
50. ? [X0] : ~humble(X0) => ~humble(sK3) [choice axiom]
51. (~humble(sK3) | ((brave(john) | ~rich(john)) & (rich(john) | ~brave(john)))) & (((~rich(john) | ~brave(john)) & (rich(john) | brave(john))) | ! [X1] : humble(X1)) [skolemisation 49,50]
60. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X1] : ((old(X1) | ~curious(X1)) & (~old(X1) | curious(X1))) | ! [X0] : (tall(X0) | curious(X0))) [nnf transformation 25]
61. (? [X0] : (~tall(X0) & ~curious(X0)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) | ! [X3] : (tall(X3) | curious(X3))) [rectify 60]
62. ? [X0] : (~tall(X0) & ~curious(X0)) => (~tall(sK6) & ~curious(sK6)) [choice axiom]
63. ? [X2] : ((old(X2) | ~curious(X2)) & (~old(X2) | curious(X2))) => ((old(sK7) | ~curious(sK7)) & (~old(sK7) | curious(sK7))) [choice axiom]
64. ((~tall(sK6) & ~curious(sK6)) | ! [X1] : ((curious(X1) | old(X1)) & (~old(X1) | ~curious(X1)))) & (((old(sK7) | ~curious(sK7)) & (~old(sK7) | curious(sK7))) | ! [X3] : (tall(X3) | curious(X3))) [skolemisation 61,63,62]
68. ! [X0] : (((patient(X0) & ~funny(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | (~patient(X0) | funny(X0)))) [nnf transformation 13]
69. ! [X0] : (((patient(X0) & ~funny(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) & (((wise(X0) | ~wise(X0)) & (~wise(X0) | wise(X0))) | ~patient(X0) | funny(X0))) [flattening 68]
84. ~humble(sK0) | ~patient(sK0) | tall(mary) | tall(mary) [cnf transformation 39]
85. ~humble(sK0) | ~patient(sK0) | ~tall(mary) | ~tall(mary) [cnf transformation 39]
98. rich(john) | brave(john) | humble(X1) [cnf transformation 51]
111. ~curious(sK6) | ~old(X1) | ~curious(X1) [cnf transformation 64]
113. ~tall(sK6) | ~old(X1) | ~curious(X1) [cnf transformation 64]
117. curious(X0) | tall(X0) [cnf transformation 30]
118. brave(X0) | curious(X0) [cnf transformation 30]
134. patient(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 69]
135. patient(X0) | wise(X0) | wise(X0) [cnf transformation 69]
138. ~rich(X0) | old(X0) [cnf transformation 35]
150. ~brave(john) [cnf transformation 23]
153. patient(X0) | ~wise(X0) [duplicate literal removal 134]
154. wise(X0) | patient(X0) [duplicate literal removal 135]
157. ~humble(sK0) | ~patient(sK0) | tall(mary) [duplicate literal removal 84]
158. ~humble(sK0) | ~patient(sK0) | ~tall(mary) [duplicate literal removal 85]
160. 1 <=> tall(mary) [avatar definition]
164. 2 <=> patient(sK0) [avatar definition]
166. ~patient(sK0) <- (~2) [avatar component clause 164]
168. 3 <=> humble(sK0) [avatar definition]
170. ~humble(sK0) <- (~3) [avatar component clause 168]
171. ~1 | ~2 | ~3 [avatar split clause 158,168,164,160]
172. 1 | ~2 | ~3 [avatar split clause 157,168,164,160]
217. 13 <=> rich(john) [avatar definition]
218. rich(john) <- (13) [avatar component clause 217]
221. 14 <=> brave(john) [avatar definition]
222. ~brave(john) <- (~14) [avatar component clause 221]
231. 16 <=> ! [X1] : humble(X1) [avatar definition]
232. humble(X1) <- (16) [avatar component clause 231]
234. 16 | 14 | 13 [avatar split clause 98,217,221,231]
277. 26 <=> tall(sK6) [avatar definition]
282. 27 <=> ! [X1] : (~old(X1) | ~curious(X1)) [avatar definition]
283. ~old(X1) | ~curious(X1) <- (27) [avatar component clause 282]
284. 27 | ~26 [avatar split clause 113,277,282]
286. 28 <=> curious(sK6) [avatar definition]
288. ~curious(sK6) <- (~28) [avatar component clause 286]
290. 27 | ~28 [avatar split clause 111,286,282]
292. 29 <=> ! [X3] : (tall(X3) | curious(X3)) [avatar definition]
293. curious(X3) | tall(X3) <- (29) [avatar component clause 292]
304. 29 [avatar split clause 117,292]
321. patient(X0) [subsumption resolution 153,154]
346. ~14 [avatar split clause 150,221]
355. curious(john) <- (~14) [resolution 118,222]
359. old(john) <- (13) [resolution 138,218]
361. tall(sK6) <- (~28, 29) [resolution 293,288]
364. 26 | 28 | ~29 [avatar split clause 361,292,286,277]
368. ~curious(john) <- (13, 27) [resolution 283,359]
370. $false <- (13, ~14, 27) [subsumption resolution 368,355]
371. ~13 | 14 | ~27 [avatar contradiction clause 370]
372. $false <- (~3, 16) [resolution 232,170]
377. 3 | ~16 [avatar contradiction clause 372]
378. $false <- (~2) [subsumption resolution 166,321]
379. 2 [avatar contradiction clause 378]
380. $false [avatar sat refutation 171,172,234,284,290,304,346,364,371,377,379]
% SZS output end Proof for 5327203191790802371226419
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not creative is curious or not creative.
If someone is not calm then someone is either not wise or not rich.
If someone is brave then someone is both happy and not happy and vice versa.
Everyone who is not funny or not creative is either not strong or rich.
Everyone who is both brave and generous is funny and vice versa.
Everyone who is either not calm or not brave is either creative or not creative and vice versa.
Everyone who is not tall is not creative and vice versa.
Everyone who is brave is either creative or not patient and vice versa.
Everyone who is quiet is both not quiet and not patient.
Everyone who is both quiet and not calm is not generous or calm.
Everyone who is not old is either rich or old.
If paul is both not curious and not funny then someone is not creative or not quiet and vice versa.
Everyone who is either not generous or not patient is either not generous or humble.
Everyone who is not tall is both generous and patient.
Everyone who is both not old and not funny is not happy or generous.
Everyone who is either old or calm is both old and not rich.
Someone is not wise or curious.
Alice is humble.
Paul is either not patient or wise.
Paul is either tall or not rich.
Someone is either old or not humble.
Someone is either not calm or not brave.
Fred is not tall.
Lucy is either not creative or humble. | Lucy is quiet. | contradiction | (![X]:((~generous(X)&~creative(X))=>(curious(X)|~creative(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~wise(X)<~>~rich(X)))))&
((?[X]:(brave(X)))<=>(?[X]:((happy(X)&~happy(X)))))&
(![X]:((~funny(X)|~creative(X))=>(~strong(X)<~>rich(X))))&
(![X]:((brave(X)&generous(X))<=>funny(X)))&
(![X]:((~calm(X)<~>~brave(X))<=>(creative(X)<~>~creative(X))))&
(![X]:(~tall(X)<=>~creative(X)))&
(![X]:(brave(X)<=>(creative(X)<~>~patient(X))))&
(![X]:(quiet(X)=>(~quiet(X)&~patient(X))))&
(![X]:((quiet(X)&~calm(X))=>(~generous(X)|calm(X))))&
(![X]:(~old(X)=>(rich(X)<~>old(X))))&
(((~curious(paul)&~funny(paul)))<=>(?[X]:((~creative(X)|~quiet(X)))))&
(![X]:((~generous(X)<~>~patient(X))=>(~generous(X)<~>humble(X))))&
(![X]:(~tall(X)=>(generous(X)&patient(X))))&
(![X]:((~old(X)&~funny(X))=>(~happy(X)|generous(X))))&
(![X]:((old(X)<~>calm(X))=>(old(X)&~rich(X))))&
(?[X]:((~wise(X)|curious(X))))&
(humble(alice))&
((~patient(paul)<~>wise(paul)))&
((tall(paul)<~>~rich(paul)))&
(?[X]:((old(X)<~>~humble(X))))&
(?[X]:((~calm(X)<~>~brave(X))))&
(~tall(fred))&
((~creative(lucy)<~>humble(lucy))) | quiet(lucy) | [
"p8",
"hypothesis"
]
| % SZS status Unsatisfiable for 4689199847227827407696075
% SZS output start Proof for 4689199847227827407696075
9. ! [X0] : (quiet(X0) => (~patient(X0) & ~quiet(X0))) [input p8]
25. quiet(lucy) [input hypothesis]
32. ! [X0] : ((~patient(X0) & ~quiet(X0)) | ~quiet(X0)) [ennf transformation 9]
102. ~quiet(X0) | ~quiet(X0) [cnf transformation 32]
136. quiet(lucy) [cnf transformation 25]
142. ~quiet(X0) [duplicate literal removal 102]
224. $false [subsumption resolution 136,142]
% SZS output end Proof for 4689199847227827407696075
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not generous or not quiet then someone is either not wise or not curious. Everyone who is both not rich and kind is not funny or old. If someone is both patient and tall then someone is not quiet or not curious. Everyone who is not kind or creative is either curious or not generous and vice versa. Everyone who is not funny or generous is kind or patient and vice versa. Everyone who is either strong or kind is not curious and vice versa. If someone is not wise then john is not funny and vice versa. Everyone who is not tall or patient is both not humble and not rich and vice versa. If someone is both not creative and not curious then susan is not creative or brave. Everyone who is either generous or funny is both rich and curious. Everyone who is quiet is both not kind and not tall. Everyone who is quiet is either patient or kind and vice versa. Everyone who is not patient or not quiet is not calm or tall and vice versa. If susan is not quiet then someone is both happy and funny. If mary is either not strong or not funny then susan is patient or not funny and vice versa. If someone is both curious and tall then mary is not patient or patient. Someone is wise or quiet. Fred is not curious or kind. Someone is both not kind and not brave. Someone is wise. Someone is either brave or humble. Susan is either patient or not calm. | Susan is not humble. | entailment | (((~generous(john)<~>~quiet(john)))=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((~rich(X)&kind(X))=>(~funny(X)|old(X))))&
((?[X]:((patient(X)&tall(X))))=>(?[X]:((~quiet(X)|~curious(X)))))&
(![X]:((~kind(X)|creative(X))<=>(curious(X)<~>~generous(X))))&
(![X]:((~funny(X)|generous(X))<=>(kind(X)|patient(X))))&
(![X]:((strong(X)<~>kind(X))<=>~curious(X)))&
((?[X]:(~wise(X)))<=>(~funny(john)))&
(![X]:((~tall(X)|patient(X))<=>(~humble(X)&~rich(X))))&
((?[X]:((~creative(X)&~curious(X))))=>((~creative(susan)|brave(susan))))&
(![X]:((generous(X)<~>funny(X))=>(rich(X)&curious(X))))&
(![X]:(quiet(X)=>(~kind(X)&~tall(X))))&
(![X]:(quiet(X)<=>(patient(X)<~>kind(X))))&
(![X]:((~patient(X)|~quiet(X))<=>(~calm(X)|tall(X))))&
((~quiet(susan))=>(?[X]:((happy(X)&funny(X)))))&
(((~strong(mary)<~>~funny(mary)))<=>((patient(susan)|~funny(susan))))&
((?[X]:((curious(X)&tall(X))))=>((~patient(mary)|patient(mary))))&
(?[X]:((wise(X)|quiet(X))))&
((~curious(fred)|kind(fred)))&
(?[X]:((~kind(X)&~brave(X))))&
(?[X]:(wise(X)))&
(?[X]:((brave(X)<~>humble(X))))&
((patient(susan)<~>~calm(susan))) | ~humble(susan) | [
"p3",
"p4",
"p7",
"p9",
"p10",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 8119456520472499821345835
% SZS output start Proof for 8119456520472499821345835
4. ! [X0] : ((creative(X0) | ~kind(X0)) <=> (curious(X0) <~> ~generous(X0))) [input p3]
5. ! [X0] : ((generous(X0) | ~funny(X0)) <=> (patient(X0) | kind(X0))) [input p4]
8. ! [X0] : ((patient(X0) | ~tall(X0)) <=> (~rich(X0) & ~humble(X0))) [input p7]
10. ! [X0] : ((generous(X0) <~> funny(X0)) => (curious(X0) & rich(X0))) [input p9]
11. ! [X0] : (quiet(X0) => (~tall(X0) & ~kind(X0))) [input p10]
12. ! [X0] : (quiet(X0) <=> (patient(X0) <~> kind(X0))) [input p11]
23. humble(susan) [input hypothesis]
31. ! [X0] : ((curious(X0) & rich(X0)) | (generous(X0) <=> funny(X0))) [ennf transformation 10]
32. ! [X0] : ((~tall(X0) & ~kind(X0)) | ~quiet(X0)) [ennf transformation 11]
42. ! [X0] : (((creative(X0) | ~kind(X0)) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~creative(X0) & kind(X0)))) [nnf transformation 4]
43. ! [X0] : ((creative(X0) | ~kind(X0) | ((curious(X0) | generous(X0)) & (~generous(X0) | ~curious(X0)))) & (((generous(X0) | ~curious(X0)) & (~generous(X0) | curious(X0))) | (~creative(X0) & kind(X0)))) [flattening 42]
44. ! [X0] : (((generous(X0) | ~funny(X0)) | (~patient(X0) & ~kind(X0))) & ((patient(X0) | kind(X0)) | (~generous(X0) & funny(X0)))) [nnf transformation 5]
45. ! [X0] : ((generous(X0) | ~funny(X0) | (~patient(X0) & ~kind(X0))) & (patient(X0) | kind(X0) | (~generous(X0) & funny(X0)))) [flattening 44]
51. ! [X0] : (((patient(X0) | ~tall(X0)) | (rich(X0) | humble(X0))) & ((~rich(X0) & ~humble(X0)) | (~patient(X0) & tall(X0)))) [nnf transformation 8]
52. ! [X0] : ((patient(X0) | ~tall(X0) | rich(X0) | humble(X0)) & ((~rich(X0) & ~humble(X0)) | (~patient(X0) & tall(X0)))) [flattening 51]
53. ! [X0] : ((curious(X0) & rich(X0)) | ((generous(X0) | ~funny(X0)) & (funny(X0) | ~generous(X0)))) [nnf transformation 31]
54. ! [X0] : ((quiet(X0) | ((patient(X0) | ~kind(X0)) & (kind(X0) | ~patient(X0)))) & (((~kind(X0) | ~patient(X0)) & (kind(X0) | patient(X0))) | ~quiet(X0))) [nnf transformation 12]
78. ~curious(X0) | generous(X0) | kind(X0) [cnf transformation 43]
82. patient(X0) | kind(X0) | funny(X0) [cnf transformation 45]
83. ~generous(X0) | kind(X0) | patient(X0) [cnf transformation 45]
93. ~humble(X0) | ~patient(X0) [cnf transformation 52]
101. ~funny(X0) | generous(X0) | curious(X0) [cnf transformation 53]
102. ~kind(X0) | ~quiet(X0) [cnf transformation 32]
107. quiet(X0) | patient(X0) | ~kind(X0) [cnf transformation 54]
129. humble(susan) [cnf transformation 23]
187. ~kind(X0) | patient(X0) [subsumption resolution 107,102]
200. 16 <=> funny(susan) [avatar definition]
202. funny(susan) <- (16) [avatar component clause 200]
213. 19 <=> patient(susan) [avatar definition]
215. ~patient(susan) <- (~19) [avatar component clause 213]
256. ~patient(susan) [resolution 93,129]
266. 27 <=> kind(susan) [avatar definition]
267. kind(susan) <- (27) [avatar component clause 266]
268. ~kind(susan) <- (~27) [avatar component clause 266]
270. 28 <=> generous(susan) [avatar definition]
271. ~generous(susan) <- (~28) [avatar component clause 270]
272. generous(susan) <- (28) [avatar component clause 270]
328. ~19 [avatar split clause 256,213]
329. kind(susan) | funny(susan) <- (~19) [resolution 215,82]
331. patient(susan) <- (27) [resolution 267,187]
334. 37 <=> curious(susan) [avatar definition]
335. curious(susan) <- (37) [avatar component clause 334]
342. $false <- (~19, 27) [subsumption resolution 331,215]
343. 19 | ~27 [avatar contradiction clause 342]
344. 16 | 27 | 19 [avatar split clause 329,213,266,200]
349. generous(susan) | curious(susan) <- (16) [resolution 101,202]
354. kind(susan) | patient(susan) <- (28) [resolution 272,83]
356. patient(susan) <- (~27, 28) [subsumption resolution 354,268]
357. $false <- (~19, ~27, 28) [subsumption resolution 356,215]
358. 19 | 27 | ~28 [avatar contradiction clause 357]
361. 37 | 28 | ~16 [avatar split clause 349,200,270,334]
392. generous(susan) | kind(susan) <- (37) [resolution 335,78]
393. kind(susan) <- (~28, 37) [subsumption resolution 392,271]
394. $false <- (~27, ~28, 37) [subsumption resolution 393,268]
395. 27 | 28 | ~37 [avatar contradiction clause 394]
396. $false [avatar sat refutation 328,343,344,358,361,395]
% SZS output end Proof for 8119456520472499821345835
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not funny is not kind or calm and vice versa.
Everyone who is either not wise or not generous is humble and vice versa.
Everyone who is not generous or calm is creative.
Everyone who is calm is not generous or not tall and vice versa.
Everyone who is rich is both not curious and not brave and vice versa.
Everyone who is curious or calm is both humble and generous and vice versa.
Everyone who is old or not kind is both not strong and not creative.
If someone is not creative then someone is rich and vice versa.
If someone is both not curious and not humble then someone is either brave or rich and vice versa.
Everyone who is tall or brave is both humble and not old and vice versa.
Everyone who is not kind or curious is not patient.
If someone is not curious then fred is either not humble or not brave.
If someone is both not happy and kind then susan is either not patient or not funny.
Everyone who is humble or not quiet is rich or quiet and vice versa.
Everyone who is both brave and funny is either brave or funny.
Alice is either not patient or not creative.
Someone is creative or not tall.
Someone is happy.
Paul is not old or kind. | Fred is not patient. | entailment | (![X]:((~wise(X)&~funny(X))<=>(~kind(X)|calm(X))))&
(![X]:((~wise(X)<~>~generous(X))<=>humble(X)))&
(![X]:((~generous(X)|calm(X))=>creative(X)))&
(![X]:(calm(X)<=>(~generous(X)|~tall(X))))&
(![X]:(rich(X)<=>(~curious(X)&~brave(X))))&
(![X]:((curious(X)|calm(X))<=>(humble(X)&generous(X))))&
(![X]:((old(X)|~kind(X))=>(~strong(X)&~creative(X))))&
((?[X]:(~creative(X)))<=>(?[X]:(rich(X))))&
((?[X]:((~curious(X)&~humble(X))))<=>(?[X]:((brave(X)<~>rich(X)))))&
(![X]:((tall(X)|brave(X))<=>(humble(X)&~old(X))))&
(![X]:((~kind(X)|curious(X))=>~patient(X)))&
((?[X]:(~curious(X)))=>((~humble(fred)<~>~brave(fred))))&
((?[X]:((~happy(X)&kind(X))))=>((~patient(susan)<~>~funny(susan))))&
(![X]:((humble(X)|~quiet(X))<=>(rich(X)|quiet(X))))&
(![X]:((brave(X)&funny(X))=>(brave(X)<~>funny(X))))&
((~patient(alice)<~>~creative(alice)))&
(?[X]:((creative(X)|~tall(X))))&
(?[X]:(happy(X)))&
((~old(paul)|kind(paul))) | ~patient(fred) | [
"p3",
"p4",
"p5",
"p8",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 1925130898900760050179845
% SZS output start Proof for 1925130898900760050179845
4. ! [X0] : (calm(X0) <=> (~tall(X0) | ~generous(X0))) [input p3]
5. ! [X0] : (rich(X0) <=> (~brave(X0) & ~curious(X0))) [input p4]
6. ! [X0] : ((calm(X0) | curious(X0)) <=> (generous(X0) & humble(X0))) [input p5]
9. ? [X0] : (~humble(X0) & ~curious(X0)) <=> ? [X0] : (brave(X0) <~> rich(X0)) [input p8]
10. ! [X0] : ((brave(X0) | tall(X0)) <=> (~old(X0) & humble(X0))) [input p9]
11. ! [X0] : ((curious(X0) | ~kind(X0)) => ~patient(X0)) [input p10]
20. patient(fred) [input hypothesis]
22. ? [X0] : (~humble(X0) & ~curious(X0)) <=> ? [X1] : (brave(X1) <~> rich(X1)) [rectify 9]
28. ! [X0] : (~patient(X0) | (~curious(X0) & kind(X0))) [ennf transformation 11]
35. ! [X0] : ((calm(X0) | (tall(X0) & generous(X0))) & ((~tall(X0) | ~generous(X0)) | ~calm(X0))) [nnf transformation 4]
36. ! [X0] : ((calm(X0) | (tall(X0) & generous(X0))) & (~tall(X0) | ~generous(X0) | ~calm(X0))) [flattening 35]
37. ! [X0] : ((rich(X0) | (brave(X0) | curious(X0))) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [nnf transformation 5]
38. ! [X0] : ((rich(X0) | brave(X0) | curious(X0)) & ((~brave(X0) & ~curious(X0)) | ~rich(X0))) [flattening 37]
39. ! [X0] : (((calm(X0) | curious(X0)) | (~generous(X0) | ~humble(X0))) & ((generous(X0) & humble(X0)) | (~calm(X0) & ~curious(X0)))) [nnf transformation 6]
40. ! [X0] : ((calm(X0) | curious(X0) | ~generous(X0) | ~humble(X0)) & ((generous(X0) & humble(X0)) | (~calm(X0) & ~curious(X0)))) [flattening 39]
46. (? [X0] : (~humble(X0) & ~curious(X0)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (? [X1] : ((~rich(X1) | ~brave(X1)) & (rich(X1) | brave(X1))) | ! [X0] : (humble(X0) | curious(X0))) [nnf transformation 22]
47. (? [X0] : (~humble(X0) & ~curious(X0)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (? [X2] : ((~rich(X2) | ~brave(X2)) & (rich(X2) | brave(X2))) | ! [X3] : (humble(X3) | curious(X3))) [rectify 46]
48. ? [X0] : (~humble(X0) & ~curious(X0)) => (~humble(sK2) & ~curious(sK2)) [choice axiom]
49. ? [X2] : ((~rich(X2) | ~brave(X2)) & (rich(X2) | brave(X2))) => ((~rich(sK3) | ~brave(sK3)) & (rich(sK3) | brave(sK3))) [choice axiom]
50. ((~humble(sK2) & ~curious(sK2)) | ! [X1] : ((brave(X1) | ~rich(X1)) & (rich(X1) | ~brave(X1)))) & (((~rich(sK3) | ~brave(sK3)) & (rich(sK3) | brave(sK3))) | ! [X3] : (humble(X3) | curious(X3))) [skolemisation 47,49,48]
51. ! [X0] : (((brave(X0) | tall(X0)) | (old(X0) | ~humble(X0))) & ((~old(X0) & humble(X0)) | (~brave(X0) & ~tall(X0)))) [nnf transformation 10]
52. ! [X0] : ((brave(X0) | tall(X0) | old(X0) | ~humble(X0)) & ((~old(X0) & humble(X0)) | (~brave(X0) & ~tall(X0)))) [flattening 51]
73. tall(X0) | calm(X0) [cnf transformation 36]
75. ~brave(X0) | ~rich(X0) [cnf transformation 38]
76. brave(X0) | rich(X0) | curious(X0) [cnf transformation 38]
78. ~calm(X0) | humble(X0) [cnf transformation 40]
90. ~humble(sK2) | rich(X1) | ~brave(X1) [cnf transformation 50]
91. ~humble(sK2) | brave(X1) | ~rich(X1) [cnf transformation 50]
92. ~tall(X0) | humble(X0) [cnf transformation 52]
98. ~patient(X0) | ~curious(X0) [cnf transformation 28]
111. patient(fred) [cnf transformation 20]
118. 1 <=> ! [X1] : ~rich(X1) [avatar definition]
119. ~rich(X1) <- (1) [avatar component clause 118]
133. ~humble(sK2) | ~rich(X1) [subsumption resolution 91,75]
135. 5 <=> humble(sK2) [avatar definition]
137. ~humble(sK2) <- (~5) [avatar component clause 135]
138. 1 | ~5 [avatar split clause 133,135,118]
139. ~humble(sK2) | ~brave(X1) [subsumption resolution 90,75]
141. 6 <=> ! [X1] : ~brave(X1) [avatar definition]
142. ~brave(X1) <- (6) [avatar component clause 141]
143. 6 | ~5 [avatar split clause 139,135,141]
154. 8 <=> ! [X3] : humble(X3) [avatar definition]
155. humble(X3) <- (8) [avatar component clause 154]
176. 13 <=> brave(fred) [avatar definition]
177. brave(fred) <- (13) [avatar component clause 176]
178. ~brave(fred) <- (~13) [avatar component clause 176]
210. $false <- (~5, 8) [subsumption resolution 137,155]
211. 5 | ~8 [avatar contradiction clause 210]
224. humble(X0) | calm(X0) [resolution 92,73]
225. humble(X0) [subsumption resolution 224,78]
226. 8 [avatar split clause 225,154]
230. ~curious(fred) [resolution 98,111]
243. rich(fred) | curious(fred) <- (~13) [resolution 76,178]
248. curious(fred) <- (1, ~13) [subsumption resolution 243,119]
249. $false <- (1, ~13) [subsumption resolution 248,230]
250. ~1 | 13 [avatar contradiction clause 249]
254. $false <- (6, 13) [subsumption resolution 177,142]
255. ~6 | ~13 [avatar contradiction clause 254]
256. $false [avatar sat refutation 138,143,211,226,250,255]
% SZS output end Proof for 1925130898900760050179845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or not humble is either curious or not patient and vice versa.
Everyone who is happy or not funny is both not happy and calm.
Everyone who is both calm and not brave is quiet or not humble.
If someone is not generous or not quiet then fred is humble.
If someone is patient then mary is either not quiet or humble and vice versa.
Everyone who is both not rich and not creative is curious.
Everyone who is either not funny or funny is not curious.
Everyone who is both not patient and not strong is calm and vice versa.
If lucy is curious then someone is either calm or wise.
Everyone who is old or generous is not kind or funny.
If someone is both curious and brave then someone is either not strong or calm and vice versa.
Everyone who is quiet or not curious is generous and vice versa.
Everyone who is not wise is not rich or not old.
Everyone who is not tall or not quiet is either not funny or curious.
If someone is not curious or patient then someone is both not happy and not rich.
If lucy is either not humble or strong then someone is not old.
Someone is both kind and humble.
John is both not creative and strong.
Lucy is either not tall or strong.
Lucy is not strong or not quiet.
Fred is not brave.
Someone is either not brave or funny. | Fred is happy. | contradiction | (![X]:((curious(X)<~>~humble(X))<=>(curious(X)<~>~patient(X))))&
(![X]:((happy(X)|~funny(X))=>(~happy(X)&calm(X))))&
(![X]:((calm(X)&~brave(X))=>(quiet(X)|~humble(X))))&
((?[X]:((~generous(X)|~quiet(X))))=>(humble(fred)))&
((?[X]:(patient(X)))<=>((~quiet(mary)<~>humble(mary))))&
(![X]:((~rich(X)&~creative(X))=>curious(X)))&
(![X]:((~funny(X)<~>funny(X))=>~curious(X)))&
(![X]:((~patient(X)&~strong(X))<=>calm(X)))&
((curious(lucy))=>(?[X]:((calm(X)<~>wise(X)))))&
(![X]:((old(X)|generous(X))=>(~kind(X)|funny(X))))&
((?[X]:((curious(X)&brave(X))))<=>(?[X]:((~strong(X)<~>calm(X)))))&
(![X]:((quiet(X)|~curious(X))<=>generous(X)))&
(![X]:(~wise(X)=>(~rich(X)|~old(X))))&
(![X]:((~tall(X)|~quiet(X))=>(~funny(X)<~>curious(X))))&
((?[X]:((~curious(X)|patient(X))))=>(?[X]:((~happy(X)&~rich(X)))))&
(((~humble(lucy)<~>strong(lucy)))=>(?[X]:(~old(X))))&
(?[X]:((kind(X)&humble(X))))&
((~creative(john)&strong(john)))&
((~tall(lucy)<~>strong(lucy)))&
((~strong(lucy)|~quiet(lucy)))&
(~brave(fred))&
(?[X]:((~brave(X)<~>funny(X)))) | happy(fred) | [
"p1",
"hypothesis"
]
| % SZS status Unsatisfiable for 1194593119440275028976686
% SZS output start Proof for 1194593119440275028976686
2. ! [X0] : ((~funny(X0) | happy(X0)) => (calm(X0) & ~happy(X0))) [input p1]
23. happy(fred) [input hypothesis]
29. ! [X0] : ((calm(X0) & ~happy(X0)) | (funny(X0) & ~happy(X0))) [ennf transformation 2]
77. ~happy(X0) | ~happy(X0) [cnf transformation 29]
124. happy(fred) [cnf transformation 23]
127. ~happy(X0) [duplicate literal removal 77]
212. $false [subsumption resolution 124,127]
% SZS output end Proof for 1194593119440275028976686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or creative is patient. Everyone who is both not wise and not generous is quiet or creative and vice versa. If someone is not rich or generous then fred is either calm or wise. Everyone who is both not curious and not rich is either happy or not tall. If someone is either tall or funny then someone is not humble. Everyone who is humble is either not humble or not happy. Everyone who is either creative or old is both not old and quiet and vice versa. Everyone who is not happy is both not funny and funny and vice versa. Everyone who is both not humble and tall is quiet. If someone is either not quiet or humble then someone is both not curious and not happy and vice versa. If someone is either calm or not quiet then susan is either generous or rich and vice versa. Everyone who is generous or not funny is not funny. If mary is funny or not humble then someone is happy and vice versa. Someone is both strong and brave. Someone is not patient or not wise. Susan is rich or not curious. Someone is either kind or happy. Alice is not happy or quiet. Alice is strong. Someone is either generous or curious. | Fred is wise. | contradiction | (![X]:((~rich(X)<~>creative(X))=>patient(X)))&
(![X]:((~wise(X)&~generous(X))<=>(quiet(X)|creative(X))))&
((?[X]:((~rich(X)|generous(X))))=>((calm(fred)<~>wise(fred))))&
(![X]:((~curious(X)&~rich(X))=>(happy(X)<~>~tall(X))))&
((?[X]:((tall(X)<~>funny(X))))=>(?[X]:(~humble(X))))&
(![X]:(humble(X)=>(~humble(X)<~>~happy(X))))&
(![X]:((creative(X)<~>old(X))<=>(~old(X)&quiet(X))))&
(![X]:(~happy(X)<=>(~funny(X)&funny(X))))&
(![X]:((~humble(X)&tall(X))=>quiet(X)))&
((?[X]:((~quiet(X)<~>humble(X))))<=>(?[X]:((~curious(X)&~happy(X)))))&
((?[X]:((calm(X)<~>~quiet(X))))<=>((generous(susan)<~>rich(susan))))&
(![X]:((generous(X)|~funny(X))=>~funny(X)))&
(((funny(mary)|~humble(mary)))<=>(?[X]:(happy(X))))&
(?[X]:((strong(X)&brave(X))))&
(?[X]:((~patient(X)|~wise(X))))&
((rich(susan)|~curious(susan)))&
(?[X]:((kind(X)<~>happy(X))))&
((~happy(alice)|quiet(alice)))&
(strong(alice))&
(?[X]:((generous(X)<~>curious(X)))) | wise(fred) | [
"p1",
"p5",
"p7",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 926613554233089613762658
% SZS output start Proof for 926613554233089613762658
2. ! [X0] : ((~generous(X0) & ~wise(X0)) <=> (creative(X0) | quiet(X0))) [input p1]
6. ! [X0] : (humble(X0) => (~humble(X0) <~> ~happy(X0))) [input p5]
8. ! [X0] : (~happy(X0) <=> (funny(X0) & ~funny(X0))) [input p7]
10. ? [X0] : (~quiet(X0) <~> humble(X0)) <=> ? [X0] : (~happy(X0) & ~curious(X0)) [input p9]
21. wise(fred) [input hypothesis]
23. ? [X0] : (~quiet(X0) <~> humble(X0)) <=> ? [X1] : (~happy(X1) & ~curious(X1)) [rectify 10]
32. ! [X0] : ((~humble(X0) <~> ~happy(X0)) | ~humble(X0)) [ennf transformation 6]
37. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~creative(X0) & ~quiet(X0))) & ((creative(X0) | quiet(X0)) | (generous(X0) | wise(X0)))) [nnf transformation 2]
38. ! [X0] : (((~generous(X0) & ~wise(X0)) | (~creative(X0) & ~quiet(X0))) & (creative(X0) | quiet(X0) | generous(X0) | wise(X0))) [flattening 37]
45. ! [X0] : (((happy(X0) | humble(X0)) & (~happy(X0) | ~humble(X0))) | ~humble(X0)) [nnf transformation 32]
48. ! [X0] : ((~happy(X0) | (~funny(X0) | funny(X0))) & ((funny(X0) & ~funny(X0)) | happy(X0))) [nnf transformation 8]
49. ! [X0] : ((~happy(X0) | ~funny(X0) | funny(X0)) & ((funny(X0) & ~funny(X0)) | happy(X0))) [flattening 48]
50. (? [X0] : ((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | curious(X1))) & (? [X1] : (~happy(X1) & ~curious(X1)) | ! [X0] : ((~quiet(X0) | ~humble(X0)) & (humble(X0) | quiet(X0)))) [nnf transformation 23]
51. (? [X0] : ((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) | ! [X1] : (happy(X1) | curious(X1))) & (? [X2] : (~happy(X2) & ~curious(X2)) | ! [X3] : ((~quiet(X3) | ~humble(X3)) & (humble(X3) | quiet(X3)))) [rectify 50]
52. ? [X0] : ((~humble(X0) | quiet(X0)) & (humble(X0) | ~quiet(X0))) => ((~humble(sK1) | quiet(sK1)) & (humble(sK1) | ~quiet(sK1))) [choice axiom]
53. ? [X2] : (~happy(X2) & ~curious(X2)) => (~happy(sK2) & ~curious(sK2)) [choice axiom]
54. (((~humble(sK1) | quiet(sK1)) & (humble(sK1) | ~quiet(sK1))) | ! [X1] : (happy(X1) | curious(X1))) & ((~happy(sK2) & ~curious(sK2)) | ! [X3] : ((~quiet(X3) | ~humble(X3)) & (humble(X3) | quiet(X3)))) [skolemisation 51,53,52]
75. ~quiet(X0) | ~wise(X0) [cnf transformation 38]
87. ~happy(X0) | ~humble(X0) | ~humble(X0) [cnf transformation 45]
95. ~funny(X0) | happy(X0) [cnf transformation 49]
96. funny(X0) | happy(X0) [cnf transformation 49]
101. ~happy(sK2) | humble(X3) | quiet(X3) [cnf transformation 54]
125. wise(fred) [cnf transformation 21]
128. ~humble(X0) | ~happy(X0) [duplicate literal removal 87]
137. 3 <=> wise(fred) [avatar definition]
138. wise(fred) <- (3) [avatar component clause 137]
159. happy(X0) [subsumption resolution 95,96]
161. humble(X3) | quiet(X3) [subsumption resolution 101,159]
228. 3 [avatar split clause 125,137]
237. quiet(X1) | ~happy(X1) [resolution 161,128]
238. quiet(X1) [subsumption resolution 237,159]
245. ~wise(X1) [resolution 238,75]
255. $false <- (3) [resolution 245,138]
256. ~3 [avatar contradiction clause 255]
257. $false [avatar sat refutation 228,256]
% SZS output end Proof for 926613554233089613762658
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either not calm or not kind then fred is strong or creative and vice versa.
If someone is either not brave or brave then mary is not wise.
Everyone who is both not strong and not curious is both not strong and happy.
Everyone who is either generous or not calm is not curious.
Everyone who is humble or not humble is not quiet and vice versa.
If someone is both not strong and humble then someone is patient.
If someone is both creative and not patient then mary is both happy and old.
If paul is both not strong and not rich then someone is either not quiet or happy.
If lucy is not creative or not generous then someone is either calm or not quiet and vice versa.
Everyone who is either curious or not creative is happy or not patient and vice versa.
Everyone who is not calm or not creative is not quiet and vice versa.
If susan is both not curious and not generous then someone is generous or patient and vice versa.
If john is not rich then lucy is kind.
Everyone who is not calm is happy or not calm and vice versa.
If someone is wise or generous then paul is not funny or not tall and vice versa.
If lucy is either not creative or strong then someone is either not brave or curious.
Mary is funny.
Someone is both not calm and not curious.
Fred is either not old or calm.
Susan is creative.
Fred is wise.
Mary is rich.
Paul is either funny or quiet.
Someone is wise or not strong. | Paul is tall. | contradiction | (((~calm(mary)<~>~kind(mary)))<=>((strong(fred)|creative(fred))))&
((?[X]:((~brave(X)<~>brave(X))))=>(~wise(mary)))&
(![X]:((~strong(X)&~curious(X))=>(~strong(X)&happy(X))))&
(![X]:((generous(X)<~>~calm(X))=>~curious(X)))&
(![X]:((humble(X)|~humble(X))<=>~quiet(X)))&
((?[X]:((~strong(X)&humble(X))))=>(?[X]:(patient(X))))&
((?[X]:((creative(X)&~patient(X))))=>((happy(mary)&old(mary))))&
(((~strong(paul)&~rich(paul)))=>(?[X]:((~quiet(X)<~>happy(X)))))&
(((~creative(lucy)|~generous(lucy)))<=>(?[X]:((calm(X)<~>~quiet(X)))))&
(![X]:((curious(X)<~>~creative(X))<=>(happy(X)|~patient(X))))&
(![X]:((~calm(X)|~creative(X))<=>~quiet(X)))&
(((~curious(susan)&~generous(susan)))<=>(?[X]:((generous(X)|patient(X)))))&
((~rich(john))=>(kind(lucy)))&
(![X]:(~calm(X)<=>(happy(X)|~calm(X))))&
((?[X]:((wise(X)|generous(X))))<=>((~funny(paul)|~tall(paul))))&
(((~creative(lucy)<~>strong(lucy)))=>(?[X]:((~brave(X)<~>curious(X)))))&
(funny(mary))&
(?[X]:((~calm(X)&~curious(X))))&
((~old(fred)<~>calm(fred)))&
(creative(susan))&
(wise(fred))&
(rich(mary))&
((funny(paul)<~>quiet(paul)))&
(?[X]:((wise(X)|~strong(X)))) | tall(paul) | [
"p4",
"p14",
"p20",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 6913310339416907218204119
% SZS output start Proof for 6913310339416907218204119
5. ! [X0] : ((~humble(X0) | humble(X0)) <=> ~quiet(X0)) [input p4]
15. ? [X0] : (generous(X0) | wise(X0)) <=> (~tall(paul) | ~funny(paul)) [input p14]
21. wise(fred) [input p20]
23. funny(paul) <~> quiet(paul) [input p22]
25. tall(paul) [input hypothesis]
41. ! [X0] : (((~humble(X0) | humble(X0)) | quiet(X0)) & (~quiet(X0) | (humble(X0) & ~humble(X0)))) [nnf transformation 5]
42. ! [X0] : ((~humble(X0) | humble(X0) | quiet(X0)) & (~quiet(X0) | (humble(X0) & ~humble(X0)))) [flattening 41]
62. (? [X0] : (generous(X0) | wise(X0)) | (tall(paul) & funny(paul))) & ((~tall(paul) | ~funny(paul)) | ! [X0] : (~generous(X0) & ~wise(X0))) [nnf transformation 15]
63. (? [X0] : (generous(X0) | wise(X0)) | (tall(paul) & funny(paul))) & (~tall(paul) | ~funny(paul) | ! [X0] : (~generous(X0) & ~wise(X0))) [flattening 62]
64. (? [X0] : (generous(X0) | wise(X0)) | (tall(paul) & funny(paul))) & (~tall(paul) | ~funny(paul) | ! [X1] : (~generous(X1) & ~wise(X1))) [rectify 63]
65. ? [X0] : (generous(X0) | wise(X0)) => (generous(sK3) | wise(sK3)) [choice axiom]
66. ((generous(sK3) | wise(sK3)) | (tall(paul) & funny(paul))) & (~tall(paul) | ~funny(paul) | ! [X1] : (~generous(X1) & ~wise(X1))) [skolemisation 64,65]
73. (~quiet(paul) | ~funny(paul)) & (quiet(paul) | funny(paul)) [nnf transformation 23]
88. ~quiet(X0) | ~humble(X0) [cnf transformation 42]
89. ~quiet(X0) | humble(X0) [cnf transformation 42]
117. ~tall(paul) | ~funny(paul) | ~wise(X1) [cnf transformation 66]
131. wise(fred) [cnf transformation 21]
132. quiet(paul) | funny(paul) [cnf transformation 73]
135. tall(paul) [cnf transformation 25]
172. ~quiet(X0) [subsumption resolution 88,89]
244. 23 <=> tall(paul) [avatar definition]
257. 26 <=> funny(paul) [avatar definition]
263. 27 <=> ! [X1] : ~wise(X1) [avatar definition]
264. ~wise(X1) <- (27) [avatar component clause 263]
265. 27 | ~26 | ~23 [avatar split clause 117,244,257,263]
292. funny(paul) [subsumption resolution 132,172]
293. 26 [avatar split clause 292,257]
303. 23 [avatar split clause 135,244]
307. $false <- (27) [resolution 264,131]
308. ~27 [avatar contradiction clause 307]
309. $false [avatar sat refutation 265,293,303,308]
% SZS output end Proof for 6913310339416907218204119
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 someone is generous then fred is either not happy or not patient and vice versa.
Everyone who is not creative or not humble is funny and vice versa.
Everyone who is either curious or kind is brave and vice versa.
Everyone who is wise or curious is humble or not calm.
If lucy is quiet or brave then someone is funny.
If someone is both not funny and not curious then alice is funny and vice versa.
Everyone who is not wise or quiet is both curious and not humble and vice versa.
If john is both calm and not tall then paul is both calm and happy.
If mary is both not strong and old then fred is both funny and not brave and vice versa.
If someone is patient or not humble then paul is happy or wise.
Everyone who is either humble or funny is not kind or not strong.
If susan is not kind then susan is both generous and not old and vice versa.
Everyone who is funny or tall is patient and vice versa.
Everyone who is either happy or humble is either not brave or not calm.
Everyone who is generous or not calm is both funny and strong and vice versa.
Everyone who is generous or not calm is patient or curious and vice versa.
Someone is not wise or old.
Someone is either not strong or curious.
Paul is not generous or humble.
Susan is either curious or not humble.
Alice is not quiet or kind.
Mary is strong or not tall.
Fred is not wise or generous.
Someone is wise or not calm. | Fred is strong. | entailment | ((?[X]:(generous(X)))<=>((~happy(fred)<~>~patient(fred))))&
(![X]:((~creative(X)|~humble(X))<=>funny(X)))&
(![X]:((curious(X)<~>kind(X))<=>brave(X)))&
(![X]:((wise(X)|curious(X))=>(humble(X)|~calm(X))))&
(((quiet(lucy)|brave(lucy)))=>(?[X]:(funny(X))))&
((?[X]:((~funny(X)&~curious(X))))<=>(funny(alice)))&
(![X]:((~wise(X)|quiet(X))<=>(curious(X)&~humble(X))))&
(((calm(john)&~tall(john)))=>((calm(paul)&happy(paul))))&
(((~strong(mary)&old(mary)))<=>((funny(fred)&~brave(fred))))&
((?[X]:((patient(X)|~humble(X))))=>((happy(paul)|wise(paul))))&
(![X]:((humble(X)<~>funny(X))=>(~kind(X)|~strong(X))))&
((~kind(susan))<=>((generous(susan)&~old(susan))))&
(![X]:((funny(X)|tall(X))<=>patient(X)))&
(![X]:((happy(X)<~>humble(X))=>(~brave(X)<~>~calm(X))))&
(![X]:((generous(X)|~calm(X))<=>(funny(X)&strong(X))))&
(![X]:((generous(X)|~calm(X))<=>(patient(X)|curious(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((~strong(X)<~>curious(X))))&
((~generous(paul)|humble(paul)))&
((curious(susan)<~>~humble(susan)))&
((~quiet(alice)|kind(alice)))&
((strong(mary)|~tall(mary)))&
((~wise(fred)|generous(fred)))&
(?[X]:((wise(X)|~calm(X)))) | strong(fred) | [
"p3",
"p6",
"p14",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 4816308397428832679210092
% SZS output start Proof for 4816308397428832679210092
4. ! [X0] : ((curious(X0) | wise(X0)) => (~calm(X0) | humble(X0))) [input p3]
7. ! [X0] : ((quiet(X0) | ~wise(X0)) <=> (~humble(X0) & curious(X0))) [input p6]
15. ! [X0] : ((~calm(X0) | generous(X0)) <=> (strong(X0) & funny(X0))) [input p14]
23. generous(fred) | ~wise(fred) [input p22]
25. ~strong(fred) [input hypothesis]
26. ! [X0] : ((~calm(X0) | humble(X0)) | (~curious(X0) & ~wise(X0))) [ennf transformation 4]
27. ! [X0] : (~calm(X0) | humble(X0) | (~curious(X0) & ~wise(X0))) [flattening 26]
49. ! [X0] : (((quiet(X0) | ~wise(X0)) | (humble(X0) | ~curious(X0))) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [nnf transformation 7]
50. ! [X0] : ((quiet(X0) | ~wise(X0) | humble(X0) | ~curious(X0)) & ((~humble(X0) & curious(X0)) | (~quiet(X0) & wise(X0)))) [flattening 49]
59. ! [X0] : (((~calm(X0) | generous(X0)) | (~strong(X0) | ~funny(X0))) & ((strong(X0) & funny(X0)) | (calm(X0) & ~generous(X0)))) [nnf transformation 15]
60. ! [X0] : ((~calm(X0) | generous(X0) | ~strong(X0) | ~funny(X0)) & ((strong(X0) & funny(X0)) | (calm(X0) & ~generous(X0)))) [flattening 59]
83. ~calm(X0) | humble(X0) | ~curious(X0) [cnf transformation 27]
89. wise(X0) | curious(X0) [cnf transformation 50]
91. ~humble(X0) | wise(X0) [cnf transformation 50]
116. ~generous(X0) | strong(X0) [cnf transformation 60]
117. strong(X0) | calm(X0) [cnf transformation 60]
131. generous(fred) | ~wise(fred) [cnf transformation 23]
133. ~strong(fred) [cnf transformation 25]
305. 37 <=> wise(fred) [avatar definition]
307. ~wise(fred) <- (~37) [avatar component clause 305]
309. 38 <=> generous(fred) [avatar definition]
311. generous(fred) <- (38) [avatar component clause 309]
312. ~37 | 38 [avatar split clause 131,309,305]
359. strong(fred) <- (38) [resolution 116,311]
360. $false <- (38) [subsumption resolution 359,133]
361. ~38 [avatar contradiction clause 360]
362. curious(fred) <- (~37) [resolution 307,89]
364. calm(fred) [resolution 117,133]
376. 41 <=> humble(fred) [avatar definition]
377. humble(fred) <- (41) [avatar component clause 376]
447. humble(fred) | ~curious(fred) [resolution 83,364]
452. humble(fred) <- (~37) [subsumption resolution 447,362]
453. 41 | 37 [avatar split clause 452,305,376]
454. wise(fred) <- (41) [resolution 377,91]
455. $false <- (~37, 41) [subsumption resolution 454,307]
456. 37 | ~41 [avatar contradiction clause 455]
457. $false [avatar sat refutation 312,361,453,456]
% SZS output end Proof for 4816308397428832679210092
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not brave or not patient is either curious or not patient. Everyone who is rich is both rich and not strong. Everyone who is not strong is not curious or not brave and vice versa. Everyone who is either not funny or old is both tall and patient. Everyone who is generous is not funny and vice versa. If someone is not patient then someone is old and vice versa. Everyone who is both not brave and not kind is either creative or kind and vice versa. If someone is patient then someone is either not quiet or quiet. Everyone who is either kind or brave is both brave and curious. Everyone who is either brave or not old is either not funny or not rich. Everyone who is both humble and not funny is both not curious and brave and vice versa. Everyone who is happy or quiet is generous or not creative and vice versa. If someone is humble then lucy is either not kind or creative. Everyone who is either not happy or not funny is both kind and not generous and vice versa. Everyone who is both not tall and generous is quiet or happy and vice versa. Everyone who is either quiet or brave is both not generous and happy and vice versa. Someone is rich. Someone is not rich or not calm. Someone is not happy. Someone is not tall or curious. | Lucy is not humble. | contradiction | (![X]:((~brave(X)|~patient(X))=>(curious(X)<~>~patient(X))))&
(![X]:(rich(X)=>(rich(X)&~strong(X))))&
(![X]:(~strong(X)<=>(~curious(X)|~brave(X))))&
(![X]:((~funny(X)<~>old(X))=>(tall(X)&patient(X))))&
(![X]:(generous(X)<=>~funny(X)))&
((?[X]:(~patient(X)))<=>(?[X]:(old(X))))&
(![X]:((~brave(X)&~kind(X))<=>(creative(X)<~>kind(X))))&
((?[X]:(patient(X)))=>(?[X]:((~quiet(X)<~>quiet(X)))))&
(![X]:((kind(X)<~>brave(X))=>(brave(X)&curious(X))))&
(![X]:((brave(X)<~>~old(X))=>(~funny(X)<~>~rich(X))))&
(![X]:((humble(X)&~funny(X))<=>(~curious(X)&brave(X))))&
(![X]:((happy(X)|quiet(X))<=>(generous(X)|~creative(X))))&
((?[X]:(humble(X)))=>((~kind(lucy)<~>creative(lucy))))&
(![X]:((~happy(X)<~>~funny(X))<=>(kind(X)&~generous(X))))&
(![X]:((~tall(X)&generous(X))<=>(quiet(X)|happy(X))))&
(![X]:((quiet(X)<~>brave(X))<=>(~generous(X)&happy(X))))&
(?[X]:(rich(X)))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)|curious(X)))) | ~humble(lucy) | [
"p1",
"p2",
"p3",
"p4",
"p8",
"p9",
"p10",
"p11",
"p13",
"p14",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 255116951179040802238222
% SZS output start Proof for 255116951179040802238222
2. ! [X0] : (rich(X0) => (~strong(X0) & rich(X0))) [input p1]
3. ! [X0] : (~strong(X0) <=> (~brave(X0) | ~curious(X0))) [input p2]
4. ! [X0] : ((~funny(X0) <~> old(X0)) => (patient(X0) & tall(X0))) [input p3]
5. ! [X0] : (generous(X0) <=> ~funny(X0)) [input p4]
9. ! [X0] : ((kind(X0) <~> brave(X0)) => (curious(X0) & brave(X0))) [input p8]
10. ! [X0] : ((brave(X0) <~> ~old(X0)) => (~funny(X0) <~> ~rich(X0))) [input p9]
11. ! [X0] : ((~funny(X0) & humble(X0)) <=> (brave(X0) & ~curious(X0))) [input p10]
12. ! [X0] : ((quiet(X0) | happy(X0)) <=> (~creative(X0) | generous(X0))) [input p11]
14. ! [X0] : ((~happy(X0) <~> ~funny(X0)) <=> (~generous(X0) & kind(X0))) [input p13]
15. ! [X0] : ((generous(X0) & ~tall(X0)) <=> (happy(X0) | quiet(X0))) [input p14]
16. ! [X0] : ((quiet(X0) <~> brave(X0)) <=> (happy(X0) & ~generous(X0))) [input p15]
21. ~humble(lucy) [input hypothesis]
24. ! [X0] : (~strong(X0) => (~brave(X0) | ~curious(X0))) [unused predicate definition removal 3]
27. ! [X0] : ((~strong(X0) & rich(X0)) | ~rich(X0)) [ennf transformation 2]
28. ! [X0] : ((~brave(X0) | ~curious(X0)) | strong(X0)) [ennf transformation 24]
29. ! [X0] : (~brave(X0) | ~curious(X0) | strong(X0)) [flattening 28]
30. ! [X0] : ((patient(X0) & tall(X0)) | (~funny(X0) <=> old(X0))) [ennf transformation 4]
32. ! [X0] : ((curious(X0) & brave(X0)) | (kind(X0) <=> brave(X0))) [ennf transformation 9]
33. ! [X0] : ((~funny(X0) <~> ~rich(X0)) | (brave(X0) <=> ~old(X0))) [ennf transformation 10]
36. ! [X0] : ((patient(X0) & tall(X0)) | ((~funny(X0) | ~old(X0)) & (old(X0) | funny(X0)))) [nnf transformation 30]
37. ! [X0] : ((generous(X0) | funny(X0)) & (~funny(X0) | ~generous(X0))) [nnf transformation 5]
49. ! [X0] : ((curious(X0) & brave(X0)) | ((kind(X0) | ~brave(X0)) & (brave(X0) | ~kind(X0)))) [nnf transformation 32]
50. ! [X0] : (((rich(X0) | funny(X0)) & (~rich(X0) | ~funny(X0))) | ((brave(X0) | old(X0)) & (~old(X0) | ~brave(X0)))) [nnf transformation 33]
51. ! [X0] : (((~funny(X0) & humble(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (funny(X0) | ~humble(X0)))) [nnf transformation 11]
52. ! [X0] : (((~funny(X0) & humble(X0)) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | funny(X0) | ~humble(X0))) [flattening 51]
53. ! [X0] : (((quiet(X0) | happy(X0)) | (creative(X0) & ~generous(X0))) & ((~creative(X0) | generous(X0)) | (~quiet(X0) & ~happy(X0)))) [nnf transformation 12]
54. ! [X0] : ((quiet(X0) | happy(X0) | (creative(X0) & ~generous(X0))) & (~creative(X0) | generous(X0) | (~quiet(X0) & ~happy(X0)))) [flattening 53]
56. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | (generous(X0) | ~kind(X0))) & ((~generous(X0) & kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [nnf transformation 14]
57. ! [X0] : ((((funny(X0) | happy(X0)) & (~funny(X0) | ~happy(X0))) | generous(X0) | ~kind(X0)) & ((~generous(X0) & kind(X0)) | ((~happy(X0) | funny(X0)) & (~funny(X0) | happy(X0))))) [flattening 56]
58. ! [X0] : (((generous(X0) & ~tall(X0)) | (~happy(X0) & ~quiet(X0))) & ((happy(X0) | quiet(X0)) | (~generous(X0) | tall(X0)))) [nnf transformation 15]
59. ! [X0] : (((generous(X0) & ~tall(X0)) | (~happy(X0) & ~quiet(X0))) & (happy(X0) | quiet(X0) | ~generous(X0) | tall(X0))) [flattening 58]
60. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | (~happy(X0) | generous(X0))) & ((happy(X0) & ~generous(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [nnf transformation 16]
61. ! [X0] : ((((~brave(X0) | ~quiet(X0)) & (brave(X0) | quiet(X0))) | ~happy(X0) | generous(X0)) & ((happy(X0) & ~generous(X0)) | ((quiet(X0) | ~brave(X0)) & (brave(X0) | ~quiet(X0))))) [flattening 60]
73. ~strong(X0) | ~rich(X0) [cnf transformation 27]
74. ~curious(X0) | ~brave(X0) | strong(X0) [cnf transformation 29]
75. tall(X0) | old(X0) | funny(X0) [cnf transformation 36]
79. ~generous(X0) | ~funny(X0) [cnf transformation 37]
80. generous(X0) | funny(X0) [cnf transformation 37]
91. brave(X0) | brave(X0) | ~kind(X0) [cnf transformation 49]
97. ~old(X0) | funny(X0) | rich(X0) | ~brave(X0) [cnf transformation 50]
101. ~brave(X0) | humble(X0) | curious(X0) [cnf transformation 52]
104. ~quiet(X0) | generous(X0) | ~creative(X0) [cnf transformation 54]
105. ~generous(X0) | happy(X0) | quiet(X0) [cnf transformation 54]
106. happy(X0) | quiet(X0) | creative(X0) [cnf transformation 54]
109. ~funny(X0) | kind(X0) | happy(X0) [cnf transformation 57]
112. ~generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 57]
116. ~quiet(X0) | ~tall(X0) [cnf transformation 59]
118. ~quiet(X0) | generous(X0) [cnf transformation 59]
119. generous(X0) | ~happy(X0) [cnf transformation 59]
122. happy(X0) | brave(X0) | ~quiet(X0) [cnf transformation 61]
123. happy(X0) | quiet(X0) | ~brave(X0) [cnf transformation 61]
129. ~humble(lucy) [cnf transformation 21]
130. ~kind(X0) | brave(X0) [duplicate literal removal 91]
164. ~happy(X0) | ~generous(X0) [subsumption resolution 112,79]
165. ~happy(X0) [subsumption resolution 119,164]
166. ~brave(X0) | quiet(X0) [subsumption resolution 123,165]
167. ~quiet(X0) | brave(X0) [subsumption resolution 122,165]
220. happy(X0) | quiet(X0) | funny(X0) [resolution 105,80]
221. quiet(X0) | funny(X0) [subsumption resolution 220,165]
223. funny(X1) | brave(X1) [resolution 221,167]
228. quiet(X2) | creative(X2) [resolution 106,165]
231. creative(X2) | generous(X2) [resolution 228,118]
268. brave(X1) | kind(X1) | happy(X1) [resolution 223,109]
272. brave(X1) | kind(X1) [subsumption resolution 268,165]
273. brave(X1) [subsumption resolution 272,130]
275. humble(X0) | curious(X0) [resolution 273,101]
277. quiet(X2) [resolution 273,166]
284. generous(X0) | ~creative(X0) [resolution 277,104]
287. ~tall(X3) [resolution 277,116]
288. generous(X0) [subsumption resolution 284,231]
308. old(X0) | funny(X0) [resolution 287,75]
347. ~funny(X2) [resolution 288,79]
354. curious(lucy) [resolution 275,129]
361. ~brave(lucy) | strong(lucy) [resolution 354,74]
363. strong(lucy) [subsumption resolution 361,273]
366. ~rich(lucy) [resolution 363,73]
368. funny(X0) | funny(X0) | rich(X0) | ~brave(X0) [resolution 308,97]
372. funny(X0) | rich(X0) | ~brave(X0) [duplicate literal removal 368]
373. rich(X0) | ~brave(X0) [subsumption resolution 372,347]
374. rich(X0) [subsumption resolution 373,273]
376. $false [resolution 374,366]
% SZS output end Proof for 255116951179040802238222
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not strong is both calm and kind. If alice is both quiet and creative then john is both calm and tall. If lucy is both not humble and curious then paul is not patient and vice versa. If mary is both not creative and old then lucy is either not tall or generous. Everyone who is both not quiet and not creative is both tall and kind and vice versa. If lucy is both old and not rich then fred is not brave and vice versa. Everyone who is not kind or not wise is generous. Everyone who is creative or humble is both humble and old and vice versa. Everyone who is either not generous or rich is either not quiet or curious. Everyone who is calm or brave is either not patient or rich and vice versa. Everyone who is not rich is both brave and tall. Everyone who is both not curious and not wise is kind or not rich and vice versa. If someone is both not old and not tall then alice is either funny or not wise and vice versa. If someone is either not creative or quiet then someone is not patient and vice versa. Everyone who is not curious is both patient and old and vice versa. Everyone who is curious is not kind. Someone is either not calm or humble. Someone is not calm or happy. Someone is curious. Alice is both brave and not calm. Someone is either not humble or generous. Alice is either not humble or rich. Paul is both not calm and not tall. Susan is both tall and not calm. | Fred is rich. | entailment | (![X]:((~quiet(X)&~strong(X))=>(calm(X)&kind(X))))&
(((quiet(alice)&creative(alice)))=>((calm(john)&tall(john))))&
(((~humble(lucy)&curious(lucy)))<=>(~patient(paul)))&
(((~creative(mary)&old(mary)))=>((~tall(lucy)<~>generous(lucy))))&
(![X]:((~quiet(X)&~creative(X))<=>(tall(X)&kind(X))))&
(((old(lucy)&~rich(lucy)))<=>(~brave(fred)))&
(![X]:((~kind(X)|~wise(X))=>generous(X)))&
(![X]:((creative(X)|humble(X))<=>(humble(X)&old(X))))&
(![X]:((~generous(X)<~>rich(X))=>(~quiet(X)<~>curious(X))))&
(![X]:((calm(X)|brave(X))<=>(~patient(X)<~>rich(X))))&
(![X]:(~rich(X)=>(brave(X)&tall(X))))&
(![X]:((~curious(X)&~wise(X))<=>(kind(X)|~rich(X))))&
((?[X]:((~old(X)&~tall(X))))<=>((funny(alice)<~>~wise(alice))))&
((?[X]:((~creative(X)<~>quiet(X))))<=>(?[X]:(~patient(X))))&
(![X]:(~curious(X)<=>(patient(X)&old(X))))&
(![X]:(curious(X)=>~kind(X)))&
(?[X]:((~calm(X)<~>humble(X))))&
(?[X]:((~calm(X)|happy(X))))&
(?[X]:(curious(X)))&
((brave(alice)&~calm(alice)))&
(?[X]:((~humble(X)<~>generous(X))))&
((~humble(alice)<~>rich(alice)))&
((~calm(paul)&~tall(paul)))&
((tall(susan)&~calm(susan))) | rich(fred) | [
"p9",
"p10",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 4696182323647205558223034
% SZS output start Proof for 4696182323647205558223034
10. ! [X0] : ((brave(X0) | calm(X0)) <=> (~patient(X0) <~> rich(X0))) [input p9]
11. ! [X0] : (~rich(X0) => (tall(X0) & brave(X0))) [input p10]
12. ! [X0] : ((~wise(X0) & ~curious(X0)) <=> (~rich(X0) | kind(X0))) [input p11]
15. ! [X0] : (~curious(X0) <=> (old(X0) & patient(X0))) [input p14]
25. ~rich(fred) [input hypothesis]
35. ! [X0] : ((tall(X0) & brave(X0)) | rich(X0)) [ennf transformation 11]
47. ! [X0] : (((brave(X0) | calm(X0)) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~brave(X0) & ~calm(X0)))) [nnf transformation 10]
48. ! [X0] : ((brave(X0) | calm(X0) | ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0)))) & (((~rich(X0) | patient(X0)) & (rich(X0) | ~patient(X0))) | (~brave(X0) & ~calm(X0)))) [flattening 47]
49. ! [X0] : (((~wise(X0) & ~curious(X0)) | (rich(X0) & ~kind(X0))) & ((~rich(X0) | kind(X0)) | (wise(X0) | curious(X0)))) [nnf transformation 12]
50. ! [X0] : (((~wise(X0) & ~curious(X0)) | (rich(X0) & ~kind(X0))) & (~rich(X0) | kind(X0) | wise(X0) | curious(X0))) [flattening 49]
60. ! [X0] : ((~curious(X0) | (~old(X0) | ~patient(X0))) & ((old(X0) & patient(X0)) | curious(X0))) [nnf transformation 15]
61. ! [X0] : ((~curious(X0) | ~old(X0) | ~patient(X0)) & ((old(X0) & patient(X0)) | curious(X0))) [flattening 60]
97. ~brave(X0) | ~patient(X0) | rich(X0) [cnf transformation 48]
102. brave(X0) | rich(X0) [cnf transformation 35]
106. ~curious(X0) | rich(X0) [cnf transformation 50]
119. patient(X0) | curious(X0) [cnf transformation 61]
136. ~rich(fred) [cnf transformation 25]
387. ~patient(X0) | rich(X0) | rich(X0) [resolution 97,102]
388. ~patient(X0) | rich(X0) [duplicate literal removal 387]
500. rich(X0) | curious(X0) [resolution 388,119]
501. rich(X0) [subsumption resolution 500,106]
589. $false [resolution 501,136]
% SZS output end Proof for 4696182323647205558223034
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny is both not funny and not happy.
Everyone who is both not creative and calm is both not rich and kind and vice versa.
Everyone who is either creative or not brave is either not happy or not rich and vice versa.
If john is not tall or not quiet then alice is creative or tall.
Everyone who is either curious or not rich is either not creative or not humble.
Everyone who is patient or not humble is both kind and funny.
Everyone who is either quiet or not happy is tall.
If someone is kind or not creative then mary is both funny and happy and vice versa.
If someone is tall or creative then lucy is creative and vice versa.
If someone is either humble or not strong then someone is patient and vice versa.
Everyone who is wise or humble is creative and vice versa.
Everyone who is not creative or kind is both not curious and happy.
If alice is either not brave or not calm then john is strong and vice versa.
If susan is both not calm and not creative then alice is both happy and wise and vice versa.
Everyone who is not strong or not kind is both not happy and tall.
If someone is not patient or not calm then someone is not quiet and vice versa.
Fred is not brave or calm.
Someone is not happy.
Someone is either not curious or not humble.
Susan is not old.
Someone is both brave and not calm.
Someone is generous.
Lucy is not quiet or not rich. | Mary is happy. | contradiction | (![X]:((curious(X)<~>funny(X))=>(~funny(X)&~happy(X))))&
(![X]:((~creative(X)&calm(X))<=>(~rich(X)&kind(X))))&
(![X]:((creative(X)<~>~brave(X))<=>(~happy(X)<~>~rich(X))))&
(((~tall(john)|~quiet(john)))=>((creative(alice)|tall(alice))))&
(![X]:((curious(X)<~>~rich(X))=>(~creative(X)<~>~humble(X))))&
(![X]:((patient(X)|~humble(X))=>(kind(X)&funny(X))))&
(![X]:((quiet(X)<~>~happy(X))=>tall(X)))&
((?[X]:((kind(X)|~creative(X))))<=>((funny(mary)&happy(mary))))&
((?[X]:((tall(X)|creative(X))))<=>(creative(lucy)))&
((?[X]:((humble(X)<~>~strong(X))))<=>(?[X]:(patient(X))))&
(![X]:((wise(X)|humble(X))<=>creative(X)))&
(![X]:((~creative(X)|kind(X))=>(~curious(X)&happy(X))))&
(((~brave(alice)<~>~calm(alice)))<=>(strong(john)))&
(((~calm(susan)&~creative(susan)))<=>((happy(alice)&wise(alice))))&
(![X]:((~strong(X)|~kind(X))=>(~happy(X)&tall(X))))&
((?[X]:((~patient(X)|~calm(X))))<=>(?[X]:(~quiet(X))))&
((~brave(fred)|calm(fred)))&
(?[X]:(~happy(X)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(~old(susan))&
(?[X]:((brave(X)&~calm(X))))&
(?[X]:(generous(X)))&
((~quiet(lucy)|~rich(lucy))) | happy(mary) | [
"p0",
"p7",
"p11",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5220755908305165971281473
% SZS output start Proof for 5220755908305165971281473
1. ! [X0] : ((curious(X0) <~> funny(X0)) => (~happy(X0) & ~funny(X0))) [input p0]
8. ? [X0] : (~creative(X0) | kind(X0)) <=> (happy(mary) & funny(mary)) [input p7]
12. ! [X0] : ((kind(X0) | ~creative(X0)) => (happy(X0) & ~curious(X0))) [input p11]
15. ! [X0] : ((~kind(X0) | ~strong(X0)) => (tall(X0) & ~happy(X0))) [input p14]
24. happy(mary) [input hypothesis]
29. ! [X0] : ((~happy(X0) & ~funny(X0)) | (curious(X0) <=> funny(X0))) [ennf transformation 1]
35. ! [X0] : ((happy(X0) & ~curious(X0)) | (~kind(X0) & creative(X0))) [ennf transformation 12]
36. ! [X0] : ((tall(X0) & ~happy(X0)) | (kind(X0) & strong(X0))) [ennf transformation 15]
37. ! [X0] : ((~happy(X0) & ~funny(X0)) | ((curious(X0) | ~funny(X0)) & (funny(X0) | ~curious(X0)))) [nnf transformation 29]
43. (? [X0] : (~creative(X0) | kind(X0)) | (~happy(mary) | ~funny(mary))) & ((happy(mary) & funny(mary)) | ! [X0] : (creative(X0) & ~kind(X0))) [nnf transformation 8]
44. (? [X0] : (~creative(X0) | kind(X0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X0] : (creative(X0) & ~kind(X0))) [flattening 43]
45. (? [X0] : (~creative(X0) | kind(X0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X1] : (creative(X1) & ~kind(X1))) [rectify 44]
46. ? [X0] : (~creative(X0) | kind(X0)) => (~creative(sK0) | kind(sK0)) [choice axiom]
47. ((~creative(sK0) | kind(sK0)) | ~happy(mary) | ~funny(mary)) & ((happy(mary) & funny(mary)) | ! [X1] : (creative(X1) & ~kind(X1))) [skolemisation 45,46]
75. ~funny(X0) | curious(X0) | ~funny(X0) [cnf transformation 37]
102. funny(mary) | ~kind(X1) [cnf transformation 47]
118. ~kind(X0) | ~curious(X0) [cnf transformation 35]
130. ~happy(X0) | kind(X0) [cnf transformation 36]
143. happy(mary) [cnf transformation 24]
144. ~funny(X0) | curious(X0) [duplicate literal removal 75]
164. 5 <=> funny(mary) [avatar definition]
165. funny(mary) <- (5) [avatar component clause 164]
168. 6 <=> happy(mary) [avatar definition]
169. happy(mary) <- (6) [avatar component clause 168]
185. 10 <=> ! [X1] : ~kind(X1) [avatar definition]
186. ~kind(X1) <- (10) [avatar component clause 185]
189. 10 | 5 [avatar split clause 102,164,185]
324. 6 [avatar split clause 143,168]
350. kind(mary) <- (6) [resolution 130,169]
359. curious(mary) <- (5) [resolution 144,165]
376. ~curious(mary) <- (6) [resolution 350,118]
377. $false <- (5, 6) [subsumption resolution 376,359]
378. ~5 | ~6 [avatar contradiction clause 377]
384. $false <- (6, 10) [resolution 186,350]
385. ~6 | ~10 [avatar contradiction clause 384]
387. $false [avatar sat refutation 189,324,378,385]
% SZS output end Proof for 5220755908305165971281473
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not generous then someone is either calm or happy.
Everyone who is both rich and not humble is not quiet or not happy and vice versa.
Everyone who is both old and not quiet is not tall or not curious.
Everyone who is either not funny or wise is either kind or not creative and vice versa.
If someone is both not wise and not patient then someone is either not old or funny.
If someone is old or not humble then paul is both not calm and curious.
If john is funny then susan is both kind and not patient and vice versa.
If paul is both tall and rich then someone is not wise or quiet.
If someone is tall then someone is both not strong and tall.
If someone is quiet then someone is old or not strong and vice versa.
Everyone who is not creative or quiet is either not curious or not old and vice versa.
If mary is both not old and not brave then someone is not funny or happy.
Everyone who is both humble and not tall is either brave or patient.
If someone is creative then someone is strong.
Everyone who is not strong is kind and vice versa.
Everyone who is both not curious and kind is not old and vice versa.
Alice is not kind.
Paul is both patient and funny.
John is not happy.
Susan is strong.
Alice is either old or not quiet.
Someone is either not brave or kind.
Someone is either not curious or not wise.
Susan is not tall. | Alice is strong. | entailment | ((?[X]:(~generous(X)))=>(?[X]:((calm(X)<~>happy(X)))))&
(![X]:((rich(X)&~humble(X))<=>(~quiet(X)|~happy(X))))&
(![X]:((old(X)&~quiet(X))=>(~tall(X)|~curious(X))))&
(![X]:((~funny(X)<~>wise(X))<=>(kind(X)<~>~creative(X))))&
((?[X]:((~wise(X)&~patient(X))))=>(?[X]:((~old(X)<~>funny(X)))))&
((?[X]:((old(X)|~humble(X))))=>((~calm(paul)&curious(paul))))&
((funny(john))<=>((kind(susan)&~patient(susan))))&
(((tall(paul)&rich(paul)))=>(?[X]:((~wise(X)|quiet(X)))))&
((?[X]:(tall(X)))=>(?[X]:((~strong(X)&tall(X)))))&
((?[X]:(quiet(X)))<=>(?[X]:((old(X)|~strong(X)))))&
(![X]:((~creative(X)|quiet(X))<=>(~curious(X)<~>~old(X))))&
(((~old(mary)&~brave(mary)))=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((humble(X)&~tall(X))=>(brave(X)<~>patient(X))))&
((?[X]:(creative(X)))=>(?[X]:(strong(X))))&
(![X]:(~strong(X)<=>kind(X)))&
(![X]:((~curious(X)&kind(X))<=>~old(X)))&
(~kind(alice))&
((patient(paul)&funny(paul)))&
(~happy(john))&
(strong(susan))&
((old(alice)<~>~quiet(alice)))&
(?[X]:((~brave(X)<~>kind(X))))&
(?[X]:((~curious(X)<~>~wise(X))))&
(~tall(susan)) | strong(alice) | [
"p14",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 6435517560029136441536299
% SZS output start Proof for 6435517560029136441536299
15. ! [X0] : (~strong(X0) <=> kind(X0)) [input p14]
17. ~kind(alice) [input p16]
25. ~strong(alice) [input hypothesis]
72. ! [X0] : ((~strong(X0) | ~kind(X0)) & (kind(X0) | strong(X0))) [nnf transformation 15]
119. strong(X0) | kind(X0) [cnf transformation 72]
124. ~kind(alice) [cnf transformation 17]
136. ~strong(alice) [cnf transformation 25]
290. kind(alice) [resolution 119,136]
292. $false [subsumption resolution 290,124]
% SZS output end Proof for 6435517560029136441536299
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or not patient is not old and vice versa.
Everyone who is not quiet is both not patient and not curious.
Everyone who is not happy or not rich is curious and vice versa.
If someone is strong or not brave then alice is not funny or not humble.
Everyone who is both old and not old is not creative or not wise and vice versa.
If alice is generous then paul is both strong and old and vice versa.
Everyone who is not funny is not old and vice versa.
Everyone who is both not strong and not patient is strong or not patient and vice versa.
Everyone who is both not kind and brave is either curious or not old and vice versa.
Everyone who is either not rich or not patient is either strong or not humble and vice versa.
Everyone who is both strong and not kind is old or brave and vice versa.
If lucy is not wise then mary is both not curious and not funny.
Everyone who is not curious is humble and vice versa.
If someone is not brave or calm then fred is either tall or calm and vice versa.
Everyone who is either not wise or not curious is either not wise or rich.
If someone is either curious or not rich then alice is not generous and vice versa.
John is either wise or not kind.
Someone is not kind or not brave.
Paul is curious or generous.
John is either not strong or brave.
Mary is tall. | John is not humble. | entailment | (![X]:((~wise(X)<~>~patient(X))<=>~old(X)))&
(![X]:(~quiet(X)=>(~patient(X)&~curious(X))))&
(![X]:((~happy(X)|~rich(X))<=>curious(X)))&
((?[X]:((strong(X)|~brave(X))))=>((~funny(alice)|~humble(alice))))&
(![X]:((old(X)&~old(X))<=>(~creative(X)|~wise(X))))&
((generous(alice))<=>((strong(paul)&old(paul))))&
(![X]:(~funny(X)<=>~old(X)))&
(![X]:((~strong(X)&~patient(X))<=>(strong(X)|~patient(X))))&
(![X]:((~kind(X)&brave(X))<=>(curious(X)<~>~old(X))))&
(![X]:((~rich(X)<~>~patient(X))<=>(strong(X)<~>~humble(X))))&
(![X]:((strong(X)&~kind(X))<=>(old(X)|brave(X))))&
((~wise(lucy))=>((~curious(mary)&~funny(mary))))&
(![X]:(~curious(X)<=>humble(X)))&
((?[X]:((~brave(X)|calm(X))))<=>((tall(fred)<~>calm(fred))))&
(![X]:((~wise(X)<~>~curious(X))=>(~wise(X)<~>rich(X))))&
((?[X]:((curious(X)<~>~rich(X))))<=>(~generous(alice)))&
((wise(john)<~>~kind(john)))&
(?[X]:((~kind(X)|~brave(X))))&
((curious(paul)|generous(paul)))&
((~strong(john)<~>brave(john)))&
(tall(mary)) | ~humble(john) | [
"p4",
"p8",
"p10",
"p12",
"p16",
"hypothesis"
]
| % SZS status Unsatisfiable for 2577100950645199375136931
% SZS output start Proof for 2577100950645199375136931
5. ! [X0] : ((~old(X0) & old(X0)) <=> (~wise(X0) | ~creative(X0))) [input p4]
9. ! [X0] : ((brave(X0) & ~kind(X0)) <=> (curious(X0) <~> ~old(X0))) [input p8]
11. ! [X0] : ((~kind(X0) & strong(X0)) <=> (brave(X0) | old(X0))) [input p10]
13. ! [X0] : (~curious(X0) <=> humble(X0)) [input p12]
17. wise(john) <~> ~kind(john) [input p16]
22. humble(john) [input hypothesis]
33. ! [X0] : (((~old(X0) & old(X0)) | (wise(X0) & creative(X0))) & ((~wise(X0) | ~creative(X0)) | (old(X0) | ~old(X0)))) [nnf transformation 5]
34. ! [X0] : (((~old(X0) & old(X0)) | (wise(X0) & creative(X0))) & (~wise(X0) | ~creative(X0) | old(X0) | ~old(X0))) [flattening 33]
39. ! [X0] : (((brave(X0) & ~kind(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (~brave(X0) | kind(X0)))) [nnf transformation 9]
40. ! [X0] : (((brave(X0) & ~kind(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | ~brave(X0) | kind(X0))) [flattening 39]
42. ! [X0] : (((~kind(X0) & strong(X0)) | (~brave(X0) & ~old(X0))) & ((brave(X0) | old(X0)) | (kind(X0) | ~strong(X0)))) [nnf transformation 11]
43. ! [X0] : (((~kind(X0) & strong(X0)) | (~brave(X0) & ~old(X0))) & (brave(X0) | old(X0) | kind(X0) | ~strong(X0))) [flattening 42]
44. ! [X0] : ((~curious(X0) | ~humble(X0)) & (humble(X0) | curious(X0))) [nnf transformation 13]
54. (kind(john) | ~wise(john)) & (~kind(john) | wise(john)) [nnf transformation 17]
69. old(X0) | wise(X0) [cnf transformation 34]
71. ~old(X0) | wise(X0) [cnf transformation 34]
84. ~kind(X0) | curious(X0) | old(X0) [cnf transformation 40]
98. ~kind(X0) | ~old(X0) [cnf transformation 43]
103. ~humble(X0) | ~curious(X0) [cnf transformation 44]
119. kind(john) | ~wise(john) [cnf transformation 54]
125. humble(john) [cnf transformation 22]
146. wise(X0) [subsumption resolution 69,71]
211. kind(john) [subsumption resolution 119,146]
230. ~old(john) [resolution 98,211]
234. ~curious(john) [resolution 103,125]
252. curious(john) | old(john) [resolution 84,211]
253. old(john) [subsumption resolution 252,234]
254. $false [subsumption resolution 253,230]
% SZS output end Proof for 2577100950645199375136931
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not strong is either generous or creative and vice versa.
If paul is brave or not quiet then someone is both not old and not calm and vice versa.
If alice is kind then someone is both kind and calm and vice versa.
If alice is wise then lucy is not happy or not patient.
If someone is rich then someone is both not quiet and not generous and vice versa.
Everyone who is not old is both creative and not tall and vice versa.
Everyone who is not creative is either not wise or quiet.
Everyone who is either not brave or brave is strong and vice versa.
Everyone who is not rich is both not strong and strong and vice versa.
If someone is both not happy and not tall then paul is tall and vice versa.
Everyone who is both not brave and patient is either humble or not rich and vice versa.
Everyone who is not funny is not strong and vice versa.
Everyone who is either quiet or not tall is not generous and vice versa.
Everyone who is patient or happy is both not happy and not funny.
If alice is either not quiet or not tall then susan is not humble or not happy.
Someone is creative.
Someone is happy or generous.
Someone is kind.
Paul is both not quiet and not patient.
John is humble or quiet.
Someone is either calm or not quiet. | Paul is not funny. | contradiction | (![X]:((strong(X)<~>~strong(X))<=>(generous(X)<~>creative(X))))&
(((brave(paul)|~quiet(paul)))<=>(?[X]:((~old(X)&~calm(X)))))&
((kind(alice))<=>(?[X]:((kind(X)&calm(X)))))&
((wise(alice))=>((~happy(lucy)|~patient(lucy))))&
((?[X]:(rich(X)))<=>(?[X]:((~quiet(X)&~generous(X)))))&
(![X]:(~old(X)<=>(creative(X)&~tall(X))))&
(![X]:(~creative(X)=>(~wise(X)<~>quiet(X))))&
(![X]:((~brave(X)<~>brave(X))<=>strong(X)))&
(![X]:(~rich(X)<=>(~strong(X)&strong(X))))&
((?[X]:((~happy(X)&~tall(X))))<=>(tall(paul)))&
(![X]:((~brave(X)&patient(X))<=>(humble(X)<~>~rich(X))))&
(![X]:(~funny(X)<=>~strong(X)))&
(![X]:((quiet(X)<~>~tall(X))<=>~generous(X)))&
(![X]:((patient(X)|happy(X))=>(~happy(X)&~funny(X))))&
(((~quiet(alice)<~>~tall(alice)))=>((~humble(susan)|~happy(susan))))&
(?[X]:(creative(X)))&
(?[X]:((happy(X)|generous(X))))&
(?[X]:(kind(X)))&
((~quiet(paul)&~patient(paul)))&
((humble(john)|quiet(john)))&
(?[X]:((calm(X)<~>~quiet(X)))) | ~funny(paul) | [
"p7",
"p11",
"hypothesis"
]
| % SZS status Unsatisfiable for 4452079466870332389567910
% SZS output start Proof for 4452079466870332389567910
8. ! [X0] : ((~brave(X0) <~> brave(X0)) <=> strong(X0)) [input p7]
12. ! [X0] : (~funny(X0) <=> ~strong(X0)) [input p11]
22. ~funny(paul) [input hypothesis]
24. ! [X0] : (~funny(X0) => ~strong(X0)) [unused predicate definition removal 12]
28. ! [X0] : (~strong(X0) | funny(X0)) [ennf transformation 24]
50. ! [X0] : ((((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~strong(X0)) & (strong(X0) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0))))) [nnf transformation 8]
95. strong(X0) | brave(X0) | brave(X0) [cnf transformation 50]
96. strong(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 50]
111. ~strong(X0) | funny(X0) [cnf transformation 28]
130. ~funny(paul) [cnf transformation 22]
132. strong(X0) | brave(X0) [duplicate literal removal 95]
133. strong(X0) | ~brave(X0) [duplicate literal removal 96]
216. strong(X0) [subsumption resolution 132,133]
239. funny(X0) [subsumption resolution 111,216]
263. $false [subsumption resolution 130,239]
% SZS output end Proof for 4452079466870332389567910
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise or happy is both curious and not kind and vice versa.
If john is not brave or not rich then susan is either calm or kind and vice versa.
Everyone who is either brave or quiet is wise or calm and vice versa.
Everyone who is both not happy and not kind is creative or not brave and vice versa.
Everyone who is not curious or creative is calm and vice versa.
Everyone who is both calm and creative is not creative or not old.
Everyone who is both not humble and quiet is patient and vice versa.
Everyone who is strong is patient or not old and vice versa.
If someone is both not tall and happy then alice is rich or strong and vice versa.
Everyone who is not humble is not old or not happy.
If someone is both creative and happy then john is either happy or not curious and vice versa.
If john is brave then someone is not strong or kind.
If someone is both kind and rich then someone is either kind or happy.
Everyone who is both not strong and not tall is either not humble or curious.
If alice is old or rich then someone is rich and vice versa.
Everyone who is funny or not wise is not strong or kind.
Someone is both kind and not funny.
Someone is both old and calm.
Someone is not quiet.
Paul is not rich or not happy.
Susan is not brave or wise.
Someone is either curious or not quiet.
Someone is either not rich or not happy. | Paul is calm. | neutral | (![X]:((wise(X)<~>happy(X))<=>(curious(X)&~kind(X))))&
(((~brave(john)|~rich(john)))<=>((calm(susan)<~>kind(susan))))&
(![X]:((brave(X)<~>quiet(X))<=>(wise(X)|calm(X))))&
(![X]:((~happy(X)&~kind(X))<=>(creative(X)|~brave(X))))&
(![X]:((~curious(X)|creative(X))<=>calm(X)))&
(![X]:((calm(X)&creative(X))=>(~creative(X)|~old(X))))&
(![X]:((~humble(X)&quiet(X))<=>patient(X)))&
(![X]:(strong(X)<=>(patient(X)|~old(X))))&
((?[X]:((~tall(X)&happy(X))))<=>((rich(alice)|strong(alice))))&
(![X]:(~humble(X)=>(~old(X)|~happy(X))))&
((?[X]:((creative(X)&happy(X))))<=>((happy(john)<~>~curious(john))))&
((brave(john))=>(?[X]:((~strong(X)|kind(X)))))&
((?[X]:((kind(X)&rich(X))))=>(?[X]:((kind(X)<~>happy(X)))))&
(![X]:((~strong(X)&~tall(X))=>(~humble(X)<~>curious(X))))&
(((old(alice)|rich(alice)))<=>(?[X]:(rich(X))))&
(![X]:((funny(X)|~wise(X))=>(~strong(X)|kind(X))))&
(?[X]:((kind(X)&~funny(X))))&
(?[X]:((old(X)&calm(X))))&
(?[X]:(~quiet(X)))&
((~rich(paul)|~happy(paul)))&
((~brave(susan)|wise(susan)))&
(?[X]:((curious(X)<~>~quiet(X))))&
(?[X]:((~rich(X)<~>~happy(X)))) | calm(paul) | []
| null | 0 |
If someone is not calm or not happy then someone is both not funny and creative.
If lucy is humble then susan is happy and vice versa.
Everyone who is not rich or humble is either creative or not rich.
If someone is either strong or not calm then someone is either rich or humble and vice versa.
If alice is quiet then alice is creative or quiet and vice versa.
Everyone who is either not curious or curious is both happy and wise.
If someone is both not funny and wise then john is not rich and vice versa.
If someone is either not patient or not tall then someone is both not tall and brave.
Everyone who is not quiet is not creative and vice versa.
If someone is either humble or not generous then mary is strong and vice versa.
Everyone who is creative is either funny or quiet and vice versa.
Everyone who is both not brave and generous is not patient or tall and vice versa.
Everyone who is either generous or not humble is old.
Everyone who is both generous and wise is both not old and patient and vice versa.
If john is both tall and not happy then mary is either kind or not generous and vice versa.
If fred is creative then someone is not curious.
John is brave.
Someone is either not quiet or not kind.
Someone is quiet.
Someone is humble or wise.
Fred is either not wise or not rich.
Fred is not kind or happy. | Mary is patient. | entailment | ((?[X]:((~calm(X)|~happy(X))))=>(?[X]:((~funny(X)&creative(X)))))&
((humble(lucy))<=>(happy(susan)))&
(![X]:((~rich(X)|humble(X))=>(creative(X)<~>~rich(X))))&
((?[X]:((strong(X)<~>~calm(X))))<=>(?[X]:((rich(X)<~>humble(X)))))&
((quiet(alice))<=>((creative(alice)|quiet(alice))))&
(![X]:((~curious(X)<~>curious(X))=>(happy(X)&wise(X))))&
((?[X]:((~funny(X)&wise(X))))<=>(~rich(john)))&
((?[X]:((~patient(X)<~>~tall(X))))=>(?[X]:((~tall(X)&brave(X)))))&
(![X]:(~quiet(X)<=>~creative(X)))&
((?[X]:((humble(X)<~>~generous(X))))<=>(strong(mary)))&
(![X]:(creative(X)<=>(funny(X)<~>quiet(X))))&
(![X]:((~brave(X)&generous(X))<=>(~patient(X)|tall(X))))&
(![X]:((generous(X)<~>~humble(X))=>old(X)))&
(![X]:((generous(X)&wise(X))<=>(~old(X)&patient(X))))&
(((tall(john)&~happy(john)))<=>((kind(mary)<~>~generous(mary))))&
((creative(fred))=>(?[X]:(~curious(X))))&
(brave(john))&
(?[X]:((~quiet(X)<~>~kind(X))))&
(?[X]:(quiet(X)))&
(?[X]:((humble(X)|wise(X))))&
((~wise(fred)<~>~rich(fred)))&
((~kind(fred)|happy(fred))) | patient(mary) | [
"p5",
"p11",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 4225116726174760296360673
% SZS output start Proof for 4225116726174760296360673
6. ! [X0] : ((~curious(X0) <~> curious(X0)) => (wise(X0) & happy(X0))) [input p5]
12. ! [X0] : ((generous(X0) & ~brave(X0)) <=> (tall(X0) | ~patient(X0))) [input p11]
14. ! [X0] : ((wise(X0) & generous(X0)) <=> (patient(X0) & ~old(X0))) [input p13]
23. ~patient(mary) [input hypothesis]
29. ! [X0] : ((wise(X0) & happy(X0)) | (~curious(X0) <=> curious(X0))) [ennf transformation 6]
45. ! [X0] : ((wise(X0) & happy(X0)) | ((~curious(X0) | ~curious(X0)) & (curious(X0) | curious(X0)))) [nnf transformation 29]
60. ! [X0] : (((generous(X0) & ~brave(X0)) | (~tall(X0) & patient(X0))) & ((tall(X0) | ~patient(X0)) | (~generous(X0) | brave(X0)))) [nnf transformation 12]
61. ! [X0] : (((generous(X0) & ~brave(X0)) | (~tall(X0) & patient(X0))) & (tall(X0) | ~patient(X0) | ~generous(X0) | brave(X0))) [flattening 60]
63. ! [X0] : (((wise(X0) & generous(X0)) | (~patient(X0) | old(X0))) & ((patient(X0) & ~old(X0)) | (~wise(X0) | ~generous(X0)))) [nnf transformation 14]
64. ! [X0] : (((wise(X0) & generous(X0)) | ~patient(X0) | old(X0)) & ((patient(X0) & ~old(X0)) | ~wise(X0) | ~generous(X0))) [flattening 63]
100. wise(X0) | curious(X0) | curious(X0) [cnf transformation 45]
101. wise(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
122. generous(X0) | patient(X0) [cnf transformation 61]
127. patient(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 64]
145. ~patient(mary) [cnf transformation 23]
148. wise(X0) | curious(X0) [duplicate literal removal 100]
149. wise(X0) | ~curious(X0) [duplicate literal removal 101]
224. wise(X0) [subsumption resolution 148,149]
284. patient(X0) | ~generous(X0) [subsumption resolution 127,224]
285. patient(X0) [subsumption resolution 284,122]
338. $false [subsumption resolution 145,285]
% SZS output end Proof for 4225116726174760296360673
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or wise is happy and vice versa. Everyone who is tall or not humble is happy or not humble and vice versa. If mary is both brave and not creative then someone is both funny and not rich and vice versa. If someone is either not strong or calm then someone is both not funny and not creative and vice versa. Everyone who is either patient or strong is kind and vice versa. If john is rich or not happy then alice is kind. If mary is either creative or tall then someone is kind and vice versa. Everyone who is either not happy or rich is either not humble or curious. Everyone who is funny is patient. Everyone who is calm or quiet is not curious and vice versa. If lucy is both not wise and quiet then someone is either generous or brave and vice versa. If someone is either not generous or brave then paul is not quiet or wise and vice versa. Everyone who is both not generous and not humble is not old or quiet and vice versa. Everyone who is patient or brave is both generous and not calm and vice versa. If someone is either calm or not kind then someone is not quiet. Everyone who is generous or patient is both brave and not old. Someone is not rich or quiet. Someone is either not humble or not curious. Someone is both not calm and old. Susan is not creative or strong. Paul is not brave. John is not generous or rich. Paul is both old and not creative. Paul is not funny or not calm. | Susan is wise. | entailment | (![X]:((~happy(X)<~>wise(X))<=>happy(X)))&
(![X]:((tall(X)|~humble(X))<=>(happy(X)|~humble(X))))&
(((brave(mary)&~creative(mary)))<=>(?[X]:((funny(X)&~rich(X)))))&
((?[X]:((~strong(X)<~>calm(X))))<=>(?[X]:((~funny(X)&~creative(X)))))&
(![X]:((patient(X)<~>strong(X))<=>kind(X)))&
(((rich(john)|~happy(john)))=>(kind(alice)))&
(((creative(mary)<~>tall(mary)))<=>(?[X]:(kind(X))))&
(![X]:((~happy(X)<~>rich(X))=>(~humble(X)<~>curious(X))))&
(![X]:(funny(X)=>patient(X)))&
(![X]:((calm(X)|quiet(X))<=>~curious(X)))&
(((~wise(lucy)&quiet(lucy)))<=>(?[X]:((generous(X)<~>brave(X)))))&
((?[X]:((~generous(X)<~>brave(X))))<=>((~quiet(paul)|wise(paul))))&
(![X]:((~generous(X)&~humble(X))<=>(~old(X)|quiet(X))))&
(![X]:((patient(X)|brave(X))<=>(generous(X)&~calm(X))))&
((?[X]:((calm(X)<~>~kind(X))))=>(?[X]:(~quiet(X))))&
(![X]:((generous(X)|patient(X))=>(brave(X)&~old(X))))&
(?[X]:((~rich(X)|quiet(X))))&
(?[X]:((~humble(X)<~>~curious(X))))&
(?[X]:((~calm(X)&old(X))))&
((~creative(susan)|strong(susan)))&
(~brave(paul))&
((~generous(john)|rich(john)))&
((old(paul)&~creative(paul)))&
((~funny(paul)|~calm(paul))) | wise(susan) | [
"p0",
"hypothesis"
]
| % SZS status Unsatisfiable for 3415863706235795741405511
% SZS output start Proof for 3415863706235795741405511
1. ! [X0] : ((~happy(X0) <~> wise(X0)) <=> happy(X0)) [input p0]
25. ~wise(susan) [input hypothesis]
33. ! [X0] : ((((~wise(X0) | happy(X0)) & (wise(X0) | ~happy(X0))) | ~happy(X0)) & (happy(X0) | ((~happy(X0) | ~wise(X0)) & (wise(X0) | happy(X0))))) [nnf transformation 1]
79. happy(X0) | wise(X0) | happy(X0) [cnf transformation 33]
81. wise(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 33]
154. ~wise(susan) [cnf transformation 25]
155. happy(X0) | wise(X0) [duplicate literal removal 79]
156. wise(X0) | ~happy(X0) [duplicate literal removal 81]
157. wise(X0) [subsumption resolution 155,156]
326. $false [subsumption resolution 154,157]
% SZS output end Proof for 3415863706235795741405511
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or not wise then someone is either strong or funny and vice versa.
If mary is old or strong then fred is either not quiet or creative and vice versa.
Everyone who is humble or not kind is both creative and happy.
If someone is not tall or not funny then john is calm and vice versa.
Everyone who is either not kind or curious is kind and vice versa.
If alice is quiet or old then someone is either not creative or not calm.
If mary is not curious or not wise then someone is either not generous or not wise.
Everyone who is both not rich and not generous is rich or tall.
Everyone who is tall is creative and vice versa.
Everyone who is both wise and not tall is either not tall or strong and vice versa.
Everyone who is not generous is patient and vice versa.
If someone is both humble and not patient then someone is both kind and not old.
Everyone who is either not generous or tall is brave and vice versa.
Everyone who is either not kind or quiet is both not brave and calm.
If someone is either patient or generous then someone is not patient and vice versa.
If someone is either not humble or generous then alice is not calm or happy and vice versa.
John is either happy or not rich.
Someone is generous or not rich.
Someone is both funny and not tall.
Someone is old.
Alice is both curious and not brave.
Fred is both not calm and not quiet. | Mary is not creative. | neutral | ((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((strong(X)<~>funny(X)))))&
(((old(mary)|strong(mary)))<=>((~quiet(fred)<~>creative(fred))))&
(![X]:((humble(X)|~kind(X))=>(creative(X)&happy(X))))&
((?[X]:((~tall(X)|~funny(X))))<=>(calm(john)))&
(![X]:((~kind(X)<~>curious(X))<=>kind(X)))&
(((quiet(alice)|old(alice)))=>(?[X]:((~creative(X)<~>~calm(X)))))&
(((~curious(mary)|~wise(mary)))=>(?[X]:((~generous(X)<~>~wise(X)))))&
(![X]:((~rich(X)&~generous(X))=>(rich(X)|tall(X))))&
(![X]:(tall(X)<=>creative(X)))&
(![X]:((wise(X)&~tall(X))<=>(~tall(X)<~>strong(X))))&
(![X]:(~generous(X)<=>patient(X)))&
((?[X]:((humble(X)&~patient(X))))=>(?[X]:((kind(X)&~old(X)))))&
(![X]:((~generous(X)<~>tall(X))<=>brave(X)))&
(![X]:((~kind(X)<~>quiet(X))=>(~brave(X)&calm(X))))&
((?[X]:((patient(X)<~>generous(X))))<=>(?[X]:(~patient(X))))&
((?[X]:((~humble(X)<~>generous(X))))<=>((~calm(alice)|happy(alice))))&
((happy(john)<~>~rich(john)))&
(?[X]:((generous(X)|~rich(X))))&
(?[X]:((funny(X)&~tall(X))))&
(?[X]:(old(X)))&
((curious(alice)&~brave(alice)))&
((~calm(fred)&~quiet(fred))) | ~creative(mary) | []
| null | 0 |
If mary is not calm then someone is old.
Everyone who is not quiet or not humble is wise and vice versa.
If paul is either old or happy then lucy is not generous or kind.
If someone is old then someone is not happy.
If alice is either curious or generous then someone is funny and vice versa.
Everyone who is both not creative and not rich is kind and vice versa.
If someone is not curious or not quiet then someone is not happy.
If paul is both curious and kind then fred is not kind.
Everyone who is not funny is either not strong or tall and vice versa.
Everyone who is not funny is either not patient or not rich and vice versa.
If someone is not humble or kind then someone is happy or calm and vice versa.
Everyone who is not curious or happy is either not calm or happy and vice versa.
If mary is either not brave or patient then someone is both not kind and not rich.
Everyone who is quiet is wise and vice versa.
If alice is both calm and humble then alice is either not happy or not strong and vice versa.
Everyone who is brave is quiet or generous and vice versa.
Fred is both not funny and old.
Someone is not brave or patient.
Someone is wise or not kind.
Someone is not funny.
Fred is both not funny and not happy.
John is either funny or not humble.
John is patient.
Lucy is both strong and not funny. | Paul is brave. | entailment | ((~calm(mary))=>(?[X]:(old(X))))&
(![X]:((~quiet(X)|~humble(X))<=>wise(X)))&
(((old(paul)<~>happy(paul)))=>((~generous(lucy)|kind(lucy))))&
((?[X]:(old(X)))=>(?[X]:(~happy(X))))&
(((curious(alice)<~>generous(alice)))<=>(?[X]:(funny(X))))&
(![X]:((~creative(X)&~rich(X))<=>kind(X)))&
((?[X]:((~curious(X)|~quiet(X))))=>(?[X]:(~happy(X))))&
(((curious(paul)&kind(paul)))=>(~kind(fred)))&
(![X]:(~funny(X)<=>(~strong(X)<~>tall(X))))&
(![X]:(~funny(X)<=>(~patient(X)<~>~rich(X))))&
((?[X]:((~humble(X)|kind(X))))<=>(?[X]:((happy(X)|calm(X)))))&
(![X]:((~curious(X)|happy(X))<=>(~calm(X)<~>happy(X))))&
(((~brave(mary)<~>patient(mary)))=>(?[X]:((~kind(X)&~rich(X)))))&
(![X]:(quiet(X)<=>wise(X)))&
(((calm(alice)&humble(alice)))<=>((~happy(alice)<~>~strong(alice))))&
(![X]:(brave(X)<=>(quiet(X)|generous(X))))&
((~funny(fred)&old(fred)))&
(?[X]:((~brave(X)|patient(X))))&
(?[X]:((wise(X)|~kind(X))))&
(?[X]:(~funny(X)))&
((~funny(fred)&~happy(fred)))&
((funny(john)<~>~humble(john)))&
(patient(john))&
((strong(lucy)&~funny(lucy))) | brave(paul) | [
"p1",
"p13",
"p15",
"hypothesis"
]
| % SZS status Unsatisfiable for 5719079805537435844884106
% SZS output start Proof for 5719079805537435844884106
2. ! [X0] : ((~humble(X0) | ~quiet(X0)) <=> wise(X0)) [input p1]
14. ! [X0] : (quiet(X0) <=> wise(X0)) [input p13]
16. ! [X0] : (brave(X0) <=> (generous(X0) | quiet(X0))) [input p15]
25. ~brave(paul) [input hypothesis]
39. ! [X0] : (((~humble(X0) | ~quiet(X0)) | ~wise(X0)) & (wise(X0) | (humble(X0) & quiet(X0)))) [nnf transformation 2]
40. ! [X0] : ((~humble(X0) | ~quiet(X0) | ~wise(X0)) & (wise(X0) | (humble(X0) & quiet(X0)))) [flattening 39]
66. ! [X0] : ((quiet(X0) | ~wise(X0)) & (wise(X0) | ~quiet(X0))) [nnf transformation 14]
69. ! [X0] : ((brave(X0) | (~generous(X0) & ~quiet(X0))) & ((generous(X0) | quiet(X0)) | ~brave(X0))) [nnf transformation 16]
70. ! [X0] : ((brave(X0) | (~generous(X0) & ~quiet(X0))) & (generous(X0) | quiet(X0) | ~brave(X0))) [flattening 69]
79. wise(X0) | quiet(X0) [cnf transformation 40]
118. quiet(X0) | ~wise(X0) [cnf transformation 66]
126. ~quiet(X0) | brave(X0) [cnf transformation 70]
140. ~brave(paul) [cnf transformation 25]
198. 13 <=> ! [X1] : quiet(X1) [avatar definition]
199. quiet(X1) <- (13) [avatar component clause 198]
274. quiet(X0) [subsumption resolution 118,79]
275. 13 [avatar split clause 274,198]
319. brave(X0) <- (13) [resolution 126,199]
320. $false <- (13) [resolution 319,140]
325. ~13 [avatar contradiction clause 320]
326. $false [avatar sat refutation 275,325]
% SZS output end Proof for 5719079805537435844884106
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and not generous is not funny or creative and vice versa.
If someone is not patient then lucy is tall or kind.
Everyone who is not creative or not kind is either not generous or not funny.
Everyone who is either funny or brave is both not old and not quiet and vice versa.
Everyone who is not calm is both generous and not tall.
Everyone who is either not kind or not generous is both not rich and not quiet and vice versa.
Everyone who is both calm and rich is either patient or calm.
Everyone who is not creative is curious or wise and vice versa.
Everyone who is either not creative or not old is either kind or not rich and vice versa.
Everyone who is either generous or happy is both funny and not happy.
Everyone who is humble is either not wise or not patient.
If someone is either not happy or old then someone is not tall or not wise and vice versa.
If someone is calm or not tall then mary is not calm or humble and vice versa.
Everyone who is either not strong or not quiet is both calm and not humble and vice versa.
Everyone who is creative or strong is not tall and vice versa.
Someone is old.
Fred is either not patient or happy.
Paul is either patient or not quiet.
Lucy is either kind or brave.
Someone is not old or calm. | Lucy is funny. | neutral | (![X]:((~quiet(X)&~generous(X))<=>(~funny(X)|creative(X))))&
((?[X]:(~patient(X)))=>((tall(lucy)|kind(lucy))))&
(![X]:((~creative(X)|~kind(X))=>(~generous(X)<~>~funny(X))))&
(![X]:((funny(X)<~>brave(X))<=>(~old(X)&~quiet(X))))&
(![X]:(~calm(X)=>(generous(X)&~tall(X))))&
(![X]:((~kind(X)<~>~generous(X))<=>(~rich(X)&~quiet(X))))&
(![X]:((calm(X)&rich(X))=>(patient(X)<~>calm(X))))&
(![X]:(~creative(X)<=>(curious(X)|wise(X))))&
(![X]:((~creative(X)<~>~old(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((generous(X)<~>happy(X))=>(funny(X)&~happy(X))))&
(![X]:(humble(X)=>(~wise(X)<~>~patient(X))))&
((?[X]:((~happy(X)<~>old(X))))<=>(?[X]:((~tall(X)|~wise(X)))))&
((?[X]:((calm(X)|~tall(X))))<=>((~calm(mary)|humble(mary))))&
(![X]:((~strong(X)<~>~quiet(X))<=>(calm(X)&~humble(X))))&
(![X]:((creative(X)|strong(X))<=>~tall(X)))&
(?[X]:(old(X)))&
((~patient(fred)<~>happy(fred)))&
((patient(paul)<~>~quiet(paul)))&
((kind(lucy)<~>brave(lucy)))&
(?[X]:((~old(X)|calm(X)))) | funny(lucy) | []
| null | 0 |
If mary is not brave then mary is either tall or kind and vice versa.
Everyone who is not old is kind or old and vice versa.
Everyone who is quiet or happy is either patient or old and vice versa.
If fred is either tall or humble then susan is kind or brave and vice versa.
Everyone who is both not rich and quiet is either strong or not curious and vice versa.
If lucy is funny then paul is tall.
If someone is generous then lucy is both not generous and brave.
Everyone who is either old or kind is happy and vice versa.
Everyone who is either curious or not rich is either brave or not wise and vice versa.
If fred is not humble or not patient then someone is not curious or not tall.
Everyone who is both quiet and tall is either calm or quiet and vice versa.
Everyone who is either funny or strong is either not patient or humble.
If someone is not curious then lucy is both quiet and wise and vice versa.
If someone is both not rich and not strong then someone is either happy or not kind.
Everyone who is both happy and not old is not patient or calm.
Everyone who is both not brave and not generous is either not curious or happy.
Susan is not kind or not old.
Someone is both rich and not curious.
Someone is brave.
Someone is creative or generous.
Paul is either funny or not wise. | Mary is calm. | entailment | ((~brave(mary))<=>((tall(mary)<~>kind(mary))))&
(![X]:(~old(X)<=>(kind(X)|old(X))))&
(![X]:((quiet(X)|happy(X))<=>(patient(X)<~>old(X))))&
(((tall(fred)<~>humble(fred)))<=>((kind(susan)|brave(susan))))&
(![X]:((~rich(X)&quiet(X))<=>(strong(X)<~>~curious(X))))&
((funny(lucy))=>(tall(paul)))&
((?[X]:(generous(X)))=>((~generous(lucy)&brave(lucy))))&
(![X]:((old(X)<~>kind(X))<=>happy(X)))&
(![X]:((curious(X)<~>~rich(X))<=>(brave(X)<~>~wise(X))))&
(((~humble(fred)|~patient(fred)))=>(?[X]:((~curious(X)|~tall(X)))))&
(![X]:((quiet(X)&tall(X))<=>(calm(X)<~>quiet(X))))&
(![X]:((funny(X)<~>strong(X))=>(~patient(X)<~>humble(X))))&
((?[X]:(~curious(X)))<=>((quiet(lucy)&wise(lucy))))&
((?[X]:((~rich(X)&~strong(X))))=>(?[X]:((happy(X)<~>~kind(X)))))&
(![X]:((happy(X)&~old(X))=>(~patient(X)|calm(X))))&
(![X]:((~brave(X)&~generous(X))=>(~curious(X)<~>happy(X))))&
((~kind(susan)|~old(susan)))&
(?[X]:((rich(X)&~curious(X))))&
(?[X]:(brave(X)))&
(?[X]:((creative(X)|generous(X))))&
((funny(paul)<~>~wise(paul))) | calm(mary) | [
"p1",
"p2",
"p7",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 7355405545270590132991265
% SZS output start Proof for 7355405545270590132991265
2. ! [X0] : (~old(X0) <=> (old(X0) | kind(X0))) [input p1]
3. ! [X0] : ((happy(X0) | quiet(X0)) <=> (patient(X0) <~> old(X0))) [input p2]
8. ! [X0] : ((old(X0) <~> kind(X0)) <=> happy(X0)) [input p7]
15. ! [X0] : ((~old(X0) & happy(X0)) => (calm(X0) | ~patient(X0))) [input p14]
22. ~calm(mary) [input hypothesis]
30. ! [X0] : ((calm(X0) | ~patient(X0)) | (old(X0) | ~happy(X0))) [ennf transformation 15]
31. ! [X0] : (calm(X0) | ~patient(X0) | old(X0) | ~happy(X0)) [flattening 30]
35. ! [X0] : ((~old(X0) | (~old(X0) & ~kind(X0))) & ((old(X0) | kind(X0)) | old(X0))) [nnf transformation 2]
36. ! [X0] : ((~old(X0) | (~old(X0) & ~kind(X0))) & (old(X0) | kind(X0) | old(X0))) [flattening 35]
37. ! [X0] : (((happy(X0) | quiet(X0)) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~happy(X0) & ~quiet(X0)))) [nnf transformation 3]
38. ! [X0] : ((happy(X0) | quiet(X0) | ((patient(X0) | ~old(X0)) & (old(X0) | ~patient(X0)))) & (((~old(X0) | ~patient(X0)) & (old(X0) | patient(X0))) | (~happy(X0) & ~quiet(X0)))) [flattening 37]
43. ! [X0] : ((((~kind(X0) | ~old(X0)) & (kind(X0) | old(X0))) | ~happy(X0)) & (happy(X0) | ((old(X0) | ~kind(X0)) & (kind(X0) | ~old(X0))))) [nnf transformation 8]
69. old(X0) | kind(X0) | old(X0) [cnf transformation 36]
71. ~old(X0) | ~old(X0) [cnf transformation 36]
73. old(X0) | patient(X0) | ~happy(X0) [cnf transformation 38]
94. happy(X0) | old(X0) | ~kind(X0) [cnf transformation 43]
122. calm(X0) | ~patient(X0) | old(X0) | ~happy(X0) [cnf transformation 31]
131. ~calm(mary) [cnf transformation 22]
134. old(X0) | kind(X0) [duplicate literal removal 69]
135. ~old(X0) [duplicate literal removal 71]
152. kind(X0) [subsumption resolution 134,135]
154. ~happy(X0) | patient(X0) [subsumption resolution 73,135]
196. happy(X0) | ~kind(X0) [subsumption resolution 94,135]
197. happy(X0) [subsumption resolution 196,152]
231. calm(X0) | ~patient(X0) | ~happy(X0) [subsumption resolution 122,135]
232. ~patient(X0) | calm(X0) [subsumption resolution 231,197]
246. patient(X0) [resolution 154,197]
248. calm(X0) [resolution 232,246]
249. $false [resolution 248,131]
% SZS output end Proof for 7355405545270590132991265
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or not strong then susan is both not curious and patient. Everyone who is not happy is creative. If lucy is both not old and not funny then someone is either humble or not curious and vice versa. Everyone who is both wise and brave is either funny or rich and vice versa. Everyone who is both patient and curious is generous and vice versa. Everyone who is calm is creative and vice versa. Everyone who is both not calm and not humble is both wise and not curious and vice versa. Everyone who is both not strong and old is both curious and not happy. Everyone who is not wise or not curious is not old and vice versa. Everyone who is generous or not strong is either curious or wise. If someone is calm or not generous then john is happy or brave. Everyone who is old is brave or not generous. Everyone who is either quiet or not creative is not humble or not curious and vice versa. If someone is not tall then someone is funny or not rich and vice versa. If someone is generous then someone is either humble or calm. If someone is both not tall and old then alice is not curious and vice versa. Mary is either not happy or happy. Someone is either not old or not tall. Someone is either not rich or kind. Someone is not patient. Someone is both not calm and not quiet. Someone is either patient or calm. Someone is either not patient or generous. Lucy is both not wise and not tall. | Alice is curious. | neutral | ((?[X]:((~wise(X)|~strong(X))))=>((~curious(susan)&patient(susan))))&
(![X]:(~happy(X)=>creative(X)))&
(((~old(lucy)&~funny(lucy)))<=>(?[X]:((humble(X)<~>~curious(X)))))&
(![X]:((wise(X)&brave(X))<=>(funny(X)<~>rich(X))))&
(![X]:((patient(X)&curious(X))<=>generous(X)))&
(![X]:(calm(X)<=>creative(X)))&
(![X]:((~calm(X)&~humble(X))<=>(wise(X)&~curious(X))))&
(![X]:((~strong(X)&old(X))=>(curious(X)&~happy(X))))&
(![X]:((~wise(X)|~curious(X))<=>~old(X)))&
(![X]:((generous(X)|~strong(X))=>(curious(X)<~>wise(X))))&
((?[X]:((calm(X)|~generous(X))))=>((happy(john)|brave(john))))&
(![X]:(old(X)=>(brave(X)|~generous(X))))&
(![X]:((quiet(X)<~>~creative(X))<=>(~humble(X)|~curious(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((funny(X)|~rich(X)))))&
((?[X]:(generous(X)))=>(?[X]:((humble(X)<~>calm(X)))))&
((?[X]:((~tall(X)&old(X))))<=>(~curious(alice)))&
((~happy(mary)<~>happy(mary)))&
(?[X]:((~old(X)<~>~tall(X))))&
(?[X]:((~rich(X)<~>kind(X))))&
(?[X]:(~patient(X)))&
(?[X]:((~calm(X)&~quiet(X))))&
(?[X]:((patient(X)<~>calm(X))))&
(?[X]:((~patient(X)<~>generous(X))))&
((~wise(lucy)&~tall(lucy))) | curious(alice) | []
| null | 0 |
Everyone who is not quiet or not patient is not happy and vice versa. Everyone who is not curious or not calm is not brave. Everyone who is either humble or not patient is both not rich and old. If someone is both not quiet and rich then someone is humble and vice versa. Everyone who is both not kind and not brave is rich. If someone is either brave or patient then someone is not curious. Everyone who is both funny and not kind is both tall and creative and vice versa. Everyone who is patient is brave or wise. Everyone who is kind is either kind or calm. Everyone who is not happy or funny is both not creative and not tall. If mary is both tall and calm then paul is either old or not wise. If john is generous then someone is both not creative and old and vice versa. If someone is both tall and not quiet then someone is brave or calm. Everyone who is both not tall and happy is both brave and rich and vice versa. Everyone who is both not brave and patient is not tall and vice versa. Everyone who is either brave or not humble is quiet or calm. Fred is both not quiet and kind. Someone is either not strong or not generous. Susan is brave or quiet. Alice is not old. Someone is both not calm and not funny. Someone is humble. John is kind or not old. Mary is not happy or happy. | John is not creative. | entailment | (![X]:((~quiet(X)|~patient(X))<=>~happy(X)))&
(![X]:((~curious(X)|~calm(X))=>~brave(X)))&
(![X]:((humble(X)<~>~patient(X))=>(~rich(X)&old(X))))&
((?[X]:((~quiet(X)&rich(X))))<=>(?[X]:(humble(X))))&
(![X]:((~kind(X)&~brave(X))=>rich(X)))&
((?[X]:((brave(X)<~>patient(X))))=>(?[X]:(~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(tall(X)&creative(X))))&
(![X]:(patient(X)=>(brave(X)|wise(X))))&
(![X]:(kind(X)=>(kind(X)<~>calm(X))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)&~tall(X))))&
(((tall(mary)&calm(mary)))=>((old(paul)<~>~wise(paul))))&
((generous(john))<=>(?[X]:((~creative(X)&old(X)))))&
((?[X]:((tall(X)&~quiet(X))))=>(?[X]:((brave(X)|calm(X)))))&
(![X]:((~tall(X)&happy(X))<=>(brave(X)&rich(X))))&
(![X]:((~brave(X)&patient(X))<=>~tall(X)))&
(![X]:((brave(X)<~>~humble(X))=>(quiet(X)|calm(X))))&
((~quiet(fred)&kind(fred)))&
(?[X]:((~strong(X)<~>~generous(X))))&
((brave(susan)|quiet(susan)))&
(~old(alice))&
(?[X]:((~calm(X)&~funny(X))))&
(?[X]:(humble(X)))&
((kind(john)|~old(john)))&
((~happy(mary)|happy(mary))) | ~creative(john) | [
"p6",
"p9",
"p13",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 5463107984220366637168438
% SZS output start Proof for 5463107984220366637168438
7. ! [X0] : ((~kind(X0) & funny(X0)) <=> (creative(X0) & tall(X0))) [input p6]
10. ! [X0] : ((funny(X0) | ~happy(X0)) => (~tall(X0) & ~creative(X0))) [input p9]
14. ! [X0] : ((happy(X0) & ~tall(X0)) <=> (rich(X0) & brave(X0))) [input p13]
15. ! [X0] : ((patient(X0) & ~brave(X0)) <=> ~tall(X0)) [input p14]
25. creative(john) [input hypothesis]
37. ! [X0] : ((~tall(X0) & ~creative(X0)) | (~funny(X0) & happy(X0))) [ennf transformation 10]
55. ! [X0] : (((~kind(X0) & funny(X0)) | (~creative(X0) | ~tall(X0))) & ((creative(X0) & tall(X0)) | (kind(X0) | ~funny(X0)))) [nnf transformation 7]
56. ! [X0] : (((~kind(X0) & funny(X0)) | ~creative(X0) | ~tall(X0)) & ((creative(X0) & tall(X0)) | kind(X0) | ~funny(X0))) [flattening 55]
66. ! [X0] : (((happy(X0) & ~tall(X0)) | (~rich(X0) | ~brave(X0))) & ((rich(X0) & brave(X0)) | (~happy(X0) | tall(X0)))) [nnf transformation 14]
67. ! [X0] : (((happy(X0) & ~tall(X0)) | ~rich(X0) | ~brave(X0)) & ((rich(X0) & brave(X0)) | ~happy(X0) | tall(X0))) [flattening 66]
68. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | (~patient(X0) | brave(X0)))) [nnf transformation 15]
69. ! [X0] : (((patient(X0) & ~brave(X0)) | tall(X0)) & (~tall(X0) | ~patient(X0) | brave(X0))) [flattening 68]
95. ~creative(X0) | funny(X0) | ~tall(X0) [cnf transformation 56]
100. ~creative(X0) | happy(X0) [cnf transformation 37]
101. ~creative(X0) | ~funny(X0) [cnf transformation 37]
110. ~happy(X0) | brave(X0) | tall(X0) [cnf transformation 67]
115. ~brave(X0) | tall(X0) [cnf transformation 69]
130. creative(john) [cnf transformation 25]
241. happy(john) [resolution 100,130]
242. ~funny(john) [resolution 101,130]
293. funny(john) | ~tall(john) [resolution 95,130]
296. ~tall(john) [subsumption resolution 293,242]
311. 28 <=> brave(john) [avatar definition]
313. brave(john) <- (28) [avatar component clause 311]
327. brave(john) | tall(john) [resolution 110,241]
329. brave(john) [subsumption resolution 327,296]
330. 28 [avatar split clause 329,311]
456. tall(john) <- (28) [resolution 313,115]
459. $false <- (28) [subsumption resolution 456,296]
460. ~28 [avatar contradiction clause 459]
461. $false [avatar sat refutation 330,460]
% SZS output end Proof for 5463107984220366637168438
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny or patient is either kind or quiet. Everyone who is either happy or not strong is both not calm and not kind and vice versa. If mary is not rich then alice is either strong or not curious. Everyone who is both humble and not funny is happy or creative. If paul is not kind or old then someone is not calm or not wise. If john is both not generous and kind then alice is brave and vice versa. If alice is either not creative or patient then someone is wise or not humble and vice versa. Everyone who is either not curious or old is either tall or not brave and vice versa. Everyone who is both rich and not humble is both not funny and not happy. If lucy is not generous then lucy is either humble or not curious and vice versa. Everyone who is both not wise and rich is both not curious and patient and vice versa. Everyone who is not patient or not humble is not curious or not wise. If someone is both curious and strong then mary is humble. Everyone who is either not creative or wise is humble and vice versa. If someone is not funny then paul is curious or creative and vice versa. If fred is not quiet or kind then someone is kind and vice versa. Alice is not creative. Someone is either old or happy. Lucy is not curious or wise. Fred is calm or creative. Someone is calm or not strong. Susan is both not creative and old. Paul is not wise. John is both not funny and not curious. | Fred is not kind. | neutral | (![X]:((funny(X)|patient(X))=>(kind(X)<~>quiet(X))))&
(![X]:((happy(X)<~>~strong(X))<=>(~calm(X)&~kind(X))))&
((~rich(mary))=>((strong(alice)<~>~curious(alice))))&
(![X]:((humble(X)&~funny(X))=>(happy(X)|creative(X))))&
(((~kind(paul)|old(paul)))=>(?[X]:((~calm(X)|~wise(X)))))&
(((~generous(john)&kind(john)))<=>(brave(alice)))&
(((~creative(alice)<~>patient(alice)))<=>(?[X]:((wise(X)|~humble(X)))))&
(![X]:((~curious(X)<~>old(X))<=>(tall(X)<~>~brave(X))))&
(![X]:((rich(X)&~humble(X))=>(~funny(X)&~happy(X))))&
((~generous(lucy))<=>((humble(lucy)<~>~curious(lucy))))&
(![X]:((~wise(X)&rich(X))<=>(~curious(X)&patient(X))))&
(![X]:((~patient(X)|~humble(X))=>(~curious(X)|~wise(X))))&
((?[X]:((curious(X)&strong(X))))=>(humble(mary)))&
(![X]:((~creative(X)<~>wise(X))<=>humble(X)))&
((?[X]:(~funny(X)))<=>((curious(paul)|creative(paul))))&
(((~quiet(fred)|kind(fred)))<=>(?[X]:(kind(X))))&
(~creative(alice))&
(?[X]:((old(X)<~>happy(X))))&
((~curious(lucy)|wise(lucy)))&
((calm(fred)|creative(fred)))&
(?[X]:((calm(X)|~strong(X))))&
((~creative(susan)&old(susan)))&
(~wise(paul))&
((~funny(john)&~curious(john))) | ~kind(fred) | []
| null | 0 |
If someone is not happy or patient then lucy is both quiet and not old and vice versa.
Everyone who is either wise or not creative is either quiet or humble and vice versa.
Everyone who is not strong is not happy and vice versa.
If someone is either strong or not kind then someone is either not wise or quiet and vice versa.
Everyone who is either not kind or wise is wise.
If someone is not wise then someone is both not wise and not creative.
Everyone who is both not kind and not tall is both not patient and not curious.
If lucy is either not rich or curious then someone is both not funny and happy and vice versa.
If john is either not wise or creative then fred is not curious and vice versa.
If someone is not patient then someone is not generous or not calm.
Everyone who is not happy or not curious is either brave or not curious.
Everyone who is either not generous or not curious is both tall and wise and vice versa.
If someone is generous then someone is both wise and patient.
If someone is not creative or not happy then someone is both not tall and curious and vice versa.
If fred is either patient or not humble then mary is not wise or not rich.
Everyone who is not old or not patient is either not quiet or rich and vice versa.
Paul is both not rich and brave.
Fred is either not humble or not calm.
Someone is creative or humble.
Lucy is wise.
Susan is quiet or creative.
Someone is not humble or patient.
Paul is both kind and generous.
Someone is not old. | Lucy is rich. | entailment | ((?[X]:((~happy(X)|patient(X))))<=>((quiet(lucy)&~old(lucy))))&
(![X]:((wise(X)<~>~creative(X))<=>(quiet(X)<~>humble(X))))&
(![X]:(~strong(X)<=>~happy(X)))&
((?[X]:((strong(X)<~>~kind(X))))<=>(?[X]:((~wise(X)<~>quiet(X)))))&
(![X]:((~kind(X)<~>wise(X))=>wise(X)))&
((?[X]:(~wise(X)))=>(?[X]:((~wise(X)&~creative(X)))))&
(![X]:((~kind(X)&~tall(X))=>(~patient(X)&~curious(X))))&
(((~rich(lucy)<~>curious(lucy)))<=>(?[X]:((~funny(X)&happy(X)))))&
(((~wise(john)<~>creative(john)))<=>(~curious(fred)))&
((?[X]:(~patient(X)))=>(?[X]:((~generous(X)|~calm(X)))))&
(![X]:((~happy(X)|~curious(X))=>(brave(X)<~>~curious(X))))&
(![X]:((~generous(X)<~>~curious(X))<=>(tall(X)&wise(X))))&
((?[X]:(generous(X)))=>(?[X]:((wise(X)&patient(X)))))&
((?[X]:((~creative(X)|~happy(X))))<=>(?[X]:((~tall(X)&curious(X)))))&
(((patient(fred)<~>~humble(fred)))=>((~wise(mary)|~rich(mary))))&
(![X]:((~old(X)|~patient(X))<=>(~quiet(X)<~>rich(X))))&
((~rich(paul)&brave(paul)))&
((~humble(fred)<~>~calm(fred)))&
(?[X]:((creative(X)|humble(X))))&
(wise(lucy))&
((quiet(susan)|creative(susan)))&
(?[X]:((~humble(X)|patient(X))))&
((kind(paul)&generous(paul)))&
(?[X]:(~old(X))) | rich(lucy) | [
"p0",
"p12",
"p15",
"p22",
"hypothesis"
]
| % SZS status Unsatisfiable for 1487247146492747216549641
% SZS output start Proof for 1487247146492747216549641
1. ? [X0] : (patient(X0) | ~happy(X0)) <=> (~old(lucy) & quiet(lucy)) [input p0]
13. ? [X0] : generous(X0) => ? [X0] : (patient(X0) & wise(X0)) [input p12]
16. ! [X0] : ((~patient(X0) | ~old(X0)) <=> (~quiet(X0) <~> rich(X0))) [input p15]
23. generous(paul) & kind(paul) [input p22]
25. ~rich(lucy) [input hypothesis]
29. ? [X0] : generous(X0) => ? [X1] : (patient(X1) & wise(X1)) [rectify 13]
37. ? [X1] : (patient(X1) & wise(X1)) | ! [X0] : ~generous(X0) [ennf transformation 29]
40. (? [X0] : (patient(X0) | ~happy(X0)) | (old(lucy) | ~quiet(lucy))) & ((~old(lucy) & quiet(lucy)) | ! [X0] : (~patient(X0) & happy(X0))) [nnf transformation 1]
41. (? [X0] : (patient(X0) | ~happy(X0)) | old(lucy) | ~quiet(lucy)) & ((~old(lucy) & quiet(lucy)) | ! [X0] : (~patient(X0) & happy(X0))) [flattening 40]
42. (? [X0] : (patient(X0) | ~happy(X0)) | old(lucy) | ~quiet(lucy)) & ((~old(lucy) & quiet(lucy)) | ! [X1] : (~patient(X1) & happy(X1))) [rectify 41]
43. ? [X0] : (patient(X0) | ~happy(X0)) => (patient(sK0) | ~happy(sK0)) [choice axiom]
44. ((patient(sK0) | ~happy(sK0)) | old(lucy) | ~quiet(lucy)) & ((~old(lucy) & quiet(lucy)) | ! [X1] : (~patient(X1) & happy(X1))) [skolemisation 42,43]
67. ? [X0] : (patient(X0) & wise(X0)) | ! [X1] : ~generous(X1) [rectify 37]
68. ? [X0] : (patient(X0) & wise(X0)) => (patient(sK6) & wise(sK6)) [choice axiom]
69. (patient(sK6) & wise(sK6)) | ! [X1] : ~generous(X1) [skolemisation 67,68]
76. ! [X0] : (((~patient(X0) | ~old(X0)) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (patient(X0) & old(X0)))) [nnf transformation 16]
77. ! [X0] : ((~patient(X0) | ~old(X0) | ((~quiet(X0) | ~rich(X0)) & (rich(X0) | quiet(X0)))) & (((~rich(X0) | quiet(X0)) & (rich(X0) | ~quiet(X0))) | (patient(X0) & old(X0)))) [flattening 76]
86. quiet(lucy) | ~patient(X1) [cnf transformation 44]
88. ~old(lucy) | ~patient(X1) [cnf transformation 44]
136. patient(sK6) | ~generous(X1) [cnf transformation 69]
144. ~quiet(X0) | rich(X0) | old(X0) [cnf transformation 77]
159. generous(paul) [cnf transformation 23]
161. ~rich(lucy) [cnf transformation 25]
165. 1 <=> quiet(lucy) [avatar definition]
166. quiet(lucy) <- (1) [avatar component clause 165]
169. 2 <=> old(lucy) [avatar definition]
170. ~old(lucy) <- (~2) [avatar component clause 169]
182. 5 <=> ! [X1] : ~patient(X1) [avatar definition]
183. ~patient(X1) <- (5) [avatar component clause 182]
184. 5 | ~2 [avatar split clause 88,169,182]
189. 5 | 1 [avatar split clause 86,165,182]
244. 19 <=> rich(lucy) [avatar definition]
245. ~rich(lucy) <- (~19) [avatar component clause 244]
294. 29 <=> ! [X1] : ~generous(X1) [avatar definition]
295. ~generous(X1) <- (29) [avatar component clause 294]
297. 30 <=> patient(sK6) [avatar definition]
299. patient(sK6) <- (30) [avatar component clause 297]
300. 29 | 30 [avatar split clause 136,297,294]
384. ~19 [avatar split clause 161,244]
385. $false <- (29) [resolution 295,159]
386. ~29 [avatar contradiction clause 385]
387. $false <- (5, 30) [subsumption resolution 299,183]
388. ~5 | ~30 [avatar contradiction clause 387]
498. rich(lucy) | old(lucy) <- (1) [resolution 144,166]
500. old(lucy) <- (1, ~19) [subsumption resolution 498,245]
501. $false <- (1, ~2, ~19) [subsumption resolution 500,170]
502. ~1 | 2 | 19 [avatar contradiction clause 501]
512. $false [avatar sat refutation 184,189,300,384,386,388,502]
% SZS output end Proof for 1487247146492747216549641
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not creative then someone is not old and vice versa.
If lucy is either not generous or not humble then someone is both not generous and strong and vice versa.
Everyone who is both patient and not curious is both calm and not quiet.
If someone is not tall then someone is not funny.
If mary is not wise or quiet then alice is both happy and calm and vice versa.
Everyone who is either not strong or not humble is either tall or brave and vice versa.
Everyone who is both not curious and generous is either not patient or not kind.
Everyone who is both not curious and humble is either not kind or strong.
If lucy is generous then mary is tall.
Everyone who is either happy or wise is not generous or not calm and vice versa.
Everyone who is either old or not happy is both humble and quiet and vice versa.
If john is strong then mary is not curious and vice versa.
Everyone who is both not funny and brave is either not calm or not funny and vice versa.
Everyone who is humble or not quiet is funny and vice versa.
If someone is either tall or not strong then lucy is both not tall and not quiet and vice versa.
If alice is both curious and funny then someone is both not kind and curious and vice versa.
Someone is not patient or not funny.
Someone is not kind or not happy.
Someone is quiet.
John is either not brave or not creative.
Lucy is both wise and not patient.
Fred is not funny or not quiet.
Alice is both humble and not strong.
Paul is not strong. | John is not humble. | neutral | ((?[X]:((~patient(X)|~creative(X))))<=>(?[X]:(~old(X))))&
(((~generous(lucy)<~>~humble(lucy)))<=>(?[X]:((~generous(X)&strong(X)))))&
(![X]:((patient(X)&~curious(X))=>(calm(X)&~quiet(X))))&
((?[X]:(~tall(X)))=>(?[X]:(~funny(X))))&
(((~wise(mary)|quiet(mary)))<=>((happy(alice)&calm(alice))))&
(![X]:((~strong(X)<~>~humble(X))<=>(tall(X)<~>brave(X))))&
(![X]:((~curious(X)&generous(X))=>(~patient(X)<~>~kind(X))))&
(![X]:((~curious(X)&humble(X))=>(~kind(X)<~>strong(X))))&
((generous(lucy))=>(tall(mary)))&
(![X]:((happy(X)<~>wise(X))<=>(~generous(X)|~calm(X))))&
(![X]:((old(X)<~>~happy(X))<=>(humble(X)&quiet(X))))&
((strong(john))<=>(~curious(mary)))&
(![X]:((~funny(X)&brave(X))<=>(~calm(X)<~>~funny(X))))&
(![X]:((humble(X)|~quiet(X))<=>funny(X)))&
((?[X]:((tall(X)<~>~strong(X))))<=>((~tall(lucy)&~quiet(lucy))))&
(((curious(alice)&funny(alice)))<=>(?[X]:((~kind(X)&curious(X)))))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((~kind(X)|~happy(X))))&
(?[X]:(quiet(X)))&
((~brave(john)<~>~creative(john)))&
((wise(lucy)&~patient(lucy)))&
((~funny(fred)|~quiet(fred)))&
((humble(alice)&~strong(alice)))&
(~strong(paul)) | ~humble(john) | []
| null | 0 |
Everyone who is either not wise or not curious is not kind.
If john is rich or not quiet then someone is both not creative and not rich.
Everyone who is not calm is funny and vice versa.
If someone is quiet or not calm then someone is not kind and vice versa.
If someone is both generous and humble then someone is both not funny and brave and vice versa.
If alice is either old or not strong then someone is tall.
If lucy is both not kind and not creative then susan is either not humble or creative and vice versa.
Everyone who is quiet or not strong is rich.
If mary is either brave or not brave then someone is not curious and vice versa.
Everyone who is funny or patient is both patient and not funny and vice versa.
If someone is either not wise or not old then alice is either patient or generous.
If john is creative or not wise then someone is curious.
If mary is brave then someone is both not calm and brave and vice versa.
Everyone who is either not humble or funny is not old or not rich and vice versa.
Susan is either not wise or not curious.
Paul is either not kind or kind.
Paul is both not wise and curious.
Someone is either not creative or generous.
Someone is either tall or not tall.
Alice is either not strong or rich.
John is not tall. | Susan is kind. | contradiction | (![X]:((~wise(X)<~>~curious(X))=>~kind(X)))&
(((rich(john)|~quiet(john)))=>(?[X]:((~creative(X)&~rich(X)))))&
(![X]:(~calm(X)<=>funny(X)))&
((?[X]:((quiet(X)|~calm(X))))<=>(?[X]:(~kind(X))))&
((?[X]:((generous(X)&humble(X))))<=>(?[X]:((~funny(X)&brave(X)))))&
(((old(alice)<~>~strong(alice)))=>(?[X]:(tall(X))))&
(((~kind(lucy)&~creative(lucy)))<=>((~humble(susan)<~>creative(susan))))&
(![X]:((quiet(X)|~strong(X))=>rich(X)))&
(((brave(mary)<~>~brave(mary)))<=>(?[X]:(~curious(X))))&
(![X]:((funny(X)|patient(X))<=>(patient(X)&~funny(X))))&
((?[X]:((~wise(X)<~>~old(X))))=>((patient(alice)<~>generous(alice))))&
(((creative(john)|~wise(john)))=>(?[X]:(curious(X))))&
((brave(mary))<=>(?[X]:((~calm(X)&brave(X)))))&
(![X]:((~humble(X)<~>funny(X))<=>(~old(X)|~rich(X))))&
((~wise(susan)<~>~curious(susan)))&
((~kind(paul)<~>kind(paul)))&
((~wise(paul)&curious(paul)))&
(?[X]:((~creative(X)<~>generous(X))))&
(?[X]:((tall(X)<~>~tall(X))))&
((~strong(alice)<~>rich(alice)))&
(~tall(john)) | kind(susan) | [
"p0",
"p14",
"hypothesis"
]
| % SZS status Unsatisfiable for 3098597863985178347436314
% SZS output start Proof for 3098597863985178347436314
1. ! [X0] : ((~wise(X0) <~> ~curious(X0)) => ~kind(X0)) [input p0]
15. ~wise(susan) <~> ~curious(susan) [input p14]
22. kind(susan) [input hypothesis]
25. ! [X0] : (~kind(X0) | (~wise(X0) <=> ~curious(X0))) [ennf transformation 1]
31. ! [X0] : (~kind(X0) | ((~wise(X0) | curious(X0)) & (~curious(X0) | wise(X0)))) [nnf transformation 25]
65. (curious(susan) | wise(susan)) & (~curious(susan) | ~wise(susan)) [nnf transformation 15]
74. ~kind(X0) | ~curious(X0) | wise(X0) [cnf transformation 31]
75. ~kind(X0) | ~wise(X0) | curious(X0) [cnf transformation 31]
123. ~curious(susan) | ~wise(susan) [cnf transformation 65]
124. curious(susan) | wise(susan) [cnf transformation 65]
136. kind(susan) [cnf transformation 22]
307. 36 <=> wise(susan) [avatar definition]
311. 37 <=> curious(susan) [avatar definition]
314. 36 | 37 [avatar split clause 124,311,307]
315. ~36 | ~37 [avatar split clause 123,311,307]
337. ~curious(susan) | wise(susan) [resolution 74,136]
338. ~wise(susan) | curious(susan) [resolution 75,136]
342. 37 | ~36 [avatar split clause 338,307,311]
343. 36 | ~37 [avatar split clause 337,311,307]
344. $false [avatar sat refutation 314,315,342,343]
% SZS output end Proof for 3098597863985178347436314
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich or calm is rich or not quiet.
If paul is both happy and calm then mary is not tall or happy and vice versa.
If mary is not funny or old then paul is both not kind and patient.
If john is not calm or not strong then someone is either calm or humble.
If someone is creative or calm then susan is either not happy or not humble and vice versa.
If john is both not wise and happy then someone is patient and vice versa.
Everyone who is both humble and not strong is both happy and kind.
Everyone who is both not happy and not funny is funny and vice versa.
If alice is wise then someone is both quiet and creative.
Everyone who is both calm and generous is not funny or not strong and vice versa.
If someone is kind then someone is either strong or not happy.
If someone is not generous or creative then someone is both creative and not kind.
Everyone who is not strong or brave is rich or tall and vice versa.
If lucy is patient then someone is either not patient or calm.
If paul is both funny and not brave then lucy is not old or creative and vice versa.
Fred is both not funny and not quiet.
Susan is both tall and not brave.
Someone is not patient or quiet.
Susan is either not creative or not patient.
Someone is not tall.
John is not rich or curious.
Someone is creative or not humble. | John is not generous. | contradiction | (![X]:((rich(X)|calm(X))=>(rich(X)|~quiet(X))))&
(((happy(paul)&calm(paul)))<=>((~tall(mary)|happy(mary))))&
(((~funny(mary)|old(mary)))=>((~kind(paul)&patient(paul))))&
(((~calm(john)|~strong(john)))=>(?[X]:((calm(X)<~>humble(X)))))&
((?[X]:((creative(X)|calm(X))))<=>((~happy(susan)<~>~humble(susan))))&
(((~wise(john)&happy(john)))<=>(?[X]:(patient(X))))&
(![X]:((humble(X)&~strong(X))=>(happy(X)&kind(X))))&
(![X]:((~happy(X)&~funny(X))<=>funny(X)))&
((wise(alice))=>(?[X]:((quiet(X)&creative(X)))))&
(![X]:((calm(X)&generous(X))<=>(~funny(X)|~strong(X))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)<~>~happy(X)))))&
((?[X]:((~generous(X)|creative(X))))=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:((~strong(X)|brave(X))<=>(rich(X)|tall(X))))&
((patient(lucy))=>(?[X]:((~patient(X)<~>calm(X)))))&
(((funny(paul)&~brave(paul)))<=>((~old(lucy)|creative(lucy))))&
((~funny(fred)&~quiet(fred)))&
((tall(susan)&~brave(susan)))&
(?[X]:((~patient(X)|quiet(X))))&
((~creative(susan)<~>~patient(susan)))&
(?[X]:(~tall(X)))&
((~rich(john)|curious(john)))&
(?[X]:((creative(X)|~humble(X)))) | ~generous(john) | [
"p7",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 5204349595295423329409603
% SZS output start Proof for 5204349595295423329409603
8. ! [X0] : ((~funny(X0) & ~happy(X0)) <=> funny(X0)) [input p7]
10. ! [X0] : ((generous(X0) & calm(X0)) <=> (~strong(X0) | ~funny(X0))) [input p9]
23. ~generous(john) [input hypothesis]
51. ! [X0] : (((~funny(X0) & ~happy(X0)) | ~funny(X0)) & (funny(X0) | (funny(X0) | happy(X0)))) [nnf transformation 8]
52. ! [X0] : (((~funny(X0) & ~happy(X0)) | ~funny(X0)) & (funny(X0) | funny(X0) | happy(X0))) [flattening 51]
55. ! [X0] : (((generous(X0) & calm(X0)) | (strong(X0) & funny(X0))) & ((~strong(X0) | ~funny(X0)) | (~generous(X0) | ~calm(X0)))) [nnf transformation 10]
56. ! [X0] : (((generous(X0) & calm(X0)) | (strong(X0) & funny(X0))) & (~strong(X0) | ~funny(X0) | ~generous(X0) | ~calm(X0))) [flattening 55]
106. ~funny(X0) | ~funny(X0) [cnf transformation 52]
112. generous(X0) | funny(X0) [cnf transformation 56]
140. ~generous(john) [cnf transformation 23]
142. ~funny(X0) [duplicate literal removal 106]
265. generous(X0) [subsumption resolution 112,142]
342. $false [subsumption resolution 140,265]
% SZS output end Proof for 5204349595295423329409603
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet and kind is tall or not rich and vice versa. If someone is rich or brave then someone is not old and vice versa. Everyone who is either not kind or kind is curious and vice versa. Everyone who is patient is happy and vice versa. Everyone who is not wise or not calm is calm or not generous. If lucy is generous then someone is both humble and brave and vice versa. If john is not strong or not brave then someone is kind or strong and vice versa. Everyone who is rich is either creative or calm and vice versa. If someone is both funny and not funny then someone is both not patient and not tall and vice versa. If someone is either calm or not tall then someone is either generous or not wise. Everyone who is kind or not generous is quiet or creative and vice versa. If mary is both wise and calm then lucy is brave or not funny. Everyone who is both humble and not quiet is both wise and not humble and vice versa. Everyone who is either not rich or brave is either quiet or happy and vice versa. Everyone who is not old or humble is not rich or strong and vice versa. If john is either not patient or funny then someone is both not tall and generous and vice versa. John is both calm and not kind. Someone is not patient or not funny. Someone is wise or patient. Alice is either humble or not curious. Someone is both not rich and not old. Someone is either generous or funny. | Alice is not patient. | contradiction | (![X]:((~quiet(X)&kind(X))<=>(tall(X)|~rich(X))))&
((?[X]:((rich(X)|brave(X))))<=>(?[X]:(~old(X))))&
(![X]:((~kind(X)<~>kind(X))<=>curious(X)))&
(![X]:(patient(X)<=>happy(X)))&
(![X]:((~wise(X)|~calm(X))=>(calm(X)|~generous(X))))&
((generous(lucy))<=>(?[X]:((humble(X)&brave(X)))))&
(((~strong(john)|~brave(john)))<=>(?[X]:((kind(X)|strong(X)))))&
(![X]:(rich(X)<=>(creative(X)<~>calm(X))))&
((?[X]:((funny(X)&~funny(X))))<=>(?[X]:((~patient(X)&~tall(X)))))&
((?[X]:((calm(X)<~>~tall(X))))=>(?[X]:((generous(X)<~>~wise(X)))))&
(![X]:((kind(X)|~generous(X))<=>(quiet(X)|creative(X))))&
(((wise(mary)&calm(mary)))=>((brave(lucy)|~funny(lucy))))&
(![X]:((humble(X)&~quiet(X))<=>(wise(X)&~humble(X))))&
(![X]:((~rich(X)<~>brave(X))<=>(quiet(X)<~>happy(X))))&
(![X]:((~old(X)|humble(X))<=>(~rich(X)|strong(X))))&
(((~patient(john)<~>funny(john)))<=>(?[X]:((~tall(X)&generous(X)))))&
((calm(john)&~kind(john)))&
(?[X]:((~patient(X)|~funny(X))))&
(?[X]:((wise(X)|patient(X))))&
((humble(alice)<~>~curious(alice)))&
(?[X]:((~rich(X)&~old(X))))&
(?[X]:((generous(X)<~>funny(X)))) | ~patient(alice) | [
"p0",
"p2",
"p8",
"p12",
"p19",
"hypothesis"
]
| % SZS status Unsatisfiable for 2731441216323939395261292
% SZS output start Proof for 2731441216323939395261292
1. ! [X0] : ((kind(X0) & ~quiet(X0)) <=> (~rich(X0) | tall(X0))) [input p0]
3. ! [X0] : ((~kind(X0) <~> kind(X0)) <=> curious(X0)) [input p2]
9. ? [X0] : (~funny(X0) & funny(X0)) <=> ? [X0] : (~tall(X0) & ~patient(X0)) [input p8]
13. ! [X0] : ((~quiet(X0) & humble(X0)) <=> (~humble(X0) & wise(X0))) [input p12]
20. humble(alice) <~> ~curious(alice) [input p19]
23. ~patient(alice) [input hypothesis]
25. ? [X0] : (~funny(X0) & funny(X0)) <=> ? [X1] : (~tall(X1) & ~patient(X1)) [rectify 9]
32. ! [X0] : (((kind(X0) & ~quiet(X0)) | (rich(X0) & ~tall(X0))) & ((~rich(X0) | tall(X0)) | (~kind(X0) | quiet(X0)))) [nnf transformation 1]
33. ! [X0] : (((kind(X0) & ~quiet(X0)) | (rich(X0) & ~tall(X0))) & (~rich(X0) | tall(X0) | ~kind(X0) | quiet(X0))) [flattening 32]
39. ! [X0] : ((((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~curious(X0)) & (curious(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0))))) [nnf transformation 3]
51. (? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : (tall(X1) | patient(X1))) & (? [X1] : (~tall(X1) & ~patient(X1)) | ! [X0] : (funny(X0) | ~funny(X0))) [nnf transformation 25]
52. (? [X0] : (~funny(X0) & funny(X0)) | ! [X1] : (tall(X1) | patient(X1))) & (? [X2] : (~tall(X2) & ~patient(X2)) | ! [X3] : (funny(X3) | ~funny(X3))) [rectify 51]
53. ? [X0] : (~funny(X0) & funny(X0)) => (~funny(sK4) & funny(sK4)) [choice axiom]
54. ? [X2] : (~tall(X2) & ~patient(X2)) => (~tall(sK5) & ~patient(sK5)) [choice axiom]
55. ((~funny(sK4) & funny(sK4)) | ! [X1] : (tall(X1) | patient(X1))) & ((~tall(sK5) & ~patient(sK5)) | ! [X3] : (funny(X3) | ~funny(X3))) [skolemisation 52,54,53]
62. ! [X0] : (((~quiet(X0) & humble(X0)) | (humble(X0) | ~wise(X0))) & ((~humble(X0) & wise(X0)) | (quiet(X0) | ~humble(X0)))) [nnf transformation 13]
63. ! [X0] : (((~quiet(X0) & humble(X0)) | humble(X0) | ~wise(X0)) & ((~humble(X0) & wise(X0)) | quiet(X0) | ~humble(X0))) [flattening 62]
75. (curious(alice) | ~humble(alice)) & (~curious(alice) | humble(alice)) [nnf transformation 20]
82. ~tall(X0) | ~quiet(X0) [cnf transformation 33]
89. curious(X0) | kind(X0) | kind(X0) [cnf transformation 39]
90. curious(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 39]
110. funny(sK4) | tall(X1) | patient(X1) [cnf transformation 55]
111. ~funny(sK4) | tall(X1) | patient(X1) [cnf transformation 55]
122. ~humble(X0) | quiet(X0) | ~humble(X0) [cnf transformation 63]
147. ~curious(alice) | humble(alice) [cnf transformation 75]
153. ~patient(alice) [cnf transformation 23]
154. ~humble(X0) | quiet(X0) [duplicate literal removal 122]
157. curious(X0) | kind(X0) [duplicate literal removal 89]
158. ~kind(X0) | curious(X0) [duplicate literal removal 90]
183. curious(X0) [subsumption resolution 157,158]
229. 17 <=> ! [X1] : (tall(X1) | patient(X1)) [avatar definition]
230. patient(X1) | tall(X1) <- (17) [avatar component clause 229]
232. 18 <=> funny(sK4) [avatar definition]
235. 17 | ~18 [avatar split clause 111,232,229]
236. 17 | 18 [avatar split clause 110,232,229]
319. humble(alice) [subsumption resolution 147,183]
337. quiet(alice) [resolution 154,319]
346. tall(alice) <- (17) [resolution 230,153]
350. ~quiet(alice) <- (17) [resolution 346,82]
351. $false <- (17) [subsumption resolution 350,337]
352. ~17 [avatar contradiction clause 351]
353. $false [avatar sat refutation 235,236,352]
% SZS output end Proof for 2731441216323939395261292
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet or brave is curious or generous.
Everyone who is both not brave and generous is not rich and vice versa.
If someone is either not quiet or creative then someone is patient and vice versa.
Everyone who is not funny or strong is strong or not generous and vice versa.
If someone is not quiet or curious then lucy is humble or happy.
Everyone who is either humble or curious is not humble.
Everyone who is calm or strong is both strong and not strong.
Everyone who is both brave and not funny is not strong or creative and vice versa.
Everyone who is wise is rich.
Everyone who is either creative or old is patient or not creative and vice versa.
Everyone who is both not strong and not old is either rich or creative and vice versa.
If paul is both not kind and brave then paul is either strong or not patient.
If mary is not happy or not calm then someone is kind.
Everyone who is not rich is both not calm and kind.
If paul is curious then susan is calm or old.
If someone is wise then mary is happy.
Someone is both not wise and humble.
Someone is either old or not kind.
Someone is both not humble and curious.
Someone is not wise or not humble.
Someone is both not happy and not kind. | Lucy is creative. | entailment | (![X]:((~quiet(X)|brave(X))=>(curious(X)|generous(X))))&
(![X]:((~brave(X)&generous(X))<=>~rich(X)))&
((?[X]:((~quiet(X)<~>creative(X))))<=>(?[X]:(patient(X))))&
(![X]:((~funny(X)|strong(X))<=>(strong(X)|~generous(X))))&
((?[X]:((~quiet(X)|curious(X))))=>((humble(lucy)|happy(lucy))))&
(![X]:((humble(X)<~>curious(X))=>~humble(X)))&
(![X]:((calm(X)|strong(X))=>(strong(X)&~strong(X))))&
(![X]:((brave(X)&~funny(X))<=>(~strong(X)|creative(X))))&
(![X]:(wise(X)=>rich(X)))&
(![X]:((creative(X)<~>old(X))<=>(patient(X)|~creative(X))))&
(![X]:((~strong(X)&~old(X))<=>(rich(X)<~>creative(X))))&
(((~kind(paul)&brave(paul)))=>((strong(paul)<~>~patient(paul))))&
(((~happy(mary)|~calm(mary)))=>(?[X]:(kind(X))))&
(![X]:(~rich(X)=>(~calm(X)&kind(X))))&
((curious(paul))=>((calm(susan)|old(susan))))&
((?[X]:(wise(X)))=>(happy(mary)))&
(?[X]:((~wise(X)&humble(X))))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((~humble(X)&curious(X))))&
(?[X]:((~wise(X)|~humble(X))))&
(?[X]:((~happy(X)&~kind(X)))) | creative(lucy) | [
"p1",
"p6",
"p7",
"p9",
"p10",
"hypothesis"
]
| % SZS status Unsatisfiable for 7453983342142558232188485
% SZS output start Proof for 7453983342142558232188485
2. ! [X0] : ((generous(X0) & ~brave(X0)) <=> ~rich(X0)) [input p1]
7. ! [X0] : ((strong(X0) | calm(X0)) => (~strong(X0) & strong(X0))) [input p6]
8. ! [X0] : ((~funny(X0) & brave(X0)) <=> (creative(X0) | ~strong(X0))) [input p7]
10. ! [X0] : ((creative(X0) <~> old(X0)) <=> (~creative(X0) | patient(X0))) [input p9]
11. ! [X0] : ((~old(X0) & ~strong(X0)) <=> (rich(X0) <~> creative(X0))) [input p10]
22. ~creative(lucy) [input hypothesis]
33. ! [X0] : ((~strong(X0) & strong(X0)) | (~strong(X0) & ~calm(X0))) [ennf transformation 7]
40. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | (~generous(X0) | brave(X0)))) [nnf transformation 2]
41. ! [X0] : (((generous(X0) & ~brave(X0)) | rich(X0)) & (~rich(X0) | ~generous(X0) | brave(X0))) [flattening 40]
50. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & ((creative(X0) | ~strong(X0)) | (funny(X0) | ~brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((~funny(X0) & brave(X0)) | (~creative(X0) & strong(X0))) & (creative(X0) | ~strong(X0) | funny(X0) | ~brave(X0))) [flattening 50]
52. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (creative(X0) & ~patient(X0))) & ((~creative(X0) | patient(X0)) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [nnf transformation 10]
53. ! [X0] : ((((~old(X0) | ~creative(X0)) & (old(X0) | creative(X0))) | (creative(X0) & ~patient(X0))) & (~creative(X0) | patient(X0) | ((creative(X0) | ~old(X0)) & (old(X0) | ~creative(X0))))) [flattening 52]
54. ! [X0] : (((~old(X0) & ~strong(X0)) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | (old(X0) | strong(X0)))) [nnf transformation 11]
55. ! [X0] : (((~old(X0) & ~strong(X0)) | ((rich(X0) | ~creative(X0)) & (creative(X0) | ~rich(X0)))) & (((~creative(X0) | ~rich(X0)) & (creative(X0) | rich(X0))) | old(X0) | strong(X0))) [flattening 54]
71. ~brave(X0) | rich(X0) [cnf transformation 41]
88. ~strong(X0) | ~strong(X0) [cnf transformation 33]
90. brave(X0) | strong(X0) [cnf transformation 51]
97. old(X0) | creative(X0) | creative(X0) [cnf transformation 53]
104. ~old(X0) | creative(X0) | ~rich(X0) [cnf transformation 55]
120. ~creative(lucy) [cnf transformation 22]
122. old(X0) | creative(X0) [duplicate literal removal 97]
123. ~strong(X0) [duplicate literal removal 88]
168. brave(X0) [subsumption resolution 90,123]
170. ~rich(X0) | creative(X0) [subsumption resolution 104,122]
205. rich(X0) [resolution 71,168]
214. creative(X1) [resolution 170,205]
217. $false [resolution 214,120]
% SZS output end Proof for 7453983342142558232188485
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If mary is either funny or not happy then fred is either rich or not patient.
If john is both not happy and rich then paul is either not creative or not tall.
If someone is brave then someone is either old or curious.
Everyone who is brave or patient is either not wise or not old and vice versa.
Everyone who is either happy or humble is patient.
Everyone who is not creative or not humble is both not generous and not quiet.
Everyone who is either not brave or not rich is either generous or curious.
Everyone who is either not calm or not creative is calm or not humble and vice versa.
Everyone who is wise or not brave is not rich and vice versa.
Everyone who is both not quiet and quiet is either humble or brave.
If lucy is either not wise or curious then paul is either calm or not tall.
If someone is not generous then lucy is either kind or not quiet and vice versa.
Everyone who is both not strong and not patient is not funny or brave and vice versa.
Everyone who is not happy or quiet is rich or happy and vice versa.
Everyone who is not patient or not kind is not humble and vice versa.
Paul is calm or not curious.
Susan is both not strong and not wise.
John is either not creative or happy.
Someone is either not patient or not old.
Someone is both not strong and not patient.
Someone is either happy or not strong. | Lucy is rich. | entailment | (((funny(mary)<~>~happy(mary)))=>((rich(fred)<~>~patient(fred))))&
(((~happy(john)&rich(john)))=>((~creative(paul)<~>~tall(paul))))&
((?[X]:(brave(X)))=>(?[X]:((old(X)<~>curious(X)))))&
(![X]:((brave(X)|patient(X))<=>(~wise(X)<~>~old(X))))&
(![X]:((happy(X)<~>humble(X))=>patient(X)))&
(![X]:((~creative(X)|~humble(X))=>(~generous(X)&~quiet(X))))&
(![X]:((~brave(X)<~>~rich(X))=>(generous(X)<~>curious(X))))&
(![X]:((~calm(X)<~>~creative(X))<=>(calm(X)|~humble(X))))&
(![X]:((wise(X)|~brave(X))<=>~rich(X)))&
(![X]:((~quiet(X)&quiet(X))=>(humble(X)<~>brave(X))))&
(((~wise(lucy)<~>curious(lucy)))=>((calm(paul)<~>~tall(paul))))&
((?[X]:(~generous(X)))<=>((kind(lucy)<~>~quiet(lucy))))&
(![X]:((~strong(X)&~patient(X))<=>(~funny(X)|brave(X))))&
(![X]:((~happy(X)|quiet(X))<=>(rich(X)|happy(X))))&
(![X]:((~patient(X)|~kind(X))<=>~humble(X)))&
((calm(paul)|~curious(paul)))&
((~strong(susan)&~wise(susan)))&
((~creative(john)<~>happy(john)))&
(?[X]:((~patient(X)<~>~old(X))))&
(?[X]:((~strong(X)&~patient(X))))&
(?[X]:((happy(X)<~>~strong(X)))) | rich(lucy) | [
"p5",
"p7",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 5197684540337000862701656
% SZS output start Proof for 5197684540337000862701656
6. ! [X0] : ((~humble(X0) | ~creative(X0)) => (~quiet(X0) & ~generous(X0))) [input p5]
8. ! [X0] : ((~calm(X0) <~> ~creative(X0)) <=> (~humble(X0) | calm(X0))) [input p7]
14. ! [X0] : ((quiet(X0) | ~happy(X0)) <=> (happy(X0) | rich(X0))) [input p13]
22. ~rich(lucy) [input hypothesis]
29. ! [X0] : ((~quiet(X0) & ~generous(X0)) | (humble(X0) & creative(X0))) [ennf transformation 6]
44. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (humble(X0) & ~calm(X0))) & ((~humble(X0) | calm(X0)) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [nnf transformation 8]
45. ! [X0] : ((((creative(X0) | calm(X0)) & (~creative(X0) | ~calm(X0))) | (humble(X0) & ~calm(X0))) & (~humble(X0) | calm(X0) | ((~calm(X0) | creative(X0)) & (~creative(X0) | calm(X0))))) [flattening 44]
56. ! [X0] : (((quiet(X0) | ~happy(X0)) | (~happy(X0) & ~rich(X0))) & ((happy(X0) | rich(X0)) | (~quiet(X0) & happy(X0)))) [nnf transformation 14]
57. ! [X0] : ((quiet(X0) | ~happy(X0) | (~happy(X0) & ~rich(X0))) & (happy(X0) | rich(X0) | (~quiet(X0) & happy(X0)))) [flattening 56]
87. ~quiet(X0) | creative(X0) [cnf transformation 29]
88. ~quiet(X0) | humble(X0) [cnf transformation 29]
93. ~humble(X0) | calm(X0) | ~creative(X0) | calm(X0) [cnf transformation 45]
95. ~creative(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
117. happy(X0) | rich(X0) | happy(X0) [cnf transformation 57]
120. quiet(X0) | ~happy(X0) | ~happy(X0) [cnf transformation 57]
135. ~rich(lucy) [cnf transformation 22]
136. rich(X0) | happy(X0) [duplicate literal removal 117]
137. ~happy(X0) | quiet(X0) [duplicate literal removal 120]
138. ~humble(X0) | calm(X0) | ~creative(X0) [duplicate literal removal 93]
139. ~calm(X0) | ~creative(X0) [duplicate literal removal 95]
191. ~humble(X0) | ~creative(X0) [subsumption resolution 138,139]
209. 15 <=> quiet(lucy) [avatar definition]
211. quiet(lucy) <- (15) [avatar component clause 209]
262. happy(lucy) [resolution 136,135]
274. quiet(lucy) [resolution 262,137]
277. 15 [avatar split clause 274,209]
278. humble(lucy) <- (15) [resolution 211,88]
279. creative(lucy) <- (15) [resolution 211,87]
281. ~creative(lucy) <- (15) [resolution 278,191]
284. $false <- (15) [subsumption resolution 281,279]
285. ~15 [avatar contradiction clause 284]
286. $false [avatar sat refutation 277,285]
% SZS output end Proof for 5197684540337000862701656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 john is either not generous or not happy then lucy is both not rich and generous.
Everyone who is either quiet or brave is either tall or wise and vice versa.
If someone is not tall then someone is strong or not brave.
Everyone who is either old or not curious is both old and calm.
If paul is tall then lucy is both not wise and generous and vice versa.
Everyone who is either tall or not old is either happy or not creative and vice versa.
If someone is either not patient or not generous then someone is not old or not quiet and vice versa.
If someone is not happy then alice is either not brave or rich.
Everyone who is generous is not wise or not generous and vice versa.
Everyone who is either humble or wise is either not rich or not quiet and vice versa.
Everyone who is both not curious and strong is not curious and vice versa.
If john is not strong then john is either not quiet or not humble and vice versa.
If mary is either not generous or kind then fred is not generous.
If lucy is both not quiet and not calm then mary is not funny.
Everyone who is wise or curious is either humble or not brave and vice versa.
Everyone who is kind or tall is calm or generous.
Mary is either quiet or not funny.
Fred is calm.
Someone is both not wise and not patient.
Someone is both strong and not patient.
Alice is both happy and not kind.
Someone is not kind.
Someone is either not old or brave. | Alice is happy. | entailment | (((~generous(john)<~>~happy(john)))=>((~rich(lucy)&generous(lucy))))&
(![X]:((quiet(X)<~>brave(X))<=>(tall(X)<~>wise(X))))&
((?[X]:(~tall(X)))=>(?[X]:((strong(X)|~brave(X)))))&
(![X]:((old(X)<~>~curious(X))=>(old(X)&calm(X))))&
((tall(paul))<=>((~wise(lucy)&generous(lucy))))&
(![X]:((tall(X)<~>~old(X))<=>(happy(X)<~>~creative(X))))&
((?[X]:((~patient(X)<~>~generous(X))))<=>(?[X]:((~old(X)|~quiet(X)))))&
((?[X]:(~happy(X)))=>((~brave(alice)<~>rich(alice))))&
(![X]:(generous(X)<=>(~wise(X)|~generous(X))))&
(![X]:((humble(X)<~>wise(X))<=>(~rich(X)<~>~quiet(X))))&
(![X]:((~curious(X)&strong(X))<=>~curious(X)))&
((~strong(john))<=>((~quiet(john)<~>~humble(john))))&
(((~generous(mary)<~>kind(mary)))=>(~generous(fred)))&
(((~quiet(lucy)&~calm(lucy)))=>(~funny(mary)))&
(![X]:((wise(X)|curious(X))<=>(humble(X)<~>~brave(X))))&
(![X]:((kind(X)|tall(X))=>(calm(X)|generous(X))))&
((quiet(mary)<~>~funny(mary)))&
(calm(fred))&
(?[X]:((~wise(X)&~patient(X))))&
(?[X]:((strong(X)&~patient(X))))&
((happy(alice)&~kind(alice)))&
(?[X]:(~kind(X)))&
(?[X]:((~old(X)<~>brave(X)))) | happy(alice) | [
"p20",
"hypothesis"
]
| % SZS status Unsatisfiable for 3273746915850366657283105
% SZS output start Proof for 3273746915850366657283105
21. ~kind(alice) & happy(alice) [input p20]
24. ~happy(alice) [input hypothesis]
136. happy(alice) [cnf transformation 21]
141. ~happy(alice) [cnf transformation 24]
280. $false [subsumption resolution 141,136]
% SZS output end Proof for 3273746915850366657283105
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If mary is not curious then john is either funny or not brave. Everyone who is happy is not patient and vice versa. Everyone who is happy or not old is not curious. Everyone who is both brave and happy is both rich and not funny and vice versa. If someone is both not patient and not rich then someone is generous. Everyone who is not kind is funny and vice versa. Everyone who is humble is either old or not brave and vice versa. If someone is either not humble or not rich then someone is both not humble and humble. If john is brave then someone is both generous and creative and vice versa. If john is not patient then lucy is funny and vice versa. If fred is either tall or strong then someone is not curious and vice versa. Everyone who is both happy and not old is creative and vice versa. Everyone who is either old or not creative is not curious or not brave and vice versa. If someone is either not strong or strong then someone is either not quiet or wise. If someone is not kind then alice is curious and vice versa. If someone is not generous or strong then someone is not generous. Someone is not happy or not brave. Someone is generous. John is calm or not strong. Paul is not calm or not creative. Someone is humble or not brave. Lucy is either not quiet or kind. Paul is not generous or humble. John is rich. | Alice is not happy. | entailment | ((~curious(mary))=>((funny(john)<~>~brave(john))))&
(![X]:(happy(X)<=>~patient(X)))&
(![X]:((happy(X)|~old(X))=>~curious(X)))&
(![X]:((brave(X)&happy(X))<=>(rich(X)&~funny(X))))&
((?[X]:((~patient(X)&~rich(X))))=>(?[X]:(generous(X))))&
(![X]:(~kind(X)<=>funny(X)))&
(![X]:(humble(X)<=>(old(X)<~>~brave(X))))&
((?[X]:((~humble(X)<~>~rich(X))))=>(?[X]:((~humble(X)&humble(X)))))&
((brave(john))<=>(?[X]:((generous(X)&creative(X)))))&
((~patient(john))<=>(funny(lucy)))&
(((tall(fred)<~>strong(fred)))<=>(?[X]:(~curious(X))))&
(![X]:((happy(X)&~old(X))<=>creative(X)))&
(![X]:((old(X)<~>~creative(X))<=>(~curious(X)|~brave(X))))&
((?[X]:((~strong(X)<~>strong(X))))=>(?[X]:((~quiet(X)<~>wise(X)))))&
((?[X]:(~kind(X)))<=>(curious(alice)))&
((?[X]:((~generous(X)|strong(X))))=>(?[X]:(~generous(X))))&
(?[X]:((~happy(X)|~brave(X))))&
(?[X]:(generous(X)))&
((calm(john)|~strong(john)))&
((~calm(paul)|~creative(paul)))&
(?[X]:((humble(X)|~brave(X))))&
((~quiet(lucy)<~>kind(lucy)))&
((~generous(paul)|humble(paul)))&
(rich(john)) | ~happy(alice) | [
"p1",
"p2",
"p3",
"p5",
"p9",
"p14",
"p23",
"hypothesis"
]
| % SZS status Unsatisfiable for 6714954267862882727157483
% SZS output start Proof for 6714954267862882727157483
2. ! [X0] : (happy(X0) <=> ~patient(X0)) [input p1]
3. ! [X0] : ((~old(X0) | happy(X0)) => ~curious(X0)) [input p2]
4. ! [X0] : ((happy(X0) & brave(X0)) <=> (~funny(X0) & rich(X0))) [input p3]
6. ! [X0] : (~kind(X0) <=> funny(X0)) [input p5]
10. ~patient(john) <=> funny(lucy) [input p9]
15. ? [X0] : ~kind(X0) <=> curious(alice) [input p14]
24. rich(john) [input p23]
25. happy(alice) [input hypothesis]
31. ! [X0] : (~curious(X0) | (old(X0) & ~happy(X0))) [ennf transformation 3]
37. ! [X0] : ((happy(X0) | patient(X0)) & (~patient(X0) | ~happy(X0))) [nnf transformation 2]
38. ! [X0] : (((happy(X0) & brave(X0)) | (funny(X0) | ~rich(X0))) & ((~funny(X0) & rich(X0)) | (~happy(X0) | ~brave(X0)))) [nnf transformation 4]
39. ! [X0] : (((happy(X0) & brave(X0)) | funny(X0) | ~rich(X0)) & ((~funny(X0) & rich(X0)) | ~happy(X0) | ~brave(X0))) [flattening 38]
43. ! [X0] : ((~kind(X0) | ~funny(X0)) & (funny(X0) | kind(X0))) [nnf transformation 6]
53. (~patient(john) | ~funny(lucy)) & (funny(lucy) | patient(john)) [nnf transformation 10]
66. (? [X0] : ~kind(X0) | ~curious(alice)) & (curious(alice) | ! [X0] : kind(X0)) [nnf transformation 15]
67. (? [X0] : ~kind(X0) | ~curious(alice)) & (curious(alice) | ! [X1] : kind(X1)) [rectify 66]
68. ? [X0] : ~kind(X0) => ~kind(sK5) [choice axiom]
69. (~kind(sK5) | ~curious(alice)) & (curious(alice) | ! [X1] : kind(X1)) [skolemisation 67,68]
82. ~patient(X0) | ~happy(X0) [cnf transformation 37]
84. ~happy(X0) | ~curious(X0) [cnf transformation 31]
89. ~rich(X0) | funny(X0) | happy(X0) [cnf transformation 39]
92. ~kind(X0) | ~funny(X0) [cnf transformation 43]
104. funny(lucy) | patient(john) [cnf transformation 53]
123. curious(alice) | kind(X1) [cnf transformation 69]
135. rich(john) [cnf transformation 24]
136. happy(alice) [cnf transformation 25]
192. 12 <=> funny(lucy) [avatar definition]
193. funny(lucy) <- (12) [avatar component clause 192]
196. 13 <=> patient(john) [avatar definition]
197. patient(john) <- (13) [avatar component clause 196]
200. 13 | 12 [avatar split clause 104,192,196]
243. 22 <=> curious(alice) [avatar definition]
252. 24 <=> ! [X1] : kind(X1) [avatar definition]
253. kind(X1) <- (24) [avatar component clause 252]
254. 24 | 22 [avatar split clause 123,243,252]
323. ~curious(alice) [resolution 84,136]
326. ~22 [avatar split clause 323,243]
333. ~funny(X1) <- (24) [resolution 92,253]
334. $false <- (12, 24) [resolution 333,193]
335. ~12 | ~24 [avatar contradiction clause 334]
336. ~happy(john) <- (13) [resolution 197,82]
372. funny(john) | happy(john) [resolution 89,135]
374. happy(john) <- (24) [subsumption resolution 372,333]
375. $false <- (13, 24) [subsumption resolution 374,336]
376. ~13 | ~24 [avatar contradiction clause 375]
377. $false [avatar sat refutation 200,254,326,335,376]
% SZS output end Proof for 6714954267862882727157483
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient is not wise or not happy. If someone is both rich and not rich then someone is happy or old and vice versa. Everyone who is either quiet or not rich is quiet or rich and vice versa. Everyone who is not tall or strong is either not funny or not wise. Everyone who is either happy or funny is either curious or not curious. If susan is wise or not brave then susan is tall. Everyone who is not happy or happy is either not quiet or not calm and vice versa. If someone is not quiet or calm then someone is both not kind and not funny. Everyone who is either strong or kind is wise or not humble and vice versa. Everyone who is both tall and not generous is not old and vice versa. If alice is either not strong or not rich then someone is either not humble or generous. If someone is not kind or strong then mary is either not curious or strong. If someone is both rich and not strong then someone is both strong and calm. Everyone who is both not strong and curious is either patient or not wise and vice versa. Everyone who is old is both not patient and brave and vice versa. Everyone who is strong is either not strong or not humble. Mary is creative or not rich. Lucy is both funny and not brave. Fred is either rich or not creative. John is not kind. Someone is both not calm and not patient. Susan is not calm or not generous. | Fred is not generous. | entailment | (![X]:(patient(X)=>(~wise(X)|~happy(X))))&
((?[X]:((rich(X)&~rich(X))))<=>(?[X]:((happy(X)|old(X)))))&
(![X]:((quiet(X)<~>~rich(X))<=>(quiet(X)|rich(X))))&
(![X]:((~tall(X)|strong(X))=>(~funny(X)<~>~wise(X))))&
(![X]:((happy(X)<~>funny(X))=>(curious(X)<~>~curious(X))))&
(((wise(susan)|~brave(susan)))=>(tall(susan)))&
(![X]:((~happy(X)|happy(X))<=>(~quiet(X)<~>~calm(X))))&
((?[X]:((~quiet(X)|calm(X))))=>(?[X]:((~kind(X)&~funny(X)))))&
(![X]:((strong(X)<~>kind(X))<=>(wise(X)|~humble(X))))&
(![X]:((tall(X)&~generous(X))<=>~old(X)))&
(((~strong(alice)<~>~rich(alice)))=>(?[X]:((~humble(X)<~>generous(X)))))&
((?[X]:((~kind(X)|strong(X))))=>((~curious(mary)<~>strong(mary))))&
((?[X]:((rich(X)&~strong(X))))=>(?[X]:((strong(X)&calm(X)))))&
(![X]:((~strong(X)&curious(X))<=>(patient(X)<~>~wise(X))))&
(![X]:(old(X)<=>(~patient(X)&brave(X))))&
(![X]:(strong(X)=>(~strong(X)<~>~humble(X))))&
((creative(mary)|~rich(mary)))&
((funny(lucy)&~brave(lucy)))&
((rich(fred)<~>~creative(fred)))&
(~kind(john))&
(?[X]:((~calm(X)&~patient(X))))&
((~calm(susan)|~generous(susan))) | ~generous(fred) | [
"p1",
"p9",
"hypothesis"
]
| % SZS status Unsatisfiable for 9184865677097485719292374
% SZS output start Proof for 9184865677097485719292374
2. ? [X0] : (~rich(X0) & rich(X0)) <=> ? [X0] : (old(X0) | happy(X0)) [input p1]
10. ! [X0] : ((~generous(X0) & tall(X0)) <=> ~old(X0)) [input p9]
23. generous(fred) [input hypothesis]
24. ? [X0] : (~rich(X0) & rich(X0)) <=> ? [X1] : (old(X1) | happy(X1)) [rectify 2]
37. (? [X0] : (~rich(X0) & rich(X0)) | ! [X1] : (~old(X1) & ~happy(X1))) & (? [X1] : (old(X1) | happy(X1)) | ! [X0] : (rich(X0) | ~rich(X0))) [nnf transformation 24]
38. (? [X0] : (~rich(X0) & rich(X0)) | ! [X1] : (~old(X1) & ~happy(X1))) & (? [X2] : (old(X2) | happy(X2)) | ! [X3] : (rich(X3) | ~rich(X3))) [rectify 37]
39. ? [X0] : (~rich(X0) & rich(X0)) => (~rich(sK0) & rich(sK0)) [choice axiom]
40. ? [X2] : (old(X2) | happy(X2)) => (old(sK1) | happy(sK1)) [choice axiom]
41. ((~rich(sK0) & rich(sK0)) | ! [X1] : (~old(X1) & ~happy(X1))) & ((old(sK1) | happy(sK1)) | ! [X3] : (rich(X3) | ~rich(X3))) [skolemisation 38,40,39]
53. ! [X0] : (((~generous(X0) & tall(X0)) | old(X0)) & (~old(X0) | (generous(X0) | ~tall(X0)))) [nnf transformation 10]
54. ! [X0] : (((~generous(X0) & tall(X0)) | old(X0)) & (~old(X0) | generous(X0) | ~tall(X0))) [flattening 53]
73. rich(sK0) | ~old(X1) [cnf transformation 41]
75. ~rich(sK0) | ~old(X1) [cnf transformation 41]
110. ~generous(X0) | old(X0) [cnf transformation 54]
141. generous(fred) [cnf transformation 23]
147. 1 <=> ! [X1] : ~old(X1) [avatar definition]
148. ~old(X1) <- (1) [avatar component clause 147]
150. 2 <=> rich(sK0) [avatar definition]
153. 1 | ~2 [avatar split clause 75,150,147]
158. 1 | 2 [avatar split clause 73,150,147]
236. old(fred) [resolution 110,141]
237. $false <- (1) [subsumption resolution 236,148]
238. ~1 [avatar contradiction clause 237]
239. $false [avatar sat refutation 153,158,238]
% SZS output end Proof for 9184865677097485719292374
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not humble or strong is either not funny or not creative.
If mary is not creative then someone is not curious or wise and vice versa.
Everyone who is both humble and not creative is either not calm or rich and vice versa.
Everyone who is not kind is either not kind or creative and vice versa.
Everyone who is quiet or not tall is kind or curious.
If someone is happy then someone is both wise and rich.
If someone is patient then someone is not generous or not rich and vice versa.
Everyone who is quiet or brave is both not tall and not brave.
Everyone who is generous or kind is tall and vice versa.
Everyone who is either not calm or creative is either not happy or strong and vice versa.
If alice is kind or rich then someone is not calm or patient and vice versa.
Everyone who is either not kind or generous is not strong.
If mary is wise or not rich then someone is either not funny or not humble.
If susan is not strong or not tall then mary is either not tall or strong and vice versa.
If someone is calm then someone is both not rich and not strong.
Everyone who is both not rich and wise is both not creative and not strong.
Fred is quiet or calm.
Mary is rich or not generous.
Susan is both generous and humble.
Someone is not calm or not strong.
Mary is both not happy and not humble.
Susan is both kind and not calm.
Someone is either not old or happy. | Mary is not generous. | entailment | (![X]:((~humble(X)|strong(X))=>(~funny(X)<~>~creative(X))))&
((~creative(mary))<=>(?[X]:((~curious(X)|wise(X)))))&
(![X]:((humble(X)&~creative(X))<=>(~calm(X)<~>rich(X))))&
(![X]:(~kind(X)<=>(~kind(X)<~>creative(X))))&
(![X]:((quiet(X)|~tall(X))=>(kind(X)|curious(X))))&
((?[X]:(happy(X)))=>(?[X]:((wise(X)&rich(X)))))&
((?[X]:(patient(X)))<=>(?[X]:((~generous(X)|~rich(X)))))&
(![X]:((quiet(X)|brave(X))=>(~tall(X)&~brave(X))))&
(![X]:((generous(X)|kind(X))<=>tall(X)))&
(![X]:((~calm(X)<~>creative(X))<=>(~happy(X)<~>strong(X))))&
(((kind(alice)|rich(alice)))<=>(?[X]:((~calm(X)|patient(X)))))&
(![X]:((~kind(X)<~>generous(X))=>~strong(X)))&
(((wise(mary)|~rich(mary)))=>(?[X]:((~funny(X)<~>~humble(X)))))&
(((~strong(susan)|~tall(susan)))<=>((~tall(mary)<~>strong(mary))))&
((?[X]:(calm(X)))=>(?[X]:((~rich(X)&~strong(X)))))&
(![X]:((~rich(X)&wise(X))=>(~creative(X)&~strong(X))))&
((quiet(fred)|calm(fred)))&
((rich(mary)|~generous(mary)))&
((generous(susan)&humble(susan)))&
(?[X]:((~calm(X)|~strong(X))))&
((~happy(mary)&~humble(mary)))&
((kind(susan)&~calm(susan)))&
(?[X]:((~old(X)<~>happy(X)))) | ~generous(mary) | [
"p2",
"p3",
"p8",
"p9",
"p11",
"p13",
"p17",
"p18",
"p20",
"p21",
"hypothesis"
]
| % SZS status Unsatisfiable for 5683991413671758054310345
% SZS output start Proof for 5683991413671758054310345
3. ! [X0] : ((~creative(X0) & humble(X0)) <=> (~calm(X0) <~> rich(X0))) [input p2]
4. ! [X0] : (~kind(X0) <=> (~kind(X0) <~> creative(X0))) [input p3]
9. ! [X0] : ((kind(X0) | generous(X0)) <=> tall(X0)) [input p8]
10. ! [X0] : ((~calm(X0) <~> creative(X0)) <=> (~happy(X0) <~> strong(X0))) [input p9]
12. ! [X0] : ((~kind(X0) <~> generous(X0)) => ~strong(X0)) [input p11]
14. (~tall(susan) | ~strong(susan)) <=> (~tall(mary) <~> strong(mary)) [input p13]
18. ~generous(mary) | rich(mary) [input p17]
19. humble(susan) & generous(susan) [input p18]
21. ~humble(mary) & ~happy(mary) [input p20]
22. ~calm(susan) & kind(susan) [input p21]
24. generous(mary) [input hypothesis]
34. ! [X0] : (~strong(X0) | (~kind(X0) <=> generous(X0))) [ennf transformation 12]
44. ! [X0] : (((~creative(X0) & humble(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (creative(X0) | ~humble(X0)))) [nnf transformation 3]
45. ! [X0] : (((~creative(X0) & humble(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | creative(X0) | ~humble(X0))) [flattening 44]
46. ! [X0] : ((~kind(X0) | ((~kind(X0) | ~creative(X0)) & (creative(X0) | kind(X0)))) & (((~creative(X0) | kind(X0)) & (creative(X0) | ~kind(X0))) | kind(X0))) [nnf transformation 4]
55. ! [X0] : (((kind(X0) | generous(X0)) | ~tall(X0)) & (tall(X0) | (~kind(X0) & ~generous(X0)))) [nnf transformation 9]
56. ! [X0] : ((kind(X0) | generous(X0) | ~tall(X0)) & (tall(X0) | (~kind(X0) & ~generous(X0)))) [flattening 55]
57. ! [X0] : ((((~creative(X0) | calm(X0)) & (creative(X0) | ~calm(X0))) | ((~happy(X0) | ~strong(X0)) & (strong(X0) | happy(X0)))) & (((~strong(X0) | happy(X0)) & (strong(X0) | ~happy(X0))) | ((~calm(X0) | ~creative(X0)) & (creative(X0) | calm(X0))))) [nnf transformation 10]
63. ! [X0] : (~strong(X0) | ((~kind(X0) | ~generous(X0)) & (generous(X0) | kind(X0)))) [nnf transformation 34]
67. ((~tall(susan) | ~strong(susan)) | ((~tall(mary) | ~strong(mary)) & (strong(mary) | tall(mary)))) & (((~strong(mary) | tall(mary)) & (strong(mary) | ~tall(mary))) | (tall(susan) & strong(susan))) [nnf transformation 14]
68. (~tall(susan) | ~strong(susan) | ((~tall(mary) | ~strong(mary)) & (strong(mary) | tall(mary)))) & (((~strong(mary) | tall(mary)) & (strong(mary) | ~tall(mary))) | (tall(susan) & strong(susan))) [flattening 67]
87. ~rich(X0) | ~calm(X0) | humble(X0) [cnf transformation 45]
91. ~creative(X0) | kind(X0) | kind(X0) [cnf transformation 46]
93. ~kind(X0) | ~kind(X0) | ~creative(X0) [cnf transformation 46]
102. ~generous(X0) | tall(X0) [cnf transformation 56]
107. ~strong(X0) | happy(X0) | creative(X0) | calm(X0) [cnf transformation 57]
118. ~generous(X0) | ~kind(X0) | ~strong(X0) [cnf transformation 63]
123. strong(mary) | ~tall(mary) | strong(susan) [cnf transformation 68]
134. ~generous(mary) | rich(mary) [cnf transformation 18]
135. generous(susan) [cnf transformation 19]
138. ~happy(mary) [cnf transformation 21]
139. ~humble(mary) [cnf transformation 21]
140. kind(susan) [cnf transformation 22]
144. generous(mary) [cnf transformation 24]
145. ~creative(X0) | kind(X0) [duplicate literal removal 91]
146. ~kind(X0) | ~creative(X0) [duplicate literal removal 93]
168. ~creative(X0) [subsumption resolution 145,146]
208. ~strong(X0) | happy(X0) | calm(X0) [subsumption resolution 107,168]
234. 20 <=> rich(mary) [avatar definition]
236. rich(mary) <- (20) [avatar component clause 234]
254. 24 <=> strong(mary) [avatar definition]
255. strong(mary) <- (24) [avatar component clause 254]
258. 25 <=> tall(mary) [avatar definition]
262. 26 <=> strong(susan) [avatar definition]
274. 26 | ~25 | 24 [avatar split clause 123,254,258,262]
298. 33 <=> generous(mary) [avatar definition]
299. generous(mary) <- (33) [avatar component clause 298]
301. 20 | ~33 [avatar split clause 134,298,234]
321. 33 [avatar split clause 144,298]
323. tall(mary) <- (33) [resolution 102,299]
327. 25 | ~33 [avatar split clause 323,298,258]
362. ~calm(mary) | humble(mary) <- (20) [resolution 87,236]
384. ~calm(mary) <- (20) [subsumption resolution 362,139]
393. ~kind(susan) | ~strong(susan) [resolution 118,135]
403. happy(mary) | calm(mary) <- (24) [resolution 208,255]
404. calm(mary) <- (24) [subsumption resolution 403,138]
405. $false <- (20, 24) [subsumption resolution 404,384]
406. ~20 | ~24 [avatar contradiction clause 405]
412. ~strong(susan) [subsumption resolution 393,140]
413. ~26 [avatar split clause 412,262]
414. $false [avatar sat refutation 274,301,321,327,406,413]
% SZS output end Proof for 5683991413671758054310345
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 calm or quiet is not generous or generous and vice versa.
Everyone who is either funny or calm is either generous or quiet and vice versa.
If someone is either not tall or funny then john is either not quiet or not funny and vice versa.
Everyone who is both patient and tall is not tall and vice versa.
Everyone who is not creative is brave and vice versa.
If mary is wise then someone is either not old or generous and vice versa.
If paul is not old then alice is both creative and not quiet.
Everyone who is curious or creative is both quiet and creative.
If lucy is not wise or strong then someone is both not calm and not funny and vice versa.
Everyone who is both not funny and not brave is not old or not quiet and vice versa.
Everyone who is both humble and patient is both calm and not old and vice versa.
If mary is both not rich and old then fred is both not creative and old.
If someone is both patient and humble then alice is not creative and vice versa.
Everyone who is not creative is either not quiet or tall.
If someone is both humble and not generous then john is either funny or old.
Someone is humble or rich.
Fred is not brave.
Someone is brave.
Someone is not generous.
Someone is both old and quiet.
Paul is either strong or not generous. | John is not quiet. | contradiction | (![X]:((~calm(X)|quiet(X))<=>(~generous(X)|generous(X))))&
(![X]:((funny(X)<~>calm(X))<=>(generous(X)<~>quiet(X))))&
((?[X]:((~tall(X)<~>funny(X))))<=>((~quiet(john)<~>~funny(john))))&
(![X]:((patient(X)&tall(X))<=>~tall(X)))&
(![X]:(~creative(X)<=>brave(X)))&
((wise(mary))<=>(?[X]:((~old(X)<~>generous(X)))))&
((~old(paul))=>((creative(alice)&~quiet(alice))))&
(![X]:((curious(X)|creative(X))=>(quiet(X)&creative(X))))&
(((~wise(lucy)|strong(lucy)))<=>(?[X]:((~calm(X)&~funny(X)))))&
(![X]:((~funny(X)&~brave(X))<=>(~old(X)|~quiet(X))))&
(![X]:((humble(X)&patient(X))<=>(calm(X)&~old(X))))&
(((~rich(mary)&old(mary)))=>((~creative(fred)&old(fred))))&
((?[X]:((patient(X)&humble(X))))<=>(~creative(alice)))&
(![X]:(~creative(X)=>(~quiet(X)<~>tall(X))))&
((?[X]:((humble(X)&~generous(X))))=>((funny(john)<~>old(john))))&
(?[X]:((humble(X)|rich(X))))&
(~brave(fred))&
(?[X]:(brave(X)))&
(?[X]:(~generous(X)))&
(?[X]:((old(X)&quiet(X))))&
((strong(paul)<~>~generous(paul))) | ~quiet(john) | [
"p3",
"p7",
"p13",
"hypothesis"
]
| % SZS status Unsatisfiable for 4179701414556847703650748
% SZS output start Proof for 4179701414556847703650748
4. ! [X0] : ((tall(X0) & patient(X0)) <=> ~tall(X0)) [input p3]
8. ! [X0] : ((creative(X0) | curious(X0)) => (creative(X0) & quiet(X0))) [input p7]
14. ! [X0] : (~creative(X0) => (~quiet(X0) <~> tall(X0))) [input p13]
22. ~quiet(john) [input hypothesis]
25. ! [X0] : (creative(X0) => (creative(X0) & quiet(X0))) [pure predicate removal 8]
27. ! [X0] : ((creative(X0) & quiet(X0)) | ~creative(X0)) [ennf transformation 25]
28. ! [X0] : ((~quiet(X0) <~> tall(X0)) | creative(X0)) [ennf transformation 14]
37. ! [X0] : (((tall(X0) & patient(X0)) | tall(X0)) & (~tall(X0) | (~tall(X0) | ~patient(X0)))) [nnf transformation 4]
38. ! [X0] : (((tall(X0) & patient(X0)) | tall(X0)) & (~tall(X0) | ~tall(X0) | ~patient(X0))) [flattening 37]
57. ! [X0] : (((~tall(X0) | quiet(X0)) & (tall(X0) | ~quiet(X0))) | creative(X0)) [nnf transformation 28]
88. tall(X0) | tall(X0) [cnf transformation 38]
97. quiet(X0) | ~creative(X0) [cnf transformation 27]
117. ~tall(X0) | quiet(X0) | creative(X0) [cnf transformation 57]
127. ~quiet(john) [cnf transformation 22]
129. tall(X0) [duplicate literal removal 88]
234. quiet(X0) | creative(X0) [subsumption resolution 117,129]
235. quiet(X0) [subsumption resolution 234,97]
257. $false [subsumption resolution 127,235]
% SZS output end Proof for 4179701414556847703650748
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 |
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