premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
|
|---|---|---|---|---|---|---|---|
Everyone who is quiet is generous or not old.
If someone is both not generous and not wise then someone is old or not curious.
If someone is either funny or not old then john is both humble and not wise.
Everyone who is brave is both not tall and calm and vice versa.
Everyone who is not quiet is not patient and vice versa.
Everyone who is either not generous or not kind is either strong or not rich.
If someone is not quiet then lucy is not quiet and vice versa.
If john is both strong and not generous then alice is not rich or not wise.
Everyone who is both curious and patient is not old or not calm and vice versa.
If someone is both not rich and kind then paul is both generous and quiet and vice versa.
If someone is both not calm and not patient then someone is not kind or not calm.
Everyone who is not calm is humble or old.
Everyone who is not happy or old is not funny.
Everyone who is either patient or not brave is both not calm and not tall.
If john is old then someone is not old and vice versa.
Everyone who is either wise or not happy is happy and vice versa.
John is strong or not kind.
Someone is happy or not rich.
Someone is both patient and kind.
Someone is either brave or not old.
Susan is not kind or not old.
Someone is either patient or brave.
Lucy is generous or not rich.
Someone is not patient or strong. | Alice is not wise. | contradiction | (![X]:(quiet(X)=>(generous(X)|~old(X))))&
((?[X]:((~generous(X)&~wise(X))))=>(?[X]:((old(X)|~curious(X)))))&
((?[X]:((funny(X)<~>~old(X))))=>((humble(john)&~wise(john))))&
(![X]:(brave(X)<=>(~tall(X)&calm(X))))&
(![X]:(~quiet(X)<=>~patient(X)))&
(![X]:((~generous(X)<~>~kind(X))=>(strong(X)<~>~rich(X))))&
((?[X]:(~quiet(X)))<=>(~quiet(lucy)))&
(((strong(john)&~generous(john)))=>((~rich(alice)|~wise(alice))))&
(![X]:((curious(X)&patient(X))<=>(~old(X)|~calm(X))))&
((?[X]:((~rich(X)&kind(X))))<=>((generous(paul)&quiet(paul))))&
((?[X]:((~calm(X)&~patient(X))))=>(?[X]:((~kind(X)|~calm(X)))))&
(![X]:(~calm(X)=>(humble(X)|old(X))))&
(![X]:((~happy(X)|old(X))=>~funny(X)))&
(![X]:((patient(X)<~>~brave(X))=>(~calm(X)&~tall(X))))&
((old(john))<=>(?[X]:(~old(X))))&
(![X]:((wise(X)<~>~happy(X))<=>happy(X)))&
((strong(john)|~kind(john)))&
(?[X]:((happy(X)|~rich(X))))&
(?[X]:((patient(X)&kind(X))))&
(?[X]:((brave(X)<~>~old(X))))&
((~kind(susan)|~old(susan)))&
(?[X]:((patient(X)<~>brave(X))))&
((generous(lucy)|~rich(lucy)))&
(?[X]:((~patient(X)|strong(X)))) | ~wise(alice) | [
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8744204869070973132712990
% SZS output start Proof for 8744204869070973132712990
16. ! [X0] : ((wise(X0) <~> ~happy(X0)) <=> happy(X0)) [input p15]
25. ~wise(alice) [input hypothesis]
67. ! [X0] : ((((happy(X0) | ~wise(X0)) & (~happy(X0) | wise(X0))) | ~happy(X0)) & (happy(X0) | ((wise(X0) | happy(X0)) & (~happy(X0) | ~wise(X0))))) [nnf transformation 16]
115. happy(X0) | wise(X0) | happy(X0) [cnf transformation 67]
116. ~happy(X0) | wise(X0) | ~happy(X0) [cnf transformation 67]
129. ~wise(alice) [cnf transformation 25]
130. happy(X0) | wise(X0) [duplicate literal removal 115]
131. ~happy(X0) | wise(X0) [duplicate literal removal 116]
226. wise(X0) [subsumption resolution 130,131]
278. $false [subsumption resolution 129,226]
% SZS output end Proof for 8744204869070973132712990
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is happy or old is not wise or not tall and vice versa.
Everyone who is not tall is happy or not humble.
Everyone who is either not tall or humble is either strong or not quiet.
Everyone who is both not brave and not generous is strong or rich.
Everyone who is not old is both calm and rich.
Everyone who is not tall is either creative or not humble and vice versa.
If paul is not calm or not quiet then alice is either not funny or strong.
Everyone who is not funny or wise is not tall or not strong and vice versa.
If someone is either curious or not funny then someone is curious or happy.
If someone is either tall or calm then paul is both generous and not calm and vice versa.
Everyone who is brave or not humble is both wise and patient and vice versa.
If someone is either tall or wise then susan is not calm.
Everyone who is both not patient and not wise is curious or not curious.
If lucy is not curious or not old then john is both tall and not generous and vice versa.
Everyone who is both quiet and funny is not brave and vice versa.
Everyone who is both not wise and not kind is not old or not funny.
Someone is either funny or happy.
Paul is both not tall and not generous.
Paul is either old or generous.
Alice is both kind and not wise.
Someone is not generous.
Someone is not patient.
Someone is either old or wise.
Alice is not curious. | Alice is strong. | entailment | (![X]:((happy(X)|old(X))<=>(~wise(X)|~tall(X))))&
(![X]:(~tall(X)=>(happy(X)|~humble(X))))&
(![X]:((~tall(X)<~>humble(X))=>(strong(X)<~>~quiet(X))))&
(![X]:((~brave(X)&~generous(X))=>(strong(X)|rich(X))))&
(![X]:(~old(X)=>(calm(X)&rich(X))))&
(![X]:(~tall(X)<=>(creative(X)<~>~humble(X))))&
(((~calm(paul)|~quiet(paul)))=>((~funny(alice)<~>strong(alice))))&
(![X]:((~funny(X)|wise(X))<=>(~tall(X)|~strong(X))))&
((?[X]:((curious(X)<~>~funny(X))))=>(?[X]:((curious(X)|happy(X)))))&
((?[X]:((tall(X)<~>calm(X))))<=>((generous(paul)&~calm(paul))))&
(![X]:((brave(X)|~humble(X))<=>(wise(X)&patient(X))))&
((?[X]:((tall(X)<~>wise(X))))=>(~calm(susan)))&
(![X]:((~patient(X)&~wise(X))=>(curious(X)|~curious(X))))&
(((~curious(lucy)|~old(lucy)))<=>((tall(john)&~generous(john))))&
(![X]:((quiet(X)&funny(X))<=>~brave(X)))&
(![X]:((~wise(X)&~kind(X))=>(~old(X)|~funny(X))))&
(?[X]:((funny(X)<~>happy(X))))&
((~tall(paul)&~generous(paul)))&
((old(paul)<~>generous(paul)))&
((kind(alice)&~wise(alice)))&
(?[X]:(~generous(X)))&
(?[X]:(~patient(X)))&
(?[X]:((old(X)<~>wise(X))))&
(~curious(alice)) | strong(alice) | [
"p6",
"p9",
"p10",
"p14",
"p17",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 3113517349377285603245908
% SZS output start Proof for 3113517349377285603245908
7. (~quiet(paul) | ~calm(paul)) => (~funny(alice) <~> strong(alice)) [input p6]
10. ? [X0] : (tall(X0) <~> calm(X0)) <=> (~calm(paul) & generous(paul)) [input p9]
11. ! [X0] : ((~humble(X0) | brave(X0)) <=> (patient(X0) & wise(X0))) [input p10]
15. ! [X0] : ((funny(X0) & quiet(X0)) <=> ~brave(X0)) [input p14]
18. ~generous(paul) & ~tall(paul) [input p17]
20. ~wise(alice) & kind(alice) [input p19]
25. ~strong(alice) [input hypothesis]
28. ~wise(alice) [pure predicate removal 20]
35. (~funny(alice) <~> strong(alice)) | (quiet(paul) & calm(paul)) [ennf transformation 7]
44. ((~strong(alice) | funny(alice)) & (strong(alice) | ~funny(alice))) | (quiet(paul) & calm(paul)) [nnf transformation 35]
51. (? [X0] : ((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | (calm(paul) | ~generous(paul))) & ((~calm(paul) & generous(paul)) | ! [X0] : ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0)))) [nnf transformation 10]
52. (? [X0] : ((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | calm(paul) | ~generous(paul)) & ((~calm(paul) & generous(paul)) | ! [X0] : ((tall(X0) | ~calm(X0)) & (calm(X0) | ~tall(X0)))) [flattening 51]
53. (? [X0] : ((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) | calm(paul) | ~generous(paul)) & ((~calm(paul) & generous(paul)) | ! [X1] : ((tall(X1) | ~calm(X1)) & (calm(X1) | ~tall(X1)))) [rectify 52]
54. ? [X0] : ((~calm(X0) | ~tall(X0)) & (calm(X0) | tall(X0))) => ((~calm(sK1) | ~tall(sK1)) & (calm(sK1) | tall(sK1))) [choice axiom]
55. (((~calm(sK1) | ~tall(sK1)) & (calm(sK1) | tall(sK1))) | calm(paul) | ~generous(paul)) & ((~calm(paul) & generous(paul)) | ! [X1] : ((tall(X1) | ~calm(X1)) & (calm(X1) | ~tall(X1)))) [skolemisation 53,54]
56. ! [X0] : (((~humble(X0) | brave(X0)) | (~patient(X0) | ~wise(X0))) & ((patient(X0) & wise(X0)) | (humble(X0) & ~brave(X0)))) [nnf transformation 11]
57. ! [X0] : ((~humble(X0) | brave(X0) | ~patient(X0) | ~wise(X0)) & ((patient(X0) & wise(X0)) | (humble(X0) & ~brave(X0)))) [flattening 56]
61. ! [X0] : (((funny(X0) & quiet(X0)) | brave(X0)) & (~brave(X0) | (~funny(X0) | ~quiet(X0)))) [nnf transformation 15]
62. ! [X0] : (((funny(X0) & quiet(X0)) | brave(X0)) & (~brave(X0) | ~funny(X0) | ~quiet(X0))) [flattening 61]
88. strong(alice) | ~funny(alice) | calm(paul) [cnf transformation 44]
99. generous(paul) | tall(X1) | ~calm(X1) [cnf transformation 55]
104. ~brave(X0) | wise(X0) [cnf transformation 57]
119. funny(X0) | brave(X0) [cnf transformation 62]
122. ~tall(paul) [cnf transformation 18]
123. ~generous(paul) [cnf transformation 18]
126. ~wise(alice) [cnf transformation 28]
132. ~strong(alice) [cnf transformation 25]
138. 2 <=> funny(alice) [avatar definition]
139. ~funny(alice) <- (~2) [avatar component clause 138]
142. 3 <=> strong(alice) [avatar definition]
147. 4 <=> calm(paul) [avatar definition]
149. calm(paul) <- (4) [avatar component clause 147]
152. 4 | ~2 | 3 [avatar split clause 88,142,138,147]
170. 9 <=> generous(paul) [avatar definition]
184. 12 <=> ! [X1] : (tall(X1) | ~calm(X1)) [avatar definition]
185. ~calm(X1) | tall(X1) <- (12) [avatar component clause 184]
191. 12 | 9 [avatar split clause 99,170,184]
236. ~9 [avatar split clause 123,170]
253. ~3 [avatar split clause 132,142]
258. brave(alice) <- (~2) [resolution 119,139]
261. wise(alice) <- (~2) [resolution 258,104]
262. $false <- (~2) [subsumption resolution 261,126]
263. 2 [avatar contradiction clause 262]
264. tall(paul) <- (4, 12) [resolution 149,185]
265. $false <- (4, 12) [subsumption resolution 264,122]
266. ~4 | ~12 [avatar contradiction clause 265]
267. $false [avatar sat refutation 152,191,236,253,263,266]
% SZS output end Proof for 3113517349377285603245908
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is both curious and calm and vice versa.
If fred is both not rich and not quiet then john is either generous or calm and vice versa.
Everyone who is either strong or old is both not quiet and not old and vice versa.
Everyone who is either not quiet or strong is either not creative or not funny and vice versa.
If mary is brave or not brave then lucy is brave.
If alice is both not tall and happy then lucy is not kind.
Everyone who is quiet or creative is not creative or not curious.
If lucy is both strong and tall then someone is tall.
Everyone who is patient or happy is not funny and vice versa.
Everyone who is funny or not kind is not creative or not humble.
Everyone who is either rich or brave is both generous and not rich.
If someone is either generous or not quiet then mary is curious and vice versa.
If fred is both generous and not tall then fred is not happy or humble.
Everyone who is both brave and happy is not curious or not old and vice versa.
If john is creative or not strong then lucy is not generous or not strong and vice versa.
Everyone who is not patient is not quiet or not creative.
Mary is not creative.
Someone is either tall or kind.
Paul is wise.
John is both patient and strong.
Someone is generous.
Lucy is both rich and wise.
Someone is both not tall and curious. | Alice is tall. | neutral | (![X]:(funny(X)<=>(curious(X)&calm(X))))&
(((~rich(fred)&~quiet(fred)))<=>((generous(john)<~>calm(john))))&
(![X]:((strong(X)<~>old(X))<=>(~quiet(X)&~old(X))))&
(![X]:((~quiet(X)<~>strong(X))<=>(~creative(X)<~>~funny(X))))&
(((brave(mary)|~brave(mary)))=>(brave(lucy)))&
(((~tall(alice)&happy(alice)))=>(~kind(lucy)))&
(![X]:((quiet(X)|creative(X))=>(~creative(X)|~curious(X))))&
(((strong(lucy)&tall(lucy)))=>(?[X]:(tall(X))))&
(![X]:((patient(X)|happy(X))<=>~funny(X)))&
(![X]:((funny(X)|~kind(X))=>(~creative(X)|~humble(X))))&
(![X]:((rich(X)<~>brave(X))=>(generous(X)&~rich(X))))&
((?[X]:((generous(X)<~>~quiet(X))))<=>(curious(mary)))&
(((generous(fred)&~tall(fred)))=>((~happy(fred)|humble(fred))))&
(![X]:((brave(X)&happy(X))<=>(~curious(X)|~old(X))))&
(((creative(john)|~strong(john)))<=>((~generous(lucy)|~strong(lucy))))&
(![X]:(~patient(X)=>(~quiet(X)|~creative(X))))&
(~creative(mary))&
(?[X]:((tall(X)<~>kind(X))))&
(wise(paul))&
((patient(john)&strong(john)))&
(?[X]:(generous(X)))&
((rich(lucy)&wise(lucy)))&
(?[X]:((~tall(X)&curious(X)))) | tall(alice) | [] | null | 0 |
Everyone who is both not strong and not patient is creative and vice versa.
Everyone who is both kind and not kind is both old and not wise.
If someone is either quiet or not patient then someone is both generous and not brave and vice versa.
If someone is calm or curious then paul is kind or rich.
If someone is not quiet or wise then someone is both strong and brave.
If mary is both happy and curious then susan is not curious.
Everyone who is not patient or not old is either generous or rich and vice versa.
If mary is either creative or humble then someone is patient or not funny.
Everyone who is wise or not humble is either old or not brave and vice versa.
Everyone who is old or not old is both not generous and not curious.
Everyone who is humble or generous is either not generous or not strong.
If someone is either not patient or rich then mary is both not quiet and not strong.
Everyone who is both not curious and not old is not quiet and vice versa.
Everyone who is old is kind.
If mary is not patient or old then paul is not happy or strong.
Everyone who is not strong or happy is either not kind or not happy and vice versa.
John is either rich or calm.
Someone is both not happy and not kind.
Mary is not funny.
Someone is creative.
Lucy is kind or not rich.
Someone is not happy or not quiet. | Mary is patient. | entailment | (![X]:((~strong(X)&~patient(X))<=>creative(X)))&
(![X]:((kind(X)&~kind(X))=>(old(X)&~wise(X))))&
((?[X]:((quiet(X)<~>~patient(X))))<=>(?[X]:((generous(X)&~brave(X)))))&
((?[X]:((calm(X)|curious(X))))=>((kind(paul)|rich(paul))))&
((?[X]:((~quiet(X)|wise(X))))=>(?[X]:((strong(X)&brave(X)))))&
(((happy(mary)&curious(mary)))=>(~curious(susan)))&
(![X]:((~patient(X)|~old(X))<=>(generous(X)<~>rich(X))))&
(((creative(mary)<~>humble(mary)))=>(?[X]:((patient(X)|~funny(X)))))&
(![X]:((wise(X)|~humble(X))<=>(old(X)<~>~brave(X))))&
(![X]:((old(X)|~old(X))=>(~generous(X)&~curious(X))))&
(![X]:((humble(X)|generous(X))=>(~generous(X)<~>~strong(X))))&
((?[X]:((~patient(X)<~>rich(X))))=>((~quiet(mary)&~strong(mary))))&
(![X]:((~curious(X)&~old(X))<=>~quiet(X)))&
(![X]:(old(X)=>kind(X)))&
(((~patient(mary)|old(mary)))=>((~happy(paul)|strong(paul))))&
(![X]:((~strong(X)|happy(X))<=>(~kind(X)<~>~happy(X))))&
((rich(john)<~>calm(john)))&
(?[X]:((~happy(X)&~kind(X))))&
(~funny(mary))&
(?[X]:(creative(X)))&
((kind(lucy)|~rich(lucy)))&
(?[X]:((~happy(X)|~quiet(X)))) | patient(mary) | [
"p2",
"p6",
"p9",
"p11",
"p12",
"p13",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 3362282052360617008194828
% SZS output start Proof for 3362282052360617008194828
3. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ? [X0] : (~brave(X0) & generous(X0)) [input p2]
7. ! [X0] : ((~old(X0) | ~patient(X0)) <=> (generous(X0) <~> rich(X0))) [input p6]
10. ! [X0] : ((~old(X0) | old(X0)) => (~curious(X0) & ~generous(X0))) [input p9]
12. ? [X0] : (~patient(X0) <~> rich(X0)) => (~strong(mary) & ~quiet(mary)) [input p11]
13. ! [X0] : ((~old(X0) & ~curious(X0)) <=> ~quiet(X0)) [input p12]
14. ! [X0] : (old(X0) => kind(X0)) [input p13]
18. ? [X0] : (~kind(X0) & ~happy(X0)) [input p17]
23. ~patient(mary) [input hypothesis]
24. ? [X0] : (quiet(X0) <~> ~patient(X0)) <=> ? [X1] : (~brave(X1) & generous(X1)) [rectify 3]
37. ! [X0] : ((~curious(X0) & ~generous(X0)) | (old(X0) & ~old(X0))) [ennf transformation 10]
39. (~strong(mary) & ~quiet(mary)) | ! [X0] : (~patient(X0) <=> rich(X0)) [ennf transformation 12]
40. ! [X0] : (kind(X0) | ~old(X0)) [ennf transformation 14]
43. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ! [X1] : (brave(X1) | ~generous(X1))) & (? [X1] : (~brave(X1) & generous(X1)) | ! [X0] : ((quiet(X0) | patient(X0)) & (~patient(X0) | ~quiet(X0)))) [nnf transformation 24]
44. (? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) | ! [X1] : (brave(X1) | ~generous(X1))) & (? [X2] : (~brave(X2) & generous(X2)) | ! [X3] : ((quiet(X3) | patient(X3)) & (~patient(X3) | ~quiet(X3)))) [rectify 43]
45. ? [X0] : ((patient(X0) | ~quiet(X0)) & (~patient(X0) | quiet(X0))) => ((patient(sK0) | ~quiet(sK0)) & (~patient(sK0) | quiet(sK0))) [choice axiom]
46. ? [X2] : (~brave(X2) & generous(X2)) => (~brave(sK1) & generous(sK1)) [choice axiom]
47. (((patient(sK0) | ~quiet(sK0)) & (~patient(sK0) | quiet(sK0))) | ! [X1] : (brave(X1) | ~generous(X1))) & ((~brave(sK1) & generous(sK1)) | ! [X3] : ((quiet(X3) | patient(X3)) & (~patient(X3) | ~quiet(X3)))) [skolemisation 44,46,45]
51. ! [X0] : (((~old(X0) | ~patient(X0)) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0)))) & (((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | (old(X0) & patient(X0)))) [nnf transformation 7]
52. ! [X0] : ((~old(X0) | ~patient(X0) | ((generous(X0) | ~rich(X0)) & (rich(X0) | ~generous(X0)))) & (((~rich(X0) | ~generous(X0)) & (rich(X0) | generous(X0))) | (old(X0) & patient(X0)))) [flattening 51]
56. (~strong(mary) & ~quiet(mary)) | ! [X0] : ((~patient(X0) | ~rich(X0)) & (rich(X0) | patient(X0))) [nnf transformation 39]
57. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | (old(X0) | curious(X0)))) [nnf transformation 13]
58. ! [X0] : (((~old(X0) & ~curious(X0)) | quiet(X0)) & (~quiet(X0) | old(X0) | curious(X0))) [flattening 57]
62. ? [X0] : (~kind(X0) & ~happy(X0)) => (~kind(sK3) & ~happy(sK3)) [choice axiom]
63. ~kind(sK3) & ~happy(sK3) [skolemisation 18,62]
73. generous(sK1) | quiet(X3) | patient(X3) [cnf transformation 47]
86. rich(X0) | generous(X0) | old(X0) [cnf transformation 52]
97. ~generous(X0) | ~old(X0) [cnf transformation 37]
98. ~generous(X0) | old(X0) [cnf transformation 37]
100. ~curious(X0) | old(X0) [cnf transformation 37]
106. ~quiet(mary) | ~patient(X0) | ~rich(X0) [cnf transformation 56]
109. ~quiet(X0) | old(X0) | curious(X0) [cnf transformation 58]
112. ~old(X0) | kind(X0) [cnf transformation 40]
124. ~kind(sK3) [cnf transformation 63]
128. ~patient(mary) [cnf transformation 23]
146. 4 <=> ! [X3] : (quiet(X3) | patient(X3)) [avatar definition]
147. quiet(X3) | patient(X3) <- (4) [avatar component clause 146]
158. 7 <=> generous(sK1) [avatar definition]
160. generous(sK1) <- (7) [avatar component clause 158]
161. 4 | 7 [avatar split clause 73,158,146]
212. ~generous(X0) [subsumption resolution 97,98]
215. 19 <=> ! [X0] : (~patient(X0) | ~rich(X0)) [avatar definition]
216. ~rich(X0) | ~patient(X0) <- (19) [avatar component clause 215]
227. 22 <=> quiet(mary) [avatar definition]
229. ~quiet(mary) <- (~22) [avatar component clause 227]
230. 19 | ~22 [avatar split clause 106,227,215]
232. ~quiet(X0) | old(X0) [subsumption resolution 109,100]
247. 26 <=> patient(mary) [avatar definition]
248. ~patient(mary) <- (~26) [avatar component clause 247]
279. ~26 [avatar split clause 128,247]
286. patient(mary) <- (4, ~22) [resolution 147,229]
290. $false <- (4, ~22, ~26) [subsumption resolution 286,248]
291. ~4 | 22 | 26 [avatar contradiction clause 290]
292. $false <- (7) [subsumption resolution 160,212]
293. ~7 [avatar contradiction clause 292]
306. old(X0) | patient(X0) <- (4) [resolution 232,147]
313. generous(X0) | old(X0) | ~patient(X0) <- (19) [resolution 86,216]
315. old(X0) | ~patient(X0) <- (19) [subsumption resolution 313,212]
316. old(X0) <- (4, 19) [subsumption resolution 315,306]
333. kind(X0) <- (4, 19) [resolution 316,112]
347. $false <- (4, 19) [resolution 333,124]
348. ~4 | ~19 [avatar contradiction clause 347]
349. $false [avatar sat refutation 161,230,279,291,293,348]
% SZS output end Proof for 3362282052360617008194828
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not generous and not rich is not calm or wise. If paul is wise or strong then someone is not calm or funny and vice versa. Everyone who is both brave and rich is not rich. If someone is both creative and not brave then susan is either not quiet or patient. Everyone who is both funny and patient is either happy or not brave and vice versa. If paul is either creative or not brave then someone is either not calm or not old. If someone is either not wise or not old then someone is rich or not calm. If paul is not strong or tall then someone is happy. If someone is both not strong and not generous then lucy is both not quiet and not humble. Everyone who is both not wise and creative is both wise and not old and vice versa. If someone is creative or not humble then fred is not happy or old. Everyone who is either not tall or not quiet is generous or not tall. If someone is humble or not kind then someone is both not generous and not calm. If someone is either tall or not strong then lucy is quiet or not calm and vice versa. Everyone who is either calm or old is both wise and not rich. If someone is both not patient and not tall then someone is both not wise and rich and vice versa. Someone is tall. Someone is either generous or not creative. Paul is rich. Someone is not generous or tall. Someone is not curious. Someone is rich or curious. Someone is kind. John is patient or not tall. | Paul is rich. | entailment | (![X]:((~generous(X)&~rich(X))=>(~calm(X)|wise(X))))&
(((wise(paul)|strong(paul)))<=>(?[X]:((~calm(X)|funny(X)))))&
(![X]:((brave(X)&rich(X))=>~rich(X)))&
((?[X]:((creative(X)&~brave(X))))=>((~quiet(susan)<~>patient(susan))))&
(![X]:((funny(X)&patient(X))<=>(happy(X)<~>~brave(X))))&
(((creative(paul)<~>~brave(paul)))=>(?[X]:((~calm(X)<~>~old(X)))))&
((?[X]:((~wise(X)<~>~old(X))))=>(?[X]:((rich(X)|~calm(X)))))&
(((~strong(paul)|tall(paul)))=>(?[X]:(happy(X))))&
((?[X]:((~strong(X)&~generous(X))))=>((~quiet(lucy)&~humble(lucy))))&
(![X]:((~wise(X)&creative(X))<=>(wise(X)&~old(X))))&
((?[X]:((creative(X)|~humble(X))))=>((~happy(fred)|old(fred))))&
(![X]:((~tall(X)<~>~quiet(X))=>(generous(X)|~tall(X))))&
((?[X]:((humble(X)|~kind(X))))=>(?[X]:((~generous(X)&~calm(X)))))&
((?[X]:((tall(X)<~>~strong(X))))<=>((quiet(lucy)|~calm(lucy))))&
(![X]:((calm(X)<~>old(X))=>(wise(X)&~rich(X))))&
((?[X]:((~patient(X)&~tall(X))))<=>(?[X]:((~wise(X)&rich(X)))))&
(?[X]:(tall(X)))&
(?[X]:((generous(X)<~>~creative(X))))&
(rich(paul))&
(?[X]:((~generous(X)|tall(X))))&
(?[X]:(~curious(X)))&
(?[X]:((rich(X)|curious(X))))&
(?[X]:(kind(X)))&
((patient(john)|~tall(john))) | rich(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 4416847319508473264791796
% SZS output start Proof for 4416847319508473264791796
19. rich(paul) [input p18]
25. ~rich(paul) [input hypothesis]
142. rich(paul) [cnf transformation 19]
147. ~rich(paul) [cnf transformation 25]
367. $false [subsumption resolution 147,142]
% SZS output end Proof for 4416847319508473264791796
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall and old is brave or happy. Everyone who is wise is either not generous or generous and vice versa. If fred is not funny then susan is either tall or quiet and vice versa. If someone is old or not generous then lucy is not rich or quiet. If someone is both not curious and not quiet then susan is either humble or not creative and vice versa. Everyone who is either calm or not generous is either humble or not calm. If mary is both brave and not patient then someone is happy or not brave and vice versa. Everyone who is both curious and quiet is not funny. If someone is both not rich and kind then fred is generous or funny. If someone is both quiet and not patient then susan is not curious or not calm and vice versa. Everyone who is not wise or not tall is not calm. Everyone who is brave is not strong or old. If john is either strong or old then someone is either not funny or not creative. Everyone who is not happy or humble is either not generous or not wise. If alice is rich or not happy then alice is quiet. Everyone who is both brave and not wise is both rich and not curious and vice versa. Someone is not strong. John is old or tall. Someone is patient. Fred is both not strong and quiet. Someone is either brave or calm. John is not calm. Someone is not curious. | Alice is quiet. | neutral | (![X]:((~tall(X)&old(X))=>(brave(X)|happy(X))))&
(![X]:(wise(X)<=>(~generous(X)<~>generous(X))))&
((~funny(fred))<=>((tall(susan)<~>quiet(susan))))&
((?[X]:((old(X)|~generous(X))))=>((~rich(lucy)|quiet(lucy))))&
((?[X]:((~curious(X)&~quiet(X))))<=>((humble(susan)<~>~creative(susan))))&
(![X]:((calm(X)<~>~generous(X))=>(humble(X)<~>~calm(X))))&
(((brave(mary)&~patient(mary)))<=>(?[X]:((happy(X)|~brave(X)))))&
(![X]:((curious(X)&quiet(X))=>~funny(X)))&
((?[X]:((~rich(X)&kind(X))))=>((generous(fred)|funny(fred))))&
((?[X]:((quiet(X)&~patient(X))))<=>((~curious(susan)|~calm(susan))))&
(![X]:((~wise(X)|~tall(X))=>~calm(X)))&
(![X]:(brave(X)=>(~strong(X)|old(X))))&
(((strong(john)<~>old(john)))=>(?[X]:((~funny(X)<~>~creative(X)))))&
(![X]:((~happy(X)|humble(X))=>(~generous(X)<~>~wise(X))))&
(((rich(alice)|~happy(alice)))=>(quiet(alice)))&
(![X]:((brave(X)&~wise(X))<=>(rich(X)&~curious(X))))&
(?[X]:(~strong(X)))&
((old(john)|tall(john)))&
(?[X]:(patient(X)))&
((~strong(fred)&quiet(fred)))&
(?[X]:((brave(X)<~>calm(X))))&
(~calm(john))&
(?[X]:(~curious(X))) | quiet(alice) | [] | null | 0 |
If john is generous or not kind then lucy is not quiet and vice versa.
Everyone who is either not quiet or not brave is not curious and vice versa.
If someone is not wise or not patient then someone is both not funny and not kind and vice versa.
If someone is either not curious or old then someone is both quiet and not creative.
Everyone who is either not creative or old is not creative and vice versa.
If someone is either humble or old then alice is not tall or not old.
Everyone who is either rich or not wise is funny and vice versa.
If someone is either not happy or not tall then someone is either not old or not generous and vice versa.
If someone is either humble or not quiet then someone is not generous or curious.
Everyone who is either not creative or happy is both happy and tall and vice versa.
Everyone who is both not happy and not creative is not kind or not tall.
If someone is old then susan is funny and vice versa.
If someone is either not rich or tall then paul is not funny or not humble.
Everyone who is generous or not old is creative and vice versa.
Everyone who is rich or tall is not rich.
Everyone who is both not creative and not funny is either not tall or not curious.
Fred is strong or not quiet.
Someone is not creative or not funny.
Mary is not funny.
Mary is either not curious or not calm.
Someone is humble.
Someone is not strong or calm. | Lucy is old. | contradiction | (((generous(john)|~kind(john)))<=>(~quiet(lucy)))&
(![X]:((~quiet(X)<~>~brave(X))<=>~curious(X)))&
((?[X]:((~wise(X)|~patient(X))))<=>(?[X]:((~funny(X)&~kind(X)))))&
((?[X]:((~curious(X)<~>old(X))))=>(?[X]:((quiet(X)&~creative(X)))))&
(![X]:((~creative(X)<~>old(X))<=>~creative(X)))&
((?[X]:((humble(X)<~>old(X))))=>((~tall(alice)|~old(alice))))&
(![X]:((rich(X)<~>~wise(X))<=>funny(X)))&
((?[X]:((~happy(X)<~>~tall(X))))<=>(?[X]:((~old(X)<~>~generous(X)))))&
((?[X]:((humble(X)<~>~quiet(X))))=>(?[X]:((~generous(X)|curious(X)))))&
(![X]:((~creative(X)<~>happy(X))<=>(happy(X)&tall(X))))&
(![X]:((~happy(X)&~creative(X))=>(~kind(X)|~tall(X))))&
((?[X]:(old(X)))<=>(funny(susan)))&
((?[X]:((~rich(X)<~>tall(X))))=>((~funny(paul)|~humble(paul))))&
(![X]:((generous(X)|~old(X))<=>creative(X)))&
(![X]:((rich(X)|tall(X))=>~rich(X)))&
(![X]:((~creative(X)&~funny(X))=>(~tall(X)<~>~curious(X))))&
((strong(fred)|~quiet(fred)))&
(?[X]:((~creative(X)|~funny(X))))&
(~funny(mary))&
((~curious(mary)<~>~calm(mary)))&
(?[X]:(humble(X)))&
(?[X]:((~strong(X)|calm(X)))) | old(lucy) | [
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3984838048607448102354807
% SZS output start Proof for 3984838048607448102354807
5. ! [X0] : ((~creative(X0) <~> old(X0)) <=> ~creative(X0)) [input p4]
23. old(lucy) [input hypothesis]
51. ! [X0] : ((((~old(X0) | creative(X0)) & (old(X0) | ~creative(X0))) | creative(X0)) & (~creative(X0) | ((~creative(X0) | ~old(X0)) & (old(X0) | creative(X0))))) [nnf transformation 5]
97. ~creative(X0) | ~creative(X0) | ~old(X0) [cnf transformation 51]
99. ~old(X0) | creative(X0) | creative(X0) [cnf transformation 51]
141. old(lucy) [cnf transformation 23]
145. ~creative(X0) | ~old(X0) [duplicate literal removal 97]
146. ~old(X0) | creative(X0) [duplicate literal removal 99]
210. ~old(X0) [subsumption resolution 145,146]
304. $false [subsumption resolution 141,210]
% SZS output end Proof for 3984838048607448102354807
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 wise is either calm or funny and vice versa.
If mary is not kind then someone is both calm and old.
If someone is either not calm or not tall then someone is either tall or not rich.
Everyone who is old or not calm is either not brave or creative and vice versa.
Everyone who is either not wise or strong is kind or not brave.
Everyone who is both not patient and rich is old or not strong.
If someone is both not patient and not brave then someone is both not curious and brave and vice versa.
If someone is both not quiet and creative then fred is generous or tall and vice versa.
Everyone who is not wise or not old is either not creative or calm.
Everyone who is both not patient and not quiet is rich.
If someone is both not patient and curious then someone is happy and vice versa.
Everyone who is either not tall or kind is not funny.
Everyone who is both not calm and not patient is both not happy and not kind.
If fred is funny or humble then someone is either not creative or old and vice versa.
Everyone who is either generous or not tall is not old or not creative.
If alice is curious then paul is both rich and creative and vice versa.
Lucy is both funny and not quiet.
Someone is both rich and not old.
Someone is not funny.
Someone is both not humble and calm.
Someone is both generous and rich.
Someone is both tall and not brave.
Someone is generous.
Mary is creative or happy. | Alice is not curious. | neutral | (![X]:(~wise(X)<=>(calm(X)<~>funny(X))))&
((~kind(mary))=>(?[X]:((calm(X)&old(X)))))&
((?[X]:((~calm(X)<~>~tall(X))))=>(?[X]:((tall(X)<~>~rich(X)))))&
(![X]:((old(X)|~calm(X))<=>(~brave(X)<~>creative(X))))&
(![X]:((~wise(X)<~>strong(X))=>(kind(X)|~brave(X))))&
(![X]:((~patient(X)&rich(X))=>(old(X)|~strong(X))))&
((?[X]:((~patient(X)&~brave(X))))<=>(?[X]:((~curious(X)&brave(X)))))&
((?[X]:((~quiet(X)&creative(X))))<=>((generous(fred)|tall(fred))))&
(![X]:((~wise(X)|~old(X))=>(~creative(X)<~>calm(X))))&
(![X]:((~patient(X)&~quiet(X))=>rich(X)))&
((?[X]:((~patient(X)&curious(X))))<=>(?[X]:(happy(X))))&
(![X]:((~tall(X)<~>kind(X))=>~funny(X)))&
(![X]:((~calm(X)&~patient(X))=>(~happy(X)&~kind(X))))&
(((funny(fred)|humble(fred)))<=>(?[X]:((~creative(X)<~>old(X)))))&
(![X]:((generous(X)<~>~tall(X))=>(~old(X)|~creative(X))))&
((curious(alice))<=>((rich(paul)&creative(paul))))&
((funny(lucy)&~quiet(lucy)))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:(~funny(X)))&
(?[X]:((~humble(X)&calm(X))))&
(?[X]:((generous(X)&rich(X))))&
(?[X]:((tall(X)&~brave(X))))&
(?[X]:(generous(X)))&
((creative(mary)|happy(mary))) | ~curious(alice) | [] | null | 0 |
Everyone who is not curious or not generous is either not curious or not brave.
Everyone who is not generous or curious is not curious or funny.
If someone is either curious or rich then someone is either not brave or not calm and vice versa.
Everyone who is not quiet or rich is either old or not humble.
Everyone who is funny is not strong.
Everyone who is either strong or not happy is patient or quiet.
Everyone who is tall is either kind or happy.
Everyone who is happy or tall is not brave.
If someone is humble then someone is patient or not wise and vice versa.
If mary is both not happy and creative then someone is tall or not funny.
Everyone who is not happy or creative is both happy and generous and vice versa.
If john is both not brave and not calm then someone is either curious or funny.
Everyone who is not funny or tall is not humble or strong and vice versa.
If paul is either generous or not old then someone is not patient or old and vice versa.
Everyone who is not calm or wise is tall and vice versa.
If mary is patient then someone is either kind or not quiet and vice versa.
Someone is either creative or strong.
Susan is kind or not happy.
Someone is either quiet or not strong.
Paul is both not generous and rich.
Someone is both creative and quiet.
Someone is old or kind. | John is generous. | neutral | (![X]:((~curious(X)|~generous(X))=>(~curious(X)<~>~brave(X))))&
(![X]:((~generous(X)|curious(X))=>(~curious(X)|funny(X))))&
((?[X]:((curious(X)<~>rich(X))))<=>(?[X]:((~brave(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|rich(X))=>(old(X)<~>~humble(X))))&
(![X]:(funny(X)=>~strong(X)))&
(![X]:((strong(X)<~>~happy(X))=>(patient(X)|quiet(X))))&
(![X]:(tall(X)=>(kind(X)<~>happy(X))))&
(![X]:((happy(X)|tall(X))=>~brave(X)))&
((?[X]:(humble(X)))<=>(?[X]:((patient(X)|~wise(X)))))&
(((~happy(mary)&creative(mary)))=>(?[X]:((tall(X)|~funny(X)))))&
(![X]:((~happy(X)|creative(X))<=>(happy(X)&generous(X))))&
(((~brave(john)&~calm(john)))=>(?[X]:((curious(X)<~>funny(X)))))&
(![X]:((~funny(X)|tall(X))<=>(~humble(X)|strong(X))))&
(((generous(paul)<~>~old(paul)))<=>(?[X]:((~patient(X)|old(X)))))&
(![X]:((~calm(X)|wise(X))<=>tall(X)))&
((patient(mary))<=>(?[X]:((kind(X)<~>~quiet(X)))))&
(?[X]:((creative(X)<~>strong(X))))&
((kind(susan)|~happy(susan)))&
(?[X]:((quiet(X)<~>~strong(X))))&
((~generous(paul)&rich(paul)))&
(?[X]:((creative(X)&quiet(X))))&
(?[X]:((old(X)|kind(X)))) | generous(john) | [] | null | 0 |
If alice is not curious then someone is either not generous or curious.
Everyone who is both not generous and not old is both not calm and not quiet.
Everyone who is creative is either not kind or kind and vice versa.
Everyone who is quiet is wise.
Everyone who is both creative and brave is both not tall and not happy.
Everyone who is not old is funny.
If someone is creative then susan is either creative or happy and vice versa.
Everyone who is either wise or not strong is not quiet.
Everyone who is both wise and generous is either not generous or creative.
If alice is not creative then someone is humble or old.
If someone is both not calm and not patient then someone is patient and vice versa.
If someone is generous or funny then alice is not creative or rich.
Everyone who is both not curious and not funny is wise and vice versa.
Everyone who is both funny and brave is not quiet or not funny and vice versa.
If fred is kind or not rich then someone is generous or not funny.
Everyone who is curious or not old is either patient or not generous.
Alice is not wise or not calm.
Someone is either rich or not rich.
Someone is kind.
Someone is either tall or not kind.
Someone is not curious.
Someone is either not rich or patient. | Alice is creative. | entailment | ((~curious(alice))=>(?[X]:((~generous(X)<~>curious(X)))))&
(![X]:((~generous(X)&~old(X))=>(~calm(X)&~quiet(X))))&
(![X]:(creative(X)<=>(~kind(X)<~>kind(X))))&
(![X]:(quiet(X)=>wise(X)))&
(![X]:((creative(X)&brave(X))=>(~tall(X)&~happy(X))))&
(![X]:(~old(X)=>funny(X)))&
((?[X]:(creative(X)))<=>((creative(susan)<~>happy(susan))))&
(![X]:((wise(X)<~>~strong(X))=>~quiet(X)))&
(![X]:((wise(X)&generous(X))=>(~generous(X)<~>creative(X))))&
((~creative(alice))=>(?[X]:((humble(X)|old(X)))))&
((?[X]:((~calm(X)&~patient(X))))<=>(?[X]:(patient(X))))&
((?[X]:((generous(X)|funny(X))))=>((~creative(alice)|rich(alice))))&
(![X]:((~curious(X)&~funny(X))<=>wise(X)))&
(![X]:((funny(X)&brave(X))<=>(~quiet(X)|~funny(X))))&
(((kind(fred)|~rich(fred)))=>(?[X]:((generous(X)|~funny(X)))))&
(![X]:((curious(X)|~old(X))=>(patient(X)<~>~generous(X))))&
((~wise(alice)|~calm(alice)))&
(?[X]:((rich(X)<~>~rich(X))))&
(?[X]:(kind(X)))&
(?[X]:((tall(X)<~>~kind(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~rich(X)<~>patient(X)))) | creative(alice) | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable for 2004106441071914383814656
% SZS output start Proof for 2004106441071914383814656
3. ! [X0] : (creative(X0) <=> (~kind(X0) <~> kind(X0))) [input p2]
23. ~creative(alice) [input hypothesis]
43. ! [X0] : ((creative(X0) | ((~kind(X0) | ~kind(X0)) & (kind(X0) | kind(X0)))) & (((~kind(X0) | kind(X0)) & (kind(X0) | ~kind(X0))) | ~creative(X0))) [nnf transformation 3]
79. creative(X0) | kind(X0) | kind(X0) [cnf transformation 43]
80. creative(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 43]
118. ~creative(alice) [cnf transformation 23]
122. creative(X0) | kind(X0) [duplicate literal removal 79]
123. creative(X0) | ~kind(X0) [duplicate literal removal 80]
138. creative(X0) [subsumption resolution 122,123]
225. $false [subsumption resolution 118,138]
% SZS output end Proof for 2004106441071914383814656
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.026 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not creative then someone is brave.
If someone is either not creative or not kind then fred is both not funny and calm.
Everyone who is rich is either happy or generous.
Everyone who is both not tall and creative is rich.
If someone is old or not calm then someone is calm.
If paul is generous then alice is not tall or humble.
If someone is not calm then someone is not humble.
Everyone who is not humble or happy is calm or not patient.
Everyone who is not patient is not creative and vice versa.
If someone is not funny or not rich then paul is either brave or funny.
Everyone who is both happy and not creative is either not strong or not rich.
Everyone who is either not brave or not patient is both not creative and not wise.
If john is either humble or creative then susan is both old and not generous and vice versa.
Everyone who is patient is not humble and vice versa.
Everyone who is not humble is either patient or creative.
If someone is both wise and not funny then someone is either not kind or not humble.
Someone is either not humble or not happy.
Someone is either not calm or generous.
Alice is both generous and not brave.
Someone is either rich or patient.
John is both not patient and kind.
Mary is tall or not strong.
Someone is curious.
Susan is not creative. | Paul is not calm. | contradiction | ((?[X]:(~creative(X)))=>(?[X]:(brave(X))))&
((?[X]:((~creative(X)<~>~kind(X))))=>((~funny(fred)&calm(fred))))&
(![X]:(rich(X)=>(happy(X)<~>generous(X))))&
(![X]:((~tall(X)&creative(X))=>rich(X)))&
((?[X]:((old(X)|~calm(X))))=>(?[X]:(calm(X))))&
((generous(paul))=>((~tall(alice)|humble(alice))))&
((?[X]:(~calm(X)))=>(?[X]:(~humble(X))))&
(![X]:((~humble(X)|happy(X))=>(calm(X)|~patient(X))))&
(![X]:(~patient(X)<=>~creative(X)))&
((?[X]:((~funny(X)|~rich(X))))=>((brave(paul)<~>funny(paul))))&
(![X]:((happy(X)&~creative(X))=>(~strong(X)<~>~rich(X))))&
(![X]:((~brave(X)<~>~patient(X))=>(~creative(X)&~wise(X))))&
(((humble(john)<~>creative(john)))<=>((old(susan)&~generous(susan))))&
(![X]:(patient(X)<=>~humble(X)))&
(![X]:(~humble(X)=>(patient(X)<~>creative(X))))&
((?[X]:((wise(X)&~funny(X))))=>(?[X]:((~kind(X)<~>~humble(X)))))&
(?[X]:((~humble(X)<~>~happy(X))))&
(?[X]:((~calm(X)<~>generous(X))))&
((generous(alice)&~brave(alice)))&
(?[X]:((rich(X)<~>patient(X))))&
((~patient(john)&kind(john)))&
((tall(mary)|~strong(mary)))&
(?[X]:(curious(X)))&
(~creative(susan)) | ~calm(paul) | [
"p6",
"p8",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 5212796678906344981133305
% SZS output start Proof for 5212796678906344981133305
7. ? [X0] : ~calm(X0) => ? [X0] : ~humble(X0) [input p6]
9. ! [X0] : (~patient(X0) <=> ~creative(X0)) [input p8]
14. ! [X0] : (patient(X0) <=> ~humble(X0)) [input p13]
15. ! [X0] : (~humble(X0) => (patient(X0) <~> creative(X0))) [input p14]
25. ~calm(paul) [input hypothesis]
28. ? [X0] : ~calm(X0) => ? [X1] : ~humble(X1) [rectify 7]
41. ? [X1] : ~humble(X1) | ! [X0] : calm(X0) [ennf transformation 28]
48. ! [X0] : ((patient(X0) <~> creative(X0)) | humble(X0)) [ennf transformation 15]
57. ? [X0] : ~humble(X0) | ! [X1] : calm(X1) [rectify 41]
58. ? [X0] : ~humble(X0) => ~humble(sK2) [choice axiom]
59. ~humble(sK2) | ! [X1] : calm(X1) [skolemisation 57,58]
60. ! [X0] : ((~patient(X0) | creative(X0)) & (~creative(X0) | patient(X0))) [nnf transformation 9]
66. ! [X0] : ((patient(X0) | humble(X0)) & (~humble(X0) | ~patient(X0))) [nnf transformation 14]
67. ! [X0] : (((~creative(X0) | ~patient(X0)) & (creative(X0) | patient(X0))) | humble(X0)) [nnf transformation 48]
88. ~humble(sK2) | calm(X1) [cnf transformation 59]
92. ~patient(X0) | creative(X0) [cnf transformation 60]
107. ~patient(X0) | ~humble(X0) [cnf transformation 66]
108. patient(X0) | humble(X0) [cnf transformation 66]
110. ~creative(X0) | ~patient(X0) | humble(X0) [cnf transformation 67]
123. ~calm(paul) [cnf transformation 25]
151. 7 <=> ! [X1] : calm(X1) [avatar definition]
152. calm(X1) <- (7) [avatar component clause 151]
176. 13 <=> humble(sK2) [avatar definition]
178. ~humble(sK2) <- (~13) [avatar component clause 176]
179. 7 | ~13 [avatar split clause 88,176,151]
221. ~patient(X0) | humble(X0) [subsumption resolution 110,92]
222. ~patient(X0) [subsumption resolution 221,107]
255. humble(X2) [resolution 108,222]
257. $false <- (~13) [resolution 255,178]
260. 13 [avatar contradiction clause 257]
261. $false <- (7) [resolution 152,123]
264. ~7 [avatar contradiction clause 261]
265. $false [avatar sat refutation 179,260,264]
% SZS output end Proof for 5212796678906344981133305
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or creative is both not happy and old. If someone is not creative or not brave then susan is not generous. If someone is either not rich or creative then john is not funny. Everyone who is calm is funny and vice versa. If someone is both rich and not patient then someone is not happy or quiet and vice versa. Everyone who is both not curious and curious is either kind or not kind. Everyone who is not strong or wise is both funny and not funny and vice versa. If lucy is either generous or not rich then fred is either strong or not calm and vice versa. If someone is either not wise or old then john is both kind and not strong. Everyone who is either not old or not patient is either quiet or wise. Everyone who is kind or not funny is both not kind and not happy and vice versa. Everyone who is both brave and curious is kind. Everyone who is strong or creative is curious. Everyone who is curious is both not calm and not tall. John is not happy or not quiet. Someone is either curious or tall. Someone is both not funny and not kind. Mary is rich. Susan is either happy or not generous. Someone is not kind or not rich. Paul is both not funny and old. Someone is either not calm or wise. | Paul is brave. | contradiction | (![X]:((old(X)|creative(X))=>(~happy(X)&old(X))))&
((?[X]:((~creative(X)|~brave(X))))=>(~generous(susan)))&
((?[X]:((~rich(X)<~>creative(X))))=>(~funny(john)))&
(![X]:(calm(X)<=>funny(X)))&
((?[X]:((rich(X)&~patient(X))))<=>(?[X]:((~happy(X)|quiet(X)))))&
(![X]:((~curious(X)&curious(X))=>(kind(X)<~>~kind(X))))&
(![X]:((~strong(X)|wise(X))<=>(funny(X)&~funny(X))))&
(((generous(lucy)<~>~rich(lucy)))<=>((strong(fred)<~>~calm(fred))))&
((?[X]:((~wise(X)<~>old(X))))=>((kind(john)&~strong(john))))&
(![X]:((~old(X)<~>~patient(X))=>(quiet(X)<~>wise(X))))&
(![X]:((kind(X)|~funny(X))<=>(~kind(X)&~happy(X))))&
(![X]:((brave(X)&curious(X))=>kind(X)))&
(![X]:((strong(X)|creative(X))=>curious(X)))&
(![X]:(curious(X)=>(~calm(X)&~tall(X))))&
((~happy(john)|~quiet(john)))&
(?[X]:((curious(X)<~>tall(X))))&
(?[X]:((~funny(X)&~kind(X))))&
(rich(mary))&
((happy(susan)<~>~generous(susan)))&
(?[X]:((~kind(X)|~rich(X))))&
((~funny(paul)&old(paul)))&
(?[X]:((~calm(X)<~>wise(X)))) | brave(paul) | [
"p6",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5957990839974432417393657
% SZS output start Proof for 5957990839974432417393657
7. ! [X0] : ((wise(X0) | ~strong(X0)) <=> (~funny(X0) & funny(X0))) [input p6]
11. ! [X0] : ((~funny(X0) | kind(X0)) <=> (~happy(X0) & ~kind(X0))) [input p10]
12. ! [X0] : ((curious(X0) & brave(X0)) => kind(X0)) [input p11]
13. ! [X0] : ((creative(X0) | strong(X0)) => curious(X0)) [input p12]
23. brave(paul) [input hypothesis]
32. ! [X0] : (kind(X0) | (~curious(X0) | ~brave(X0))) [ennf transformation 12]
33. ! [X0] : (kind(X0) | ~curious(X0) | ~brave(X0)) [flattening 32]
34. ! [X0] : (curious(X0) | (~creative(X0) & ~strong(X0))) [ennf transformation 13]
44. ! [X0] : (((wise(X0) | ~strong(X0)) | (funny(X0) | ~funny(X0))) & ((~funny(X0) & funny(X0)) | (~wise(X0) & strong(X0)))) [nnf transformation 7]
45. ! [X0] : ((wise(X0) | ~strong(X0) | funny(X0) | ~funny(X0)) & ((~funny(X0) & funny(X0)) | (~wise(X0) & strong(X0)))) [flattening 44]
49. ! [X0] : (((~funny(X0) | kind(X0)) | (happy(X0) | kind(X0))) & ((~happy(X0) & ~kind(X0)) | (funny(X0) & ~kind(X0)))) [nnf transformation 11]
50. ! [X0] : ((~funny(X0) | kind(X0) | happy(X0) | kind(X0)) & ((~happy(X0) & ~kind(X0)) | (funny(X0) & ~kind(X0)))) [flattening 49]
79. funny(X0) | strong(X0) [cnf transformation 45]
81. ~funny(X0) | strong(X0) [cnf transformation 45]
100. ~kind(X0) | ~kind(X0) [cnf transformation 50]
105. kind(X0) | ~curious(X0) | ~brave(X0) [cnf transformation 33]
106. curious(X0) | ~strong(X0) [cnf transformation 34]
123. brave(paul) [cnf transformation 23]
124. ~kind(X0) [duplicate literal removal 100]
181. strong(X0) [subsumption resolution 79,81]
206. ~curious(X0) | ~brave(X0) [subsumption resolution 105,124]
207. curious(X0) [subsumption resolution 106,181]
232. ~brave(X0) [resolution 206,207]
233. $false [resolution 232,123]
% SZS output end Proof for 5957990839974432417393657
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is brave is kind or not old. If someone is either not curious or not happy then mary is strong. If fred is both patient and not humble then someone is either not wise or kind and vice versa. Everyone who is curious or wise is not quiet. If someone is both not funny and not rich then someone is both not kind and old and vice versa. Everyone who is both not funny and not tall is rich or funny and vice versa. If mary is not generous or not rich then alice is quiet or not humble. If fred is creative or not funny then alice is not creative or strong. If someone is both brave and happy then lucy is not kind or not happy and vice versa. Everyone who is both happy and rich is either happy or generous. If alice is creative or not quiet then lucy is not quiet. If fred is both not old and not rich then someone is brave and vice versa. Everyone who is both not generous and wise is either not generous or not patient and vice versa. If someone is not strong or kind then john is not rich. Everyone who is either not wise or kind is both not funny and not wise and vice versa. Everyone who is not generous is curious or not patient. Susan is calm or funny. John is both not curious and not calm. Alice is either humble or wise. Someone is both not strong and not creative. Someone is both not creative and not kind. Alice is strong. Someone is wise or not funny. | Lucy is not kind. | entailment | (![X]:(brave(X)=>(kind(X)|~old(X))))&
((?[X]:((~curious(X)<~>~happy(X))))=>(strong(mary)))&
(((patient(fred)&~humble(fred)))<=>(?[X]:((~wise(X)<~>kind(X)))))&
(![X]:((curious(X)|wise(X))=>~quiet(X)))&
((?[X]:((~funny(X)&~rich(X))))<=>(?[X]:((~kind(X)&old(X)))))&
(![X]:((~funny(X)&~tall(X))<=>(rich(X)|funny(X))))&
(((~generous(mary)|~rich(mary)))=>((quiet(alice)|~humble(alice))))&
(((creative(fred)|~funny(fred)))=>((~creative(alice)|strong(alice))))&
((?[X]:((brave(X)&happy(X))))<=>((~kind(lucy)|~happy(lucy))))&
(![X]:((happy(X)&rich(X))=>(happy(X)<~>generous(X))))&
(((creative(alice)|~quiet(alice)))=>(~quiet(lucy)))&
(((~old(fred)&~rich(fred)))<=>(?[X]:(brave(X))))&
(![X]:((~generous(X)&wise(X))<=>(~generous(X)<~>~patient(X))))&
((?[X]:((~strong(X)|kind(X))))=>(~rich(john)))&
(![X]:((~wise(X)<~>kind(X))<=>(~funny(X)&~wise(X))))&
(![X]:(~generous(X)=>(curious(X)|~patient(X))))&
((calm(susan)|funny(susan)))&
((~curious(john)&~calm(john)))&
((humble(alice)<~>wise(alice)))&
(?[X]:((~strong(X)&~creative(X))))&
(?[X]:((~creative(X)&~kind(X))))&
(strong(alice))&
(?[X]:((wise(X)|~funny(X)))) | ~kind(lucy) | [
"p5",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 2910728233796164633942581
% SZS output start Proof for 2910728233796164633942581
6. ! [X0] : ((~tall(X0) & ~funny(X0)) <=> (funny(X0) | rich(X0))) [input p5]
15. ! [X0] : ((~wise(X0) <~> kind(X0)) <=> (~wise(X0) & ~funny(X0))) [input p14]
24. kind(lucy) [input hypothesis]
53. ! [X0] : (((~tall(X0) & ~funny(X0)) | (~funny(X0) & ~rich(X0))) & ((funny(X0) | rich(X0)) | (tall(X0) | funny(X0)))) [nnf transformation 6]
54. ! [X0] : (((~tall(X0) & ~funny(X0)) | (~funny(X0) & ~rich(X0))) & (funny(X0) | rich(X0) | tall(X0) | funny(X0))) [flattening 53]
68. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | (wise(X0) | funny(X0))) & ((~wise(X0) & ~funny(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [nnf transformation 15]
69. ! [X0] : ((((~kind(X0) | wise(X0)) & (kind(X0) | ~wise(X0))) | wise(X0) | funny(X0)) & ((~wise(X0) & ~funny(X0)) | ((~wise(X0) | ~kind(X0)) & (kind(X0) | wise(X0))))) [flattening 68]
94. ~funny(X0) | ~funny(X0) [cnf transformation 54]
121. ~wise(X0) | ~wise(X0) | ~kind(X0) [cnf transformation 69]
123. ~kind(X0) | wise(X0) | wise(X0) | funny(X0) [cnf transformation 69]
134. kind(lucy) [cnf transformation 24]
135. ~wise(X0) | ~kind(X0) [duplicate literal removal 121]
136. ~kind(X0) | wise(X0) | funny(X0) [duplicate literal removal 123]
141. ~funny(X0) [duplicate literal removal 94]
237. 22 <=> kind(lucy) [avatar definition]
239. kind(lucy) <- (22) [avatar component clause 237]
276. 30 <=> ! [X0] : ~kind(X0) [avatar definition]
277. ~kind(X0) <- (30) [avatar component clause 276]
287. ~kind(X0) | wise(X0) [subsumption resolution 136,141]
288. ~kind(X0) [subsumption resolution 135,287]
289. 30 [avatar split clause 288,276]
297. 22 [avatar split clause 134,237]
300. $false <- (22, 30) [subsumption resolution 239,277]
301. ~22 | ~30 [avatar contradiction clause 300]
306. $false [avatar sat refutation 289,297,301]
% SZS output end Proof for 2910728233796164633942581
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 or not generous is not curious or wise.
Everyone who is either not humble or not generous is either humble or old and vice versa.
Everyone who is patient is brave.
If mary is both curious and not rich then someone is calm.
If susan is both not generous and not humble then susan is both not humble and generous.
If lucy is creative or not curious then susan is curious.
Everyone who is humble is curious or kind and vice versa.
Everyone who is not strong or not wise is either generous or not generous and vice versa.
Everyone who is both not wise and not tall is not calm.
If alice is both kind and not patient then someone is not quiet or not humble and vice versa.
Everyone who is curious or not patient is happy and vice versa.
Everyone who is both not old and not patient is generous or tall and vice versa.
If someone is not curious or not calm then john is generous.
Everyone who is either not creative or not curious is not curious or rich and vice versa.
Everyone who is both not patient and not strong is not tall or not strong.
If someone is generous then fred is either not curious or not strong.
Someone is either not brave or not happy.
Paul is both humble and not funny.
Someone is happy.
Someone is either brave or not patient.
Mary is either not patient or curious.
Someone is not creative or not old.
Someone is both not patient and rich. | Mary is not humble. | contradiction | (![X]:((~calm(X)|~generous(X))=>(~curious(X)|wise(X))))&
(![X]:((~humble(X)<~>~generous(X))<=>(humble(X)<~>old(X))))&
(![X]:(patient(X)=>brave(X)))&
(((curious(mary)&~rich(mary)))=>(?[X]:(calm(X))))&
(((~generous(susan)&~humble(susan)))=>((~humble(susan)&generous(susan))))&
(((creative(lucy)|~curious(lucy)))=>(curious(susan)))&
(![X]:(humble(X)<=>(curious(X)|kind(X))))&
(![X]:((~strong(X)|~wise(X))<=>(generous(X)<~>~generous(X))))&
(![X]:((~wise(X)&~tall(X))=>~calm(X)))&
(((kind(alice)&~patient(alice)))<=>(?[X]:((~quiet(X)|~humble(X)))))&
(![X]:((curious(X)|~patient(X))<=>happy(X)))&
(![X]:((~old(X)&~patient(X))<=>(generous(X)|tall(X))))&
((?[X]:((~curious(X)|~calm(X))))=>(generous(john)))&
(![X]:((~creative(X)<~>~curious(X))<=>(~curious(X)|rich(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)|~strong(X))))&
((?[X]:(generous(X)))=>((~curious(fred)<~>~strong(fred))))&
(?[X]:((~brave(X)<~>~happy(X))))&
((humble(paul)&~funny(paul)))&
(?[X]:(happy(X)))&
(?[X]:((brave(X)<~>~patient(X))))&
((~patient(mary)<~>curious(mary)))&
(?[X]:((~creative(X)|~old(X))))&
(?[X]:((~patient(X)&rich(X)))) | ~humble(mary) | [
"p1",
"p6",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 8536489464892577533687352
% SZS output start Proof for 8536489464892577533687352
2. ! [X0] : ((~humble(X0) <~> ~generous(X0)) <=> (humble(X0) <~> old(X0))) [input p1]
7. ! [X0] : (humble(X0) <=> (kind(X0) | curious(X0))) [input p6]
12. ! [X0] : ((~patient(X0) & ~old(X0)) <=> (tall(X0) | generous(X0))) [input p11]
13. ? [X0] : (~calm(X0) | ~curious(X0)) => generous(john) [input p12]
24. ~humble(mary) [input hypothesis]
36. generous(john) | ! [X0] : (calm(X0) & curious(X0)) [ennf transformation 13]
40. ! [X0] : ((((generous(X0) | humble(X0)) & (~generous(X0) | ~humble(X0))) | ((humble(X0) | ~old(X0)) & (old(X0) | ~humble(X0)))) & (((~old(X0) | ~humble(X0)) & (old(X0) | humble(X0))) | ((~humble(X0) | generous(X0)) & (~generous(X0) | humble(X0))))) [nnf transformation 2]
43. ! [X0] : ((humble(X0) | (~kind(X0) & ~curious(X0))) & ((kind(X0) | curious(X0)) | ~humble(X0))) [nnf transformation 7]
44. ! [X0] : ((humble(X0) | (~kind(X0) & ~curious(X0))) & (kind(X0) | curious(X0) | ~humble(X0))) [flattening 43]
54. ! [X0] : (((~patient(X0) & ~old(X0)) | (~tall(X0) & ~generous(X0))) & ((tall(X0) | generous(X0)) | (patient(X0) | old(X0)))) [nnf transformation 12]
55. ! [X0] : (((~patient(X0) & ~old(X0)) | (~tall(X0) & ~generous(X0))) & (tall(X0) | generous(X0) | patient(X0) | old(X0))) [flattening 54]
74. old(X0) | humble(X0) | ~generous(X0) | humble(X0) [cnf transformation 40]
77. ~old(X0) | ~humble(X0) | ~humble(X0) | generous(X0) [cnf transformation 40]
78. ~generous(X0) | ~humble(X0) | old(X0) | ~humble(X0) [cnf transformation 40]
81. generous(X0) | humble(X0) | humble(X0) | ~old(X0) [cnf transformation 40]
89. ~curious(X0) | humble(X0) [cnf transformation 44]
107. ~old(X0) | ~generous(X0) [cnf transformation 55]
111. generous(john) | curious(X0) [cnf transformation 36]
133. ~humble(mary) [cnf transformation 24]
139. old(X0) | humble(X0) | ~generous(X0) [duplicate literal removal 74]
140. ~old(X0) | ~humble(X0) | generous(X0) [duplicate literal removal 77]
141. ~generous(X0) | ~humble(X0) | old(X0) [duplicate literal removal 78]
142. generous(X0) | humble(X0) | ~old(X0) [duplicate literal removal 81]
143. ~old(X0) | generous(X0) [subsumption resolution 140,142]
144. ~generous(X0) | old(X0) [subsumption resolution 139,141]
183. 9 <=> ! [X0] : humble(X0) [avatar definition]
184. humble(X0) <- (9) [avatar component clause 183]
209. ~old(X0) [subsumption resolution 107,143]
215. 16 <=> generous(john) [avatar definition]
217. generous(john) <- (16) [avatar component clause 215]
220. 17 <=> ! [X0] : curious(X0) [avatar definition]
221. curious(X0) <- (17) [avatar component clause 220]
222. 17 | 16 [avatar split clause 111,215,220]
264. $false <- (9) [resolution 184,133]
265. ~9 [avatar contradiction clause 264]
279. old(john) <- (16) [resolution 144,217]
280. $false <- (16) [subsumption resolution 279,209]
281. ~16 [avatar contradiction clause 280]
283. humble(X1) <- (17) [resolution 221,89]
284. 9 | ~17 [avatar split clause 283,220,183]
285. $false [avatar sat refutation 222,265,281,284]
% SZS output end Proof for 8536489464892577533687352
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not calm or not wise then fred is both not funny and patient. Everyone who is either curious or not funny is brave and vice versa. Everyone who is both not humble and rich is not generous or patient. Everyone who is generous or curious is not old and vice versa. If fred is either not quiet or not tall then someone is both creative and quiet and vice versa. Everyone who is not rich is humble. Everyone who is either not humble or brave is both not quiet and brave. Everyone who is not happy or kind is not generous. Everyone who is either not brave or old is both quiet and not creative and vice versa. Everyone who is both brave and rich is not curious or humble and vice versa. Everyone who is quiet or not creative is generous. Everyone who is both not brave and not calm is either strong or patient. If lucy is tall then someone is either not old or not tall. If alice is either not patient or wise then john is either curious or not funny. If fred is not rich then fred is both not humble and curious and vice versa. Everyone who is either not humble or quiet is not curious. Lucy is not generous or patient. Someone is either not strong or old. Someone is funny or happy. Someone is both not tall and generous. Mary is curious or not curious. Someone is either rich or not kind. | Mary is old. | contradiction | (((~calm(susan)|~wise(susan)))=>((~funny(fred)&patient(fred))))&
(![X]:((curious(X)<~>~funny(X))<=>brave(X)))&
(![X]:((~humble(X)&rich(X))=>(~generous(X)|patient(X))))&
(![X]:((generous(X)|curious(X))<=>~old(X)))&
(((~quiet(fred)<~>~tall(fred)))<=>(?[X]:((creative(X)&quiet(X)))))&
(![X]:(~rich(X)=>humble(X)))&
(![X]:((~humble(X)<~>brave(X))=>(~quiet(X)&brave(X))))&
(![X]:((~happy(X)|kind(X))=>~generous(X)))&
(![X]:((~brave(X)<~>old(X))<=>(quiet(X)&~creative(X))))&
(![X]:((brave(X)&rich(X))<=>(~curious(X)|humble(X))))&
(![X]:((quiet(X)|~creative(X))=>generous(X)))&
(![X]:((~brave(X)&~calm(X))=>(strong(X)<~>patient(X))))&
((tall(lucy))=>(?[X]:((~old(X)<~>~tall(X)))))&
(((~patient(alice)<~>wise(alice)))=>((curious(john)<~>~funny(john))))&
((~rich(fred))<=>((~humble(fred)&curious(fred))))&
(![X]:((~humble(X)<~>quiet(X))=>~curious(X)))&
((~generous(lucy)|patient(lucy)))&
(?[X]:((~strong(X)<~>old(X))))&
(?[X]:((funny(X)|happy(X))))&
(?[X]:((~tall(X)&generous(X))))&
((curious(mary)|~curious(mary)))&
(?[X]:((rich(X)<~>~kind(X)))) | old(mary) | [
"p3",
"p6",
"p8",
"p9",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 2158423336534587242334580
% SZS output start Proof for 2158423336534587242334580
4. ! [X0] : ((curious(X0) | generous(X0)) <=> ~old(X0)) [input p3]
7. ! [X0] : ((~humble(X0) <~> brave(X0)) => (brave(X0) & ~quiet(X0))) [input p6]
9. ! [X0] : ((~brave(X0) <~> old(X0)) <=> (~creative(X0) & quiet(X0))) [input p8]
10. ! [X0] : ((rich(X0) & brave(X0)) <=> (humble(X0) | ~curious(X0))) [input p9]
11. ! [X0] : ((~creative(X0) | quiet(X0)) => generous(X0)) [input p10]
23. old(mary) [input hypothesis]
32. ! [X0] : ((brave(X0) & ~quiet(X0)) | (~humble(X0) <=> brave(X0))) [ennf transformation 7]
34. ! [X0] : (generous(X0) | (creative(X0) & ~quiet(X0))) [ennf transformation 11]
39. ! [X0] : (((curious(X0) | generous(X0)) | old(X0)) & (~old(X0) | (~curious(X0) & ~generous(X0)))) [nnf transformation 4]
40. ! [X0] : ((curious(X0) | generous(X0) | old(X0)) & (~old(X0) | (~curious(X0) & ~generous(X0)))) [flattening 39]
45. ! [X0] : ((brave(X0) & ~quiet(X0)) | ((~humble(X0) | ~brave(X0)) & (brave(X0) | humble(X0)))) [nnf transformation 32]
46. ! [X0] : ((((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | (creative(X0) | ~quiet(X0))) & ((~creative(X0) & quiet(X0)) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0))))) [nnf transformation 9]
47. ! [X0] : ((((~old(X0) | brave(X0)) & (old(X0) | ~brave(X0))) | creative(X0) | ~quiet(X0)) & ((~creative(X0) & quiet(X0)) | ((~brave(X0) | ~old(X0)) & (old(X0) | brave(X0))))) [flattening 46]
48. ! [X0] : (((rich(X0) & brave(X0)) | (~humble(X0) & curious(X0))) & ((humble(X0) | ~curious(X0)) | (~rich(X0) | ~brave(X0)))) [nnf transformation 10]
49. ! [X0] : (((rich(X0) & brave(X0)) | (~humble(X0) & curious(X0))) & (humble(X0) | ~curious(X0) | ~rich(X0) | ~brave(X0))) [flattening 48]
72. ~old(X0) | ~generous(X0) [cnf transformation 40]
84. brave(X0) | brave(X0) | humble(X0) [cnf transformation 45]
88. ~old(X0) | ~brave(X0) | quiet(X0) [cnf transformation 47]
95. brave(X0) | ~humble(X0) [cnf transformation 49]
98. ~quiet(X0) | generous(X0) [cnf transformation 34]
119. old(mary) [cnf transformation 23]
120. humble(X0) | brave(X0) [duplicate literal removal 84]
161. brave(X0) [subsumption resolution 95,120]
219. ~generous(mary) [resolution 72,119]
249. ~brave(mary) | quiet(mary) [resolution 88,119]
252. quiet(mary) [subsumption resolution 249,161]
258. generous(mary) [resolution 252,98]
260. $false [subsumption resolution 258,219]
% SZS output end Proof for 2158423336534587242334580
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 kind or not generous is both not generous and humble.
Everyone who is either rich or not generous is not funny and vice versa.
Everyone who is calm or tall is not creative and vice versa.
Everyone who is quiet or wise is both not brave and old.
If someone is not wise or curious then someone is not humble or not tall and vice versa.
Everyone who is either humble or curious is not curious.
If alice is both happy and creative then someone is not old or not funny.
If fred is both curious and not wise then someone is kind.
If someone is quiet then john is not calm and vice versa.
Everyone who is generous is either creative or not rich and vice versa.
If someone is both tall and old then someone is either wise or not brave and vice versa.
Everyone who is not curious is not kind or not patient.
Everyone who is not wise or not creative is either not funny or not creative.
If someone is both not generous and not humble then someone is happy or not quiet and vice versa.
Everyone who is rich is strong or not patient and vice versa.
If lucy is both not brave and not patient then someone is either humble or patient.
Someone is kind or not curious.
Mary is both old and not curious.
Paul is patient.
Someone is not creative.
Paul is either creative or patient.
Someone is not tall.
Someone is both not patient and creative.
Someone is both tall and patient. | Alice is happy. | contradiction | (![X]:((~kind(X)|~generous(X))=>(~generous(X)&humble(X))))&
(![X]:((rich(X)<~>~generous(X))<=>~funny(X)))&
(![X]:((calm(X)|tall(X))<=>~creative(X)))&
(![X]:((quiet(X)|wise(X))=>(~brave(X)&old(X))))&
((?[X]:((~wise(X)|curious(X))))<=>(?[X]:((~humble(X)|~tall(X)))))&
(![X]:((humble(X)<~>curious(X))=>~curious(X)))&
(((happy(alice)&creative(alice)))=>(?[X]:((~old(X)|~funny(X)))))&
(((curious(fred)&~wise(fred)))=>(?[X]:(kind(X))))&
((?[X]:(quiet(X)))<=>(~calm(john)))&
(![X]:(generous(X)<=>(creative(X)<~>~rich(X))))&
((?[X]:((tall(X)&old(X))))<=>(?[X]:((wise(X)<~>~brave(X)))))&
(![X]:(~curious(X)=>(~kind(X)|~patient(X))))&
(![X]:((~wise(X)|~creative(X))=>(~funny(X)<~>~creative(X))))&
((?[X]:((~generous(X)&~humble(X))))<=>(?[X]:((happy(X)|~quiet(X)))))&
(![X]:(rich(X)<=>(strong(X)|~patient(X))))&
(((~brave(lucy)&~patient(lucy)))=>(?[X]:((humble(X)<~>patient(X)))))&
(?[X]:((kind(X)|~curious(X))))&
((old(mary)&~curious(mary)))&
(patient(paul))&
(?[X]:(~creative(X)))&
((creative(paul)<~>patient(paul)))&
(?[X]:(~tall(X)))&
(?[X]:((~patient(X)&creative(X))))&
(?[X]:((tall(X)&patient(X)))) | happy(alice) | [
"p0",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 5922049981581467587353035
% SZS output start Proof for 5922049981581467587353035
1. ! [X0] : ((~generous(X0) | ~kind(X0)) => (humble(X0) & ~generous(X0))) [input p0]
14. ? [X0] : (~humble(X0) & ~generous(X0)) <=> ? [X0] : (~quiet(X0) | happy(X0)) [input p13]
25. happy(alice) [input hypothesis]
28. ? [X0] : (~humble(X0) & ~generous(X0)) <=> ? [X1] : (~quiet(X1) | happy(X1)) [rectify 14]
29. ! [X0] : ((humble(X0) & ~generous(X0)) | (generous(X0) & kind(X0))) [ennf transformation 1]
65. (? [X0] : (~humble(X0) & ~generous(X0)) | ! [X1] : (quiet(X1) & ~happy(X1))) & (? [X1] : (~quiet(X1) | happy(X1)) | ! [X0] : (humble(X0) | generous(X0))) [nnf transformation 28]
66. (? [X0] : (~humble(X0) & ~generous(X0)) | ! [X1] : (quiet(X1) & ~happy(X1))) & (? [X2] : (~quiet(X2) | happy(X2)) | ! [X3] : (humble(X3) | generous(X3))) [rectify 65]
67. ? [X0] : (~humble(X0) & ~generous(X0)) => (~humble(sK7) & ~generous(sK7)) [choice axiom]
68. ? [X2] : (~quiet(X2) | happy(X2)) => (~quiet(sK8) | happy(sK8)) [choice axiom]
69. ((~humble(sK7) & ~generous(sK7)) | ! [X1] : (quiet(X1) & ~happy(X1))) & ((~quiet(sK8) | happy(sK8)) | ! [X3] : (humble(X3) | generous(X3))) [skolemisation 66,68,67]
89. humble(X0) | generous(X0) [cnf transformation 29]
127. ~generous(sK7) | ~happy(X1) [cnf transformation 69]
129. ~humble(sK7) | ~happy(X1) [cnf transformation 69]
148. happy(alice) [cnf transformation 25]
184. 9 <=> happy(alice) [avatar definition]
185. happy(alice) <- (9) [avatar component clause 184]
258. 26 <=> humble(sK7) [avatar definition]
260. ~humble(sK7) <- (~26) [avatar component clause 258]
263. 27 <=> ! [X1] : ~happy(X1) [avatar definition]
264. ~happy(X1) <- (27) [avatar component clause 263]
265. 27 | ~26 [avatar split clause 129,258,263]
267. 28 <=> generous(sK7) [avatar definition]
269. ~generous(sK7) <- (~28) [avatar component clause 267]
271. 27 | ~28 [avatar split clause 127,267,263]
300. 9 [avatar split clause 148,184]
304. generous(sK7) <- (~26) [resolution 89,260]
305. $false <- (~26, ~28) [subsumption resolution 304,269]
306. 26 | 28 [avatar contradiction clause 305]
307. $false <- (9, 27) [resolution 264,185]
308. ~9 | ~27 [avatar contradiction clause 307]
309. $false [avatar sat refutation 265,271,300,306,308]
% SZS output end Proof for 5922049981581467587353035
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 alice is not happy or not generous then lucy is either not humble or old and vice versa.
Everyone who is both not strong and not quiet is both tall and not strong and vice versa.
Everyone who is either not funny or not kind is either brave or patient and vice versa.
If someone is both not strong and not patient then someone is both brave and not curious and vice versa.
Everyone who is either generous or not happy is rich and vice versa.
Everyone who is both not calm and tall is brave.
Everyone who is both not funny and strong is either patient or tall.
If someone is either patient or not generous then john is either not creative or not patient and vice versa.
If someone is not brave then paul is both curious and quiet and vice versa.
Everyone who is both not wise and not happy is either creative or not strong.
If lucy is both not creative and kind then fred is humble or kind.
If someone is either not happy or funny then someone is either not quiet or not strong.
Everyone who is brave or calm is not brave or tall and vice versa.
If someone is either not creative or not humble then someone is humble.
Everyone who is either not tall or calm is both not brave and not rich.
Everyone who is both humble and not tall is wise or calm.
Someone is not tall or not funny.
Someone is tall or not creative.
Paul is both not funny and humble.
Alice is creative.
Someone is both not rich and generous.
Lucy is creative.
Someone is not curious.
Fred is both not funny and not generous. | Paul is humble. | entailment | (((~happy(alice)|~generous(alice)))<=>((~humble(lucy)<~>old(lucy))))&
(![X]:((~strong(X)&~quiet(X))<=>(tall(X)&~strong(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(brave(X)<~>patient(X))))&
((?[X]:((~strong(X)&~patient(X))))<=>(?[X]:((brave(X)&~curious(X)))))&
(![X]:((generous(X)<~>~happy(X))<=>rich(X)))&
(![X]:((~calm(X)&tall(X))=>brave(X)))&
(![X]:((~funny(X)&strong(X))=>(patient(X)<~>tall(X))))&
((?[X]:((patient(X)<~>~generous(X))))<=>((~creative(john)<~>~patient(john))))&
((?[X]:(~brave(X)))<=>((curious(paul)&quiet(paul))))&
(![X]:((~wise(X)&~happy(X))=>(creative(X)<~>~strong(X))))&
(((~creative(lucy)&kind(lucy)))=>((humble(fred)|kind(fred))))&
((?[X]:((~happy(X)<~>funny(X))))=>(?[X]:((~quiet(X)<~>~strong(X)))))&
(![X]:((brave(X)|calm(X))<=>(~brave(X)|tall(X))))&
((?[X]:((~creative(X)<~>~humble(X))))=>(?[X]:(humble(X))))&
(![X]:((~tall(X)<~>calm(X))=>(~brave(X)&~rich(X))))&
(![X]:((humble(X)&~tall(X))=>(wise(X)|calm(X))))&
(?[X]:((~tall(X)|~funny(X))))&
(?[X]:((tall(X)|~creative(X))))&
((~funny(paul)&humble(paul)))&
(creative(alice))&
(?[X]:((~rich(X)&generous(X))))&
(creative(lucy))&
(?[X]:(~curious(X)))&
((~funny(fred)&~generous(fred))) | humble(paul) | [
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8610100102483986634754952
% SZS output start Proof for 8610100102483986634754952
19. humble(paul) & ~funny(paul) [input p18]
25. ~humble(paul) [input hypothesis]
138. humble(paul) [cnf transformation 19]
146. ~humble(paul) [cnf transformation 25]
312. $false [subsumption resolution 146,138]
% SZS output end Proof for 8610100102483986634754952
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.028 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or old then paul is both old and not patient.
Everyone who is quiet is both not calm and old and vice versa.
Everyone who is both kind and not happy is brave and vice versa.
Everyone who is either happy or not humble is not funny or rich and vice versa.
Everyone who is not patient is happy and vice versa.
Everyone who is old or wise is tall and vice versa.
Everyone who is not kind or not generous is brave.
Everyone who is either wise or not curious is either old or funny.
Everyone who is both happy and not wise is both not tall and not wise.
If someone is not patient then someone is either happy or not tall and vice versa.
If alice is rich or wise then lucy is tall or not wise.
If mary is wise then someone is not brave or not tall.
If mary is not curious then someone is not kind.
Everyone who is both not wise and not curious is old and vice versa.
Everyone who is creative or not old is either creative or wise.
If fred is not generous then john is not humble and vice versa.
Lucy is kind.
Someone is both not wise and kind.
Alice is both curious and not calm.
Mary is not old.
Someone is not brave or rich.
Someone is not brave or creative.
Someone is both not humble and happy. | Alice is not patient. | entailment | ((?[X]:((brave(X)<~>old(X))))=>((old(paul)&~patient(paul))))&
(![X]:(quiet(X)<=>(~calm(X)&old(X))))&
(![X]:((kind(X)&~happy(X))<=>brave(X)))&
(![X]:((happy(X)<~>~humble(X))<=>(~funny(X)|rich(X))))&
(![X]:(~patient(X)<=>happy(X)))&
(![X]:((old(X)|wise(X))<=>tall(X)))&
(![X]:((~kind(X)|~generous(X))=>brave(X)))&
(![X]:((wise(X)<~>~curious(X))=>(old(X)<~>funny(X))))&
(![X]:((happy(X)&~wise(X))=>(~tall(X)&~wise(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(((rich(alice)|wise(alice)))=>((tall(lucy)|~wise(lucy))))&
((wise(mary))=>(?[X]:((~brave(X)|~tall(X)))))&
((~curious(mary))=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)&~curious(X))<=>old(X)))&
(![X]:((creative(X)|~old(X))=>(creative(X)<~>wise(X))))&
((~generous(fred))<=>(~humble(john)))&
(kind(lucy))&
(?[X]:((~wise(X)&kind(X))))&
((curious(alice)&~calm(alice)))&
(~old(mary))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((~humble(X)&happy(X)))) | ~patient(alice) | [
"p0",
"p2",
"p4",
"p5",
"p6",
"p8",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2222949691500125070203020
% SZS output start Proof for 2222949691500125070203020
1. ? [X0] : (brave(X0) <~> old(X0)) => (~patient(paul) & old(paul)) [input p0]
3. ! [X0] : ((~happy(X0) & kind(X0)) <=> brave(X0)) [input p2]
5. ! [X0] : (~patient(X0) <=> happy(X0)) [input p4]
6. ! [X0] : ((wise(X0) | old(X0)) <=> tall(X0)) [input p5]
7. ! [X0] : ((~generous(X0) | ~kind(X0)) => brave(X0)) [input p6]
9. ! [X0] : ((~wise(X0) & happy(X0)) => (~wise(X0) & ~tall(X0))) [input p8]
14. ! [X0] : ((~curious(X0) & ~wise(X0)) <=> old(X0)) [input p13]
19. ~calm(alice) & curious(alice) [input p18]
24. patient(alice) [input hypothesis]
26. curious(alice) [pure predicate removal 19]
27. (~patient(paul) & old(paul)) | ! [X0] : (brave(X0) <=> old(X0)) [ennf transformation 1]
28. ! [X0] : (brave(X0) | (generous(X0) & kind(X0))) [ennf transformation 7]
30. ! [X0] : ((~wise(X0) & ~tall(X0)) | (wise(X0) | ~happy(X0))) [ennf transformation 9]
31. ! [X0] : ((~wise(X0) & ~tall(X0)) | wise(X0) | ~happy(X0)) [flattening 30]
37. (~patient(paul) & old(paul)) | ! [X0] : ((brave(X0) | ~old(X0)) & (old(X0) | ~brave(X0))) [nnf transformation 27]
38. ! [X0] : (((~happy(X0) & kind(X0)) | ~brave(X0)) & (brave(X0) | (happy(X0) | ~kind(X0)))) [nnf transformation 3]
39. ! [X0] : (((~happy(X0) & kind(X0)) | ~brave(X0)) & (brave(X0) | happy(X0) | ~kind(X0))) [flattening 38]
42. ! [X0] : ((~patient(X0) | ~happy(X0)) & (happy(X0) | patient(X0))) [nnf transformation 5]
43. ! [X0] : (((wise(X0) | old(X0)) | ~tall(X0)) & (tall(X0) | (~wise(X0) & ~old(X0)))) [nnf transformation 6]
44. ! [X0] : ((wise(X0) | old(X0) | ~tall(X0)) & (tall(X0) | (~wise(X0) & ~old(X0)))) [flattening 43]
55. ! [X0] : (((~curious(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | (curious(X0) | wise(X0)))) [nnf transformation 14]
56. ! [X0] : (((~curious(X0) & ~wise(X0)) | ~old(X0)) & (old(X0) | curious(X0) | wise(X0))) [flattening 55]
67. old(paul) | old(X0) | ~brave(X0) [cnf transformation 37]
69. ~patient(paul) | old(X0) | ~brave(X0) [cnf transformation 37]
71. ~kind(X0) | happy(X0) | brave(X0) [cnf transformation 39]
72. ~brave(X0) | kind(X0) [cnf transformation 39]
80. happy(X0) | patient(X0) [cnf transformation 42]
81. ~happy(X0) | ~patient(X0) [cnf transformation 42]
82. ~old(X0) | tall(X0) [cnf transformation 44]
85. brave(X0) | kind(X0) [cnf transformation 28]
91. ~tall(X0) | wise(X0) | ~happy(X0) [cnf transformation 31]
102. ~wise(X0) | ~old(X0) [cnf transformation 56]
103. ~curious(X0) | ~old(X0) [cnf transformation 56]
113. curious(alice) [cnf transformation 26]
119. patient(alice) [cnf transformation 24]
125. 2 <=> patient(paul) [avatar definition]
127. ~patient(paul) <- (~2) [avatar component clause 125]
130. 3 <=> ! [X0] : (old(X0) | ~brave(X0)) [avatar definition]
131. ~brave(X0) | old(X0) <- (3) [avatar component clause 130]
132. 3 | ~2 [avatar split clause 69,125,130]
134. 4 <=> old(paul) [avatar definition]
136. old(paul) <- (4) [avatar component clause 134]
138. 3 | 4 [avatar split clause 67,134,130]
139. kind(X0) [subsumption resolution 85,72]
213. tall(paul) <- (4) [resolution 82,136]
216. ~old(alice) [resolution 103,113]
219. happy(X0) | brave(X0) [resolution 71,139]
221. ~patient(X0) | brave(X0) [resolution 219,81]
229. brave(alice) [resolution 221,119]
235. wise(paul) | ~happy(paul) <- (4) [resolution 91,213]
237. 20 <=> happy(paul) [avatar definition]
239. ~happy(paul) <- (~20) [avatar component clause 237]
241. 21 <=> wise(paul) [avatar definition]
243. wise(paul) <- (21) [avatar component clause 241]
244. ~20 | 21 | ~4 [avatar split clause 235,134,241,237]
246. patient(paul) <- (~20) [resolution 239,80]
247. $false <- (~2, ~20) [subsumption resolution 246,127]
248. 2 | 20 [avatar contradiction clause 247]
266. ~old(paul) <- (21) [resolution 243,102]
268. $false <- (4, 21) [subsumption resolution 266,136]
269. ~4 | ~21 [avatar contradiction clause 268]
272. old(alice) <- (3) [resolution 131,229]
273. $false <- (3) [subsumption resolution 272,216]
274. ~3 [avatar contradiction clause 273]
275. $false [avatar sat refutation 132,138,244,248,269,274]
% SZS output end Proof for 2222949691500125070203020
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either brave or patient then susan is not patient and vice versa.
Everyone who is either not strong or not patient is both rich and curious and vice versa.
Everyone who is both strong and not kind is funny and vice versa.
Everyone who is not curious is either not brave or not rich and vice versa.
Everyone who is both humble and brave is both generous and kind.
Everyone who is both not funny and generous is either wise or not curious.
If someone is calm then someone is not happy or tall.
If lucy is both happy and brave then fred is curious.
Everyone who is both quiet and kind is curious.
If fred is either kind or not curious then someone is either not kind or not humble.
If susan is not happy or not curious then someone is both not funny and not creative and vice versa.
If someone is either not brave or strong then someone is either generous or curious and vice versa.
Everyone who is not wise or not tall is tall and vice versa.
Everyone who is strong is either tall or generous and vice versa.
Everyone who is funny or not generous is not wise or quiet.
Everyone who is both kind and generous is not curious and vice versa.
Mary is not kind.
Someone is either humble or not wise.
Someone is not funny.
Alice is not kind.
Alice is quiet.
Susan is old. | Susan is curious. | neutral | ((?[X]:((brave(X)<~>patient(X))))<=>(~patient(susan)))&
(![X]:((~strong(X)<~>~patient(X))<=>(rich(X)&curious(X))))&
(![X]:((strong(X)&~kind(X))<=>funny(X)))&
(![X]:(~curious(X)<=>(~brave(X)<~>~rich(X))))&
(![X]:((humble(X)&brave(X))=>(generous(X)&kind(X))))&
(![X]:((~funny(X)&generous(X))=>(wise(X)<~>~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~happy(X)|tall(X)))))&
(((happy(lucy)&brave(lucy)))=>(curious(fred)))&
(![X]:((quiet(X)&kind(X))=>curious(X)))&
(((kind(fred)<~>~curious(fred)))=>(?[X]:((~kind(X)<~>~humble(X)))))&
(((~happy(susan)|~curious(susan)))<=>(?[X]:((~funny(X)&~creative(X)))))&
((?[X]:((~brave(X)<~>strong(X))))<=>(?[X]:((generous(X)<~>curious(X)))))&
(![X]:((~wise(X)|~tall(X))<=>tall(X)))&
(![X]:(strong(X)<=>(tall(X)<~>generous(X))))&
(![X]:((funny(X)|~generous(X))=>(~wise(X)|quiet(X))))&
(![X]:((kind(X)&generous(X))<=>~curious(X)))&
(~kind(mary))&
(?[X]:((humble(X)<~>~wise(X))))&
(?[X]:(~funny(X)))&
(~kind(alice))&
(quiet(alice))&
(old(susan)) | curious(susan) | [] | null | 0 |
Everyone who is not old is either calm or old and vice versa. Everyone who is curious is not brave or curious and vice versa. Everyone who is not curious is either brave or patient. Everyone who is either funny or not tall is curious or patient. If paul is not brave or brave then someone is not funny or not humble. If someone is not patient then susan is either not old or not kind. If fred is not tall then paul is kind. Everyone who is not curious or not brave is not creative or patient. Everyone who is tall is not calm or tall and vice versa. If someone is not calm or not brave then someone is either not funny or curious. If fred is creative or not funny then someone is either tall or calm and vice versa. Everyone who is not calm or not creative is both not strong and old and vice versa. Everyone who is strong is both not happy and humble and vice versa. If paul is not rich or calm then someone is rich or not calm. If lucy is rich or old then paul is not patient or not strong and vice versa. If alice is either not old or brave then someone is humble and vice versa. Fred is calm or old. Fred is not creative or not tall. Alice is both tall and kind. Someone is both not brave and patient. John is not happy or brave. Lucy is not creative. Alice is either happy or quiet. Someone is calm or not curious. | Fred is not old. | neutral | (![X]:(~old(X)<=>(calm(X)<~>old(X))))&
(![X]:(curious(X)<=>(~brave(X)|curious(X))))&
(![X]:(~curious(X)=>(brave(X)<~>patient(X))))&
(![X]:((funny(X)<~>~tall(X))=>(curious(X)|patient(X))))&
(((~brave(paul)|brave(paul)))=>(?[X]:((~funny(X)|~humble(X)))))&
((?[X]:(~patient(X)))=>((~old(susan)<~>~kind(susan))))&
((~tall(fred))=>(kind(paul)))&
(![X]:((~curious(X)|~brave(X))=>(~creative(X)|patient(X))))&
(![X]:(tall(X)<=>(~calm(X)|tall(X))))&
((?[X]:((~calm(X)|~brave(X))))=>(?[X]:((~funny(X)<~>curious(X)))))&
(((creative(fred)|~funny(fred)))<=>(?[X]:((tall(X)<~>calm(X)))))&
(![X]:((~calm(X)|~creative(X))<=>(~strong(X)&old(X))))&
(![X]:(strong(X)<=>(~happy(X)&humble(X))))&
(((~rich(paul)|calm(paul)))=>(?[X]:((rich(X)|~calm(X)))))&
(((rich(lucy)|old(lucy)))<=>((~patient(paul)|~strong(paul))))&
(((~old(alice)<~>brave(alice)))<=>(?[X]:(humble(X))))&
((calm(fred)|old(fred)))&
((~creative(fred)|~tall(fred)))&
((tall(alice)&kind(alice)))&
(?[X]:((~brave(X)&patient(X))))&
((~happy(john)|brave(john)))&
(~creative(lucy))&
((happy(alice)<~>quiet(alice)))&
(?[X]:((calm(X)|~curious(X)))) | ~old(fred) | [] | null | 0 |
If someone is not calm or tall then someone is both not curious and old and vice versa. Everyone who is either tall or brave is both not creative and not curious and vice versa. Everyone who is both not curious and patient is patient or not humble. Everyone who is both not generous and old is generous or brave and vice versa. Everyone who is not tall is funny and vice versa. Everyone who is both not patient and tall is not creative and vice versa. If paul is not brave or calm then susan is either wise or not humble. If someone is old then someone is not humble. If someone is not curious or wise then alice is humble or happy and vice versa. Everyone who is not quiet or not humble is either tall or not rich and vice versa. Everyone who is not generous is not patient or not old and vice versa. Everyone who is curious or not tall is wise or not calm. If someone is both wise and calm then lucy is either not patient or not happy and vice versa. If paul is not generous then someone is either not curious or not rich. If alice is happy then someone is either curious or not creative and vice versa. If susan is both patient and not calm then someone is not quiet. Someone is either not brave or quiet. Someone is either not patient or not calm. Paul is strong or happy. Fred is quiet. Lucy is wise. Lucy is either not old or humble. | Fred is not happy. | neutral | ((?[X]:((~calm(X)|tall(X))))<=>(?[X]:((~curious(X)&old(X)))))&
(![X]:((tall(X)<~>brave(X))<=>(~creative(X)&~curious(X))))&
(![X]:((~curious(X)&patient(X))=>(patient(X)|~humble(X))))&
(![X]:((~generous(X)&old(X))<=>(generous(X)|brave(X))))&
(![X]:(~tall(X)<=>funny(X)))&
(![X]:((~patient(X)&tall(X))<=>~creative(X)))&
(((~brave(paul)|calm(paul)))=>((wise(susan)<~>~humble(susan))))&
((?[X]:(old(X)))=>(?[X]:(~humble(X))))&
((?[X]:((~curious(X)|wise(X))))<=>((humble(alice)|happy(alice))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)<~>~rich(X))))&
(![X]:(~generous(X)<=>(~patient(X)|~old(X))))&
(![X]:((curious(X)|~tall(X))=>(wise(X)|~calm(X))))&
((?[X]:((wise(X)&calm(X))))<=>((~patient(lucy)<~>~happy(lucy))))&
((~generous(paul))=>(?[X]:((~curious(X)<~>~rich(X)))))&
((happy(alice))<=>(?[X]:((curious(X)<~>~creative(X)))))&
(((patient(susan)&~calm(susan)))=>(?[X]:(~quiet(X))))&
(?[X]:((~brave(X)<~>quiet(X))))&
(?[X]:((~patient(X)<~>~calm(X))))&
((strong(paul)|happy(paul)))&
(quiet(fred))&
(wise(lucy))&
((~old(lucy)<~>humble(lucy))) | ~happy(fred) | [] | null | 0 |
Everyone who is either happy or not happy is both happy and strong.
If alice is not generous then someone is not patient.
Everyone who is not generous is old or not humble and vice versa.
If someone is both quiet and not calm then someone is both generous and happy.
Everyone who is brave is either curious or not funny and vice versa.
If lucy is tall then someone is not old or not generous.
If mary is both tall and rich then alice is quiet or rich.
Everyone who is patient or not happy is both old and not kind and vice versa.
If someone is not brave or generous then someone is either rich or not strong.
Everyone who is not tall or quiet is either not strong or quiet and vice versa.
If john is funny or not old then paul is either not wise or not happy and vice versa.
Everyone who is both quiet and not old is rich and vice versa.
If lucy is not tall or not old then someone is either not strong or curious and vice versa.
If susan is either generous or not curious then mary is kind and vice versa.
Everyone who is humble is both kind and not humble.
If someone is patient or tall then someone is both not calm and generous.
Someone is either not brave or not curious.
Someone is both happy and not humble.
Lucy is both curious and not old.
Someone is both not old and creative.
Someone is either not quiet or funny.
Alice is both happy and not humble. | Paul is humble. | contradiction | (![X]:((happy(X)<~>~happy(X))=>(happy(X)&strong(X))))&
((~generous(alice))=>(?[X]:(~patient(X))))&
(![X]:(~generous(X)<=>(old(X)|~humble(X))))&
((?[X]:((quiet(X)&~calm(X))))=>(?[X]:((generous(X)&happy(X)))))&
(![X]:(brave(X)<=>(curious(X)<~>~funny(X))))&
((tall(lucy))=>(?[X]:((~old(X)|~generous(X)))))&
(((tall(mary)&rich(mary)))=>((quiet(alice)|rich(alice))))&
(![X]:((patient(X)|~happy(X))<=>(old(X)&~kind(X))))&
((?[X]:((~brave(X)|generous(X))))=>(?[X]:((rich(X)<~>~strong(X)))))&
(![X]:((~tall(X)|quiet(X))<=>(~strong(X)<~>quiet(X))))&
(((funny(john)|~old(john)))<=>((~wise(paul)<~>~happy(paul))))&
(![X]:((quiet(X)&~old(X))<=>rich(X)))&
(((~tall(lucy)|~old(lucy)))<=>(?[X]:((~strong(X)<~>curious(X)))))&
(((generous(susan)<~>~curious(susan)))<=>(kind(mary)))&
(![X]:(humble(X)=>(kind(X)&~humble(X))))&
((?[X]:((patient(X)|tall(X))))=>(?[X]:((~calm(X)&generous(X)))))&
(?[X]:((~brave(X)<~>~curious(X))))&
(?[X]:((happy(X)&~humble(X))))&
((curious(lucy)&~old(lucy)))&
(?[X]:((~old(X)&creative(X))))&
(?[X]:((~quiet(X)<~>funny(X))))&
((happy(alice)&~humble(alice))) | humble(paul) | [
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 1067893021096311565613175
% SZS output start Proof for 1067893021096311565613175
15. ! [X0] : (humble(X0) => (~humble(X0) & kind(X0))) [input p14]
23. humble(paul) [input hypothesis]
35. ! [X0] : ((~humble(X0) & kind(X0)) | ~humble(X0)) [ennf transformation 15]
130. ~humble(X0) | ~humble(X0) [cnf transformation 35]
146. humble(paul) [cnf transformation 23]
147. ~humble(X0) [duplicate literal removal 130]
299. $false [subsumption resolution 146,147]
% SZS output end Proof for 1067893021096311565613175
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny or not happy is either old or happy. If susan is both not patient and not old then john is either quiet or generous and vice versa. Everyone who is not old or rich is generous or patient. If someone is either funny or not rich then fred is both not quiet and calm. Everyone who is either not creative or not calm is kind and vice versa. If someone is not curious then someone is both funny and creative. Everyone who is not creative or not kind is not patient and vice versa. Everyone who is not rich or rich is not strong. If fred is happy or quiet then susan is both not quiet and not old. Everyone who is not happy is not quiet or funny. Everyone who is funny or humble is not calm or kind and vice versa. Everyone who is both not generous and generous is both not calm and not strong and vice versa. Everyone who is patient is either not kind or not patient. If someone is kind or not funny then someone is not brave. Everyone who is old is not kind or not humble and vice versa. If mary is either not strong or not quiet then someone is not strong or funny. Susan is humble. Alice is not quiet or not rich. Alice is both calm and tall. Someone is either wise or not curious. Lucy is not curious or not brave. Someone is happy or not tall. Susan is both curious and funny. Someone is both not strong and curious. | Susan is kind. | entailment | (![X]:((~funny(X)|~happy(X))=>(old(X)<~>happy(X))))&
(((~patient(susan)&~old(susan)))<=>((quiet(john)<~>generous(john))))&
(![X]:((~old(X)|rich(X))=>(generous(X)|patient(X))))&
((?[X]:((funny(X)<~>~rich(X))))=>((~quiet(fred)&calm(fred))))&
(![X]:((~creative(X)<~>~calm(X))<=>kind(X)))&
((?[X]:(~curious(X)))=>(?[X]:((funny(X)&creative(X)))))&
(![X]:((~creative(X)|~kind(X))<=>~patient(X)))&
(![X]:((~rich(X)|rich(X))=>~strong(X)))&
(((happy(fred)|quiet(fred)))=>((~quiet(susan)&~old(susan))))&
(![X]:(~happy(X)=>(~quiet(X)|funny(X))))&
(![X]:((funny(X)|humble(X))<=>(~calm(X)|kind(X))))&
(![X]:((~generous(X)&generous(X))<=>(~calm(X)&~strong(X))))&
(![X]:(patient(X)=>(~kind(X)<~>~patient(X))))&
((?[X]:((kind(X)|~funny(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>(~kind(X)|~humble(X))))&
(((~strong(mary)<~>~quiet(mary)))=>(?[X]:((~strong(X)|funny(X)))))&
(humble(susan))&
((~quiet(alice)|~rich(alice)))&
((calm(alice)&tall(alice)))&
(?[X]:((wise(X)<~>~curious(X))))&
((~curious(lucy)|~brave(lucy)))&
(?[X]:((happy(X)|~tall(X))))&
((curious(susan)&funny(susan)))&
(?[X]:((~strong(X)&curious(X)))) | kind(susan) | [
"p7",
"p10",
"p11",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 1711695856440172603161010
% SZS output start Proof for 1711695856440172603161010
8. ! [X0] : ((rich(X0) | ~rich(X0)) => ~strong(X0)) [input p7]
11. ! [X0] : ((humble(X0) | funny(X0)) <=> (kind(X0) | ~calm(X0))) [input p10]
12. ! [X0] : ((generous(X0) & ~generous(X0)) <=> (~strong(X0) & ~calm(X0))) [input p11]
17. humble(susan) [input p16]
25. ~kind(susan) [input hypothesis]
35. ! [X0] : (~strong(X0) | (~rich(X0) & rich(X0))) [ennf transformation 8]
51. ! [X0] : (((humble(X0) | funny(X0)) | (~kind(X0) & calm(X0))) & ((kind(X0) | ~calm(X0)) | (~humble(X0) & ~funny(X0)))) [nnf transformation 11]
52. ! [X0] : ((humble(X0) | funny(X0) | (~kind(X0) & calm(X0))) & (kind(X0) | ~calm(X0) | (~humble(X0) & ~funny(X0)))) [flattening 51]
53. ! [X0] : (((generous(X0) & ~generous(X0)) | (strong(X0) | calm(X0))) & ((~strong(X0) & ~calm(X0)) | (~generous(X0) | generous(X0)))) [nnf transformation 12]
54. ! [X0] : (((generous(X0) & ~generous(X0)) | strong(X0) | calm(X0)) & ((~strong(X0) & ~calm(X0)) | ~generous(X0) | generous(X0))) [flattening 53]
93. ~strong(X0) | rich(X0) [cnf transformation 35]
94. ~strong(X0) | ~rich(X0) [cnf transformation 35]
101. ~humble(X0) | ~calm(X0) | kind(X0) [cnf transformation 52]
106. ~generous(X0) | strong(X0) | calm(X0) [cnf transformation 54]
107. generous(X0) | strong(X0) | calm(X0) [cnf transformation 54]
115. humble(susan) [cnf transformation 17]
126. ~kind(susan) [cnf transformation 25]
182. ~strong(X0) [subsumption resolution 93,94]
195. calm(X0) | generous(X0) [subsumption resolution 107,182]
196. ~generous(X0) | calm(X0) [subsumption resolution 106,182]
197. calm(X0) [subsumption resolution 196,195]
267. ~calm(susan) | kind(susan) [resolution 101,115]
269. kind(susan) [subsumption resolution 267,197]
270. $false [subsumption resolution 269,126]
% SZS output end Proof for 1711695856440172603161010
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 generous is either strong or not generous and vice versa.
Everyone who is both not rich and not generous is either not old or rich and vice versa.
If someone is not generous then lucy is old or not kind.
Everyone who is tall is either not quiet or not curious.
If lucy is either tall or not humble then someone is both not brave and not wise and vice versa.
Everyone who is either not old or generous is either kind or strong.
Everyone who is not humble or wise is both humble and not curious and vice versa.
Everyone who is either humble or happy is both brave and not tall and vice versa.
Everyone who is either not brave or calm is both strong and not rich and vice versa.
If fred is either not quiet or not patient then someone is not rich or creative.
Everyone who is both happy and not funny is both not rich and humble.
Everyone who is not happy or curious is not patient.
If susan is patient then someone is both not quiet and rich and vice versa.
Everyone who is calm or not strong is not creative.
Everyone who is either generous or not quiet is either wise or not rich.
Everyone who is patient or not kind is not curious or creative and vice versa.
Someone is brave or quiet.
Lucy is either not strong or not rich.
John is not curious or creative.
Someone is not patient or brave.
Someone is creative or not brave.
Someone is both not wise and not rich.
Someone is generous or kind. | Susan is not generous. | neutral | (![X]:(~generous(X)<=>(strong(X)<~>~generous(X))))&
(![X]:((~rich(X)&~generous(X))<=>(~old(X)<~>rich(X))))&
((?[X]:(~generous(X)))=>((old(lucy)|~kind(lucy))))&
(![X]:(tall(X)=>(~quiet(X)<~>~curious(X))))&
(((tall(lucy)<~>~humble(lucy)))<=>(?[X]:((~brave(X)&~wise(X)))))&
(![X]:((~old(X)<~>generous(X))=>(kind(X)<~>strong(X))))&
(![X]:((~humble(X)|wise(X))<=>(humble(X)&~curious(X))))&
(![X]:((humble(X)<~>happy(X))<=>(brave(X)&~tall(X))))&
(![X]:((~brave(X)<~>calm(X))<=>(strong(X)&~rich(X))))&
(((~quiet(fred)<~>~patient(fred)))=>(?[X]:((~rich(X)|creative(X)))))&
(![X]:((happy(X)&~funny(X))=>(~rich(X)&humble(X))))&
(![X]:((~happy(X)|curious(X))=>~patient(X)))&
((patient(susan))<=>(?[X]:((~quiet(X)&rich(X)))))&
(![X]:((calm(X)|~strong(X))=>~creative(X)))&
(![X]:((generous(X)<~>~quiet(X))=>(wise(X)<~>~rich(X))))&
(![X]:((patient(X)|~kind(X))<=>(~curious(X)|creative(X))))&
(?[X]:((brave(X)|quiet(X))))&
((~strong(lucy)<~>~rich(lucy)))&
((~curious(john)|creative(john)))&
(?[X]:((~patient(X)|brave(X))))&
(?[X]:((creative(X)|~brave(X))))&
(?[X]:((~wise(X)&~rich(X))))&
(?[X]:((generous(X)|kind(X)))) | ~generous(susan) | [] | null | 0 |
Everyone who is old is creative or not strong. If someone is not strong or not patient then someone is not patient or calm and vice versa. Everyone who is either not curious or not old is old. Everyone who is curious or brave is both quiet and calm and vice versa. If someone is generous or tall then someone is not wise. Everyone who is not generous is both not brave and not generous. Everyone who is either not wise or generous is both not wise and not funny and vice versa. Everyone who is both tall and not wise is not generous or tall and vice versa. Everyone who is either patient or happy is either happy or wise. Everyone who is either patient or humble is not funny or quiet and vice versa. If susan is either not quiet or calm then someone is not kind and vice versa. If someone is kind then mary is not calm and vice versa. Everyone who is funny is curious or not curious and vice versa. If someone is not wise or not creative then someone is either happy or old and vice versa. If paul is not wise or humble then john is either not old or happy. If someone is either curious or not calm then lucy is kind and vice versa. Alice is both patient and not strong. Someone is not happy or kind. Mary is either not quiet or curious. Someone is both not kind and strong. Lucy is either strong or not old. Someone is not calm or patient. Someone is either not calm or not happy. Alice is old or not generous. | Alice is happy. | entailment | (![X]:(old(X)=>(creative(X)|~strong(X))))&
((?[X]:((~strong(X)|~patient(X))))<=>(?[X]:((~patient(X)|calm(X)))))&
(![X]:((~curious(X)<~>~old(X))=>old(X)))&
(![X]:((curious(X)|brave(X))<=>(quiet(X)&calm(X))))&
((?[X]:((generous(X)|tall(X))))=>(?[X]:(~wise(X))))&
(![X]:(~generous(X)=>(~brave(X)&~generous(X))))&
(![X]:((~wise(X)<~>generous(X))<=>(~wise(X)&~funny(X))))&
(![X]:((tall(X)&~wise(X))<=>(~generous(X)|tall(X))))&
(![X]:((patient(X)<~>happy(X))=>(happy(X)<~>wise(X))))&
(![X]:((patient(X)<~>humble(X))<=>(~funny(X)|quiet(X))))&
(((~quiet(susan)<~>calm(susan)))<=>(?[X]:(~kind(X))))&
((?[X]:(kind(X)))<=>(~calm(mary)))&
(![X]:(funny(X)<=>(curious(X)|~curious(X))))&
((?[X]:((~wise(X)|~creative(X))))<=>(?[X]:((happy(X)<~>old(X)))))&
(((~wise(paul)|humble(paul)))=>((~old(john)<~>happy(john))))&
((?[X]:((curious(X)<~>~calm(X))))<=>(kind(lucy)))&
((patient(alice)&~strong(alice)))&
(?[X]:((~happy(X)|kind(X))))&
((~quiet(mary)<~>curious(mary)))&
(?[X]:((~kind(X)&strong(X))))&
((strong(lucy)<~>~old(lucy)))&
(?[X]:((~calm(X)|patient(X))))&
(?[X]:((~calm(X)<~>~happy(X))))&
((old(alice)|~generous(alice))) | happy(alice) | [
"p6",
"p7",
"p8",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6592896854161519550511325
% SZS output start Proof for 6592896854161519550511325
7. ! [X0] : ((~wise(X0) <~> generous(X0)) <=> (~funny(X0) & ~wise(X0))) [input p6]
8. ! [X0] : ((~wise(X0) & tall(X0)) <=> (tall(X0) | ~generous(X0))) [input p7]
9. ! [X0] : ((patient(X0) <~> happy(X0)) => (happy(X0) <~> wise(X0))) [input p8]
17. ~strong(alice) & patient(alice) [input p16]
25. ~happy(alice) [input hypothesis]
34. ! [X0] : ((happy(X0) <~> wise(X0)) | (patient(X0) <=> happy(X0))) [ennf transformation 9]
47. ! [X0] : ((((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | (funny(X0) | wise(X0))) & ((~funny(X0) & ~wise(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))))) [nnf transformation 7]
48. ! [X0] : ((((~generous(X0) | wise(X0)) & (generous(X0) | ~wise(X0))) | funny(X0) | wise(X0)) & ((~funny(X0) & ~wise(X0)) | ((~wise(X0) | ~generous(X0)) & (generous(X0) | wise(X0))))) [flattening 47]
49. ! [X0] : (((~wise(X0) & tall(X0)) | (~tall(X0) & generous(X0))) & ((tall(X0) | ~generous(X0)) | (wise(X0) | ~tall(X0)))) [nnf transformation 8]
50. ! [X0] : (((~wise(X0) & tall(X0)) | (~tall(X0) & generous(X0))) & (tall(X0) | ~generous(X0) | wise(X0) | ~tall(X0))) [flattening 49]
51. ! [X0] : (((~wise(X0) | ~happy(X0)) & (wise(X0) | happy(X0))) | ((patient(X0) | ~happy(X0)) & (happy(X0) | ~patient(X0)))) [nnf transformation 34]
102. ~wise(X0) | ~wise(X0) | ~generous(X0) [cnf transformation 48]
110. ~wise(X0) | generous(X0) [cnf transformation 50]
112. wise(X0) | happy(X0) | happy(X0) | ~patient(X0) [cnf transformation 51]
145. patient(alice) [cnf transformation 17]
158. ~happy(alice) [cnf transformation 25]
159. wise(X0) | happy(X0) | ~patient(X0) [duplicate literal removal 112]
161. ~wise(X0) | ~generous(X0) [duplicate literal removal 102]
205. ~wise(X0) [subsumption resolution 110,161]
206. ~patient(X0) | happy(X0) [subsumption resolution 159,205]
354. happy(alice) [resolution 206,145]
355. $false [subsumption resolution 354,158]
% SZS output end Proof for 6592896854161519550511325
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave then someone is either not tall or not humble and vice versa. Everyone who is not strong or creative is old. Everyone who is tall or wise is rich or not happy and vice versa. If mary is humble then alice is tall. If alice is either not curious or wise then mary is not old and vice versa. Everyone who is generous or not generous is not calm or humble and vice versa. Everyone who is patient is happy or not tall. Everyone who is strong is not creative and vice versa. If someone is either not creative or happy then someone is both not brave and not calm. If someone is both humble and calm then someone is either not wise or rich. If someone is not generous then susan is not strong or old. If paul is either creative or not generous then lucy is wise or kind and vice versa. Everyone who is either not tall or funny is both curious and not humble. Everyone who is either humble or creative is both happy and not wise and vice versa. Everyone who is not strong or patient is either not creative or not generous. Everyone who is either calm or not humble is both wise and not curious and vice versa. Mary is rich. Fred is either not creative or not strong. Someone is brave or curious. Lucy is not strong or not happy. Mary is either patient or not quiet. Someone is either not quiet or old. Someone is either curious or not rich. | Alice is curious. | neutral | ((?[X]:(brave(X)))<=>(?[X]:((~tall(X)<~>~humble(X)))))&
(![X]:((~strong(X)|creative(X))=>old(X)))&
(![X]:((tall(X)|wise(X))<=>(rich(X)|~happy(X))))&
((humble(mary))=>(tall(alice)))&
(((~curious(alice)<~>wise(alice)))<=>(~old(mary)))&
(![X]:((generous(X)|~generous(X))<=>(~calm(X)|humble(X))))&
(![X]:(patient(X)=>(happy(X)|~tall(X))))&
(![X]:(strong(X)<=>~creative(X)))&
((?[X]:((~creative(X)<~>happy(X))))=>(?[X]:((~brave(X)&~calm(X)))))&
((?[X]:((humble(X)&calm(X))))=>(?[X]:((~wise(X)<~>rich(X)))))&
((?[X]:(~generous(X)))=>((~strong(susan)|old(susan))))&
(((creative(paul)<~>~generous(paul)))<=>((wise(lucy)|kind(lucy))))&
(![X]:((~tall(X)<~>funny(X))=>(curious(X)&~humble(X))))&
(![X]:((humble(X)<~>creative(X))<=>(happy(X)&~wise(X))))&
(![X]:((~strong(X)|patient(X))=>(~creative(X)<~>~generous(X))))&
(![X]:((calm(X)<~>~humble(X))<=>(wise(X)&~curious(X))))&
(rich(mary))&
((~creative(fred)<~>~strong(fred)))&
(?[X]:((brave(X)|curious(X))))&
((~strong(lucy)|~happy(lucy)))&
((patient(mary)<~>~quiet(mary)))&
(?[X]:((~quiet(X)<~>old(X))))&
(?[X]:((curious(X)<~>~rich(X)))) | curious(alice) | [] | null | 0 |
If mary is either strong or rich then paul is both wise and not old.
Everyone who is both curious and not humble is kind or not brave and vice versa.
Everyone who is both not strong and not old is both not rich and not tall.
Everyone who is both not brave and kind is either not creative or curious and vice versa.
Everyone who is funny or curious is not old or not wise.
If someone is wise then lucy is either brave or not strong.
If someone is either not brave or brave then someone is either curious or wise.
Everyone who is either brave or not kind is either not quiet or humble.
Everyone who is either not generous or quiet is not wise or not funny.
Everyone who is happy or not happy is either curious or creative and vice versa.
If someone is both not tall and curious then alice is both funny and rich and vice versa.
If lucy is both wise and not strong then someone is humble or funny.
Everyone who is either not creative or happy is both kind and not kind and vice versa.
Everyone who is not rich is calm or not rich.
If someone is not humble or curious then paul is either old or happy.
If someone is both not funny and not calm then someone is not tall.
Someone is either not patient or not humble.
Someone is either old or calm.
Fred is not humble or not wise.
Paul is not patient.
Susan is not curious or not happy.
Someone is generous.
Paul is humble or not rich.
Lucy is kind or not rich. | Susan is not kind. | entailment | (((strong(mary)<~>rich(mary)))=>((wise(paul)&~old(paul))))&
(![X]:((curious(X)&~humble(X))<=>(kind(X)|~brave(X))))&
(![X]:((~strong(X)&~old(X))=>(~rich(X)&~tall(X))))&
(![X]:((~brave(X)&kind(X))<=>(~creative(X)<~>curious(X))))&
(![X]:((funny(X)|curious(X))=>(~old(X)|~wise(X))))&
((?[X]:(wise(X)))=>((brave(lucy)<~>~strong(lucy))))&
((?[X]:((~brave(X)<~>brave(X))))=>(?[X]:((curious(X)<~>wise(X)))))&
(![X]:((brave(X)<~>~kind(X))=>(~quiet(X)<~>humble(X))))&
(![X]:((~generous(X)<~>quiet(X))=>(~wise(X)|~funny(X))))&
(![X]:((happy(X)|~happy(X))<=>(curious(X)<~>creative(X))))&
((?[X]:((~tall(X)&curious(X))))<=>((funny(alice)&rich(alice))))&
(((wise(lucy)&~strong(lucy)))=>(?[X]:((humble(X)|funny(X)))))&
(![X]:((~creative(X)<~>happy(X))<=>(kind(X)&~kind(X))))&
(![X]:(~rich(X)=>(calm(X)|~rich(X))))&
((?[X]:((~humble(X)|curious(X))))=>((old(paul)<~>happy(paul))))&
((?[X]:((~funny(X)&~calm(X))))=>(?[X]:(~tall(X))))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((old(X)<~>calm(X))))&
((~humble(fred)|~wise(fred)))&
(~patient(paul))&
((~curious(susan)|~happy(susan)))&
(?[X]:(generous(X)))&
((humble(paul)|~rich(paul)))&
((kind(lucy)|~rich(lucy))) | ~kind(susan) | [
"p1",
"p9",
"p12",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 503009629557264419224563
% SZS output start Proof for 503009629557264419224563
2. ! [X0] : ((~humble(X0) & curious(X0)) <=> (~brave(X0) | kind(X0))) [input p1]
10. ! [X0] : ((~happy(X0) | happy(X0)) <=> (curious(X0) <~> creative(X0))) [input p9]
13. ! [X0] : ((~creative(X0) <~> happy(X0)) <=> (~kind(X0) & kind(X0))) [input p12]
21. ~happy(susan) | ~curious(susan) [input p20]
25. kind(susan) [input hypothesis]
45. ! [X0] : (((~humble(X0) & curious(X0)) | (brave(X0) & ~kind(X0))) & ((~brave(X0) | kind(X0)) | (humble(X0) | ~curious(X0)))) [nnf transformation 2]
46. ! [X0] : (((~humble(X0) & curious(X0)) | (brave(X0) & ~kind(X0))) & (~brave(X0) | kind(X0) | humble(X0) | ~curious(X0))) [flattening 45]
56. ! [X0] : (((~happy(X0) | happy(X0)) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (happy(X0) & ~happy(X0)))) [nnf transformation 10]
57. ! [X0] : ((~happy(X0) | happy(X0) | ((curious(X0) | ~creative(X0)) & (creative(X0) | ~curious(X0)))) & (((~creative(X0) | ~curious(X0)) & (creative(X0) | curious(X0))) | (happy(X0) & ~happy(X0)))) [flattening 56]
65. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | (kind(X0) | ~kind(X0))) & ((~kind(X0) & kind(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [nnf transformation 13]
66. ! [X0] : ((((~happy(X0) | creative(X0)) & (happy(X0) | ~creative(X0))) | kind(X0) | ~kind(X0)) & ((~kind(X0) & kind(X0)) | ((~creative(X0) | ~happy(X0)) & (happy(X0) | creative(X0))))) [flattening 65]
84. ~kind(X0) | curious(X0) [cnf transformation 46]
112. ~creative(X0) | ~curious(X0) | ~happy(X0) [cnf transformation 57]
113. ~creative(X0) | ~curious(X0) | happy(X0) [cnf transformation 57]
121. kind(X0) | happy(X0) | creative(X0) [cnf transformation 66]
123. ~kind(X0) | happy(X0) | creative(X0) [cnf transformation 66]
139. ~happy(susan) | ~curious(susan) [cnf transformation 21]
143. kind(susan) [cnf transformation 25]
203. ~creative(X0) | ~curious(X0) [subsumption resolution 112,113]
241. happy(X0) | creative(X0) [subsumption resolution 121,123]
294. 31 <=> curious(susan) [avatar definition]
295. curious(susan) <- (31) [avatar component clause 294]
298. 32 <=> happy(susan) [avatar definition]
300. ~happy(susan) <- (~32) [avatar component clause 298]
301. ~31 | ~32 [avatar split clause 139,298,294]
320. curious(susan) [resolution 84,143]
323. 31 [avatar split clause 320,294]
328. creative(susan) <- (~32) [resolution 241,300]
350. ~curious(susan) <- (~32) [resolution 328,203]
352. $false <- (31, ~32) [subsumption resolution 350,295]
353. ~31 | 32 [avatar contradiction clause 352]
354. $false [avatar sat refutation 301,323,353]
% SZS output end Proof for 503009629557264419224563
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 patient or not generous is not strong or not funny and vice versa.
If someone is generous then paul is both not generous and not kind and vice versa.
If someone is either not tall or happy then fred is not patient and vice versa.
Everyone who is wise or kind is brave.
Everyone who is brave is either not generous or humble and vice versa.
Everyone who is either not calm or not curious is generous or not strong and vice versa.
Everyone who is either quiet or curious is both curious and happy and vice versa.
Everyone who is creative or not wise is brave.
Everyone who is not strong or not generous is strong and vice versa.
If someone is both not wise and not generous then susan is either not rich or not kind and vice versa.
Everyone who is patient is not generous or not wise.
If someone is both generous and not funny then someone is curious and vice versa.
If someone is both not old and curious then fred is either not kind or quiet.
If paul is both not generous and not humble then john is funny.
Everyone who is either not humble or not wise is either not old or generous and vice versa.
If paul is patient or not curious then susan is not happy or happy.
Someone is not patient or not generous.
Lucy is not curious or not calm.
Someone is both not calm and creative.
Susan is not kind or curious.
Someone is old.
Someone is not humble. | Fred is calm. | contradiction | (![X]:((~patient(X)<~>~generous(X))<=>(~strong(X)|~funny(X))))&
((?[X]:(generous(X)))<=>((~generous(paul)&~kind(paul))))&
((?[X]:((~tall(X)<~>happy(X))))<=>(~patient(fred)))&
(![X]:((wise(X)|kind(X))=>brave(X)))&
(![X]:(brave(X)<=>(~generous(X)<~>humble(X))))&
(![X]:((~calm(X)<~>~curious(X))<=>(generous(X)|~strong(X))))&
(![X]:((quiet(X)<~>curious(X))<=>(curious(X)&happy(X))))&
(![X]:((creative(X)|~wise(X))=>brave(X)))&
(![X]:((~strong(X)|~generous(X))<=>strong(X)))&
((?[X]:((~wise(X)&~generous(X))))<=>((~rich(susan)<~>~kind(susan))))&
(![X]:(patient(X)=>(~generous(X)|~wise(X))))&
((?[X]:((generous(X)&~funny(X))))<=>(?[X]:(curious(X))))&
((?[X]:((~old(X)&curious(X))))=>((~kind(fred)<~>quiet(fred))))&
(((~generous(paul)&~humble(paul)))=>(funny(john)))&
(![X]:((~humble(X)<~>~wise(X))<=>(~old(X)<~>generous(X))))&
(((patient(paul)|~curious(paul)))=>((~happy(susan)|happy(susan))))&
(?[X]:((~patient(X)|~generous(X))))&
((~curious(lucy)|~calm(lucy)))&
(?[X]:((~calm(X)&creative(X))))&
((~kind(susan)|curious(susan)))&
(?[X]:(old(X)))&
(?[X]:(~humble(X))) | calm(fred) | [
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 79636812022603452247011
% SZS output start Proof for 79636812022603452247011
6. ! [X0] : ((~calm(X0) <~> ~curious(X0)) <=> (~strong(X0) | generous(X0))) [input p5]
9. ! [X0] : ((~generous(X0) | ~strong(X0)) <=> strong(X0)) [input p8]
12. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X0] : curious(X0) [input p11]
23. calm(fred) [input hypothesis]
24. ? [X0] : (~funny(X0) & generous(X0)) <=> ? [X1] : curious(X1) [rectify 12]
48. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & ((~strong(X0) | generous(X0)) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [nnf transformation 6]
49. ! [X0] : ((((curious(X0) | calm(X0)) & (~curious(X0) | ~calm(X0))) | (strong(X0) & ~generous(X0))) & (~strong(X0) | generous(X0) | ((~calm(X0) | curious(X0)) & (~curious(X0) | calm(X0))))) [flattening 48]
52. ! [X0] : (((~generous(X0) | ~strong(X0)) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [nnf transformation 9]
53. ! [X0] : ((~generous(X0) | ~strong(X0) | ~strong(X0)) & (strong(X0) | (generous(X0) & strong(X0)))) [flattening 52]
58. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X1] : curious(X1) | ! [X0] : (funny(X0) | ~generous(X0))) [nnf transformation 24]
59. (? [X0] : (~funny(X0) & generous(X0)) | ! [X1] : ~curious(X1)) & (? [X2] : curious(X2) | ! [X3] : (funny(X3) | ~generous(X3))) [rectify 58]
60. ? [X0] : (~funny(X0) & generous(X0)) => (~funny(sK3) & generous(sK3)) [choice axiom]
61. ? [X2] : curious(X2) => curious(sK4) [choice axiom]
62. ((~funny(sK3) & generous(sK3)) | ! [X1] : ~curious(X1)) & (curious(sK4) | ! [X3] : (funny(X3) | ~generous(X3))) [skolemisation 59,61,60]
91. ~calm(X0) | generous(X0) | ~strong(X0) | curious(X0) [cnf transformation 49]
104. strong(X0) | strong(X0) [cnf transformation 53]
106. ~generous(X0) | ~strong(X0) | ~strong(X0) [cnf transformation 53]
115. generous(sK3) | ~curious(X1) [cnf transformation 62]
137. calm(fred) [cnf transformation 23]
138. strong(X0) [duplicate literal removal 104]
139. ~strong(X0) | ~generous(X0) [duplicate literal removal 106]
156. 4 <=> ! [X1] : ~generous(X1) [avatar definition]
157. ~generous(X1) <- (4) [avatar component clause 156]
209. 15 <=> ! [X1] : ~curious(X1) [avatar definition]
210. ~curious(X1) <- (15) [avatar component clause 209]
217. 17 <=> generous(sK3) [avatar definition]
219. generous(sK3) <- (17) [avatar component clause 217]
220. 15 | 17 [avatar split clause 115,217,209]
275. ~generous(X1) [resolution 139,138]
276. 4 [avatar split clause 275,156]
302. generous(fred) | ~strong(fred) | curious(fred) [resolution 91,137]
303. ~strong(fred) | curious(fred) <- (4) [subsumption resolution 302,157]
304. curious(fred) <- (4) [subsumption resolution 303,138]
305. $false <- (4, 15) [subsumption resolution 304,210]
306. ~4 | ~15 [avatar contradiction clause 305]
307. $false <- (4, 17) [subsumption resolution 219,157]
308. ~4 | ~17 [avatar contradiction clause 307]
309. $false [avatar sat refutation 220,276,306,308]
% SZS output end Proof for 79636812022603452247011
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 susan is not kind or not rich then fred is wise or old and vice versa.
Everyone who is either not creative or old is either not happy or not wise and vice versa.
Everyone who is either rich or strong is both humble and not strong.
Everyone who is not kind or generous is curious or not calm.
If john is not wise then paul is both rich and patient.
Everyone who is rich is either not rich or generous.
Everyone who is either not funny or old is not creative or not wise and vice versa.
Everyone who is funny or rich is calm.
If someone is either happy or not quiet then someone is not wise.
Everyone who is happy is not funny or happy.
If mary is both not calm and kind then someone is not quiet and vice versa.
Everyone who is either not generous or not rich is both not humble and funny and vice versa.
Everyone who is not curious is strong or brave and vice versa.
Everyone who is either not patient or tall is either strong or not wise and vice versa.
If someone is generous or not humble then someone is either strong or not brave.
If someone is not tall or not funny then someone is both not humble and wise and vice versa.
Someone is either generous or not creative.
Someone is funny or not creative.
Fred is curious or tall.
Someone is both rich and funny.
Paul is creative.
Someone is not creative.
Susan is not patient or creative.
Fred is not wise. | Mary is not strong. | entailment | (((~kind(susan)|~rich(susan)))<=>((wise(fred)|old(fred))))&
(![X]:((~creative(X)<~>old(X))<=>(~happy(X)<~>~wise(X))))&
(![X]:((rich(X)<~>strong(X))=>(humble(X)&~strong(X))))&
(![X]:((~kind(X)|generous(X))=>(curious(X)|~calm(X))))&
((~wise(john))=>((rich(paul)&patient(paul))))&
(![X]:(rich(X)=>(~rich(X)<~>generous(X))))&
(![X]:((~funny(X)<~>old(X))<=>(~creative(X)|~wise(X))))&
(![X]:((funny(X)|rich(X))=>calm(X)))&
((?[X]:((happy(X)<~>~quiet(X))))=>(?[X]:(~wise(X))))&
(![X]:(happy(X)=>(~funny(X)|happy(X))))&
(((~calm(mary)&kind(mary)))<=>(?[X]:(~quiet(X))))&
(![X]:((~generous(X)<~>~rich(X))<=>(~humble(X)&funny(X))))&
(![X]:(~curious(X)<=>(strong(X)|brave(X))))&
(![X]:((~patient(X)<~>tall(X))<=>(strong(X)<~>~wise(X))))&
((?[X]:((generous(X)|~humble(X))))=>(?[X]:((strong(X)<~>~brave(X)))))&
((?[X]:((~tall(X)|~funny(X))))<=>(?[X]:((~humble(X)&wise(X)))))&
(?[X]:((generous(X)<~>~creative(X))))&
(?[X]:((funny(X)|~creative(X))))&
((curious(fred)|tall(fred)))&
(?[X]:((rich(X)&funny(X))))&
(creative(paul))&
(?[X]:(~creative(X)))&
((~patient(susan)|creative(susan)))&
(~wise(fred)) | ~strong(mary) | [
"p2",
"p3",
"p5",
"p7",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1180115064374946058119959
% SZS output start Proof for 1180115064374946058119959
3. ! [X0] : ((rich(X0) <~> strong(X0)) => (~strong(X0) & humble(X0))) [input p2]
4. ! [X0] : ((generous(X0) | ~kind(X0)) => (~calm(X0) | curious(X0))) [input p3]
6. ! [X0] : (rich(X0) => (~rich(X0) <~> generous(X0))) [input p5]
8. ! [X0] : ((rich(X0) | funny(X0)) => calm(X0)) [input p7]
13. ! [X0] : (~curious(X0) <=> (brave(X0) | strong(X0))) [input p12]
25. strong(mary) [input hypothesis]
29. ! [X0] : ((brave(X0) | strong(X0)) => ~curious(X0)) [unused predicate definition removal 13]
30. ! [X0] : ((~strong(X0) & humble(X0)) | (rich(X0) <=> strong(X0))) [ennf transformation 3]
31. ! [X0] : ((~calm(X0) | curious(X0)) | (~generous(X0) & kind(X0))) [ennf transformation 4]
32. ! [X0] : (~calm(X0) | curious(X0) | (~generous(X0) & kind(X0))) [flattening 31]
34. ! [X0] : ((~rich(X0) <~> generous(X0)) | ~rich(X0)) [ennf transformation 6]
35. ! [X0] : (calm(X0) | (~rich(X0) & ~funny(X0))) [ennf transformation 8]
39. ! [X0] : (~curious(X0) | (~brave(X0) & ~strong(X0))) [ennf transformation 29]
44. ! [X0] : ((~strong(X0) & humble(X0)) | ((rich(X0) | ~strong(X0)) & (strong(X0) | ~rich(X0)))) [nnf transformation 30]
45. ! [X0] : (((~generous(X0) | rich(X0)) & (generous(X0) | ~rich(X0))) | ~rich(X0)) [nnf transformation 34]
93. ~strong(X0) | rich(X0) | ~strong(X0) [cnf transformation 44]
95. ~calm(X0) | curious(X0) | ~generous(X0) [cnf transformation 32]
98. generous(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 45]
107. ~rich(X0) | calm(X0) [cnf transformation 35]
120. ~curious(X0) | ~strong(X0) [cnf transformation 39]
149. strong(mary) [cnf transformation 25]
150. ~rich(X0) | generous(X0) [duplicate literal removal 98]
151. ~strong(X0) | rich(X0) [duplicate literal removal 93]
207. 13 <=> calm(mary) [avatar definition]
208. calm(mary) <- (13) [avatar component clause 207]
310. rich(mary) [resolution 151,149]
332. generous(mary) [resolution 310,150]
333. calm(mary) [resolution 310,107]
334. 13 [avatar split clause 333,207]
351. 40 <=> curious(mary) [avatar definition]
353. curious(mary) <- (40) [avatar component clause 351]
356. curious(mary) | ~generous(mary) <- (13) [resolution 95,208]
359. curious(mary) <- (13) [subsumption resolution 356,332]
360. 40 | ~13 [avatar split clause 359,207,351]
361. ~strong(mary) <- (40) [resolution 353,120]
362. $false <- (40) [subsumption resolution 361,149]
363. ~40 [avatar contradiction clause 362]
364. $false [avatar sat refutation 334,360,363]
% SZS output end Proof for 1180115064374946058119959
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong and not tall is brave.
Everyone who is either generous or curious is not curious and vice versa.
Everyone who is both not calm and not generous is not rich or wise and vice versa.
Everyone who is curious is either old or not calm.
Everyone who is generous is not funny and vice versa.
If mary is either quiet or happy then mary is not brave or generous and vice versa.
If lucy is happy then someone is wise and vice versa.
If someone is not humble then someone is either not kind or not humble and vice versa.
Everyone who is both not wise and not kind is either funny or humble and vice versa.
If someone is both not kind and not brave then someone is either rich or brave and vice versa.
Everyone who is either not creative or quiet is not calm.
Everyone who is happy is either not old or not kind.
Everyone who is not humble or not happy is both not old and not happy and vice versa.
If someone is not wise then someone is either not strong or happy and vice versa.
Everyone who is wise or not wise is wise or not curious.
If mary is not kind or funny then someone is not wise.
Someone is curious or not old.
Mary is either funny or calm.
Lucy is either tall or not curious.
Someone is not wise.
Paul is not wise or not humble.
Someone is not generous or calm.
Mary is curious or not strong.
Someone is not humble or funny. | Paul is generous. | entailment | (![X]:((strong(X)&~tall(X))=>brave(X)))&
(![X]:((generous(X)<~>curious(X))<=>~curious(X)))&
(![X]:((~calm(X)&~generous(X))<=>(~rich(X)|wise(X))))&
(![X]:(curious(X)=>(old(X)<~>~calm(X))))&
(![X]:(generous(X)<=>~funny(X)))&
(((quiet(mary)<~>happy(mary)))<=>((~brave(mary)|generous(mary))))&
((happy(lucy))<=>(?[X]:(wise(X))))&
((?[X]:(~humble(X)))<=>(?[X]:((~kind(X)<~>~humble(X)))))&
(![X]:((~wise(X)&~kind(X))<=>(funny(X)<~>humble(X))))&
((?[X]:((~kind(X)&~brave(X))))<=>(?[X]:((rich(X)<~>brave(X)))))&
(![X]:((~creative(X)<~>quiet(X))=>~calm(X)))&
(![X]:(happy(X)=>(~old(X)<~>~kind(X))))&
(![X]:((~humble(X)|~happy(X))<=>(~old(X)&~happy(X))))&
((?[X]:(~wise(X)))<=>(?[X]:((~strong(X)<~>happy(X)))))&
(![X]:((wise(X)|~wise(X))=>(wise(X)|~curious(X))))&
(((~kind(mary)|funny(mary)))=>(?[X]:(~wise(X))))&
(?[X]:((curious(X)|~old(X))))&
((funny(mary)<~>calm(mary)))&
((tall(lucy)<~>~curious(lucy)))&
(?[X]:(~wise(X)))&
((~wise(paul)|~humble(paul)))&
(?[X]:((~generous(X)|calm(X))))&
((curious(mary)|~strong(mary)))&
(?[X]:((~humble(X)|funny(X)))) | generous(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 890346791942311660123655
% SZS output start Proof for 890346791942311660123655
2. ! [X0] : ((generous(X0) <~> curious(X0)) <=> ~curious(X0)) [input p1]
25. ~generous(paul) [input hypothesis]
37. ! [X0] : ((((~curious(X0) | ~generous(X0)) & (curious(X0) | generous(X0))) | curious(X0)) & (~curious(X0) | ((generous(X0) | ~curious(X0)) & (curious(X0) | ~generous(X0))))) [nnf transformation 2]
83. ~curious(X0) | generous(X0) | ~curious(X0) [cnf transformation 37]
84. curious(X0) | generous(X0) | curious(X0) [cnf transformation 37]
146. ~generous(paul) [cnf transformation 25]
148. ~curious(X0) | generous(X0) [duplicate literal removal 83]
149. curious(X0) | generous(X0) [duplicate literal removal 84]
150. generous(X0) [subsumption resolution 148,149]
244. $false [subsumption resolution 146,150]
% SZS output end Proof for 890346791942311660123655
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 funny then someone is both not generous and not humble and vice versa.
Everyone who is not happy or quiet is either not creative or creative and vice versa.
If someone is either patient or not humble then someone is either tall or creative.
Everyone who is both strong and not wise is generous or not creative.
If someone is both wise and tall then someone is either strong or patient and vice versa.
Everyone who is both humble and not happy is both wise and patient.
Everyone who is either generous or not generous is not old.
If fred is not happy or not kind then alice is old and vice versa.
If someone is either patient or not strong then paul is happy.
Everyone who is both not strong and not patient is quiet or not wise and vice versa.
Everyone who is not funny or rich is either not humble or calm and vice versa.
Everyone who is not funny or not strong is strong or not humble.
If john is not tall then susan is not curious or quiet and vice versa.
If someone is both not quiet and not happy then john is not happy.
Lucy is generous.
Someone is either strong or not generous.
Someone is either creative or not curious.
Someone is either not happy or not strong.
Someone is not calm.
Someone is curious.
Someone is either happy or kind. | Paul is not happy. | contradiction | ((funny(mary))<=>(?[X]:((~generous(X)&~humble(X)))))&
(![X]:((~happy(X)|quiet(X))<=>(~creative(X)<~>creative(X))))&
((?[X]:((patient(X)<~>~humble(X))))=>(?[X]:((tall(X)<~>creative(X)))))&
(![X]:((strong(X)&~wise(X))=>(generous(X)|~creative(X))))&
((?[X]:((wise(X)&tall(X))))<=>(?[X]:((strong(X)<~>patient(X)))))&
(![X]:((humble(X)&~happy(X))=>(wise(X)&patient(X))))&
(![X]:((generous(X)<~>~generous(X))=>~old(X)))&
(((~happy(fred)|~kind(fred)))<=>(old(alice)))&
((?[X]:((patient(X)<~>~strong(X))))=>(happy(paul)))&
(![X]:((~strong(X)&~patient(X))<=>(quiet(X)|~wise(X))))&
(![X]:((~funny(X)|rich(X))<=>(~humble(X)<~>calm(X))))&
(![X]:((~funny(X)|~strong(X))=>(strong(X)|~humble(X))))&
((~tall(john))<=>((~curious(susan)|quiet(susan))))&
((?[X]:((~quiet(X)&~happy(X))))=>(~happy(john)))&
(generous(lucy))&
(?[X]:((strong(X)<~>~generous(X))))&
(?[X]:((creative(X)<~>~curious(X))))&
(?[X]:((~happy(X)<~>~strong(X))))&
(?[X]:(~calm(X)))&
(?[X]:(curious(X)))&
(?[X]:((happy(X)<~>kind(X)))) | ~happy(paul) | [
"p1",
"p6",
"p7",
"p8",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 7331148486674402139765682
% SZS output start Proof for 7331148486674402139765682
2. ! [X0] : ((quiet(X0) | ~happy(X0)) <=> (~creative(X0) <~> creative(X0))) [input p1]
7. ! [X0] : ((generous(X0) <~> ~generous(X0)) => ~old(X0)) [input p6]
8. (~kind(fred) | ~happy(fred)) <=> old(alice) [input p7]
9. ? [X0] : (patient(X0) <~> ~strong(X0)) => happy(paul) [input p8]
10. ! [X0] : ((~patient(X0) & ~strong(X0)) <=> (~wise(X0) | quiet(X0))) [input p9]
22. ~happy(paul) [input hypothesis]
30. ! [X0] : (~old(X0) | (generous(X0) <=> ~generous(X0))) [ennf transformation 7]
31. happy(paul) | ! [X0] : (patient(X0) <=> ~strong(X0)) [ennf transformation 9]
39. ! [X0] : (((quiet(X0) | ~happy(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~quiet(X0) & happy(X0)))) [nnf transformation 2]
40. ! [X0] : ((quiet(X0) | ~happy(X0) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0)))) & (((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~quiet(X0) & happy(X0)))) [flattening 39]
50. ! [X0] : (~old(X0) | ((generous(X0) | generous(X0)) & (~generous(X0) | ~generous(X0)))) [nnf transformation 30]
51. ((~kind(fred) | ~happy(fred)) | ~old(alice)) & (old(alice) | (kind(fred) & happy(fred))) [nnf transformation 8]
52. (~kind(fred) | ~happy(fred) | ~old(alice)) & (old(alice) | (kind(fred) & happy(fred))) [flattening 51]
53. happy(paul) | ! [X0] : ((patient(X0) | strong(X0)) & (~strong(X0) | ~patient(X0))) [nnf transformation 31]
54. ! [X0] : (((~patient(X0) & ~strong(X0)) | (wise(X0) & ~quiet(X0))) & ((~wise(X0) | quiet(X0)) | (patient(X0) | strong(X0)))) [nnf transformation 10]
55. ! [X0] : (((~patient(X0) & ~strong(X0)) | (wise(X0) & ~quiet(X0))) & (~wise(X0) | quiet(X0) | patient(X0) | strong(X0))) [flattening 54]
83. quiet(X0) | ~happy(X0) | creative(X0) | creative(X0) [cnf transformation 40]
84. quiet(X0) | ~happy(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 40]
98. ~old(X0) | ~generous(X0) | ~generous(X0) [cnf transformation 50]
99. ~old(X0) | generous(X0) | generous(X0) [cnf transformation 50]
100. old(alice) | happy(fred) [cnf transformation 52]
104. happy(paul) | patient(X0) | strong(X0) [cnf transformation 53]
106. ~strong(X0) | ~quiet(X0) [cnf transformation 55]
108. ~patient(X0) | ~quiet(X0) [cnf transformation 55]
133. ~happy(paul) [cnf transformation 22]
135. ~old(X0) | ~generous(X0) [duplicate literal removal 98]
136. ~old(X0) | generous(X0) [duplicate literal removal 99]
137. quiet(X0) | ~happy(X0) | creative(X0) [duplicate literal removal 83]
138. quiet(X0) | ~happy(X0) | ~creative(X0) [duplicate literal removal 84]
157. ~happy(X0) | quiet(X0) [subsumption resolution 137,138]
207. ~old(X0) [subsumption resolution 135,136]
209. happy(fred) [subsumption resolution 100,207]
211. 16 <=> ! [X0] : (patient(X0) | strong(X0)) [avatar definition]
212. strong(X0) | patient(X0) <- (16) [avatar component clause 211]
214. 17 <=> happy(paul) [avatar definition]
217. 16 | 17 [avatar split clause 104,214,211]
286. ~17 [avatar split clause 133,214]
289. quiet(fred) [resolution 157,209]
295. patient(X1) | ~quiet(X1) <- (16) [resolution 212,106]
322. ~quiet(X1) <- (16) [subsumption resolution 295,108]
330. $false <- (16) [resolution 322,289]
335. ~16 [avatar contradiction clause 330]
336. $false [avatar sat refutation 217,286,335]
% SZS output end Proof for 7331148486674402139765682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 quiet or not calm is not creative.
If paul is both generous and creative then someone is not funny or happy and vice versa.
Everyone who is patient or not wise is not curious.
If someone is either old or not wise then someone is both not calm and not strong and vice versa.
Everyone who is patient or strong is both kind and happy and vice versa.
Everyone who is both not calm and rich is both quiet and humble and vice versa.
If someone is kind or not old then mary is not rich.
Everyone who is both strong and patient is not rich or wise.
Everyone who is either not kind or not generous is either wise or not funny.
Everyone who is both not brave and curious is strong or brave and vice versa.
If someone is patient or not calm then mary is either happy or humble and vice versa.
If someone is both humble and not old then someone is both wise and not old and vice versa.
If someone is happy then lucy is both not wise and curious and vice versa.
Everyone who is both strong and not patient is not wise or not calm and vice versa.
If john is either tall or not funny then someone is either tall or not humble.
Everyone who is not curious is either not brave or creative and vice versa.
Someone is either not generous or not happy.
Someone is not generous or strong.
Susan is not quiet or not strong.
Someone is patient or not strong.
Susan is both funny and not humble.
Someone is not tall or brave. | John is tall. | neutral | (![X]:((quiet(X)<~>~calm(X))=>~creative(X)))&
(((generous(paul)&creative(paul)))<=>(?[X]:((~funny(X)|happy(X)))))&
(![X]:((patient(X)|~wise(X))=>~curious(X)))&
((?[X]:((old(X)<~>~wise(X))))<=>(?[X]:((~calm(X)&~strong(X)))))&
(![X]:((patient(X)|strong(X))<=>(kind(X)&happy(X))))&
(![X]:((~calm(X)&rich(X))<=>(quiet(X)&humble(X))))&
((?[X]:((kind(X)|~old(X))))=>(~rich(mary)))&
(![X]:((strong(X)&patient(X))=>(~rich(X)|wise(X))))&
(![X]:((~kind(X)<~>~generous(X))=>(wise(X)<~>~funny(X))))&
(![X]:((~brave(X)&curious(X))<=>(strong(X)|brave(X))))&
((?[X]:((patient(X)|~calm(X))))<=>((happy(mary)<~>humble(mary))))&
((?[X]:((humble(X)&~old(X))))<=>(?[X]:((wise(X)&~old(X)))))&
((?[X]:(happy(X)))<=>((~wise(lucy)&curious(lucy))))&
(![X]:((strong(X)&~patient(X))<=>(~wise(X)|~calm(X))))&
(((tall(john)<~>~funny(john)))=>(?[X]:((tall(X)<~>~humble(X)))))&
(![X]:(~curious(X)<=>(~brave(X)<~>creative(X))))&
(?[X]:((~generous(X)<~>~happy(X))))&
(?[X]:((~generous(X)|strong(X))))&
((~quiet(susan)|~strong(susan)))&
(?[X]:((patient(X)|~strong(X))))&
((funny(susan)&~humble(susan)))&
(?[X]:((~tall(X)|brave(X)))) | tall(john) | [] | null | 0 |
Everyone who is not strong or happy is either calm or not strong and vice versa.
Everyone who is generous is either quiet or not generous and vice versa.
Everyone who is both creative and not tall is either not funny or not strong.
Everyone who is either wise or patient is patient and vice versa.
Everyone who is happy or not quiet is both generous and not old and vice versa.
If susan is both wise and rich then lucy is either tall or not brave and vice versa.
If someone is generous or wise then someone is not calm and vice versa.
Everyone who is either strong or not kind is both not curious and strong.
If fred is either patient or not wise then susan is either not curious or tall.
If paul is strong or not rich then someone is not patient.
Everyone who is either not calm or quiet is both curious and kind and vice versa.
Everyone who is not quiet is kind and vice versa.
Everyone who is both rich and creative is both curious and not old and vice versa.
If susan is not quiet or calm then someone is both old and tall and vice versa.
If someone is both not funny and not calm then someone is funny.
Someone is old or curious.
Mary is not generous.
Paul is either not quiet or not wise.
Someone is either quiet or not brave.
Someone is curious or wise.
Fred is funny or not calm.
Someone is both rich and not patient. | Lucy is not strong. | contradiction | (![X]:((~strong(X)|happy(X))<=>(calm(X)<~>~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((happy(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(((wise(susan)&rich(susan)))<=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(((patient(fred)<~>~wise(fred)))=>((~curious(susan)<~>tall(susan))))&
(((strong(paul)|~rich(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(curious(X)&kind(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
((?[X]:((~funny(X)&~calm(X))))=>(?[X]:(funny(X))))&
(?[X]:((old(X)|curious(X))))&
(~generous(mary))&
((~quiet(paul)<~>~wise(paul)))&
(?[X]:((quiet(X)<~>~brave(X))))&
(?[X]:((curious(X)|wise(X))))&
((funny(fred)|~calm(fred)))&
(?[X]:((rich(X)&~patient(X)))) | ~strong(lucy) | [
"p1",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8095486709487182042167248
% SZS output start Proof for 8095486709487182042167248
2. ! [X0] : (generous(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p1]
8. ! [X0] : ((strong(X0) <~> ~kind(X0)) => (strong(X0) & ~curious(X0))) [input p7]
12. ! [X0] : (~quiet(X0) <=> kind(X0)) [input p11]
23. ~strong(lucy) [input hypothesis]
28. ! [X0] : ((strong(X0) & ~curious(X0)) | (strong(X0) <=> ~kind(X0))) [ennf transformation 8]
34. ! [X0] : ((generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~generous(X0))) [nnf transformation 2]
46. ! [X0] : ((strong(X0) & ~curious(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 28]
52. ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))) [nnf transformation 12]
79. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 34]
82. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 34]
106. strong(X0) | strong(X0) | kind(X0) [cnf transformation 46]
120. ~quiet(X0) | ~kind(X0) [cnf transformation 52]
141. ~strong(lucy) [cnf transformation 23]
142. kind(X0) | strong(X0) [duplicate literal removal 106]
145. ~generous(X0) | quiet(X0) [duplicate literal removal 79]
146. generous(X0) | quiet(X0) [duplicate literal removal 82]
149. quiet(X0) [subsumption resolution 145,146]
220. ~kind(X0) [subsumption resolution 120,149]
271. strong(X0) [resolution 142,220]
272. $false [resolution 271,141]
% SZS output end Proof for 8095486709487182042167248
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is not calm or old.
If fred is both rich and funny then someone is wise or curious and vice versa.
Everyone who is not generous or curious is happy and vice versa.
If someone is both not old and strong then alice is either quiet or generous and vice versa.
If someone is wise then john is strong or wise.
Everyone who is humble is not tall or not patient and vice versa.
If someone is not calm or quiet then someone is either patient or rich.
If susan is brave then mary is not quiet or creative and vice versa.
Everyone who is curious or not quiet is happy and vice versa.
Everyone who is rich is either humble or not creative and vice versa.
Everyone who is not creative is either not strong or calm.
If john is both wise and not curious then fred is both happy and not tall.
Everyone who is both not creative and not strong is both happy and not quiet.
Everyone who is both tall and not patient is quiet and vice versa.
Everyone who is not tall is not kind or patient and vice versa.
If paul is not curious or old then lucy is either funny or not tall and vice versa.
Lucy is not strong.
Someone is both calm and funny.
Paul is either not wise or not generous.
Paul is either not patient or tall.
Lucy is either strong or not quiet.
Someone is not old or not generous.
Paul is humble. | Alice is kind. | neutral | (![X]:(~generous(X)=>(~calm(X)|old(X))))&
(((rich(fred)&funny(fred)))<=>(?[X]:((wise(X)|curious(X)))))&
(![X]:((~generous(X)|curious(X))<=>happy(X)))&
((?[X]:((~old(X)&strong(X))))<=>((quiet(alice)<~>generous(alice))))&
((?[X]:(wise(X)))=>((strong(john)|wise(john))))&
(![X]:(humble(X)<=>(~tall(X)|~patient(X))))&
((?[X]:((~calm(X)|quiet(X))))=>(?[X]:((patient(X)<~>rich(X)))))&
((brave(susan))<=>((~quiet(mary)|creative(mary))))&
(![X]:((curious(X)|~quiet(X))<=>happy(X)))&
(![X]:(rich(X)<=>(humble(X)<~>~creative(X))))&
(![X]:(~creative(X)=>(~strong(X)<~>calm(X))))&
(((wise(john)&~curious(john)))=>((happy(fred)&~tall(fred))))&
(![X]:((~creative(X)&~strong(X))=>(happy(X)&~quiet(X))))&
(![X]:((tall(X)&~patient(X))<=>quiet(X)))&
(![X]:(~tall(X)<=>(~kind(X)|patient(X))))&
(((~curious(paul)|old(paul)))<=>((funny(lucy)<~>~tall(lucy))))&
(~strong(lucy))&
(?[X]:((calm(X)&funny(X))))&
((~wise(paul)<~>~generous(paul)))&
((~patient(paul)<~>tall(paul)))&
((strong(lucy)<~>~quiet(lucy)))&
(?[X]:((~old(X)|~generous(X))))&
(humble(paul)) | kind(alice) | [] | null | 0 |
If susan is not wise then fred is either not curious or funny.
If alice is not quiet then someone is happy and vice versa.
Everyone who is not wise or generous is either not rich or not old.
If someone is quiet then paul is happy and vice versa.
Everyone who is not humble is both not happy and not curious and vice versa.
If someone is both not rich and not quiet then someone is not creative or patient and vice versa.
If someone is wise or humble then john is tall and vice versa.
If someone is quiet or not rich then someone is either not tall or not calm.
If lucy is either happy or not kind then john is either not funny or funny.
If mary is both tall and not old then mary is patient or rich and vice versa.
If someone is either not tall or kind then someone is either creative or kind.
If john is both kind and old then john is both brave and not generous.
Everyone who is either calm or generous is either curious or generous and vice versa.
Everyone who is either generous or tall is not tall and vice versa.
If mary is not quiet then lucy is either not funny or happy.
Everyone who is curious or not old is either not calm or rich and vice versa.
Mary is calm or strong.
Someone is both not patient and funny.
Someone is not strong or not old.
Alice is either wise or patient. | Lucy is not calm. | contradiction | ((~wise(susan))=>((~curious(fred)<~>funny(fred))))&
((~quiet(alice))<=>(?[X]:(happy(X))))&
(![X]:((~wise(X)|generous(X))=>(~rich(X)<~>~old(X))))&
((?[X]:(quiet(X)))<=>(happy(paul)))&
(![X]:(~humble(X)<=>(~happy(X)&~curious(X))))&
((?[X]:((~rich(X)&~quiet(X))))<=>(?[X]:((~creative(X)|patient(X)))))&
((?[X]:((wise(X)|humble(X))))<=>(tall(john)))&
((?[X]:((quiet(X)|~rich(X))))=>(?[X]:((~tall(X)<~>~calm(X)))))&
(((happy(lucy)<~>~kind(lucy)))=>((~funny(john)<~>funny(john))))&
(((tall(mary)&~old(mary)))<=>((patient(mary)|rich(mary))))&
((?[X]:((~tall(X)<~>kind(X))))=>(?[X]:((creative(X)<~>kind(X)))))&
(((kind(john)&old(john)))=>((brave(john)&~generous(john))))&
(![X]:((calm(X)<~>generous(X))<=>(curious(X)<~>generous(X))))&
(![X]:((generous(X)<~>tall(X))<=>~tall(X)))&
((~quiet(mary))=>((~funny(lucy)<~>happy(lucy))))&
(![X]:((curious(X)|~old(X))<=>(~calm(X)<~>rich(X))))&
((calm(mary)|strong(mary)))&
(?[X]:((~patient(X)&funny(X))))&
(?[X]:((~strong(X)|~old(X))))&
((wise(alice)<~>patient(alice))) | ~calm(lucy) | [
"p2",
"p12",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 659319858748962530835291
% SZS output start Proof for 659319858748962530835291
3. ! [X0] : ((generous(X0) | ~wise(X0)) => (~rich(X0) <~> ~old(X0))) [input p2]
13. ! [X0] : ((calm(X0) <~> generous(X0)) <=> (curious(X0) <~> generous(X0))) [input p12]
14. ! [X0] : ((generous(X0) <~> tall(X0)) <=> ~tall(X0)) [input p13]
16. ! [X0] : ((~old(X0) | curious(X0)) <=> (~calm(X0) <~> rich(X0))) [input p15]
21. ~calm(lucy) [input hypothesis]
27. ! [X0] : ((~rich(X0) <~> ~old(X0)) | (~generous(X0) & wise(X0))) [ennf transformation 3]
39. ! [X0] : (((old(X0) | rich(X0)) & (~old(X0) | ~rich(X0))) | (~generous(X0) & wise(X0))) [nnf transformation 27]
66. ! [X0] : ((((~generous(X0) | ~calm(X0)) & (generous(X0) | calm(X0))) | ((curious(X0) | ~generous(X0)) & (generous(X0) | ~curious(X0)))) & (((~generous(X0) | ~curious(X0)) & (generous(X0) | curious(X0))) | ((calm(X0) | ~generous(X0)) & (generous(X0) | ~calm(X0))))) [nnf transformation 13]
67. ! [X0] : ((((~tall(X0) | ~generous(X0)) & (tall(X0) | generous(X0))) | tall(X0)) & (~tall(X0) | ((generous(X0) | ~tall(X0)) & (tall(X0) | ~generous(X0))))) [nnf transformation 14]
69. ! [X0] : (((~old(X0) | curious(X0)) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (old(X0) & ~curious(X0)))) [nnf transformation 16]
70. ! [X0] : ((~old(X0) | curious(X0) | ((~calm(X0) | ~rich(X0)) & (rich(X0) | calm(X0)))) & (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | (old(X0) & ~curious(X0)))) [flattening 69]
81. ~old(X0) | ~rich(X0) | ~generous(X0) [cnf transformation 39]
83. ~generous(X0) | rich(X0) | old(X0) [cnf transformation 39]
115. generous(X0) | curious(X0) | generous(X0) | ~calm(X0) [cnf transformation 66]
118. ~generous(X0) | ~curious(X0) | calm(X0) | ~generous(X0) [cnf transformation 66]
119. generous(X0) | calm(X0) | generous(X0) | ~curious(X0) [cnf transformation 66]
122. ~generous(X0) | ~calm(X0) | curious(X0) | ~generous(X0) [cnf transformation 66]
124. ~tall(X0) | generous(X0) | ~tall(X0) [cnf transformation 67]
125. tall(X0) | generous(X0) | tall(X0) [cnf transformation 67]
129. rich(X0) | ~calm(X0) | ~curious(X0) [cnf transformation 70]
132. ~rich(X0) | calm(X0) | old(X0) [cnf transformation 70]
133. ~old(X0) | curious(X0) | rich(X0) | calm(X0) [cnf transformation 70]
141. ~calm(lucy) [cnf transformation 21]
142. ~tall(X0) | generous(X0) [duplicate literal removal 124]
143. tall(X0) | generous(X0) [duplicate literal removal 125]
144. generous(X0) | curious(X0) | ~calm(X0) [duplicate literal removal 115]
145. ~generous(X0) | ~curious(X0) | calm(X0) [duplicate literal removal 118]
146. ~curious(X0) | calm(X0) | generous(X0) [duplicate literal removal 119]
147. ~calm(X0) | ~generous(X0) | curious(X0) [duplicate literal removal 122]
240. 22 <=> ! [X1] : rich(X1) [avatar definition]
241. rich(X1) <- (22) [avatar component clause 240]
306. ~curious(X0) | calm(X0) [subsumption resolution 145,146]
307. ~calm(X0) | curious(X0) [subsumption resolution 144,147]
308. generous(X0) [subsumption resolution 142,143]
323. ~old(X0) | rich(X0) | calm(X0) [subsumption resolution 133,306]
324. ~calm(X0) | rich(X0) [subsumption resolution 129,307]
402. old(X0) | rich(X0) [resolution 83,308]
428. rich(X0) | calm(X0) | rich(X0) [resolution 323,402]
431. rich(X0) | calm(X0) [duplicate literal removal 428]
432. rich(X0) [subsumption resolution 431,324]
433. 22 [avatar split clause 432,240]
435. calm(X0) | old(X0) <- (22) [resolution 241,132]
440. old(lucy) <- (22) [resolution 435,141]
449. ~rich(lucy) | ~generous(lucy) <- (22) [resolution 440,81]
451. ~generous(lucy) <- (22) [subsumption resolution 449,241]
452. $false <- (22) [subsumption resolution 451,308]
453. ~22 [avatar contradiction clause 452]
455. $false [avatar sat refutation 433,453]
% SZS output end Proof for 659319858748962530835291
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative is both not generous and old.
Everyone who is not generous is both kind and not wise.
If someone is quiet then lucy is either not quiet or not strong.
Everyone who is both curious and not old is funny.
If susan is not rich then mary is either not creative or not funny.
If someone is either humble or not patient then someone is either not old or old and vice versa.
Everyone who is both kind and humble is both not calm and creative.
If john is either not brave or not wise then someone is either strong or not calm.
Everyone who is not quiet or not humble is either strong or not creative.
If susan is brave then someone is both humble and kind and vice versa.
Everyone who is brave is both not wise and not generous and vice versa.
If someone is happy then paul is generous or not rich.
If john is calm or not patient then someone is both rich and not rich and vice versa.
Everyone who is either not funny or tall is both calm and not calm and vice versa.
Everyone who is either not humble or rich is wise or not tall.
Everyone who is not quiet is either quiet or strong.
Alice is either not wise or funny.
Mary is either not brave or not generous.
Fred is both strong and not calm.
Paul is both old and calm.
Someone is both not humble and quiet.
John is not quiet or not funny.
Lucy is strong or kind.
Mary is not creative or creative. | Lucy is not kind. | contradiction | (![X]:(creative(X)=>(~generous(X)&old(X))))&
(![X]:(~generous(X)=>(kind(X)&~wise(X))))&
((?[X]:(quiet(X)))=>((~quiet(lucy)<~>~strong(lucy))))&
(![X]:((curious(X)&~old(X))=>funny(X)))&
((~rich(susan))=>((~creative(mary)<~>~funny(mary))))&
((?[X]:((humble(X)<~>~patient(X))))<=>(?[X]:((~old(X)<~>old(X)))))&
(![X]:((kind(X)&humble(X))=>(~calm(X)&creative(X))))&
(((~brave(john)<~>~wise(john)))=>(?[X]:((strong(X)<~>~calm(X)))))&
(![X]:((~quiet(X)|~humble(X))=>(strong(X)<~>~creative(X))))&
((brave(susan))<=>(?[X]:((humble(X)&kind(X)))))&
(![X]:(brave(X)<=>(~wise(X)&~generous(X))))&
((?[X]:(happy(X)))=>((generous(paul)|~rich(paul))))&
(((calm(john)|~patient(john)))<=>(?[X]:((rich(X)&~rich(X)))))&
(![X]:((~funny(X)<~>tall(X))<=>(calm(X)&~calm(X))))&
(![X]:((~humble(X)<~>rich(X))=>(wise(X)|~tall(X))))&
(![X]:(~quiet(X)=>(quiet(X)<~>strong(X))))&
((~wise(alice)<~>funny(alice)))&
((~brave(mary)<~>~generous(mary)))&
((strong(fred)&~calm(fred)))&
((old(paul)&calm(paul)))&
(?[X]:((~humble(X)&quiet(X))))&
((~quiet(john)|~funny(john)))&
((strong(lucy)|kind(lucy)))&
((~creative(mary)|creative(mary))) | ~kind(lucy) | [
"p0",
"p1",
"p2",
"p8",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 5611211921341367160396197
% SZS output start Proof for 5611211921341367160396197
1. ! [X0] : (creative(X0) => (old(X0) & ~generous(X0))) [input p0]
2. ! [X0] : (~generous(X0) => (~wise(X0) & kind(X0))) [input p1]
3. ? [X0] : quiet(X0) => (~quiet(lucy) <~> ~strong(lucy)) [input p2]
9. ! [X0] : ((~humble(X0) | ~quiet(X0)) => (strong(X0) <~> ~creative(X0))) [input p8]
21. ? [X0] : (quiet(X0) & ~humble(X0)) [input p20]
23. kind(lucy) | strong(lucy) [input p22]
25. ~kind(lucy) [input hypothesis]
29. ! [X0] : ((old(X0) & ~generous(X0)) | ~creative(X0)) [ennf transformation 1]
30. ! [X0] : ((~wise(X0) & kind(X0)) | generous(X0)) [ennf transformation 2]
31. (~quiet(lucy) <~> ~strong(lucy)) | ! [X0] : ~quiet(X0) [ennf transformation 3]
36. ! [X0] : ((strong(X0) <~> ~creative(X0)) | (humble(X0) & quiet(X0))) [ennf transformation 9]
40. ((strong(lucy) | quiet(lucy)) & (~strong(lucy) | ~quiet(lucy))) | ! [X0] : ~quiet(X0) [nnf transformation 31]
50. ! [X0] : (((creative(X0) | ~strong(X0)) & (~creative(X0) | strong(X0))) | (humble(X0) & quiet(X0))) [nnf transformation 36]
68. ? [X0] : (quiet(X0) & ~humble(X0)) => (quiet(sK5) & ~humble(sK5)) [choice axiom]
69. quiet(sK5) & ~humble(sK5) [skolemisation 21,68]
70. ~generous(X0) | ~creative(X0) [cnf transformation 29]
72. kind(X0) | generous(X0) [cnf transformation 30]
74. ~strong(lucy) | ~quiet(lucy) | ~quiet(X0) [cnf transformation 40]
94. ~strong(X0) | creative(X0) | quiet(X0) [cnf transformation 50]
126. quiet(sK5) [cnf transformation 69]
128. kind(lucy) | strong(lucy) [cnf transformation 23]
130. ~kind(lucy) [cnf transformation 25]
137. 1 <=> ! [X0] : ~quiet(X0) [avatar definition]
138. ~quiet(X0) <- (1) [avatar component clause 137]
140. 2 <=> quiet(lucy) [avatar definition]
144. 3 <=> strong(lucy) [avatar definition]
146. strong(lucy) <- (3) [avatar component clause 144]
148. 1 | ~2 | ~3 [avatar split clause 74,144,140,137]
258. 26 <=> kind(lucy) [avatar definition]
259. ~kind(lucy) <- (~26) [avatar component clause 258]
261. 3 | 26 [avatar split clause 128,258,144]
262. ~26 [avatar split clause 130,258]
263. generous(lucy) <- (~26) [resolution 72,259]
264. ~creative(lucy) <- (~26) [resolution 263,70]
274. creative(lucy) | quiet(lucy) <- (3) [resolution 94,146]
286. quiet(lucy) <- (3, ~26) [subsumption resolution 274,264]
289. 2 | ~3 | 26 [avatar split clause 286,258,144,140]
290. $false <- (1) [resolution 138,126]
291. ~1 [avatar contradiction clause 290]
292. $false [avatar sat refutation 148,261,262,289,291]
% SZS output end Proof for 5611211921341367160396197
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise then someone is not funny or not happy and vice versa.
Everyone who is humble is patient or strong and vice versa.
If someone is wise or not calm then someone is not curious or not calm and vice versa.
Everyone who is both tall and not wise is either not creative or not tall and vice versa.
Everyone who is both tall and curious is not wise and vice versa.
Everyone who is either not rich or not old is not quiet.
If mary is either not funny or rich then john is rich and vice versa.
Everyone who is either humble or generous is not humble or not generous.
Everyone who is calm or happy is both funny and wise.
Everyone who is either patient or not creative is both not creative and brave and vice versa.
Everyone who is curious is both calm and not kind and vice versa.
Everyone who is not generous is either strong or not strong and vice versa.
If someone is not old or generous then alice is not generous.
Everyone who is either not rich or humble is kind and vice versa.
Everyone who is not generous is not happy or tall and vice versa.
Everyone who is either not humble or not brave is kind or tall.
Someone is not kind.
Mary is humble or not quiet.
Someone is either not old or not tall.
Alice is both kind and not calm.
Someone is not creative or not old.
John is either not humble or creative. | Mary is not happy. | contradiction | ((?[X]:(~wise(X)))<=>(?[X]:((~funny(X)|~happy(X)))))&
(![X]:(humble(X)<=>(patient(X)|strong(X))))&
((?[X]:((wise(X)|~calm(X))))<=>(?[X]:((~curious(X)|~calm(X)))))&
(![X]:((tall(X)&~wise(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((tall(X)&curious(X))<=>~wise(X)))&
(![X]:((~rich(X)<~>~old(X))=>~quiet(X)))&
(((~funny(mary)<~>rich(mary)))<=>(rich(john)))&
(![X]:((humble(X)<~>generous(X))=>(~humble(X)|~generous(X))))&
(![X]:((calm(X)|happy(X))=>(funny(X)&wise(X))))&
(![X]:((patient(X)<~>~creative(X))<=>(~creative(X)&brave(X))))&
(![X]:(curious(X)<=>(calm(X)&~kind(X))))&
(![X]:(~generous(X)<=>(strong(X)<~>~strong(X))))&
((?[X]:((~old(X)|generous(X))))=>(~generous(alice)))&
(![X]:((~rich(X)<~>humble(X))<=>kind(X)))&
(![X]:(~generous(X)<=>(~happy(X)|tall(X))))&
(![X]:((~humble(X)<~>~brave(X))=>(kind(X)|tall(X))))&
(?[X]:(~kind(X)))&
((humble(mary)|~quiet(mary)))&
(?[X]:((~old(X)<~>~tall(X))))&
((kind(alice)&~calm(alice)))&
(?[X]:((~creative(X)|~old(X))))&
((~humble(john)<~>creative(john))) | ~happy(mary) | [
"p0",
"p4",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4530204672454310045327001
% SZS output start Proof for 4530204672454310045327001
1. ? [X0] : ~wise(X0) <=> ? [X0] : (~happy(X0) | ~funny(X0)) [input p0]
5. ! [X0] : ((curious(X0) & tall(X0)) <=> ~wise(X0)) [input p4]
9. ! [X0] : ((happy(X0) | calm(X0)) => (wise(X0) & funny(X0))) [input p8]
11. ! [X0] : (curious(X0) <=> (~kind(X0) & calm(X0))) [input p10]
23. ~happy(mary) [input hypothesis]
24. ? [X0] : ~wise(X0) <=> ? [X1] : (~happy(X1) | ~funny(X1)) [rectify 1]
30. ! [X0] : ((wise(X0) & funny(X0)) | (~happy(X0) & ~calm(X0))) [ennf transformation 9]
34. (? [X0] : ~wise(X0) | ! [X1] : (happy(X1) & funny(X1))) & (? [X1] : (~happy(X1) | ~funny(X1)) | ! [X0] : wise(X0)) [nnf transformation 24]
35. (? [X0] : ~wise(X0) | ! [X1] : (happy(X1) & funny(X1))) & (? [X2] : (~happy(X2) | ~funny(X2)) | ! [X3] : wise(X3)) [rectify 34]
36. ? [X0] : ~wise(X0) => ~wise(sK0) [choice axiom]
37. ? [X2] : (~happy(X2) | ~funny(X2)) => (~happy(sK1) | ~funny(sK1)) [choice axiom]
38. (~wise(sK0) | ! [X1] : (happy(X1) & funny(X1))) & ((~happy(sK1) | ~funny(sK1)) | ! [X3] : wise(X3)) [skolemisation 35,37,36]
48. ! [X0] : (((curious(X0) & tall(X0)) | wise(X0)) & (~wise(X0) | (~curious(X0) | ~tall(X0)))) [nnf transformation 5]
49. ! [X0] : (((curious(X0) & tall(X0)) | wise(X0)) & (~wise(X0) | ~curious(X0) | ~tall(X0))) [flattening 48]
54. ! [X0] : ((curious(X0) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | ~curious(X0))) [nnf transformation 11]
55. ! [X0] : ((curious(X0) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | ~curious(X0))) [flattening 54]
71. ~wise(sK0) | happy(X1) [cnf transformation 38]
87. curious(X0) | wise(X0) [cnf transformation 49]
96. ~calm(X0) | wise(X0) [cnf transformation 30]
104. ~curious(X0) | calm(X0) [cnf transformation 55]
130. ~happy(mary) [cnf transformation 23]
140. 1 <=> ! [X1] : happy(X1) [avatar definition]
141. happy(X1) <- (1) [avatar component clause 140]
143. 2 <=> wise(sK0) [avatar definition]
145. ~wise(sK0) <- (~2) [avatar component clause 143]
146. 1 | ~2 [avatar split clause 71,143,140]
152. 4 <=> ! [X3] : wise(X3) [avatar definition]
153. wise(X3) <- (4) [avatar component clause 152]
242. calm(X0) | wise(X0) [resolution 104,87]
243. wise(X0) [subsumption resolution 242,96]
244. 4 [avatar split clause 243,152]
245. $false <- (~2, 4) [resolution 153,145]
246. 2 | ~4 [avatar contradiction clause 245]
247. $false <- (1) [resolution 141,130]
252. ~1 [avatar contradiction clause 247]
253. $false [avatar sat refutation 146,244,246,252]
% SZS output end Proof for 4530204672454310045327001
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not humble then mary is not tall or not happy and vice versa.
If someone is both calm and generous then mary is not calm.
If someone is either calm or not strong then lucy is both rich and calm and vice versa.
If someone is either not calm or not generous then john is not brave.
Everyone who is not kind is both calm and not funny.
If someone is happy then someone is both creative and tall.
Everyone who is not brave is creative and vice versa.
If paul is both brave and not strong then someone is not patient and vice versa.
Everyone who is funny or not strong is kind and vice versa.
Everyone who is kind or generous is both not funny and not curious.
Everyone who is curious or not rich is both old and not wise.
Everyone who is happy is either not rich or wise.
Everyone who is either not quiet or not creative is either not quiet or not humble and vice versa.
If alice is either not curious or kind then someone is funny or old and vice versa.
Everyone who is calm or not humble is not happy or rich and vice versa.
Paul is both quiet and generous.
Alice is not tall.
Someone is not generous.
Someone is both curious and not tall.
Mary is both not humble and not patient.
Paul is both wise and not humble.
Someone is both tall and not humble.
Someone is either not strong or patient. | Lucy is calm. | entailment | ((~humble(mary))<=>((~tall(mary)|~happy(mary))))&
((?[X]:((calm(X)&generous(X))))=>(~calm(mary)))&
((?[X]:((calm(X)<~>~strong(X))))<=>((rich(lucy)&calm(lucy))))&
((?[X]:((~calm(X)<~>~generous(X))))=>(~brave(john)))&
(![X]:(~kind(X)=>(calm(X)&~funny(X))))&
((?[X]:(happy(X)))=>(?[X]:((creative(X)&tall(X)))))&
(![X]:(~brave(X)<=>creative(X)))&
(((brave(paul)&~strong(paul)))<=>(?[X]:(~patient(X))))&
(![X]:((funny(X)|~strong(X))<=>kind(X)))&
(![X]:((kind(X)|generous(X))=>(~funny(X)&~curious(X))))&
(![X]:((curious(X)|~rich(X))=>(old(X)&~wise(X))))&
(![X]:(happy(X)=>(~rich(X)<~>wise(X))))&
(![X]:((~quiet(X)<~>~creative(X))<=>(~quiet(X)<~>~humble(X))))&
(((~curious(alice)<~>kind(alice)))<=>(?[X]:((funny(X)|old(X)))))&
(![X]:((calm(X)|~humble(X))<=>(~happy(X)|rich(X))))&
((quiet(paul)&generous(paul)))&
(~tall(alice))&
(?[X]:(~generous(X)))&
(?[X]:((curious(X)&~tall(X))))&
((~humble(mary)&~patient(mary)))&
((wise(paul)&~humble(paul)))&
(?[X]:((tall(X)&~humble(X))))&
(?[X]:((~strong(X)<~>patient(X)))) | calm(lucy) | [
"p2",
"p4",
"p8",
"p9",
"p10",
"p13",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 616584211648436728843436
% SZS output start Proof for 616584211648436728843436
3. ? [X0] : (calm(X0) <~> ~strong(X0)) <=> (calm(lucy) & rich(lucy)) [input p2]
5. ! [X0] : (~kind(X0) => (~funny(X0) & calm(X0))) [input p4]
9. ! [X0] : ((~strong(X0) | funny(X0)) <=> kind(X0)) [input p8]
10. ! [X0] : ((generous(X0) | kind(X0)) => (~curious(X0) & ~funny(X0))) [input p9]
11. ! [X0] : ((~rich(X0) | curious(X0)) => (~wise(X0) & old(X0))) [input p10]
14. (~curious(alice) <~> kind(alice)) <=> ? [X0] : (old(X0) | funny(X0)) [input p13]
19. ? [X0] : (~tall(X0) & curious(X0)) [input p18]
24. ~calm(lucy) [input hypothesis]
28. ! [X0] : ((~funny(X0) & calm(X0)) | kind(X0)) [ennf transformation 5]
30. ! [X0] : ((~curious(X0) & ~funny(X0)) | (~generous(X0) & ~kind(X0))) [ennf transformation 10]
31. ! [X0] : ((~wise(X0) & old(X0)) | (rich(X0) & ~curious(X0))) [ennf transformation 11]
35. (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | (~calm(lucy) | ~rich(lucy))) & ((calm(lucy) & rich(lucy)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) [nnf transformation 3]
36. (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ~calm(lucy) | ~rich(lucy)) & ((calm(lucy) & rich(lucy)) | ! [X0] : ((calm(X0) | strong(X0)) & (~strong(X0) | ~calm(X0)))) [flattening 35]
37. (? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) | ~calm(lucy) | ~rich(lucy)) & ((calm(lucy) & rich(lucy)) | ! [X1] : ((calm(X1) | strong(X1)) & (~strong(X1) | ~calm(X1)))) [rectify 36]
38. ? [X0] : ((strong(X0) | ~calm(X0)) & (~strong(X0) | calm(X0))) => ((strong(sK0) | ~calm(sK0)) & (~strong(sK0) | calm(sK0))) [choice axiom]
39. (((strong(sK0) | ~calm(sK0)) & (~strong(sK0) | calm(sK0))) | ~calm(lucy) | ~rich(lucy)) & ((calm(lucy) & rich(lucy)) | ! [X1] : ((calm(X1) | strong(X1)) & (~strong(X1) | ~calm(X1)))) [skolemisation 37,38]
50. ! [X0] : (((~strong(X0) | funny(X0)) | ~kind(X0)) & (kind(X0) | (strong(X0) & ~funny(X0)))) [nnf transformation 9]
51. ! [X0] : ((~strong(X0) | funny(X0) | ~kind(X0)) & (kind(X0) | (strong(X0) & ~funny(X0)))) [flattening 50]
54. (((~kind(alice) | curious(alice)) & (kind(alice) | ~curious(alice))) | ! [X0] : (~old(X0) & ~funny(X0))) & (? [X0] : (old(X0) | funny(X0)) | ((~curious(alice) | ~kind(alice)) & (kind(alice) | curious(alice)))) [nnf transformation 14]
55. (((~kind(alice) | curious(alice)) & (kind(alice) | ~curious(alice))) | ! [X0] : (~old(X0) & ~funny(X0))) & (? [X1] : (old(X1) | funny(X1)) | ((~curious(alice) | ~kind(alice)) & (kind(alice) | curious(alice)))) [rectify 54]
56. ? [X1] : (old(X1) | funny(X1)) => (old(sK3) | funny(sK3)) [choice axiom]
57. (((~kind(alice) | curious(alice)) & (kind(alice) | ~curious(alice))) | ! [X0] : (~old(X0) & ~funny(X0))) & ((old(sK3) | funny(sK3)) | ((~curious(alice) | ~kind(alice)) & (kind(alice) | curious(alice)))) [skolemisation 55,56]
62. ? [X0] : (~tall(X0) & curious(X0)) => (~tall(sK5) & curious(sK5)) [choice axiom]
63. ~tall(sK5) & curious(sK5) [skolemisation 19,62]
75. calm(lucy) | ~strong(X1) | ~calm(X1) [cnf transformation 39]
81. kind(X0) | calm(X0) [cnf transformation 28]
91. kind(X0) | strong(X0) [cnf transformation 51]
95. ~curious(X0) | ~kind(X0) [cnf transformation 30]
97. ~curious(X0) | old(X0) [cnf transformation 31]
116. ~kind(alice) | curious(alice) | ~old(X0) [cnf transformation 57]
125. curious(sK5) [cnf transformation 63]
135. ~calm(lucy) [cnf transformation 24]
168. 7 <=> calm(lucy) [avatar definition]
186. 11 <=> ! [X1] : (~strong(X1) | ~calm(X1)) [avatar definition]
187. ~strong(X1) | ~calm(X1) <- (11) [avatar component clause 186]
188. 11 | 7 [avatar split clause 75,168,186]
237. ~kind(alice) | ~old(X0) [subsumption resolution 116,95]
239. 22 <=> ! [X0] : ~old(X0) [avatar definition]
240. ~old(X0) <- (22) [avatar component clause 239]
242. 23 <=> kind(alice) [avatar definition]
244. ~kind(alice) <- (~23) [avatar component clause 242]
245. 22 | ~23 [avatar split clause 237,242,239]
269. ~7 [avatar split clause 135,168]
277. old(sK5) [resolution 97,125]
278. $false <- (22) [subsumption resolution 277,240]
279. ~22 [avatar contradiction clause 278]
280. strong(alice) <- (~23) [resolution 244,91]
281. calm(alice) <- (~23) [resolution 244,81]
286. ~calm(alice) <- (11, ~23) [resolution 187,280]
288. $false <- (11, ~23) [subsumption resolution 286,281]
289. ~11 | 23 [avatar contradiction clause 288]
290. $false [avatar sat refutation 188,245,269,279,289]
% SZS output end Proof for 616584211648436728843436
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or funny is both not funny and rich.
Everyone who is either funny or creative is not rich and vice versa.
If mary is strong then someone is both not calm and creative.
If fred is rich or not funny then someone is either not kind or not tall.
If someone is either tall or not kind then someone is generous.
If susan is not generous then susan is either not strong or not patient and vice versa.
If fred is not curious then lucy is both not funny and kind.
Everyone who is both happy and strong is kind or not wise.
Everyone who is both not strong and creative is funny or calm and vice versa.
Everyone who is rich is either not patient or not wise and vice versa.
If someone is either not calm or not humble then someone is both funny and rich.
Everyone who is both happy and not old is not generous.
If fred is both happy and not kind then susan is either generous or wise.
Everyone who is either funny or not strong is not rich or not happy and vice versa.
Everyone who is not funny or tall is both creative and not curious and vice versa.
If john is tall then fred is wise or not strong and vice versa.
Paul is either not happy or not humble.
Paul is not tall or strong.
Someone is either not tall or strong.
Someone is not calm or not generous.
Fred is kind. | Susan is not generous. | neutral | (![X]:((~calm(X)|funny(X))=>(~funny(X)&rich(X))))&
(![X]:((funny(X)<~>creative(X))<=>~rich(X)))&
((strong(mary))=>(?[X]:((~calm(X)&creative(X)))))&
(((rich(fred)|~funny(fred)))=>(?[X]:((~kind(X)<~>~tall(X)))))&
((?[X]:((tall(X)<~>~kind(X))))=>(?[X]:(generous(X))))&
((~generous(susan))<=>((~strong(susan)<~>~patient(susan))))&
((~curious(fred))=>((~funny(lucy)&kind(lucy))))&
(![X]:((happy(X)&strong(X))=>(kind(X)|~wise(X))))&
(![X]:((~strong(X)&creative(X))<=>(funny(X)|calm(X))))&
(![X]:(rich(X)<=>(~patient(X)<~>~wise(X))))&
((?[X]:((~calm(X)<~>~humble(X))))=>(?[X]:((funny(X)&rich(X)))))&
(![X]:((happy(X)&~old(X))=>~generous(X)))&
(((happy(fred)&~kind(fred)))=>((generous(susan)<~>wise(susan))))&
(![X]:((funny(X)<~>~strong(X))<=>(~rich(X)|~happy(X))))&
(![X]:((~funny(X)|tall(X))<=>(creative(X)&~curious(X))))&
((tall(john))<=>((wise(fred)|~strong(fred))))&
((~happy(paul)<~>~humble(paul)))&
((~tall(paul)|strong(paul)))&
(?[X]:((~tall(X)<~>strong(X))))&
(?[X]:((~calm(X)|~generous(X))))&
(kind(fred)) | ~generous(susan) | [] | null | 0 |
Everyone who is both creative and tall is both wise and not tall and vice versa. Everyone who is either rich or not curious is either happy or old. If someone is generous or happy then someone is not humble. Everyone who is both not brave and not calm is not rich or humble. Everyone who is not happy or rich is both patient and curious. If susan is happy then mary is either not funny or not curious. Everyone who is humble or funny is funny or not rich and vice versa. If lucy is either tall or not kind then fred is not quiet. Everyone who is both not wise and brave is both not quiet and not brave and vice versa. Everyone who is creative is both patient and happy. If lucy is happy then fred is either humble or not brave. If lucy is not calm or strong then susan is creative or calm. If someone is creative then susan is both not strong and strong and vice versa. Everyone who is funny is tall. If john is either quiet or happy then fred is quiet or curious and vice versa. Everyone who is both creative and not curious is curious and vice versa. Someone is kind. Someone is strong. Paul is either generous or happy. Someone is not curious or old. Someone is not curious or not strong. Mary is humble. Fred is quiet. | John is not quiet. | entailment | (![X]:((creative(X)&tall(X))<=>(wise(X)&~tall(X))))&
(![X]:((rich(X)<~>~curious(X))=>(happy(X)<~>old(X))))&
((?[X]:((generous(X)|happy(X))))=>(?[X]:(~humble(X))))&
(![X]:((~brave(X)&~calm(X))=>(~rich(X)|humble(X))))&
(![X]:((~happy(X)|rich(X))=>(patient(X)&curious(X))))&
((happy(susan))=>((~funny(mary)<~>~curious(mary))))&
(![X]:((humble(X)|funny(X))<=>(funny(X)|~rich(X))))&
(((tall(lucy)<~>~kind(lucy)))=>(~quiet(fred)))&
(![X]:((~wise(X)&brave(X))<=>(~quiet(X)&~brave(X))))&
(![X]:(creative(X)=>(patient(X)&happy(X))))&
((happy(lucy))=>((humble(fred)<~>~brave(fred))))&
(((~calm(lucy)|strong(lucy)))=>((creative(susan)|calm(susan))))&
((?[X]:(creative(X)))<=>((~strong(susan)&strong(susan))))&
(![X]:(funny(X)=>tall(X)))&
(((quiet(john)<~>happy(john)))<=>((quiet(fred)|curious(fred))))&
(![X]:((creative(X)&~curious(X))<=>curious(X)))&
(?[X]:(kind(X)))&
(?[X]:(strong(X)))&
((generous(paul)<~>happy(paul)))&
(?[X]:((~curious(X)|old(X))))&
(?[X]:((~curious(X)|~strong(X))))&
(humble(mary))&
(quiet(fred)) | ~quiet(john) | [
"p4",
"p14",
"p15",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 6658547806045687107747371
% SZS output start Proof for 6658547806045687107747371
5. ! [X0] : ((rich(X0) | ~happy(X0)) => (curious(X0) & patient(X0))) [input p4]
15. (quiet(john) <~> happy(john)) <=> (curious(fred) | quiet(fred)) [input p14]
16. ! [X0] : ((~curious(X0) & creative(X0)) <=> curious(X0)) [input p15]
23. quiet(fred) [input p22]
24. quiet(john) [input hypothesis]
27. ! [X0] : ((rich(X0) | ~happy(X0)) => curious(X0)) [pure predicate removal 5]
32. ! [X0] : (curious(X0) | (~rich(X0) & happy(X0))) [ennf transformation 27]
56. (((~happy(john) | ~quiet(john)) & (happy(john) | quiet(john))) | (~curious(fred) & ~quiet(fred))) & ((curious(fred) | quiet(fred)) | ((quiet(john) | ~happy(john)) & (happy(john) | ~quiet(john)))) [nnf transformation 15]
57. (((~happy(john) | ~quiet(john)) & (happy(john) | quiet(john))) | (~curious(fred) & ~quiet(fred))) & (curious(fred) | quiet(fred) | ((quiet(john) | ~happy(john)) & (happy(john) | ~quiet(john)))) [flattening 56]
58. ! [X0] : (((~curious(X0) & creative(X0)) | ~curious(X0)) & (curious(X0) | (curious(X0) | ~creative(X0)))) [nnf transformation 16]
59. ! [X0] : (((~curious(X0) & creative(X0)) | ~curious(X0)) & (curious(X0) | curious(X0) | ~creative(X0))) [flattening 58]
79. happy(X0) | curious(X0) [cnf transformation 32]
104. ~happy(john) | ~quiet(john) | ~quiet(fred) [cnf transformation 57]
108. ~curious(X0) | ~curious(X0) [cnf transformation 59]
116. quiet(fred) [cnf transformation 23]
117. quiet(john) [cnf transformation 24]
119. ~curious(X0) [duplicate literal removal 108]
159. 9 <=> quiet(fred) [avatar definition]
192. 16 <=> quiet(john) [avatar definition]
196. 17 <=> happy(john) [avatar definition]
198. ~happy(john) <- (~17) [avatar component clause 196]
200. ~9 | ~16 | ~17 [avatar split clause 104,196,192,159]
217. 9 [avatar split clause 116,159]
218. 16 [avatar split clause 117,192]
221. curious(john) <- (~17) [resolution 79,198]
227. $false <- (~17) [subsumption resolution 221,119]
228. 17 [avatar contradiction clause 227]
231. $false [avatar sat refutation 200,217,218,228]
% SZS output end Proof for 6658547806045687107747371
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not patient or not curious is quiet or funny.
If paul is both strong and not wise then john is either funny or curious.
Everyone who is curious is not humble.
Everyone who is not generous or generous is humble.
Everyone who is both not brave and not humble is not tall and vice versa.
Everyone who is both rich and strong is wise or not patient and vice versa.
Everyone who is calm is either strong or calm.
If someone is strong then paul is not humble or patient.
If someone is both not wise and not kind then someone is both not strong and generous.
If someone is both not humble and not funny then lucy is humble.
Everyone who is patient or not funny is either not brave or curious and vice versa.
If someone is not creative then someone is rich or not tall.
Everyone who is either not humble or not patient is strong and vice versa.
Everyone who is tall is quiet or not funny and vice versa.
Everyone who is wise or not strong is old or kind.
If someone is either brave or curious then mary is generous or not quiet and vice versa.
Someone is not creative.
Someone is not tall or not creative.
Lucy is either not quiet or rich.
Alice is not creative.
Mary is not creative.
Susan is either not happy or generous. | Paul is old. | neutral | (![X]:((~patient(X)<~>~curious(X))=>(quiet(X)|funny(X))))&
(((strong(paul)&~wise(paul)))=>((funny(john)<~>curious(john))))&
(![X]:(curious(X)=>~humble(X)))&
(![X]:((~generous(X)|generous(X))=>humble(X)))&
(![X]:((~brave(X)&~humble(X))<=>~tall(X)))&
(![X]:((rich(X)&strong(X))<=>(wise(X)|~patient(X))))&
(![X]:(calm(X)=>(strong(X)<~>calm(X))))&
((?[X]:(strong(X)))=>((~humble(paul)|patient(paul))))&
((?[X]:((~wise(X)&~kind(X))))=>(?[X]:((~strong(X)&generous(X)))))&
((?[X]:((~humble(X)&~funny(X))))=>(humble(lucy)))&
(![X]:((patient(X)|~funny(X))<=>(~brave(X)<~>curious(X))))&
((?[X]:(~creative(X)))=>(?[X]:((rich(X)|~tall(X)))))&
(![X]:((~humble(X)<~>~patient(X))<=>strong(X)))&
(![X]:(tall(X)<=>(quiet(X)|~funny(X))))&
(![X]:((wise(X)|~strong(X))=>(old(X)|kind(X))))&
((?[X]:((brave(X)<~>curious(X))))<=>((generous(mary)|~quiet(mary))))&
(?[X]:(~creative(X)))&
(?[X]:((~tall(X)|~creative(X))))&
((~quiet(lucy)<~>rich(lucy)))&
(~creative(alice))&
(~creative(mary))&
((~happy(susan)<~>generous(susan))) | old(paul) | [] | null | 0 |
If lucy is wise then someone is either not creative or not calm.
If john is not patient then someone is not brave or happy and vice versa.
If someone is not quiet then someone is not happy or creative and vice versa.
Everyone who is both not wise and not patient is both not rich and wise and vice versa.
Everyone who is both not generous and funny is either not generous or not wise.
If lucy is tall or not curious then someone is both not happy and not generous and vice versa.
If someone is not curious or not old then alice is both creative and not kind and vice versa.
Everyone who is both not curious and not old is both not old and not brave and vice versa.
Everyone who is either brave or not strong is creative.
Everyone who is either wise or not curious is either curious or not quiet.
Everyone who is patient or not calm is not rich and vice versa.
Everyone who is either generous or not kind is either creative or not strong.
If someone is either not funny or not curious then john is both not humble and not strong.
Everyone who is not wise or not rich is not strong and vice versa.
If fred is not quiet then fred is not funny.
Everyone who is not strong is generous or curious.
Fred is curious.
Someone is not calm or kind.
Mary is humble or not quiet.
Someone is not patient.
Susan is happy or not old.
Mary is patient or not kind.
Lucy is not humble. | Susan is not creative. | neutral | ((wise(lucy))=>(?[X]:((~creative(X)<~>~calm(X)))))&
((~patient(john))<=>(?[X]:((~brave(X)|happy(X)))))&
((?[X]:(~quiet(X)))<=>(?[X]:((~happy(X)|creative(X)))))&
(![X]:((~wise(X)&~patient(X))<=>(~rich(X)&wise(X))))&
(![X]:((~generous(X)&funny(X))=>(~generous(X)<~>~wise(X))))&
(((tall(lucy)|~curious(lucy)))<=>(?[X]:((~happy(X)&~generous(X)))))&
((?[X]:((~curious(X)|~old(X))))<=>((creative(alice)&~kind(alice))))&
(![X]:((~curious(X)&~old(X))<=>(~old(X)&~brave(X))))&
(![X]:((brave(X)<~>~strong(X))=>creative(X)))&
(![X]:((wise(X)<~>~curious(X))=>(curious(X)<~>~quiet(X))))&
(![X]:((patient(X)|~calm(X))<=>~rich(X)))&
(![X]:((generous(X)<~>~kind(X))=>(creative(X)<~>~strong(X))))&
((?[X]:((~funny(X)<~>~curious(X))))=>((~humble(john)&~strong(john))))&
(![X]:((~wise(X)|~rich(X))<=>~strong(X)))&
((~quiet(fred))=>(~funny(fred)))&
(![X]:(~strong(X)=>(generous(X)|curious(X))))&
(curious(fred))&
(?[X]:((~calm(X)|kind(X))))&
((humble(mary)|~quiet(mary)))&
(?[X]:(~patient(X)))&
((happy(susan)|~old(susan)))&
((patient(mary)|~kind(mary)))&
(~humble(lucy)) | ~creative(susan) | [] | null | 0 |
Everyone who is either not rich or not generous is either not tall or creative.
Everyone who is both not brave and not rich is not humble and vice versa.
If someone is either kind or not calm then susan is either not patient or not quiet.
If john is either not old or strong then someone is quiet.
Everyone who is either not generous or not rich is both quiet and curious.
Everyone who is either not creative or not patient is happy or funny and vice versa.
If someone is both not old and brave then lucy is both not calm and not kind and vice versa.
If someone is either tall or not quiet then john is not tall or not old.
Everyone who is either humble or not curious is not wise or not quiet and vice versa.
Everyone who is rich or not kind is both funny and kind.
Everyone who is both not wise and wise is either not humble or not kind.
Everyone who is both kind and not curious is either patient or not generous.
Everyone who is both not wise and generous is both not strong and rich and vice versa.
Everyone who is not creative or brave is not strong.
Everyone who is both not kind and wise is not rich and vice versa.
If someone is either not curious or not quiet then fred is both not strong and not patient.
Someone is not funny or wise.
Someone is either humble or not tall.
Someone is rich or happy.
John is kind or creative.
Alice is either curious or brave.
John is either not strong or rich. | Fred is curious. | entailment | (![X]:((~rich(X)<~>~generous(X))=>(~tall(X)<~>creative(X))))&
(![X]:((~brave(X)&~rich(X))<=>~humble(X)))&
((?[X]:((kind(X)<~>~calm(X))))=>((~patient(susan)<~>~quiet(susan))))&
(((~old(john)<~>strong(john)))=>(?[X]:(quiet(X))))&
(![X]:((~generous(X)<~>~rich(X))=>(quiet(X)&curious(X))))&
(![X]:((~creative(X)<~>~patient(X))<=>(happy(X)|funny(X))))&
((?[X]:((~old(X)&brave(X))))<=>((~calm(lucy)&~kind(lucy))))&
((?[X]:((tall(X)<~>~quiet(X))))=>((~tall(john)|~old(john))))&
(![X]:((humble(X)<~>~curious(X))<=>(~wise(X)|~quiet(X))))&
(![X]:((rich(X)|~kind(X))=>(funny(X)&kind(X))))&
(![X]:((~wise(X)&wise(X))=>(~humble(X)<~>~kind(X))))&
(![X]:((kind(X)&~curious(X))=>(patient(X)<~>~generous(X))))&
(![X]:((~wise(X)&generous(X))<=>(~strong(X)&rich(X))))&
(![X]:((~creative(X)|brave(X))=>~strong(X)))&
(![X]:((~kind(X)&wise(X))<=>~rich(X)))&
((?[X]:((~curious(X)<~>~quiet(X))))=>((~strong(fred)&~patient(fred))))&
(?[X]:((~funny(X)|wise(X))))&
(?[X]:((humble(X)<~>~tall(X))))&
(?[X]:((rich(X)|happy(X))))&
((kind(john)|creative(john)))&
((curious(alice)<~>brave(alice)))&
((~strong(john)<~>rich(john))) | curious(fred) | [
"p1",
"p4",
"p8",
"p9",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 2020973054093304900295223
% SZS output start Proof for 2020973054093304900295223
2. ! [X0] : ((~rich(X0) & ~brave(X0)) <=> ~humble(X0)) [input p1]
5. ! [X0] : ((~generous(X0) <~> ~rich(X0)) => (curious(X0) & quiet(X0))) [input p4]
9. ! [X0] : ((humble(X0) <~> ~curious(X0)) <=> (~quiet(X0) | ~wise(X0))) [input p8]
10. ! [X0] : ((~kind(X0) | rich(X0)) => (kind(X0) & funny(X0))) [input p9]
12. ! [X0] : ((~curious(X0) & kind(X0)) => (patient(X0) <~> ~generous(X0))) [input p11]
15. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~rich(X0)) [input p14]
16. ? [X0] : (~curious(X0) <~> ~quiet(X0)) => (~patient(fred) & ~strong(fred)) [input p15]
23. ~curious(fred) [input hypothesis]
27. ! [X0] : ((curious(X0) & quiet(X0)) | (~generous(X0) <=> ~rich(X0))) [ennf transformation 5]
30. ! [X0] : ((kind(X0) & funny(X0)) | (kind(X0) & ~rich(X0))) [ennf transformation 10]
33. ! [X0] : ((patient(X0) <~> ~generous(X0)) | (curious(X0) | ~kind(X0))) [ennf transformation 12]
34. ! [X0] : ((patient(X0) <~> ~generous(X0)) | curious(X0) | ~kind(X0)) [flattening 33]
36. (~patient(fred) & ~strong(fred)) | ! [X0] : (~curious(X0) <=> ~quiet(X0)) [ennf transformation 16]
38. ! [X0] : (((~rich(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | (rich(X0) | brave(X0)))) [nnf transformation 2]
39. ! [X0] : (((~rich(X0) & ~brave(X0)) | humble(X0)) & (~humble(X0) | rich(X0) | brave(X0))) [flattening 38]
44. ! [X0] : ((curious(X0) & quiet(X0)) | ((~generous(X0) | rich(X0)) & (~rich(X0) | generous(X0)))) [nnf transformation 27]
53. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) & ((~quiet(X0) | ~wise(X0)) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [nnf transformation 9]
54. ! [X0] : ((((curious(X0) | ~humble(X0)) & (~curious(X0) | humble(X0))) | (quiet(X0) & wise(X0))) & (~quiet(X0) | ~wise(X0) | ((humble(X0) | curious(X0)) & (~curious(X0) | ~humble(X0))))) [flattening 53]
56. ! [X0] : (((generous(X0) | ~patient(X0)) & (~generous(X0) | patient(X0))) | curious(X0) | ~kind(X0)) [nnf transformation 34]
59. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0)) & (~rich(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 15]
60. ! [X0] : (((wise(X0) & ~kind(X0)) | rich(X0)) & (~rich(X0) | ~wise(X0) | kind(X0))) [flattening 59]
61. (~patient(fred) & ~strong(fred)) | ! [X0] : ((~curious(X0) | quiet(X0)) & (~quiet(X0) | curious(X0))) [nnf transformation 36]
77. ~rich(X0) | humble(X0) [cnf transformation 39]
86. ~rich(X0) | curious(X0) | generous(X0) [cnf transformation 44]
105. ~humble(X0) | curious(X0) | quiet(X0) [cnf transformation 54]
109. kind(X0) | kind(X0) [cnf transformation 30]
112. ~generous(X0) | patient(X0) | curious(X0) | ~kind(X0) [cnf transformation 56]
121. ~kind(X0) | rich(X0) [cnf transformation 60]
125. ~patient(fred) | ~quiet(X0) | curious(X0) [cnf transformation 61]
136. ~curious(fred) [cnf transformation 23]
137. kind(X0) [duplicate literal removal 109]
206. ~generous(X0) | patient(X0) | curious(X0) [subsumption resolution 112,137]
207. rich(X0) [subsumption resolution 121,137]
212. 17 <=> patient(fred) [avatar definition]
217. 18 <=> ! [X0] : (~quiet(X0) | curious(X0)) [avatar definition]
218. ~quiet(X0) | curious(X0) <- (18) [avatar component clause 217]
219. 18 | ~17 [avatar split clause 125,212,217]
260. humble(X0) [resolution 77,207]
275. curious(X0) | generous(X0) [resolution 86,207]
276. generous(fred) [resolution 275,136]
290. curious(X0) | quiet(X0) [resolution 105,260]
319. patient(fred) | curious(fred) [resolution 206,276]
323. patient(fred) [subsumption resolution 319,136]
324. 17 [avatar split clause 323,212]
325. curious(X0) <- (18) [subsumption resolution 218,290]
329. $false <- (18) [resolution 325,136]
332. ~18 [avatar contradiction clause 329]
333. $false [avatar sat refutation 219,324,332]
% SZS output end Proof for 2020973054093304900295223
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall or funny then mary is not funny and vice versa. If someone is either not wise or not rich then susan is quiet. If someone is not quiet or tall then someone is kind or wise and vice versa. Everyone who is curious or generous is both not rich and not humble and vice versa. If someone is both not happy and happy then john is not curious or funny. Everyone who is not creative or not patient is happy or humble. Everyone who is both not curious and strong is either not humble or not quiet. If lucy is either tall or not patient then susan is strong or brave and vice versa. If someone is not tall then someone is brave or not quiet. Everyone who is generous is either humble or old. Everyone who is not rich or not generous is either curious or strong. If mary is not kind then fred is generous or not wise and vice versa. Everyone who is either not brave or calm is not calm and vice versa. If someone is patient or not creative then mary is creative. Everyone who is not creative is either curious or creative and vice versa. If someone is humble then susan is either not old or not rich and vice versa. Someone is not happy. Someone is not funny. Susan is either not creative or not generous. Someone is not old or old. Someone is both funny and not quiet. Someone is rich or not old. Someone is either funny or not funny. | Alice is not old. | neutral | (((~tall(alice)|funny(alice)))<=>(~funny(mary)))&
((?[X]:((~wise(X)<~>~rich(X))))=>(quiet(susan)))&
((?[X]:((~quiet(X)|tall(X))))<=>(?[X]:((kind(X)|wise(X)))))&
(![X]:((curious(X)|generous(X))<=>(~rich(X)&~humble(X))))&
((?[X]:((~happy(X)&happy(X))))=>((~curious(john)|funny(john))))&
(![X]:((~creative(X)|~patient(X))=>(happy(X)|humble(X))))&
(![X]:((~curious(X)&strong(X))=>(~humble(X)<~>~quiet(X))))&
(((tall(lucy)<~>~patient(lucy)))<=>((strong(susan)|brave(susan))))&
((?[X]:(~tall(X)))=>(?[X]:((brave(X)|~quiet(X)))))&
(![X]:(generous(X)=>(humble(X)<~>old(X))))&
(![X]:((~rich(X)|~generous(X))=>(curious(X)<~>strong(X))))&
((~kind(mary))<=>((generous(fred)|~wise(fred))))&
(![X]:((~brave(X)<~>calm(X))<=>~calm(X)))&
((?[X]:((patient(X)|~creative(X))))=>(creative(mary)))&
(![X]:(~creative(X)<=>(curious(X)<~>creative(X))))&
((?[X]:(humble(X)))<=>((~old(susan)<~>~rich(susan))))&
(?[X]:(~happy(X)))&
(?[X]:(~funny(X)))&
((~creative(susan)<~>~generous(susan)))&
(?[X]:((~old(X)|old(X))))&
(?[X]:((funny(X)&~quiet(X))))&
(?[X]:((rich(X)|~old(X))))&
(?[X]:((funny(X)<~>~funny(X)))) | ~old(alice) | [] | null | 0 |
Everyone who is not humble is old or not strong and vice versa.
If someone is either humble or generous then fred is either quiet or old.
Everyone who is both not brave and not calm is both tall and not old.
Everyone who is not humble or brave is not generous or rich and vice versa.
If lucy is both not wise and not curious then someone is both creative and patient and vice versa.
Everyone who is either not tall or not kind is quiet or not tall and vice versa.
If someone is not kind then paul is either not brave or quiet.
Everyone who is either not tall or patient is old or patient.
If someone is humble or not rich then mary is both not patient and not humble.
Everyone who is either strong or brave is both quiet and generous and vice versa.
Everyone who is either not quiet or patient is not generous or happy and vice versa.
If paul is not curious then john is both not calm and not humble and vice versa.
Everyone who is both calm and old is not kind or not old.
Everyone who is either curious or not strong is rich or funny.
If someone is not creative then susan is both generous and happy.
Everyone who is either not humble or not creative is not humble and vice versa.
Susan is either not humble or wise.
Someone is both not kind and not funny.
Paul is either quiet or not humble.
Someone is not calm.
Lucy is not humble.
Someone is wise.
Alice is both humble and not happy.
Someone is both not tall and not calm. | Alice is not strong. | contradiction | (![X]:(~humble(X)<=>(old(X)|~strong(X))))&
((?[X]:((humble(X)<~>generous(X))))=>((quiet(fred)<~>old(fred))))&
(![X]:((~brave(X)&~calm(X))=>(tall(X)&~old(X))))&
(![X]:((~humble(X)|brave(X))<=>(~generous(X)|rich(X))))&
(((~wise(lucy)&~curious(lucy)))<=>(?[X]:((creative(X)&patient(X)))))&
(![X]:((~tall(X)<~>~kind(X))<=>(quiet(X)|~tall(X))))&
((?[X]:(~kind(X)))=>((~brave(paul)<~>quiet(paul))))&
(![X]:((~tall(X)<~>patient(X))=>(old(X)|patient(X))))&
((?[X]:((humble(X)|~rich(X))))=>((~patient(mary)&~humble(mary))))&
(![X]:((strong(X)<~>brave(X))<=>(quiet(X)&generous(X))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~generous(X)|happy(X))))&
((~curious(paul))<=>((~calm(john)&~humble(john))))&
(![X]:((calm(X)&old(X))=>(~kind(X)|~old(X))))&
(![X]:((curious(X)<~>~strong(X))=>(rich(X)|funny(X))))&
((?[X]:(~creative(X)))=>((generous(susan)&happy(susan))))&
(![X]:((~humble(X)<~>~creative(X))<=>~humble(X)))&
((~humble(susan)<~>wise(susan)))&
(?[X]:((~kind(X)&~funny(X))))&
((quiet(paul)<~>~humble(paul)))&
(?[X]:(~calm(X)))&
(~humble(lucy))&
(?[X]:(wise(X)))&
((humble(alice)&~happy(alice)))&
(?[X]:((~tall(X)&~calm(X)))) | ~strong(alice) | [
"p0",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 1189752258811346115620626
% SZS output start Proof for 1189752258811346115620626
1. ! [X0] : (~humble(X0) <=> (~strong(X0) | old(X0))) [input p0]
23. ~happy(alice) & humble(alice) [input p22]
25. ~strong(alice) [input hypothesis]
38. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & ((~strong(X0) | old(X0)) | humble(X0))) [nnf transformation 1]
39. ! [X0] : ((~humble(X0) | (strong(X0) & ~old(X0))) & (~strong(X0) | old(X0) | humble(X0))) [flattening 38]
72. ~humble(X0) | strong(X0) [cnf transformation 39]
134. humble(alice) [cnf transformation 23]
138. ~strong(alice) [cnf transformation 25]
265. strong(alice) [resolution 72,134]
266. $false [subsumption resolution 265,138]
% SZS output end Proof for 1189752258811346115620626
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 rich and kind is both not creative and rich and vice versa. Everyone who is not quiet is wise or not calm and vice versa. Everyone who is either tall or calm is not quiet and vice versa. Everyone who is tall is not funny or not rich and vice versa. Everyone who is not strong is either rich or wise. Everyone who is not old is not kind. If paul is either calm or not rich then john is not humble or kind. If lucy is not funny then someone is rich. Everyone who is rich or not tall is both tall and old. Everyone who is both happy and humble is not generous. Everyone who is both generous and not creative is not old or not humble. Everyone who is either generous or not generous is either not curious or funny and vice versa. Everyone who is both not strong and humble is not humble and vice versa. If someone is either tall or funny then someone is both kind and strong. If someone is old or not patient then fred is not patient. If alice is happy then fred is not rich and vice versa. Mary is not funny or not brave. Someone is either not generous or humble. Someone is both happy and not generous. Paul is both not curious and not old. Mary is wise or tall. Susan is either not wise or happy. | John is curious. | neutral | (![X]:((rich(X)&kind(X))<=>(~creative(X)&rich(X))))&
(![X]:(~quiet(X)<=>(wise(X)|~calm(X))))&
(![X]:((tall(X)<~>calm(X))<=>~quiet(X)))&
(![X]:(tall(X)<=>(~funny(X)|~rich(X))))&
(![X]:(~strong(X)=>(rich(X)<~>wise(X))))&
(![X]:(~old(X)=>~kind(X)))&
(((calm(paul)<~>~rich(paul)))=>((~humble(john)|kind(john))))&
((~funny(lucy))=>(?[X]:(rich(X))))&
(![X]:((rich(X)|~tall(X))=>(tall(X)&old(X))))&
(![X]:((happy(X)&humble(X))=>~generous(X)))&
(![X]:((generous(X)&~creative(X))=>(~old(X)|~humble(X))))&
(![X]:((generous(X)<~>~generous(X))<=>(~curious(X)<~>funny(X))))&
(![X]:((~strong(X)&humble(X))<=>~humble(X)))&
((?[X]:((tall(X)<~>funny(X))))=>(?[X]:((kind(X)&strong(X)))))&
((?[X]:((old(X)|~patient(X))))=>(~patient(fred)))&
((happy(alice))<=>(~rich(fred)))&
((~funny(mary)|~brave(mary)))&
(?[X]:((~generous(X)<~>humble(X))))&
(?[X]:((happy(X)&~generous(X))))&
((~curious(paul)&~old(paul)))&
((wise(mary)|tall(mary)))&
((~wise(susan)<~>happy(susan))) | curious(john) | [] | null | 0 |
Everyone who is old is funny and vice versa.
If alice is not calm then paul is both not calm and not happy and vice versa.
Everyone who is strong or not creative is either creative or strong.
Everyone who is calm or kind is both tall and quiet.
If susan is not old then mary is not happy or calm.
Everyone who is not rich or tall is happy or brave.
If someone is not quiet or old then someone is either not wise or creative.
Everyone who is either funny or not old is both humble and not funny and vice versa.
Everyone who is both rich and happy is patient or not creative and vice versa.
If alice is both creative and tall then susan is either curious or generous and vice versa.
If john is both not curious and not calm then someone is either happy or not tall and vice versa.
If someone is either creative or calm then someone is either generous or patient and vice versa.
Everyone who is happy is not calm or happy and vice versa.
Everyone who is rich is rich or calm and vice versa.
If paul is either quiet or not curious then mary is calm or curious.
If someone is either wise or not generous then someone is either not wise or not humble.
Lucy is not patient.
Lucy is happy or not tall.
Fred is not strong.
Mary is either not funny or not calm.
Susan is creative.
Someone is wise.
Someone is brave. | Mary is not old. | entailment | (![X]:(old(X)<=>funny(X)))&
((~calm(alice))<=>((~calm(paul)&~happy(paul))))&
(![X]:((strong(X)|~creative(X))=>(creative(X)<~>strong(X))))&
(![X]:((calm(X)|kind(X))=>(tall(X)&quiet(X))))&
((~old(susan))=>((~happy(mary)|calm(mary))))&
(![X]:((~rich(X)|tall(X))=>(happy(X)|brave(X))))&
((?[X]:((~quiet(X)|old(X))))=>(?[X]:((~wise(X)<~>creative(X)))))&
(![X]:((funny(X)<~>~old(X))<=>(humble(X)&~funny(X))))&
(![X]:((rich(X)&happy(X))<=>(patient(X)|~creative(X))))&
(((creative(alice)&tall(alice)))<=>((curious(susan)<~>generous(susan))))&
(((~curious(john)&~calm(john)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
((?[X]:((creative(X)<~>calm(X))))<=>(?[X]:((generous(X)<~>patient(X)))))&
(![X]:(happy(X)<=>(~calm(X)|happy(X))))&
(![X]:(rich(X)<=>(rich(X)|calm(X))))&
(((quiet(paul)<~>~curious(paul)))=>((calm(mary)|curious(mary))))&
((?[X]:((wise(X)<~>~generous(X))))=>(?[X]:((~wise(X)<~>~humble(X)))))&
(~patient(lucy))&
((happy(lucy)|~tall(lucy)))&
(~strong(fred))&
((~funny(mary)<~>~calm(mary)))&
(creative(susan))&
(?[X]:(wise(X)))&
(?[X]:(brave(X))) | ~old(mary) | [
"p0",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 3842783594598028252534547
% SZS output start Proof for 3842783594598028252534547
1. ! [X0] : (old(X0) <=> funny(X0)) [input p0]
8. ! [X0] : ((funny(X0) <~> ~old(X0)) <=> (~funny(X0) & humble(X0))) [input p7]
24. old(mary) [input hypothesis]
39. ! [X0] : ((old(X0) | ~funny(X0)) & (funny(X0) | ~old(X0))) [nnf transformation 1]
47. ! [X0] : ((((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | (funny(X0) | ~humble(X0))) & ((~funny(X0) & humble(X0)) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0))))) [nnf transformation 8]
48. ! [X0] : ((((old(X0) | ~funny(X0)) & (~old(X0) | funny(X0))) | funny(X0) | ~humble(X0)) & ((~funny(X0) & humble(X0)) | ((funny(X0) | old(X0)) & (~old(X0) | ~funny(X0))))) [flattening 47]
75. funny(X0) | ~old(X0) [cnf transformation 39]
93. ~funny(X0) | ~old(X0) | ~funny(X0) [cnf transformation 48]
141. old(mary) [cnf transformation 24]
142. ~funny(X0) | ~old(X0) [duplicate literal removal 93]
175. 7 <=> ! [X1] : ~old(X1) [avatar definition]
176. ~old(X1) <- (7) [avatar component clause 175]
192. ~old(X0) [subsumption resolution 142,75]
193. 7 [avatar split clause 192,175]
329. $false <- (7) [resolution 176,141]
330. ~7 [avatar contradiction clause 329]
331. $false [avatar sat refutation 193,330]
% SZS output end Proof for 3842783594598028252534547
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not wise or funny then someone is happy or tall. If someone is not humble then fred is humble or kind and vice versa. Everyone who is either calm or wise is happy or not rich and vice versa. If someone is either strong or not strong then someone is quiet or strong and vice versa. Everyone who is brave is both curious and not happy and vice versa. If someone is rich then someone is both humble and rich. Everyone who is both not patient and not happy is not tall or not calm. If someone is curious or not kind then someone is not funny or not tall and vice versa. If mary is not quiet or not funny then someone is not quiet or quiet and vice versa. If someone is not brave then someone is either generous or calm and vice versa. Everyone who is either rich or old is both calm and not quiet and vice versa. If someone is both old and not old then fred is both not old and not wise and vice versa. Everyone who is funny is not quiet. Everyone who is both not wise and happy is both not funny and tall. Everyone who is not tall is not funny or not patient. Everyone who is kind or quiet is both not old and not brave. Fred is kind. Someone is not strong. Someone is either wise or not old. Susan is both not old and not funny. Lucy is calm or not old. Someone is not funny. Someone is both rich and calm. Someone is not brave or happy. | Lucy is not generous. | neutral | ((?[X]:((~wise(X)|funny(X))))=>(?[X]:((happy(X)|tall(X)))))&
((?[X]:(~humble(X)))<=>((humble(fred)|kind(fred))))&
(![X]:((calm(X)<~>wise(X))<=>(happy(X)|~rich(X))))&
((?[X]:((strong(X)<~>~strong(X))))<=>(?[X]:((quiet(X)|strong(X)))))&
(![X]:(brave(X)<=>(curious(X)&~happy(X))))&
((?[X]:(rich(X)))=>(?[X]:((humble(X)&rich(X)))))&
(![X]:((~patient(X)&~happy(X))=>(~tall(X)|~calm(X))))&
((?[X]:((curious(X)|~kind(X))))<=>(?[X]:((~funny(X)|~tall(X)))))&
(((~quiet(mary)|~funny(mary)))<=>(?[X]:((~quiet(X)|quiet(X)))))&
((?[X]:(~brave(X)))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((rich(X)<~>old(X))<=>(calm(X)&~quiet(X))))&
((?[X]:((old(X)&~old(X))))<=>((~old(fred)&~wise(fred))))&
(![X]:(funny(X)=>~quiet(X)))&
(![X]:((~wise(X)&happy(X))=>(~funny(X)&tall(X))))&
(![X]:(~tall(X)=>(~funny(X)|~patient(X))))&
(![X]:((kind(X)|quiet(X))=>(~old(X)&~brave(X))))&
(kind(fred))&
(?[X]:(~strong(X)))&
(?[X]:((wise(X)<~>~old(X))))&
((~old(susan)&~funny(susan)))&
((calm(lucy)|~old(lucy)))&
(?[X]:(~funny(X)))&
(?[X]:((rich(X)&calm(X))))&
(?[X]:((~brave(X)|happy(X)))) | ~generous(lucy) | [] | null | 0 |
Everyone who is not brave is old. Everyone who is not calm is both funny and not patient. If someone is not curious or generous then lucy is either curious or kind. Everyone who is either calm or not funny is not kind or not brave and vice versa. Everyone who is humble or not creative is either patient or happy. If john is not humble or strong then someone is not happy. If someone is both not quiet and not calm then susan is both generous and not quiet and vice versa. Everyone who is not funny is not quiet. Everyone who is either not quiet or not kind is either happy or not kind and vice versa. If john is either calm or generous then someone is curious and vice versa. Everyone who is not kind or happy is both not humble and happy. Everyone who is kind is humble and vice versa. Everyone who is both not wise and not patient is either not happy or not quiet. Everyone who is strong or not quiet is not old. If fred is both not strong and curious then someone is not humble or kind and vice versa. Everyone who is either old or not kind is both funny and not happy and vice versa. Someone is not funny or not tall. John is either not generous or generous. Lucy is both curious and creative. Alice is kind or happy. Someone is wise. Fred is both kind and calm. | Lucy is generous. | contradiction | (![X]:(~brave(X)=>old(X)))&
(![X]:(~calm(X)=>(funny(X)&~patient(X))))&
((?[X]:((~curious(X)|generous(X))))=>((curious(lucy)<~>kind(lucy))))&
(![X]:((calm(X)<~>~funny(X))<=>(~kind(X)|~brave(X))))&
(![X]:((humble(X)|~creative(X))=>(patient(X)<~>happy(X))))&
(((~humble(john)|strong(john)))=>(?[X]:(~happy(X))))&
((?[X]:((~quiet(X)&~calm(X))))<=>((generous(susan)&~quiet(susan))))&
(![X]:(~funny(X)=>~quiet(X)))&
(![X]:((~quiet(X)<~>~kind(X))<=>(happy(X)<~>~kind(X))))&
(((calm(john)<~>generous(john)))<=>(?[X]:(curious(X))))&
(![X]:((~kind(X)|happy(X))=>(~humble(X)&happy(X))))&
(![X]:(kind(X)<=>humble(X)))&
(![X]:((~wise(X)&~patient(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|~quiet(X))=>~old(X)))&
(((~strong(fred)&curious(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(funny(X)&~happy(X))))&
(?[X]:((~funny(X)|~tall(X))))&
((~generous(john)<~>generous(john)))&
((curious(lucy)&creative(lucy)))&
((kind(alice)|happy(alice)))&
(?[X]:(wise(X)))&
((kind(fred)&calm(fred))) | generous(lucy) | [
"p2",
"p8",
"p10",
"p13",
"p15",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 1697361154714929503843746
% SZS output start Proof for 1697361154714929503843746
3. ? [X0] : (generous(X0) | ~curious(X0)) => (curious(lucy) <~> kind(lucy)) [input p2]
9. ! [X0] : ((~quiet(X0) <~> ~kind(X0)) <=> (happy(X0) <~> ~kind(X0))) [input p8]
11. ! [X0] : ((happy(X0) | ~kind(X0)) => (happy(X0) & ~humble(X0))) [input p10]
14. ! [X0] : ((~quiet(X0) | strong(X0)) => ~old(X0)) [input p13]
16. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> (~happy(X0) & funny(X0))) [input p15]
19. creative(lucy) & curious(lucy) [input p18]
23. generous(lucy) [input hypothesis]
27. curious(lucy) [pure predicate removal 19]
31. (curious(lucy) <~> kind(lucy)) | ! [X0] : (~generous(X0) & curious(X0)) [ennf transformation 3]
35. ! [X0] : ((happy(X0) & ~humble(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 11]
36. ! [X0] : (~old(X0) | (quiet(X0) & ~strong(X0))) [ennf transformation 14]
37. ((~kind(lucy) | ~curious(lucy)) & (kind(lucy) | curious(lucy))) | ! [X0] : (~generous(X0) & curious(X0)) [nnf transformation 31]
48. ! [X0] : ((((kind(X0) | quiet(X0)) & (~kind(X0) | ~quiet(X0))) | ((happy(X0) | kind(X0)) & (~kind(X0) | ~happy(X0)))) & (((kind(X0) | ~happy(X0)) & (~kind(X0) | happy(X0))) | ((~quiet(X0) | kind(X0)) & (~kind(X0) | quiet(X0))))) [nnf transformation 9]
59. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 16]
60. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [flattening 59]
68. ~kind(lucy) | ~curious(lucy) | ~generous(X0) [cnf transformation 37]
87. kind(X0) | ~happy(X0) | ~quiet(X0) | kind(X0) [cnf transformation 48]
88. ~kind(X0) | ~quiet(X0) | ~kind(X0) | ~happy(X0) [cnf transformation 48]
98. happy(X0) | kind(X0) [cnf transformation 35]
103. ~old(X0) | quiet(X0) [cnf transformation 36]
112. ~happy(X0) | old(X0) | kind(X0) [cnf transformation 60]
117. curious(lucy) [cnf transformation 27]
121. generous(lucy) [cnf transformation 23]
123. kind(X0) | ~happy(X0) | ~quiet(X0) [duplicate literal removal 87]
124. ~quiet(X0) | ~kind(X0) | ~happy(X0) [duplicate literal removal 88]
127. 1 <=> ! [X0] : ~generous(X0) [avatar definition]
128. ~generous(X0) <- (1) [avatar component clause 127]
130. 2 <=> curious(lucy) [avatar definition]
134. 3 <=> kind(lucy) [avatar definition]
136. ~kind(lucy) <- (~3) [avatar component clause 134]
137. 1 | ~2 | ~3 [avatar split clause 68,134,130,127]
185. ~quiet(X0) | ~happy(X0) [subsumption resolution 123,124]
225. kind(X0) | old(X0) [subsumption resolution 112,98]
227. 2 [avatar split clause 117,130]
246. old(lucy) <- (~3) [resolution 225,136]
264. quiet(lucy) <- (~3) [resolution 246,103]
297. ~happy(lucy) <- (~3) [resolution 264,185]
444. kind(lucy) <- (~3) [resolution 297,98]
445. $false <- (~3) [subsumption resolution 444,136]
446. 3 [avatar contradiction clause 445]
447. $false <- (1) [resolution 128,121]
450. ~1 [avatar contradiction clause 447]
451. $false [avatar sat refutation 137,227,446,450]
% SZS output end Proof for 1697361154714929503843746
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious is not old.
Everyone who is generous is either not calm or brave.
Everyone who is funny or patient is not tall and vice versa.
Everyone who is either old or not old is either funny or happy and vice versa.
If susan is humble then mary is not patient and vice versa.
Everyone who is not wise is not funny.
Everyone who is either curious or humble is not generous or wise and vice versa.
If someone is not rich or quiet then someone is either humble or tall.
If someone is both quiet and curious then susan is not happy and vice versa.
Everyone who is brave or rich is both not brave and happy.
If susan is not funny or strong then someone is either not wise or humble.
Everyone who is not brave or funny is both tall and curious and vice versa.
Everyone who is either curious or not happy is either not old or quiet and vice versa.
If alice is both wise and strong then paul is not curious or not tall.
Everyone who is both happy and kind is either quiet or not wise and vice versa.
Everyone who is either not calm or rich is either old or not rich and vice versa.
Fred is not generous.
Someone is both kind and generous.
Someone is both strong and not rich.
Someone is either not generous or not creative. | Fred is not strong. | neutral | (![X]:(~curious(X)=>~old(X)))&
(![X]:(generous(X)=>(~calm(X)<~>brave(X))))&
(![X]:((funny(X)|patient(X))<=>~tall(X)))&
(![X]:((old(X)<~>~old(X))<=>(funny(X)<~>happy(X))))&
((humble(susan))<=>(~patient(mary)))&
(![X]:(~wise(X)=>~funny(X)))&
(![X]:((curious(X)<~>humble(X))<=>(~generous(X)|wise(X))))&
((?[X]:((~rich(X)|quiet(X))))=>(?[X]:((humble(X)<~>tall(X)))))&
((?[X]:((quiet(X)&curious(X))))<=>(~happy(susan)))&
(![X]:((brave(X)|rich(X))=>(~brave(X)&happy(X))))&
(((~funny(susan)|strong(susan)))=>(?[X]:((~wise(X)<~>humble(X)))))&
(![X]:((~brave(X)|funny(X))<=>(tall(X)&curious(X))))&
(![X]:((curious(X)<~>~happy(X))<=>(~old(X)<~>quiet(X))))&
(((wise(alice)&strong(alice)))=>((~curious(paul)|~tall(paul))))&
(![X]:((happy(X)&kind(X))<=>(quiet(X)<~>~wise(X))))&
(![X]:((~calm(X)<~>rich(X))<=>(old(X)<~>~rich(X))))&
(~generous(fred))&
(?[X]:((kind(X)&generous(X))))&
(?[X]:((strong(X)&~rich(X))))&
(?[X]:((~generous(X)<~>~creative(X)))) | ~strong(fred) | [] | null | 0 |
If susan is both not funny and not strong then someone is either wise or calm.
Everyone who is either not humble or brave is not old and vice versa.
Everyone who is not humble or not funny is both patient and not wise.
If someone is patient or strong then someone is patient.
Everyone who is both patient and not humble is either not curious or humble and vice versa.
If lucy is both funny and not wise then alice is either not quiet or wise and vice versa.
Everyone who is either not funny or rich is both patient and funny and vice versa.
Everyone who is both wise and not patient is not calm or wise and vice versa.
Everyone who is strong is not rich or not strong.
Everyone who is generous is not patient and vice versa.
Everyone who is generous or not curious is generous or rich.
If mary is either strong or generous then mary is not funny or not tall.
If mary is not calm then alice is both happy and wise and vice versa.
Everyone who is both not wise and humble is kind or not kind.
If someone is tall then lucy is not wise and vice versa.
If someone is tall then lucy is kind or humble.
Lucy is humble or funny.
Someone is both wise and not tall.
Susan is both not curious and quiet.
Alice is both not kind and not calm.
Someone is either not rich or not old.
Mary is both not calm and not old.
Someone is old or not tall.
Someone is not curious or not patient. | Lucy is strong. | neutral | (((~funny(susan)&~strong(susan)))=>(?[X]:((wise(X)<~>calm(X)))))&
(![X]:((~humble(X)<~>brave(X))<=>~old(X)))&
(![X]:((~humble(X)|~funny(X))=>(patient(X)&~wise(X))))&
((?[X]:((patient(X)|strong(X))))=>(?[X]:(patient(X))))&
(![X]:((patient(X)&~humble(X))<=>(~curious(X)<~>humble(X))))&
(((funny(lucy)&~wise(lucy)))<=>((~quiet(alice)<~>wise(alice))))&
(![X]:((~funny(X)<~>rich(X))<=>(patient(X)&funny(X))))&
(![X]:((wise(X)&~patient(X))<=>(~calm(X)|wise(X))))&
(![X]:(strong(X)=>(~rich(X)|~strong(X))))&
(![X]:(generous(X)<=>~patient(X)))&
(![X]:((generous(X)|~curious(X))=>(generous(X)|rich(X))))&
(((strong(mary)<~>generous(mary)))=>((~funny(mary)|~tall(mary))))&
((~calm(mary))<=>((happy(alice)&wise(alice))))&
(![X]:((~wise(X)&humble(X))=>(kind(X)|~kind(X))))&
((?[X]:(tall(X)))<=>(~wise(lucy)))&
((?[X]:(tall(X)))=>((kind(lucy)|humble(lucy))))&
((humble(lucy)|funny(lucy)))&
(?[X]:((wise(X)&~tall(X))))&
((~curious(susan)&quiet(susan)))&
((~kind(alice)&~calm(alice)))&
(?[X]:((~rich(X)<~>~old(X))))&
((~calm(mary)&~old(mary)))&
(?[X]:((old(X)|~tall(X))))&
(?[X]:((~curious(X)|~patient(X)))) | strong(lucy) | [] | null | 0 |
If someone is both not quiet and rich then someone is either not generous or not curious.
Everyone who is either strong or not tall is quiet.
If someone is either generous or not creative then susan is both not happy and not funny and vice versa.
Everyone who is not patient or old is not patient or not kind.
If lucy is not strong then someone is old or calm.
If lucy is both not kind and brave then someone is not kind or not happy and vice versa.
If someone is both not happy and not tall then fred is not strong or not curious.
Everyone who is rich or not brave is either strong or quiet and vice versa.
Everyone who is both not generous and creative is both not curious and creative and vice versa.
If someone is not quiet or patient then someone is not rich and vice versa.
Everyone who is both not rich and not creative is both generous and creative and vice versa.
Everyone who is curious or not curious is either calm or not strong.
If someone is either happy or patient then susan is either funny or not humble.
Everyone who is either not brave or wise is either not funny or not curious and vice versa.
If someone is either not calm or not wise then someone is either tall or not tall.
Everyone who is either not quiet or patient is not old or funny and vice versa.
Susan is both not patient and not old.
Lucy is old or not wise.
Paul is both patient and brave.
Someone is old.
Someone is wise or not rich.
Alice is humble.
John is not strong.
Someone is not wise or patient. | Susan is not old. | entailment | ((?[X]:((~quiet(X)&rich(X))))=>(?[X]:((~generous(X)<~>~curious(X)))))&
(![X]:((strong(X)<~>~tall(X))=>quiet(X)))&
((?[X]:((generous(X)<~>~creative(X))))<=>((~happy(susan)&~funny(susan))))&
(![X]:((~patient(X)|old(X))=>(~patient(X)|~kind(X))))&
((~strong(lucy))=>(?[X]:((old(X)|calm(X)))))&
(((~kind(lucy)&brave(lucy)))<=>(?[X]:((~kind(X)|~happy(X)))))&
((?[X]:((~happy(X)&~tall(X))))=>((~strong(fred)|~curious(fred))))&
(![X]:((rich(X)|~brave(X))<=>(strong(X)<~>quiet(X))))&
(![X]:((~generous(X)&creative(X))<=>(~curious(X)&creative(X))))&
((?[X]:((~quiet(X)|patient(X))))<=>(?[X]:(~rich(X))))&
(![X]:((~rich(X)&~creative(X))<=>(generous(X)&creative(X))))&
(![X]:((curious(X)|~curious(X))=>(calm(X)<~>~strong(X))))&
((?[X]:((happy(X)<~>patient(X))))=>((funny(susan)<~>~humble(susan))))&
(![X]:((~brave(X)<~>wise(X))<=>(~funny(X)<~>~curious(X))))&
((?[X]:((~calm(X)<~>~wise(X))))=>(?[X]:((tall(X)<~>~tall(X)))))&
(![X]:((~quiet(X)<~>patient(X))<=>(~old(X)|funny(X))))&
((~patient(susan)&~old(susan)))&
((old(lucy)|~wise(lucy)))&
((patient(paul)&brave(paul)))&
(?[X]:(old(X)))&
(?[X]:((wise(X)|~rich(X))))&
(humble(alice))&
(~strong(john))&
(?[X]:((~wise(X)|patient(X)))) | ~old(susan) | [
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 6625458085765033763432992
% SZS output start Proof for 6625458085765033763432992
17. ~old(susan) & ~patient(susan) [input p16]
25. old(susan) [input hypothesis]
145. ~old(susan) [cnf transformation 17]
154. old(susan) [cnf transformation 25]
318. $false [subsumption resolution 154,145]
% SZS output end Proof for 6625458085765033763432992
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny or rich then alice is brave.
If someone is either wise or patient then someone is humble and vice versa.
Everyone who is both tall and happy is both rich and not calm and vice versa.
Everyone who is not patient or curious is either old or wise and vice versa.
If someone is not tall then someone is wise or old and vice versa.
If someone is either wise or humble then mary is not tall or not patient.
Everyone who is funny or tall is both humble and funny.
If paul is both not funny and calm then someone is both not strong and not tall and vice versa.
If someone is not funny or old then lucy is either not funny or not wise and vice versa.
If fred is either not wise or generous then someone is not kind or creative and vice versa.
Everyone who is not strong or strong is brave or calm.
Everyone who is both not humble and not calm is not happy or quiet and vice versa.
Everyone who is not strong is either strong or humble and vice versa.
If someone is either not rich or tall then someone is both brave and generous and vice versa.
Everyone who is both humble and not wise is quiet or not wise and vice versa.
If lucy is not quiet or tall then someone is either not creative or quiet.
Someone is curious.
Someone is wise.
Someone is either not humble or calm.
Someone is either generous or not rich.
Mary is not patient.
Someone is not happy or kind. | Alice is tall. | neutral | (((funny(alice)|rich(alice)))=>(brave(alice)))&
((?[X]:((wise(X)<~>patient(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)&happy(X))<=>(rich(X)&~calm(X))))&
(![X]:((~patient(X)|curious(X))<=>(old(X)<~>wise(X))))&
((?[X]:(~tall(X)))<=>(?[X]:((wise(X)|old(X)))))&
((?[X]:((wise(X)<~>humble(X))))=>((~tall(mary)|~patient(mary))))&
(![X]:((funny(X)|tall(X))=>(humble(X)&funny(X))))&
(((~funny(paul)&calm(paul)))<=>(?[X]:((~strong(X)&~tall(X)))))&
((?[X]:((~funny(X)|old(X))))<=>((~funny(lucy)<~>~wise(lucy))))&
(((~wise(fred)<~>generous(fred)))<=>(?[X]:((~kind(X)|creative(X)))))&
(![X]:((~strong(X)|strong(X))=>(brave(X)|calm(X))))&
(![X]:((~humble(X)&~calm(X))<=>(~happy(X)|quiet(X))))&
(![X]:(~strong(X)<=>(strong(X)<~>humble(X))))&
((?[X]:((~rich(X)<~>tall(X))))<=>(?[X]:((brave(X)&generous(X)))))&
(![X]:((humble(X)&~wise(X))<=>(quiet(X)|~wise(X))))&
(((~quiet(lucy)|tall(lucy)))=>(?[X]:((~creative(X)<~>quiet(X)))))&
(?[X]:(curious(X)))&
(?[X]:(wise(X)))&
(?[X]:((~humble(X)<~>calm(X))))&
(?[X]:((generous(X)<~>~rich(X))))&
(~patient(mary))&
(?[X]:((~happy(X)|kind(X)))) | tall(alice) | [] | null | 0 |
If someone is curious then alice is not happy.
Everyone who is not humble or not kind is not curious or not strong and vice versa.
Everyone who is tall or not quiet is not happy or not kind and vice versa.
If someone is not curious then someone is strong and vice versa.
Everyone who is not rich or not happy is either patient or not rich.
Everyone who is either not calm or not humble is not rich or kind and vice versa.
If someone is brave or not quiet then someone is either not curious or not patient.
Everyone who is not creative or brave is both brave and not patient and vice versa.
Everyone who is curious or not quiet is not humble and vice versa.
If mary is kind or not old then someone is either funny or patient.
If someone is generous or rich then fred is not creative.
Everyone who is not curious is both not happy and tall and vice versa.
Everyone who is both kind and curious is tall or not funny and vice versa.
If someone is not funny then someone is not kind or not rich and vice versa.
If someone is not calm then mary is both not creative and old.
Everyone who is both not tall and brave is patient or not calm and vice versa.
Someone is not creative or wise.
Someone is funny or not happy.
Mary is generous or not calm.
Someone is both old and curious.
Someone is either not brave or not creative.
Paul is rich. | Mary is humble. | contradiction | ((?[X]:(curious(X)))=>(~happy(alice)))&
(![X]:((~humble(X)|~kind(X))<=>(~curious(X)|~strong(X))))&
(![X]:((tall(X)|~quiet(X))<=>(~happy(X)|~kind(X))))&
((?[X]:(~curious(X)))<=>(?[X]:(strong(X))))&
(![X]:((~rich(X)|~happy(X))=>(patient(X)<~>~rich(X))))&
(![X]:((~calm(X)<~>~humble(X))<=>(~rich(X)|kind(X))))&
((?[X]:((brave(X)|~quiet(X))))=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((~creative(X)|brave(X))<=>(brave(X)&~patient(X))))&
(![X]:((curious(X)|~quiet(X))<=>~humble(X)))&
(((kind(mary)|~old(mary)))=>(?[X]:((funny(X)<~>patient(X)))))&
((?[X]:((generous(X)|rich(X))))=>(~creative(fred)))&
(![X]:(~curious(X)<=>(~happy(X)&tall(X))))&
(![X]:((kind(X)&curious(X))<=>(tall(X)|~funny(X))))&
((?[X]:(~funny(X)))<=>(?[X]:((~kind(X)|~rich(X)))))&
((?[X]:(~calm(X)))=>((~creative(mary)&old(mary))))&
(![X]:((~tall(X)&brave(X))<=>(patient(X)|~calm(X))))&
(?[X]:((~creative(X)|wise(X))))&
(?[X]:((funny(X)|~happy(X))))&
((generous(mary)|~calm(mary)))&
(?[X]:((old(X)&curious(X))))&
(?[X]:((~brave(X)<~>~creative(X))))&
(rich(paul)) | humble(mary) | [
"p8",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 1428823257627430457212666
% SZS output start Proof for 1428823257627430457212666
9. ! [X0] : ((~quiet(X0) | curious(X0)) <=> ~humble(X0)) [input p8]
12. ! [X0] : (~curious(X0) <=> (tall(X0) & ~happy(X0))) [input p11]
13. ! [X0] : ((curious(X0) & kind(X0)) <=> (~funny(X0) | tall(X0))) [input p12]
23. humble(mary) [input hypothesis]
55. ! [X0] : (((~quiet(X0) | curious(X0)) | humble(X0)) & (~humble(X0) | (quiet(X0) & ~curious(X0)))) [nnf transformation 9]
56. ! [X0] : ((~quiet(X0) | curious(X0) | humble(X0)) & (~humble(X0) | (quiet(X0) & ~curious(X0)))) [flattening 55]
60. ! [X0] : ((~curious(X0) | (~tall(X0) | happy(X0))) & ((tall(X0) & ~happy(X0)) | curious(X0))) [nnf transformation 12]
61. ! [X0] : ((~curious(X0) | ~tall(X0) | happy(X0)) & ((tall(X0) & ~happy(X0)) | curious(X0))) [flattening 60]
62. ! [X0] : (((curious(X0) & kind(X0)) | (funny(X0) & ~tall(X0))) & ((~funny(X0) | tall(X0)) | (~curious(X0) | ~kind(X0)))) [nnf transformation 13]
63. ! [X0] : (((curious(X0) & kind(X0)) | (funny(X0) & ~tall(X0))) & (~funny(X0) | tall(X0) | ~curious(X0) | ~kind(X0))) [flattening 62]
108. ~humble(X0) | ~curious(X0) [cnf transformation 56]
116. tall(X0) | curious(X0) [cnf transformation 61]
121. curious(X0) | ~tall(X0) [cnf transformation 63]
138. humble(mary) [cnf transformation 23]
157. 5 <=> ! [X3] : curious(X3) [avatar definition]
158. curious(X3) <- (5) [avatar component clause 157]
208. curious(X0) [subsumption resolution 121,116]
209. 5 [avatar split clause 208,157]
281. ~curious(mary) [resolution 108,138]
282. $false <- (5) [subsumption resolution 281,158]
283. ~5 [avatar contradiction clause 282]
284. $false [avatar sat refutation 209,283]
% SZS output end Proof for 1428823257627430457212666
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is 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. Everyone who is both generous and tall is both funny and not generous. Everyone who is not patient or not creative is both not rich and creative and vice versa. Everyone who is either not kind or patient is both strong and brave. If susan is not strong then fred is not generous and vice versa. If john is curious or brave then someone is either humble or generous and vice versa. Everyone who is not old or generous is both curious and not calm and vice versa. Someone is old. Someone is strong or patient. Alice is either not patient or not calm. Fred is not calm or not creative. Someone is both not kind and not curious. Someone is not calm. Someone is not generous or not patient. | Alice is generous. | neutral | (![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)&tall(X))=>(funny(X)&~generous(X))))&
(![X]:((~patient(X)|~creative(X))<=>(~rich(X)&creative(X))))&
(![X]:((~kind(X)<~>patient(X))=>(strong(X)&brave(X))))&
((~strong(susan))<=>(~generous(fred)))&
(((curious(john)|brave(john)))<=>(?[X]:((humble(X)<~>generous(X)))))&
(![X]:((~old(X)|generous(X))<=>(curious(X)&~calm(X))))&
(?[X]:(old(X)))&
(?[X]:((strong(X)|patient(X))))&
((~patient(alice)<~>~calm(alice)))&
((~calm(fred)|~creative(fred)))&
(?[X]:((~kind(X)&~curious(X))))&
(?[X]:(~calm(X)))&
(?[X]:((~generous(X)|~patient(X)))) | generous(alice) | [] | null | 0 |
Everyone who is not humble or not happy is both patient and not curious and vice versa.
Everyone who is not old is both generous and not brave and vice versa.
Everyone who is old or not funny is either old or calm.
Everyone who is either rich or not tall is either patient or not brave and vice versa.
Everyone who is both funny and rich is both not calm and not generous and vice versa.
Everyone who is both not calm and curious is either not calm or calm and vice versa.
If fred is both not old and brave then someone is both wise and not quiet.
Everyone who is creative is either not humble or wise.
If someone is old or patient then someone is creative.
If susan is not quiet then someone is either generous or calm and vice versa.
Everyone who is not brave or humble is wise and vice versa.
Everyone who is both not strong and old is either not strong or curious.
If paul is either not kind or quiet then someone is both quiet and patient.
If john is funny then susan is both not curious and creative and vice versa.
If someone is funny or rich then alice is tall or rich.
If someone is not calm or humble then susan is not strong.
Someone is brave.
Someone is generous.
Susan is wise.
Mary is wise or not funny.
Someone is calm or happy.
Someone is not calm.
Someone is brave or not quiet.
Someone is either generous or funny. | Fred is not happy. | contradiction | (![X]:((~humble(X)|~happy(X))<=>(patient(X)&~curious(X))))&
(![X]:(~old(X)<=>(generous(X)&~brave(X))))&
(![X]:((old(X)|~funny(X))=>(old(X)<~>calm(X))))&
(![X]:((rich(X)<~>~tall(X))<=>(patient(X)<~>~brave(X))))&
(![X]:((funny(X)&rich(X))<=>(~calm(X)&~generous(X))))&
(![X]:((~calm(X)&curious(X))<=>(~calm(X)<~>calm(X))))&
(((~old(fred)&brave(fred)))=>(?[X]:((wise(X)&~quiet(X)))))&
(![X]:(creative(X)=>(~humble(X)<~>wise(X))))&
((?[X]:((old(X)|patient(X))))=>(?[X]:(creative(X))))&
((~quiet(susan))<=>(?[X]:((generous(X)<~>calm(X)))))&
(![X]:((~brave(X)|humble(X))<=>wise(X)))&
(![X]:((~strong(X)&old(X))=>(~strong(X)<~>curious(X))))&
(((~kind(paul)<~>quiet(paul)))=>(?[X]:((quiet(X)&patient(X)))))&
((funny(john))<=>((~curious(susan)&creative(susan))))&
((?[X]:((funny(X)|rich(X))))=>((tall(alice)|rich(alice))))&
((?[X]:((~calm(X)|humble(X))))=>(~strong(susan)))&
(?[X]:(brave(X)))&
(?[X]:(generous(X)))&
(wise(susan))&
((wise(mary)|~funny(mary)))&
(?[X]:((calm(X)|happy(X))))&
(?[X]:(~calm(X)))&
(?[X]:((brave(X)|~quiet(X))))&
(?[X]:((generous(X)<~>funny(X)))) | ~happy(fred) | [
"p0",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1206931447734045353519330
% SZS output start Proof for 1206931447734045353519330
1. ! [X0] : ((~happy(X0) | ~humble(X0)) <=> (~curious(X0) & patient(X0))) [input p0]
6. ! [X0] : ((curious(X0) & ~calm(X0)) <=> (~calm(X0) <~> calm(X0))) [input p5]
25. ~happy(fred) [input hypothesis]
38. ! [X0] : (((~happy(X0) | ~humble(X0)) | (curious(X0) | ~patient(X0))) & ((~curious(X0) & patient(X0)) | (happy(X0) & humble(X0)))) [nnf transformation 1]
39. ! [X0] : ((~happy(X0) | ~humble(X0) | curious(X0) | ~patient(X0)) & ((~curious(X0) & patient(X0)) | (happy(X0) & humble(X0)))) [flattening 38]
46. ! [X0] : (((curious(X0) & ~calm(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | (~curious(X0) | calm(X0)))) [nnf transformation 6]
47. ! [X0] : (((curious(X0) & ~calm(X0)) | ((~calm(X0) | ~calm(X0)) & (calm(X0) | calm(X0)))) & (((~calm(X0) | calm(X0)) & (calm(X0) | ~calm(X0))) | ~curious(X0) | calm(X0))) [flattening 46]
82. ~curious(X0) | happy(X0) [cnf transformation 39]
107. curious(X0) | calm(X0) | calm(X0) [cnf transformation 47]
108. curious(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 47]
144. ~happy(fred) [cnf transformation 25]
150. curious(X0) | calm(X0) [duplicate literal removal 107]
151. curious(X0) | ~calm(X0) [duplicate literal removal 108]
153. curious(X0) [subsumption resolution 150,151]
271. happy(X0) [resolution 82,153]
272. $false [resolution 271,144]
% SZS output end Proof for 1206931447734045353519330
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not brave is either tall or not quiet.
Everyone who is not wise or not funny is generous or not quiet and vice versa.
Everyone who is generous is not wise.
Everyone who is either funny or not tall is kind or curious.
Everyone who is funny or strong is brave.
Everyone who is not patient is calm or not calm.
Everyone who is not strong or not tall is rich or creative and vice versa.
Everyone who is not kind is both wise and generous and vice versa.
If mary is not kind or calm then someone is either not humble or tall.
Everyone who is either old or generous is either not calm or not creative and vice versa.
Everyone who is not patient or patient is both tall and not humble and vice versa.
Everyone who is not tall or kind is not happy and vice versa.
Everyone who is not curious or happy is both strong and not tall.
If someone is brave then someone is both humble and not old.
Everyone who is not rich is not calm.
Everyone who is both not wise and not quiet is either not brave or not kind.
Susan is not brave.
Susan is either not generous or quiet.
John is calm or not wise.
Lucy is not quiet or kind.
Someone is calm.
Someone is both not old and not happy. | Lucy is not generous. | contradiction | (![X]:((~strong(X)|~brave(X))=>(tall(X)<~>~quiet(X))))&
(![X]:((~wise(X)|~funny(X))<=>(generous(X)|~quiet(X))))&
(![X]:(generous(X)=>~wise(X)))&
(![X]:((funny(X)<~>~tall(X))=>(kind(X)|curious(X))))&
(![X]:((funny(X)|strong(X))=>brave(X)))&
(![X]:(~patient(X)=>(calm(X)|~calm(X))))&
(![X]:((~strong(X)|~tall(X))<=>(rich(X)|creative(X))))&
(![X]:(~kind(X)<=>(wise(X)&generous(X))))&
(((~kind(mary)|calm(mary)))=>(?[X]:((~humble(X)<~>tall(X)))))&
(![X]:((old(X)<~>generous(X))<=>(~calm(X)<~>~creative(X))))&
(![X]:((~patient(X)|patient(X))<=>(tall(X)&~humble(X))))&
(![X]:((~tall(X)|kind(X))<=>~happy(X)))&
(![X]:((~curious(X)|happy(X))=>(strong(X)&~tall(X))))&
((?[X]:(brave(X)))=>(?[X]:((humble(X)&~old(X)))))&
(![X]:(~rich(X)=>~calm(X)))&
(![X]:((~wise(X)&~quiet(X))=>(~brave(X)<~>~kind(X))))&
(~brave(susan))&
((~generous(susan)<~>quiet(susan)))&
((calm(john)|~wise(john)))&
((~quiet(lucy)|kind(lucy)))&
(?[X]:(calm(X)))&
(?[X]:((~old(X)&~happy(X)))) | ~generous(lucy) | [
"p0",
"p1",
"p4",
"p10",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1261691915426252869987682
% SZS output start Proof for 1261691915426252869987682
1. ! [X0] : ((~brave(X0) | ~strong(X0)) => (tall(X0) <~> ~quiet(X0))) [input p0]
2. ! [X0] : ((~funny(X0) | ~wise(X0)) <=> (~quiet(X0) | generous(X0))) [input p1]
5. ! [X0] : ((strong(X0) | funny(X0)) => brave(X0)) [input p4]
11. ! [X0] : ((patient(X0) | ~patient(X0)) <=> (~humble(X0) & tall(X0))) [input p10]
14. ? [X0] : brave(X0) => ? [X0] : (~old(X0) & humble(X0)) [input p13]
23. ~generous(lucy) [input hypothesis]
24. ? [X0] : brave(X0) => ? [X1] : (~old(X1) & humble(X1)) [rectify 14]
28. ! [X0] : ((tall(X0) <~> ~quiet(X0)) | (brave(X0) & strong(X0))) [ennf transformation 1]
30. ! [X0] : (brave(X0) | (~strong(X0) & ~funny(X0))) [ennf transformation 5]
37. ? [X1] : (~old(X1) & humble(X1)) | ! [X0] : ~brave(X0) [ennf transformation 24]
41. ! [X0] : (((quiet(X0) | ~tall(X0)) & (~quiet(X0) | tall(X0))) | (brave(X0) & strong(X0))) [nnf transformation 28]
42. ! [X0] : (((~funny(X0) | ~wise(X0)) | (quiet(X0) & ~generous(X0))) & ((~quiet(X0) | generous(X0)) | (funny(X0) & wise(X0)))) [nnf transformation 2]
43. ! [X0] : ((~funny(X0) | ~wise(X0) | (quiet(X0) & ~generous(X0))) & (~quiet(X0) | generous(X0) | (funny(X0) & wise(X0)))) [flattening 42]
52. ! [X0] : (((patient(X0) | ~patient(X0)) | (humble(X0) | ~tall(X0))) & ((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0)))) [nnf transformation 11]
53. ! [X0] : ((patient(X0) | ~patient(X0) | humble(X0) | ~tall(X0)) & ((~humble(X0) & tall(X0)) | (~patient(X0) & patient(X0)))) [flattening 52]
54. ? [X0] : (~old(X0) & humble(X0)) | ! [X1] : ~brave(X1) [rectify 37]
55. ? [X0] : (~old(X0) & humble(X0)) => (~old(sK1) & humble(sK1)) [choice axiom]
56. (~old(sK1) & humble(sK1)) | ! [X1] : ~brave(X1) [skolemisation 54,55]
66. ~tall(X0) | quiet(X0) | brave(X0) [cnf transformation 41]
68. ~quiet(X0) | generous(X0) | funny(X0) [cnf transformation 43]
72. ~funny(X0) | brave(X0) [cnf transformation 30]
94. tall(X0) | patient(X0) [cnf transformation 53]
95. ~patient(X0) | tall(X0) [cnf transformation 53]
96. ~humble(X0) | patient(X0) [cnf transformation 53]
97. ~humble(X0) | ~patient(X0) [cnf transformation 53]
102. humble(sK1) | ~brave(X1) [cnf transformation 56]
115. ~generous(lucy) [cnf transformation 23]
136. ~humble(X0) [subsumption resolution 96,97]
137. tall(X0) [subsumption resolution 94,95]
141. 5 <=> ! [X1] : ~brave(X1) [avatar definition]
142. ~brave(X1) <- (5) [avatar component clause 141]
148. ~brave(X1) [subsumption resolution 102,136]
149. 5 [avatar split clause 148,141]
189. quiet(X0) | brave(X0) [resolution 66,137]
190. quiet(X0) <- (5) [subsumption resolution 189,142]
202. generous(X0) | funny(X0) <- (5) [resolution 68,190]
206. funny(lucy) <- (5) [resolution 202,115]
210. brave(lucy) <- (5) [resolution 206,72]
211. $false <- (5) [subsumption resolution 210,142]
212. ~5 [avatar contradiction clause 211]
213. $false [avatar sat refutation 149,212]
% SZS output end Proof for 1261691915426252869987682
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 not old then lucy is both creative and generous.
Everyone who is either not tall or creative is tall or kind and vice versa.
Everyone who is both not calm and not humble is funny and vice versa.
Everyone who is not creative or happy is brave.
Everyone who is either not humble or wise is not kind or strong.
Everyone who is either not generous or strong is both not brave and not wise and vice versa.
Everyone who is either not wise or not patient is not creative or creative and vice versa.
If someone is either quiet or wise then someone is either rich or not patient.
Everyone who is both not tall and not quiet is both not quiet and strong and vice versa.
Everyone who is both not creative and tall is either not quiet or not creative.
Everyone who is not quiet or not brave is either not curious or old and vice versa.
Everyone who is strong or not tall is both not calm and not creative.
Everyone who is both humble and not happy is humble and vice versa.
Everyone who is either not old or not kind is both not happy and curious.
Everyone who is brave or not quiet is not patient or curious and vice versa.
Everyone who is both not funny and curious is not happy and vice versa.
Susan is either not quiet or not generous.
Mary is both calm and not wise.
Someone is generous or not strong.
Alice is not humble or old.
Someone is humble or tall.
Alice is either humble or not patient.
Someone is patient or quiet. | Alice is not patient. | neutral | ((?[X]:(~old(X)))=>((creative(lucy)&generous(lucy))))&
(![X]:((~tall(X)<~>creative(X))<=>(tall(X)|kind(X))))&
(![X]:((~calm(X)&~humble(X))<=>funny(X)))&
(![X]:((~creative(X)|happy(X))=>brave(X)))&
(![X]:((~humble(X)<~>wise(X))=>(~kind(X)|strong(X))))&
(![X]:((~generous(X)<~>strong(X))<=>(~brave(X)&~wise(X))))&
(![X]:((~wise(X)<~>~patient(X))<=>(~creative(X)|creative(X))))&
((?[X]:((quiet(X)<~>wise(X))))=>(?[X]:((rich(X)<~>~patient(X)))))&
(![X]:((~tall(X)&~quiet(X))<=>(~quiet(X)&strong(X))))&
(![X]:((~creative(X)&tall(X))=>(~quiet(X)<~>~creative(X))))&
(![X]:((~quiet(X)|~brave(X))<=>(~curious(X)<~>old(X))))&
(![X]:((strong(X)|~tall(X))=>(~calm(X)&~creative(X))))&
(![X]:((humble(X)&~happy(X))<=>humble(X)))&
(![X]:((~old(X)<~>~kind(X))=>(~happy(X)&curious(X))))&
(![X]:((brave(X)|~quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~funny(X)&curious(X))<=>~happy(X)))&
((~quiet(susan)<~>~generous(susan)))&
((calm(mary)&~wise(mary)))&
(?[X]:((generous(X)|~strong(X))))&
((~humble(alice)|old(alice)))&
(?[X]:((humble(X)|tall(X))))&
((humble(alice)<~>~patient(alice)))&
(?[X]:((patient(X)|quiet(X)))) | ~patient(alice) | [] | null | 0 |
Everyone who is strong is not humble.
Everyone who is either not strong or not brave is not quiet or not calm.
Everyone who is rich or not old is either not funny or not old and vice versa.
If fred is not patient or not old then alice is either strong or not old.
If someone is not tall then lucy is both old and creative and vice versa.
If mary is both not brave and not rich then paul is not happy or rich and vice versa.
If someone is rich then someone is old or not humble.
If someone is both not brave and not quiet then someone is not generous and vice versa.
Everyone who is either not funny or not patient is both strong and not tall.
Everyone who is both creative and quiet is funny and vice versa.
If fred is either not kind or quiet then someone is both not wise and funny.
If someone is either not tall or not creative then someone is both generous and not curious.
Everyone who is quiet or tall is strong and vice versa.
If lucy is quiet then someone is strong and vice versa.
If someone is either not brave or calm then paul is either not creative or not curious.
Everyone who is either quiet or strong is either generous or not curious and vice versa.
Lucy is rich or not kind.
Someone is not wise or rich.
John is not calm or not patient.
Someone is either creative or not brave.
Someone is not humble or not curious.
Fred is either generous or old.
Someone is kind. | Lucy is not humble. | entailment | (![X]:(strong(X)=>~humble(X)))&
(![X]:((~strong(X)<~>~brave(X))=>(~quiet(X)|~calm(X))))&
(![X]:((rich(X)|~old(X))<=>(~funny(X)<~>~old(X))))&
(((~patient(fred)|~old(fred)))=>((strong(alice)<~>~old(alice))))&
((?[X]:(~tall(X)))<=>((old(lucy)&creative(lucy))))&
(((~brave(mary)&~rich(mary)))<=>((~happy(paul)|rich(paul))))&
((?[X]:(rich(X)))=>(?[X]:((old(X)|~humble(X)))))&
((?[X]:((~brave(X)&~quiet(X))))<=>(?[X]:(~generous(X))))&
(![X]:((~funny(X)<~>~patient(X))=>(strong(X)&~tall(X))))&
(![X]:((creative(X)&quiet(X))<=>funny(X)))&
(((~kind(fred)<~>quiet(fred)))=>(?[X]:((~wise(X)&funny(X)))))&
((?[X]:((~tall(X)<~>~creative(X))))=>(?[X]:((generous(X)&~curious(X)))))&
(![X]:((quiet(X)|tall(X))<=>strong(X)))&
((quiet(lucy))<=>(?[X]:(strong(X))))&
((?[X]:((~brave(X)<~>calm(X))))=>((~creative(paul)<~>~curious(paul))))&
(![X]:((quiet(X)<~>strong(X))<=>(generous(X)<~>~curious(X))))&
((rich(lucy)|~kind(lucy)))&
(?[X]:((~wise(X)|rich(X))))&
((~calm(john)|~patient(john)))&
(?[X]:((creative(X)<~>~brave(X))))&
(?[X]:((~humble(X)|~curious(X))))&
((generous(fred)<~>old(fred)))&
(?[X]:(kind(X))) | ~humble(lucy) | [
"p0",
"p2",
"p3",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 3392920691589138597787540
% SZS output start Proof for 3392920691589138597787540
1. ! [X0] : (strong(X0) => ~humble(X0)) [input p0]
3. ! [X0] : ((~old(X0) | rich(X0)) <=> (~funny(X0) <~> ~old(X0))) [input p2]
4. (~old(fred) | ~patient(fred)) => (strong(alice) <~> ~old(alice)) [input p3]
9. ! [X0] : ((~funny(X0) <~> ~patient(X0)) => (~tall(X0) & strong(X0))) [input p8]
10. ! [X0] : ((quiet(X0) & creative(X0)) <=> funny(X0)) [input p9]
13. ! [X0] : ((tall(X0) | quiet(X0)) <=> strong(X0)) [input p12]
14. quiet(lucy) <=> ? [X0] : strong(X0) [input p13]
24. humble(lucy) [input hypothesis]
30. ! [X0] : (~humble(X0) | ~strong(X0)) [ennf transformation 1]
33. (strong(alice) <~> ~old(alice)) | (old(fred) & patient(fred)) [ennf transformation 4]
35. ! [X0] : ((~tall(X0) & strong(X0)) | (~funny(X0) <=> ~patient(X0))) [ennf transformation 9]
40. ! [X0] : (((~old(X0) | rich(X0)) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (old(X0) & ~rich(X0)))) [nnf transformation 3]
41. ! [X0] : ((~old(X0) | rich(X0) | ((~funny(X0) | old(X0)) & (~old(X0) | funny(X0)))) & (((old(X0) | funny(X0)) & (~old(X0) | ~funny(X0))) | (old(X0) & ~rich(X0)))) [flattening 40]
42. ((old(alice) | ~strong(alice)) & (~old(alice) | strong(alice))) | (old(fred) & patient(fred)) [nnf transformation 33]
58. ! [X0] : ((~tall(X0) & strong(X0)) | ((~funny(X0) | patient(X0)) & (~patient(X0) | funny(X0)))) [nnf transformation 35]
59. ! [X0] : (((quiet(X0) & creative(X0)) | ~funny(X0)) & (funny(X0) | (~quiet(X0) | ~creative(X0)))) [nnf transformation 10]
60. ! [X0] : (((quiet(X0) & creative(X0)) | ~funny(X0)) & (funny(X0) | ~quiet(X0) | ~creative(X0))) [flattening 59]
68. ! [X0] : (((tall(X0) | quiet(X0)) | ~strong(X0)) & (strong(X0) | (~tall(X0) & ~quiet(X0)))) [nnf transformation 13]
69. ! [X0] : ((tall(X0) | quiet(X0) | ~strong(X0)) & (strong(X0) | (~tall(X0) & ~quiet(X0)))) [flattening 68]
70. (quiet(lucy) | ! [X0] : ~strong(X0)) & (? [X0] : strong(X0) | ~quiet(lucy)) [nnf transformation 14]
71. (quiet(lucy) | ! [X0] : ~strong(X0)) & (? [X1] : strong(X1) | ~quiet(lucy)) [rectify 70]
72. ? [X1] : strong(X1) => strong(sK6) [choice axiom]
73. (quiet(lucy) | ! [X0] : ~strong(X0)) & (strong(sK6) | ~quiet(lucy)) [skolemisation 71,72]
84. ~humble(X0) | ~strong(X0) [cnf transformation 30]
90. old(X0) | funny(X0) | old(X0) [cnf transformation 41]
93. ~old(alice) | strong(alice) | patient(fred) [cnf transformation 42]
109. ~patient(X0) | strong(X0) | funny(X0) [cnf transformation 58]
115. ~funny(X0) | quiet(X0) [cnf transformation 60]
122. ~quiet(X0) | strong(X0) [cnf transformation 69]
126. quiet(lucy) | ~strong(X0) [cnf transformation 73]
147. humble(lucy) [cnf transformation 24]
148. funny(X0) | old(X0) [duplicate literal removal 90]
155. 2 <=> strong(alice) [avatar definition]
156. strong(alice) <- (2) [avatar component clause 155]
157. ~strong(alice) <- (~2) [avatar component clause 155]
159. 3 <=> old(alice) [avatar definition]
160. ~old(alice) <- (~3) [avatar component clause 159]
164. 4 <=> patient(fred) [avatar definition]
166. patient(fred) <- (4) [avatar component clause 164]
169. 4 | 2 | ~3 [avatar split clause 93,159,155,164]
243. 21 <=> quiet(fred) [avatar definition]
244. quiet(fred) <- (21) [avatar component clause 243]
245. ~quiet(fred) <- (~21) [avatar component clause 243]
275. 28 <=> ! [X0] : ~strong(X0) [avatar definition]
276. ~strong(X0) <- (28) [avatar component clause 275]
278. 29 <=> quiet(lucy) [avatar definition]
280. quiet(lucy) <- (29) [avatar component clause 278]
281. 28 | 29 [avatar split clause 126,278,275]
352. ~strong(lucy) [resolution 84,147]
353. strong(fred) <- (21) [resolution 122,244]
354. $false <- (21, 28) [subsumption resolution 353,276]
355. ~21 | ~28 [avatar contradiction clause 354]
356. old(X0) | quiet(X0) [resolution 148,115]
371. quiet(alice) <- (~3) [resolution 356,160]
376. strong(lucy) <- (29) [resolution 280,122]
377. $false <- (29) [subsumption resolution 376,352]
378. ~29 [avatar contradiction clause 377]
382. strong(alice) <- (~3) [resolution 371,122]
383. $false <- (~2, ~3) [subsumption resolution 382,157]
384. 2 | 3 [avatar contradiction clause 383]
385. strong(fred) | funny(fred) <- (4) [resolution 109,166]
386. funny(fred) <- (4, 28) [subsumption resolution 385,276]
388. quiet(fred) <- (4, 28) [resolution 386,115]
391. $false <- (4, ~21, 28) [subsumption resolution 388,245]
392. ~4 | 21 | ~28 [avatar contradiction clause 391]
393. $false <- (2, 28) [subsumption resolution 156,276]
394. ~2 | ~28 [avatar contradiction clause 393]
395. $false [avatar sat refutation 169,281,355,378,384,392,394]
% SZS output end Proof for 3392920691589138597787540
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 happy or not quiet is both not happy and happy and vice versa. Everyone who is either kind or generous is either not wise or funny. Everyone who is either not funny or rich is humble or quiet. If alice is not creative then someone is funny and vice versa. Everyone who is humble or not wise is not quiet and vice versa. If lucy is not brave then lucy is not kind and vice versa. Everyone who is quiet is not generous. If susan is not happy then someone is generous or kind and vice versa. If john is either generous or strong then alice is not generous or not strong and vice versa. If paul is wise then alice is strong or humble. If susan is rich then someone is not tall and vice versa. If fred is both not brave and not calm then john is both not rich and generous. Everyone who is either happy or not calm is not kind or humble and vice versa. If john is not funny or generous then john is not quiet and vice versa. If susan is tall or humble then fred is tall. If paul is either funny or not creative then someone is not kind or not generous and vice versa. John is either not calm or humble. Someone is not wise or funny. Someone is not kind or not tall. Someone is not kind or not calm. John is either old or not generous. Lucy is quiet. | Susan is not strong. | neutral | (![X]:((happy(X)|~quiet(X))<=>(~happy(X)&happy(X))))&
(![X]:((kind(X)<~>generous(X))=>(~wise(X)<~>funny(X))))&
(![X]:((~funny(X)<~>rich(X))=>(humble(X)|quiet(X))))&
((~creative(alice))<=>(?[X]:(funny(X))))&
(![X]:((humble(X)|~wise(X))<=>~quiet(X)))&
((~brave(lucy))<=>(~kind(lucy)))&
(![X]:(quiet(X)=>~generous(X)))&
((~happy(susan))<=>(?[X]:((generous(X)|kind(X)))))&
(((generous(john)<~>strong(john)))<=>((~generous(alice)|~strong(alice))))&
((wise(paul))=>((strong(alice)|humble(alice))))&
((rich(susan))<=>(?[X]:(~tall(X))))&
(((~brave(fred)&~calm(fred)))=>((~rich(john)&generous(john))))&
(![X]:((happy(X)<~>~calm(X))<=>(~kind(X)|humble(X))))&
(((~funny(john)|generous(john)))<=>(~quiet(john)))&
(((tall(susan)|humble(susan)))=>(tall(fred)))&
(((funny(paul)<~>~creative(paul)))<=>(?[X]:((~kind(X)|~generous(X)))))&
((~calm(john)<~>humble(john)))&
(?[X]:((~wise(X)|funny(X))))&
(?[X]:((~kind(X)|~tall(X))))&
(?[X]:((~kind(X)|~calm(X))))&
((old(john)<~>~generous(john)))&
(quiet(lucy)) | ~strong(susan) | [] | null | 0 |
If lucy is not patient then lucy is both not funny and calm. If fred is tall or not generous then lucy is not brave and vice versa. Everyone who is funny or not tall is either not creative or generous and vice versa. If fred is wise then susan is either curious or not strong. Everyone who is both patient and strong is patient or tall. If someone is not rich then susan is either not humble or not happy. If someone is either not humble or not old then someone is calm. Everyone who is both curious and patient is humble and vice versa. If lucy is not calm or not tall then mary is either generous or not generous and vice versa. Everyone who is both not calm and old is not brave or wise and vice versa. If john is either kind or not creative then someone is both rich and old and vice versa. If someone is either tall or not calm then john is both not brave and funny and vice versa. If john is brave then someone is not patient or old and vice versa. If someone is either kind or not tall then someone is brave or not tall. If fred is both not wise and calm then paul is either kind or wise. Everyone who is either happy or not wise is both not funny and old and vice versa. Someone is not curious or brave. Someone is creative. John is both strong and not creative. Mary is generous or not humble. Alice is both old and curious. Susan is either rich or not curious. Fred is both not creative and not funny. Someone is either not wise or not funny. | Lucy is not tall. | contradiction | ((~patient(lucy))=>((~funny(lucy)&calm(lucy))))&
(((tall(fred)|~generous(fred)))<=>(~brave(lucy)))&
(![X]:((funny(X)|~tall(X))<=>(~creative(X)<~>generous(X))))&
((wise(fred))=>((curious(susan)<~>~strong(susan))))&
(![X]:((patient(X)&strong(X))=>(patient(X)|tall(X))))&
((?[X]:(~rich(X)))=>((~humble(susan)<~>~happy(susan))))&
((?[X]:((~humble(X)<~>~old(X))))=>(?[X]:(calm(X))))&
(![X]:((curious(X)&patient(X))<=>humble(X)))&
(((~calm(lucy)|~tall(lucy)))<=>((generous(mary)<~>~generous(mary))))&
(![X]:((~calm(X)&old(X))<=>(~brave(X)|wise(X))))&
(((kind(john)<~>~creative(john)))<=>(?[X]:((rich(X)&old(X)))))&
((?[X]:((tall(X)<~>~calm(X))))<=>((~brave(john)&funny(john))))&
((brave(john))<=>(?[X]:((~patient(X)|old(X)))))&
((?[X]:((kind(X)<~>~tall(X))))=>(?[X]:((brave(X)|~tall(X)))))&
(((~wise(fred)&calm(fred)))=>((kind(paul)<~>wise(paul))))&
(![X]:((happy(X)<~>~wise(X))<=>(~funny(X)&old(X))))&
(?[X]:((~curious(X)|brave(X))))&
(?[X]:(creative(X)))&
((strong(john)&~creative(john)))&
((generous(mary)|~humble(mary)))&
((old(alice)&curious(alice)))&
((rich(susan)<~>~curious(susan)))&
((~creative(fred)&~funny(fred)))&
(?[X]:((~wise(X)<~>~funny(X)))) | ~tall(lucy) | [
"p1",
"p2",
"p9",
"p11",
"p12",
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 4413189128032147638390767
% SZS output start Proof for 4413189128032147638390767
2. (~generous(fred) | tall(fred)) <=> ~brave(lucy) [input p1]
3. ! [X0] : ((~tall(X0) | funny(X0)) <=> (~creative(X0) <~> generous(X0))) [input p2]
10. ! [X0] : ((old(X0) & ~calm(X0)) <=> (wise(X0) | ~brave(X0))) [input p9]
12. ? [X0] : (tall(X0) <~> ~calm(X0)) <=> (funny(john) & ~brave(john)) [input p11]
13. brave(john) <=> ? [X0] : (old(X0) | ~patient(X0)) [input p12]
21. curious(alice) & old(alice) [input p20]
23. ~funny(fred) & ~creative(fred) [input p22]
25. ~tall(lucy) [input hypothesis]
37. ((~generous(fred) | tall(fred)) | brave(lucy)) & (~brave(lucy) | (generous(fred) & ~tall(fred))) [nnf transformation 2]
38. (~generous(fred) | tall(fred) | brave(lucy)) & (~brave(lucy) | (generous(fred) & ~tall(fred))) [flattening 37]
39. ! [X0] : (((~tall(X0) | funny(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (tall(X0) & ~funny(X0)))) [nnf transformation 3]
40. ! [X0] : ((~tall(X0) | funny(X0) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0)))) & (((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (tall(X0) & ~funny(X0)))) [flattening 39]
51. ! [X0] : (((old(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) & ((wise(X0) | ~brave(X0)) | (~old(X0) | calm(X0)))) [nnf transformation 10]
52. ! [X0] : (((old(X0) & ~calm(X0)) | (~wise(X0) & brave(X0))) & (wise(X0) | ~brave(X0) | ~old(X0) | calm(X0))) [flattening 51]
57. (? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | (~funny(john) | brave(john))) & ((funny(john) & ~brave(john)) | ! [X0] : ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0)))) [nnf transformation 12]
58. (? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ~funny(john) | brave(john)) & ((funny(john) & ~brave(john)) | ! [X0] : ((tall(X0) | calm(X0)) & (~calm(X0) | ~tall(X0)))) [flattening 57]
59. (? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) | ~funny(john) | brave(john)) & ((funny(john) & ~brave(john)) | ! [X1] : ((tall(X1) | calm(X1)) & (~calm(X1) | ~tall(X1)))) [rectify 58]
60. ? [X0] : ((calm(X0) | ~tall(X0)) & (~calm(X0) | tall(X0))) => ((calm(sK2) | ~tall(sK2)) & (~calm(sK2) | tall(sK2))) [choice axiom]
61. (((calm(sK2) | ~tall(sK2)) & (~calm(sK2) | tall(sK2))) | ~funny(john) | brave(john)) & ((funny(john) & ~brave(john)) | ! [X1] : ((tall(X1) | calm(X1)) & (~calm(X1) | ~tall(X1)))) [skolemisation 59,60]
62. (brave(john) | ! [X0] : (~old(X0) & patient(X0))) & (? [X0] : (old(X0) | ~patient(X0)) | ~brave(john)) [nnf transformation 13]
63. (brave(john) | ! [X0] : (~old(X0) & patient(X0))) & (? [X1] : (old(X1) | ~patient(X1)) | ~brave(john)) [rectify 62]
64. ? [X1] : (old(X1) | ~patient(X1)) => (old(sK3) | ~patient(sK3)) [choice axiom]
65. (brave(john) | ! [X0] : (~old(X0) & patient(X0))) & ((old(sK3) | ~patient(sK3)) | ~brave(john)) [skolemisation 63,64]
83. ~brave(lucy) | ~tall(fred) [cnf transformation 38]
84. ~brave(lucy) | generous(fred) [cnf transformation 38]
89. ~generous(X0) | creative(X0) | tall(X0) [cnf transformation 40]
109. ~calm(X0) | brave(X0) [cnf transformation 52]
120. ~brave(john) | tall(X1) | calm(X1) [cnf transformation 61]
127. brave(john) | ~old(X0) [cnf transformation 65]
143. old(alice) [cnf transformation 21]
147. ~creative(fred) [cnf transformation 23]
151. ~tall(lucy) [cnf transformation 25]
159. 2 <=> calm(lucy) [avatar definition]
160. ~calm(lucy) <- (~2) [avatar component clause 159]
161. calm(lucy) <- (2) [avatar component clause 159]
169. 4 <=> brave(lucy) [avatar definition]
170. ~brave(lucy) <- (~4) [avatar component clause 169]
173. 5 <=> tall(fred) [avatar definition]
174. ~tall(fred) <- (~5) [avatar component clause 173]
177. 6 <=> generous(fred) [avatar definition]
178. generous(fred) <- (6) [avatar component clause 177]
181. 6 | ~4 [avatar split clause 84,169,177]
182. ~5 | ~4 [avatar split clause 83,169,173]
227. 17 <=> tall(lucy) [avatar definition]
229. ~tall(lucy) <- (~17) [avatar component clause 227]
258. 23 <=> brave(john) [avatar definition]
276. 27 <=> ! [X1] : (tall(X1) | calm(X1)) [avatar definition]
277. tall(X1) | calm(X1) <- (27) [avatar component clause 276]
283. 27 | ~23 [avatar split clause 120,258,276]
286. 29 <=> ! [X0] : ~old(X0) [avatar definition]
287. ~old(X0) <- (29) [avatar component clause 286]
288. 29 | 23 [avatar split clause 127,258,286]
367. ~17 [avatar split clause 151,227]
373. brave(lucy) <- (2) [resolution 109,161]
375. $false <- (2, ~4) [subsumption resolution 373,170]
376. ~2 | 4 [avatar contradiction clause 375]
382. calm(lucy) <- (~17, 27) [resolution 277,229]
384. $false <- (~2, ~17, 27) [subsumption resolution 382,160]
385. 2 | 17 | ~27 [avatar contradiction clause 384]
386. $false <- (29) [resolution 287,143]
390. ~29 [avatar contradiction clause 386]
427. creative(fred) | tall(fred) <- (6) [resolution 89,178]
429. tall(fred) <- (6) [subsumption resolution 427,147]
430. $false <- (~5, 6) [subsumption resolution 429,174]
431. 5 | ~6 [avatar contradiction clause 430]
432. $false [avatar sat refutation 181,182,283,288,367,376,385,390,431]
% SZS output end Proof for 4413189128032147638390767
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not funny or funny is either not happy or generous and vice versa.
If someone is both not generous and calm then mary is quiet or happy.
If someone is either not rich or not funny then someone is not humble.
Everyone who is old or not quiet is humble and vice versa.
If someone is both not strong and wise then someone is wise and vice versa.
If paul is either humble or not tall then mary is not creative.
Everyone who is either creative or not humble is generous and vice versa.
If someone is brave or not old then someone is both wise and not wise and vice versa.
Everyone who is not kind is happy or funny.
Everyone who is both funny and old is both not curious and not calm and vice versa.
If someone is rich or funny then john is creative or not calm.
Everyone who is not old is not happy and vice versa.
Everyone who is quiet is both not humble and wise and vice versa.
Everyone who is either old or not wise is both not curious and not generous and vice versa.
Everyone who is either not kind or tall is not wise and vice versa.
Fred is either wise or happy.
Lucy is generous.
John is not humble or not brave.
Paul is wise or funny.
Someone is old or quiet. | John is not creative. | contradiction | (![X]:((~funny(X)|funny(X))<=>(~happy(X)<~>generous(X))))&
((?[X]:((~generous(X)&calm(X))))=>((quiet(mary)|happy(mary))))&
((?[X]:((~rich(X)<~>~funny(X))))=>(?[X]:(~humble(X))))&
(![X]:((old(X)|~quiet(X))<=>humble(X)))&
((?[X]:((~strong(X)&wise(X))))<=>(?[X]:(wise(X))))&
(((humble(paul)<~>~tall(paul)))=>(~creative(mary)))&
(![X]:((creative(X)<~>~humble(X))<=>generous(X)))&
((?[X]:((brave(X)|~old(X))))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~kind(X)=>(happy(X)|funny(X))))&
(![X]:((funny(X)&old(X))<=>(~curious(X)&~calm(X))))&
((?[X]:((rich(X)|funny(X))))=>((creative(john)|~calm(john))))&
(![X]:(~old(X)<=>~happy(X)))&
(![X]:(quiet(X)<=>(~humble(X)&wise(X))))&
(![X]:((old(X)<~>~wise(X))<=>(~curious(X)&~generous(X))))&
(![X]:((~kind(X)<~>tall(X))<=>~wise(X)))&
((wise(fred)<~>happy(fred)))&
(generous(lucy))&
((~humble(john)|~brave(john)))&
((wise(paul)|funny(paul)))&
(?[X]:((old(X)|quiet(X)))) | ~creative(john) | [
"p0",
"p3",
"p6",
"p7",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3432167592467379778894561
% SZS output start Proof for 3432167592467379778894561
1. ! [X0] : ((funny(X0) | ~funny(X0)) <=> (~happy(X0) <~> generous(X0))) [input p0]
4. ! [X0] : ((~quiet(X0) | old(X0)) <=> humble(X0)) [input p3]
7. ! [X0] : ((creative(X0) <~> ~humble(X0)) <=> generous(X0)) [input p6]
8. ? [X0] : (~old(X0) | brave(X0)) <=> ? [X0] : (~wise(X0) & wise(X0)) [input p7]
12. ! [X0] : (~old(X0) <=> ~happy(X0)) [input p11]
21. ~creative(john) [input hypothesis]
24. ? [X0] : (~old(X0) | brave(X0)) <=> ? [X1] : (~wise(X1) & wise(X1)) [rectify 8]
33. ! [X0] : (((funny(X0) | ~funny(X0)) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [nnf transformation 1]
34. ! [X0] : ((funny(X0) | ~funny(X0) | ((~happy(X0) | ~generous(X0)) & (generous(X0) | happy(X0)))) & (((~generous(X0) | happy(X0)) & (generous(X0) | ~happy(X0))) | (~funny(X0) & funny(X0)))) [flattening 33]
39. ! [X0] : (((~quiet(X0) | old(X0)) | ~humble(X0)) & (humble(X0) | (quiet(X0) & ~old(X0)))) [nnf transformation 4]
40. ! [X0] : ((~quiet(X0) | old(X0) | ~humble(X0)) & (humble(X0) | (quiet(X0) & ~old(X0)))) [flattening 39]
47. ! [X0] : ((((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ~generous(X0)) & (generous(X0) | ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0))))) [nnf transformation 7]
48. (? [X0] : (~old(X0) | brave(X0)) | ! [X1] : (wise(X1) | ~wise(X1))) & (? [X1] : (~wise(X1) & wise(X1)) | ! [X0] : (old(X0) & ~brave(X0))) [nnf transformation 24]
49. (? [X0] : (~old(X0) | brave(X0)) | ! [X1] : (wise(X1) | ~wise(X1))) & (? [X2] : (~wise(X2) & wise(X2)) | ! [X3] : (old(X3) & ~brave(X3))) [rectify 48]
50. ? [X0] : (~old(X0) | brave(X0)) => (~old(sK3) | brave(sK3)) [choice axiom]
51. ? [X2] : (~wise(X2) & wise(X2)) => (~wise(sK4) & wise(sK4)) [choice axiom]
52. ((~old(sK3) | brave(sK3)) | ! [X1] : (wise(X1) | ~wise(X1))) & ((~wise(sK4) & wise(sK4)) | ! [X3] : (old(X3) & ~brave(X3))) [skolemisation 49,51,50]
55. ! [X0] : ((~old(X0) | happy(X0)) & (~happy(X0) | old(X0))) [nnf transformation 12]
64. generous(X0) | ~happy(X0) | funny(X0) [cnf transformation 34]
65. ~happy(X0) | generous(X0) | ~funny(X0) [cnf transformation 34]
73. ~old(X0) | humble(X0) [cnf transformation 40]
83. ~humble(X0) | creative(X0) | ~generous(X0) [cnf transformation 47]
86. wise(sK4) | old(X3) [cnf transformation 52]
88. ~wise(sK4) | old(X3) [cnf transformation 52]
98. ~old(X0) | happy(X0) [cnf transformation 55]
118. ~creative(john) [cnf transformation 21]
120. ~happy(X0) | generous(X0) [subsumption resolution 64,65]
181. 15 <=> ! [X3] : old(X3) [avatar definition]
182. old(X3) <- (15) [avatar component clause 181]
184. 16 <=> wise(sK4) [avatar definition]
187. 15 | ~16 [avatar split clause 88,184,181]
192. 15 | 16 [avatar split clause 86,184,181]
198. 19 <=> creative(john) [avatar definition]
199. ~creative(john) <- (~19) [avatar component clause 198]
247. ~19 [avatar split clause 118,198]
252. humble(X0) <- (15) [resolution 73,182]
258. happy(X0) <- (15) [resolution 98,182]
265. generous(X0) <- (15) [resolution 120,258]
283. creative(X0) | ~generous(X0) <- (15) [resolution 83,252]
285. creative(X0) <- (15) [subsumption resolution 283,265]
287. $false <- (15, ~19) [resolution 285,199]
289. ~15 | 19 [avatar contradiction clause 287]
291. $false [avatar sat refutation 187,192,247,289]
% SZS output end Proof for 3432167592467379778894561
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not tall or not calm is not quiet or humble.
Everyone who is not strong or kind is both calm and not kind and vice versa.
Everyone who is both not calm and calm is either not quiet or not creative and vice versa.
If mary is both not strong and not funny then lucy is either wise or rich and vice versa.
If mary is both calm and not brave then paul is either not quiet or patient and vice versa.
If fred is both not humble and calm then someone is not brave or not kind and vice versa.
Everyone who is both happy and not quiet is either not brave or not humble and vice versa.
Everyone who is both not brave and creative is not kind or not generous and vice versa.
If someone is both curious and not kind then paul is either not creative or not brave.
If alice is both not humble and rich then someone is tall.
If john is either not rich or not generous then john is not happy or not funny.
If someone is both not happy and tall then paul is either not happy or happy.
Everyone who is both curious and old is both happy and not curious and vice versa.
If paul is both not calm and curious then lucy is either not old or not rich.
Everyone who is not old is either not patient or not calm.
If paul is both patient and strong then someone is funny and vice versa.
Lucy is not rich or kind.
Mary is patient or happy.
Fred is either brave or patient.
Lucy is not humble or calm.
Someone is tall.
Susan is either calm or humble. | Susan is calm. | entailment | (![X]:((~tall(X)|~calm(X))=>(~quiet(X)|humble(X))))&
(![X]:((~strong(X)|kind(X))<=>(calm(X)&~kind(X))))&
(![X]:((~calm(X)&calm(X))<=>(~quiet(X)<~>~creative(X))))&
(((~strong(mary)&~funny(mary)))<=>((wise(lucy)<~>rich(lucy))))&
(((calm(mary)&~brave(mary)))<=>((~quiet(paul)<~>patient(paul))))&
(((~humble(fred)&calm(fred)))<=>(?[X]:((~brave(X)|~kind(X)))))&
(![X]:((happy(X)&~quiet(X))<=>(~brave(X)<~>~humble(X))))&
(![X]:((~brave(X)&creative(X))<=>(~kind(X)|~generous(X))))&
((?[X]:((curious(X)&~kind(X))))=>((~creative(paul)<~>~brave(paul))))&
(((~humble(alice)&rich(alice)))=>(?[X]:(tall(X))))&
(((~rich(john)<~>~generous(john)))=>((~happy(john)|~funny(john))))&
((?[X]:((~happy(X)&tall(X))))=>((~happy(paul)<~>happy(paul))))&
(![X]:((curious(X)&old(X))<=>(happy(X)&~curious(X))))&
(((~calm(paul)&curious(paul)))=>((~old(lucy)<~>~rich(lucy))))&
(![X]:(~old(X)=>(~patient(X)<~>~calm(X))))&
(((patient(paul)&strong(paul)))<=>(?[X]:(funny(X))))&
((~rich(lucy)|kind(lucy)))&
((patient(mary)|happy(mary)))&
((brave(fred)<~>patient(fred)))&
((~humble(lucy)|calm(lucy)))&
(?[X]:(tall(X)))&
((calm(susan)<~>humble(susan))) | calm(susan) | [
"p1",
"p2",
"p6",
"p7",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2610309513778754054548752
% SZS output start Proof for 2610309513778754054548752
2. ! [X0] : ((kind(X0) | ~strong(X0)) <=> (~kind(X0) & calm(X0))) [input p1]
3. ! [X0] : ((calm(X0) & ~calm(X0)) <=> (~quiet(X0) <~> ~creative(X0))) [input p2]
7. ! [X0] : ((~quiet(X0) & happy(X0)) <=> (~brave(X0) <~> ~humble(X0))) [input p6]
8. ! [X0] : ((creative(X0) & ~brave(X0)) <=> (~generous(X0) | ~kind(X0))) [input p7]
22. calm(susan) <~> humble(susan) [input p21]
23. ~calm(susan) [input hypothesis]
35. ! [X0] : (((kind(X0) | ~strong(X0)) | (kind(X0) | ~calm(X0))) & ((~kind(X0) & calm(X0)) | (~kind(X0) & strong(X0)))) [nnf transformation 2]
36. ! [X0] : ((kind(X0) | ~strong(X0) | kind(X0) | ~calm(X0)) & ((~kind(X0) & calm(X0)) | (~kind(X0) & strong(X0)))) [flattening 35]
37. ! [X0] : (((calm(X0) & ~calm(X0)) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | (~calm(X0) | calm(X0)))) [nnf transformation 3]
38. ! [X0] : (((calm(X0) & ~calm(X0)) | ((~quiet(X0) | creative(X0)) & (~creative(X0) | quiet(X0)))) & (((creative(X0) | quiet(X0)) & (~creative(X0) | ~quiet(X0))) | ~calm(X0) | calm(X0))) [flattening 37]
48. ! [X0] : (((~quiet(X0) & happy(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | (quiet(X0) | ~happy(X0)))) [nnf transformation 7]
49. ! [X0] : (((~quiet(X0) & happy(X0)) | ((~brave(X0) | humble(X0)) & (~humble(X0) | brave(X0)))) & (((humble(X0) | brave(X0)) & (~humble(X0) | ~brave(X0))) | quiet(X0) | ~happy(X0))) [flattening 48]
50. ! [X0] : (((creative(X0) & ~brave(X0)) | (generous(X0) & kind(X0))) & ((~generous(X0) | ~kind(X0)) | (~creative(X0) | brave(X0)))) [nnf transformation 8]
51. ! [X0] : (((creative(X0) & ~brave(X0)) | (generous(X0) & kind(X0))) & (~generous(X0) | ~kind(X0) | ~creative(X0) | brave(X0))) [flattening 50]
69. (~humble(susan) | ~calm(susan)) & (humble(susan) | calm(susan)) [nnf transformation 22]
75. ~kind(X0) | ~kind(X0) [cnf transformation 36]
79. ~calm(X0) | ~creative(X0) | quiet(X0) [cnf transformation 38]
81. ~creative(X0) | calm(X0) | quiet(X0) [cnf transformation 38]
104. ~humble(X0) | ~quiet(X0) | brave(X0) [cnf transformation 49]
107. ~brave(X0) | kind(X0) [cnf transformation 51]
109. creative(X0) | kind(X0) [cnf transformation 51]
135. humble(susan) | calm(susan) [cnf transformation 69]
137. ~calm(susan) [cnf transformation 23]
140. ~kind(X0) [duplicate literal removal 75]
143. ~creative(X0) | quiet(X0) [subsumption resolution 79,81]
190. creative(X0) [subsumption resolution 109,140]
191. ~brave(X0) [subsumption resolution 107,140]
273. 26 <=> calm(susan) [avatar definition]
277. 27 <=> humble(susan) [avatar definition]
278. humble(susan) <- (27) [avatar component clause 277]
281. 26 | 27 [avatar split clause 135,277,273]
282. ~26 [avatar split clause 137,273]
285. quiet(X0) [resolution 143,190]
305. ~quiet(susan) | brave(susan) <- (27) [resolution 104,278]
308. brave(susan) <- (27) [subsumption resolution 305,285]
309. $false <- (27) [subsumption resolution 308,191]
310. ~27 [avatar contradiction clause 309]
315. $false [avatar sat refutation 281,282,310]
% SZS output end Proof for 2610309513778754054548752
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 fred is both patient and calm then someone is brave or quiet and vice versa.
Everyone who is either not humble or not happy is both calm and not tall and vice versa.
Everyone who is either not rich or not funny is both generous and not creative.
Everyone who is both curious and not tall is quiet.
If fred is both not rich and creative then someone is both not calm and not wise.
Everyone who is either wise or patient is curious or patient.
Everyone who is wise or generous is both tall and not funny and vice versa.
Everyone who is not wise is not brave or not old and vice versa.
Everyone who is not curious is generous or not creative.
If someone is both not rich and not kind then fred is both not curious and funny and vice versa.
Everyone who is not happy or curious is not kind.
Everyone who is funny is either not tall or not old.
Everyone who is not patient is not wise or generous and vice versa.
If paul is either calm or quiet then paul is strong or quiet and vice versa.
Everyone who is not brave is either quiet or not generous and vice versa.
If someone is not creative or patient then someone is generous.
Someone is either not generous or brave.
John is old or not brave.
Lucy is either quiet or not rich.
Someone is either kind or brave.
Someone is not generous.
Lucy is curious. | John is humble. | neutral | (((patient(fred)&calm(fred)))<=>(?[X]:((brave(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~happy(X))<=>(calm(X)&~tall(X))))&
(![X]:((~rich(X)<~>~funny(X))=>(generous(X)&~creative(X))))&
(![X]:((curious(X)&~tall(X))=>quiet(X)))&
(((~rich(fred)&creative(fred)))=>(?[X]:((~calm(X)&~wise(X)))))&
(![X]:((wise(X)<~>patient(X))=>(curious(X)|patient(X))))&
(![X]:((wise(X)|generous(X))<=>(tall(X)&~funny(X))))&
(![X]:(~wise(X)<=>(~brave(X)|~old(X))))&
(![X]:(~curious(X)=>(generous(X)|~creative(X))))&
((?[X]:((~rich(X)&~kind(X))))<=>((~curious(fred)&funny(fred))))&
(![X]:((~happy(X)|curious(X))=>~kind(X)))&
(![X]:(funny(X)=>(~tall(X)<~>~old(X))))&
(![X]:(~patient(X)<=>(~wise(X)|generous(X))))&
(((calm(paul)<~>quiet(paul)))<=>((strong(paul)|quiet(paul))))&
(![X]:(~brave(X)<=>(quiet(X)<~>~generous(X))))&
((?[X]:((~creative(X)|patient(X))))=>(?[X]:(generous(X))))&
(?[X]:((~generous(X)<~>brave(X))))&
((old(john)|~brave(john)))&
((quiet(lucy)<~>~rich(lucy)))&
(?[X]:((kind(X)<~>brave(X))))&
(?[X]:(~generous(X)))&
(curious(lucy)) | humble(john) | [] | null | 0 |
If someone is both generous and quiet then susan is not curious or brave.
Everyone who is not kind is both tall and not strong and vice versa.
Everyone who is both not creative and brave is either calm or not tall.
Everyone who is not creative or not quiet is not kind or curious and vice versa.
If susan is brave or curious then someone is not kind and vice versa.
Everyone who is patient is both not humble and not curious.
Everyone who is both wise and not strong is not happy and vice versa.
Everyone who is not rich is either funny or creative and vice versa.
If someone is old or not creative then mary is both old and humble.
Everyone who is both calm and not humble is creative.
Everyone who is calm is not brave.
Everyone who is both generous and kind is not generous and vice versa.
Everyone who is curious or kind is both brave and not wise.
Everyone who is both not quiet and not humble is either not creative or not brave and vice versa.
Everyone who is not funny is both patient and rich and vice versa.
Mary is not wise.
Someone is both tall and not patient.
Alice is wise or tall.
Someone is both not brave and humble.
Someone is either not tall or wise.
Someone is not kind or old. | Alice is not happy. | neutral | ((?[X]:((generous(X)&quiet(X))))=>((~curious(susan)|brave(susan))))&
(![X]:(~kind(X)<=>(tall(X)&~strong(X))))&
(![X]:((~creative(X)&brave(X))=>(calm(X)<~>~tall(X))))&
(![X]:((~creative(X)|~quiet(X))<=>(~kind(X)|curious(X))))&
(((brave(susan)|curious(susan)))<=>(?[X]:(~kind(X))))&
(![X]:(patient(X)=>(~humble(X)&~curious(X))))&
(![X]:((wise(X)&~strong(X))<=>~happy(X)))&
(![X]:(~rich(X)<=>(funny(X)<~>creative(X))))&
((?[X]:((old(X)|~creative(X))))=>((old(mary)&humble(mary))))&
(![X]:((calm(X)&~humble(X))=>creative(X)))&
(![X]:(calm(X)=>~brave(X)))&
(![X]:((generous(X)&kind(X))<=>~generous(X)))&
(![X]:((curious(X)|kind(X))=>(brave(X)&~wise(X))))&
(![X]:((~quiet(X)&~humble(X))<=>(~creative(X)<~>~brave(X))))&
(![X]:(~funny(X)<=>(patient(X)&rich(X))))&
(~wise(mary))&
(?[X]:((tall(X)&~patient(X))))&
((wise(alice)|tall(alice)))&
(?[X]:((~brave(X)&humble(X))))&
(?[X]:((~tall(X)<~>wise(X))))&
(?[X]:((~kind(X)|old(X)))) | ~happy(alice) | [] | null | 0 |
If fred is humble or rich then lucy is either not creative or wise and vice versa.
If mary is happy or not humble then mary is either curious or not rich and vice versa.
If mary is both not tall and strong then fred is funny or not quiet.
If john is both not curious and tall then someone is not tall.
Everyone who is both not humble and kind is both funny and quiet and vice versa.
Everyone who is calm is both creative and not humble and vice versa.
If someone is rich or humble then lucy is wise or not kind.
Everyone who is both not creative and not happy is not kind.
If someone is not brave or not happy then john is not patient.
Everyone who is not kind is both happy and not curious and vice versa.
Everyone who is brave or kind is either quiet or not generous.
If someone is not rich then someone is both curious and not calm and vice versa.
Everyone who is both not calm and not rich is wise or not patient.
If john is both quiet and generous then susan is strong or not rich.
Everyone who is either not happy or not creative is quiet and vice versa.
If mary is happy or tall then alice is either not quiet or not funny and vice versa.
John is calm.
Someone is both not strong and not funny.
Someone is not quiet or funny.
Alice is both not happy and generous.
Paul is both curious and brave.
Someone is both not tall and old.
Someone is both humble and generous. | John is kind. | neutral | (((humble(fred)|rich(fred)))<=>((~creative(lucy)<~>wise(lucy))))&
(((happy(mary)|~humble(mary)))<=>((curious(mary)<~>~rich(mary))))&
(((~tall(mary)&strong(mary)))=>((funny(fred)|~quiet(fred))))&
(((~curious(john)&tall(john)))=>(?[X]:(~tall(X))))&
(![X]:((~humble(X)&kind(X))<=>(funny(X)&quiet(X))))&
(![X]:(calm(X)<=>(creative(X)&~humble(X))))&
((?[X]:((rich(X)|humble(X))))=>((wise(lucy)|~kind(lucy))))&
(![X]:((~creative(X)&~happy(X))=>~kind(X)))&
((?[X]:((~brave(X)|~happy(X))))=>(~patient(john)))&
(![X]:(~kind(X)<=>(happy(X)&~curious(X))))&
(![X]:((brave(X)|kind(X))=>(quiet(X)<~>~generous(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((curious(X)&~calm(X)))))&
(![X]:((~calm(X)&~rich(X))=>(wise(X)|~patient(X))))&
(((quiet(john)&generous(john)))=>((strong(susan)|~rich(susan))))&
(![X]:((~happy(X)<~>~creative(X))<=>quiet(X)))&
(((happy(mary)|tall(mary)))<=>((~quiet(alice)<~>~funny(alice))))&
(calm(john))&
(?[X]:((~strong(X)&~funny(X))))&
(?[X]:((~quiet(X)|funny(X))))&
((~happy(alice)&generous(alice)))&
((curious(paul)&brave(paul)))&
(?[X]:((~tall(X)&old(X))))&
(?[X]:((humble(X)&generous(X)))) | kind(john) | [] | null | 0 |
If alice is not rich or not quiet then fred is generous or strong and vice versa.
If mary is not brave or not patient then lucy is both not calm and not funny and vice versa.
If susan is both patient and calm then someone is both old and curious and vice versa.
Everyone who is both not strong and creative is not humble or patient and vice versa.
If john is both creative and not calm then lucy is either calm or not rich and vice versa.
If someone is happy or not curious then alice is tall.
If susan is not happy then someone is strong or generous and vice versa.
If john is generous then someone is both curious and not brave and vice versa.
If john is either not happy or kind then someone is both not kind and not brave.
If someone is strong then someone is either not quiet or not brave and vice versa.
If someone is both tall and creative then paul is both not funny and brave and vice versa.
Everyone who is creative or tall is both not curious and brave and vice versa.
Everyone who is not funny is both not old and not curious and vice versa.
If lucy is humble then mary is curious or old and vice versa.
If lucy is both not generous and not tall then susan is not kind or humble.
Everyone who is not rich or tall is both calm and not creative.
Mary is both not funny and not happy.
Someone is either curious or patient.
Someone is humble or brave.
Someone is not kind or humble.
Someone is kind or quiet.
Someone is either kind or strong.
Fred is kind.
Lucy is kind or patient. | Lucy is tall. | contradiction | (((~rich(alice)|~quiet(alice)))<=>((generous(fred)|strong(fred))))&
(((~brave(mary)|~patient(mary)))<=>((~calm(lucy)&~funny(lucy))))&
(((patient(susan)&calm(susan)))<=>(?[X]:((old(X)&curious(X)))))&
(![X]:((~strong(X)&creative(X))<=>(~humble(X)|patient(X))))&
(((creative(john)&~calm(john)))<=>((calm(lucy)<~>~rich(lucy))))&
((?[X]:((happy(X)|~curious(X))))=>(tall(alice)))&
((~happy(susan))<=>(?[X]:((strong(X)|generous(X)))))&
((generous(john))<=>(?[X]:((curious(X)&~brave(X)))))&
(((~happy(john)<~>kind(john)))=>(?[X]:((~kind(X)&~brave(X)))))&
((?[X]:(strong(X)))<=>(?[X]:((~quiet(X)<~>~brave(X)))))&
((?[X]:((tall(X)&creative(X))))<=>((~funny(paul)&brave(paul))))&
(![X]:((creative(X)|tall(X))<=>(~curious(X)&brave(X))))&
(![X]:(~funny(X)<=>(~old(X)&~curious(X))))&
((humble(lucy))<=>((curious(mary)|old(mary))))&
(((~generous(lucy)&~tall(lucy)))=>((~kind(susan)|humble(susan))))&
(![X]:((~rich(X)|tall(X))=>(calm(X)&~creative(X))))&
((~funny(mary)&~happy(mary)))&
(?[X]:((curious(X)<~>patient(X))))&
(?[X]:((humble(X)|brave(X))))&
(?[X]:((~kind(X)|humble(X))))&
(?[X]:((kind(X)|quiet(X))))&
(?[X]:((kind(X)<~>strong(X))))&
(kind(fred))&
((kind(lucy)|patient(lucy))) | tall(lucy) | [
"p1",
"p3",
"p11",
"p12",
"p13",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 2425920601223453854426028
% SZS output start Proof for 2425920601223453854426028
2. (~patient(mary) | ~brave(mary)) <=> (~funny(lucy) & ~calm(lucy)) [input p1]
4. ! [X0] : ((creative(X0) & ~strong(X0)) <=> (patient(X0) | ~humble(X0))) [input p3]
12. ! [X0] : ((tall(X0) | creative(X0)) <=> (brave(X0) & ~curious(X0))) [input p11]
13. ! [X0] : (~funny(X0) <=> (~curious(X0) & ~old(X0))) [input p12]
14. humble(lucy) <=> (old(mary) | curious(mary)) [input p13]
16. ! [X0] : ((tall(X0) | ~rich(X0)) => (~creative(X0) & calm(X0))) [input p15]
17. ~happy(mary) & ~funny(mary) [input p16]
25. tall(lucy) [input hypothesis]
31. ! [X0] : ((~creative(X0) & calm(X0)) | (~tall(X0) & rich(X0))) [ennf transformation 16]
34. ((~patient(mary) | ~brave(mary)) | (funny(lucy) | calm(lucy))) & ((~funny(lucy) & ~calm(lucy)) | (patient(mary) & brave(mary))) [nnf transformation 2]
35. (~patient(mary) | ~brave(mary) | funny(lucy) | calm(lucy)) & ((~funny(lucy) & ~calm(lucy)) | (patient(mary) & brave(mary))) [flattening 34]
41. ! [X0] : (((creative(X0) & ~strong(X0)) | (~patient(X0) & humble(X0))) & ((patient(X0) | ~humble(X0)) | (~creative(X0) | strong(X0)))) [nnf transformation 4]
42. ! [X0] : (((creative(X0) & ~strong(X0)) | (~patient(X0) & humble(X0))) & (patient(X0) | ~humble(X0) | ~creative(X0) | strong(X0))) [flattening 41]
66. ! [X0] : (((tall(X0) | creative(X0)) | (~brave(X0) | curious(X0))) & ((brave(X0) & ~curious(X0)) | (~tall(X0) & ~creative(X0)))) [nnf transformation 12]
67. ! [X0] : ((tall(X0) | creative(X0) | ~brave(X0) | curious(X0)) & ((brave(X0) & ~curious(X0)) | (~tall(X0) & ~creative(X0)))) [flattening 66]
68. ! [X0] : ((~funny(X0) | (curious(X0) | old(X0))) & ((~curious(X0) & ~old(X0)) | funny(X0))) [nnf transformation 13]
69. ! [X0] : ((~funny(X0) | curious(X0) | old(X0)) & ((~curious(X0) & ~old(X0)) | funny(X0))) [flattening 68]
70. (humble(lucy) | (~old(mary) & ~curious(mary))) & ((old(mary) | curious(mary)) | ~humble(lucy)) [nnf transformation 14]
71. (humble(lucy) | (~old(mary) & ~curious(mary))) & (old(mary) | curious(mary) | ~humble(lucy)) [flattening 70]
89. ~calm(lucy) | patient(mary) [cnf transformation 35]
100. humble(X0) | creative(X0) [cnf transformation 42]
101. ~patient(X0) | creative(X0) [cnf transformation 42]
128. ~creative(X0) | ~curious(X0) [cnf transformation 67]
133. ~old(X0) | funny(X0) [cnf transformation 69]
136. old(mary) | curious(mary) | ~humble(lucy) [cnf transformation 71]
141. ~tall(X0) | calm(X0) [cnf transformation 31]
143. ~creative(X0) | ~tall(X0) [cnf transformation 31]
144. ~funny(mary) [cnf transformation 17]
155. tall(lucy) [cnf transformation 25]
177. 5 <=> calm(lucy) [avatar definition]
189. 8 <=> patient(mary) [avatar definition]
190. patient(mary) <- (8) [avatar component clause 189]
195. 8 | ~5 [avatar split clause 89,177,189]
350. 42 <=> ! [X1] : (~creative(X1) | ~tall(X1)) [avatar definition]
351. ~tall(X1) | ~creative(X1) <- (42) [avatar component clause 350]
355. 43 <=> old(mary) [avatar definition]
356. old(mary) <- (43) [avatar component clause 355]
359. 44 <=> humble(lucy) [avatar definition]
360. ~humble(lucy) <- (~44) [avatar component clause 359]
364. 45 <=> curious(mary) [avatar definition]
368. ~44 | 45 | 43 [avatar split clause 136,355,364,359]
374. 47 <=> tall(lucy) [avatar definition]
376. tall(lucy) <- (47) [avatar component clause 374]
386. 42 [avatar split clause 143,350]
443. 47 [avatar split clause 155,374]
447. creative(lucy) <- (~44) [resolution 100,360]
448. creative(mary) <- (8) [resolution 101,190]
450. ~curious(mary) <- (8) [resolution 128,448]
460. calm(lucy) <- (47) [resolution 141,376]
465. 5 | ~47 [avatar split clause 460,374,177]
479. ~creative(lucy) <- (42, 47) [resolution 351,376]
480. $false <- (42, ~44, 47) [subsumption resolution 479,447]
481. ~42 | 44 | ~47 [avatar contradiction clause 480]
482. funny(mary) <- (43) [resolution 356,133]
483. $false <- (43) [subsumption resolution 482,144]
484. ~43 [avatar contradiction clause 483]
485. ~45 | ~8 [avatar split clause 450,189,364]
486. $false [avatar sat refutation 195,368,386,443,465,481,484,485]
% SZS output end Proof for 2425920601223453854426028
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 mary is both not quiet and not rich then someone is either not happy or not generous and vice versa.
Everyone who is calm is both not happy and rich.
If fred is tall or not tall then someone is either not generous or quiet.
Everyone who is tall or not rich is calm or not kind and vice versa.
Everyone who is either not tall or patient is not happy and vice versa.
Everyone who is not old or tall is funny.
If susan is either not strong or strong then someone is both not patient and not curious and vice versa.
Everyone who is either not happy or not curious is either not wise or calm.
If paul is not creative or old then fred is not rich or not humble.
Everyone who is happy is quiet or not kind and vice versa.
If someone is either curious or creative then someone is both kind and generous.
If someone is not patient then susan is both patient and old.
If susan is either creative or funny then mary is not wise.
If someone is brave or funny then fred is strong or old.
If someone is both quiet and not calm then someone is either not rich or not happy and vice versa.
Everyone who is both happy and not tall is either not kind or patient.
Fred is both happy and not rich.
Someone is both rich and generous.
Someone is rich.
Susan is not curious.
Mary is not tall or rich.
Mary is both brave and not patient.
Lucy is both humble and kind.
Someone is both brave and happy. | Susan is rich. | entailment | (((~quiet(mary)&~rich(mary)))<=>(?[X]:((~happy(X)<~>~generous(X)))))&
(![X]:(calm(X)=>(~happy(X)&rich(X))))&
(((tall(fred)|~tall(fred)))=>(?[X]:((~generous(X)<~>quiet(X)))))&
(![X]:((tall(X)|~rich(X))<=>(calm(X)|~kind(X))))&
(![X]:((~tall(X)<~>patient(X))<=>~happy(X)))&
(![X]:((~old(X)|tall(X))=>funny(X)))&
(((~strong(susan)<~>strong(susan)))<=>(?[X]:((~patient(X)&~curious(X)))))&
(![X]:((~happy(X)<~>~curious(X))=>(~wise(X)<~>calm(X))))&
(((~creative(paul)|old(paul)))=>((~rich(fred)|~humble(fred))))&
(![X]:(happy(X)<=>(quiet(X)|~kind(X))))&
((?[X]:((curious(X)<~>creative(X))))=>(?[X]:((kind(X)&generous(X)))))&
((?[X]:(~patient(X)))=>((patient(susan)&old(susan))))&
(((creative(susan)<~>funny(susan)))=>(~wise(mary)))&
((?[X]:((brave(X)|funny(X))))=>((strong(fred)|old(fred))))&
((?[X]:((quiet(X)&~calm(X))))<=>(?[X]:((~rich(X)<~>~happy(X)))))&
(![X]:((happy(X)&~tall(X))=>(~kind(X)<~>patient(X))))&
((happy(fred)&~rich(fred)))&
(?[X]:((rich(X)&generous(X))))&
(?[X]:(rich(X)))&
(~curious(susan))&
((~tall(mary)|rich(mary)))&
((brave(mary)&~patient(mary)))&
((humble(lucy)&kind(lucy)))&
(?[X]:((brave(X)&happy(X)))) | rich(susan) | [
"p1",
"p3",
"p4",
"p6",
"p9",
"p11",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 9208738984523703922720219
% SZS output start Proof for 9208738984523703922720219
2. ! [X0] : (calm(X0) => (rich(X0) & ~happy(X0))) [input p1]
4. ! [X0] : ((~rich(X0) | tall(X0)) <=> (~kind(X0) | calm(X0))) [input p3]
5. ! [X0] : ((~tall(X0) <~> patient(X0)) <=> ~happy(X0)) [input p4]
7. (~strong(susan) <~> strong(susan)) <=> ? [X0] : (~curious(X0) & ~patient(X0)) [input p6]
10. ! [X0] : (happy(X0) <=> (~kind(X0) | quiet(X0))) [input p9]
12. ? [X0] : ~patient(X0) => (old(susan) & patient(susan)) [input p11]
16. ! [X0] : ((~tall(X0) & happy(X0)) => (~kind(X0) <~> patient(X0))) [input p15]
25. ~rich(susan) [input hypothesis]
28. ! [X0] : ((rich(X0) & ~happy(X0)) | ~calm(X0)) [ennf transformation 2]
35. (old(susan) & patient(susan)) | ! [X0] : patient(X0) [ennf transformation 12]
39. ! [X0] : ((~kind(X0) <~> patient(X0)) | (tall(X0) | ~happy(X0))) [ennf transformation 16]
40. ! [X0] : ((~kind(X0) <~> patient(X0)) | tall(X0) | ~happy(X0)) [flattening 39]
49. ! [X0] : (((~rich(X0) | tall(X0)) | (kind(X0) & ~calm(X0))) & ((~kind(X0) | calm(X0)) | (rich(X0) & ~tall(X0)))) [nnf transformation 4]
50. ! [X0] : ((~rich(X0) | tall(X0) | (kind(X0) & ~calm(X0))) & (~kind(X0) | calm(X0) | (rich(X0) & ~tall(X0)))) [flattening 49]
51. ! [X0] : ((((~patient(X0) | tall(X0)) & (patient(X0) | ~tall(X0))) | happy(X0)) & (~happy(X0) | ((~tall(X0) | ~patient(X0)) & (patient(X0) | tall(X0))))) [nnf transformation 5]
52. (((~strong(susan) | strong(susan)) & (strong(susan) | ~strong(susan))) | ! [X0] : (curious(X0) | patient(X0))) & (? [X0] : (~curious(X0) & ~patient(X0)) | ((~strong(susan) | ~strong(susan)) & (strong(susan) | strong(susan)))) [nnf transformation 7]
53. (((~strong(susan) | strong(susan)) & (strong(susan) | ~strong(susan))) | ! [X0] : (curious(X0) | patient(X0))) & (? [X1] : (~curious(X1) & ~patient(X1)) | ((~strong(susan) | ~strong(susan)) & (strong(susan) | strong(susan)))) [rectify 52]
54. ? [X1] : (~curious(X1) & ~patient(X1)) => (~curious(sK2) & ~patient(sK2)) [choice axiom]
55. (((~strong(susan) | strong(susan)) & (strong(susan) | ~strong(susan))) | ! [X0] : (curious(X0) | patient(X0))) & ((~curious(sK2) & ~patient(sK2)) | ((~strong(susan) | ~strong(susan)) & (strong(susan) | strong(susan)))) [skolemisation 53,54]
57. ! [X0] : ((happy(X0) | (kind(X0) & ~quiet(X0))) & ((~kind(X0) | quiet(X0)) | ~happy(X0))) [nnf transformation 10]
58. ! [X0] : ((happy(X0) | (kind(X0) & ~quiet(X0))) & (~kind(X0) | quiet(X0) | ~happy(X0))) [flattening 57]
69. ! [X0] : (((~patient(X0) | kind(X0)) & (patient(X0) | ~kind(X0))) | tall(X0) | ~happy(X0)) [nnf transformation 40]
83. ~calm(X0) | rich(X0) [cnf transformation 28]
89. ~kind(X0) | calm(X0) | rich(X0) [cnf transformation 50]
93. ~patient(X0) | ~tall(X0) | ~happy(X0) [cnf transformation 51]
98. ~patient(sK2) | strong(susan) | strong(susan) [cnf transformation 55]
99. ~patient(sK2) | ~strong(susan) | ~strong(susan) [cnf transformation 55]
112. kind(X0) | happy(X0) [cnf transformation 58]
117. patient(susan) | patient(X0) [cnf transformation 35]
130. ~patient(X0) | kind(X0) | tall(X0) | ~happy(X0) [cnf transformation 69]
144. ~rich(susan) [cnf transformation 25]
145. ~patient(sK2) | strong(susan) [duplicate literal removal 98]
146. ~patient(sK2) | ~strong(susan) [duplicate literal removal 99]
194. ~kind(X0) | rich(X0) [subsumption resolution 89,83]
196. 10 <=> strong(susan) [avatar definition]
206. 12 <=> patient(sK2) [avatar definition]
208. ~patient(sK2) <- (~12) [avatar component clause 206]
209. ~10 | ~12 [avatar split clause 146,206,196]
210. 10 | ~12 [avatar split clause 145,206,196]
250. 21 <=> ! [X0] : patient(X0) [avatar definition]
251. patient(X0) <- (21) [avatar component clause 250]
258. 23 <=> patient(susan) [avatar definition]
260. patient(susan) <- (23) [avatar component clause 258]
261. 21 | 23 [avatar split clause 117,258,250]
323. ~patient(X0) | kind(X0) | tall(X0) [subsumption resolution 130,112]
330. $false <- (~12, 21) [subsumption resolution 208,251]
331. 12 | ~21 [avatar contradiction clause 330]
333. happy(X0) | rich(X0) [resolution 194,112]
443. ~tall(susan) | ~happy(susan) <- (23) [resolution 93,260]
445. 55 <=> happy(susan) [avatar definition]
447. ~happy(susan) <- (~55) [avatar component clause 445]
449. 56 <=> tall(susan) [avatar definition]
452. ~55 | ~56 | ~23 [avatar split clause 443,258,449,445]
502. kind(susan) | tall(susan) <- (23) [resolution 323,260]
511. rich(susan) <- (~55) [resolution 333,447]
515. $false <- (~55) [subsumption resolution 511,144]
516. 55 [avatar contradiction clause 515]
519. 64 <=> kind(susan) [avatar definition]
521. kind(susan) <- (64) [avatar component clause 519]
522. 56 | 64 | ~23 [avatar split clause 502,258,519,449]
526. rich(susan) <- (64) [resolution 521,194]
528. $false <- (64) [subsumption resolution 526,144]
529. ~64 [avatar contradiction clause 528]
530. $false [avatar sat refutation 209,210,261,331,452,516,522,529]
% SZS output end Proof for 9208738984523703922720219
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not strong and not rich is not happy or not strong.
If someone is both quiet and not strong then alice is both not old and brave.
Everyone who is not funny or not humble is both rich and brave and vice versa.
If someone is not calm or old then susan is either not creative or not calm and vice versa.
If alice is both not tall and wise then john is either not humble or not strong.
If someone is kind then mary is either happy or strong.
If susan is not tall then someone is strong or not patient and vice versa.
If someone is curious or old then lucy is both not old and rich and vice versa.
Everyone who is not rich or not brave is funny and vice versa.
If someone is not generous then mary is both curious and not happy and vice versa.
Everyone who is either not strong or strong is creative or calm.
Everyone who is both not quiet and funny is not brave or generous.
Everyone who is not tall or not generous is strong or not rich and vice versa.
If someone is not calm then someone is rich or kind.
If alice is either not humble or patient then someone is calm or not happy.
Everyone who is not humble or not tall is both old and not humble and vice versa.
Someone is brave or not curious.
Someone is either funny or tall.
Lucy is funny.
Someone is happy or not tall.
Susan is not strong or not old.
Someone is both not happy and kind. | Susan is not patient. | contradiction | (![X]:((~strong(X)&~rich(X))=>(~happy(X)|~strong(X))))&
((?[X]:((quiet(X)&~strong(X))))=>((~old(alice)&brave(alice))))&
(![X]:((~funny(X)|~humble(X))<=>(rich(X)&brave(X))))&
((?[X]:((~calm(X)|old(X))))<=>((~creative(susan)<~>~calm(susan))))&
(((~tall(alice)&wise(alice)))=>((~humble(john)<~>~strong(john))))&
((?[X]:(kind(X)))=>((happy(mary)<~>strong(mary))))&
((~tall(susan))<=>(?[X]:((strong(X)|~patient(X)))))&
((?[X]:((curious(X)|old(X))))<=>((~old(lucy)&rich(lucy))))&
(![X]:((~rich(X)|~brave(X))<=>funny(X)))&
((?[X]:(~generous(X)))<=>((curious(mary)&~happy(mary))))&
(![X]:((~strong(X)<~>strong(X))=>(creative(X)|calm(X))))&
(![X]:((~quiet(X)&funny(X))=>(~brave(X)|generous(X))))&
(![X]:((~tall(X)|~generous(X))<=>(strong(X)|~rich(X))))&
((?[X]:(~calm(X)))=>(?[X]:((rich(X)|kind(X)))))&
(((~humble(alice)<~>patient(alice)))=>(?[X]:((calm(X)|~happy(X)))))&
(![X]:((~humble(X)|~tall(X))<=>(old(X)&~humble(X))))&
(?[X]:((brave(X)|~curious(X))))&
(?[X]:((funny(X)<~>tall(X))))&
(funny(lucy))&
(?[X]:((happy(X)|~tall(X))))&
((~strong(susan)|~old(susan)))&
(?[X]:((~happy(X)&kind(X)))) | ~patient(susan) | [
"p2",
"p6",
"p12",
"p15",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7319175265501515562492245
% SZS output start Proof for 7319175265501515562492245
3. ! [X0] : ((~humble(X0) | ~funny(X0)) <=> (brave(X0) & rich(X0))) [input p2]
7. ~tall(susan) <=> ? [X0] : (~patient(X0) | strong(X0)) [input p6]
13. ! [X0] : ((~generous(X0) | ~tall(X0)) <=> (~rich(X0) | strong(X0))) [input p12]
16. ! [X0] : ((~tall(X0) | ~humble(X0)) <=> (~humble(X0) & old(X0))) [input p15]
21. ~old(susan) | ~strong(susan) [input p20]
23. ~patient(susan) [input hypothesis]
36. ! [X0] : (((~humble(X0) | ~funny(X0)) | (~brave(X0) | ~rich(X0))) & ((brave(X0) & rich(X0)) | (humble(X0) & funny(X0)))) [nnf transformation 3]
37. ! [X0] : ((~humble(X0) | ~funny(X0) | ~brave(X0) | ~rich(X0)) & ((brave(X0) & rich(X0)) | (humble(X0) & funny(X0)))) [flattening 36]
43. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X0] : (~patient(X0) | strong(X0)) | tall(susan)) [nnf transformation 7]
44. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & (? [X1] : (~patient(X1) | strong(X1)) | tall(susan)) [rectify 43]
45. ? [X1] : (~patient(X1) | strong(X1)) => (~patient(sK1) | strong(sK1)) [choice axiom]
46. (~tall(susan) | ! [X0] : (patient(X0) & ~strong(X0))) & ((~patient(sK1) | strong(sK1)) | tall(susan)) [skolemisation 44,45]
60. ! [X0] : (((~generous(X0) | ~tall(X0)) | (rich(X0) & ~strong(X0))) & ((~rich(X0) | strong(X0)) | (generous(X0) & tall(X0)))) [nnf transformation 13]
61. ! [X0] : ((~generous(X0) | ~tall(X0) | (rich(X0) & ~strong(X0))) & (~rich(X0) | strong(X0) | (generous(X0) & tall(X0)))) [flattening 60]
68. ! [X0] : (((~tall(X0) | ~humble(X0)) | (humble(X0) | ~old(X0))) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [nnf transformation 16]
69. ! [X0] : ((~tall(X0) | ~humble(X0) | humble(X0) | ~old(X0)) & ((~humble(X0) & old(X0)) | (tall(X0) & humble(X0)))) [flattening 68]
83. humble(X0) | rich(X0) [cnf transformation 37]
97. ~tall(susan) | patient(X0) [cnf transformation 46]
112. ~rich(X0) | strong(X0) | tall(X0) [cnf transformation 61]
120. tall(X0) | old(X0) [cnf transformation 69]
122. ~humble(X0) | tall(X0) [cnf transformation 69]
129. ~old(susan) | ~strong(susan) [cnf transformation 21]
132. ~patient(susan) [cnf transformation 23]
190. 13 <=> ! [X0] : patient(X0) [avatar definition]
191. patient(X0) <- (13) [avatar component clause 190]
193. 14 <=> tall(susan) [avatar definition]
195. ~tall(susan) <- (~14) [avatar component clause 193]
196. 13 | ~14 [avatar split clause 97,193,190]
305. 38 <=> strong(susan) [avatar definition]
307. ~strong(susan) <- (~38) [avatar component clause 305]
309. 39 <=> old(susan) [avatar definition]
312. ~38 | ~39 [avatar split clause 129,309,305]
317. old(susan) <- (~14) [resolution 120,195]
320. 39 | 14 [avatar split clause 317,193,309]
321. $false <- (13) [resolution 191,132]
324. ~13 [avatar contradiction clause 321]
330. tall(X2) | rich(X2) [resolution 122,83]
422. rich(susan) <- (~14) [resolution 330,195]
455. strong(susan) | tall(susan) <- (~14) [resolution 422,112]
457. tall(susan) <- (~14, ~38) [subsumption resolution 455,307]
458. $false <- (~14, ~38) [subsumption resolution 457,195]
459. 14 | 38 [avatar contradiction clause 458]
460. $false [avatar sat refutation 196,312,320,324,459]
% SZS output end Proof for 7319175265501515562492245
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 tall or not strong is either patient or not happy.
Everyone who is either generous or strong is old and vice versa.
Everyone who is both not creative and humble is both generous and funny.
If someone is strong or not humble then someone is both not quiet and strong and vice versa.
If someone is brave or not humble then someone is not tall or not funny.
Everyone who is both not creative and not kind is not funny or not curious and vice versa.
Everyone who is not quiet is both not curious and not kind and vice versa.
If someone is rich then someone is quiet and vice versa.
If fred is rich then someone is not curious or not happy and vice versa.
If someone is both rich and not funny then susan is both not strong and not brave.
If paul is either not wise or not happy then alice is either calm or funny and vice versa.
Everyone who is calm is not patient and vice versa.
If someone is not rich then someone is both not brave and not wise.
Everyone who is either not tall or not happy is either kind or creative.
Everyone who is patient is either not humble or not funny.
If susan is either creative or not wise then someone is either not brave or not old and vice versa.
Susan is both not happy and not creative.
John is brave.
Someone is either not generous or not strong.
Someone is either funny or not rich.
Mary is both funny and generous.
Mary is either humble or not brave.
Mary is either not funny or tall.
Paul is generous. | Mary is tall. | entailment | (![X]:((tall(X)|~strong(X))=>(patient(X)<~>~happy(X))))&
(![X]:((generous(X)<~>strong(X))<=>old(X)))&
(![X]:((~creative(X)&humble(X))=>(generous(X)&funny(X))))&
((?[X]:((strong(X)|~humble(X))))<=>(?[X]:((~quiet(X)&strong(X)))))&
((?[X]:((brave(X)|~humble(X))))=>(?[X]:((~tall(X)|~funny(X)))))&
(![X]:((~creative(X)&~kind(X))<=>(~funny(X)|~curious(X))))&
(![X]:(~quiet(X)<=>(~curious(X)&~kind(X))))&
((?[X]:(rich(X)))<=>(?[X]:(quiet(X))))&
((rich(fred))<=>(?[X]:((~curious(X)|~happy(X)))))&
((?[X]:((rich(X)&~funny(X))))=>((~strong(susan)&~brave(susan))))&
(((~wise(paul)<~>~happy(paul)))<=>((calm(alice)<~>funny(alice))))&
(![X]:(calm(X)<=>~patient(X)))&
((?[X]:(~rich(X)))=>(?[X]:((~brave(X)&~wise(X)))))&
(![X]:((~tall(X)<~>~happy(X))=>(kind(X)<~>creative(X))))&
(![X]:(patient(X)=>(~humble(X)<~>~funny(X))))&
(((creative(susan)<~>~wise(susan)))<=>(?[X]:((~brave(X)<~>~old(X)))))&
((~happy(susan)&~creative(susan)))&
(brave(john))&
(?[X]:((~generous(X)<~>~strong(X))))&
(?[X]:((funny(X)<~>~rich(X))))&
((funny(mary)&generous(mary)))&
((humble(mary)<~>~brave(mary)))&
((~funny(mary)<~>tall(mary)))&
(generous(paul)) | tall(mary) | [
"p20",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 8522789898323482518945524
% SZS output start Proof for 8522789898323482518945524
21. generous(mary) & funny(mary) [input p20]
23. ~funny(mary) <~> tall(mary) [input p22]
25. ~tall(mary) [input hypothesis]
79. (~tall(mary) | funny(mary)) & (tall(mary) | ~funny(mary)) [nnf transformation 23]
145. funny(mary) [cnf transformation 21]
149. tall(mary) | ~funny(mary) [cnf transformation 79]
152. ~tall(mary) [cnf transformation 25]
345. tall(mary) [subsumption resolution 149,145]
346. $false [subsumption resolution 152,345]
% SZS output end Proof for 8522789898323482518945524
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or rich is both patient and not brave.
Everyone who is old is either not wise or happy.
If susan is either not quiet or not tall then susan is creative and vice versa.
Everyone who is either creative or not quiet is not quiet or curious.
Everyone who is funny is either not humble or creative and vice versa.
Everyone who is both not humble and kind is happy and vice versa.
Everyone who is not old or generous is not rich or patient and vice versa.
Everyone who is either not wise or creative is either not wise or not calm.
If alice is both calm and not brave then mary is strong.
If mary is either curious or funny then someone is either not happy or not patient and vice versa.
Everyone who is not brave or not creative is either not patient or not tall.
Everyone who is both not wise and not quiet is rich and vice versa.
If someone is both not kind and not calm then someone is quiet or calm and vice versa.
Everyone who is either generous or curious is rich and vice versa.
Everyone who is both not generous and not tall is not rich or not strong.
If susan is either patient or calm then alice is both not humble and not patient.
Fred is both funny and creative.
Lucy is either not kind or not wise.
Someone is either not old or not wise.
Susan is either not curious or not funny.
Paul is wise or not strong.
Someone is both not tall and generous.
Susan is either not strong or rich.
Someone is quiet. | Susan is not creative. | neutral | (![X]:((~strong(X)|rich(X))=>(patient(X)&~brave(X))))&
(![X]:(old(X)=>(~wise(X)<~>happy(X))))&
(((~quiet(susan)<~>~tall(susan)))<=>(creative(susan)))&
(![X]:((creative(X)<~>~quiet(X))=>(~quiet(X)|curious(X))))&
(![X]:(funny(X)<=>(~humble(X)<~>creative(X))))&
(![X]:((~humble(X)&kind(X))<=>happy(X)))&
(![X]:((~old(X)|generous(X))<=>(~rich(X)|patient(X))))&
(![X]:((~wise(X)<~>creative(X))=>(~wise(X)<~>~calm(X))))&
(((calm(alice)&~brave(alice)))=>(strong(mary)))&
(((curious(mary)<~>funny(mary)))<=>(?[X]:((~happy(X)<~>~patient(X)))))&
(![X]:((~brave(X)|~creative(X))=>(~patient(X)<~>~tall(X))))&
(![X]:((~wise(X)&~quiet(X))<=>rich(X)))&
((?[X]:((~kind(X)&~calm(X))))<=>(?[X]:((quiet(X)|calm(X)))))&
(![X]:((generous(X)<~>curious(X))<=>rich(X)))&
(![X]:((~generous(X)&~tall(X))=>(~rich(X)|~strong(X))))&
(((patient(susan)<~>calm(susan)))=>((~humble(alice)&~patient(alice))))&
((funny(fred)&creative(fred)))&
((~kind(lucy)<~>~wise(lucy)))&
(?[X]:((~old(X)<~>~wise(X))))&
((~curious(susan)<~>~funny(susan)))&
((wise(paul)|~strong(paul)))&
(?[X]:((~tall(X)&generous(X))))&
((~strong(susan)<~>rich(susan)))&
(?[X]:(quiet(X))) | ~creative(susan) | [] | null | 0 |
If mary is strong then fred is both not strong and not kind.
If someone is old or not brave then fred is patient.
Everyone who is humble or quiet is not patient and vice versa.
Everyone who is either brave or not generous is quiet or old.
Everyone who is not patient or humble is not tall and vice versa.
If someone is not happy then mary is not happy.
Everyone who is generous or rich is either curious or not funny.
Everyone who is both not happy and happy is quiet or not curious and vice versa.
If alice is not wise or not rich then susan is either calm or not quiet and vice versa.
Everyone who is either not rich or not humble is not tall or not quiet.
Everyone who is either tall or generous is not quiet and vice versa.
Everyone who is both not kind and not creative is either rich or wise and vice versa.
If lucy is both calm and tall then someone is not generous and vice versa.
Everyone who is kind is patient.
If mary is old then susan is not wise or not calm.
Everyone who is not generous is not kind and vice versa.
Paul is funny.
Someone is calm.
Someone is not humble or not curious.
Lucy is not rich or not kind.
John is not kind or not creative.
Someone is not funny.
John is curious. | Lucy is generous. | contradiction | ((strong(mary))=>((~strong(fred)&~kind(fred))))&
((?[X]:((old(X)|~brave(X))))=>(patient(fred)))&
(![X]:((humble(X)|quiet(X))<=>~patient(X)))&
(![X]:((brave(X)<~>~generous(X))=>(quiet(X)|old(X))))&
(![X]:((~patient(X)|humble(X))<=>~tall(X)))&
((?[X]:(~happy(X)))=>(~happy(mary)))&
(![X]:((generous(X)|rich(X))=>(curious(X)<~>~funny(X))))&
(![X]:((~happy(X)&happy(X))<=>(quiet(X)|~curious(X))))&
(((~wise(alice)|~rich(alice)))<=>((calm(susan)<~>~quiet(susan))))&
(![X]:((~rich(X)<~>~humble(X))=>(~tall(X)|~quiet(X))))&
(![X]:((tall(X)<~>generous(X))<=>~quiet(X)))&
(![X]:((~kind(X)&~creative(X))<=>(rich(X)<~>wise(X))))&
(((calm(lucy)&tall(lucy)))<=>(?[X]:(~generous(X))))&
(![X]:(kind(X)=>patient(X)))&
((old(mary))=>((~wise(susan)|~calm(susan))))&
(![X]:(~generous(X)<=>~kind(X)))&
(funny(paul))&
(?[X]:(calm(X)))&
(?[X]:((~humble(X)|~curious(X))))&
((~rich(lucy)|~kind(lucy)))&
((~kind(john)|~creative(john)))&
(?[X]:(~funny(X)))&
(curious(john)) | generous(lucy) | [
"p2",
"p4",
"p7",
"p10",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 3505929075010664572278319
% SZS output start Proof for 3505929075010664572278319
3. ! [X0] : ((quiet(X0) | humble(X0)) <=> ~patient(X0)) [input p2]
5. ! [X0] : ((humble(X0) | ~patient(X0)) <=> ~tall(X0)) [input p4]
8. ! [X0] : ((happy(X0) & ~happy(X0)) <=> (~curious(X0) | quiet(X0))) [input p7]
11. ! [X0] : ((tall(X0) <~> generous(X0)) <=> ~quiet(X0)) [input p10]
14. ! [X0] : (kind(X0) => patient(X0)) [input p13]
16. ! [X0] : (~generous(X0) <=> ~kind(X0)) [input p15]
24. generous(lucy) [input hypothesis]
33. ! [X0] : (patient(X0) | ~kind(X0)) [ennf transformation 14]
36. ! [X0] : (((quiet(X0) | humble(X0)) | patient(X0)) & (~patient(X0) | (~quiet(X0) & ~humble(X0)))) [nnf transformation 3]
37. ! [X0] : ((quiet(X0) | humble(X0) | patient(X0)) & (~patient(X0) | (~quiet(X0) & ~humble(X0)))) [flattening 36]
39. ! [X0] : (((humble(X0) | ~patient(X0)) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [nnf transformation 5]
40. ! [X0] : ((humble(X0) | ~patient(X0) | tall(X0)) & (~tall(X0) | (~humble(X0) & patient(X0)))) [flattening 39]
42. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & ((~curious(X0) | quiet(X0)) | (~happy(X0) | happy(X0)))) [nnf transformation 8]
43. ! [X0] : (((happy(X0) & ~happy(X0)) | (curious(X0) & ~quiet(X0))) & (~curious(X0) | quiet(X0) | ~happy(X0) | happy(X0))) [flattening 42]
47. ! [X0] : ((((~generous(X0) | ~tall(X0)) & (generous(X0) | tall(X0))) | quiet(X0)) & (~quiet(X0) | ((tall(X0) | ~generous(X0)) & (generous(X0) | ~tall(X0))))) [nnf transformation 11]
55. ! [X0] : ((~generous(X0) | kind(X0)) & (~kind(X0) | generous(X0))) [nnf transformation 16]
64. ~humble(X0) | ~patient(X0) [cnf transformation 37]
71. humble(X0) | ~patient(X0) | tall(X0) [cnf transformation 40]
78. ~happy(X0) | ~quiet(X0) [cnf transformation 43]
80. ~quiet(X0) | happy(X0) [cnf transformation 43]
93. ~generous(X0) | ~tall(X0) | quiet(X0) [cnf transformation 47]
103. ~kind(X0) | patient(X0) [cnf transformation 33]
106. ~generous(X0) | kind(X0) [cnf transformation 55]
114. generous(lucy) [cnf transformation 24]
127. ~patient(X0) | tall(X0) [subsumption resolution 71,64]
137. ~quiet(X0) [subsumption resolution 78,80]
156. ~tall(X0) | ~generous(X0) [subsumption resolution 93,137]
162. 10 <=> tall(lucy) [avatar definition]
163. ~tall(lucy) <- (~10) [avatar component clause 162]
164. tall(lucy) <- (10) [avatar component clause 162]
191. 16 <=> kind(lucy) [avatar definition]
192. kind(lucy) <- (16) [avatar component clause 191]
193. ~kind(lucy) <- (~16) [avatar component clause 191]
204. kind(lucy) [resolution 106,114]
206. $false <- (~16) [subsumption resolution 204,193]
207. 16 [avatar contradiction clause 206]
216. patient(lucy) <- (16) [resolution 192,103]
217. ~generous(lucy) <- (10) [resolution 156,164]
218. $false <- (10) [subsumption resolution 217,114]
219. ~10 [avatar contradiction clause 218]
230. tall(lucy) <- (16) [resolution 216,127]
231. $false <- (~10, 16) [subsumption resolution 230,163]
232. 10 | ~16 [avatar contradiction clause 231]
233. $false [avatar sat refutation 207,219,232]
% SZS output end Proof for 3505929075010664572278319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If fred is creative then susan is calm or rich.
Everyone who is either not brave or not funny is brave and vice versa.
Everyone who is brave is not wise and vice versa.
If mary is not wise or not generous then someone is tall or not kind and vice versa.
Everyone who is both not curious and not rich is both old and not strong and vice versa.
If someone is both not tall and not happy then someone is both happy and quiet and vice versa.
Everyone who is curious is not funny or strong and vice versa.
If someone is either not calm or tall then someone is not happy and vice versa.
Everyone who is both funny and not tall is both happy and not happy and vice versa.
If someone is both not tall and not humble then someone is both not calm and generous.
Everyone who is not funny or not generous is both happy and not generous.
Everyone who is not generous or not rich is either not brave or rich and vice versa.
If someone is rich or kind then lucy is either not wise or curious.
Everyone who is not old is either old or wise.
If paul is either not wise or humble then lucy is not happy.
Everyone who is not kind is calm or not kind and vice versa.
Someone is not creative or rich.
Someone is old.
John is both kind and not generous.
Susan is both old and calm.
Susan is either not funny or not calm.
Someone is either brave or happy.
John is either not creative or creative.
Susan is not creative. | Paul is not funny. | entailment | ((creative(fred))=>((calm(susan)|rich(susan))))&
(![X]:((~brave(X)<~>~funny(X))<=>brave(X)))&
(![X]:(brave(X)<=>~wise(X)))&
(((~wise(mary)|~generous(mary)))<=>(?[X]:((tall(X)|~kind(X)))))&
(![X]:((~curious(X)&~rich(X))<=>(old(X)&~strong(X))))&
((?[X]:((~tall(X)&~happy(X))))<=>(?[X]:((happy(X)&quiet(X)))))&
(![X]:(curious(X)<=>(~funny(X)|strong(X))))&
((?[X]:((~calm(X)<~>tall(X))))<=>(?[X]:(~happy(X))))&
(![X]:((funny(X)&~tall(X))<=>(happy(X)&~happy(X))))&
((?[X]:((~tall(X)&~humble(X))))=>(?[X]:((~calm(X)&generous(X)))))&
(![X]:((~funny(X)|~generous(X))=>(happy(X)&~generous(X))))&
(![X]:((~generous(X)|~rich(X))<=>(~brave(X)<~>rich(X))))&
((?[X]:((rich(X)|kind(X))))=>((~wise(lucy)<~>curious(lucy))))&
(![X]:(~old(X)=>(old(X)<~>wise(X))))&
(((~wise(paul)<~>humble(paul)))=>(~happy(lucy)))&
(![X]:(~kind(X)<=>(calm(X)|~kind(X))))&
(?[X]:((~creative(X)|rich(X))))&
(?[X]:(old(X)))&
((kind(john)&~generous(john)))&
((old(susan)&calm(susan)))&
((~funny(susan)<~>~calm(susan)))&
(?[X]:((brave(X)<~>happy(X))))&
((~creative(john)<~>creative(john)))&
(~creative(susan)) | ~funny(paul) | [
"p1",
"hypothesis"
] | % SZS status Unsatisfiable for 5843303918829099675565151
% SZS output start Proof for 5843303918829099675565151
2. ! [X0] : ((~brave(X0) <~> ~funny(X0)) <=> brave(X0)) [input p1]
25. funny(paul) [input hypothesis]
36. ! [X0] : ((((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | ~brave(X0)) & (brave(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0))))) [nnf transformation 2]
79. brave(X0) | ~funny(X0) | brave(X0) [cnf transformation 36]
81. ~funny(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 36]
144. funny(paul) [cnf transformation 25]
148. brave(X0) | ~funny(X0) [duplicate literal removal 79]
149. ~funny(X0) | ~brave(X0) [duplicate literal removal 81]
163. ~funny(X0) [subsumption resolution 148,149]
311. $false [subsumption resolution 144,163]
% SZS output end Proof for 5843303918829099675565151
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 paul is either not creative or not wise then mary is not happy or not tall. Everyone who is patient or happy is either brave or not calm. Everyone who is old is either not quiet or calm and vice versa. Everyone who is either not creative or generous is funny or generous and vice versa. Everyone who is either not humble or not old is both humble and not humble and vice versa. Everyone who is both generous and not generous is calm or funny and vice versa. If lucy is not rich then someone is either not wise or not strong and vice versa. If someone is either not humble or creative then susan is both generous and calm. Everyone who is not humble or not rich is not old or creative and vice versa. If someone is not humble or curious then paul is either kind or not funny. Everyone who is either not creative or not humble is either creative or not rich and vice versa. If someone is both not brave and brave then someone is strong. If someone is both funny and not quiet then someone is both not curious and not old and vice versa. If alice is both brave and not curious then someone is either not creative or not kind. If mary is rich then someone is not curious or curious and vice versa. Someone is either not kind or old. Someone is not generous or not strong. Alice is either not humble or not creative. Someone is strong or funny. Alice is either not curious or not strong. Someone is either not happy or not creative. Susan is either tall or calm. Someone is both not patient and brave. | Susan is rich. | entailment | (((~creative(paul)<~>~wise(paul)))=>((~happy(mary)|~tall(mary))))&
(![X]:((patient(X)|happy(X))=>(brave(X)<~>~calm(X))))&
(![X]:(old(X)<=>(~quiet(X)<~>calm(X))))&
(![X]:((~creative(X)<~>generous(X))<=>(funny(X)|generous(X))))&
(![X]:((~humble(X)<~>~old(X))<=>(humble(X)&~humble(X))))&
(![X]:((generous(X)&~generous(X))<=>(calm(X)|funny(X))))&
((~rich(lucy))<=>(?[X]:((~wise(X)<~>~strong(X)))))&
((?[X]:((~humble(X)<~>creative(X))))=>((generous(susan)&calm(susan))))&
(![X]:((~humble(X)|~rich(X))<=>(~old(X)|creative(X))))&
((?[X]:((~humble(X)|curious(X))))=>((kind(paul)<~>~funny(paul))))&
(![X]:((~creative(X)<~>~humble(X))<=>(creative(X)<~>~rich(X))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:(strong(X))))&
((?[X]:((funny(X)&~quiet(X))))<=>(?[X]:((~curious(X)&~old(X)))))&
(((brave(alice)&~curious(alice)))=>(?[X]:((~creative(X)<~>~kind(X)))))&
((rich(mary))<=>(?[X]:((~curious(X)|curious(X)))))&
(?[X]:((~kind(X)<~>old(X))))&
(?[X]:((~generous(X)|~strong(X))))&
((~humble(alice)<~>~creative(alice)))&
(?[X]:((strong(X)|funny(X))))&
((~curious(alice)<~>~strong(alice)))&
(?[X]:((~happy(X)<~>~creative(X))))&
((tall(susan)<~>calm(susan)))&
(?[X]:((~patient(X)&brave(X)))) | rich(susan) | [
"p3",
"p5",
"p7",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 685403025638234744948179
% SZS output start Proof for 685403025638234744948179
4. ! [X0] : ((~creative(X0) <~> generous(X0)) <=> (generous(X0) | funny(X0))) [input p3]
6. ! [X0] : ((~generous(X0) & generous(X0)) <=> (funny(X0) | calm(X0))) [input p5]
8. ? [X0] : (~humble(X0) <~> creative(X0)) => (calm(susan) & generous(susan)) [input p7]
11. ! [X0] : ((~creative(X0) <~> ~humble(X0)) <=> (creative(X0) <~> ~rich(X0))) [input p10]
24. ~rich(susan) [input hypothesis]
32. (calm(susan) & generous(susan)) | ! [X0] : (~humble(X0) <=> creative(X0)) [ennf transformation 8]
40. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~generous(X0) & ~funny(X0))) & ((generous(X0) | funny(X0)) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [nnf transformation 4]
41. ! [X0] : ((((~generous(X0) | creative(X0)) & (generous(X0) | ~creative(X0))) | (~generous(X0) & ~funny(X0))) & (generous(X0) | funny(X0) | ((~creative(X0) | ~generous(X0)) & (generous(X0) | creative(X0))))) [flattening 40]
44. ! [X0] : (((~generous(X0) & generous(X0)) | (~funny(X0) & ~calm(X0))) & ((funny(X0) | calm(X0)) | (generous(X0) | ~generous(X0)))) [nnf transformation 6]
45. ! [X0] : (((~generous(X0) & generous(X0)) | (~funny(X0) & ~calm(X0))) & (funny(X0) | calm(X0) | generous(X0) | ~generous(X0))) [flattening 44]
50. (calm(susan) & generous(susan)) | ! [X0] : ((~humble(X0) | ~creative(X0)) & (creative(X0) | humble(X0))) [nnf transformation 32]
54. ! [X0] : ((((humble(X0) | creative(X0)) & (~humble(X0) | ~creative(X0))) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | ((~creative(X0) | humble(X0)) & (~humble(X0) | creative(X0))))) [nnf transformation 11]
93. generous(X0) | funny(X0) | generous(X0) | creative(X0) [cnf transformation 41]
98. ~generous(X0) | creative(X0) | ~generous(X0) [cnf transformation 41]
106. generous(X0) | ~calm(X0) [cnf transformation 45]
107. generous(X0) | ~funny(X0) [cnf transformation 45]
108. ~generous(X0) | ~calm(X0) [cnf transformation 45]
109. ~funny(X0) | ~generous(X0) [cnf transformation 45]
116. calm(susan) | creative(X0) | humble(X0) [cnf transformation 50]
117. calm(susan) | ~humble(X0) | ~creative(X0) [cnf transformation 50]
129. rich(X0) | ~creative(X0) | ~creative(X0) | humble(X0) [cnf transformation 54]
157. ~rich(susan) [cnf transformation 24]
159. rich(X0) | ~creative(X0) | humble(X0) [duplicate literal removal 129]
166. generous(X0) | funny(X0) | creative(X0) [duplicate literal removal 93]
167. ~generous(X0) | creative(X0) [duplicate literal removal 98]
186. funny(X0) | creative(X0) [subsumption resolution 166,167]
187. ~funny(X0) [subsumption resolution 107,109]
188. ~calm(X0) [subsumption resolution 106,108]
211. ~humble(X0) | ~creative(X0) [subsumption resolution 117,188]
212. humble(X0) | creative(X0) [subsumption resolution 116,188]
227. rich(X0) | humble(X0) [subsumption resolution 159,212]
304. creative(X1) [resolution 186,187]
311. humble(susan) [resolution 227,157]
315. ~creative(susan) [resolution 311,211]
317. $false [subsumption resolution 315,304]
% SZS output end Proof for 685403025638234744948179
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 both not rich and not wise is both strong and funny and vice versa. Everyone who is creative or not happy is brave. If someone is either not generous or happy then john is either not creative or curious and vice versa. If someone is either quiet or creative then someone is both not funny and humble. If someone is both humble and creative then fred is not kind or happy. If john is patient then john is not happy or strong. Everyone who is old is not quiet or patient. If someone is kind then paul is both tall and not generous and vice versa. Everyone who is brave is both strong and funny. Everyone who is patient is both not calm and not patient and vice versa. Everyone who is creative or old is either strong or curious and vice versa. Everyone who is both curious and generous is either old or not humble. If susan is not humble then paul is funny or not calm and vice versa. If alice is both wise and not kind then paul is not kind and vice versa. Everyone who is not kind or not curious is not curious or not rich. Everyone who is not tall is both not generous and wise. Someone is tall or not old. John is both calm and strong. Someone is creative. Fred is kind. Paul is either quiet or not brave. Someone is either not funny or not humble. John is rich. Alice is either happy or brave. | John is funny. | contradiction | (![X]:((~rich(X)&~wise(X))<=>(strong(X)&funny(X))))&
(![X]:((creative(X)|~happy(X))=>brave(X)))&
((?[X]:((~generous(X)<~>happy(X))))<=>((~creative(john)<~>curious(john))))&
((?[X]:((quiet(X)<~>creative(X))))=>(?[X]:((~funny(X)&humble(X)))))&
((?[X]:((humble(X)&creative(X))))=>((~kind(fred)|happy(fred))))&
((patient(john))=>((~happy(john)|strong(john))))&
(![X]:(old(X)=>(~quiet(X)|patient(X))))&
((?[X]:(kind(X)))<=>((tall(paul)&~generous(paul))))&
(![X]:(brave(X)=>(strong(X)&funny(X))))&
(![X]:(patient(X)<=>(~calm(X)&~patient(X))))&
(![X]:((creative(X)|old(X))<=>(strong(X)<~>curious(X))))&
(![X]:((curious(X)&generous(X))=>(old(X)<~>~humble(X))))&
((~humble(susan))<=>((funny(paul)|~calm(paul))))&
(((wise(alice)&~kind(alice)))<=>(~kind(paul)))&
(![X]:((~kind(X)|~curious(X))=>(~curious(X)|~rich(X))))&
(![X]:(~tall(X)=>(~generous(X)&wise(X))))&
(?[X]:((tall(X)|~old(X))))&
((calm(john)&strong(john)))&
(?[X]:(creative(X)))&
(kind(fred))&
((quiet(paul)<~>~brave(paul)))&
(?[X]:((~funny(X)<~>~humble(X))))&
(rich(john))&
((happy(alice)<~>brave(alice))) | funny(john) | [
"p0",
"p17",
"p22",
"hypothesis"
] | % SZS status Unsatisfiable for 7557375466950793334873019
% SZS output start Proof for 7557375466950793334873019
1. ! [X0] : ((~wise(X0) & ~rich(X0)) <=> (funny(X0) & strong(X0))) [input p0]
18. strong(john) & calm(john) [input p17]
23. rich(john) [input p22]
25. funny(john) [input hypothesis]
41. ! [X0] : (((~wise(X0) & ~rich(X0)) | (~funny(X0) | ~strong(X0))) & ((funny(X0) & strong(X0)) | (wise(X0) | rich(X0)))) [nnf transformation 1]
42. ! [X0] : (((~wise(X0) & ~rich(X0)) | ~funny(X0) | ~strong(X0)) & ((funny(X0) & strong(X0)) | wise(X0) | rich(X0))) [flattening 41]
76. ~funny(X0) | ~rich(X0) | ~strong(X0) [cnf transformation 42]
123. strong(john) [cnf transformation 18]
130. rich(john) [cnf transformation 23]
133. funny(john) [cnf transformation 25]
205. 16 <=> strong(john) [avatar definition]
207. strong(john) <- (16) [avatar component clause 205]
266. 16 [avatar split clause 123,205]
333. ~rich(john) | ~strong(john) [resolution 76,133]
338. ~strong(john) [subsumption resolution 333,130]
339. $false <- (16) [subsumption resolution 338,207]
340. ~16 [avatar contradiction clause 339]
361. $false [avatar sat refutation 266,340]
% SZS output end Proof for 7557375466950793334873019
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is tall or not old then lucy is both happy and not humble and vice versa. Everyone who is patient or curious is either kind or calm. Everyone who is both not wise and not brave is either not brave or not tall. If john is both humble and not patient then john is both patient and tall. If alice is not rich then someone is both not happy and not creative. If john is either humble or not rich then alice is humble or happy and vice versa. Everyone who is both not curious and generous is rich. Everyone who is patient or kind is patient or not brave. Everyone who is both old and tall is both old and not curious. If fred is creative or generous then alice is not happy. If someone is either humble or not brave then mary is both brave and patient. Everyone who is quiet is not happy. If paul is old then susan is rich or kind and vice versa. Everyone who is both not brave and not quiet is not brave or not generous. If someone is either generous or brave then lucy is either creative or not brave and vice versa. Everyone who is patient is both happy and funny and vice versa. Paul is tall or funny. Someone is both tall and not old. Susan is happy. Someone is either wise or not old. Lucy is both curious and not quiet. Someone is both not kind and not old. Someone is quiet. Mary is generous. | Alice is not patient. | neutral | (((tall(alice)|~old(alice)))<=>((happy(lucy)&~humble(lucy))))&
(![X]:((patient(X)|curious(X))=>(kind(X)<~>calm(X))))&
(![X]:((~wise(X)&~brave(X))=>(~brave(X)<~>~tall(X))))&
(((humble(john)&~patient(john)))=>((patient(john)&tall(john))))&
((~rich(alice))=>(?[X]:((~happy(X)&~creative(X)))))&
(((humble(john)<~>~rich(john)))<=>((humble(alice)|happy(alice))))&
(![X]:((~curious(X)&generous(X))=>rich(X)))&
(![X]:((patient(X)|kind(X))=>(patient(X)|~brave(X))))&
(![X]:((old(X)&tall(X))=>(old(X)&~curious(X))))&
(((creative(fred)|generous(fred)))=>(~happy(alice)))&
((?[X]:((humble(X)<~>~brave(X))))=>((brave(mary)&patient(mary))))&
(![X]:(quiet(X)=>~happy(X)))&
((old(paul))<=>((rich(susan)|kind(susan))))&
(![X]:((~brave(X)&~quiet(X))=>(~brave(X)|~generous(X))))&
((?[X]:((generous(X)<~>brave(X))))<=>((creative(lucy)<~>~brave(lucy))))&
(![X]:(patient(X)<=>(happy(X)&funny(X))))&
((tall(paul)|funny(paul)))&
(?[X]:((tall(X)&~old(X))))&
(happy(susan))&
(?[X]:((wise(X)<~>~old(X))))&
((curious(lucy)&~quiet(lucy)))&
(?[X]:((~kind(X)&~old(X))))&
(?[X]:(quiet(X)))&
(generous(mary)) | ~patient(alice) | [] | null | 0 |
Everyone who is not strong is not wise.
Everyone who is both funny and tall is either not old or not quiet and vice versa.
If someone is creative then someone is not creative or happy.
Everyone who is not generous or patient is rich and vice versa.
Everyone who is quiet or not strong is not quiet or old.
Everyone who is not strong or curious is both not strong and strong and vice versa.
Everyone who is both not funny and brave is either not generous or not curious and vice versa.
If someone is generous or humble then someone is not kind or tall and vice versa.
Everyone who is either creative or humble is generous or not strong.
Everyone who is not happy or patient is not old.
If susan is either rich or not patient then someone is not happy or tall and vice versa.
Everyone who is creative or not curious is both not calm and generous.
Everyone who is both not funny and not brave is not quiet or not curious.
Everyone who is both not brave and not strong is either not patient or not quiet and vice versa.
Everyone who is either generous or creative is both not quiet and brave.
If john is not wise or old then john is both not old and not creative and vice versa.
Someone is not humble or not strong.
Someone is not creative or quiet.
Someone is not curious or not generous.
Someone is not happy or strong. | John is humble. | neutral | (![X]:(~strong(X)=>~wise(X)))&
(![X]:((funny(X)&tall(X))<=>(~old(X)<~>~quiet(X))))&
((?[X]:(creative(X)))=>(?[X]:((~creative(X)|happy(X)))))&
(![X]:((~generous(X)|patient(X))<=>rich(X)))&
(![X]:((quiet(X)|~strong(X))=>(~quiet(X)|old(X))))&
(![X]:((~strong(X)|curious(X))<=>(~strong(X)&strong(X))))&
(![X]:((~funny(X)&brave(X))<=>(~generous(X)<~>~curious(X))))&
((?[X]:((generous(X)|humble(X))))<=>(?[X]:((~kind(X)|tall(X)))))&
(![X]:((creative(X)<~>humble(X))=>(generous(X)|~strong(X))))&
(![X]:((~happy(X)|patient(X))=>~old(X)))&
(((rich(susan)<~>~patient(susan)))<=>(?[X]:((~happy(X)|tall(X)))))&
(![X]:((creative(X)|~curious(X))=>(~calm(X)&generous(X))))&
(![X]:((~funny(X)&~brave(X))=>(~quiet(X)|~curious(X))))&
(![X]:((~brave(X)&~strong(X))<=>(~patient(X)<~>~quiet(X))))&
(![X]:((generous(X)<~>creative(X))=>(~quiet(X)&brave(X))))&
(((~wise(john)|old(john)))<=>((~old(john)&~creative(john))))&
(?[X]:((~humble(X)|~strong(X))))&
(?[X]:((~creative(X)|quiet(X))))&
(?[X]:((~curious(X)|~generous(X))))&
(?[X]:((~happy(X)|strong(X)))) | humble(john) | [] | null | 0 |
Everyone who is both not calm and brave is both not rich and not brave and vice versa.
If lucy is not quiet or rich then alice is not rich or not funny.
Everyone who is either not kind or not humble is not brave or creative and vice versa.
If susan is both not wise and calm then someone is either generous or humble and vice versa.
Everyone who is not calm is creative.
Everyone who is brave is either not brave or funny.
Everyone who is either creative or curious is not humble and vice versa.
If someone is not rich or not creative then someone is both kind and happy.
Everyone who is not quiet or not kind is not strong and vice versa.
Everyone who is generous or not curious is both not quiet and creative and vice versa.
Everyone who is either not happy or wise is generous and vice versa.
If lucy is either not rich or not tall then someone is either generous or not funny and vice versa.
Everyone who is either not generous or not creative is both kind and not brave and vice versa.
Everyone who is both not rich and calm is both not wise and happy and vice versa.
If someone is both curious and creative then fred is not patient or not old.
If paul is both strong and not old then someone is patient and vice versa.
Alice is not kind or not wise.
Mary is either not kind or not happy.
Someone is not rich or not patient.
Susan is not calm or rich.
Lucy is brave.
Lucy is either not kind or patient.
John is both not tall and curious. | John is calm. | neutral | (![X]:((~calm(X)&brave(X))<=>(~rich(X)&~brave(X))))&
(((~quiet(lucy)|rich(lucy)))=>((~rich(alice)|~funny(alice))))&
(![X]:((~kind(X)<~>~humble(X))<=>(~brave(X)|creative(X))))&
(((~wise(susan)&calm(susan)))<=>(?[X]:((generous(X)<~>humble(X)))))&
(![X]:(~calm(X)=>creative(X)))&
(![X]:(brave(X)=>(~brave(X)<~>funny(X))))&
(![X]:((creative(X)<~>curious(X))<=>~humble(X)))&
((?[X]:((~rich(X)|~creative(X))))=>(?[X]:((kind(X)&happy(X)))))&
(![X]:((~quiet(X)|~kind(X))<=>~strong(X)))&
(![X]:((generous(X)|~curious(X))<=>(~quiet(X)&creative(X))))&
(![X]:((~happy(X)<~>wise(X))<=>generous(X)))&
(((~rich(lucy)<~>~tall(lucy)))<=>(?[X]:((generous(X)<~>~funny(X)))))&
(![X]:((~generous(X)<~>~creative(X))<=>(kind(X)&~brave(X))))&
(![X]:((~rich(X)&calm(X))<=>(~wise(X)&happy(X))))&
((?[X]:((curious(X)&creative(X))))=>((~patient(fred)|~old(fred))))&
(((strong(paul)&~old(paul)))<=>(?[X]:(patient(X))))&
((~kind(alice)|~wise(alice)))&
((~kind(mary)<~>~happy(mary)))&
(?[X]:((~rich(X)|~patient(X))))&
((~calm(susan)|rich(susan)))&
(brave(lucy))&
((~kind(lucy)<~>patient(lucy)))&
((~tall(john)&curious(john))) | calm(john) | [] | null | 0 |
If someone is wise then fred is old or not kind and vice versa. Everyone who is not brave or not tall is both not brave and not old. If someone is both not happy and not curious then paul is both quiet and curious and vice versa. Everyone who is old is brave. If someone is not wise or not strong then someone is either not wise or generous and vice versa. Everyone who is tall or not creative is quiet or not quiet and vice versa. Everyone who is both patient and curious is not rich or kind. If someone is either calm or not wise then paul is both not calm and not tall. Everyone who is either not old or not wise is strong or old. Everyone who is not funny is either strong or old and vice versa. If lucy is either happy or generous then someone is either creative or not strong. If susan is either curious or generous then someone is both not old and not strong and vice versa. Everyone who is both curious and not strong is tall and vice versa. Everyone who is not patient or not kind is not wise and vice versa. Everyone who is both not funny and calm is not patient or not old and vice versa. If someone is either not patient or quiet then lucy is patient and vice versa. Someone is both not generous and not creative. Someone is either generous or not curious. Someone is not humble. Fred is either not old or patient. Someone is either not generous or not funny. Someone is calm. Someone is funny or kind. Mary is either funny or tall. | Mary is not brave. | contradiction | ((?[X]:(wise(X)))<=>((old(fred)|~kind(fred))))&
(![X]:((~brave(X)|~tall(X))=>(~brave(X)&~old(X))))&
((?[X]:((~happy(X)&~curious(X))))<=>((quiet(paul)&curious(paul))))&
(![X]:(old(X)=>brave(X)))&
((?[X]:((~wise(X)|~strong(X))))<=>(?[X]:((~wise(X)<~>generous(X)))))&
(![X]:((tall(X)|~creative(X))<=>(quiet(X)|~quiet(X))))&
(![X]:((patient(X)&curious(X))=>(~rich(X)|kind(X))))&
((?[X]:((calm(X)<~>~wise(X))))=>((~calm(paul)&~tall(paul))))&
(![X]:((~old(X)<~>~wise(X))=>(strong(X)|old(X))))&
(![X]:(~funny(X)<=>(strong(X)<~>old(X))))&
(((happy(lucy)<~>generous(lucy)))=>(?[X]:((creative(X)<~>~strong(X)))))&
(((curious(susan)<~>generous(susan)))<=>(?[X]:((~old(X)&~strong(X)))))&
(![X]:((curious(X)&~strong(X))<=>tall(X)))&
(![X]:((~patient(X)|~kind(X))<=>~wise(X)))&
(![X]:((~funny(X)&calm(X))<=>(~patient(X)|~old(X))))&
((?[X]:((~patient(X)<~>quiet(X))))<=>(patient(lucy)))&
(?[X]:((~generous(X)&~creative(X))))&
(?[X]:((generous(X)<~>~curious(X))))&
(?[X]:(~humble(X)))&
((~old(fred)<~>patient(fred)))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((funny(X)|kind(X))))&
((funny(mary)<~>tall(mary))) | ~brave(mary) | [
"p1",
"p9",
"p12",
"p14",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 3962744933555896068708631
% SZS output start Proof for 3962744933555896068708631
2. ! [X0] : ((~tall(X0) | ~brave(X0)) => (~old(X0) & ~brave(X0))) [input p1]
10. ! [X0] : (~funny(X0) <=> (strong(X0) <~> old(X0))) [input p9]
13. ! [X0] : ((~strong(X0) & curious(X0)) <=> tall(X0)) [input p12]
15. ! [X0] : ((calm(X0) & ~funny(X0)) <=> (~old(X0) | ~patient(X0))) [input p14]
24. funny(mary) <~> tall(mary) [input p23]
25. ~brave(mary) [input hypothesis]
29. ! [X0] : ((~old(X0) & ~brave(X0)) | (tall(X0) & brave(X0))) [ennf transformation 2]
54. ! [X0] : ((~funny(X0) | ((strong(X0) | ~old(X0)) & (old(X0) | ~strong(X0)))) & (((~old(X0) | ~strong(X0)) & (old(X0) | strong(X0))) | funny(X0))) [nnf transformation 10]
62. ! [X0] : (((~strong(X0) & curious(X0)) | ~tall(X0)) & (tall(X0) | (strong(X0) | ~curious(X0)))) [nnf transformation 13]
63. ! [X0] : (((~strong(X0) & curious(X0)) | ~tall(X0)) & (tall(X0) | strong(X0) | ~curious(X0))) [flattening 62]
66. ! [X0] : (((calm(X0) & ~funny(X0)) | (old(X0) & patient(X0))) & ((~old(X0) | ~patient(X0)) | (~calm(X0) | funny(X0)))) [nnf transformation 15]
67. ! [X0] : (((calm(X0) & ~funny(X0)) | (old(X0) & patient(X0))) & (~old(X0) | ~patient(X0) | ~calm(X0) | funny(X0))) [flattening 66]
85. (~tall(mary) | ~funny(mary)) & (tall(mary) | funny(mary)) [nnf transformation 24]
91. ~old(X0) | brave(X0) [cnf transformation 29]
114. funny(X0) | strong(X0) | old(X0) [cnf transformation 54]
130. ~strong(X0) | ~tall(X0) [cnf transformation 63]
136. ~funny(X0) | old(X0) [cnf transformation 67]
153. tall(mary) | funny(mary) [cnf transformation 85]
155. ~brave(mary) [cnf transformation 25]
272. 26 <=> ! [X0] : (strong(X0) | old(X0)) [avatar definition]
273. strong(X0) | old(X0) <- (26) [avatar component clause 272]
354. 43 <=> funny(mary) [avatar definition]
355. funny(mary) <- (43) [avatar component clause 354]
358. 44 <=> tall(mary) [avatar definition]
359. tall(mary) <- (44) [avatar component clause 358]
362. 43 | 44 [avatar split clause 153,358,354]
368. old(mary) <- (43) [resolution 136,355]
374. brave(mary) <- (43) [resolution 368,91]
377. $false <- (43) [subsumption resolution 374,155]
378. ~43 [avatar contradiction clause 377]
381. ~tall(X0) | old(X0) <- (26) [resolution 273,130]
398. strong(X0) | old(X0) | old(X0) [resolution 114,136]
401. strong(X0) | old(X0) [duplicate literal removal 398]
452. old(mary) <- (26, 44) [resolution 381,359]
471. brave(mary) <- (26, 44) [resolution 452,91]
472. $false <- (26, 44) [subsumption resolution 471,155]
473. ~26 | ~44 [avatar contradiction clause 472]
492. 26 [avatar split clause 401,272]
502. $false [avatar sat refutation 362,378,473,492]
% SZS output end Proof for 3962744933555896068708631
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 curious or happy then someone is humble and vice versa. Everyone who is both tall and not patient is not patient and vice versa. If susan is quiet then john is not creative and vice versa. If susan is not calm then susan is not wise. If john is both rich and tall then alice is not strong or strong and vice versa. Everyone who is quiet is creative and vice versa. Everyone who is both not creative and rich is not calm or generous. If fred is curious then paul is both funny and not rich. Everyone who is not curious is both humble and not strong. If someone is both old and not curious then someone is not kind or not patient. If someone is kind or not rich then fred is either not happy or not funny. Everyone who is humble or funny is brave. Everyone who is not humble is calm. Everyone who is humble is calm or not brave and vice versa. Everyone who is either not patient or old is either not creative or not wise. If lucy is either not humble or strong then susan is patient. Susan is either curious or rich. Lucy is both not funny and not old. Paul is either not brave or not wise. John is curious. Someone is both brave and not funny. Someone is both not tall and creative. Paul is old. | John is brave. | entailment | ((?[X]:((curious(X)<~>happy(X))))<=>(?[X]:(humble(X))))&
(![X]:((tall(X)&~patient(X))<=>~patient(X)))&
((quiet(susan))<=>(~creative(john)))&
((~calm(susan))=>(~wise(susan)))&
(((rich(john)&tall(john)))<=>((~strong(alice)|strong(alice))))&
(![X]:(quiet(X)<=>creative(X)))&
(![X]:((~creative(X)&rich(X))=>(~calm(X)|generous(X))))&
((curious(fred))=>((funny(paul)&~rich(paul))))&
(![X]:(~curious(X)=>(humble(X)&~strong(X))))&
((?[X]:((old(X)&~curious(X))))=>(?[X]:((~kind(X)|~patient(X)))))&
((?[X]:((kind(X)|~rich(X))))=>((~happy(fred)<~>~funny(fred))))&
(![X]:((humble(X)|funny(X))=>brave(X)))&
(![X]:(~humble(X)=>calm(X)))&
(![X]:(humble(X)<=>(calm(X)|~brave(X))))&
(![X]:((~patient(X)<~>old(X))=>(~creative(X)<~>~wise(X))))&
(((~humble(lucy)<~>strong(lucy)))=>(patient(susan)))&
((curious(susan)<~>rich(susan)))&
((~funny(lucy)&~old(lucy)))&
((~brave(paul)<~>~wise(paul)))&
(curious(john))&
(?[X]:((brave(X)&~funny(X))))&
(?[X]:((~tall(X)&creative(X))))&
(old(paul)) | brave(john) | [
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 6821101828814692459632507
% SZS output start Proof for 6821101828814692459632507
12. ! [X0] : ((funny(X0) | humble(X0)) => brave(X0)) [input p11]
14. ! [X0] : (humble(X0) <=> (~brave(X0) | calm(X0))) [input p13]
24. ~brave(john) [input hypothesis]
34. ! [X0] : (brave(X0) | (~funny(X0) & ~humble(X0))) [ennf transformation 12]
50. ! [X0] : ((humble(X0) | (brave(X0) & ~calm(X0))) & ((~brave(X0) | calm(X0)) | ~humble(X0))) [nnf transformation 14]
51. ! [X0] : ((humble(X0) | (brave(X0) & ~calm(X0))) & (~brave(X0) | calm(X0) | ~humble(X0))) [flattening 50]
83. brave(X0) | ~humble(X0) [cnf transformation 34]
88. humble(X0) | brave(X0) [cnf transformation 51]
107. ~brave(john) [cnf transformation 24]
195. brave(X0) [subsumption resolution 88,83]
220. $false [subsumption resolution 107,195]
% SZS output end Proof for 6821101828814692459632507
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either kind or rich then susan is both happy and not quiet. Everyone who is both creative and not quiet is quiet and vice versa. If someone is calm then paul is both curious and strong. If paul is both wise and not humble then john is either not generous or not old. Everyone who is not kind is calm. If someone is either old or funny then someone is either tall or not creative and vice versa. If someone is both not wise and old then someone is either not rich or patient. Everyone who is funny or curious is both not kind and creative and vice versa. Everyone who is curious is either not generous or not brave. Everyone who is both not strong and patient is either quiet or not happy and vice versa. Everyone who is either wise or not generous is not brave. If someone is either happy or not tall then fred is generous or quiet. Everyone who is both strong and not curious is both kind and not tall and vice versa. If someone is not humble then someone is funny. If someone is rich or wise then someone is kind. Someone is both generous and not patient. Someone is kind. Paul is either not curious or not patient. Someone is not quiet or quiet. Someone is either not funny or strong. | Fred is kind. | entailment | (((kind(fred)<~>rich(fred)))=>((happy(susan)&~quiet(susan))))&
(![X]:((creative(X)&~quiet(X))<=>quiet(X)))&
((?[X]:(calm(X)))=>((curious(paul)&strong(paul))))&
(((wise(paul)&~humble(paul)))=>((~generous(john)<~>~old(john))))&
(![X]:(~kind(X)=>calm(X)))&
((?[X]:((old(X)<~>funny(X))))<=>(?[X]:((tall(X)<~>~creative(X)))))&
((?[X]:((~wise(X)&old(X))))=>(?[X]:((~rich(X)<~>patient(X)))))&
(![X]:((funny(X)|curious(X))<=>(~kind(X)&creative(X))))&
(![X]:(curious(X)=>(~generous(X)<~>~brave(X))))&
(![X]:((~strong(X)&patient(X))<=>(quiet(X)<~>~happy(X))))&
(![X]:((wise(X)<~>~generous(X))=>~brave(X)))&
((?[X]:((happy(X)<~>~tall(X))))=>((generous(fred)|quiet(fred))))&
(![X]:((strong(X)&~curious(X))<=>(kind(X)&~tall(X))))&
((?[X]:(~humble(X)))=>(?[X]:(funny(X))))&
((?[X]:((rich(X)|wise(X))))=>(?[X]:(kind(X))))&
(?[X]:((generous(X)&~patient(X))))&
(?[X]:(kind(X)))&
((~curious(paul)<~>~patient(paul)))&
(?[X]:((~quiet(X)|quiet(X))))&
(?[X]:((~funny(X)<~>strong(X)))) | kind(fred) | [
"p1",
"p2",
"p4",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 4784029801701556323825395
% SZS output start Proof for 4784029801701556323825395
2. ! [X0] : ((~quiet(X0) & creative(X0)) <=> quiet(X0)) [input p1]
3. ? [X0] : calm(X0) => (strong(paul) & curious(paul)) [input p2]
5. ! [X0] : (~kind(X0) => calm(X0)) [input p4]
8. ! [X0] : ((curious(X0) | funny(X0)) <=> (creative(X0) & ~kind(X0))) [input p7]
21. ~kind(fred) [input hypothesis]
29. (strong(paul) & curious(paul)) | ! [X0] : ~calm(X0) [ennf transformation 3]
30. ! [X0] : (calm(X0) | kind(X0)) [ennf transformation 5]
38. ! [X0] : (((~quiet(X0) & creative(X0)) | ~quiet(X0)) & (quiet(X0) | (quiet(X0) | ~creative(X0)))) [nnf transformation 2]
39. ! [X0] : (((~quiet(X0) & creative(X0)) | ~quiet(X0)) & (quiet(X0) | quiet(X0) | ~creative(X0))) [flattening 38]
49. ! [X0] : (((curious(X0) | funny(X0)) | (~creative(X0) | kind(X0))) & ((creative(X0) & ~kind(X0)) | (~curious(X0) & ~funny(X0)))) [nnf transformation 8]
50. ! [X0] : ((curious(X0) | funny(X0) | ~creative(X0) | kind(X0)) & ((creative(X0) & ~kind(X0)) | (~curious(X0) & ~funny(X0)))) [flattening 49]
75. quiet(X0) | quiet(X0) | ~creative(X0) [cnf transformation 39]
77. ~quiet(X0) | ~quiet(X0) [cnf transformation 39]
78. curious(paul) | ~calm(X0) [cnf transformation 29]
80. calm(X0) | kind(X0) [cnf transformation 30]
94. creative(X0) | ~curious(X0) [cnf transformation 50]
122. ~kind(fred) [cnf transformation 21]
123. quiet(X0) | ~creative(X0) [duplicate literal removal 75]
124. ~quiet(X0) [duplicate literal removal 77]
130. 2 <=> kind(fred) [avatar definition]
131. ~kind(fred) <- (~2) [avatar component clause 130]
145. ~creative(X0) [subsumption resolution 123,124]
147. 5 <=> ! [X0] : ~calm(X0) [avatar definition]
148. ~calm(X0) <- (5) [avatar component clause 147]
155. 7 <=> curious(paul) [avatar definition]
157. curious(paul) <- (7) [avatar component clause 155]
158. 5 | 7 [avatar split clause 78,155,147]
201. ~curious(X0) [subsumption resolution 94,145]
236. ~2 [avatar split clause 122,130]
239. kind(X0) <- (5) [resolution 80,148]
240. $false <- (~2, 5) [resolution 239,131]
241. 2 | ~5 [avatar contradiction clause 240]
242. $false <- (7) [subsumption resolution 157,201]
243. ~7 [avatar contradiction clause 242]
244. $false [avatar sat refutation 158,236,241,243]
% SZS output end Proof for 4784029801701556323825395
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not generous or creative is calm. Everyone who is either not patient or generous is both funny and not curious. Everyone who is both not old and old is not rich or old and vice versa. Everyone who is rich is kind. If fred is kind or not strong then someone is either calm or not strong. Everyone who is strong or not calm is generous. Everyone who is either happy or not rich is not tall and vice versa. If paul is both not rich and creative then someone is not generous or not funny and vice versa. If someone is either not tall or kind then susan is not calm or kind. If mary is both brave and old then lucy is either strong or curious. Everyone who is either not old or brave is either not patient or not brave. If lucy is funny or not kind then someone is tall or not rich and vice versa. Everyone who is both not rich and not brave is not kind and vice versa. If someone is tall then mary is quiet. Everyone who is both not humble and old is both not strong and not rich. If someone is not rich or funny then alice is tall or funny and vice versa. Someone is not humble or humble. Lucy is not curious. John is both not quiet and strong. Mary is patient. Someone is humble. Someone is brave or rich. | John is generous. | entailment | (![X]:((~generous(X)<~>creative(X))=>calm(X)))&
(![X]:((~patient(X)<~>generous(X))=>(funny(X)&~curious(X))))&
(![X]:((~old(X)&old(X))<=>(~rich(X)|old(X))))&
(![X]:(rich(X)=>kind(X)))&
(((kind(fred)|~strong(fred)))=>(?[X]:((calm(X)<~>~strong(X)))))&
(![X]:((strong(X)|~calm(X))=>generous(X)))&
(![X]:((happy(X)<~>~rich(X))<=>~tall(X)))&
(((~rich(paul)&creative(paul)))<=>(?[X]:((~generous(X)|~funny(X)))))&
((?[X]:((~tall(X)<~>kind(X))))=>((~calm(susan)|kind(susan))))&
(((brave(mary)&old(mary)))=>((strong(lucy)<~>curious(lucy))))&
(![X]:((~old(X)<~>brave(X))=>(~patient(X)<~>~brave(X))))&
(((funny(lucy)|~kind(lucy)))<=>(?[X]:((tall(X)|~rich(X)))))&
(![X]:((~rich(X)&~brave(X))<=>~kind(X)))&
((?[X]:(tall(X)))=>(quiet(mary)))&
(![X]:((~humble(X)&old(X))=>(~strong(X)&~rich(X))))&
((?[X]:((~rich(X)|funny(X))))<=>((tall(alice)|funny(alice))))&
(?[X]:((~humble(X)|humble(X))))&
(~curious(lucy))&
((~quiet(john)&strong(john)))&
(patient(mary))&
(?[X]:(humble(X)))&
(?[X]:((brave(X)|rich(X)))) | generous(john) | [
"p2",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 6176546243430533982655174
% SZS output start Proof for 6176546243430533982655174
3. ! [X0] : ((old(X0) & ~old(X0)) <=> (old(X0) | ~rich(X0))) [input p2]
8. (creative(paul) & ~rich(paul)) <=> ? [X0] : (~funny(X0) | ~generous(X0)) [input p7]
23. ~generous(john) [input hypothesis]
39. ! [X0] : (((old(X0) & ~old(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (~old(X0) | old(X0)))) [nnf transformation 3]
40. ! [X0] : (((old(X0) & ~old(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | ~old(X0) | old(X0))) [flattening 39]
45. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & (? [X0] : (~funny(X0) | ~generous(X0)) | (~creative(paul) | rich(paul))) [nnf transformation 8]
46. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & (? [X0] : (~funny(X0) | ~generous(X0)) | ~creative(paul) | rich(paul)) [flattening 45]
47. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & (? [X1] : (~funny(X1) | ~generous(X1)) | ~creative(paul) | rich(paul)) [rectify 46]
48. ? [X1] : (~funny(X1) | ~generous(X1)) => (~funny(sK1) | ~generous(sK1)) [choice axiom]
49. ((creative(paul) & ~rich(paul)) | ! [X0] : (funny(X0) & generous(X0))) & ((~funny(sK1) | ~generous(sK1)) | ~creative(paul) | rich(paul)) [skolemisation 47,48]
79. ~old(X0) | ~old(X0) [cnf transformation 40]
80. rich(X0) | old(X0) [cnf transformation 40]
94. ~rich(paul) | generous(X0) [cnf transformation 49]
127. ~generous(john) [cnf transformation 23]
131. ~old(X0) [duplicate literal removal 79]
161. 7 <=> ! [X0] : generous(X0) [avatar definition]
162. generous(X0) <- (7) [avatar component clause 161]
165. 8 <=> rich(paul) [avatar definition]
167. ~rich(paul) <- (~8) [avatar component clause 165]
169. 7 | ~8 [avatar split clause 94,165,161]
259. old(paul) <- (~8) [resolution 80,167]
262. $false <- (~8) [subsumption resolution 259,131]
263. 8 [avatar contradiction clause 262]
270. $false <- (7) [resolution 162,127]
271. ~7 [avatar contradiction clause 270]
272. $false [avatar sat refutation 169,263,271]
% SZS output end Proof for 6176546243430533982655174
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either happy or quiet is not humble or funny.
Everyone who is rich or calm is not rich and vice versa.
Everyone who is either kind or old is either rich or patient and vice versa.
If alice is either not happy or patient then someone is either not curious or tall and vice versa.
Everyone who is not kind or not curious is either not happy or funny and vice versa.
Everyone who is not tall or not brave is both not patient and tall and vice versa.
Everyone who is brave or not tall is both not brave and not quiet and vice versa.
If someone is both not old and not humble then paul is not funny or not quiet.
If lucy is either not kind or calm then susan is both funny and not kind and vice versa.
If someone is either not creative or not brave then someone is not quiet.
Everyone who is either funny or not rich is both not wise and not rich.
Everyone who is not rich is not wise and vice versa.
Everyone who is not brave or not old is wise or funny.
Everyone who is strong is not wise.
If someone is not happy then mary is wise and vice versa.
Someone is either not brave or not humble.
Someone is either humble or not kind. | Susan is not creative. | entailment | (![X]:((happy(X)<~>quiet(X))=>(~humble(X)|funny(X))))&
(![X]:((rich(X)|calm(X))<=>~rich(X)))&
(![X]:((kind(X)<~>old(X))<=>(rich(X)<~>patient(X))))&
(((~happy(alice)<~>patient(alice)))<=>(?[X]:((~curious(X)<~>tall(X)))))&
(![X]:((~kind(X)|~curious(X))<=>(~happy(X)<~>funny(X))))&
(![X]:((~tall(X)|~brave(X))<=>(~patient(X)&tall(X))))&
(![X]:((brave(X)|~tall(X))<=>(~brave(X)&~quiet(X))))&
((?[X]:((~old(X)&~humble(X))))=>((~funny(paul)|~quiet(paul))))&
(((~kind(lucy)<~>calm(lucy)))<=>((funny(susan)&~kind(susan))))&
((?[X]:((~creative(X)<~>~brave(X))))=>(?[X]:(~quiet(X))))&
(![X]:((funny(X)<~>~rich(X))=>(~wise(X)&~rich(X))))&
(![X]:(~rich(X)<=>~wise(X)))&
(![X]:((~brave(X)|~old(X))=>(wise(X)|funny(X))))&
(![X]:(strong(X)=>~wise(X)))&
((?[X]:(~happy(X)))<=>(wise(mary)))&
(?[X]:((~brave(X)<~>~humble(X))))&
(?[X]:((humble(X)<~>~kind(X)))) | ~creative(susan) | [
"p5",
"p6",
"p9",
"hypothesis"
] | % SZS status Unsatisfiable for 2355653040622427381846877
% SZS output start Proof for 2355653040622427381846877
6. ! [X0] : ((~brave(X0) | ~tall(X0)) <=> (tall(X0) & ~patient(X0))) [input p5]
7. ! [X0] : ((~tall(X0) | brave(X0)) <=> (~quiet(X0) & ~brave(X0))) [input p6]
10. ? [X0] : (~creative(X0) <~> ~brave(X0)) => ? [X0] : ~quiet(X0) [input p9]
18. creative(susan) [input hypothesis]
19. ? [X0] : (~creative(X0) <~> ~brave(X0)) => ? [X1] : ~quiet(X1) [rectify 10]
25. ? [X1] : ~quiet(X1) | ! [X0] : (~creative(X0) <=> ~brave(X0)) [ennf transformation 19]
39. ! [X0] : (((~brave(X0) | ~tall(X0)) | (~tall(X0) | patient(X0))) & ((tall(X0) & ~patient(X0)) | (brave(X0) & tall(X0)))) [nnf transformation 6]
40. ! [X0] : ((~brave(X0) | ~tall(X0) | ~tall(X0) | patient(X0)) & ((tall(X0) & ~patient(X0)) | (brave(X0) & tall(X0)))) [flattening 39]
41. ! [X0] : (((~tall(X0) | brave(X0)) | (quiet(X0) | brave(X0))) & ((~quiet(X0) & ~brave(X0)) | (tall(X0) & ~brave(X0)))) [nnf transformation 7]
42. ! [X0] : ((~tall(X0) | brave(X0) | quiet(X0) | brave(X0)) & ((~quiet(X0) & ~brave(X0)) | (tall(X0) & ~brave(X0)))) [flattening 41]
45. ? [X1] : ~quiet(X1) | ! [X0] : ((~creative(X0) | brave(X0)) & (~brave(X0) | creative(X0))) [nnf transformation 25]
46. ? [X0] : ~quiet(X0) | ! [X1] : ((~creative(X1) | brave(X1)) & (~brave(X1) | creative(X1))) [rectify 45]
47. ? [X0] : ~quiet(X0) => ~quiet(sK1) [choice axiom]
48. ~quiet(sK1) | ! [X1] : ((~creative(X1) | brave(X1)) & (~brave(X1) | creative(X1))) [skolemisation 46,47]
90. tall(X0) | tall(X0) [cnf transformation 40]
93. ~brave(X0) | ~brave(X0) [cnf transformation 42]
97. ~tall(X0) | brave(X0) | quiet(X0) | brave(X0) [cnf transformation 42]
106. ~quiet(sK1) | ~creative(X1) | brave(X1) [cnf transformation 48]
121. creative(susan) [cnf transformation 18]
123. ~brave(X0) [duplicate literal removal 93]
124. ~tall(X0) | brave(X0) | quiet(X0) [duplicate literal removal 97]
125. tall(X0) [duplicate literal removal 90]
163. brave(X0) | quiet(X0) [subsumption resolution 124,125]
198. ~quiet(sK1) | ~creative(X1) [subsumption resolution 106,123]
200. 14 <=> ! [X1] : ~creative(X1) [avatar definition]
201. ~creative(X1) <- (14) [avatar component clause 200]
203. 15 <=> quiet(sK1) [avatar definition]
205. ~quiet(sK1) <- (~15) [avatar component clause 203]
206. 14 | ~15 [avatar split clause 198,203,200]
246. quiet(X1) [resolution 163,123]
248. $false <- (~15) [resolution 246,205]
249. 15 [avatar contradiction clause 248]
251. $false <- (14) [resolution 201,121]
252. ~14 [avatar contradiction clause 251]
253. $false [avatar sat refutation 206,249,252]
% SZS output end Proof for 2355653040622427381846877
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both patient and not brave is either not creative or not old and vice versa.
Everyone who is either brave or kind is either happy or brave.
Everyone who is not kind is both not humble and generous.
If susan is both not generous and generous then lucy is not wise or not funny.
Everyone who is either old or not happy is happy.
Everyone who is both quiet and not brave is not curious or old.
Everyone who is humble is not quiet or strong.
If fred is not tall or humble then fred is not creative or humble and vice versa.
If fred is quiet or strong then someone is either funny or not creative and vice versa.
Everyone who is rich or quiet is both humble and calm.
Everyone who is both not patient and not kind is both generous and strong and vice versa.
Everyone who is not generous or not humble is not tall.
Everyone who is either kind or strong is both old and not calm.
Everyone who is old is either tall or wise and vice versa.
If alice is either not tall or not kind then someone is not brave or not calm and vice versa.
If alice is either humble or generous then fred is either wise or not wise and vice versa.
Someone is not funny or not humble.
Someone is humble or tall.
Someone is not happy or not strong.
Someone is both not humble and happy.
Susan is both not creative and not happy.
Someone is either not tall or calm.
Someone is both not curious and happy.
Someone is calm. | Susan is wise. | entailment | (![X]:((patient(X)&~brave(X))<=>(~creative(X)<~>~old(X))))&
(![X]:((brave(X)<~>kind(X))=>(happy(X)<~>brave(X))))&
(![X]:(~kind(X)=>(~humble(X)&generous(X))))&
(((~generous(susan)&generous(susan)))=>((~wise(lucy)|~funny(lucy))))&
(![X]:((old(X)<~>~happy(X))=>happy(X)))&
(![X]:((quiet(X)&~brave(X))=>(~curious(X)|old(X))))&
(![X]:(humble(X)=>(~quiet(X)|strong(X))))&
(((~tall(fred)|humble(fred)))<=>((~creative(fred)|humble(fred))))&
(((quiet(fred)|strong(fred)))<=>(?[X]:((funny(X)<~>~creative(X)))))&
(![X]:((rich(X)|quiet(X))=>(humble(X)&calm(X))))&
(![X]:((~patient(X)&~kind(X))<=>(generous(X)&strong(X))))&
(![X]:((~generous(X)|~humble(X))=>~tall(X)))&
(![X]:((kind(X)<~>strong(X))=>(old(X)&~calm(X))))&
(![X]:(old(X)<=>(tall(X)<~>wise(X))))&
(((~tall(alice)<~>~kind(alice)))<=>(?[X]:((~brave(X)|~calm(X)))))&
(((humble(alice)<~>generous(alice)))<=>((wise(fred)<~>~wise(fred))))&
(?[X]:((~funny(X)|~humble(X))))&
(?[X]:((humble(X)|tall(X))))&
(?[X]:((~happy(X)|~strong(X))))&
(?[X]:((~humble(X)&happy(X))))&
((~creative(susan)&~happy(susan)))&
(?[X]:((~tall(X)<~>calm(X))))&
(?[X]:((~curious(X)&happy(X))))&
(?[X]:(calm(X))) | wise(susan) | [
"p0",
"p1",
"p2",
"p4",
"p11",
"p13",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7609555856457217104688149
% SZS output start Proof for 7609555856457217104688149
1. ! [X0] : ((~brave(X0) & patient(X0)) <=> (~creative(X0) <~> ~old(X0))) [input p0]
2. ! [X0] : ((brave(X0) <~> kind(X0)) => (happy(X0) <~> brave(X0))) [input p1]
3. ! [X0] : (~kind(X0) => (generous(X0) & ~humble(X0))) [input p2]
5. ! [X0] : ((old(X0) <~> ~happy(X0)) => happy(X0)) [input p4]
12. ! [X0] : ((~humble(X0) | ~generous(X0)) => ~tall(X0)) [input p11]
14. ! [X0] : (old(X0) <=> (tall(X0) <~> wise(X0))) [input p13]
21. ~happy(susan) & ~creative(susan) [input p20]
25. ~wise(susan) [input hypothesis]
29. ! [X0] : ((happy(X0) <~> brave(X0)) | (brave(X0) <=> kind(X0))) [ennf transformation 2]
30. ! [X0] : ((generous(X0) & ~humble(X0)) | kind(X0)) [ennf transformation 3]
33. ! [X0] : (happy(X0) | (old(X0) <=> ~happy(X0))) [ennf transformation 5]
37. ! [X0] : (~tall(X0) | (humble(X0) & generous(X0))) [ennf transformation 12]
39. ! [X0] : (((~brave(X0) & patient(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | (brave(X0) | ~patient(X0)))) [nnf transformation 1]
40. ! [X0] : (((~brave(X0) & patient(X0)) | ((~creative(X0) | old(X0)) & (~old(X0) | creative(X0)))) & (((old(X0) | creative(X0)) & (~old(X0) | ~creative(X0))) | brave(X0) | ~patient(X0))) [flattening 39]
41. ! [X0] : (((~brave(X0) | ~happy(X0)) & (brave(X0) | happy(X0))) | ((brave(X0) | ~kind(X0)) & (kind(X0) | ~brave(X0)))) [nnf transformation 29]
42. ! [X0] : (happy(X0) | ((old(X0) | happy(X0)) & (~happy(X0) | ~old(X0)))) [nnf transformation 33]
53. ! [X0] : ((old(X0) | ((tall(X0) | ~wise(X0)) & (wise(X0) | ~tall(X0)))) & (((~wise(X0) | ~tall(X0)) & (wise(X0) | tall(X0))) | ~old(X0))) [nnf transformation 14]
78. ~old(X0) | ~brave(X0) | creative(X0) [cnf transformation 40]
81. brave(X0) | happy(X0) | brave(X0) | ~kind(X0) [cnf transformation 41]
84. ~humble(X0) | kind(X0) [cnf transformation 30]
88. happy(X0) | old(X0) | happy(X0) [cnf transformation 42]
107. ~tall(X0) | humble(X0) [cnf transformation 37]
112. ~old(X0) | tall(X0) | wise(X0) [cnf transformation 53]
135. ~creative(susan) [cnf transformation 21]
136. ~happy(susan) [cnf transformation 21]
141. ~wise(susan) [cnf transformation 25]
146. happy(X0) | old(X0) [duplicate literal removal 88]
147. ~kind(X0) | happy(X0) | brave(X0) [duplicate literal removal 81]
274. old(susan) [resolution 146,136]
288. ~brave(susan) | creative(susan) [resolution 78,274]
290. ~brave(susan) [subsumption resolution 288,135]
389. tall(susan) | wise(susan) [resolution 112,274]
393. tall(susan) [subsumption resolution 389,141]
498. humble(susan) [resolution 393,107]
520. kind(susan) [resolution 498,84]
521. happy(susan) | brave(susan) [resolution 520,147]
523. brave(susan) [subsumption resolution 521,136]
524. $false [subsumption resolution 523,290]
% SZS output end Proof for 7609555856457217104688149
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If john is either not brave or not wise then mary is strong or brave. Everyone who is not calm or not funny is not happy or not calm. Everyone who is rich or humble is creative or generous and vice versa. Everyone who is both not strong and not patient is not strong or funny and vice versa. Everyone who is patient or not curious is both curious and not calm and vice versa. If someone is either rich or not old then lucy is either not kind or not strong and vice versa. If fred is both not quiet and not brave then fred is both not tall and quiet. If someone is not tall then mary is either calm or not generous and vice versa. Everyone who is both not generous and creative is not curious and vice versa. If fred is either not happy or not humble then paul is not rich. Everyone who is not patient is quiet or not strong and vice versa. Everyone who is both not curious and not quiet is either not brave or kind and vice versa. If someone is both not generous and not calm then lucy is not curious or not humble. Everyone who is either not tall or not quiet is either creative or not humble and vice versa. Everyone who is either not patient or creative is not kind or not generous. If someone is rich then someone is either not calm or not wise and vice versa. Someone is curious or not brave. Someone is not humble. John is generous or quiet. Someone is either funny or not curious. Fred is not old. Someone is not happy or generous. Susan is both not patient and strong. | Susan is generous. | neutral | (((~brave(john)<~>~wise(john)))=>((strong(mary)|brave(mary))))&
(![X]:((~calm(X)|~funny(X))=>(~happy(X)|~calm(X))))&
(![X]:((rich(X)|humble(X))<=>(creative(X)|generous(X))))&
(![X]:((~strong(X)&~patient(X))<=>(~strong(X)|funny(X))))&
(![X]:((patient(X)|~curious(X))<=>(curious(X)&~calm(X))))&
((?[X]:((rich(X)<~>~old(X))))<=>((~kind(lucy)<~>~strong(lucy))))&
(((~quiet(fred)&~brave(fred)))=>((~tall(fred)&quiet(fred))))&
((?[X]:(~tall(X)))<=>((calm(mary)<~>~generous(mary))))&
(![X]:((~generous(X)&creative(X))<=>~curious(X)))&
(((~happy(fred)<~>~humble(fred)))=>(~rich(paul)))&
(![X]:(~patient(X)<=>(quiet(X)|~strong(X))))&
(![X]:((~curious(X)&~quiet(X))<=>(~brave(X)<~>kind(X))))&
((?[X]:((~generous(X)&~calm(X))))=>((~curious(lucy)|~humble(lucy))))&
(![X]:((~tall(X)<~>~quiet(X))<=>(creative(X)<~>~humble(X))))&
(![X]:((~patient(X)<~>creative(X))=>(~kind(X)|~generous(X))))&
((?[X]:(rich(X)))<=>(?[X]:((~calm(X)<~>~wise(X)))))&
(?[X]:((curious(X)|~brave(X))))&
(?[X]:(~humble(X)))&
((generous(john)|quiet(john)))&
(?[X]:((funny(X)<~>~curious(X))))&
(~old(fred))&
(?[X]:((~happy(X)|generous(X))))&
((~patient(susan)&strong(susan))) | generous(susan) | [] | null | 0 |
If someone is wise then someone is old or not brave.
Everyone who is quiet is both wise and patient.
If someone is either not generous or not tall then john is either rich or not humble and vice versa.
If alice is not quiet then susan is either not tall or not kind and vice versa.
Everyone who is funny or creative is kind and vice versa.
If fred is either calm or curious then john is either not tall or not kind.
If lucy is funny or not happy then someone is either not patient or not generous and vice versa.
If someone is not creative then john is calm.
Everyone who is both not tall and rich is not old or old and vice versa.
Everyone who is not strong is both not strong and strong.
Everyone who is both not quiet and funny is both happy and not tall and vice versa.
Everyone who is rich is strong or not funny.
Everyone who is both old and humble is either quiet or not rich.
If someone is not calm then lucy is brave or not curious.
Everyone who is not patient or calm is humble or old and vice versa.
If someone is both not creative and rich then paul is either not strong or not creative and vice versa.
Alice is calm.
Someone is either old or not strong.
Susan is not old.
Someone is not kind or not wise.
Fred is not calm or not brave.
Lucy is both not old and funny.
Paul is funny.
Mary is rich. | Mary is not rich. | contradiction | ((?[X]:(wise(X)))=>(?[X]:((old(X)|~brave(X)))))&
(![X]:(quiet(X)=>(wise(X)&patient(X))))&
((?[X]:((~generous(X)<~>~tall(X))))<=>((rich(john)<~>~humble(john))))&
((~quiet(alice))<=>((~tall(susan)<~>~kind(susan))))&
(![X]:((funny(X)|creative(X))<=>kind(X)))&
(((calm(fred)<~>curious(fred)))=>((~tall(john)<~>~kind(john))))&
(((funny(lucy)|~happy(lucy)))<=>(?[X]:((~patient(X)<~>~generous(X)))))&
((?[X]:(~creative(X)))=>(calm(john)))&
(![X]:((~tall(X)&rich(X))<=>(~old(X)|old(X))))&
(![X]:(~strong(X)=>(~strong(X)&strong(X))))&
(![X]:((~quiet(X)&funny(X))<=>(happy(X)&~tall(X))))&
(![X]:(rich(X)=>(strong(X)|~funny(X))))&
(![X]:((old(X)&humble(X))=>(quiet(X)<~>~rich(X))))&
((?[X]:(~calm(X)))=>((brave(lucy)|~curious(lucy))))&
(![X]:((~patient(X)|calm(X))<=>(humble(X)|old(X))))&
((?[X]:((~creative(X)&rich(X))))<=>((~strong(paul)<~>~creative(paul))))&
(calm(alice))&
(?[X]:((old(X)<~>~strong(X))))&
(~old(susan))&
(?[X]:((~kind(X)|~wise(X))))&
((~calm(fred)|~brave(fred)))&
((~old(lucy)&funny(lucy)))&
(funny(paul))&
(rich(mary)) | ~rich(mary) | [
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 8287412932423494353187064
% SZS output start Proof for 8287412932423494353187064
9. ! [X0] : ((rich(X0) & ~tall(X0)) <=> (old(X0) | ~old(X0))) [input p8]
25. ~rich(mary) [input hypothesis]
54. ! [X0] : (((rich(X0) & ~tall(X0)) | (~old(X0) & old(X0))) & ((old(X0) | ~old(X0)) | (~rich(X0) | tall(X0)))) [nnf transformation 9]
55. ! [X0] : (((rich(X0) & ~tall(X0)) | (~old(X0) & old(X0))) & (old(X0) | ~old(X0) | ~rich(X0) | tall(X0))) [flattening 54]
102. rich(X0) | old(X0) [cnf transformation 55]
103. rich(X0) | ~old(X0) [cnf transformation 55]
134. ~rich(mary) [cnf transformation 25]
250. rich(X0) [subsumption resolution 102,103]
296. $false [subsumption resolution 134,250]
% SZS output end Proof for 8287412932423494353187064
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 creative or brave then someone is both wise and happy.
Everyone who is either brave or not strong is either not old or quiet and vice versa.
Everyone who is patient is tall or not quiet and vice versa.
Everyone who is both rich and not creative is either wise or creative and vice versa.
Everyone who is both not patient and not quiet is either calm or funny and vice versa.
If someone is old or strong then someone is either generous or patient and vice versa.
Everyone who is not kind or happy is both not humble and happy.
Everyone who is kind is humble and vice versa.
Everyone who is both not wise and not patient is either not happy or not quiet.
Everyone who is strong or not quiet is not old.
If fred is both not strong and curious then someone is not humble or kind and vice versa.
Everyone who is either old or not kind is both funny and not happy and vice versa.
Everyone who is not happy is curious or not wise and vice versa.
Everyone who is both calm and funny is quiet or not calm and vice versa.
Everyone who is both not funny and calm is generous or not happy.
Susan is not curious.
Someone is not humble or not brave.
Someone is either not happy or creative.
Someone is either happy or calm.
Someone is rich.
Someone is not kind or strong.
Someone is not wise or not quiet. | Fred is old. | entailment | ((?[X]:((~creative(X)|brave(X))))=>(?[X]:((wise(X)&happy(X)))))&
(![X]:((brave(X)<~>~strong(X))<=>(~old(X)<~>quiet(X))))&
(![X]:(patient(X)<=>(tall(X)|~quiet(X))))&
(![X]:((rich(X)&~creative(X))<=>(wise(X)<~>creative(X))))&
(![X]:((~patient(X)&~quiet(X))<=>(calm(X)<~>funny(X))))&
((?[X]:((old(X)|strong(X))))<=>(?[X]:((generous(X)<~>patient(X)))))&
(![X]:((~kind(X)|happy(X))=>(~humble(X)&happy(X))))&
(![X]:(kind(X)<=>humble(X)))&
(![X]:((~wise(X)&~patient(X))=>(~happy(X)<~>~quiet(X))))&
(![X]:((strong(X)|~quiet(X))=>~old(X)))&
(((~strong(fred)&curious(fred)))<=>(?[X]:((~humble(X)|kind(X)))))&
(![X]:((old(X)<~>~kind(X))<=>(funny(X)&~happy(X))))&
(![X]:(~happy(X)<=>(curious(X)|~wise(X))))&
(![X]:((calm(X)&funny(X))<=>(quiet(X)|~calm(X))))&
(![X]:((~funny(X)&calm(X))=>(generous(X)|~happy(X))))&
(~curious(susan))&
(?[X]:((~humble(X)|~brave(X))))&
(?[X]:((~happy(X)<~>creative(X))))&
(?[X]:((happy(X)<~>calm(X))))&
(?[X]:(rich(X)))&
(?[X]:((~kind(X)|strong(X))))&
(?[X]:((~wise(X)|~quiet(X)))) | old(fred) | [
"p2",
"p4",
"p6",
"p7",
"p11",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 1374831299624024092702597
% SZS output start Proof for 1374831299624024092702597
3. ! [X0] : (patient(X0) <=> (~quiet(X0) | tall(X0))) [input p2]
5. ! [X0] : ((~quiet(X0) & ~patient(X0)) <=> (calm(X0) <~> funny(X0))) [input p4]
7. ! [X0] : ((happy(X0) | ~kind(X0)) => (happy(X0) & ~humble(X0))) [input p6]
8. ! [X0] : (kind(X0) <=> humble(X0)) [input p7]
12. ! [X0] : ((old(X0) <~> ~kind(X0)) <=> (~happy(X0) & funny(X0))) [input p11]
14. ! [X0] : ((funny(X0) & calm(X0)) <=> (~calm(X0) | quiet(X0))) [input p13]
23. ~old(fred) [input hypothesis]
27. ! [X0] : ((happy(X0) & ~humble(X0)) | (~happy(X0) & kind(X0))) [ennf transformation 7]
37. ! [X0] : ((patient(X0) | (quiet(X0) & ~tall(X0))) & ((~quiet(X0) | tall(X0)) | ~patient(X0))) [nnf transformation 3]
38. ! [X0] : ((patient(X0) | (quiet(X0) & ~tall(X0))) & (~quiet(X0) | tall(X0) | ~patient(X0))) [flattening 37]
41. ! [X0] : (((~quiet(X0) & ~patient(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | (quiet(X0) | patient(X0)))) [nnf transformation 5]
42. ! [X0] : (((~quiet(X0) & ~patient(X0)) | ((calm(X0) | ~funny(X0)) & (funny(X0) | ~calm(X0)))) & (((~funny(X0) | ~calm(X0)) & (funny(X0) | calm(X0))) | quiet(X0) | patient(X0))) [flattening 41]
48. ! [X0] : ((kind(X0) | ~humble(X0)) & (humble(X0) | ~kind(X0))) [nnf transformation 8]
55. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | (happy(X0) | ~funny(X0))) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [nnf transformation 12]
56. ! [X0] : ((((kind(X0) | ~old(X0)) & (~kind(X0) | old(X0))) | happy(X0) | ~funny(X0)) & ((~happy(X0) & funny(X0)) | ((old(X0) | kind(X0)) & (~kind(X0) | ~old(X0))))) [flattening 55]
59. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & ~quiet(X0))) & ((~calm(X0) | quiet(X0)) | (~funny(X0) | ~calm(X0)))) [nnf transformation 14]
60. ! [X0] : (((funny(X0) & calm(X0)) | (calm(X0) & ~quiet(X0))) & (~calm(X0) | quiet(X0) | ~funny(X0) | ~calm(X0))) [flattening 59]
89. patient(X0) | quiet(X0) [cnf transformation 38]
98. ~calm(X0) | funny(X0) | ~patient(X0) [cnf transformation 42]
109. ~humble(X0) | ~happy(X0) [cnf transformation 27]
110. kind(X0) | happy(X0) [cnf transformation 27]
112. ~kind(X0) | humble(X0) [cnf transformation 48]
126. ~happy(X0) | old(X0) | kind(X0) [cnf transformation 56]
127. ~kind(X0) | old(X0) | happy(X0) | ~funny(X0) [cnf transformation 56]
134. calm(X0) | calm(X0) [cnf transformation 60]
135. ~quiet(X0) | funny(X0) [cnf transformation 60]
147. ~old(fred) [cnf transformation 23]
149. calm(X0) [duplicate literal removal 134]
224. ~funny(X0) | happy(X0) | old(X0) [subsumption resolution 127,110]
225. kind(X0) | old(X0) [subsumption resolution 126,110]
279. humble(X0) | old(X0) [resolution 225,112]
316. ~patient(X0) | funny(X0) [resolution 98,149]
369. ~happy(X0) | old(X0) [resolution 279,109]
489. funny(X0) | quiet(X0) [resolution 316,89]
490. funny(X0) [subsumption resolution 489,135]
509. happy(X0) | old(X0) [resolution 490,224]
513. old(X0) [subsumption resolution 509,369]
554. $false [resolution 513,147]
% SZS output end Proof for 1374831299624024092702597
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not funny and not calm is not creative or funny.
If alice is either not quiet or not wise then john is both wise and curious.
If someone is not old or not wise then someone is not kind and vice versa.
Everyone who is either not humble or wise is not brave and vice versa.
Everyone who is both not old and not happy is both not strong and curious and vice versa.
Everyone who is not generous is either not curious or humble.
Everyone who is happy or calm is both humble and not happy and vice versa.
If someone is either quiet or not rich then susan is either wise or brave.
If paul is tall then john is both not tall and not rich and vice versa.
Everyone who is either not calm or strong is wise.
If someone is both tall and not funny then someone is not brave or rich.
Everyone who is patient or strong is rich and vice versa.
Everyone who is creative or not strong is both not calm and strong and vice versa.
If fred is both not rich and not humble then susan is both not funny and quiet and vice versa.
Everyone who is strong is tall or not funny.
If someone is happy or generous then someone is either kind or not tall and vice versa.
Someone is either rich or tall.
Someone is either not patient or not creative.
John is either brave or generous.
Alice is curious or tall.
Someone is not happy.
John is happy or not kind. | Susan is not funny. | neutral | (![X]:((~funny(X)&~calm(X))=>(~creative(X)|funny(X))))&
(((~quiet(alice)<~>~wise(alice)))=>((wise(john)&curious(john))))&
((?[X]:((~old(X)|~wise(X))))<=>(?[X]:(~kind(X))))&
(![X]:((~humble(X)<~>wise(X))<=>~brave(X)))&
(![X]:((~old(X)&~happy(X))<=>(~strong(X)&curious(X))))&
(![X]:(~generous(X)=>(~curious(X)<~>humble(X))))&
(![X]:((happy(X)|calm(X))<=>(humble(X)&~happy(X))))&
((?[X]:((quiet(X)<~>~rich(X))))=>((wise(susan)<~>brave(susan))))&
((tall(paul))<=>((~tall(john)&~rich(john))))&
(![X]:((~calm(X)<~>strong(X))=>wise(X)))&
((?[X]:((tall(X)&~funny(X))))=>(?[X]:((~brave(X)|rich(X)))))&
(![X]:((patient(X)|strong(X))<=>rich(X)))&
(![X]:((creative(X)|~strong(X))<=>(~calm(X)&strong(X))))&
(((~rich(fred)&~humble(fred)))<=>((~funny(susan)&quiet(susan))))&
(![X]:(strong(X)=>(tall(X)|~funny(X))))&
((?[X]:((happy(X)|generous(X))))<=>(?[X]:((kind(X)<~>~tall(X)))))&
(?[X]:((rich(X)<~>tall(X))))&
(?[X]:((~patient(X)<~>~creative(X))))&
((brave(john)<~>generous(john)))&
((curious(alice)|tall(alice)))&
(?[X]:(~happy(X)))&
((happy(john)|~kind(john))) | ~funny(susan) | [] | null | 0 |
If someone is either brave or old then paul is both old and not patient.
Everyone who is quiet is both not calm and old and vice versa.
Everyone who is both kind and not happy is brave and vice versa.
Everyone who is either happy or not humble is not funny or rich and vice versa.
Everyone who is not patient is happy and vice versa.
Everyone who is old or wise is tall and vice versa.
Everyone who is not kind or not generous is brave.
Everyone who is either wise or not curious is either old or funny.
Everyone who is both happy and not wise is both not tall and not wise.
If someone is not patient then someone is either happy or not tall and vice versa.
If alice is rich or wise then lucy is tall or not wise.
If mary is wise then someone is not brave or not tall.
If mary is not curious then someone is not kind.
Everyone who is both not wise and not curious is old and vice versa.
Everyone who is creative or not old is either creative or wise.
If fred is not generous then john is not humble and vice versa.
Lucy is kind.
Someone is both not wise and kind.
Alice is both curious and not calm.
Mary is not old.
Someone is not brave or rich.
Someone is not brave or creative.
Someone is both not humble and happy. | Fred is not generous. | neutral | ((?[X]:((brave(X)<~>old(X))))=>((old(paul)&~patient(paul))))&
(![X]:(quiet(X)<=>(~calm(X)&old(X))))&
(![X]:((kind(X)&~happy(X))<=>brave(X)))&
(![X]:((happy(X)<~>~humble(X))<=>(~funny(X)|rich(X))))&
(![X]:(~patient(X)<=>happy(X)))&
(![X]:((old(X)|wise(X))<=>tall(X)))&
(![X]:((~kind(X)|~generous(X))=>brave(X)))&
(![X]:((wise(X)<~>~curious(X))=>(old(X)<~>funny(X))))&
(![X]:((happy(X)&~wise(X))=>(~tall(X)&~wise(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((happy(X)<~>~tall(X)))))&
(((rich(alice)|wise(alice)))=>((tall(lucy)|~wise(lucy))))&
((wise(mary))=>(?[X]:((~brave(X)|~tall(X)))))&
((~curious(mary))=>(?[X]:(~kind(X))))&
(![X]:((~wise(X)&~curious(X))<=>old(X)))&
(![X]:((creative(X)|~old(X))=>(creative(X)<~>wise(X))))&
((~generous(fred))<=>(~humble(john)))&
(kind(lucy))&
(?[X]:((~wise(X)&kind(X))))&
((curious(alice)&~calm(alice)))&
(~old(mary))&
(?[X]:((~brave(X)|rich(X))))&
(?[X]:((~brave(X)|creative(X))))&
(?[X]:((~humble(X)&happy(X)))) | ~generous(fred) | [] | null | 0 |
Everyone who is not rich or happy is both not curious and kind and vice versa. Everyone who is either wise or curious is not funny or tall. Everyone who is both not old and not strong is either tall or brave. If someone is either not wise or not curious then paul is not creative. Everyone who is either not kind or patient is both patient and calm and vice versa. Everyone who is not patient is both tall and not funny and vice versa. Everyone who is either not humble or calm is both not curious and not creative and vice versa. Everyone who is not curious or not patient is either not wise or not quiet. Everyone who is not creative or not humble is either not quiet or wise and vice versa. If someone is brave or generous then alice is not patient or not tall. Everyone who is both not rich and patient is calm and vice versa. If someone is either not kind or wise then john is either brave or creative and vice versa. Everyone who is not patient is either not kind or not wise and vice versa. Everyone who is both not generous and not funny is either calm or not kind. If someone is both strong and not wise then someone is patient and vice versa. If john is either not calm or not brave then paul is both not calm and not funny and vice versa. Susan is both rich and not creative. Lucy is either not tall or not generous. Someone is both tall and creative. Susan is old or generous. Fred is not rich. Susan is either calm or patient. Someone is not brave or not calm. | John is humble. | entailment | (![X]:((~rich(X)|happy(X))<=>(~curious(X)&kind(X))))&
(![X]:((wise(X)<~>curious(X))=>(~funny(X)|tall(X))))&
(![X]:((~old(X)&~strong(X))=>(tall(X)<~>brave(X))))&
((?[X]:((~wise(X)<~>~curious(X))))=>(~creative(paul)))&
(![X]:((~kind(X)<~>patient(X))<=>(patient(X)&calm(X))))&
(![X]:(~patient(X)<=>(tall(X)&~funny(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(~curious(X)&~creative(X))))&
(![X]:((~curious(X)|~patient(X))=>(~wise(X)<~>~quiet(X))))&
(![X]:((~creative(X)|~humble(X))<=>(~quiet(X)<~>wise(X))))&
((?[X]:((brave(X)|generous(X))))=>((~patient(alice)|~tall(alice))))&
(![X]:((~rich(X)&patient(X))<=>calm(X)))&
((?[X]:((~kind(X)<~>wise(X))))<=>((brave(john)<~>creative(john))))&
(![X]:(~patient(X)<=>(~kind(X)<~>~wise(X))))&
(![X]:((~generous(X)&~funny(X))=>(calm(X)<~>~kind(X))))&
((?[X]:((strong(X)&~wise(X))))<=>(?[X]:(patient(X))))&
(((~calm(john)<~>~brave(john)))<=>((~calm(paul)&~funny(paul))))&
((rich(susan)&~creative(susan)))&
((~tall(lucy)<~>~generous(lucy)))&
(?[X]:((tall(X)&creative(X))))&
((old(susan)|generous(susan)))&
(~rich(fred))&
((calm(susan)<~>patient(susan)))&
(?[X]:((~brave(X)|~calm(X)))) | humble(john) | [
"p0",
"p6",
"p7",
"p8",
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 45488864349848927258005
% SZS output start Proof for 45488864349848927258005
1. ! [X0] : ((happy(X0) | ~rich(X0)) <=> (kind(X0) & ~curious(X0))) [input p0]
7. ! [X0] : ((~humble(X0) <~> calm(X0)) <=> (~creative(X0) & ~curious(X0))) [input p6]
8. ! [X0] : ((~patient(X0) | ~curious(X0)) => (~wise(X0) <~> ~quiet(X0))) [input p7]
9. ! [X0] : ((~humble(X0) | ~creative(X0)) <=> (~quiet(X0) <~> wise(X0))) [input p8]
11. ! [X0] : ((patient(X0) & ~rich(X0)) <=> calm(X0)) [input p10]
24. ~humble(john) [input hypothesis]
31. ! [X0] : ((~wise(X0) <~> ~quiet(X0)) | (patient(X0) & curious(X0))) [ennf transformation 8]
36. ! [X0] : (((happy(X0) | ~rich(X0)) | (~kind(X0) | curious(X0))) & ((kind(X0) & ~curious(X0)) | (~happy(X0) & rich(X0)))) [nnf transformation 1]
37. ! [X0] : ((happy(X0) | ~rich(X0) | ~kind(X0) | curious(X0)) & ((kind(X0) & ~curious(X0)) | (~happy(X0) & rich(X0)))) [flattening 36]
44. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | (creative(X0) | curious(X0))) & ((~creative(X0) & ~curious(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [nnf transformation 7]
45. ! [X0] : ((((~calm(X0) | humble(X0)) & (calm(X0) | ~humble(X0))) | creative(X0) | curious(X0)) & ((~creative(X0) & ~curious(X0)) | ((~humble(X0) | ~calm(X0)) & (calm(X0) | humble(X0))))) [flattening 44]
46. ! [X0] : (((quiet(X0) | wise(X0)) & (~quiet(X0) | ~wise(X0))) | (patient(X0) & curious(X0))) [nnf transformation 31]
47. ! [X0] : (((~humble(X0) | ~creative(X0)) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | (humble(X0) & creative(X0)))) [nnf transformation 9]
48. ! [X0] : ((~humble(X0) | ~creative(X0) | ((~quiet(X0) | ~wise(X0)) & (wise(X0) | quiet(X0)))) & (((~wise(X0) | quiet(X0)) & (wise(X0) | ~quiet(X0))) | (humble(X0) & creative(X0)))) [flattening 47]
49. ! [X0] : (((patient(X0) & ~rich(X0)) | ~calm(X0)) & (calm(X0) | (~patient(X0) | rich(X0)))) [nnf transformation 11]
50. ! [X0] : (((patient(X0) & ~rich(X0)) | ~calm(X0)) & (calm(X0) | ~patient(X0) | rich(X0))) [flattening 49]
70. ~curious(X0) | rich(X0) [cnf transformation 37]
88. ~curious(X0) | calm(X0) | humble(X0) [cnf transformation 45]
94. ~quiet(X0) | ~wise(X0) | curious(X0) [cnf transformation 46]
96. quiet(X0) | wise(X0) | curious(X0) [cnf transformation 46]
99. ~quiet(X0) | wise(X0) | humble(X0) [cnf transformation 48]
101. ~wise(X0) | quiet(X0) | humble(X0) [cnf transformation 48]
107. ~calm(X0) | ~rich(X0) [cnf transformation 50]
142. ~humble(john) [cnf transformation 24]
235. 21 <=> calm(john) [avatar definition]
236. ~calm(john) <- (~21) [avatar component clause 235]
237. calm(john) <- (21) [avatar component clause 235]
364. wise(X1) | humble(X1) | wise(X1) | curious(X1) [resolution 99,96]
365. humble(X1) | wise(X1) | curious(X1) [duplicate literal removal 364]
450. 47 <=> curious(john) [avatar definition]
451. ~curious(john) <- (~47) [avatar component clause 450]
452. curious(john) <- (47) [avatar component clause 450]
454. 48 <=> wise(john) [avatar definition]
456. wise(john) <- (48) [avatar component clause 454]
480. 52 <=> rich(john) [avatar definition]
481. ~rich(john) <- (~52) [avatar component clause 480]
497. ~rich(john) <- (21) [resolution 237,107]
501. ~52 | ~21 [avatar split clause 497,235,480]
573. wise(john) | curious(john) [resolution 365,142]
644. rich(john) <- (47) [resolution 452,70]
645. $false <- (47, ~52) [subsumption resolution 644,481]
646. ~47 | 52 [avatar contradiction clause 645]
671. calm(john) | humble(john) <- (47) [resolution 452,88]
674. humble(john) <- (~21, 47) [subsumption resolution 671,236]
675. $false <- (~21, 47) [subsumption resolution 674,142]
676. 21 | ~47 [avatar contradiction clause 675]
678. 47 | 48 [avatar split clause 573,454,450]
679. quiet(john) | humble(john) <- (48) [resolution 456,101]
683. quiet(john) <- (48) [subsumption resolution 679,142]
798. ~wise(john) | curious(john) <- (48) [resolution 683,94]
799. curious(john) <- (48) [subsumption resolution 798,456]
800. $false <- (~47, 48) [subsumption resolution 799,451]
801. 47 | ~48 [avatar contradiction clause 800]
802. $false [avatar sat refutation 501,646,676,678,801]
% SZS output end Proof for 45488864349848927258005
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm or not happy is happy. If someone is both not kind and not brave then alice is both calm and not humble and vice versa. If mary is both not old and not generous then someone is not quiet or not strong and vice versa. Everyone who is either not kind or humble is not strong or not humble. If lucy is not rich or not quiet then someone is not calm. Everyone who is not patient is either old or tall and vice versa. Everyone who is creative or not brave is either not generous or not happy and vice versa. If alice is either curious or calm then alice is not strong and vice versa. If someone is strong then someone is either patient or old. Everyone who is both not generous and not curious is wise. If someone is either brave or wise then paul is not rich or not brave and vice versa. If susan is wise then john is both not quiet and brave and vice versa. Everyone who is both not kind and not generous is either not patient or tall and vice versa. If lucy is not old then someone is both not creative and not humble and vice versa. Everyone who is generous or not generous is tall or patient. If someone is either not happy or not tall then paul is both not patient and not calm. Lucy is generous. Fred is either quiet or not calm. Someone is wise. Fred is not calm or humble. Paul is rich or curious. Someone is both not quiet and calm. | Paul is not tall. | contradiction | (![X]:((~calm(X)|~happy(X))=>happy(X)))&
((?[X]:((~kind(X)&~brave(X))))<=>((calm(alice)&~humble(alice))))&
(((~old(mary)&~generous(mary)))<=>(?[X]:((~quiet(X)|~strong(X)))))&
(![X]:((~kind(X)<~>humble(X))=>(~strong(X)|~humble(X))))&
(((~rich(lucy)|~quiet(lucy)))=>(?[X]:(~calm(X))))&
(![X]:(~patient(X)<=>(old(X)<~>tall(X))))&
(![X]:((creative(X)|~brave(X))<=>(~generous(X)<~>~happy(X))))&
(((curious(alice)<~>calm(alice)))<=>(~strong(alice)))&
((?[X]:(strong(X)))=>(?[X]:((patient(X)<~>old(X)))))&
(![X]:((~generous(X)&~curious(X))=>wise(X)))&
((?[X]:((brave(X)<~>wise(X))))<=>((~rich(paul)|~brave(paul))))&
((wise(susan))<=>((~quiet(john)&brave(john))))&
(![X]:((~kind(X)&~generous(X))<=>(~patient(X)<~>tall(X))))&
((~old(lucy))<=>(?[X]:((~creative(X)&~humble(X)))))&
(![X]:((generous(X)|~generous(X))=>(tall(X)|patient(X))))&
((?[X]:((~happy(X)<~>~tall(X))))=>((~patient(paul)&~calm(paul))))&
(generous(lucy))&
((quiet(fred)<~>~calm(fred)))&
(?[X]:(wise(X)))&
((~calm(fred)|humble(fred)))&
((rich(paul)|curious(paul)))&
(?[X]:((~quiet(X)&calm(X)))) | ~tall(paul) | [
"p0",
"p12",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5912366279403273296586195
% SZS output start Proof for 5912366279403273296586195
1. ! [X0] : ((~happy(X0) | ~calm(X0)) => happy(X0)) [input p0]
13. ! [X0] : ((~generous(X0) & ~kind(X0)) <=> (~patient(X0) <~> tall(X0))) [input p12]
15. ! [X0] : ((~generous(X0) | generous(X0)) => (patient(X0) | tall(X0))) [input p14]
16. ? [X0] : (~happy(X0) <~> ~tall(X0)) => (~calm(paul) & ~patient(paul)) [input p15]
23. ~tall(paul) [input hypothesis]
25. ! [X0] : (happy(X0) | (happy(X0) & calm(X0))) [ennf transformation 1]
32. ! [X0] : ((patient(X0) | tall(X0)) | (generous(X0) & ~generous(X0))) [ennf transformation 15]
33. ! [X0] : (patient(X0) | tall(X0) | (generous(X0) & ~generous(X0))) [flattening 32]
34. (~calm(paul) & ~patient(paul)) | ! [X0] : (~happy(X0) <=> ~tall(X0)) [ennf transformation 16]
63. ! [X0] : (((~generous(X0) & ~kind(X0)) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) & (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | (generous(X0) | kind(X0)))) [nnf transformation 13]
64. ! [X0] : (((~generous(X0) & ~kind(X0)) | ((~patient(X0) | ~tall(X0)) & (tall(X0) | patient(X0)))) & (((~tall(X0) | patient(X0)) & (tall(X0) | ~patient(X0))) | generous(X0) | kind(X0))) [flattening 63]
69. (~calm(paul) & ~patient(paul)) | ! [X0] : ((~happy(X0) | tall(X0)) & (~tall(X0) | happy(X0))) [nnf transformation 34]
76. happy(X0) | happy(X0) [cnf transformation 25]
120. ~generous(X0) | tall(X0) | patient(X0) [cnf transformation 64]
126. patient(X0) | tall(X0) | generous(X0) [cnf transformation 33]
128. ~patient(paul) | ~happy(X0) | tall(X0) [cnf transformation 69]
139. ~tall(paul) [cnf transformation 23]
141. happy(X0) [duplicate literal removal 76]
295. tall(X0) | patient(X0) [subsumption resolution 126,120]
298. 33 <=> ! [X0] : tall(X0) [avatar definition]
299. tall(X0) <- (33) [avatar component clause 298]
305. ~patient(paul) | tall(X0) [subsumption resolution 128,141]
307. 35 <=> patient(paul) [avatar definition]
310. 33 | ~35 [avatar split clause 305,307,298]
336. patient(paul) [resolution 295,139]
339. 35 [avatar split clause 336,307]
340. $false <- (33) [resolution 299,139]
341. ~33 [avatar contradiction clause 340]
342. $false [avatar sat refutation 310,339,341]
% SZS output end Proof for 5912366279403273296586195
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 brave and not patient is tall.
Everyone who is either not generous or not happy is both creative and calm.
Everyone who is not funny or brave is either not quiet or not humble.
Everyone who is funny is both not old and generous and vice versa.
Everyone who is not funny is both not wise and patient and vice versa.
If someone is either calm or quiet then mary is curious or not creative.
Everyone who is both not patient and not rich is both tall and creative.
If john is not happy then someone is happy and vice versa.
Everyone who is both creative and wise is not funny or strong and vice versa.
Everyone who is both patient and not humble is humble and vice versa.
Everyone who is either creative or brave is either rich or not happy and vice versa.
If fred is either not funny or patient then mary is not calm or not happy.
Everyone who is either not patient or kind is not creative or not patient and vice versa.
Everyone who is not creative is wise and vice versa.
If someone is creative then paul is not curious and vice versa.
Everyone who is either not quiet or not creative is not generous or not wise.
Someone is both not brave and not kind.
Someone is both not calm and not old.
Someone is both not patient and generous.
Someone is either not curious or not generous.
Someone is either quiet or not humble.
Alice is curious or patient.
Someone is humble or quiet. | John is kind. | contradiction | (![X]:((brave(X)&~patient(X))=>tall(X)))&
(![X]:((~generous(X)<~>~happy(X))=>(creative(X)&calm(X))))&
(![X]:((~funny(X)|brave(X))=>(~quiet(X)<~>~humble(X))))&
(![X]:(funny(X)<=>(~old(X)&generous(X))))&
(![X]:(~funny(X)<=>(~wise(X)&patient(X))))&
((?[X]:((calm(X)<~>quiet(X))))=>((curious(mary)|~creative(mary))))&
(![X]:((~patient(X)&~rich(X))=>(tall(X)&creative(X))))&
((~happy(john))<=>(?[X]:(happy(X))))&
(![X]:((creative(X)&wise(X))<=>(~funny(X)|strong(X))))&
(![X]:((patient(X)&~humble(X))<=>humble(X)))&
(![X]:((creative(X)<~>brave(X))<=>(rich(X)<~>~happy(X))))&
(((~funny(fred)<~>patient(fred)))=>((~calm(mary)|~happy(mary))))&
(![X]:((~patient(X)<~>kind(X))<=>(~creative(X)|~patient(X))))&
(![X]:(~creative(X)<=>wise(X)))&
((?[X]:(creative(X)))<=>(~curious(paul)))&
(![X]:((~quiet(X)<~>~creative(X))=>(~generous(X)|~wise(X))))&
(?[X]:((~brave(X)&~kind(X))))&
(?[X]:((~calm(X)&~old(X))))&
(?[X]:((~patient(X)&generous(X))))&
(?[X]:((~curious(X)<~>~generous(X))))&
(?[X]:((quiet(X)<~>~humble(X))))&
((curious(alice)|patient(alice)))&
(?[X]:((humble(X)|quiet(X)))) | kind(john) | [
"p9",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3608993884436752453132319
% SZS output start Proof for 3608993884436752453132319
10. ! [X0] : ((~humble(X0) & patient(X0)) <=> humble(X0)) [input p9]
13. ! [X0] : ((~patient(X0) <~> kind(X0)) <=> (~patient(X0) | ~creative(X0))) [input p12]
24. kind(john) [input hypothesis]
50. ! [X0] : (((~humble(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | (humble(X0) | ~patient(X0)))) [nnf transformation 10]
51. ! [X0] : (((~humble(X0) & patient(X0)) | ~humble(X0)) & (humble(X0) | humble(X0) | ~patient(X0))) [flattening 50]
54. ! [X0] : ((((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | (patient(X0) & creative(X0))) & ((~patient(X0) | ~creative(X0)) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))))) [nnf transformation 13]
55. ! [X0] : ((((~kind(X0) | patient(X0)) & (kind(X0) | ~patient(X0))) | (patient(X0) & creative(X0))) & (~patient(X0) | ~creative(X0) | ((~patient(X0) | ~kind(X0)) & (kind(X0) | patient(X0))))) [flattening 54]
100. humble(X0) | humble(X0) | ~patient(X0) [cnf transformation 51]
102. ~humble(X0) | ~humble(X0) [cnf transformation 51]
118. ~kind(X0) | patient(X0) | patient(X0) [cnf transformation 55]
137. kind(john) [cnf transformation 24]
139. ~kind(X0) | patient(X0) [duplicate literal removal 118]
140. humble(X0) | ~patient(X0) [duplicate literal removal 100]
141. ~humble(X0) [duplicate literal removal 102]
173. ~patient(X0) [subsumption resolution 140,141]
174. ~kind(X0) [subsumption resolution 139,173]
202. $false [subsumption resolution 137,174]
% SZS output end Proof for 3608993884436752453132319
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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 strong or not kind is both brave and not creative.
Everyone who is creative is both not happy and strong.
Everyone who is either curious or not funny is old.
If alice is not strong or not generous then someone is kind or not tall.
If mary is not wise then someone is both not tall and not wise.
Everyone who is old is both not strong and curious and vice versa.
Everyone who is brave is quiet or not generous.
If someone is either not old or curious then someone is both not patient and old and vice versa.
Everyone who is funny or not quiet is not rich.
Everyone who is both not kind and calm is kind and vice versa.
If lucy is not kind then paul is either kind or not rich and vice versa.
Everyone who is not funny or funny is both quiet and generous.
If someone is both tall and not creative then someone is patient.
Everyone who is either not curious or not quiet is both not kind and not wise and vice versa.
Everyone who is both not calm and kind is either calm or not happy.
If susan is happy or quiet then john is both strong and not rich.
Fred is rich or not old.
Someone is either not creative or tall.
Mary is either not creative or creative.
Susan is not funny.
Susan is either patient or not rich.
Someone is either rich or generous. | Fred is not old. | neutral | (![X]:((~strong(X)|~kind(X))=>(brave(X)&~creative(X))))&
(![X]:(creative(X)=>(~happy(X)&strong(X))))&
(![X]:((curious(X)<~>~funny(X))=>old(X)))&
(((~strong(alice)|~generous(alice)))=>(?[X]:((kind(X)|~tall(X)))))&
((~wise(mary))=>(?[X]:((~tall(X)&~wise(X)))))&
(![X]:(old(X)<=>(~strong(X)&curious(X))))&
(![X]:(brave(X)=>(quiet(X)|~generous(X))))&
((?[X]:((~old(X)<~>curious(X))))<=>(?[X]:((~patient(X)&old(X)))))&
(![X]:((funny(X)|~quiet(X))=>~rich(X)))&
(![X]:((~kind(X)&calm(X))<=>kind(X)))&
((~kind(lucy))<=>((kind(paul)<~>~rich(paul))))&
(![X]:((~funny(X)|funny(X))=>(quiet(X)&generous(X))))&
((?[X]:((tall(X)&~creative(X))))=>(?[X]:(patient(X))))&
(![X]:((~curious(X)<~>~quiet(X))<=>(~kind(X)&~wise(X))))&
(![X]:((~calm(X)&kind(X))=>(calm(X)<~>~happy(X))))&
(((happy(susan)|quiet(susan)))=>((strong(john)&~rich(john))))&
((rich(fred)|~old(fred)))&
(?[X]:((~creative(X)<~>tall(X))))&
((~creative(mary)<~>creative(mary)))&
(~funny(susan))&
((patient(susan)<~>~rich(susan)))&
(?[X]:((rich(X)<~>generous(X)))) | ~old(fred) | [] | null | 0 |
Everyone who is rich is both not generous and not humble and vice versa.
If lucy is tall then someone is either not calm or kind and vice versa.
If mary is both generous and not kind then alice is both not kind and happy and vice versa.
Everyone who is not calm is both not strong and not patient.
Everyone who is both not generous and wise is both not funny and humble.
Everyone who is not funny or calm is either humble or tall.
If someone is not curious then someone is either not funny or humble and vice versa.
Everyone who is old is not calm.
Everyone who is both not happy and curious is creative.
Everyone who is either creative or strong is not quiet or not creative.
If lucy is either creative or happy then alice is either not patient or not generous.
If alice is either kind or humble then susan is not curious.
If someone is brave then someone is either not happy or not calm.
Everyone who is quiet or not humble is either happy or patient and vice versa.
Everyone who is both funny and creative is quiet.
Everyone who is either not calm or not wise is humble or not strong and vice versa.
Paul is not happy or humble.
Someone is kind.
Paul is not generous.
Paul is not wise or happy.
Susan is funny or rich.
Lucy is kind or not creative.
Lucy is both not curious and happy. | Paul is not happy. | neutral | (![X]:(rich(X)<=>(~generous(X)&~humble(X))))&
((tall(lucy))<=>(?[X]:((~calm(X)<~>kind(X)))))&
(((generous(mary)&~kind(mary)))<=>((~kind(alice)&happy(alice))))&
(![X]:(~calm(X)=>(~strong(X)&~patient(X))))&
(![X]:((~generous(X)&wise(X))=>(~funny(X)&humble(X))))&
(![X]:((~funny(X)|calm(X))=>(humble(X)<~>tall(X))))&
((?[X]:(~curious(X)))<=>(?[X]:((~funny(X)<~>humble(X)))))&
(![X]:(old(X)=>~calm(X)))&
(![X]:((~happy(X)&curious(X))=>creative(X)))&
(![X]:((creative(X)<~>strong(X))=>(~quiet(X)|~creative(X))))&
(((creative(lucy)<~>happy(lucy)))=>((~patient(alice)<~>~generous(alice))))&
(((kind(alice)<~>humble(alice)))=>(~curious(susan)))&
((?[X]:(brave(X)))=>(?[X]:((~happy(X)<~>~calm(X)))))&
(![X]:((quiet(X)|~humble(X))<=>(happy(X)<~>patient(X))))&
(![X]:((funny(X)&creative(X))=>quiet(X)))&
(![X]:((~calm(X)<~>~wise(X))<=>(humble(X)|~strong(X))))&
((~happy(paul)|humble(paul)))&
(?[X]:(kind(X)))&
(~generous(paul))&
((~wise(paul)|happy(paul)))&
((funny(susan)|rich(susan)))&
((kind(lucy)|~creative(lucy)))&
((~curious(lucy)&happy(lucy))) | ~happy(paul) | [] | null | 0 |
If someone is both not curious and strong then mary is creative and vice versa.
Everyone who is not funny is not old or not quiet.
If someone is both wise and strong then someone is both not brave and not quiet.
If someone is both not wise and not funny then mary is both tall and not old and vice versa.
Everyone who is tall or not old is both calm and brave.
Everyone who is happy or not kind is not rich and vice versa.
Everyone who is both happy and not old is not calm and vice versa.
Everyone who is happy is both not creative and brave and vice versa.
If john is either not kind or calm then someone is rich and vice versa.
Everyone who is creative or not calm is funny or brave and vice versa.
Everyone who is not happy is either not calm or not humble.
Everyone who is brave or quiet is not quiet or curious and vice versa.
If fred is not wise then someone is both humble and not brave.
If someone is not creative or strong then mary is either kind or tall.
If someone is brave then paul is not patient and vice versa.
Fred is wise.
Someone is either wise or curious.
Mary is not funny or creative.
Fred is either not patient or not tall.
Susan is either funny or quiet. | Susan is not funny. | neutral | ((?[X]:((~curious(X)&strong(X))))<=>(creative(mary)))&
(![X]:(~funny(X)=>(~old(X)|~quiet(X))))&
((?[X]:((wise(X)&strong(X))))=>(?[X]:((~brave(X)&~quiet(X)))))&
((?[X]:((~wise(X)&~funny(X))))<=>((tall(mary)&~old(mary))))&
(![X]:((tall(X)|~old(X))=>(calm(X)&brave(X))))&
(![X]:((happy(X)|~kind(X))<=>~rich(X)))&
(![X]:((happy(X)&~old(X))<=>~calm(X)))&
(![X]:(happy(X)<=>(~creative(X)&brave(X))))&
(((~kind(john)<~>calm(john)))<=>(?[X]:(rich(X))))&
(![X]:((creative(X)|~calm(X))<=>(funny(X)|brave(X))))&
(![X]:(~happy(X)=>(~calm(X)<~>~humble(X))))&
(![X]:((brave(X)|quiet(X))<=>(~quiet(X)|curious(X))))&
((~wise(fred))=>(?[X]:((humble(X)&~brave(X)))))&
((?[X]:((~creative(X)|strong(X))))=>((kind(mary)<~>tall(mary))))&
((?[X]:(brave(X)))<=>(~patient(paul)))&
(wise(fred))&
(?[X]:((wise(X)<~>curious(X))))&
((~funny(mary)|creative(mary)))&
((~patient(fred)<~>~tall(fred)))&
((funny(susan)<~>quiet(susan))) | ~funny(susan) | [] | null | 0 |
Everyone who is either generous or not wise is both not curious and not patient.
Everyone who is either quiet or not happy is strong or not funny and vice versa.
Everyone who is not wise or creative is both patient and not creative and vice versa.
Everyone who is not humble is calm or funny.
If susan is both generous and tall then someone is happy.
If someone is both not humble and funny then someone is either humble or not brave.
If someone is funny or happy then someone is generous and vice versa.
Everyone who is brave or calm is either not calm or not funny and vice versa.
If paul is strong then john is generous and vice versa.
If someone is either humble or generous then someone is not rich and vice versa.
If susan is not tall then someone is both not patient and not strong and vice versa.
If fred is both generous and not funny then paul is either funny or not tall.
If someone is not humble or not kind then someone is not strong or old.
Everyone who is patient is humble or not creative.
If mary is either not tall or old then someone is not tall and vice versa.
Everyone who is not tall is either wise or humble.
Someone is either not generous or not funny.
Someone is either not happy or brave.
Someone is both not quiet and not creative.
Someone is not creative.
Someone is tall or not old.
Someone is calm.
Someone is curious or wise.
Someone is not wise. | John is generous. | neutral | (![X]:((generous(X)<~>~wise(X))=>(~curious(X)&~patient(X))))&
(![X]:((quiet(X)<~>~happy(X))<=>(strong(X)|~funny(X))))&
(![X]:((~wise(X)|creative(X))<=>(patient(X)&~creative(X))))&
(![X]:(~humble(X)=>(calm(X)|funny(X))))&
(((generous(susan)&tall(susan)))=>(?[X]:(happy(X))))&
((?[X]:((~humble(X)&funny(X))))=>(?[X]:((humble(X)<~>~brave(X)))))&
((?[X]:((funny(X)|happy(X))))<=>(?[X]:(generous(X))))&
(![X]:((brave(X)|calm(X))<=>(~calm(X)<~>~funny(X))))&
((strong(paul))<=>(generous(john)))&
((?[X]:((humble(X)<~>generous(X))))<=>(?[X]:(~rich(X))))&
((~tall(susan))<=>(?[X]:((~patient(X)&~strong(X)))))&
(((generous(fred)&~funny(fred)))=>((funny(paul)<~>~tall(paul))))&
((?[X]:((~humble(X)|~kind(X))))=>(?[X]:((~strong(X)|old(X)))))&
(![X]:(patient(X)=>(humble(X)|~creative(X))))&
(((~tall(mary)<~>old(mary)))<=>(?[X]:(~tall(X))))&
(![X]:(~tall(X)=>(wise(X)<~>humble(X))))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:((~quiet(X)&~creative(X))))&
(?[X]:(~creative(X)))&
(?[X]:((tall(X)|~old(X))))&
(?[X]:(calm(X)))&
(?[X]:((curious(X)|wise(X))))&
(?[X]:(~wise(X))) | generous(john) | [] | null | 0 |
Everyone who is not funny or not tall is generous or creative and vice versa.
If alice is not generous or not brave then someone is patient.
If someone is not funny then someone is both wise and not brave.
Everyone who is not curious is funny and vice versa.
Everyone who is both generous and kind is both not wise and not old and vice versa.
If mary is either tall or quiet then someone is both not old and not quiet.
Everyone who is either curious or not curious is not old or kind and vice versa.
Everyone who is not brave or curious is not curious and vice versa.
If someone is curious or humble then john is creative.
If someone is either not kind or not happy then alice is both funny and not humble and vice versa.
Everyone who is both generous and not generous is generous.
Everyone who is both brave and not patient is either wise or not quiet.
Everyone who is either tall or patient is both not quiet and not creative.
Everyone who is either not funny or not kind is curious or not patient and vice versa.
If someone is either creative or brave then someone is wise or kind.
Paul is not curious.
Alice is both creative and not happy.
Someone is happy or brave.
Someone is both not tall and not quiet.
Someone is both not old and not curious.
John is either curious or old. | Paul is not creative. | neutral | (![X]:((~funny(X)|~tall(X))<=>(generous(X)|creative(X))))&
(((~generous(alice)|~brave(alice)))=>(?[X]:(patient(X))))&
((?[X]:(~funny(X)))=>(?[X]:((wise(X)&~brave(X)))))&
(![X]:(~curious(X)<=>funny(X)))&
(![X]:((generous(X)&kind(X))<=>(~wise(X)&~old(X))))&
(((tall(mary)<~>quiet(mary)))=>(?[X]:((~old(X)&~quiet(X)))))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)|kind(X))))&
(![X]:((~brave(X)|curious(X))<=>~curious(X)))&
((?[X]:((curious(X)|humble(X))))=>(creative(john)))&
((?[X]:((~kind(X)<~>~happy(X))))<=>((funny(alice)&~humble(alice))))&
(![X]:((generous(X)&~generous(X))=>generous(X)))&
(![X]:((brave(X)&~patient(X))=>(wise(X)<~>~quiet(X))))&
(![X]:((tall(X)<~>patient(X))=>(~quiet(X)&~creative(X))))&
(![X]:((~funny(X)<~>~kind(X))<=>(curious(X)|~patient(X))))&
((?[X]:((creative(X)<~>brave(X))))=>(?[X]:((wise(X)|kind(X)))))&
(~curious(paul))&
((creative(alice)&~happy(alice)))&
(?[X]:((happy(X)|brave(X))))&
(?[X]:((~tall(X)&~quiet(X))))&
(?[X]:((~old(X)&~curious(X))))&
((curious(john)<~>old(john))) | ~creative(paul) | [] | null | 0 |
If someone is not humble or not wise then susan is not wise and vice versa.
Everyone who is both creative and brave is either kind or rich.
If lucy is both not patient and happy then fred is creative.
Everyone who is both not tall and not calm is both rich and not wise and vice versa.
Everyone who is quiet is happy and vice versa.
Everyone who is not quiet or not generous is either strong or not brave.
Everyone who is either not generous or not wise is both rich and calm.
If john is not creative then someone is both not patient and not brave and vice versa.
Everyone who is both not tall and not happy is funny or curious and vice versa.
Everyone who is both not curious and generous is old and vice versa.
Everyone who is not funny is either not quiet or not generous and vice versa.
Everyone who is not generous or humble is either not kind or not happy.
Everyone who is generous or not happy is rich and vice versa.
If lucy is either generous or rich then mary is calm or not patient and vice versa.
Mary is either creative or not quiet.
Lucy is both brave and funny.
John is humble or happy.
Someone is kind or not strong.
Someone is calm.
Someone is either not kind or rich.
Lucy is either strong or happy. | Lucy is not curious. | neutral | ((?[X]:((~humble(X)|~wise(X))))<=>(~wise(susan)))&
(![X]:((creative(X)&brave(X))=>(kind(X)<~>rich(X))))&
(((~patient(lucy)&happy(lucy)))=>(creative(fred)))&
(![X]:((~tall(X)&~calm(X))<=>(rich(X)&~wise(X))))&
(![X]:(quiet(X)<=>happy(X)))&
(![X]:((~quiet(X)|~generous(X))=>(strong(X)<~>~brave(X))))&
(![X]:((~generous(X)<~>~wise(X))=>(rich(X)&calm(X))))&
((~creative(john))<=>(?[X]:((~patient(X)&~brave(X)))))&
(![X]:((~tall(X)&~happy(X))<=>(funny(X)|curious(X))))&
(![X]:((~curious(X)&generous(X))<=>old(X)))&
(![X]:(~funny(X)<=>(~quiet(X)<~>~generous(X))))&
(![X]:((~generous(X)|humble(X))=>(~kind(X)<~>~happy(X))))&
(![X]:((generous(X)|~happy(X))<=>rich(X)))&
(((generous(lucy)<~>rich(lucy)))<=>((calm(mary)|~patient(mary))))&
((creative(mary)<~>~quiet(mary)))&
((brave(lucy)&funny(lucy)))&
((humble(john)|happy(john)))&
(?[X]:((kind(X)|~strong(X))))&
(?[X]:(calm(X)))&
(?[X]:((~kind(X)<~>rich(X))))&
((strong(lucy)<~>happy(lucy))) | ~curious(lucy) | [] | null | 0 |
Everyone who is either not brave or funny is rich. Everyone who is both rich and generous is not old. If paul is not quiet then someone is both not rich and rich. Everyone who is both creative and generous is either not curious or not calm. If someone is either not kind or strong then mary is tall or humble and vice versa. If someone is both not creative and humble then mary is creative. Everyone who is both not generous and generous is not happy or not patient and vice versa. If paul is either happy or tall then someone is both not happy and curious. Everyone who is both not brave and creative is rich. Everyone who is both curious and not rich is humble or funny. Everyone who is strong or not creative is humble. Everyone who is not creative or generous is calm and vice versa. Everyone who is calm or creative is quiet and vice versa. Everyone who is either humble or happy is strong. Everyone who is quiet is both rich and not calm and vice versa. If mary is either kind or not quiet then fred is strong and vice versa. Paul is not generous or not calm. Someone is not humble or humble. Someone is both kind and not tall. Lucy is not curious or not brave. | Fred is not happy. | contradiction | (![X]:((~brave(X)<~>funny(X))=>rich(X)))&
(![X]:((rich(X)&generous(X))=>~old(X)))&
((~quiet(paul))=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((creative(X)&generous(X))=>(~curious(X)<~>~calm(X))))&
((?[X]:((~kind(X)<~>strong(X))))<=>((tall(mary)|humble(mary))))&
((?[X]:((~creative(X)&humble(X))))=>(creative(mary)))&
(![X]:((~generous(X)&generous(X))<=>(~happy(X)|~patient(X))))&
(((happy(paul)<~>tall(paul)))=>(?[X]:((~happy(X)&curious(X)))))&
(![X]:((~brave(X)&creative(X))=>rich(X)))&
(![X]:((curious(X)&~rich(X))=>(humble(X)|funny(X))))&
(![X]:((strong(X)|~creative(X))=>humble(X)))&
(![X]:((~creative(X)|generous(X))<=>calm(X)))&
(![X]:((calm(X)|creative(X))<=>quiet(X)))&
(![X]:((humble(X)<~>happy(X))=>strong(X)))&
(![X]:(quiet(X)<=>(rich(X)&~calm(X))))&
(((kind(mary)<~>~quiet(mary)))<=>(strong(fred)))&
((~generous(paul)|~calm(paul)))&
(?[X]:((~humble(X)|humble(X))))&
(?[X]:((kind(X)&~tall(X))))&
((~curious(lucy)|~brave(lucy))) | ~happy(fred) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 466163927507874670674176
% SZS output start Proof for 466163927507874670674176
7. ! [X0] : ((generous(X0) & ~generous(X0)) <=> (~patient(X0) | ~happy(X0))) [input p6]
21. ~happy(fred) [input hypothesis]
44. ! [X0] : (((generous(X0) & ~generous(X0)) | (patient(X0) & happy(X0))) & ((~patient(X0) | ~happy(X0)) | (~generous(X0) | generous(X0)))) [nnf transformation 7]
45. ! [X0] : (((generous(X0) & ~generous(X0)) | (patient(X0) & happy(X0))) & (~patient(X0) | ~happy(X0) | ~generous(X0) | generous(X0))) [flattening 44]
75. ~generous(X0) | happy(X0) [cnf transformation 45]
77. generous(X0) | happy(X0) [cnf transformation 45]
107. ~happy(fred) [cnf transformation 21]
155. happy(X0) [subsumption resolution 75,77]
198. $false [subsumption resolution 107,155]
% SZS output end Proof for 466163927507874670674176
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 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: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
If fred is not tall then someone is not kind or kind and vice versa. Everyone who is rich or not happy is either not curious or not calm and vice versa. Everyone who is calm is either curious or strong. If mary is curious or kind then paul is not patient. Everyone who is not strong or patient is not generous and vice versa. If lucy is wise or funny then someone is both happy and old and vice versa. Everyone who is either not humble or not funny is not tall. Everyone who is generous or old is both not curious and tall. If someone is both not creative and not humble then susan is either not kind or generous and vice versa. Everyone who is either creative or not wise is not calm or not brave and vice versa. If mary is not rich or curious then susan is calm or not brave. If lucy is both strong and not tall then fred is old and vice versa. Everyone who is not strong is both not brave and funny and vice versa. Everyone who is calm or quiet is both not funny and wise and vice versa. Everyone who is not generous is both humble and curious and vice versa. Someone is either funny or not calm. Lucy is not wise or calm. Susan is rich. Susan is not calm. Someone is both humble and rich. Someone is generous or wise. | Lucy is not wise. | neutral | ((~tall(fred))<=>(?[X]:((~kind(X)|kind(X)))))&
(![X]:((rich(X)|~happy(X))<=>(~curious(X)<~>~calm(X))))&
(![X]:(calm(X)=>(curious(X)<~>strong(X))))&
(((curious(mary)|kind(mary)))=>(~patient(paul)))&
(![X]:((~strong(X)|patient(X))<=>~generous(X)))&
(((wise(lucy)|funny(lucy)))<=>(?[X]:((happy(X)&old(X)))))&
(![X]:((~humble(X)<~>~funny(X))=>~tall(X)))&
(![X]:((generous(X)|old(X))=>(~curious(X)&tall(X))))&
((?[X]:((~creative(X)&~humble(X))))<=>((~kind(susan)<~>generous(susan))))&
(![X]:((creative(X)<~>~wise(X))<=>(~calm(X)|~brave(X))))&
(((~rich(mary)|curious(mary)))=>((calm(susan)|~brave(susan))))&
(((strong(lucy)&~tall(lucy)))<=>(old(fred)))&
(![X]:(~strong(X)<=>(~brave(X)&funny(X))))&
(![X]:((calm(X)|quiet(X))<=>(~funny(X)&wise(X))))&
(![X]:(~generous(X)<=>(humble(X)&curious(X))))&
(?[X]:((funny(X)<~>~calm(X))))&
((~wise(lucy)|calm(lucy)))&
(rich(susan))&
(~calm(susan))&
(?[X]:((humble(X)&rich(X))))&
(?[X]:((generous(X)|wise(X)))) | ~wise(lucy) | [] | null | 0 |
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